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# Valuing the costs of climate change for agriculture: The hidden role of land-use adjustments in the Ricardian approach

François Bareille

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François Bareille. Valuing the costs of climate change for agriculture: The hidden role of land-use adjustments in the Ricardian approach. 2024. hal-04723862

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# Valuing the costs of climate change for agriculture:
The hidden role of land-use adjustments in the Ricardian approach

François Bareille¹

October 7, 2024

¹University of Paris-Saclay, INRAE, AgroParisTech, Paris-Saclay Applied Economics, Palaiseau, France.

Corresponding author: francois.bareille@inrae.fr

Preliminary version. Please do not cite without permission.

## Abstract

The Ricardian approach is a popular cross-sectional method regressing *average farmland rents* on climate across regions to assess the value of climate for agriculture. This paper theoretically shows that the Ricardian approach leads to biased estimates when agriculture operates under decreasing returns and competes for land access with other climate-sensitive sectors. Instead, the Ricardian estimates additionally reflect spillovers from non-agricultural sectors which, by adjusting to climate shocks (either by expanding or shrinking), affect regional farmland area and subsequently contaminate average farmland rents. Such situations would be characterized by Ricardian estimates for non-agricultural sectors that are of *similar signs* than those for agriculture. A simple correction allows us to recover the standard Ricardian interpretation: to regress the product of average farmland rents by regional farmland area – that is, *total farmland rents* – on climate. We test our approach on original data detailing land rents for agriculture, forest and urban sectors in France. In top of documenting climate-induced land-use changes between agriculture and the other sectors, we find that our Ricardian estimates do present evidence of related biases. Compared to our correction, the Ricardian approach significantly underestimates the projected climate change costs for agriculture and the other sectors.

**Keywords:** adaptation; climate damage; land markets; land-use changes; hedonic valuation; sorting.

**JEL Codes:** Q54, Q15, R14.
# 1 Introduction

The assessment of the costs of climate change for agriculture has constituted one of the most growing research areas for economists in these last decades. Although the literature is now built on a variety of methods (Ortiz-Bobea, 2021), those that certainly started it all is the Ricardian approach. Introduced by Mendelsohn et al. (1994), the Ricardian approach consists in a cross-sectional hedonic regression of average farmland prices (per hectare) on climates. Because farmland prices reflect the discounted stream of profits obtained by rational farmers, the obtained Ricardian estimates are commonly interpreted as climate impacts on agricultural productivity *net of the adaptation effects* (e.g., switch from one crop to another). Assuming constant returns and agricultural areas, hundreds of studies have used this intuitive approach to project the long-term welfare impacts of climate change on agriculture all around the world (Mendelsohn and Massetti, 2017). Despite severe criticisms on some of its empirical aspects (e.g., Schlenker et al., 2005), the appealing simplicity of the Ricardian approach still makes it one of the most popular tools to assess the costs of climate change for agriculture (Van Passel et al., 2017; Bozzola et al., 2018; DePaula, 2020; Fabri et al., 2022; Wang and Lewis, 2024).

This paper demonstrates that the Ricardian approach may actually lead to biased estimates that would not reflect the value of climate for agriculture. This inability comes from two facts that question the very assumptions of the Ricardian approach: (i) agriculture competes with other climate-sensitive sectors to access land and (ii) sectors – in particular agriculture – operate under decreasing returns to scale. The first fact implies that sectors differently sort themselves across climates – that is, that areas occupied by agricultural and non-agricultural sectors *endogeneously* depend on climate. The second implies that the average sectoral land rents depend on the very area occupied by the sector. Together, they mean that the differences of farmland prices across regions may not be solely attribute to differences of climate impacts on agricultural productivity (following the standard Ricardian interpretation), but, instead, by differences of climate impacts on that of the non-agricultural sectors.

We present hereafter a simple example to illustrate the overlooked role of land market competition between sectors operating under decreasing returns when assessing the value of climate for agriculture. Consider two fictitious regions similar in all respects except that region H (hot) is warmer than region C (cold). Assume that the productivity of the non-agricultural sectors increases with hot temperatures, but that of agriculture is not affected by climate. Competition for land access leads the sectors to sort within each region, with the non-agricultural sectors occupying larger areas in H than in C and, consequently, agriculture covering larger areas in C than in H. Under decreasing returns to scale, this means that farmland prices are on average *smaller* in C than in H. Consequently, comparing them across climates would here conduct the Ricardian approach to *misleadingly* conclude that agriculture benefits from hot temperatures. In plain English, the Ricardian estimates are here *biased*. Similar misleading conclusion could even be reached under the assumption that, this time, agriculture suffers from hot temperatures but that other sectors do not. Indeed, comparable sorting within the two regions would (here too) lead agriculture to occupy larger areas in C than in H. And similarly, sufficiently large decreasing returns would lead to smaller farmland prices in C than in H, and the Ricardian approach to misleadingly conclude that agriculture benefits from hot temperatures.
Based on this reasoning, we introduce climate as a land productivity shifter into a standard land market model where agriculture competes with urban and forestry to access land. We assume that land quality is heterogeneous within each region (Hardie and Parks, 1997), leading the sectors to operate under decreasing returns to scale (Roberts and Schlenker, 2013). This model yields several propositions showing that the standardly obtained Ricardian estimates cannot neither recover the climate impacts on agricultural productivity nor on agricultural welfare. The reason is that they do not solely capture true productivity effects from climate on agriculture (as in the standard Ricardian interpretation), but also some *climate-induced land-use change effects* resulting from *land competition* with the other sectors that contaminate the average farmland price (via the *decreasing returns*). Specifically, we show that the sector whose productivity is the relatively most positively affected by climate expands over the others, ultimately affecting the average land prices of all sectors. Depending on whether the sectors *similarly* or *differently* value land quality, this expansion can either *amplify* or *reduce* the initial productive shock on the affected sector's average land prices. When the climate-induced land-use change effects are large, it is even possible that the Ricardian estimates indicate positive climate impacts while the true productivity shock is negative (and *vice versa*). We derive an empirical test to see whether the Ricardian estimates traditionally obtained for agriculture are contaminated by climate-induced land-use change effects spilling from other sectors. Specifically, in the case where all sectors value differently land quality, such contamination would be characterized by sets of Ricardian estimates that are of similar signs for all sectors.

After theoretically demonstrating that the Ricardian approach cannot consistently recover the value of climate for agriculture, we propose a simple correction that allows researchers to recover such value. Formally, this consists in explaining the *product* of *average farmland prices* by the *regional farmland area* on climate. Because this prealable step consists in directly computing the agricultural welfare within the region (Lind, 1973), such a “land-adjusted Ricardian approach” rightly identifies the value of climate for agriculture. If the obtained estimates cannot recover the climate impacts on agricultural productivity (because still capturing climate-induced land-use impacts), they are theoretically of the *same signs* than the true productivity effects – constituting a sharp difference with the standard Ricardian approach. Finally, we show that the land-adjusted approach is also consistent to estimate the value of climate for urban and forestry and, overall, for the whole land sector.

The empirical part of the paper consists in estimating the standard and land-adjusted Ricardian approaches on real data and comparing the obtained estimates. Because some of our theoretical propositions rely on the examination of the Ricardian estimates for the urban and forest sectors, a challenging task is to obtain data on urban and forestland prices that are consistent with those traditionally found for farmland. For this purpose, we access exhaustive French notarial data detailing average price of farm, forest and building land at the departmental level (the second administrative level in France), for the years 2000, 2006, 2012 and 2018 – data that we completed with information on land-use areas, climate (seasonal distribution of weather over 30 years) and usual Ricardian controls.

The standard Ricardian estimates obtained on this data indicate that French agriculture benefits from warmer springs and autumns but suffers from hotter summers and winters. These estimates fully align with the literature (Mendelsohn and Massetti, 2017). They are however of the same signs than those obtained for urban and forestry, suggesting the presence of bias due to climate-induced
land-use change effects. By comparison, our land-adjusted Ricardian estimates indicate different climate impacts across sectors. They suggest in particular no impact of temperatures on agriculture. Adopting the traditional Ricardian interpretation, this means that potentially harmful impacts of high temperatures to crop yields – see Schlenker and Roberts, 2009 for example – are completely offset by farmers’ long-run adaptation. The single significantly non-null land-adjusted estimate for agriculture relates to summer precipitation, which appears positive. This is very different from the standard Ricardian results obtained on our data or in the literature (Schlenker et al., 2005), which fail to identify any impact of summer precipitation on agriculture. Robust across several specifications, the divergence between the sets of estimates obtained with the standard and land-adjusted Ricardian approaches implies that, contrary to the usual implicit assumptions, agriculture presents decreasing returns and competes with other sectors to access land. To consolidate this interpretation, we empirically show that, indeed, farmland areas do depend on climate and compete with urban and forestland areas.

In a final step, we project the welfare impacts of two IPCC scenarios on French agriculture, forest and urban sectors by the end of the century. In line with our raw estimates, we find that the standard Ricardian approach identifies similar positive impacts of climate change for all sectors, and that these benefits mainly accrue to the same locations. By comparison, the land-adjusted Ricardian predicts different costs for the three sectors, both in amplitude and over space. Overall, the standard Ricardian approach significantly underestimates the costs of climate change for the three sectors.

This article makes three contributions. First, it contributes to the literature on the valuation of climate for agriculture by joining previous criticisms of the Ricardian approach. While most of these critics relates to some of its empirical aspects (Darwin, 1999; Schlenker et al., 2005; Deschênes and Greenstone, 2007; Bareille and Chakir, 2023), we join the few papers that precise the theoretical conditions under which it can recover consistent climate impacts on agricultural welfare (Cline, 1996; Severen et al., 2018). Specifically, we explain that, instead of measuring climate impacts on agricultural productivity only, the Ricardian estimates additionally capture spillovers from non-agricultural sectors which, by adjusting to climate, affect farmland area – via land competition – and subsequently contaminate average farmland rents – via the decreasing returns. This aligns with Ortiz-Bobea (2020)'s insights on the confounding influence of the urban sector on the Ricardian estimates.<fnref n="1" /> We expand this work in two directions. On the one hand, we show that such estimates are also biased by the influence of forestry. On the second, we propose a simple correction to remove such biases. Different to those proposed by Ortiz-Bobea (2020), our land-adjusted correction does not suffer from potential selection bias and relies on readily available data (i.e., land-use data on top of commonly used farmland prices).

Second, this paper assesses the costs of climate change for urban and forestry. Doing so, we join the few previous papers that have applied the Ricardian approach to non-agricultural sectors. While we identify, in line with the single Ricardian studies on forestry (Onyekuru and Marchant, 2016;

<footnote n="1">¹Specifically, Ortiz-Bobea (2020) explains that farmland prices reflect capitalization of expected future uses, including urban ones. As such, Ortiz-Bobea (2020) prefers to use cash rents instead, which do not capitalize expected land-use changes and thus likely better reflect agricultural productivity – but which may suffer from selection bias by Ortiz-Bobea’s own admission. While his approach better matches the Mendelsohn et al.’s plot-level reasoning, we believe that ours better fits the standard cross-sectional Ricardian comparison of regional average farmland prices – computed on different farmland areas – across climates. At least, we theoretically show that the urban sector may not necessarily influence farmland price via agents’ anticipation but, instead, instantaneously affect both farmland areas and average prices – and then cash rents – via the competition of the two sectors operating under decreasing returns on land markets.</footnote>
Mihiar and Lewis, 2021), that standard Ricardian estimates suggest positive climate change impacts on forestry, our land-adjusted Ricardian estimates instead suggest large costs. Similarly, while the single existing cross-sectional studies on the urban sector all predict negative climate change impacts (Albouy et al., 2016; Fan et al., 2016; Sinha et al., 2018; Borsky et al., 2024), our land-adjusted Ricardian approach actually predicts positive (but not-significant) climate change impacts on the urban sector.

Finally, this paper contributes to the literature assessing farmers’ long-term adaptation to exoge-
nous shocks (e.g., Hornbeck, 2012), by highlighting the existence of climate-induced land-use changes
between agricultural and non-agricultural sectors. We specifically join previous studies empirically
documenting their existence (Seo and Mendelsohn, 2008; Cui, 2020a,b; Aragón et al., 2021), and addi-
tionally show how they bias the standard Ricardian estimates. Doing so, we join Aragón et al. (2021)’s
insights on the inconsistency of traditional short-term methods reasoning on a per-hectare basis to
value climate (due to the non-fixity of farmland area), and expand them to the long-term cases.

The paper is organized as follows. Section 2 develops the theoretical criticisms of the standard Ricardian approach and presents the rational for our land-adjusted correction. Section 3 details the data. Section 4 presents the empirical strategy. Section 5 describes the estimation results. Section 6 simulates the impacts of climate change on agriculture and other sectors in France. Section 7 concludes.

2 Theoretical analysis

2.1 Model description

Our analysis aims to investigate the impacts of a productive (climate) shock on competitive land market
equilibrium, both in terms of land rents and areas, when several sectors simultaneously operate and
when land is available in fixed quantity.<fnref n="2" /> There are several ways to model such equilibrium in the
literature (leaving aside the role of climate – which has not been taken into account before to our
knowledge), for which we present their specificities below (Randall and Castle, 1985).

Without loss of generality, we assume that there are three sectors producing each a different output type, denoted $i = 1, 2, 3$, that differ in terms of technologies and prices. Specifically, we assume that $i = 1$ represents *construction*, $i = 2$ is *agriculture* and $i = 3$ indicates *forestry*. Each sector is supposedly constituted of homogeneous agents producing the same output with the same technology. We suppose that land is the single production factor but that it presents heterogeneous quality (e.g. Lichtenberg, 1989; Chakravorty and Krulce, 1994; Hardie and Parks, 1997), leading the sectors to operate with decreasing returns to area (Roberts and Schlenker, 2013). The hypothesis for which literature splits up concerns the way the sectors value land quality (Randall and Castle, 1985). In the first case (e.g. Dunn, 1954; Hartwick, 1972; Lind, 1973), all sectors value land similarly. In the second (e.g. Chambers and Just, 1989; Miller and Plantinga, 1999; Hartwick et al., 2001), they value land quality differently. These two alternative assumptions imply that, while sectors compete to access the same land pieces in the first case (denoted as the “no sector-specific land quality” assumption henceforth), they compete

<footnote n="2">²The fixity of land availability leads to a specific kind of competition among landowners for land access, where an additional hectare put to one use decreases the aggregate area available for all the other uses by one hectare. This property differs from most markets where supply is unconstrained in the long run (e.g. human-made asset markets).</footnote>
for different ones in the second (“sector-specific land quality” assumption). That is, these assumptions represent two extreme cases, where reality likely locates somewhere in-between.<fnref n="3" /> Although they lead to different mathematical characterizations of the competitive land market equilibrium, they have minor impacts on our propositions (see Section 2.2). For brevity’s sake, we thus detail the land equilibrium in the first case in the following paragraphs, and present the second case in Appendix A1.

**Model assumptions when sectors value the same lands.** The assumption that all sectors similarly value the same types of land pieces allows us to rank these pieces along a single dimension $r$ (Lichtenberg, 1989), which can be though as a continuum of locations $r \in S$, where $S$ is a closed bounded set of a finite dimensional Euclidean space. Each location is thus denoted by $r$ and we assume for simplicity that the land piece of best quality is located in $r = 0$, while the worst one is in $r = S$. We assume that climate $C$ is a land productivity shifter that affects the quantity of output $i$ produced by unit of land (denoted $y_i^C \ge 0$). Presumably homogeneous within the region, one can consider $C$ as the set of long-term averages of seasonal temperature and precipitation (e.g. Mendelsohn et al., 1994).

For comparison purposes with Appendix A1, we assume that the decreasing returns to area manifests by the observed quality of the output produced, quality for which consumers are willing to pay a premium. Specifically, we assume that output prices are exogenous and equal to:

$$P_i(r) = p_i - t_i r, \qquad (1)$$

where $p_i$ is the price of output $i$ produced on the land of best quality, and $t_i$ is the price penalty as one moves by one unit from the land of best quality. If prices vary with land quality, we embrace the Ricardian tradition of exogenous prices – whose levels are independent to climate.

We assume that all output and land markets are in perfect competition at any point in space. We assume that the location of the different sectors follows a bidding procedure for which the highest bidder obtains the land piece. Producers thus compete for land access, and the maximum bid that they can offer correspond to the surplus they can generate from the particular land piece. The bid function $\Phi_i(r, C)$ thus corresponds to the surplus that sector $i$ in region with climate $C$ can extracted from the land piece in $r$, and is defined as follows:

$$\Phi_i(r, C) \equiv y_i^C (p_i - t_i r). \qquad (2)$$

We refer hereafter to $-t_i y_i^C$ as the gradient of sector $i$. Finally, to insure that all three sectors are observed on the land market, we make the following assumption.

**Assumption 1.** The area of the three sectors are strictly positive at the equilibrium, such that:

(1) The output price origins are characterized by: $p_1 y_1 > p_2 y_2 > p_3 y_3 > 0$;

(2) The sectoral gradients are characterized by: $t_1 y_1^C > t_2 y_2^C > t_3 y_3^C > 0$;

<footnote n="3">³This classification of the literature is somehow unusual, but allows presenting a unified framework where the decreasing returns are explained, for both assumptions, by consumers’ willingness to pay for quality – see equations (1) and (A1) respectively. Anyone familiar with von Thünen (1828) will quickly understand that the “no sector-specific land quality” case relates to his model of sector location and rent formation, where the price penalty linked to quality actually correspond to transportation costs with the distance to the city. Similarly, the “sector-specific land quality” case is actually a transcription of Ricardo (1817)’s model of decreasing returns with land modelled as an homogeneous resource.</footnote>
(3) The ratio of price parameters are characterized by: $p_3/t_3 > p_2/t_2 > p_1/t_1 > 0$.

Assumption 1.1. assumes that construction is the most profitable sector nearby $r = 0$, followed by agriculture and forestry. Assumption 1.2. supposes that the price of timber is the least affected by land quality, followed by agricultural and construction outputs. Finally, assumption 1.3. jointly insures that, given assumptions 1.1. and 1.2. the three sectors occupy a positive, non-null area.

**Land market equilibrium.** A competitive land market is characterized by (i) producers formulating bids to access land by maximizing their profits and (ii) landowners picking the highest bid. Formally, the profit for sector $i$ in $r$ under climate $C$ can be defined as:

$$ \pi_i(r, C) = y_i^C(p_i - t_i r) - R(r, C) = \Phi_i(r, C) - R(r, C), $$

where $R(r, C)$ is the land rent in $r$ under climate $C$. The result of the bidding procedure provides the land market competitive equilibrium, where profits are null (given the decreasing returns). Because land rent cannot be negative, equation (2) provides the following land rent function at the equilibrium:

$$ R^*(r, C) = \max\{\max_{i=1,2,3} \Phi_i(r, C), 0\} = \max\{\max_{i=1,2,3} y_i^C(p_i - t_i r), 0\}. \quad (3) $$

Equation (3) defines the competitive equilibrium, characterized by a rent function and by exclusive implementation areas for each sector (Lind, 1973; Hardie and Parks, 1997), such that each location is occupied by the producer that offered the highest bid.<fnref n="4" /> The land rent function at the equilibrium corresponds to the upper envelope of the bid functions – each sector being located where $\Phi_i(\cdot) = R^*(\cdot)$. As such, $R^*(\cdot)$ is decreasing with $r$, linear by pieces and convex, and the pivot points delimiting the frontiers between two sectors $i$ and $i + 1$, denoted $r_i^*(C)$, are characterized by:

$$ \Phi_i(r_i^*(C), C) = \Phi_{i+1}(r_i^*(C), C). \quad (4) $$

Figure 1 shows the competitive land market equilibrium depicted by equations (3) and (4) under assumption 1. Figure 1 illustrates that the ordering of the exclusive implementation areas is commanded by the distance to the best land, such that the sector with the greatest gradient – in absolute value – is located directly nearby the origin in a first segment (i.e. construction here), the second segment being occupied by the sector with the second highest gradient (agriculture), and the third segment being occupied by the last sector (forestry). No sector is profitable outside these segments. Because the pivot points verify equation (4), construction sector is specifically located within the segment $[0; r_1^*(C)]$, with:

$$ r_1^*(C) = \frac{p_1 y_1^C - p_2 y_2^C}{t_1 y_1^C - t_2 y_2^C}. \quad (5) $$

<footnote n="4">⁴That is, every point reflects the most profitable sector at this location. This property is exploited by most land-use models (Lichtenberg, 1989; Plantinga, 1996; Lubowski et al., 2006), and in particular by “structural” Ricardian ones to infer the value of climate (Seo and Mendelsohn, 2008).</footnote>
Equation (5) indicates that urban area depends on both construction and agricultural technologies and prices. Beyond this segment, agriculture establishes as its surplus becomes greater than those of construction. Agriculture occupies the segment $[r_1^*(C); r_2^*(C)]$, with $r_2^*(C)$ corresponding to:

$$r_2^*(C) = \frac{p_2 y_2^C - p_3 y_3^C}{t_2 y_2^C - t_3 y_3^C} \qquad (6)$$

Similarly, forestry establishes from $r_2^*(C)$ to $r_3^*(C)$, where $r_3^*(C)$ equals:

$$r_3^*(C) = \frac{p_3}{t_3}, \qquad (7)$$

in the case where total land in the region is not binding, which we assume here for the sake of simplicity (i.e. $r_3^*(C) < S$). The remaining of the region is occupied by marginal lands with null value (e.g. abandoned lands). By construction, the value of the last unit of forest is null, i.e. $\Phi_3(r_3^*(C), C) = 0$.

<figure><img src="image_3.png" /><figcaption>Figure 1: Land market equilibrium with three sectors in a fictitious region with climate C.</figcaption></figure>

NOTE. The figure displays the equilibrium on a competitive land market when sectors value the same types of lands. The x-axis indicates the distance from the piece of land with the highest quality ($r = 0$). The points $r_1^*(C)$, $r_2^*(C)$ and $r_3^*(C)$ delineate the exclusive implementation areas of the different sectors. The segment $[0; r_1^*(C)]$ corresponds to the urban area under climate C. The segment $[r_1^*(C); r_2^*(C)]$ corresponds to the agricultural area. The segment $[r_2^*(C); r_3^*(C)]$ corresponds to forestland. The area outside $[0; r_3^*(C)]$ is made of marginal lands with null value. The y-axis indicates the value of the bid and rent functions (expressed in monetary by area unit). The bidding functions $\Phi_1(r, C)$, $\Phi_1(r, C)$ and $\Phi_3(r, C)$ represented by dashed curves correspond respectively to the surplus of construction ($i = 1$), agriculture ($i = 2$) and forestry ($i = 3$) for each point $r$ under climate C. The rent function $R^*(r, C)$ depicted in plain curve correspond to the upper envelope of the three bidding curves. The points $\bar{R}_1^*(C)$, $\bar{R}_2^*(C)$ and $\bar{R}_3^*(C)$ correspond respectively to the average observed rent in the land markets for urban, agricultural and forestland.

**Average land rents.** A crucial aspect of the Ricardian approach is that, in practice, it does not use the full range of land rents from agriculture – that is, the full function $\Phi_2(r, C)$ between $r_1^*(C)$ and
$r_2^*(C)$ – but only the average rent observed on farmland market, denoted $\bar{R}_2^*(C)$.<fnref n="5" /> Given that this is this average value that is cross-sectionally compared across climates, we specify its expression below. Formally, the average farmland rent equals the sum of the (i) rectangle of basis $r_2^*(C) - r_1^*(C)$ and height $\Phi_2(r_2^*(C), C)$ and (ii) triangle of basis $r_2^*(C) - r_1^*(C)$ and height $\Phi_2(r_1^*(C), C) - \Phi_2(r_2^*(C), C)$, divided by (iii) farmland area $r_2^*(C) - r_1^*(C)$. Using equations (2) to (6), this simplifies to:

$$ \bar{R}_2^*(C) = p_2 y_2^C - \frac{t_2 y_2^C}{2} \left( \frac{p_1 y_1^C - p_2 y_2^C}{t_1 y_1^C - t_2 y_2^C} + \frac{p_2 y_2^C - p_3 y_3^C}{t_2 y_2^C - t_3 y_3^C} \right). \quad (8) $$

Equation (8) indicates that the average farmland rent observed at the regional level does not depend only on agricultural prices and technology. Although the first term of equation (8) does correspond to agricultural revenues on the best plot, the second shows that the average farmland rent also depends in a complex way on the prices and technologies of the construction and forestry sectors.

We obtain the average rents for urban and forestland similarly. Formally, the first equals to:

$$ \bar{R}_1^*(C) = p_1 y_1^C - \frac{t_1 y_1^C}{2} \left( \frac{p_1 y_1^C - p_2 y_2^C}{t_1 y_1^C - t_2 y_2^C} \right), \quad (9) $$

and the second to:

$$ \bar{R}_3^*(C) = \frac{p_3 y_3^C}{2} - \frac{t_3 y_3^C}{2} \left( \frac{p_2 y_2^C - p_3 y_3^C}{t_2 y_2^C - t_3 y_3^C} \right). \quad (10) $$

Equations (9) and (10) state that the average rents observed for construction and forestry do not only depend on their own technologies and prices, but also on those of agriculture.

**Summary.** The analyses above illustrate that, at the competitive land market equilibrium, sectoral land areas and (average) rents depend both on their own technologies and prices, but also on those of the other sectors. If we reach this point in the case where sectors all value the same land pieces (i.e. in the “no sector-specific land quality” case), Appendix A1 leads to similar conclusions in the case where sectors value land quality differently. Now, we formally explore in Section 2.2 how climate shocks on the productivity of at least one of the three sectors modify the competitive land market equilibrium.

## 2.2 Climate impacts on agriculture

Our aim here is to investigate whether and under which conditions the standard application of the Ricardian approach can capture what it pretends to capture, that is a change in agricultural productivity that is capitalized into land rents (*weak interpretation*) and that would inform on the value of climate for agriculture (*strong interpretation*).<fnref n="6" /> Indeed, while such interpretations are derived at

<footnote n="5">⁵For example, Ricardian studies applied to US commonly rely on average farmland rent at the county level, expressed in *monetary per area unit*, to infer the value of climate for agriculture (e.g. Mendelsohn et al., 1994; Schlenker et al., 2005; Deschênes and Greenstone, 2007; Massetti and Mendelsohn, 2011; Severen et al., 2018; Ortiz-Bobea, 2020).</footnote>

<footnote n="6">⁶While the weak interpretation is adopted by the vast majority of the Ricardian literature, the strong interpretation of the Ricardian approach is more circumspect. The latter notably arises when Ricardian studies ultimately perform simulation exercise of climate change costs for agriculture, multiplying the Ricardian estimates by the initial agricultural area (e.g. Mendelsohn et al., 1994; Schlenker et al., 2005; Van Passel et al., 2017).</footnote>
the plot level (or, at least, at *r* fixed; see Mendelsohn et al., 1994), we are not aware of any analysis examining their validity under competitive land markets (where markets adjust to shocks).

We examine two main cases hereafter, illustrated in Figures 2 and 3. In the first, the climate difference ΔC negatively impacts agricultural productivity (e.g. less precipitation decreases crop yields; see Ortiz-Bobea et al., 2019).<fnref n="7" /> In the second, it positively affects construction productivity (e.g. less precipitation improves labor productivity in urban areas; see Acevedo et al., 2020). Appendices A2 and A3 illustrate a diversity of other potential impacts of ΔC, depending on their sign, amplitude and sector affected. Because climate change is likely to affect the productivity of *all* sectors (and not one at a time), its real impacts on land market are likely a mix between all of these figures.

<figure><img src="image_4.png" /><figcaption>Figure 2: Impact of a negative agricultural shock on average land rents.</figcaption></figure>

NOTE. The figure displays the change in competitive land market equilibrium conditions due to a negative shock on agricultural productivity of −δ₂% induced by a climate difference ΔC. The x-axis indicates the distance from the land piece of best quality (*r* = 0). The y-axis indicates the value of the bid and rent functions (expressed in monetary by area unit). The bid functions are displayed in dashed lines. The rent function depicted in plain curve correspond to the upper envelope of the bidding curves. Following the climate shock, the bidding function of agriculture reduces by −δ₂% (indicated by plain arrows), while those of construction and forestry remain unaffected. It leads to a contraction of agricultural area from [*r*₁*(C)*; *r*₂*(C)*] to [*r*₁*(C + ΔC)*; *r*₂*(C + ΔC)*], and an expansion of urban and forestland on corresponding segments. The result is that observed average rents for all three sectors are modified.

**Impact on farmland rent at the margin.** To begin our investigations, we start with a thinking exercise where ΔC negatively affects the productivity of agriculture (Figure 2), reducing the amount of agricultural output per unit of land by −δ₂%. Using equation (2), this productivity shock translates into the bid function of agriculture such that:

$$ \Phi_2(r, C + \Delta C) = y_2^C (1 - \delta_2) (p_2 - t_2 r) \equiv (1 - \delta_2) \Phi_2(r, C), \quad (11) $$

implying that farmland rent in *r* reduces to a similar amount than the productivity shock.

<footnote n="7">⁷Such a climate difference can be thought as real climate change or, in the spirit of the Ricardian approach, a climate difference between our fictitious and its counterfactual region (identical in all other aspects) – the Ricardian approach fundamentally works on the space-for-time substitution principle to assess the impact of future climate on agriculture by exploiting actual spatial differences across regions.</footnote>
<figure><img src="image_5.png" /><figcaption>Figure 3: Impact of a positive urban shock on average land rents.</figcaption></figure>

NOTE. The figure displays the change in competitive equilibrium conditions of a land market following a positive productivity shock on construction of +$\delta_1$% induced by a climate difference $\Delta C$. The x-axis indicates the distance from the city ($r=0$). The y-axis indicates the value of the bid and rent functions (expressed in monetary by area unit). The bid functions are displayed in dashed lines. The rent function depicted in plain curve correspond to the upper envelope of the bidding curves. Following the climate shock, the bidding function of construction increases by +$\delta_1$% (indicated by plain arrows), while those of agriculture and forestry remain unaffected. It leads to an expansion of urban area from $[0; r_1^*(C)]$ to $[0; r_1^*(C + \Delta C)]$, and a contraction of agricultural area in the corresponding segment, disappearing from $[r_1^*(C); r_1^*(C + \Delta C)]$. The result is that observed average rents for construction and agriculture are modified. Forest area and rent are unaffected by the construction shock, because there is no urban-forest frontier.

For the purpose of our thinking exercise, we assume that we can observe the rent of all pieces of lands of the fictitious region under climate C (Figure 1) and its counterfactual under climate $C + \Delta C$ (Figure 2). A graphical analysis on these two regions lead to the following proposition.

**Proposition 1.** When the continuum of land rents on $r$ are observed, the application of the Ricardian approach leads to three distinguished cases.

(1) Its application on the segment where agriculture is always located – regardless of climate – is possible. The Ricardian estimates rightly infer the climate shock on agricultural productivity.

(2) Its application at the frontier between two sectors is possible. However, it cannot insure that the Ricardian estimates rightly represent the climate shock on agricultural productivity.

(3) Its application on the segments where agriculture is not always located is impossible.

**Proof.** See Appendix A4.1 ■

Proposition 1 implies that the application of the Ricardian approach on competitive land markets provide estimates that would not necessarily interpretable in the standard way. Actually, proposition 1.1. implies that this would be the case only if applied on the agricultural area of the smallest agricultural region – i.e. onto the segment $]r_1^*(C + \Delta C); r_2^*(C + \Delta C)]$. In this case, the Ricardian approach does capture a change in agricultural productivity that is capitalized in land rent (weak interpretation). The remaining of proposition 1 however makes clear that the Ricardian application on other segments cannot infer such changes. In particular, proposition 1.3. indicates that its application
onto the segments where agriculture is located in some situations only is conceptually incorrect.<fnref n="8" /> In plain English, the Ricardian application on these segments would lead to biased estimates, that do not reflect any climate impacts on agricultural productivity. Finally, proposition 1.2. highlights tricky situations at the agricultural frontiers. Though conceptually possible, Ricardian estimates recover from these points cannot be attributed to agriculture. As the frontiers move with climate until the land bids of the two sectors equal one to another (see proposition 2 below), the obtained estimates can either reflect a climate shock on the productivity of agriculture, or on those of the other sector.

Proposition 1 reveals the conditions under which the Ricardian approach can fully identify a climate shock on agricultural productivity. However, it only holds when the continuum of land rents on r is observed. Such a case is purely speculative, as we are not aware of any data informing on the rents of all farmlands of a region.<fnref n="9" /> Instead, researchers usually obtain Ricardian estimates exploiting cross-sectional differences of average farmland rents and climate at the regional level (e.g. US county). After showing that climate affects the extent of farmland areas under competitive land markets, we explain how these climate-induced land-use changes endogenously contaminate average farmland rents, making inappropriate such standard Ricardian applications.<fnref n="10" />

**Climate-induced land-use change.** Because it has been conceptually conceived at the plot level (that is, at r fixed), the Ricardian approach implicitly assumes that the agricultural area is orthogonal to climate. Yet, the pivot points $r_1^*(C)$ and $r_2^*(C)$ depend on climate such that the areas occupied by agriculture and the other sectors also vary with climate. Noting $y_{iC}^C$ the derivative of the production of sector i with respect to climate (which can be either positive or negative), and dropping the superscript C for the sectors no affected by the climate shock, we formulate the following proposition.

**Proposition 2.** A climate shock on the productivity of at least one sector induces land-use changes on competitive land markets, characterized by:

(1) A positive (resp. negative) shock leads to land expansion (resp. constriction) for the affected sector, to the detriments (resp. benefits) of the others.

(2) A modification of the frontiers such that, $\forall i \in \{1, 2\}$:

(i) Under the assumption that all sectors value the same land:

$$ \frac{d r_i^*(C)}{dC} = y_{iC}^C \frac{y_{i+1}(p_{i+1}t_i - p_i t_{i+1})}{(t_i y_i^C - t_{i+1} y_{i+1})^2} = -y_{i+1C}^C \frac{y_i(p_{i+1}t_i - p_i t_{i+1})}{(t_i y_i - t_{i+1} y_{i+1}^C)^2}; $$

(ii) Under the assumption that sectors value differently land quality:

$$ \frac{d q_i^{i*}(C)}{dC} = y_{iC}^C \frac{p_i t_{i+1} y_{i+1}}{(t_i y_i^C + t_{i+1} y_{i+1})^2} = -y_{i+1C}^C \frac{p_i t_{i+1} y_i}{(t_i y_i + t_{i+1} y_{i+1}^C)^2}. $$

<footnote n="8">⁸As an illustration, the segments $[r_1^*(C); r_1^*(C + \Delta C)]$ and $[r_2^*(C + \Delta C); r_2^*(C)]$ [in Figure 2 correspond to areas where agriculture is located under climate C, but absent under climate C + $\Delta C$. These segments are not suitable for the Ricardian approach, as it would compare farmland rent to urban and forestland rents respectively.</footnote>

<footnote n="9">⁹Proposition 1 works when the Ricardian approach is applied on individual observations, either at the farm or plot level (e.g. Fezzi and Bateman, 2015; Bozzola et al., 2018; Bareille and Chakir, 2023). However, performing analyses on such agricultural units inherently assume that they remain observed under counterfactual climate, which is unlikely.</footnote>

<footnote n="10">¹⁰A graphical reasoning based on Figure 2 allows us to get the intuition of the mechanisms behind this assertion. Indeed, the average farmland rent is the integral of farmland rent divided by the corresponding area. Proposition 1 shows that proceeding to the integral on $[r_1^*(C); r_1^*(C + \Delta C)]$ and $[r_2^*(C + \Delta C); r_2^*(C)]$ [is conceptually wrong.</footnote>
**Proof.** See Appendix A4.2 ■

Proposition 2 implies that, on competitive land markets, the agricultural area changes in response to a climate shock on the productivity of at least one sector, whether agricultural or not. Indeed, the climate shock on productivity affects the bidding curves, resulting in a change of the pivot points and, ultimately, in climate-induced land-use changes compensating for each other (given the fixity of land availability). Looking for example to Figure 2, the negative shock on agricultural productivity reduces the agricultural area from $[r_1^*(C); r_2^*(C)]$ to $[r_1^*(C + \Delta C); r_2^*(C + \Delta C)]$, reductions that are exactly compensated by the expansions of urban and forest areas.<fnref n="11" />

Proposition 2 has implications for the Ricardian approach. Indeed, the strong interpretation of the Ricardian literature assumes that the observed agricultural area is orthogonal to climate, such that the multiplication of the Ricardian estimates by the observed agricultural area would indicate the total costs of climate change for agriculture. By indicating that agricultural area does depend on climate,<fnref n="12" /> proposition 2 makes clear that such interpretation cannot be supported.

**Average analysis.** We examine hereafter the impacts of a climate difference on average farmland rents, which, contrary to the continuum of land rents, are commonly observed by econometricians. The derivatives of average farmland rent with respect to a climate shock affecting the productivity of either the agricultural or a non-agricultural sector lead to the following proposition.

**Proposition 3.** When average farmland rents are observed, the application of the Ricardian approach cannot infer the climate impact on agricultural productivity or welfare. Instead:

(1) In the case where all sectors value the same lands:

(i) A climate shock on urban productivity turns into Ricardian estimates of the opposite signs.

(ii) A climate shock on forest productivity turns into Ricardian estimates of the same signs.

(iii) A climate shock on agricultural productivity turns into Ricardian estimates that can be either null or of the same or opposite sign. The latter case occurs when agricultural prices are small enough compared to construction prices, or when the forest gradient is small enough.

(2) In the case where the sectors value differently land quality, the Ricardian estimates are of same signs than the climate shock, whatever the affected sector.

**Proof.** See Appendix A4.3 ■

Proposition 3 has major consequences for the Ricardian approach. Propositions 3.1.i., 3.1.ii. and 3.2. notably imply that, while agricultural productivity is unaffected by climate, the Ricardian estimates can be non-null. Instead, the estimates would actually reflect a climate shock on the productivity of a non-agricultural sector that *spills over* farmland rents by the mean of a *climate-induced land-use change effect* (see proposition 2), but in no case a climate shock on agricultural productivity. Such

<footnote n="11">¹¹While some studies already showed that climate affects land uses empirically (Seo and Mendelsohn, 2008; Cui, 2020a,b; Aragón et al., 2021), Section 5.4 demonstrates that such climate-induced land-use changes also occur in our data.</footnote>

<footnote n="12">¹²This result can be extended to the case of a partially regulated land market where some (but not all) land-use changes are forbidden by the regulator. The expressions would be slightly modify to add a viscosity term linked to the land regulation.</footnote>
a climate-induced land-use change effect can be illustrated by noting that the derivative of average farmland rent with respect to a climate shock affecting construction productivity only is equal to:

$$ \frac{d\bar{R}_2^*(C)}{dC} = -\frac{t_2y_2}{2} \frac{r_1^*(C)}{dC} = \underbrace{-\frac{t_2y_2}{2} y_{1C}^C \left( \frac{y_2(p_2t_1 - p_1t_2)}{(t_1y_1^C - t_2y_2)^2} \right)}_{\text{Climate-induced land-use change effect}}, \quad (12) $$

when all sectors value the same lands. Equation (12) shows that the derivative of the average farmland rent on climate is an affine function of the climate-induced land-use change, equals to half of the agriculture gradient multiplied by the climate-induced land-use change – the gradient thus indicates its sensitivity to climate-induced land-use changes.<fnref n="13" /> Because $r_1^*(C)$ increases here (urban expands over farmland, see proposition 2), equation (12) implies that the new urban-agriculture frontier is characterized by smaller bid values, such that average farmland rents decrease (see Figure 3).

Proposition 3.1.iii. extends the implications of the climate-induced land-use change effects to the case where a climate shock affects the agricultural productivity. In this case, the Ricardian estimates would reflect both a true productivity effect – as traditionally interpreted in the Ricardian approach – plus some climate-induced land-use change effects. The accumulation of these two effects clearly appear in the derivative of average farmland rent with respect to climate, which equals:

$$ \frac{d\bar{R}_2^*(C)}{dC} = \underbrace{p_2 y_{2C}^C}_{\text{Productivity effect}} + \underbrace{\frac{t_2}{2} \left( \frac{p_2 t_2 (y_2^C)^2 - p_1 t_1 (y_1)^2}{(t_1 y_1 - t_2 y_2^C)^2} + \frac{p_2 t_2 (y_2^C)^2 - p_3 t_3 (y_3)^2}{(t_2 y_2 - t_3 y_3)^2} \right)}_{\text{Climate-induced land-use change effect}}. \quad (13) $$

Equation (13) indicates that the climate-induced land-use change effects can be so large that the Ricardian estimates may actually be of opposite signs than the true shock on agricultural productivity. This latter case can happen when (i) the construction prices are so high that there is almost no climate-induced land-use expansion of agriculture on urban lands, or (ii) the forest gradient is small enough to allow forestland to quickly expand following the shock.

Appendix A4.3 shows that the productivity and climate-induced land-use change effects also coexist in response to a climate shock on agricultural productivity when lands differently value land quality. However, contrary to the “no sector-specific land quality” case, proposition 3.2. indicates that the climate-induced land-use change effects are here of the same sign than the productivity effect. Indeed, because the rent function is not strictly decreasing along $q^i(C)$, a climate-induced land-use change actually amplify the climate shock. For example, a positive climate shock on agricultural productivity expands agricultural area, leading to the nibbling of the least valuable forestland pieces – initially more profitable than agriculture, see Figure A6a (with sector i and i+1 being respectively agriculture and forestry). In response, both average farmland and forestland rents increase.

$$ \frac{d\bar{R}_2^*(C)}{dC} = -\frac{t_2y_2}{2} \frac{dr_2^*(C)}{dC} = -\frac{t_2y_2}{2} y_{3C}^C \left( \frac{y_2(p_2t_3 - p_3t_2)}{(t_2y_2 - t_3y_3)^2} \right), $$

<footnote n="13">¹³When all sectors value the same lands, a climate shock on forest productivity leads to similar relationship. Formally:</footnote>

<footnote>where the climate-induced land-use change is here of the opposite sign than the climate shock – i.e. forestry expands over farmlands in case of a positive shock on forest productivity. Note additionally that one can write the derivative of average farmland rent with respect to climate when sectors differently value land quality (see Appendix A4.3).</footnote>
To sum up, the Ricardian estimates obtained on average farmland rents do not capture only climate impacts on agricultural productivity, but additionally capture several *climate-induced land-use change effects* coming from agriculture and other sectors, that could either *accumulate* or (partially) *offset* each other. Worst, the Ricardian approach is unable to infer which sector(s) was initially affected by climate. Proposition 3 thus clearly shows that the usual Ricardian interpretation is not supported, whether in its weakest or strongest version. In plain English, as long as the average farmland rents are computed on different total agricultural areas, the standard Ricardian approach can neither inform on the climate impacts on agricultural productivity nor on agricultural welfare. We explain hereafter how a simple correction can however retrieve the latter interpretation.

**Correction.** Specifically, because the welfare of each sector corresponds to their total rents,<fnref n="14" /> one can retrieve the standard Ricardian interpretation by regressing the *total farmland rent* at the regional level on climate. Such a “land-adjusted” Ricardian approach would conceptually retrieve the climate impacts on agriculture welfare, that is the strong Ricardian interpretation. Formally, comparative statistics on the total farmland rents lead to the following proposition.

**Proposition 4.** *When total farmland rents are observed, the application of the land-adjusted Ricardian approach infer the value of climate for agriculture. Although the land-adjusted Ricardian estimates do not fully recover the climate impacts on productivity, they evolve in the same direction than those on agriculture, and in the opposite direction to those on the non-agricultural sectors.*

**Proof.** See Appendix A4.4 ■

Proposition 4 implies that measuring total farmland rents allows retrieving the initial Ricardian interpretation. If such measurements are usually not available, they can be easily recovered by *multiplying average farmland rents by their corresponding areas*. Our correction thus reverses the standard Ricardian procedure: while Ricardian studies traditionally infer the costs of climate change by first estimating Ricardian function on average farmland rents before to multiply the obtained estimates by the corresponding agricultural area, we propose here to proceed to such a multiplication *before* the Ricardian estimation. Directly multiplying these two elements allows the land-adjusted Ricardian approach to capture both the *productivity* and the *climate-induced land-use change effects* at the same time and, ultimately, to rightly and directly estimate the climate impacts on agricultural welfare. Proposition 4 however indicates that it can not isolate the climate impacts on agricultural productivity (i.e. the weak Ricardian interpretation). A major difference with the standard Ricardian approach is that, under the assumption that climate only affects agricultural productivity, the land-adjusted estimates evolve in similar direction than their impacts on agricultural productivity. Yet, the land-adjusted approach remains unable to rightly assess which sectoral productivity is initially affected by climate (agriculture, construction or forestry, or a mix of the three).

<footnote n="14">¹⁴This property is an extension of insights by Dunn (1954) and Lind (1973), who noted that the welfare in the whole economy equals to the integral of all land rents. We thus split this reasoning by sector. Specifically, the welfare of the construction sector corresponds to the integral of the bidding curve $\Phi_1(r, C)$ on the segment $[0; r_1^*(C)]$. Similar computations can be done for agriculture and forestry on $[r_1^*(C); r_2^*(C)]$ and $[r_2^*(C); r_3^*(C)]$ respectively.</footnote>
## 2.3 Climate impacts on the whole land sector

We examined so far how marginal, average and total farmland rents and areas evolve when climate affects the productivity of one sector, whether agricultural or not. These analyses led to propositions 1 to 4. One can easily prove that, if these propositions hold for agriculture, they also hold for the non-agricultural sectors. In particular, it is possible to obtain similar relations than in equations (9) and (10) to expand propositions 3 and 4 to construction and forest sectors. Figures 2 and 3 illustrate the interest of these propositions for them. Figure 2 shows for example that, while the average urban rent decreases following a negative climate shock on agricultural productivity, the total urban rent does increase (as one could intuitively expect). On the contrary, Figure 3 shows that a positive climate shock on construction productivity does not necessarily lead to an increase of average urban rent, while it necessarily increases total urban rent. These examples show that, under the assumption that urban and forestland rents are observed, (i) the application of the standard Ricardian approach cannot retrieve the welfare impacts of climate change on these two sectors, but (ii) the application of the land-adjusted Ricardian approach can.<fnref n="15" /> Proposition 3 notably implies the following corollary.

**Corollary 1.** A situation where the standard Ricardian estimates are of the same signs for all sectors implies that (i) sectors differently value land quality and (ii) it is impossible to distinguish which sectoral productivity depends on climate.

Indeed, when the standard Ricardian approach is applied to all sectors one by one, a situation where the resulting estimates are all of the same signs would imply, following proposition 3.2., that sectors differently value land quality. Corollary 1 suggests that, in such a situation, the Ricardian estimates traditionally assigned to agriculture may actually reflect spillovers from non-agricultural sectors (via climate-induced land-use change effects).

Because proposition 4 hold for all sectors, it is also possible to apply it for the whole land sector, without sectoral distinction. This means that, instead of applying the land-adjusted Ricardian approach for the different segments $[0; r_1^*(C)]$, $[r_1^*(C); r_2^*(C)]$ and $[r_2^*(C); r_3^*(C)]$ (Figure 1), one could actually apply it to the whole segment $[0; r_3^*(C)]$ directly. Indeed, because land rents correspond to the upper envelope of the sectoral bid functions, it is not necessary to distinguish the sectors to infer the value of climate for the whole land sector. This remark leads to the following corollary.

**Corollary 2.** Under the assumption that land rents are observed for all sectors, the application of the land-adjusted Ricardian approach on the total rents aggregated for all sectors rightly infer the value of climate for the whole land sector. It can however not identify the initial sectoral productive shock(s).

Corollary 2 implies that one can recover the aggregated climate impacts on the welfare of the whole land sector by explaining the climate impacts of the sum of the total rents for (i) urban, (ii) farm and (iii) forestland – that is on the whole welfare of the economy (i.e. on the integral of the whole rent function on $[0; r_3^*(C)]$ in Figure 1). Such an approach allows aggregating all sectoral climate impacts, accounting for both the initial productivity shock and the compensating climate-induced

<footnote n="15">¹⁵Propositions 3 and 4 matter for previous Ricardian attempts on urban and forestry (e.g. Sinha et al., 2018; Mihiar and Lewis, 2021, respectively). It notably means that previous applications using their average rents did not rightly infer the sectoral climate impacts. Instead, they have measured a mix between potentially true climate impacts on sectoral productivity, and climate-induced land-use change effects that could have spilled from all the sectors.</footnote>
land-use change effects between sectors. It actually reestablishes the initial Ricardian idea developed by Mendelsohn et al. (1994), but to the case where farmers not only adapt to climate change by adjusting their crop allocation (as commonly though), but also by adjusting the total farmland area.<fnref n="16" />

Based on the above analyses, we estimate in the following of the paper the land-adjusted Ricardian functions on (i) agriculture, (ii) construction, (iii) forestry and (iv) the whole land sector, and examine whether and to what extent they empirically differ from the standard Ricardian estimates.

# 3 Data

The empirical part of the article relies on longitudinal data collection of farmland prices, climate and control variables for French departments in successive cross-sections. For the purpose of the land-adjusted approach, we complete these data by observations on forest and urban prices, and data on the land area of the four considered uses (agriculture, forest, urban, other lands). We hereafter present our main data sources and variables of interest. Summary statistics are provided at the department level (for a representative area of about 78 km × 78 km).

## 3.1 Data sources

**Land prices.** The Ricardian literature commonly relies on average (farm)land prices observed at a regional level to proxy (farm)land rents (Fezzi and Bateman, 2015; Bigelow and Jodlowski, 2023). We proceed similarly in this paper, purchasing transaction-level information from the PERVAL database aggregated at the departmental level (the second administrative level in France). Provided by ADNOV, a company affiliated to the French notaries, PERVAL provides exhaustive information about all real estate transactions that have occurred since 1996 in France.<fnref n="17" /> On top of providing information on transaction price, transaction date, property size and location, PERVAL provides the key information on land uses, distinguishing houses from flats, building farm and forestland. We specifically purchase departmental-level aggregated information on (i) agricultural, (ii) forest and (iii) urban sectors, for which we restrain the transactions to building lots (which stands for the land value without buildings). Our information covers prices for the three uses (minimum, average, median, maximum and standard deviation) as well as sales volume in 2000, 2006, 2012 and 2018 for all French metropolitan departments (except those in the ‘*Corsica*’ and ‘*Ile-de-France*’ regions). To obtain complete information despite the constraints of French legislation on statistical secret, these cross-sections actually represent three-year averages (e.g. the cross-section in 2000 aggregates information from 1998, 1999 and 2000).<fnref n="18" />

Figure 4 shows the average land prices for the three alternative uses across France in 2012. As theoretically depicted in Figure 1, building lots are the most expensive lands, followed by farmland and, then, forestland. Reassuringly for our Ricardian application, Figure 4 shows that farmland prices

<footnote n="16">¹⁶The initial presentation of the Ricardian approach by Mendelsohn et al. (1994) did include non-agricultural uses (via the ‘retirement home’ example). However, because the large bulk of the Ricardian literature has applied this approach to farmland only, it actually misses – by construction – such adjustments outside agriculture (Cui, 2020a,b).</footnote>

<footnote n="17">¹⁷Notaries are legally obliged to report such data to PERVAL at the time of the signature of the notarial deed for fiscal purposes. ADNOV is authorized to sell aggregated statistics on such transactions to third parties for research purposes.</footnote>

<footnote n="18">¹⁸According to French legislation, statistical secret applies since there are less than three transactions within the department, or if a single transaction represents more than 85% of the total value. This particularly constrains us for forestland, which sometimes presents less than three annual transactions by department (in the west of France notably).</footnote>
are spatially heterogeneous, as are urban and forestland prices. Interestingly, Figure 4 suggests that land prices are positively correlated among uses, with the Mediterranean area presenting the highest prices for all land uses, and the center France presenting the cheapest ones. Table A1 in the Appendices provides additional summary statistics on the raw land price data.

<figure><img src="image_6.png" /><figcaption>Figure 4: Land prices for the different uses. NOTE. The figures show the average land price per department in 2012 for agriculture, forestry and urban, expressed in euros per hectare. The scale for building land (Figure 4c) is different from those for farmland and forestland (Figures 4a and 4b) – the brakes of the first scale are settled at 100 times the value of the second. Missing values are displayed in white. Finally, note that we assume that other land uses – made of wetlands and waters – are assumed to present null value on land markets.</figcaption></figure>

**Land areas.** We obtain departmental-level data on land use areas in France for the years 2000, 2006, 2012 and 2018 from the TERUTI survey. Provided by the French Ministry of Agriculture, it specifically distinguishes (i) urban, (ii) agricultural and (iii) forest and natural areas at the departmental-level since 1982 following the same two-stage sampling methodology coupling photointerpretation and on-site surveys. To separate natural from forestland, we couple these data to Corine Land Cover (CLC) survey for corresponding years,<fnref n="19" /> which additionally provide information on wetlands and water courses but whose methodology has changed between 2000 and 2018.

Figure 5 shows the distribution of the four considered land use areas in 2012 across France. It shows that agriculture is the main use in the two northernmost thirds of France, forest occupying the largest share in the remaining third. Primarily located along the coasts, urban and other uses never exceed more than 20% and 13% of the departmental area respectively. Following our assumption in Section 2, other uses always occupy a strictly positive area.

**Climate.** We compute departmental-level climate variables from weather information provided by Météo France. Available since 1959, the database relies on historical daily measurements for the 8,604 French stations to spatialize the weather conditions on 8×8 km² grid squares, that we further aggregate at the departmental level. Such aggregation is standard in the Ricardian literature. A more debated

<footnote n="19">¹⁹CLC is a biophysical land cover inventory at a 25ha scale according to a 44-item nomenclature, produced by visual interpretation of satellite images. Contrary to TERUTI, it is only available for 1990, 2000, 2006, 2012 and 2018.</footnote>
<figure><img src="image_7.png" /><figcaption>Figure 5: Area shares occupied by the different land uses. NOTE. The figures show the proportion of departmental area occupied by for agriculture, forestry and urban in 2012, as recomputed from TERUTI and CLC surveys. Other uses include wetlands and water resources, as reported in CLC survey. Missing values are displayed in white (for the Corsican and Parisian regions).</figcaption></figure>

choice regards the climate variables’ construction. A common practice consists of measuring climate variables as 30-year temperature and precipitation averages for each season (Mendelsohn and Massetti, 2017). However, many Ricardian studies have preferred to use degree days over the growing season instead (e.g. Schlenker et al., 2006; Severen et al., 2018; Ortiz-Bobea, 2020). While this alternative makes sense when applied to annual crops, it is more subject to debate when looking at urban and forestry, whose values may be affected by autumn and winter temperatures and precipitation (as for permanent crops; see Bareille and Chakir, 2023, for example). We thus follow the initial Ricardian literature and estimate a four-season model with climate measured as 30-year averages.

Figures A7 and A8 in the Appendices respectively show the seasonal 30-year averages of temperature and precipitation across France in 2012. They underline a great heterogeneity of climates over space. For example, the Mediterranean basin presents the highest temperatures in all seasons. Mountain areas in the Alps, the Pyrenees, the Massif Central and, to a lesser extent, the Jura display the
lowest temperatures. The remainder of France presents rather similar 30-year temperature averages. However, the Atlantic coast benefits from higher precipitation than the remainder of France.

**Controls.** Because it consists in cross-sectional analyses, previous Ricardian applications have traditionally added several control variables. We account here for the most common ones such as population and soil and topographic conditions (Mendelsohn and Massetti, 2017). Population data comes from the French institute of Economics and Statistics. Data on soil texture conditions (four levels) come from the Joint Research Centre at a scale of 1:1,000,000 (Panagos et al., 2012), and further aggregated at the departmental level. Relief data (altitude and slope) are derived from the digital elevation model GTOPO at the 30 arc seconds scale, and further aggregated at the departmental level.

## 3.2 Summary statistics

Our sample consists of 86 French departments for which we observed land prices and areas for the four distinguished uses – i.e. urban, agriculture, forest and other uses – as well as climate and control variables in 2000, 2006, 2012 and 2018. Table 1 presents the summary statistics of our variables. As displayed in Section 3.1, these statistics show that urban is the most valuable land on average (by about 50 to 90 times more than farm or forestland respectively), but that it is the most marginal area (by a factor about five to seven more than forest and farmland respectively – leaving aside other uses), representing about 8% of French territory. Farmland is on average the most common use, occupying about 52% of French territory, with an average value of about 6,000 €/ha. Finally, forestland is the least valuable use with an average value of about 3,5000 €/ha (leaving aside other uses that we assume present null value on land markets), and represent about 38% of French territory. By difference, the other use category represents only 1% of French territory.

# 4 Empirical analysis

This section presents how we exploit our data to test our theoretical propositions. We first develop in Section 4.1 the details of our econometric modelling to implement the standard and land-adjusted Ricardian approaches. We then explain the identification strategy for both methods in Section 4.2.

## 4.1 Econometric modelling

The literature traditionally estimated Ricardian models for a single cross-section (e.g. Mendelsohn et al., 1994; Schlenker et al., 2005; Severen et al., 2018). However, in face of the instability of Ricardian estimates over time (Deschênes and Greenstone, 2007), Massetti and Mendelsohn (2011) showed that estimating pooled Ricardian models on panel data with the inclusion of both time-varying controls and time fixed effects on top of usual time-invariant controls (e.g. soil and topographic conditions) allows stabilizing the Ricardian estimates over time. Following this work, numerous studies have embraced this pooled approach to estimate standard Ricardian models (e.g., Fezzi and Bateman, 2015; Bareille and Chakir, 2023). We proceed similarly in this paper.
<table><caption>Table 1: Summary Statistics (N=344)</caption><thead><tr><th></th><th>Mean</th><th>S.D.</th><th>Min</th><th>Median</th><th>Max</th></tr></thead><tbody><tr><td>Farmland price (euro/ha)</td><td>5,901.92</td><td>3,727.97</td><td>1,911.98</td><td>4,957.13</td><td>32,225.23</td></tr><tr><td>Forestland price (euro/ha)</td><td>3,528.52</td><td>2,295.35</td><td>896.10</td><td>2,967.56</td><td>20,668.22</td></tr><tr><td>Building land price (euro/ha)</td><td>313,837.01</td><td>267,709.57</td><td>32,479.06</td><td>226,921.17</td><td>1,757,449.49</td></tr><tr><td>log(Farmland price) (euro/ha)</td><td>8.56</td><td>0.45</td><td>7.56</td><td>8.51</td><td>10.38</td></tr><tr><td>log(Forestland price) (euro/ha)</td><td>8.03</td><td>0.50</td><td>6.80</td><td>8.00</td><td>9.94</td></tr><tr><td>log(Building land price) (euro/ha)</td><td>12.36</td><td>0.76</td><td>10.39</td><td>12.33</td><td>14.38</td></tr><tr><td>Farmland area (ha)</td><td>327,066.51</td><td>127,438.80</td><td>20,898.00</td><td>331,652.00</td><td>587,334.00</td></tr><tr><td>Forestland area (ha)</td><td>232,178.68</td><td>113,303.30</td><td>30,264.18</td><td>210,036.39</td><td>625,898.24</td></tr><tr><td>Urban area (ha)</td><td>48,479.06</td><td>20,790.69</td><td>7,911.00</td><td>46,009.50</td><td>129,127.00</td></tr><tr><td>Other area (ha)</td><td>6,701.13</td><td>10,450.38</td><td>441.48</td><td>3,746.15</td><td>68,753.17</td></tr><tr><td>Spring temperature (°C)</td><td>9.47</td><td>1.66</td><td>2.80</td><td>9.52</td><td>12.87</td></tr><tr><td>Summer temperature (°C)</td><td>17.76</td><td>1.71</td><td>11.78</td><td>17.78</td><td>22.16</td></tr><tr><td>Autumn temperature (°C)</td><td>10.81</td><td>1.62</td><td>5.06</td><td>10.81</td><td>14.12</td></tr><tr><td>Winter temperature (°C)</td><td>3.70</td><td>1.86</td><td>-2.50</td><td>3.81</td><td>6.56</td></tr><tr><td>Spring precipitation (cm/month)</td><td>7.04</td><td>1.35</td><td>4.64</td><td>6.85</td><td>12.30</td></tr><tr><td>Summer precipitation (cm/month)</td><td>6.49</td><td>1.70</td><td>2.51</td><td>6.28</td><td>12.74</td></tr><tr><td>Autumn precipitation (cm/month)</td><td>8.47</td><td>1.86</td><td>5.51</td><td>8.13</td><td>16.17</td></tr><tr><td>Winter precipitation (cm/month))</td><td>6.98</td><td>1.74</td><td>2.28</td><td>6.77</td><td>12.06</td></tr><tr><td>Annual temperature (°C)</td><td>10.47</td><td>1.62</td><td>4.31</td><td>10.46</td><td>13.88</td></tr><tr><td>Annual precipitation (cm/month)</td><td>7.24</td><td>1.27</td><td>4.87</td><td>6.97</td><td>11.28</td></tr><tr><td>Population density (inhabitants/km²)</td><td>1.05</td><td>0.91</td><td>0.15</td><td>0.73</td><td>5.66</td></tr><tr><td>Altitude (m)</td><td>365.48</td><td>342.27</td><td>34.97</td><td>257.61</td><td>1,641.05</td></tr><tr><td>Slope (%)</td><td>4.64</td><td>5.22</td><td>0.57</td><td>2.49</td><td>26.02</td></tr><tr><td>Soil category 1 (%)</td><td>0.15</td><td>0.15</td><td>0.00</td><td>0.10</td><td>0.66</td></tr><tr><td>Soil category 2 (%)</td><td>0.47</td><td>0.26</td><td>0.03</td><td>0.44</td><td>1.00</td></tr><tr><td>Soil category 3 (%)</td><td>0.25</td><td>0.25</td><td>0.00</td><td>0.17</td><td>0.85</td></tr><tr><td>Soil category 4 (%)</td><td>0.12</td><td>0.14</td><td>0.00</td><td>0.05</td><td>0.63</td></tr></tbody></table>

NOTE. The figures provide the summary statistics of our sample on which we performed our preferred analyses. Data sources are described in Section 3.1. All land prices have been previously deflated by ADNOV using historical inflation rate series from the French Institute of Economics and Statistics. It is assumed that other land uses present null value on land markets.

**Standard Ricardian model.** Following the large bulk of the Ricardian literature (e.g. Massetti and Mendelsohn, 2011; Fezzi and Bateman, 2015; Bareille and Chakir, 2023), we formalize the Ricardian function with a log-quadratic specification. This specification has numerous benefits, allowing us to (i) linearize equation (11), (ii) capture the skewed distribution of farmland prices and (iii) account for the non-linearities of the marginal value of climate as one moves away from averages (Mendelsohn et al., 1994). We formally write a pooled log-quadratic Ricardian model as follows:

$$ \log(\bar{R}_{i,j,t}^*) = \alpha_i + \beta_i C_{j,t} + \gamma_i z_{j,t} + \theta_{i,t} + \epsilon_{i,j,t}, \quad (14) $$

where $\bar{R}_{i,j,t}^*$ corresponds to the average land rent – price – of sector $i$ (as depicted in Section 2) in department $j$ and year $t$ ($i=2$ corresponds to the standard Ricardian application on agriculture). The sectoral Ricardian function depends on the vector of seasonal temperature and precipitation averages between $t-30$ and $t-1$ in department $j$ in both linear and squared terms (i.e. a vector of $16 = 2 \times 2 \times 4$ variables) and on the set of time-varying and time-invariant controls in $j$ and $t$ (here population as well as average altitude, slope and soil conditions), as well as their associated sectoral parameters $\beta_i$ and $\gamma_i$. The sectoral Ricardian function depends also on a set of year fixed effects $\theta_{i,t}$ and on a error term $\epsilon_{i,j,t}$. We estimate equation (14) with ordinary least squares (OLS). Spatial dependence in
the error terms is corrected using Conley (1999)'s procedure to obtain spatial heteroscedasticity and autocorrelation consistent estimator of the variance-covariance matrix.

**Land-adjusted Ricardian model.** The land-adjusted Ricardian estimation follows a similar approach, replacing the regional average land rents by the total land rents as new dependent variable. That is, our land-adjusted Ricardian approach simply consists in regressing:

$$ \log(A_{i,j,t}^* \times \bar{R}_{i,j,t}^*) = \tilde{\alpha}_i + \tilde{\beta}_i C_{j,t} + \tilde{\gamma}_i z_{j,t} + \tilde{\theta}_{i,t} + \tilde{\epsilon}_{i,j,t}, \quad (15) $$

where $A_{i,j,t}^*$ is the area of the sector $i$ in department $j$ and year $t$ (i.e. corresponding to the difference between $r_i^*(C)$ and $r_{i-1}^*(C)$ in Section 2), all other elements being similar to equation (14). The multiplication of average sectoral land rents by the corresponding areas lead to the total sectoral land rents at the origin of proposition 4. The set $\{\tilde{\alpha}_i; \tilde{\beta}_i; \tilde{\gamma}_i; \tilde{\theta}_{i,t}\}$ consists in the parameters to be estimated. We estimate them in equation (15) using OLS coupled to spatially clustered standard errors obtained with the Conley (1999)'s correction. Any statistically significant difference between $\beta_2$ and $\tilde{\beta}_2$ would indicate that the standard Ricardian estimates are biased.

## 4.2 Identification strategy

The Ricardian approach typically exploits cross-sectional data on farmland prices across space to evaluate how they vary with climate. Both our standard and land-adjusted Ricardian approaches develop in equations (14) and (15) proceed similarly, with some specificities.

The first is that we depart from the cardinal cross-sectional framework by using four successive cross-sections to increase the number of observations. Yet, because our pooled analyses include time fixed effects, they rely on similar identification principle than pure cross-sectional analyses, exploiting spatial variations only (Massetti and Mendelsohn, 2011). This is typically depicted by Figures 4, A7 and A8, where departmental-level land prices in 2012 are explained by corresponding climates.

One potential issue with this strategy is that, because France is smaller than other areas where the Ricardian approach has been applied, the amount of variations used for the identification can be more limited. Figures A7 and A8 show that the maximum differences in long-term temperatures and precipitation across French departments were about 10°C and 10 cm/month for each season in 2012. These differences more than cover the temperature and precipitation changes predicted by climatologists, even in the most pessimistic scenario (Masson-Delmotte et al., 2021). Our Ricardian application thus conserves its suitability regarding the “time for space substitution” principle. Looking at the variability around the averages, Table 1 indicates that the coefficients of variations of long-term seasonal temperature and precipitation are comprised between 0.08 and 0.44. These variation levels typically correspond to those observed in previous Ricardian studies performed in France (Bareille and Chakir, 2023), or even on larger countries (such as Ortiz-Bobea, 2020, in the US for example).

We also stand from the remaining of the Ricardian literature with regard to our dependent variables, for which we present two originalities. In the first hand, we not only use data on farmland prices, but also on land prices from other sectors. The coefficient of variations for average farmland prices in Table 1 is equal to 0.63, but to 0.65 and 0.85 for forest and building lands. That is, the land prices of
these two sectors present as least as much spatial variations than those of agriculture. Figure 4 shows
that they do vary over space, with lowest and highest values respectively reach in similar departments
than farmland prices. We use these additional sources of variation to apply the Ricardian approach
on these two alternative sectors – in addition to the standard agricultural application.

In the second hand, our land-adjusted Ricardian approach additionally use land areas on top of average land prices as primary source of variation. This means that, while our standard Ricardian approach regresses land prices (Figure 4) on climates (Figures A7 and A8), our land-adjusted Ricardian approach actually regresses land prices *preliminary multiplied* by corresponding areas (Figure 5) on climates. This conducts to additional sources of variations, which manifests by overall higher coefficients of variation – equal to 0.45, 0.75 and 1.05 for agriculture, forestry and urban respectively. Figure A9 in Appendices shows the distribution of total rents for the alternative sectors across France. It clearly indicates that the variations of total rents differ from those of average rents. For example, while Figure 4 indicates that the most valuable farmlands are located in the south-eastern France, Figure A9 shows that, actually, the departments with the largest agricultural sector are located in northern France. This is because, even if they present smaller average farmland prices (in euro per hectare), the farmland area is much larger there (Figure 5). We find similar differences for urban and forestry. These alternative sources of variations in our dependent variables reflect the main difference in identification strategy between the standard Ricardian approach and the land-adjusted one.

# 5 Results

We report hereafter our empirical results. Specifically, Section 5.1 displays the marginal climate effects recomputed with our preferred standard and land-adjusted Ricardian estimates for each sector. Section 5.2 details the marginal climate effects for the whole land sector. Section 5.3 describes some sensitivity analyses. Finally, Section 5.4 documents climate-induced land-use changes, mechanism at the origin of the non-consistency of the standard Ricardian approach (see Section 2).

## 5.1 Climate impacts: Standard vs. land-adjusted Ricardian estimates

Our main task consists in comparing the standard and land-adjusted Ricardian estimates obtained on our data for agricultural, forest and urban sectors. Tables A3, A4 and A5 in Appendices display the obtained estimates for our preferred specifications – equations (14) and (15) – as well as alternative specifications dropping either year fixed effects, controls or both. Table 2 reports the marginal impacts of seasonal climate conditions on the alternative sectors, recomputed from our preferred standard and land-adjusted Ricardian estimates.<fnref n="20" /> We successively interpret these marginal impacts in the following.

**Agriculture.** The leftest-hand column of Table 2 makes clear that the climate impacts estimated for agriculture with the standard Ricardian approach are fully in line with the literature. Indeed, most of the Ricardian literature identifies beneficial effects of warmer springs and autumns but harmful effects

<footnote n="20">²⁰Tables A6, A7 and A8 details – for agricultural, forest and urban sectors respectively – the marginal climate impacts recomputed from the raw standard and land-adjusted Ricardian estimates. See Fezzi and Bateman (2015) for an example of the computation of the marginal climate impacts with log-quadratic Ricardian models.</footnote>
<table><caption>Table 2: Marginal climate impacts by sector with the standard and land-adjusted Ricardian approaches</caption><thead><tr><th rowspan="3"></th><th colspan="3">Dependent variable:<br>log(land price of type <i>i</i>)</th><th colspan="4">Dependent variable:<br>log(land price of type <i>i</i> × area of type <i>i</i>)</th></tr><tr><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th><th>(7)</th></tr><tr><th>Agriculture</th><th>Forest</th><th>Urban</th><th>Agriculture</th><th>Forest</th><th>Urban</th><th>Total</th></tr></thead><tbody><tr><td><strong>Temperature (°C)</strong></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Spring</td><td>0.80 ***<br>(0.21)</td><td>-0.27<br>(0.38)</td><td>1.14 ***<br>(0.39)</td><td>-0.37<br>(0.26)</td><td>-0.26<br>(0.36)</td><td>0.98 ***<br>(0.32)</td><td>0.75 ***<br>(0.30)</td></tr><tr><td>Summer</td><td>-0.62 ***<br>(0.14)</td><td>-0.10<br>(0.22)</td><td>-0.76 ***<br>(0.18)</td><td>0.05<br>(0.26)</td><td>0.73 **<br>(0.36)</td><td>-0.54 ***<br>(0.16)</td><td>-0.37 **<br>(0.16)</td></tr><tr><td>Autumn</td><td>0.58 ***<br>(0.21)</td><td>0.56 **<br>(0.28)</td><td>0.81<br>(0.53)</td><td>-0.02<br>(0.48)</td><td>-1.32 **<br>(0.66)</td><td>0.35<br>(0.74)</td><td>0.12<br>(0.63)</td></tr><tr><td>Winter</td><td>-0.54 ***<br>(0.17)</td><td>-0.28<br>(0.21)</td><td>-0.93 ***<br>(0.30)</td><td>0.26<br>(0.41)</td><td>1.02 **<br>(0.52)</td><td>-0.44<br>(0.46)</td><td>-0.22<br>(0.40)</td></tr><tr><td><strong>Precipitation (cm/month)</strong></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Spring</td><td>-0.28 ***<br>(0.05)</td><td>-0.37 ***<br>(0.08)</td><td>-0.38 ***<br>(0.06)</td><td>0.08<br>(0.09)</td><td>-0.28 ***<br>(0.10)</td><td>-0.28 ***<br>(0.09)</td><td>-0.24 **<br>(0.09)</td></tr><tr><td>Summer</td><td>0.05<br>(0.04)</td><td>0.15 **<br>(0.07)</td><td>-0.13 **<br>(0.06)</td><td>0.12 ***<br>(0.03)</td><td>0.22 ***<br>(0.08)</td><td>-0.06<br>(0.10)</td><td>-0.02<br>(0.08)</td></tr><tr><td>Autumn</td><td>0.01<br>(0.04)</td><td>0.07<br>(0.05)</td><td>0.00<br>(0.05)</td><td>-0.05<br>(0.04)</td><td>0.19 **<br>(0.07)</td><td>0.02<br>(0.07)</td><td>0.03<br>(0.06)</td></tr><tr><td>Winter</td><td>0.04<br>(0.05)</td><td>0.07<br>(0.05)</td><td>0.14 ***<br>(0.05)</td><td>-0.18 *<br>(0.10)</td><td>0.01<br>(0.09)</td><td>0.01<br>(0.07)</td><td>-0.01<br>(0.08)</td></tr><tr><td><strong>Number of observations</strong></td><td>344</td><td>344</td><td>344</td><td>344</td><td>344</td><td>344</td><td>344</td></tr><tr><td><strong>Controls</strong></td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td><strong>Year fixed effects</strong></td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td><strong>Adjusted R<sup>2</sup></strong></td><td>0.63</td><td>0.54</td><td>0.73</td><td>0.54</td><td>0.38</td><td>0.81</td><td>0.81</td></tr></tbody></table>

NOTE. The figures report the recomputed marginal impacts of seasonal climate variables on land price of type *i* in left-hand columns, in the spirit of the standard Ricardian approach, and on the multiplication of area of type *i* by price in right-hand columns, in line with the land-adjusted Ricardian approach. The computations use the estimates obtained with the log-quadratic models and the average variable values in our sample. Climate variables are computed using 30-year averages. Controls include population, average altitude and soil conditions. Standard errors adjusted for spatial dependence and computed using the delta method are displayed in brackets. *, ** and *** indicate a p-value lower than 0.1, 0.05 and 0.01 respectively.

of hotter summers and winters (Massetti and Mendelsohn, 2011; Van Passel et al., 2017; Bareille and Chakir, 2023). This is also what we identify here. Our results regarding precipitation are closely related to those in Bareille and Chakir (2023), indicating negative impacts of precipitation on farmland prices in spring, but positive impacts in other seasons (though not significantly distinct from zero at the critical threshold of 90% with our preferred specification). Table A6 in the Appendices show that these results are globally conserved when changing the specification at the margin. Although varying in terms of amplitude of estimates, they always remain of the same signs than those presented in Table 2. Our standard Ricardian estimates are thus apparently robust and consistent with the literature.

However, standard Ricardian estimates may be theoretically biased (see Section 2). Following corollary 1, such a situation would be characterized by Ricardian estimates for agriculture that are of similar signs than those obtained for urban and forestry – under the assumption that they value land quality differently. Results from columns (2) and (3) in Table 2 indicate that this is indeed the case here. Specifically, we do find that all of the significantly identified climate impacts for agriculture are also significantly estimated – and of the same sign – for urban and forestry. This is particularly true for the urban sector: all of the five significantly estimated impacts for agriculture are significantly of the same sign than the urban sector (significantly non-null at the critical threshold of 85% for autumn temperatures), while only two of them are also significantly estimated for forestry. Given these similar
results, corollary 1 suggests that the Ricardian estimates traditionally assigned to agriculture are
actually biased, reflecting climate-induced land-use change spillovers from non-agricultural sectors.

By comparison, our land-adjusted Ricardian approach theoretically recovers the climate impacts on agricultural welfare even in the presence of climate-induced land-use changes (see Section 2). Column (4) of Table 2 shows the marginal climate impacts obtained for agriculture with such an approach. They indicate that, actually, none of the significantly non-null estimates identified with the standard Ricardian approach remain statistically non-null with the land-adjusted approach. In particular, temperature impacts for all seasons are statistical zeros in column (4).

Table 2 shows that, compared to our land-adjusted Ricardian estimates, the standard estimates can even hide some significant climate impacts on agriculture. This is notably the case for summer precipitation, which appears to benefit agriculture in our land-adjusted Ricardian approach, but to harm agriculture in the standard approach – this apparently inconsistent result for summer precipitation is often documented in the Ricardian literature (Schlenker et al., 2005).<fnref n="21" /> Such a positive impact however aligns with studies estimating beneficial effects of summer precipitation on agricultural productivity (e.g. Ortiz-Bobea et al., 2019), and more closely reflects common intuition (Schlenker et al., 2005).<fnref n="22" /> We find similar differences between the land-adjusted and the standard Ricardian approaches for winter precipitation. The systematic difference for seven out of eight of the climate impacts – the exception stands for autumn precipitation – does confirm that our standard Ricardian estimates are biased and, instead, likely reflect spillovers from non-agricultural uses.

**Forest.** Table 2 shows that our preferred standard and land-adjusted Ricardian estimates identify different climate impacts for forestry. For example, while the standard approach identifies a beneficial effect of autumn temperature on forestry, the land-adjusted approach rather identifies a detrimental effect. Table A7 in the Appendices shows that this holds with other specifications. For example, it reports negative impacts of both summer and winter temperature with the standard Ricardian approach, but positive impacts with the land-adjusted one. Although the difference between the two approaches is particularly marked for temperature estimates, Table A7 shows that the precipitation estimates are also sensitive to the choice of the approaches and specifications.

As for agriculture, the theoretical insights from Section 2 suggests that the standard Ricardian estimates obtained from forestry could actually reflect climate-induced land-use change effects from other sectors. Specifically, because assumption 1 supposes that forestry is only adjacent to agriculture (i.e. there is no frontier between urban and forestry; see Figure 1), our theoretical results suggest that such impacts would come from agricultural spillovers only. Our results in Table 2 support this interpretation. Indeed, all of the significantly non-null climate impacts identified for forestry with the standard Ricardian approach in Table 2 are also significantly estimated (and of similar sign) for

<footnote n="21">²¹Table A6 indicates that this result is robust: while none of the standard Ricardian specifications found a positive effect of summer precipitation, all land-adjusted Ricardian specifications identified such positive impacts.</footnote>

<footnote n="22">²²Similarly, our land-adjusted Ricardian results indicate that, contrary to what suggests the standard Ricardian approach, spring precipitation does not harm agriculture. Indeed, while alternative studies investigating weather impacts on agricultural productivity have documented beneficial effects of spring precipitation (e.g., Ortiz-Bobea et al., 2019), previous Ricardian studies have instead documented – like us – negative impacts of spring precipitation on farmland value (e.g., Bareille and Chakir, 2023). This counter-intuitive results disappear in the land-adjusted Ricardian approach, suggesting that the previous results were probably an artefact induced by climate-induced land-use changes.</footnote>
agriculture.<fnref n="23" /> This equality between the two sets of estimates confirm that it is virtually impossible to distinguish true productivity from climate-induced land-use change effects, or even to identify the sectoral productivity initially affected by climate (agriculture, forestry or both).

**Urban.** Table 2 shows that our preferred standard and land-adjusted Ricardian estimates indicate sensibly similar sets of climate impacts on the urban sector. This sector thus differs from the others regarding its consistency between the two approaches (verified whatever the considered functional forms, see Table A8 in the Appendices). This suggests that climate-induced land-use changes in or out of the urban sector are *limited* – in line with assumption 1, where the high urban gradient leads to limited land-use changes in theory (see Figure 3 for example). This consistency also means that standard Ricardian estimates obtained for the urban sector *mainly* reflect true productivity effects.

This latter assertion helps us in re-interpreting the standard Ricardian estimates obtained for agriculture – column (1) of Table 2. Indeed, because agriculture is adjacent to both urban and forestry, the climate-induced land-use effects can come from/on these two sectors. However, because all of the standard agricultural Ricardian estimates are of the same signs than the standard Ricardian estimates for the urban sector, they likely mainly reflect confounding effects from urban spillovers, which could be large even if the climated-induced land-use changes are limited (see Figure 3). This result is particularly likely to hold for temperature estimates as, except for autumn temperatures, standard Ricardian estimates for forestry are not even significantly non-null. The main doubt regards the impacts of summer precipitation for which agriculture slightly benefits (but, in the tradition of the Ricardian literature, are not significantly non-null), while urban estimates indicate a negative effect. Because those obtained for forestry are positive, the traditional lack of significantly estimated impact of summer precipitation on farmland value is likely due to opposite climate-induced land-use change effects from/on urban and forest sectors offsetting each other. Finally, note that Table 2 shows that the land-adjusted Ricardian estimates for agriculture are systematically opposite to the urban ones, suggesting that the land-adjusted approach does correct for climate-induced land-use effects.

**Summary.** Table 2 shows that the standard Ricardian estimates present clear signs of bias. In particular, it suggests that traditional Ricardian results attributed to agriculture partly reflect spillovers from urban (and to a lesser extent forestry), but in no case true productivity effects. By comparison, Table 2 shows that Ricardian estimates for urban likely reflect true productivity effects, while those for forestry likely reflects climate-induced land-use changes between agriculture and forestry. More importantly, all of these results are consistent with our theoretical results. In particular, although the sets of standard Ricardian estimates present similar signs for all sectors (as theoretically predicted; see proposition 3), the sectoral land-adjusted Ricardian estimates do present their proper signs.

<footnote n="23">²³Because there is in principle no frontier between urban and forestry, the standard Ricardian estimates for these two sectors can however be of opposite signs in theory. This is the case for summer precipitation, which benefits forestry but harms urban (Table 2).</footnote>
## 5.2 Climate impacts on the whole land sector

Now that we have examined the results of the Ricardian approaches by sector, we turn to the analysis for the whole land sector. Indeed, corollary 2 indicates that the land-adjusted application on the sum of urban, forest and farmland rents would recover the aggregated climate impacts on the whole land sector. The result of such an analysis is depicted in the rightest-hand column of Table 2, and further developed for alternative specifications in Tables A9 and A10 in the Appendices.

The land-adjusted Ricardian estimates in Table 2 suggest that the profitability of the whole land sector depends mainly on climate in spring and summer. These estimates closely align to those obtained for urban, suggesting – in line with Figure A9 – that the total land value is mostly made of urban land. Reassuringly, they however (slightly) differ, Table 2 indicating that they are always slightly smaller in amplitude than those obtained for urban. Because the land-adjusted Ricardian estimates for agriculture and forestry are (almost) systematically of opposite signs than those for urban, this result reflects the compensating effects of the climate impacts on these two alternative sectors. As explained in Section 2, these total effects of climate reflect the spirit of the Ricardian approach, where landowners adjust not only their acreage (crop allocation), but also their total farmland area. As such, these climate impacts on the whole land sector reflect the originally conceived estimates of the Ricardian approach where landowners are not restricted to the agricultural sector. An analysis of the coefficient of determination actually suggests that, among all of our standard and land-adjusted Ricardian estimations, the one with the greatest proportion of rent variation that is explained by the Ricardian approach is those conduct on the whole land sector. In other words, the land-adjusted Ricardian approach on the whole land sector is the analysis that best fits our data.

## 5.3 Sensitivity analyses

We investigate here whether our results above are influenced by specific empirical choices related to (i) the log-quadratic functional form as preferred Ricardian specification, (ii) the use of long-term seasonal temperature and precipitation as preferred climate measurements, (iii) the use of average departmental land prices as preferred proxy of land rents and (iv) the absence of any weighting procedure.

**Specification.** Our preferred estimates above could be biased if the functional form is mis-specified. In particular, while most Ricardian studies have relied on log-quadratic models (Massetti and Mendelsohn, 2011; Bareille and Chakir, 2023), the initial Mendelsohn et al. (1994)'s application did not use the logarithmic transformation on land prices but, instead, relied on strict quadratic models. Appendix A15 displays the recomputed marginal climate impacts using the standard and land-adjusted Ricardian approaches with such quadratic specification. Despite a drop in the quality of adjustment for all sectors and approaches, the estimates obtained with the quadratic specifications are overall in line with those obtained with the log-quadratic ones.

**Climate variables.** Our preferred analyses use a definition of climate as 30-years seasonal averages. Other studies have however embraced alternative climate definitions. For example, annual temperature and precipitation averages instead of seasonal ones have sometimes been considered as suitable climate
measurements for the Ricardian approach (e.g., Bozzola et al., 2018). Appendix A16 displays the estimates obtained with such climate variables. Despite a drop in the quality of adjustment for all sectors and models, the results remain in line with those reported in Sections 5.1 and 5.2, with significant differences between the standard and land-adjusted Ricardian estimates.

**Average prices for rents.** We obtained our preferred estimates using *average* departmental land price as proxy for land rents. However, because the distribution of land price is not normal (Schlenker et al., 2005), one could prefer alternative metrics. Appendix A16 displays the Ricardian estimates obtained with the *median* departmental land prices as proxy for land rents. All of the reported estimates are very similar to our preferred ones. The main difference is that those for forestry are less precisely estimated with the median departmental prices, reflecting the low number of transactions for forestland in France in many departments (see Table A1 in the Appendices).

**Weights.** We obtained our preferred estimates with OLS, while the Ricardian literature has often relied on weighting least squares (WLS), weighting the observations by the farmland area to reflect the regional agricultural specialization (e.g., Schlenker et al., 2005; Deschênes and Greenstone, 2007). Appendix A18 displays the standard and land-adjusted Ricardian estimates, weighting the observations by their sector-specific departmental area. Ricardian estimates that correspond to those reported for the land-adjusted Ricardian approach would imply that a weighting procedure scheme empirically recover the land-adjusted approach, and would thus rightly assess the climate change costs for agriculture (without the need to run the land-adjusted Ricardian approach). However, while the amplitude and precision of most of the standard Ricardian estimates for agriculture are affected by the weighting procedure, they remain significantly different from those obtained with the land-adjusted Ricardian approach. Estimates for the forest and urban sectors are less affected by the weighting procedure.

Moreover, we obtained our land-adjusted Ricardian estimates implicitly assuming that the total departmental area is sensibly the same across the whole France. While this is true that the size of such administrative division is much less varying that the US counties (or states), departmental areas differ across France – Table 1 indicates a coefficient of variation of 0.21 for the total departmental area. Even if there is no reason to assume that these differences are correlated to climate (French departments have been inherited from the French revolution, and have not evolved since 1922 in mainland France), such small variations can bias our estimates. To formally test whether our land-adjusted Ricardian estimates are sensitive to the differential departmental areas, we proceed to two alternative weighting procedure schemes. In the first one, we weight all the observations by the total departmental area. In the second, we weight them by the *inverse* of the total departmental area. That is, while the first procedure gives more weights to the largest departments, the second gives more weights to the smallest ones. Appendix A19 shows that the obtained land-adjusted Ricardian estimates differ from the standard ones in the two weighting procedures (for agriculture and forestry), confirming the presence of bias in the standard Ricardian approach.

To sum up, the sensitivity analyses suggest that our results in Sections 5.1 and 5.2 are not driven by specific empirical choices. Rather, the robust differences between the standard and land-adjusted
Ricardian estimates reflect true differences in the approaches. In particular, they suggest that the former is unable to infer true climate impacts on agriculture and forest welfare (or productivity).

## 5.4 Mechanisms: climate-induced land-use changes

Our point in this paper is to highlight the fallacy of the standard Ricardian approach in identifying consistent climate impacts on agriculture, because of the existence of climate-induced land-use change effects between agriculture and non-agricultural sectors. To investigate whether such effects exist in our data, we now regress the land-use shares of the four considered categories on climate following the same strategy than in equation (14). Table 3 reports the recomputed climate impacts.

<table><caption>Table 3: Marginal climate impacts on land-use shares</caption><thead><tr><th></th><th colspan="4">Dependent variable:<br>Land share occupied by use of type i</th></tr><tr><th></th><th>Agriculture</th><th>Forest</th><th>Urban</th><th>Other uses</th></tr></thead><tbody><tr><td><strong>Temperature (°C)</strong></td><td></td><td></td><td></td><td></td></tr><tr><td>Spring</td><td>-0.48 ***<br>(0.12)</td><td>0.57 ***<br>(0.18)</td><td>0.29<br>(0.21)</td><td>1.20 *<br>(0.74)</td></tr><tr><td>Summer</td><td>0.01<br>(0.07)</td><td>0.07<br>(0.10)</td><td>-0.34 **<br>(0.16)</td><td>-0.52<br>(0.64)</td></tr><tr><td>Autumn</td><td>0.33 **<br>(0.15)</td><td>-0.59 ***<br>(0.20)</td><td>0.57 ***<br>(0.19)</td><td>0.51<br>(1.16)</td></tr><tr><td>Winter</td><td>-0.08<br>(0.10)</td><td>0.23 *<br>(0.14)</td><td>-0.48 **<br>(0.19)</td><td>-0.80<br>(0.92)</td></tr><tr><td><strong>Precipitation (cm/month)</strong></td><td></td><td></td><td></td><td></td></tr><tr><td>Spring</td><td>0.12 ***<br>(0.04)</td><td>-0.15<br>(0.05)</td><td>-0.02<br>(0.04)</td><td>-0.57 **<br>(0.28)</td></tr><tr><td>Summer</td><td>-0.01<br>(0.03)</td><td>0.02<br>(0.04)</td><td>-0.02<br>(0.03)</td><td>-0.17<br>(0.21)</td></tr><tr><td>Autumn</td><td>-0.07 ***<br>(0.02)</td><td>0.10 **<br>(0.04)</td><td>-0.05 *<br>(0.03)</td><td>0.23<br>(0.18)</td></tr><tr><td>Winter</td><td>-0.07 **<br>(0.03)</td><td>0.08 **<br>(0.04)</td><td>0.04<br>(0.04)</td><td>0.18<br>(0.16)</td></tr><tr><td><strong>Number of observations</strong></td><td>344</td><td>344</td><td>344</td><td>344</td></tr><tr><td><strong>Controls</strong></td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td><strong>Year fixed effects</strong></td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td><strong>Adjusted R<sup>2</sup></strong></td><td>0.52</td><td>0.56</td><td>0.77</td><td>0.81</td></tr></tbody></table>

NOTE. The figures report the recomputed marginal impacts of seasonal climate variables on land shares of alternative land uses. The computations use the estimates obtained with the log-quadratic models and the average variable values in our sample. Climate variables are computed using 30-year averages. Controls include population, average altitude and soil conditions. Standard errors adjusted for spatial dependence and computed using the delta method are displayed in brackets. *, ** and *** indicate a p-value lower than 0.1, 0.05 and 0.01 respectively.

Table 3 makes clear that land uses are not orthogonal to climate. Instead, it highlights land-use substitution patterns for each marginal deviation of seasonal climate variable. For each marginal deviation, there is at least one land use that increases and at least another that decreases (not to mention significance of the effects). For example, Table 3 shows that an increase of spring temperature reduces agricultural area, in favour of more marginal lands – forest and other uses – whose area increases, urban remaining unaffected. The empirical confirmation of the existence of such climate-induced land-use changes highlighted in Section 2 clearly demonstrate that the standard Ricardian approach yields biased estimates.
Actually, these land-use substitution patterns induced by climate could explain some previous contradictory results between the standard and land-adjusted Ricardian approaches. Looking at the effect of spring temperature on agriculture for example, Table 2 shows that the standard Ricardian approach predicts an increase in agricultural profitability, while the land-adjusted one predicts no significant impact on agriculture. This means that the intensive margin effect – i.e., true productivity effects – of spring temperature on average land price is (more than) offset by the extensive margin effect on agricultural area. By comparison, Table 2 indicates no statistically significant impact of spring temperature on forest value with neither of the two methods. This means that the absence of significant effect at the intensive margin – left-hand column of Table 2 – dominates the extensive margin effect (Table 3), such that the overall impact of spring temperature on forest is null (right-hand column of Table 2). Finally, Table 2 indicates significant (and equal) positive impact of spring temperature on urban value with the two methods. This equality is consistent with the fact that urban area is really orthogonal to spring temperatures.

These climate-induced land-use substitution patterns can actually explained more subtly the differences between the standard and land-adjusted Ricardian results. Looking for example to the case of spring precipitation, the land-adjusted Ricardian results in Table 2 indicate that only agriculture benefits from them, which goes in the opposite direction than standard Ricardian results. This means that, as spring precipitation increases, agricultural value increase (as indicated by the land-adjusted Ricardian estimates), which leads farmers to expand over other sectors (notably by doing it predominantly on land pieces of fewer quality; see assumption 1), apparently reducing average farmland rents (as indicated by the standard Ricardian estimates). This expansion results in a reduction of the value of urban and forestry (see land-adjusted Ricardian results). Climate-induced land-use changes thus appear as a plausible consistent mechanism explaining the differences between standard and land-adjusted Ricardian results, at the source of biases for the standard approach.

# 6 Simulating climate change impacts

So far, we have theoretically shown that the standard Ricardian approach exploiting differences of average farmland rents on climates leads to biased estimates as long as farmland areas depend on the very climate conditions, but that a land-adjusted Ricardian approach exploiting total farmland rents can actually recover the value of climate for agriculture (Section 2). Our empirical results depicted in Section 5 confirmed such theoretical results, showing that the standard and land-adjusted Ricardian approaches lead to different climate estimates. Although striking, these results are only valid when looking at marginal changes in seasonal climate conditions. Climate change will however involve heterogeneous and non-marginal changes of temperatures and precipitation, such that one could wonder whether such divergent results remain under meaningful future climate. This is the purpose of this section. In particular, we compare the estimated impacts of two IPCC climate change scenarios using the standard and land-adjusted Ricardian approaches for agriculture, urban and forestry. Our aim here is not to produce a precise forecast of the impacts of future climate in France but, rather, to compare the estimated climate change impacts with the two approaches.
Specifically, we study the impacts of long-term outcomes (2070–2099) under low (RCP 2.6) and medium (RCP 4.5) emission pathways on the value of agriculture, urban and forestry in France, assuming all other factors to be constant. We compute these impacts by multiplying, for each observation, our preferred standard and land-adjusted Ricardian estimates in Table 2 by the differences between future climate conditions, as predicted from Météo-France’s ALADIN climate model, and those historically measured. The results of the simulations are displayed in Figure 6 for agriculture, and in Figures A10 and A11 for the forest and urban sectors.

<figure><img src="image_8.png" /><figcaption>Figure 6: Departmental projections of farmland value change by the end of the century under RCP2.6 and RCP 4.5 climate change scenario with the standard and land-adjusted Ricardian approaches. NOTE. Figures display estimated changes of value of agriculture in percentage if departments are exposed to hypothetical changes in temperature and precipitation, according to our preferred estimates and to the information provided by the ALADIN climate model for the RCP 2.6 and 4.5 emission pathways scenario between 2070 and 2099.</figcaption></figure>

Figure 6 shows contrasting climate change impacts on agriculture across France. While Figure 6a shows that the standard Ricardian approach predicts that all French departments should benefit from a RCP2.6 scenario, Figure 6b shows instead that, for the land-adjusted Ricardian approach, most departments would suffer from such a related warming. The land-adjusted Ricardian approach actually only predicts noticeable benefits for agriculture in some southern departments. The estimated
benefits with the land-adjusted Ricardian approach are larger for a RCP4.5 scenario, covering a larger part of France (notably in the west; see Figure 6d), but remain much smaller than those estimated with the standard Ricardian approach (Figure 6c). In other words, the standard Ricardian approach largely underestimates the costs of climate change for agriculture compared to the land-adjusted one.

Figures A10 and A11 underline similar underestimation with the standard Ricardian approach for forestry and urban. Specifically, while Figure A10 indicates that forestry in most departments is predicted to benefit from climate change with the standard Ricardian approach, our land-adjusted Ricardian approach instead predicts significant costs for forestry in the majority of France. The difference between the two methods is less pronounced for urban, but Figure A11 clearly shows that the standard Ricardian approach underestimates the costs of climate change for this sector.

Comparing the climate impacts for the three sectors across France with the two methods brings out an interesting pattern. Indeed, the standard Ricardian approach identifies *similar* beneficial climate impacts across France for the three sectors. This is particularly noticeable for the RCP2.6 scenario, where Figures 6a, A10a and A11a identify the same beneficiary arc-shaped area around the Massif Central, with benefits exceeding +75% of initial land value. Also identified in the RCP4.5 scenario (although to a lesser extent), this result reflects the similarity of the standard Ricardian estimates for the alternative sectors (Table 2), revealing signs of biases (corollary 1). By comparison, the predicted climate change impacts with the land-adjusted Ricardian approach are heterogeneous over space for the three sectors. Specifically, Figure 6 indicates that the land-adjusted Ricardian approach predicts beneficial climate impacts for agriculture in a small south-eastern part of France, while Figure A10 indicates beneficial climate impacts for forestry on a large southern part of France, and Figure A11 reports beneficial climate impacts for urban on the north-western France (and in the Alps). That is, the climate change benefits estimated with the land-adjusted Ricardian approach for the three sectors occur to *distinct regions* – which is in sharp contrast with what predicted by the standard Ricardian approach. To sum up the impacts over all sectors, Figure 7 displays the predicted climate change impacts as obtained with the land-adjusted Ricardian approach for the whole land sector (corollary 2). Figure 7 shows a clear partitioned situation, with the north-western part of France likely benefiting from climate change and eastern France largely suffering from it (with a few exceptions).

Figure 8 shows the estimated distribution of climate change impacts obtained with the standard and land-adjusted Ricardian approaches for the different sectors under RCP2.6 and RCP4.5 scenarios by the end of the century. It shows that the ranges of estimated climate impacts differ between the two approaches. Specifically, Figure 8a shows that, for agriculture and forestry, the estimated impacts of a RCP2.6 scenario are significantly smaller with the land-adjusted Ricardian approach than with the standard one (respectively at the 90% and 95% statistical thresholds). Indeed, while the standard approach indicates positive climate change impacts for the two sectors on average in France, the land-adjusted approach rather determines negative climate impacts (significantly distinct from zero for forestry, but not for agriculture). We find similar overestimation for urban in the RCP2.6 scenario case – although the difference between the two approaches is not significant. Figure 8a actually shows that the ranges of climate impacts estimated with the standard Ricardian approach are similar for the three sectors (between +30% to +130%), which reflects the initial similarity of the sectoral standard Ricardian estimates (Table 2) and reveals related signs of biases (corollary 1). Similar overestimation
<figure><img src="image_9.png" /><figcaption>Figure 7: Departmental projections of total land value change by the end of the century under RCP2.6 and RCP 4.5 climate change scenario with the standard and land-adjusted Ricardian approaches. NOTE. Figures display estimated changes of value for the whole land sector in percent if departments are exposed to hypothetical changes in temperature and precipitation, according to our preferred estimates and to the information provided by the ALADIN climate model for the RCP 2.6 and 4.5 emission pathways scenario between between 2070 and 2099.</figcaption></figure>

of the costs of climate change with the standard Ricardian approach is identified for all sectors under a RCP4.5 scenario (only significant for agriculture; see Figure 8b). Our land-adjusted approach actually indicates that the whole land sector will only slightly benefit from climate change on average (not statistically distinct from zero), but that all of the benefits should accrue to the urban sector.

# 7 Concluding remarks

Consisting in a cross-sectional regression of average farmland prices on climates across locations (Mendelsohn et al., 1994), the Ricardian approach is a cornerstone of the literature assessing the value of climate for agriculture (Mendelsohn and Massetti, 2017). This article theoretically and empirically shows that the Ricardian approach cannot recover such value. As long as farmland area depends on climate, we show that the Ricardian estimates are biased and, instead, additionally reflect spillovers from non-agricultural sectors which, by adjusting to climate shocks (either by expanding or contracting), affect farmland area – via land competition – and subsequently contaminate average farmland rents – via the decreasing returns. Our Ricardian estimates for France present signs of related biased, coming from both urban and forestry (whose area does statistically depend on climate). We propose a simple correction to retrieve unbiased climate impacts on agricultural welfare within this framework. It consists in preliminarily multiplying the average farmland rents by farmland area, before to explain such total farmland rents by climate across regions. Because this correction does inherently account for climate-induced land-use changes, we show that such a “land-adjusted” Ricardian approach does theoretically recover the climate impacts on agricultural welfare. Empirically, the obtained estimates with this correction are different than those traditionally obtained. While standard Ricardian estimates suggest that French agriculture will benefit from climate change, our land-adjusted Ricardian approach instead predicts no impact of climate change on agriculture.
<figure><img src="image_10.png" /><figcaption>Figure 8: Projected land value changes for the alternative sectors by the end of the century under RCP2.6 and RCP4.5 climate change scenario. NOTE. Graphs display estimated changes of land value of agriculture, forest, urban and total uses in percent if departments are exposed to hypothetical changes in temperature and precipitation, according to our preferred estimates and to the information provided by the ALADIN climate model for the RCP 2.6 and 4.5 emission pathways scenario between between 2070 and 2099. Dots represent point estimates. Solid and dotted whiskers respectively show the 90% and 95% confidence interval. The blue lines correspond to standard Ricardian models with year fixed effects and controls. The yellow lines indicate land-adjusted Ricardian models with year fixed effects and controls.</figcaption></figure>

In top of applying the Ricardian approach to agriculture, we also apply it to urban and forestry.
Our results similarly show that it underestimates the costs of climate change for these two sectors.
In line with our theoretical analysis, we notably show that it conducts to similar projections of the
costs of climate change for the three sectors, both in amplitude and over space. Once corrected, our
land-adjusted Ricardian approach instead identifies different climate change costs between sectors.
Overall, our land-adjusted approach suggests that the whole land sector will slightly benefit from
climate change, but that all of the benefits should accrue to the urban sector.

By specifically integrating the impacts of land competition between climate-sensitive sectors within
the Ricardian reasoning, our results provide several enlightenments. However, several caveats still
apply to this study. For example, while our estimates are obtained conditional on usual Ricardian
controls, one cannot ruled out potential remaining omitted variables (Deschênes and Greenstone, 2007),
particularly from those varying within the department (Bareille and Chakir, 2023). Also, while our
land-adjusted Ricardian approach accounts for long-term adjustment of farmland area, the obtained
results rely on the implicit but contestable assumption that agricultural prices and technologies will
remain constant under climate change (Cline, 1996; Gouel and Laborde, 2021). Future research should
investigate how these elements could be accounted for within the (land-adjusted) Ricardian framework
in order to provide robust and consistent estimates of climate change costs for agriculture.
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# A Appendices

## A1 Theoretical model with sector-specific land quality

This appendix presents the competitive equilibrium on land markets when the sectors value differently land quality. This assumption is notably made in all most recent land-use models working on aggregate data as Miller and Plantinga (1999) or Hartwick et al. (2001) – though more or less explicitly. As for the presentation of the alternative “no sector-specific land quality” case in Section 2.1 of the main text, we first present model assumptions when the sectors do not value the same lands, before to turn to the examination of the competitive equilibrium conditions on land markets.

**Model assumptions when sectors differently value the same lands.** As for the alternative “no sector-specific land quality” assumption, we assume that land is the single production factor. However, contrary to the “no sector-specific land quality” case, the hypothesis that all sectors do not value the same types of land pieces prevent us to rank these pieces along a single dimension without any further assumption. Instead, we assume that each piece of land is characterized by land quality $q^i$ for each sector $i = 1, 2, 3$, that is a same piece of land differ in quality depending on its use. We also assume that there are multiple demands (Chakravorty and Krulce, 1994; Chakravorty et al., 2005), where output prices are exogenous and equal to:

$$P_i(r) = p_i - t_i q^i, \qquad (A1)$$

where $p_i$ is the price of output $i$ produced on the land of best quality for sector $i$ (that is in $q^i = 0$), and $t_i$ is the price penalty as one moves by one unit from the best sector-specific land quality $q^i$. We here assume that the full set of assumptions on the parameters described in assumption 1 remains. For the sake of simplicity, we hereafter reason at the frontier between two sectors only, allowing us to represent the land market equilibrium on a two-dimensions graph.

**Land market equilibrium.** Specifically, we assume for the following that the land occupied by two sectors $i$ and $i + 1$ is at the maximum $Q$ and that the two sectors compete for land access on the segment $[0; Q]$ (Lichtenberg, 1989; Miller and Plantinga, 1999). We assume here that, contrary to the “no sector-specific land quality” case where the two sectors value the same types of land, the two sectors value here land quality on $[0; Q]$ in a strict opposite way (Hardie and Parks, 1997). That is, sector $i$ receives the highest price for $q^i = 0$, which corresponds to the case of $q^{i+1} = Q$, and it is possible to express $q^{i+1}$ as a function of $q^i$ in every point. Specifically, we assume that:

$$q^{i+1} = Q - q^i. \qquad (A2)$$

This hypothesis allows us to rank the two sectors along the segment $q_i \in [0; Q]$, where first lands in the segments are the most profitable for sector $i$, but the least valuable for sector $i + 1$, and vice versa. Note that the area $Q$ corresponds to the maximum potential area occupied by one sector alone, that is, given assumption 1, by sector $i + 1$. Furthermore, given that the last piece of land devoted to this
area is null under our model, this means that assumption 1 additionnaly ensures that the total land area occupied by sector i and i + 1 corresponds to $Q = p_{i+1}/t_{i+1}$.

The consequence of equation (A2) is that, assuming that the land markets otherwise work as in Section 2.1, this difference of land quality translates into the bid function of sector i – denoted $\Phi_i(\cdot)$ – such that:

$$ \Phi_i(q_i, C) \equiv y_i^C (p_i - t_i q^i), \qquad (A3) $$

where $y_i^C$ is the production of output i by unit of land that depends on climate as in Section 2.1. Equation (A3) is exactly similar to equation (2) in the main text, to the difference that the land quality is here specific to the sector. However, because we can note the land quality of sector of i + 1 as a function of land quality for sector i, we have also:

$$ \Phi_{i+1}(q_i, C) \equiv y_{i+1}^C (p_{i+1} - t_{i+1}(Q - q^i)). \qquad (A4) $$

As for the “no sector-specific land quality” case, we assume that landowners seek to maximize the profit from their lands, such that they will receive bids from alternative producers and select the highest bid. The result of the bidding procedure is the land market competitive equilibrium, defined by a rent function and by exclusive implementation areas for each sector. Noting $R(q^i, C)$ is the land rent at distance $q^i$ under climate C, equation (A3) provides the following land rent function at the equilibrium:

$$ R^*(q^i, C) \equiv \max\{\max_{j=i,i+1} \Phi_j(q^i, C), 0\}. \qquad (A5) $$

Equation (A5) states that, at the end of the bidding procedure, each location is occupied by the producer that offered the highest bid, that is by the most profitable sector at this location (Hardie and Parks, 1997). The land rent function at the equilibrium $R^*(\cdot)$ thus corresponds to the upper envelope of the land bidding curves along $q^i \in [0; Q]$, and each sector is located where its bid equals the land rent. The difference with Section 2.1 is that, given that the bidding curves are not linearly decreasing with $q^i$ (but decreasing for sector i and increasing for sector i + 1), the land rent function at the equilibrium is first decreasing and then increasing with $q^i$. The pivot points delimiting the frontiers between two uses i and i + 1 are characterized by the equality:

$$ \Phi_i(q_i^*(C), C) = \Phi_{i+1}(Q - q_i^*(C), C), $$

that is, when the bid functions between the two uses are equal. Noting that $\Phi_{i+1}(Q, C)$ is null, this leads to the following formula for the pivot point $q_i^{i*}$ separating sectors i and i + 1 under competitive land market equilibrium:

$$ q_i^{i*}(C) = \frac{p_i y_i^C}{t_i y_i^C + t_{i+1} y_{i+1}^C}. \qquad (A6) $$
As such, sector *i* establishes on the segment $[0; q_i^{i*}(C)]$, while sector *i* + 1 establishes on the segment $[q_i^{i*}(C); Q]$. Although the expression of the pivot point in equation (A6) is different from the expressions displayed in equations (5) to (7) in Section 2.1, it clearly shows that the frontiers between the two sectors dependent on the technologies and prices of the two sectors.

To characterize the difference between equations (1) and (A1) and related assumptions on the valuation of land quality, we present in Figure A1 the difference of bidding curves in the two alternative assumptions. Figure A1a presents the case where the two sectors *i* and *i* + 1 value the same types of land, while Figure A1b shows the case where the two sectors *i* and *i* + 1 differently value land. While functioning similarly, the competitive land market leads to two different equilibrium with these two alternative assumptions. For example, the area occupied by the two sectors differ in the two examples. Also, while the land rents are strictly decreasing with *r* in Figure A1a, the land rents are first decreasing and then increasing with *q*<sup>*i*</sup> in Figure A1b, with a minimum reached in q<sub>*i*</sub><sup>*i*\*</sup>(C), that is when the land bid functions of the two sectors equal each other.<sup>A1</sup>

<figure><img src="image_11.png" /><figcaption>Figure A1: Competitive land market equilibrium with alternative assumptions on the valuation of lands by the different sectors.</figcaption></figure>

NOTE. The figure displays the competitive equilibrium conditions of a land market when (a) sectors value the same type of land (i.e. “no sector-specific land quality” assumption) and (b) sectors differently value land (i.e. case with the “sector-specific land quality” assumption). The x-axis indicates the ranking of land pieces along the dimension *r* in (a), and along the dimensions *q*<sup>*i*</sup> and *q*<sup>*i*+1</sup> in (b). The origin *r* = 0 indicates the land of best quality in (a). The origins *q*<sup>*i*</sup> = 0 and *q*<sup>*i*+1</sup> = 0 designate the land of best quality for sector *i* and for sector *i* + 1 respectively in (b). Under the assumption that the two sectors value land quality in a strict opposite way, *q*<sup>*i*</sup> = 0 and *q*<sup>*i*+1</sup> = 0 also respectively indicate the land of worst quality for sector *i* + 1 and for sector *i*. The points *r*<sub>*i*</sub><sup>*</sup>(C) and *q*<sub>*i*</sub><sup>*</sup>(C) respectively delineate the exclusive implementation areas of the two sectors in (a) and (b). The segment [*r*<sub>*i*−1</sub><sup>*</sup>(C); *r*<sub>*i*</sub><sup>*</sup>(C)] [in (a) corresponds to the area occupied by sector *i* under climate conditions *C*, while the segment [*r*<sub>*i*</sub><sup>*</sup>(C); *r*<sub>*i*+1</sub><sup>*</sup>(C)] [correspond to those for sector *i* + 1. The segment [0; *q*<sub>*i*</sub><sup>*</sup>(C)] [in (b) corresponds to the area occupied by sector *i* under climate conditions *C*, while the segment [*q*<sub>*i*</sub><sup>*</sup>(C); *Q*] correspond to those for sector *i* + 1. The y-axis indicates the value of the bid and rent functions (expressed in monetary by area unit). The bid functions are displayed in dashed lines. The rent function depicted in plain curve correspond to the upper envelope of the bidding curves. The bidding functions *Φ*<sub>*i*</sub>(*r*, *C*) and *Φ*<sub>*i*+1</sub>(*r*, *C*) represented by dashed curves correspond respectively to the surplus of sectors *i* and *i* + 1 in (a), while *Φ*<sub>*i*</sub>(*q*<sup>*i*</sup>, *C*) and *Φ*<sub>*i*+1</sub>(*Q* − *q*<sup>*i*</sup>, *C*) correspond respectively to the surplus of sectors *i* and *i* + 1 in (b). The rent functions *R*<sup>*</sup>(*r*, *C*) and *R*<sup>*</sup>(*q*<sup>*i*</sup>, *C*) depicted in plain curve correspond to the upper envelope of the bidding curves. The points *R*<sub>*i*</sub><sup>*</sup>(C) and *R*<sub>*i*+1</sub><sup>*</sup>(C) correspond respectively to the average observed rent in the land markets for sectors *i* and *i* + 1.

<footnote><sup>A1</sup>One could also note that this “sector-specific land quality” framework develop in this Appendix also corresponds to a case where there is no land quality, and that sectors only operate under decreasing return to scale. In other words, the “sector-specific land quality” could also correspond to a case where land present no quality, where the decrease of the land bid functions would only come from decreasing return to scale strictly attached to the sectoral technology.</footnote>
**Average land rents.** The final step of this appendix is to compute the average land rents of sector $i$ and sector $i+1$ under competitive land market equilibrium, to allow us to examine the impact of climate shock on average rents observed on competitive land markets. Formally, the average rent of sector $i$ equals the sum of the (i) rectangle of basis $q_i^{i*}$ and height $\Phi_i(q_i^{i*}(C), C)$ and (ii) triangle of basis $q_i^{i*}$ and height $\Phi_i(0, C) - \Phi_2(q_i^{i*}(C), C)$, divided by (iii) area $q_i^{i*}(C)$ occupied by sector $i$. Using equations (A3) to (A6), this simplifies to:

$$ \bar{R}_i^*(C) = p_i y_2^i - \frac{t_i y_i^C}{2} \left( \frac{p_i y_i^C}{t_i y_i^C + t_{i+1} y_{i+1}^C} \right). \quad (A7) $$

Equation (A7) makes clear that the average rent observed at the regional level for sector $i$ does not depend only on prices and technology of sector $i$. Indeed, although the first term of equation (A7) typically corresponds to the revenues in point $q^i = 0$, the second term indicates that the average rent also depends in a complex way on the prices and technologies of the other sector.

Similarly, we can obtain the average observed rents for sector $i+1$ using a similar approach. Formally, the average rent of sector $i+1$ equals to the sum of (i) the rectangle of basis $Q - q_i^{i*}$ and height $\Phi_{i+1}(Q - q_i^{i*}, C)$ and (ii) the triangle of basis $Q - q_i^{i*}$ and height $\Phi_{i+1}(Q, C) - \Phi_{i+1}(Q - q_i^{i*}, C)$, divided by (iii) the area $Q - q_i^{i*}(C)$. Using equations (A3) to (A6), this simplifies to:

$$ \bar{R}_{i+1}^*(C) = p_{i+1} y_{i+1}^C + \frac{t_{i+1} y_{i+1}^C}{2} \left( \frac{p_i y_i^C}{t_i y_i^C + t_{i+1} y_{i+1}^C} \right). \quad (A8) $$

As for the case of sector $i$, equation (A8) shows that the average observed rents of sector $i+1$ on the land markets of sector $i$ do not only depend on its technology and prices, but also on those of sector $i$.

These average rents observed for the two sectors when they do not value the same type of lands are displayed in Figure A1b. Although the average rent observed for the sector $i+1$ is smaller than those of sector $i$, the difference between the two is much smaller than for the assumption when the two sectors value the same type of lands (see Figure A1a). Indeed, while the sector $i+1$ is necessarily implemented on the land of intrinsically least quality in this latter case, it is implemented on land of best quality in the “sector-specific land quality” assumption. This lead to average rents for sector $i+1$ that are strictly greater for sector $i+1$ with the “sector-specific land quality” assumption (compared to the “no sector-specific land quality” assumption). The difference of average rents observed for sector $i$ between the two alternative assumptions is much smaller. The sign of the difference depends on the difference in area devoted to $i$, that is, in the levels of $r_i^*(C)$ with respect to $q_i^{i*}(C)$.
## A2 Theoretical analysis: alternative climate shocks without sector-specific land quality

This appendix displays alternative cases than those primarily investigated in the main text. The figures illustrate the impact of climate difference $\Delta C$ affecting the productivity of one sector on the overall equilibrium on the land market. Specifically, Figure A2 displays the impact of a climate difference negatively affecting the productivity of forestry on the land market equilibrium. Figure A3 displays the impact of a climate difference negatively affecting the productivity of the construction sector on the land market equilibrium. Figure A4 displays the impact of a climate difference positively affecting the productivity of forestry on the land market equilibrium. Finally, Figure A5 shows the impact of a climate difference positively affecting the productivity of agriculture on the land market equilibrium.

<figure><img src="image_12.png" /><figcaption>Figure A2: Impact of a negative forestry shock on average land rents.</figcaption></figure>

NOTE. The figure displays the change in competitive equilibrium conditions of a land market following a negative productivity shock on forestry of $-\delta_3\%$ induced by a climate difference $\Delta C$. The x-axis indicates the distance from the city ($r=0$). The y-axis indicates the value of the bid and rent functions (expressed in monetary by area unit). The bid functions are displayed in dashed lines. The rent function depicted in plain curve correspond to the upper envelope of the bidding curves. Following the climate shock, the bidding function of forestry increases by $-\delta_3\%$ (indicated by plain arrows), while those of construction and agriculture remain unaffected. It results in a contraction of forest areas from $[r_2^*(C); r_3^*(C)]$ to $[r_2^*(C + \Delta C); r_3^*(C + \Delta C)]$, and an expansion of agricultural and marginal lands in the corresponding segments, respectively $[r_2^*(C); r_2^*(C + \Delta C)]$ and $[r_3^*(C); r_3^*(C + \Delta C)]$. The consequence is that observed average rents for forest and agriculture are modified. Urban area and rent are unaffected by this shock on forest productivity, because there is no frontier between urban and forest areas.
<figure><img src="image_13.png" /><figcaption>Figure A3: Impact of a negative urban shock on average land rents.</figcaption></figure>

NOTE. The figure displays the change in competitive equilibrium conditions of a land market following a negative productivity shock on the construction sector of –$\delta_1$% induced by a climate difference $\Delta C$. The x-axis indicates the distance from the city ($r=0$). The y-axis indicates the value of the bid and rent functions (expressed in monetary by area unit). The bid functions are displayed in dashed lines. The rent function depicted in plain curve correspond to the upper envelope of the bidding curves. Following the climate shock, the bidding function of forestry increases by –$\delta_1$% (indicated by plain arrows), while those of agriculture and forestry remain unaffected. It results in a contraction of urban areas from $[0; r_1^*(C)]$ to $[0; r_1^*(C + \Delta C)]$, and an expansion of agricultural on the corresponding segment $[r_1^*(C); r_1^*(C + \Delta C)]$. The consequence is that observed average rents for urban and agriculture are modified. Forestland area and rent are unaffected by this shock on construction productivity, because there is no frontier between urban and forest areas.
<figure><img src="image_14.png" /><figcaption>Figure A4: Impact of a positive forestry shock on average land rents.</figcaption></figure>

NOTE. The figure displays the change in competitive equilibrium conditions of a land market following a positive productivity shock on forestry of +$\delta_3$% induced by a climate difference $\Delta C$. The x-axis indicates the distance from the city ($r=0$). The y-axis indicates the value of the bid and rent functions (expressed in monetary by area unit). The bid functions are displayed in dashed lines. The rent function depicted in plain curve correspond to the upper envelope of the bidding curves. Following the climate shock, the bidding function of forestry increases by $\delta_3$% (indicated by plain arrows), while those of construction and agriculture remain unaffected. It results in an expansion of forest areas from $[r_2^*(C); r_3^*(C)]$ to $[r_2^*(C + \Delta C); r_3^*(C + \Delta C)]$, and a reduction of agricultural and marginal lands in the corresponding segments, respectively $[r_2^*(C); r_2^*(C + \Delta C)]$ and $[r_3^*(C); r_3^*(C + \Delta C)]$. The consequence is that observed average rents for forest and agriculture are modified. Urban area and rent are unaffected by this shock on forest productivity, because there is no frontier between urban and forest areas.
<figure><img src="image_15.png" /><figcaption>Figure A5: Impact of a positive agricultural shock on average land rents.</figcaption></figure>

NOTE. The figure displays the change in competitive equilibrium conditions of a land market following a positive productivity shock on agriculture of +$\delta_2$% induced by a climate difference $\Delta C$. The x-axis indicates the distance from the city ($r=0$). The y-axis indicates the value of the bid and rent functions (expressed in monetary by area unit). The bid functions are displayed in dashed lines. The rent function depicted in plain curve correspond to the upper envelope of the bidding curves. Following the climate shock, the bidding function of agriculture increases by $\delta_2$% (indicated by plain arrows), while those of construction and forestry remain unaffected. It results in an expansion of agricultural areas from [$r_1^*(C)$; $r_2^*(C)$] to [$r_1^*(C+\Delta C)$; $r_2^*(C+\Delta C)$], and a reduction of urban and forestland in the corresponding segments, respectively [$r_1^*(C)$; $r_1^*(C+\Delta C)$] and [$r_2^*(C)$; $r_2^*(C+\Delta C)$]. The consequence is that observed average rents for all uses are modified.
A3 Theoretical analysis: climate shocks with sector-specific land quality

Figure A6 displays the consequences of a positive climate shock on either sector *i* or *i* + 1 when the sectors differently value land quality. As for the “no sector-specific land quality” case, the areas occupied by the two sectors change following a climate shock on productivity. Specifically, the area of sector *i* expands in case of either a positive shock on sector *i* or a negative shock on sector *i* + 1, while those of sector *i* + 1 reacts in an opposite way. The consequences of these climate-induced land-use changes is however different in the “sector-specific land quality” case compared to the “no sector-specific land quality” one. Indeed, while the average rents of the two sectors do not necessarily evolve in the same direction following a shock on the productivity of one of the two sectors in the latter case, they do change in the same direction in the former case. This is what is depicted in Figure A6, where both average rents of sectors *i* and *i* + 1 increase in response to a positive shock on the productivity of one of the two sectors.
<figure><img src="image_16.png" /><figcaption>(a) Positive climate shock on sector i.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>(b) Positive climate shock on sector $i + 1$.</figcaption></figure>

<caption>Figure A6: Competitive land market equilibrium with positive climate shocks when sectors differently value land quality.</caption>

NOTE. The figure displays the competitive equilibrium conditions of a land market when sectors differently value land quality (i.e. case with the “sector-specific land quality” assumption), following a positive shock on sector *i* in (a) and *i* + 1 in (b) induced by a climate difference ΔC. The x-axis indicates the ranking of land pieces along the dimensions *q*<sup>*i*</sup> and *q*<sup>*i*+1</sup>. The origins *q*<sup>*i*</sup> = 0 and *q*<sup>*i*+1</sup> = 0 designate the land of best quality for sector *i* and for sector *i* + 1 respectively. Under the assumption that the two sectors value land quality in a strict opposite way, *q*<sup>*i*</sup> = 0 and *q*<sup>*i*+1</sup> = 0 also respectively indicate the land of worst quality for sector *i* + 1 and for sector *i*. The point *q*<sub>*i*</sub><sup>*</sup>(*C*) delineates the exclusive implementation areas of the two sectors. The segment [*0; q*<sub>*i*</sub><sup>*</sup>(*C*)[*] corresponds to the area occupied by sector *i* under climate conditions *C*, while the segment [*q*<sub>*i*</sub><sup>*</sup>(*C*); *Q*[*] correspond to those for sector *i* + 1. The y-axis indicates the value of the bid and rent functions (expressed in monetary by area unit). The bid functions are displayed in dashed lines. The rent function depicted in plain curve correspond to the upper envelope of the bidding curves. The bidding functions Φ<sub>*i*</sub>(*q*<sup>*i*</sup>, *C*) and Φ<sub>*i*+1</sub>(*Q* − *q*<sup>*i*</sup>, *C*) correspond respectively to the surplus of sectors *i* and *i* + 1. The rent function R<sup>*</sup>(*q*<sup>*i*</sup>, *C*) depicted in plain curve correspond to the upper envelope of the bidding curves. Following the climate shock, the bidding function of sector *i* increases by δ<sub>*i*</sub>% (indicated by plain arrows), while those of sector *i* + 1 remains unaffected in (a) – and the opposite in (b). It results in an expansion of area of sector *i* from [*0; q*<sub>*i*</sub><sup>*</sup>(*C*)[*] to [*0; q*<sub>*i*</sub><sup>*</sup>(*C* + ΔC)*], and a contraction of the area occupied by sector *i* + 1 on corresponding segments in (a) – and the opposite in (b). The consequence is that observed average rents for the two sectors are modified. In the case where all sectors differently value land quality, the average rents of all sectors move in the same direction than the climate shock (positive here), regardless of the affected sector.
# A4 Theoretical model

This appendix provides the proofs of the theoretical propositions presented in Section 2.

## A4.1 Theoretical model: proof of proposition 1

We hereafter prove proposition 1 in both the “no sector-specific land quality” and “sector-specific land quality” cases by the mean of graphical analyses.

**Proof when sectors value the same lands.** The proof relies on a graphical analysis on the two fictitious regions represented by Figures 1 and 2. Formally, Figure 2 graphically shows that, on the segment $]r_1^*(C + \Delta C); r_2^*(C + \Delta C)[$, the reduction in farmland rent corresponds exactly at the margin to the reduction in agricultural productivity. The application of the Ricardian approach on all pieces of farmlands on this segment – corresponding to the segment where agriculture is located on the smallest agricultural region – lead to Ricardian estimates that capture what they claim to capture, that is a change in agricultural productivity that is capitalized in land rent. The problem arises for the cases where agricultural is not always located (i.e. for which agricultural area changes between $C$ and $C + \Delta C$). If the area $[r_1^*(C + \Delta C); r_2^*(C + \Delta C)]$ is under agriculture for both climate $C$ and $C + \Delta C$, it additionally covers $[r_1^*(C); r_1^*(C + \Delta C)]$ and $[r_2^*(C + \Delta C); r_2^*(C)]$ under $C$ compared to $C + \Delta C$. In these two latter segments, the researchers can only observe agriculture under climate conditions $C$, but miss the counterfactual for $C + \Delta C$. The Ricardian approach thus cannot be applied on these segments. Finally, two particular points of interest for our analysis are the urban-agriculture and forest-agriculture frontiers located at $r_1^*(C + \Delta C)$ and $r_2^*(C + \Delta C)$ respectively. As explained in equation (4), the bids of agriculture respectively equal those of the construction and forestry sectors in such locations. If this is not an issue in Figure 2, Figure 3 shows that the climate shock on urban productivity modifies the agricultural fringe $r_1^*$, such that the Ricardian application at the urban-agriculture (resp. forest-agriculture) frontier is identical for the two sectors. A generalization of this reasoning obtained to the case of $N = 2$ regions to the case of $N > 2$ regions conducts to proposition 1 in the case where all sectors value the same lands.

**Proof when sectors differently value land quality.** The proof relies on a graphical analysis on the two fictitious regions represented by Figures A1b and A6a, where we assume that agriculture is represented by sector $i$. Formally, Figure A6a graphically shows that, on the segment $[0; q_i^{i*}(C)]$, the augmentation in farmland rent corresponds exactly at the margin to the increase in agricultural productivity. The application of the Ricardian approach on all pieces of farmlands on this segment – corresponding to the segment where agriculture is located on the smallest agricultural region – lead to Ricardian estimates that capture what they claim to capture, that is a change in agricultural productivity that is capitalized in land rent. The problem arises for the cases where agricultural is not always located (i.e. for which agricultural area changes between $C$ and $C + \Delta C$). If the area $[0; q_i^{i*}(C)]$ is under agriculture for both climate $C$ and $C + \Delta C$, it additionally covers $[q_i^{i*}(C); q_i^{i*}(C + \Delta C)]$ under $C + \Delta C$ (compared to $C$). In this latter segment, the researchers can only observe agriculture under climate conditions $C + \Delta C$, but miss the counterfactual for $C$. The Ricardian approach thus cannot
be applied on this segments. Finally, Figure A6 clearly indicates that the bids of the two sectors are equal at the frontier $q_i^*(C + \Delta C)$ between agriculture and sector $i + 1$. If this is not an issue in Figure A6a, Figure A6b shows that the climate shock on the productivity of sector $i + 1$ modifies $q_i^*$, such that the Ricardian application at the frontier would lead identical estimates for the two sectors. A generalization of this reasoning obtained to the case of $N = 2$ regions to the case of $N > 2$ regions conducts to proposition 1 in the case where sectors differently value land quality.

## A4.2 Theoretical model: proof of proposition 2

This appendix proves proposition 2 in both the “no sector-specific land quality” and “sector-specific land quality” cases by the mean of comparative statics. For this, we denote $y_{iC}^C$ the derivative of the production of sector $i$ with respect to climate when the climate shock affects the productivity of one sector only (which can be either positive or negative). We correspondly drop the superscript $C$ for the sectors no affected by the climate shock.

**Proof when sectors value the same lands.** Using similar notations than the paragraph above, the formula of the pivot points separating two sectors provided in equations (5) to (7) can be generalized to the formulation:

$$r_i^*(C) = \frac{p_i y_i^C - p_{i+1} y_{i+1}^C}{t_i y_i^C - t_{i+1} y_{i+1}^C},$$

where the superscript $C$ can be indifferently removed to $y_i^C$ and $y_{i+1}^C$. In the case of a climate shock on the productivity of at least one of these two sectors (that is either $\partial y_i^C / \partial C = y_{iC}^C \neq 0$ or $\partial y_{i+1}^C / \partial C = y_{i+1C}^C \neq 0$), the derivative of this latter equation with respect to $C$ is non-null. In other words, this means that a climate shock on the productivity of at least one sector induces land-use changes on the competitive land markets, as introduced by proposition 2.

Moreover, the derivative of the previous relation with respect to $C$ in the case of either $y_{iC}^C = y_{iC} = 0$ or $y_{i+1C}^C = y_{i+1C} = 0$ leads to the following:

$$\frac{\mathrm{d}r_i^*(C)}{\mathrm{d}C} = y_{iC}^C \frac{y_{i+1}(p_{i+1}t_i - p_i t_{i+1})}{(t_i y_i^C - t_{i+1} y_{i+1})^2} = -y_{i+1C}^C \frac{y_i(p_{i+1}t_i - p_i t_{i+1})}{(t_i y_i - t_{i+1} y_{i+1})^2}, \quad (A9)$$

which proves the second part of proposition 2, under the assumption that all sectors similarly value the same types of land. Note that, given assumption 1.3., equation (A9) indicates that $r_i^*(C)$ evolves in the same direction than $y_{iC}^C$ but on the opposite direction than $y_{i+1C}^C$.

Finally, noting that the urban area is $r_1^*(C)$, the agricultural area corresponds to $r_2^*(C) - r_1^*(C)$ and the forest area corresponds to $r_3^*(C) - r_2^*(C)$, one can generalize the expression to the area of the sector $i + 1$ to:

$$r_{i+1}^*(C) - r_i^*(C) = \frac{p_i y_i^C - p_{i+1} y_{i+1}^C}{t_i y_i^C - t_{i+1} y_{i+1}^C} - \frac{p_{i-1} y_{i-1}^C - p_i y_i^C}{t_{i-1} y_{i-1}^C - t_i y_i^C}.$$

The derivative of this last expression with respect to climate on the model of equation (A9) proves the first part of proposition 2. Formally, a positive shock leads to land expansion of the affected sector,
to the detriments of the other sectors. On the opposite, a negative shock leads to land expansion constriction of the affected sector, to the benefits of the others.

**Proof when sectors differently value land quality.** In the case of a climate shock on the productivity of either sector *i* or sector *i* + 1 (that is either $\partial y_i^C / \partial C = y_{iC}^C \neq 0$ or $\partial y_{i+1}^C / \partial C = y_{i+1C}^C \neq 0$), the derivative of the formula of the pivot point separating the two sectors provided in equation (A6) with respect to *C* is non-null. In other words, this means that a climate shock on the productivity of at least one sector induces land-use changes on the competitive land markets, as introduced by proposition 2.

Moreover, the derivative of equation (A6) with respect to *C* in the case of either $y_{iC}^C = y_{iC} = 0$ or $y_{i+1C}^C = y_{i+1C} = 0$ leads to the following:

$$ \frac{d q_i^{i*}(C)}{dC} = y_{iC}^C \frac{p_1 t_{i+1} y_{i+1}}{(t_i y_i^C + t_{i+1} y_{i+1})^2} = -y_{i+1C}^C \frac{p_i t_{i+1} y_i}{(t_i y_i + t_{i+1} y_{i+1})^2}, \quad (A10) $$

which proves the second part of proposition 2, under the assumption that all sectors value differently land quality. Note that, given assumption 1.3., equation (A10) indicates that $q_i^{i*}(C)$ evolves in the same direction than $y_{iC}^C$, but on the opposite direction than $y_{i+1C}^C$.

Finally, noting that the area of sector *i* is directly $q_i^{i*}(C)$ and that of sector *i* + 1 is $Q - q_i^{i*}(C)$, the derivative of this last expression with respect to climate on the model of equation (A10) proves the first part of proposition 2. Formally, a positive shock leads to land expansion of the affected sector, to the detriments of the other sectors. On the opposite, a negative shock leads to land expansion constriction of the affected sector, to the benefits of the others.

### A4.3 Theoretical model: proof of proposition 3

This appendix proves proposition 3 in both the “no sector-specific land quality” and “sector-specific land quality” cases.

**Proof when sectors value the same lands.** Proposition 3.1. considers the case where the climate shocks affect either the agricultural or a non agricultural sector. We consider the three different cases distinguished in proposition 3.1. hereafter.

Let us first consider the case where a marginal difference in climate $dC$ affects the productivity of construction only, and examine how it affects average farmland rent. We thus note $y_{1C}^C$ the derivative of construction production with respect to climate, and consider that production of agriculture and forestry are orthogonal to climate differences. A marginal difference in climate affecting construction productivity impacts average farmland rent in equation (8) in the main text such that:

$$ \frac{d \bar{R}_2^*(C)}{dC} = -y_{1C}^C \underbrace{\frac{t_2 y_2}{2} \left( \frac{y_2(p_2 t_1 - p_1 t_2)}{(t_1 y_1^C - t_2 y_2)^2} \right)}_{>0} \quad (A11) $$

The sign of the average farmland rent derivative with respect to climate in equation (A11) depends both on the derivative of construction production with respect to climate and on the sign of the
numerator of the term within brackets. Using assumption 1.3. the sign of this last term is positive. In other words, this means that under the assumption that a marginal difference in climate only affects the productivity of the construction sector, the average farmland rent evolves in the opposite direction than the climate shock. This proves the first part of proposition 3.1.

Let us now consider the case where the climate shock only impacts the forest productivity instead. Formally, a marginal difference in climate affecting forest productivity impacts average farmland rent in equation (8) in the main text such that:

$$ \frac{d\bar{R}_2^*(C)}{dC} = y_{3C}^C \underbrace{\frac{t_2y_2}{2} \left( \frac{y_2(p_3t_2 - p_2t_3)}{(t_2y_2 - t_3y_3^C)^2} \right)}_{>0}, \quad (A12) $$

where $y_{3C}^C$ denotes the derivative of forest production with respect to climate, which can be either positive or negative. Using assumption 1.3. equation (A12) indicates that the average farmland rent evolves in the same direction than the climate shock on forestry. A2 This proves the second part of proposition 3.1.

Let us finally consider the case where the climate shock affects the agricultural productivity only. Formally, a marginal difference in climate affecting agricultural productivity impacts average farmland rent in equation (8) in the main text such that:

$$ \frac{d\bar{R}_2^*(C)}{dC} = y_{2C}^C \underbrace{p_2 + \frac{t_2}{2} \left( \underbrace{\frac{p_2t_2(y_2^C)^2 - p_1t_1(y_1)^2}{(t_1y_1 - t_2y_2^C)^2}}_{<0} + \underbrace{\frac{p_2t_2(y_2^C)^2 - p_3t_3(y_3)^2}{(t_2y_2^C - t_3y_3)^2}}_{>0} \right)}_{\ge 0}, \quad (A13) $$

where $y_{2C}^C$ denotes the derivative of agricultural production with respect to climate, which can be either positive or negative. The full derivative of average farmland rent in equation (A13) is made of this term multiplying two main components. The first, equal to $p_2$, is positive. The sign of the second term is more ambiguous as it is made out of two elements that are not of the same signs. Indeed, assumptions 1.1. and 1.2. indicate that the first difference is negative while the second is positive. As such, depending on the parameters of the problem, the full derivative of average farmland rent in response to a positive shock on agricultural productivity can be either positive, negative or null – similar results can appear in the case of a negative shock on agricultural productivity. An analysis of equation (A13) indicates that the case where the average farmland rent evolves in the opposite direction than the agricultural productivity shock notably appears when agricultural prices are low compared to construction prices. It can also appear when the forest gradient $t_3y_3$ is sufficiently small. This proves the last part of proposition 3.1.

<footnote>A2 This is what is depicted in Figures A2 and A4 in the Appendix, where the climate-induced land-use change effects consecutive to the change of the forest-agriculture frontier modify the apparent average rent for agriculture.</footnote>
**Proof when sectors differently value land quality.** Proposition 3.2. considers the case where the climate shocks affect either the agricultural or a non agricultural sector. We here work on two sectors, i and i + 1, where agriculture can be either one of the two. If agriculture is sector i, then sector i + 1 is forestry, while, if agriculture is sector i + 1, then sector i is construction. We formally investigate the two cases where the climate shock affects the productivity of either sector i or sector i + 1, and how it translates into the average observed rents for the two sectors.

Let us first consider the case where a marginal difference in climate dC affects the productivity of sector i only, and examine how it affects average rent of sectors i and i + 1. A marginal difference in climate affecting productivity of sector i only impacts average rent of sector i in equation (A7) such that:

$$ \frac{d\bar{R}_i^*(C)}{dC} = y_{iC}^C \frac{\overbrace{p_i(t_{i+1}y_{i+1})^2 + t_i y_i^C t_{i+1}y_{i+1} + 0.5(t_i y_i)^2}^{>0}}{(t_i y_i^C + t_{i+1} y_{i+1})^2}. \quad (A14) $$

The sign of the average farmland rent derivative with respect to climate in equation (A14) depends thus only on the derivative of production of sector i with respect to climate. Similarly, this shock translates into average rent of sector i + 1 – see equation (A8) – such that:

$$ \frac{d\bar{R}_{i+1}^*(C)}{dC} = y_{iC}^C \overbrace{\frac{t_{i+1}y_{i+1}}{2} \left( \frac{p_i t_{i+1} y_{i+1}}{(t_i y_i^C + t_{i+1} y_{i+1})^2} \right)}^{>0}, \quad (A15) $$

which is also of the same sign than the derivative of production of sector i with respect to climate.

Let us now consider the case where a marginal difference in climate dC affects the productivity of sector i + 1 only, and examine how it affects average rent of sectors i and i + 1. A marginal difference in climate affecting productivity of sector i + 1 only impacts average rent of sector i in equation (A7) such that:

$$ \frac{d\bar{R}_i^*(C)}{dC} = y_{i+1C}^C \overbrace{\frac{t_i y_i}{2} \left( \frac{p_i t_{i+1} y_i}{(t_i y_i + t_{i+1} y_{i+1}^C)^2} \right)}^{>0}, \quad (A16) $$

The sign of the average farmland rent derivative with respect to climate in equation (A16) depends thus only on the derivative of production of sector i + 1 with respect to climate. Similarly, this shock translates into average rent of sector i + 1 – see equation (A8) – such that:

$$ \frac{d\bar{R}_{i+1}^*(C)}{dC} = y_{i+1C}^C \overbrace{\frac{(0.5p_{i+1}t_i + 0.5p_i t_{i+1})t_i y_i^2 + p_{i+1}t_i t_{i+1}y_i y_{i+1}^C + 0.5p_{i+1}(t_{i+1}y_{i+1}^C)^2}{(t_i y_i + t_{i+1} y_{i+1}^C)^2}}^{>0}, \quad (A17) $$

which is also of the same sign than the derivative of production of sector i + 1 with respect to climate. Equations (A14) to (A17) jointly proves proposition 3.2.
A4.4 Theoretical model: proof of Proposition 4

This appendix proves proposition 4 in both the “no sector-specific land quality” and “sector-specific land quality” cases.

**Proof when sectors value the same lands.** To prove proposition 4, we first note that because the total farmland rent is the integral of all farmland rents, it also corresponds to the average farmland rent multiplied by the total agricultural area (see Figure 1).

Let us now investigate the case where climate affects agricultural productivity only. Formally, a marginal difference in climate affecting agricultural productivity only – but not the construction and forest sectors – impacts total farmland rent such that:

$$ \frac{d \int_{r_1^*(C)}^{r_2^*(C)} R_2^*(C) dr(C)}{dC} = \frac{d \bar{R}_2^*(C) \times (r_1^*(C) - r_2^*(C))}{dC}, \\ = \frac{d \bar{R}_2^*(C)}{dC} \times (r_1^*(C) - r_2^*(C)) + \bar{R}_2^*(C) \times \frac{d(r_1^*(C) - r_2^*(C))}{dC}. $$

After derivation of the terms and factorization, this leads to:

$$ \frac{d \int_{r_1^*(C)}^{r_2^*(C)} R_2^*(C) dr(C)}{dC} = y_{2C}^C \left( \left( \frac{p_2 y_2^C - p_3 y_3}{t_2 y_2^C - t_3 y_3} - \frac{p_1 y_1 - p_2 y_2^C}{t_1 y_1 - t_2 y_2^C} \right) \left( p_2 - \frac{t_2}{2} \left( \frac{p_1 y_1 - p_2 y_2^C}{t_1 y_1 - t_2 y_2^C} + \frac{p_2 y_2^C - p_3 y_3}{t_2 y_2^C - t_3 y_3} \right) \right) \right. \\ \left. + \left( p_2 - t_2 \frac{p_1 y_1 - p_2 y_2^C}{t_1 y_1 - t_2 y_2^C} \right) \left( \frac{p_2 y_2^C t_1 y_1 - p_1 y_1 t_2 y_2^C}{(t_1 y_1 - t_2 y_2^C)^2} \right) \right. \\ \left. + \left( p_2 - t_2 \frac{p_2 y_2^C - p_3 y_3}{t_2 y_2^C - t_3 y_3} \right) \left( \frac{p_3 y_3 t_2 y_2^C - p_2 y_2^C t_3 y_3}{(t_2 y_2^C - t_3 y_3)^2} \right), $$

which corresponds to:

$$ \frac{d \int_{r_1^*(C)}^{r_2^*(C)} R_2^*(C) dr(C)}{dC} = y_{2C}^C \left( \underbrace{\bar{R}_2^*(C) (r_2^* - r_1^*)}_{>0} + \underbrace{\Phi_2(r_1^*, C) \left( \frac{y_1(p_2 t_1 - p_1 t_2)}{(t_1 y_1 - t_2 y_2^C)^2} \right)}_{>0} + \underbrace{\Phi_2(r_2^*, C) \left( \frac{y_3(p_3 t_2 - p_2 t_3)}{(t_2 y_2^C - t_3 y_3)^2} \right)}_{>0} \right). \quad (A18) $$

Equation (A18) consists in the multiplication of the marginal climate-induced change in agricultural productivity by three terms. The first term corresponds to the initial total rent of agriculture, while the second and third terms correspond to the value of marginal expansion of agricultural lands on urban and forest areas. A3 All these terms are positive (see assumption 1 for the determination of the signs of the last two terms). As such, equation (A18) shows that total farmland rent evolves in similar

<footnote>A3 These second and third terms consist of the value of bidding curve for agriculture multiplied by terms displayed in brackets, these latter corresponding to the marginal change in $r_1^*(C)$ and $r_2^*(C)$ consecutively to marginal climate impact on agricultural productivity. By symmetry with equations (12), the derivative of $r_1^*$ and $r_2^*$ consecutive to a marginal difference of climate affecting agricultural productivity is equal to $\frac{dr_1^*(C)}{dC} = -y_{2C}^C \left( \frac{y_1(p_2 t_1 - p_1 t_2)}{(t_1 y_1 - t_2 y_2^C)^2} \right) < 0$ and $\frac{dr_2^*(C)}{dC} = y_{2C}^C \left( \frac{y_3(p_3 t_2 - p_2 t_3)}{(t_2 y_2^C - t_3 y_3)^2} \right) > 0$. In other words, farmland expands on both urban and forestland when the climate shock positively affects agricultural productivity.</footnote>
way than the derivative of agricultural production with respect to climate. This proves the first part of proposition 4.

Let us now consider the case where the climate shock affects the productivity of a non-agricultural sector. For example, in the case where climate affects the construction productivity, the total farmland rents evolve such that:

$$ \frac{\mathrm{d} \int_{r_1^*(C)}^{r_2^*(C)} R_2^*(C) \mathrm{d}r(C)}{\mathrm{d}C} = -y_{1C}^C \overbrace{\left( p_2 y_2 \left( \frac{y_2(p_2 t_1 - p_1 t_2)}{(t_1 y_1^C - t_2 y_2)^2} \right) \right)}^{>0} . \quad (A19) $$

Equation (A19) consists in the multiplication of the opposite of the marginal change in construction productivity induced by the climate shock by a factor of two positive terms (see assumption 1). As such, the total farmland rents evolve in an opposite way to the climate shock on construction productivity. This is because the farmland area evolves in an opposite way to the climate shock on construction productivity. So, if the shock is positive as in Figure 3, then agricultural area shrinks and total farmland rent decreases. Actually, equation (A19) makes clear that the derivative of total farmland rent with respect to climate when this latter one only affects construction productivity is equal to the opposite of agricultural profitability ($-p2y2$) multiplied by the derivative of $r_1^*(C)$ with respect to climate – see equation (A11). The evolution of total farmland rent in this context is thus only due to a climate-induced land-use change effect. Similar result can be obtained in the case of a climate shock on forest productivity. This proves the second part of proposition 4.

**Proof when sectors differently value land quality.** Proposition 4 considers the case where the climate shocks affect either the agricultural or a non agricultural sector. We here work on two sectors, $i$ and $i+1$, where agriculture can be either one of the two. If agriculture is sector $i$, then sector $i+1$ is forestry, while, if agriculture is sector $i+1$, then sector $i$ is construction. We formally investigate the two cases where the climate shock affects the productivity of either sector $i$ or sector $i+1$, and how it translates into the total rents for the two sectors.

Let us first consider the case where a marginal difference in climate $dC$ affects the productivity of sector $i$ only, and examine how it affects average rent of sectors $i$ and $i+1$. A marginal difference in climate affecting productivity of sector $i$ only impacts total rent of sector $i$ in equation (A7) such that:

$$ \frac{\mathrm{d} \int_{0}^{q_i^*(C) R_i^*(q^i, C) dq^i(C)} 0}{\mathrm{d}C} = y_{iC}^C \overbrace{\frac{p_i^2 y_i^C (2t_{i+1}y_{i+1})^2 + 1.5t_i t_{i+1} + y_i^C y_{i+1} + 0.5(t_i y_i^C)^2}{(t_i y_i^C + t_{i+1} y_{i+1})^2}}^{>0} . \quad (A20) $$

The sign of the total farmland rent derivative with respect to climate in equation (A14) depends thus only on the derivative of production of sector $i$ with respect to climate.

Similarly, this shock translates into total rent of sector $i+1$ – see equation (A8) – such that:

$$ \frac{\mathrm{d} \int_{q_i^*(C)}^{q_{i+1}^*(C)} R_{i+1}^*(q^i, C) dq^i(C)}{\mathrm{d}C} = -y_{iC}^C \overbrace{\frac{(p_i t_{i+1} y_{i+1})^2 y_i^C}{(t_i y_i^C + t_{i+1} y_{i+1})^2}}^{>0} . \quad (A21) $$
which is of the opposite sign than the derivative of production of sector *i* with respect to climate.

Let us now consider the case where a marginal difference in climate *dC* affects the productivity of sector *i* + 1 only, and examine how it affects total rent of sectors *i* and *i* + 1. A marginal difference in climate affecting productivity of sector *i* + 1 only impacts total rent of sector *i* in equation (A7) such that:

$$ \frac{\mathrm{d} \int_{0}^{q_{i}^{i*}(C)} R_{i}^{*}(q^{i}, C) \mathrm{d}q^{i}(C)}{\mathrm{d}C} = -y_{i+1C}^{C} \frac{\underbrace{(p_{i} t_{i+1} y_{i})^{2} y_{i+1}^{C}}_{>0}}{(t_{i} y_{i}^{C} + t_{i+1} y_{i+1})^{2}}, \quad (A22) $$

The sign of the average farmland rent derivative with respect to climate in equation (A22) depends thus only in the opposite way to the derivative of production of sector *i* + 1 with respect to climate. Similarly, this shock translates into average rent of sector *i* + 1 – see equation (A8) – such that:

$$ \frac{\mathrm{d} \int_{q_{i}^{i*}(C)}^{Q} R_{i+1}^{*}(q^{i}, C) \mathrm{d}q^{i}(C)}{\mathrm{d}C} = y_{i+1C}^{C} \underbrace{\frac{t_{i}(0.5 p_{i+1}^{2} t_{i}^{2} - 0.5 p_{i}^{2} t_{i+1}^{2}) y_{i}^{3} + t_{i+1}(1.5 p_{i+1}^{2} t_{i}^{2} + 0.5 p_{i}^{2} t_{i+1}^{2}) y_{i}^{2} y_{i+1}^{C}}{(t_{i} y_{i} + t_{i+1} y_{i+1}^{C})^{3}}}_{>0} \\ + y_{i+1C}^{C} \underbrace{\frac{1.5 p_{i+1}^{2} t_{i} t_{i+1}^{2} y_{i} (y_{i+1}^{C})^{2} + 0.5 p_{i+1}^{2} (t_{i+1} y_{i+1}^{C})^{3}}{(t_{i} y_{i} + t_{i+1} y_{i+1}^{C})^{3}}}_{>0}, \quad (A23) $$

which is also of the same sign than the derivative of production of sector *i* + 1 with respect to climate, given the strict increasing property of the square function and the fact that $p_{i+1}t_{i} > p_{i}t_{i+1}$ by definition (see assumption 1.3.). Equations (A20) to (A23) jointly proves proposition 4 in the case where sectors value differently land quality.

### A4.5 Theoretical model: proof of Corollary 2

The proof of corollary 2 directly follows those of proposition 4. Noting that the total welfare of the economy is equal to the sum of the total rents of construction, plus those of agriculture and those of forestry, the application of the Ricardian approach on this sum leads to the welfare impacts of climate on the whole land sector. The aggregation of the total rents of alternative uses in this single term however prevents from identify from where comes the initial productive shock(s).
A5 Departmental land prices: additional statistics on the PERVAL database

Table A1 presents the summary statistics of all the variables from the initial PERVAL database that we purchased from ADNOV. All prices have been previously deflated by ADNOV using historical inflation rate series from the French Institute of Economics and Statistics.

<table><caption>Table A1: Summary statistics of the initial departmental-level PERVAL database (N=344)</caption><thead><tr><th></th><th>Mean</th><th>S.D.</th><th>Min</th><th>Median</th><th>Max</th></tr></thead><tbody><tr><td colspan="6" style="text-align: center; font-weight: bold;">A. FARMLAND</td></tr><tr><td>Minimum price in the department (euro/ha)</td><td>522.01</td><td>392.36</td><td>0.00</td><td>431.039</td><td>2,600.83</td></tr><tr><td>Median price in the department (euro/ha)</td><td>3923.87</td><td>2248.29</td><td>1291.41</td><td>3,363.46</td><td>15,923.84</td></tr><tr><td>Average price in the department (euro/ha)</td><td>5,901.92</td><td>3,727.97</td><td>1,911.98</td><td>4,957.13</td><td>32,225.23</td></tr><tr><td>Maximum price in the department (euro/ha)</td><td>532,679.75</td><td>625,233.81</td><td>67,964.09</td><td>320,849.01</td><td>5,699,005.41</td></tr><tr><td>Number of transactions in the department per cross-section</td><td>1,051.95</td><td>638.04</td><td>83.00</td><td>941.50</td><td>3,966.00</td></tr><tr><td colspan="6" style="text-align: center; font-weight: bold;">B. FORESTLAND</td></tr><tr><td>Minimum price in the department (euro/ha)</td><td>436.95</td><td>415.02</td><td>0.00</td><td>349.67</td><td>4,008.80</td></tr><tr><td>Median price in the department (euro/ha)</td><td>2757.72</td><td>2,094.45</td><td>845.07</td><td>2,199.82</td><td>21,769.22</td></tr><tr><td>Average price in the department (euro/ha)</td><td>3,528.52</td><td>2,295.35</td><td>896.10</td><td>2,967.56</td><td>20,668.22</td></tr><tr><td>Maximum price in the department (euro/ha)</td><td>75,216.54</td><td>16,8662.58</td><td>2,366.94</td><td>35252.729</td><td>2,715,016.92</td></tr><tr><td>Number of transactions in the department per cross-section</td><td>188.22</td><td>165.12</td><td>3.00</td><td>144.00</td><td>959.00</td></tr><tr><td colspan="6" style="text-align: center; font-weight: bold;">C. BUILDING LANDS</td></tr><tr><td>Minimum price in the department (euro/ha)</td><td>6,884.50</td><td>7,973.34</td><td>0.00</td><td>4239.68</td><td>47,533.53</td></tr><tr><td>Median in the department (euro/ha)</td><td>418290.43</td><td>355,230.30</td><td>33,880.34</td><td>292,318.14</td><td>2,020,677.11</td></tr><tr><td>Average in the department (euro/ha)</td><td>313,837.01</td><td>267,709.57</td><td>32,479.06</td><td>226,921.17</td><td>1,757,449.49</td></tr><tr><td>Maximum in the department (euro/ha)</td><td>2,537,831.90</td><td>3,172,528.67</td><td>315,290.50</td><td>1,555,272.70</td><td>29,032,874.00</td></tr><tr><td>Number of transactions in the department per cross-section</td><td>2,108.65</td><td>1,760.18</td><td>99.00</td><td>1,587.00</td><td>9,135.00</td></tr></tbody></table>

<footnote>NOTE. The figures provide the summary statistics of the initial PERVAL database aggregated at the departmental level, for the four distinctive cross-sections 2000, 2006, 2012 and 2018. The prices are deflated by the national inflation rate.</footnote>
A6 Climate conditions in France

Figure A7 present the 30-year seasonal averages of temperature for the mainland French departments in 2012 (seasonal averages between 1981 and 2011). Similarly, Figure A8 present the 30-year seasonal averages of precipitation for the mainland French departments in 2012 (seasonal averages between 1981 and 2011).

<figure><img src="image_18.png" /></figure>

Figure A7: Seasonal temperature averages in France. NOTE. The figures show the 30-year seasonal averages of temperature in 2012, expressed in degree Celsius. Spring temperatures are computed as the average of daily temperatures in March-May (respectively June-August, September-November and December-February for summer, autumn and winter). Missing values are displayed in white (for the Corsican and Parisian regions).
<figure><img src="image_19.png" /><figcaption>Figure A8: Seasonal temperature averages in France. NOTE. The figures show the 30-year seasonal averages of temperature in 2012, expressed in degree Celsius. Spring temperatures are computed as the average of daily temperatures in March-May (respectively June-August, September-November and December-February for summer, autumn and winter). Missing values are displayed in white (for the Corsican and Parisian regions).</figcaption></figure>
## A7 Correlation

Table A2 shows the matrix of correlation between farmland prices with forest and building land prices, as well as with land areas of the different categories and climate.

<table><caption>Table A2: Coefficients of correlation between land prices, land areas and climate</caption><thead><tr><th></th><th>Farmland price</th><th>Forestland price</th><th>Building land price</th><th>Farmland area</th><th>Forest area</th><th>Urban area</th><th>Other area</th><th>Annual temp.</th><th>Annual prec.</th></tr></thead><tbody><tr><td>Farmland price</td><td>1.00</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Forestland price</td><td>0.34</td><td>1.00</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Building land price</td><td>0.72</td><td>0.35</td><td>1.00</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Farmland area</td><td>-0.42</td><td>0.25</td><td>-0.44</td><td>1.00</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Forest area</td><td>0.13</td><td>-0.25</td><td>0.14</td><td>-0.40</td><td>1.00</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Urban area</td><td>0.14</td><td>0.26</td><td>0.27</td><td>0.37</td><td>-0.06</td><td>1.00</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Other area</td><td>0.15</td><td>0.20</td><td>0.29</td><td>-0.07</td><td>0.19</td><td>0.46</td><td>1.00</td><td>-</td><td>-</td></tr><tr><td>Annual temperature</td><td>0.01</td><td>-0.01</td><td>0.00</td><td>0.21</td><td>-0.08</td><td>0.44</td><td>0.36</td><td>1.00</td><td>-</td></tr><tr><td>Annual precipitation</td><td>-0.02</td><td>-0.20</td><td>-0.08</td><td>-0.31</td><td>0.30</td><td>-0.20</td><td>-0.13</td><td>-0.17</td><td>1.00</td></tr></tbody></table>

NOTE. The figures are the coefficients of correlations between the land price (in €/ha) and land area (in ha) for the different land uses, as well as climate conditions (measured as 30-year averages of annual temperature (in °C) and precipitation (in cm). It is assumed that other land uses present null value on land markets.
A8 Total rent values by uses

Figure A9 displays the total rent values for farmland, forestland and building lands. This measurement corresponds to the product of average land prices depicted in Figure 4 by the area occupied by the considered uses (see Figure 5).

<figure><img src="image_20.png" /></figure>

Figure A9: Total value of the different land uses. NOTE. The figures show the total value of agriculture, forest and urban in 2012, expressed in million euro. The figures in panels a. b. and c. are obtained multiplying the average departmental price of the different land uses in 2012 (as displayed in Figure 4) by their corresponding occupied area (as displayed in Figure 5). Obtained as the sum of the figures in the three first panels, figures in panel d. indicate the total value of the land sector under the assumption that other land uses – made of wetlands and waters – present null value on land markets. Missing values are displayed in white (for the Corsican and Parisian regions).
## A9 Standard vs. land-adjusted Ricardian estimates for alternative sectors

Table A3 shows the estimates obtained for agriculture in our sample with the standard and land-adjusted Ricardian approaches, including or not controls and year fixed effects. Similarly, Table A4 shows the estimates obtained for forestry in our sample with the standard and land-adjusted Ricardian approaches, including or not controls and year fixed effects. Finally, Table A5 shows the estimates obtained for the urban sector in our sample with the standard and land-adjusted Ricardian approaches, including or not controls and year fixed effects.

<table><caption>Table A3: Standard and land-adjusted Ricardian estimates for agriculture</caption><thead><tr><th rowspan="2"></th><th colspan="4">Dependent variable:<br>log(farmland price)</th><th colspan="4">Dependent variable:<br>log(farmland price × agricultural area)</th></tr><tr><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th><th>(7)</th><th>(8)</th></tr></thead><tbody><tr><td>Spring Temperature</td><td>1.97 ***<br>(0.49)</td><td>1.73 ***<br>(0.50)</td><td>2.58 ***<br>(0.54)</td><td>2.74 ***<br>(0.52)</td><td>1.89 ***<br>(0.41)</td><td>1.67 ***<br>(0.41)</td><td>2.02 ***<br>(0.51)</td><td>0.61<br>(0.58)</td></tr><tr><td>Spring Temperature Squared</td><td>-0.09 ***<br>(0.03)</td><td>-0.09 ***<br>(0.03)</td><td>-0.10 ***<br>(0.03)</td><td>-0.10 ***<br>(0.03)</td><td>-0.08 ***<br>(0.02)</td><td>-0.08 ***<br>(0.02)</td><td>-0.08 ***<br>(0.02)</td><td>-0.05 *<br>(0.03)</td></tr><tr><td>Summer Temperature</td><td>-2.76 ***<br>(0.46)</td><td>-2.82 ***<br>(0.44)</td><td>-3.83 ***<br>(0.47)</td><td>-4.21 ***<br>(0.46)</td><td>-3.25 ***<br>(0.45)</td><td>-3.27 ***<br>(0.40)</td><td>-2.33 ***<br>(0.52)</td><td>-1.58 ***<br>(0.58)</td></tr><tr><td>Summer Temperature Squared</td><td>0.07 ***<br>(0.01)</td><td>0.07 ***<br>(0.01)</td><td>0.09 ***<br>(0.01)</td><td>0.10 ***<br>(0.01)</td><td>0.08 ***<br>(0.01)</td><td>0.08 ***<br>(0.01)</td><td>0.06 ***<br>(0.01)</td><td>0.05 ***<br>(0.01)</td></tr><tr><td>Autumn Temperature</td><td>-0.99<br>(0.98)</td><td>-0.33<br>(0.97)</td><td>-0.13<br>(0.98)</td><td>0.42<br>(0.89)</td><td>0.86<br>(1.00)</td><td>1.35<br>(0.93)</td><td>-0.67<br>(1.14)</td><td>0.22<br>(1.09)</td></tr><tr><td>Autumn Temperature Squared</td><td>0.06 *<br>(0.04)</td><td>0.04<br>(0.04)</td><td>0.02<br>(0.04)</td><td>0.01<br>(0.04)</td><td>-0.04<br>(0.04)</td><td>-0.05<br>(0.04)</td><td>0.03<br>(0.04)</td><td>-0.01<br>(0.04)</td></tr><tr><td>Winter Temperature</td><td>-0.07<br>(0.22)</td><td>-0.22<br>(0.23)</td><td>-0.30<br>(0.20)</td><td>-0.49 **<br>(0.20)</td><td>-0.37<br>(0.29)</td><td>-0.45 *<br>(0.28)</td><td>-0.21<br>(0.31)</td><td>-0.17<br>(0.33)</td></tr><tr><td>Winter Temperature Squared</td><td>-0.02<br>(0.02)</td><td>-0.01<br>(0.02)</td><td>-0.01<br>(0.02)</td><td>-0.01<br>(0.02)</td><td>0.06 **<br>(0.03)</td><td>0.07 ***<br>(0.02)</td><td>0.04 **<br>(0.02)</td><td>0.06 ***<br>(0.02)</td></tr><tr><td>Spring Precipitation</td><td>-0.29<br>(0.19)</td><td>-0.34 **<br>(0.19)</td><td>-0.48 ***<br>(0.19)</td><td>-0.63 ***<br>(0.19)</td><td>-0.89 ***<br>(0.24)</td><td>-0.97 ***<br>(0.26)</td><td>-0.32<br>(0.25)</td><td>-0.26<br>(0.26)</td></tr><tr><td>Spring Precipitation Squared</td><td>0.01 *<br>(0.01)</td><td>0.01 *<br>(0.01)</td><td>0.02 ***<br>(0.01)</td><td>0.03 ***<br>(0.01)</td><td>0.06 ***<br>(0.01)</td><td>0.06 ***<br>(0.02)</td><td>0.02<br>(0.02)</td><td>0.02<br>(0.02)</td></tr><tr><td>Summer Precipitation</td><td>-0.13<br>(0.16)</td><td>-0.11<br>(0.16)</td><td>-0.11<br>(0.15)</td><td>-0.06<br>(0.15)</td><td>0.37 **<br>(0.18)</td><td>0.41 **<br>(0.19)</td><td>0.36 *<br>(0.19)</td><td>0.29<br>(0.19)</td></tr><tr><td>Summer Precipitation Squared</td><td>0.01 *<br>(0.01)</td><td>0.01 *<br>(0.01)</td><td>0.01 *<br>(0.01)</td><td>0.01 *<br>(0.01)</td><td>-0.02 **<br>(0.01)</td><td>-0.02 **<br>(0.01)</td><td>-0.02 **<br>(0.01)</td><td>-0.01 *<br>(0.01)</td></tr><tr><td>Autumn Precipitation</td><td>0.21 **<br>(0.09)</td><td>0.08<br>(0.09)</td><td>-0.15<br>(0.11)</td><td>-0.24 **<br>(0.11)</td><td>0.10<br>(0.11)</td><td>-0.01<br>(0.11)</td><td>-0.03<br>(0.11)</td><td>-0.05<br>(0.12)</td></tr><tr><td>Autumn Precipitation Squared</td><td>0.00<br>(0.00)</td><td>0.00<br>(0.00)</td><td>0.01<br>(0.01)</td><td>0.01<br>(0.01)</td><td>0.00<br>(0.00)</td><td>0.00<br>(0.00)</td><td>0.00<br>(0.00)</td><td>0.00<br>(0.01)</td></tr><tr><td>Winter Precipitation</td><td>-0.20 **<br>(0.10)</td><td>-0.14<br>(0.10)</td><td>0.16 *<br>(0.10)</td><td>0.20 **<br>(0.10)</td><td>0.35 ***<br>(0.12)</td><td>0.40 ***<br>(0.12)</td><td>0.17<br>(0.12)</td><td>0.13<br>(0.11)</td></tr><tr><td>Winter Precipitation Squared</td><td>0.00<br>(0.01)</td><td>0.00<br>(0.01)</td><td>-0.01<br>(0.01)</td><td>-0.01<br>(0.01)</td><td>-0.04 ***<br>(0.01)</td><td>-0.04 ***<br>(0.01)</td><td>-0.02 **<br>(0.01)</td><td>-0.02 **<br>(0.01)</td></tr><tr><td>Number of observations</td><td>344</td><td>344</td><td>344</td><td>344</td><td>344</td><td>344</td><td>344</td><td>344</td></tr><tr><td>Controls</td><td>No</td><td>No</td><td>Yes</td><td>Yes</td><td>No</td><td>No</td><td>Yes</td><td>Yes</td></tr><tr><td>Year fixed effects</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td></tr><tr><td>Adjusted R<sup>2</sup></td><td>0.46</td><td>0.53</td><td>0.57</td><td>0.63</td><td>0.41</td><td>0.47</td><td>0.47</td><td>0.54</td></tr></tbody></table>

NOTE. The figures report the estimates seasonal climate variables on farmland price in columns (1) to (4), in the spirit of the standard Ricardian approach, and on the multiplication of farmland area by farmland price in columns (5) to (8), in line with the land-adjusted Ricardian approach. Climate variables are computed using 30-year averages. Controls include population, average altitude and soil conditions. Standard errors adjusted for spatial dependence and computed using the delta method are displayed in brackets.
<table><caption>Table A4: Standard and land-adjusted Ricardian estimates for forestry</caption><thead><tr><th rowspan="2"></th><th colspan="4">Dependent variable:<br>log(forestland price)</th><th colspan="4">Dependent variable:<br>log(forestland price × forest area)</th></tr><tr><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th><th>(7)</th><th>(8)</th></tr></thead><tbody><tr><td>Spring Temperature</td><td>1.34 ***<br>(0.46)</td><td>1.15 **<br>(0.45)</td><td>1.18 **<br>(0.51)</td><td>0.12<br>(0.58)</td><td>0.94<br>(0.59)</td><td>0.97<br>(0.60)</td><td>0.94<br>(0.62)</td><td>0.31<br>(0.73)</td></tr><tr><td>Spring Temperature Squared</td><td>-0.05 ***<br>(0.02)</td><td>-0.05 ***<br>(0.02)</td><td>-0.04 *<br>(0.03)</td><td>-0.02<br>(0.03)</td><td>-0.04<br>(0.03)</td><td>-0.06 *<br>(0.04)</td><td>-0.04<br>(0.03)</td><td>-0.03<br>(0.03)</td></tr><tr><td>Summer Temperature</td><td>-1.08 *<br>(0.61)</td><td>-1.10 *<br>(0.58)</td><td>-1.08 *<br>(0.65)</td><td>-0.53<br>(0.65)</td><td>0.46<br>(0.84)</td><td>0.53<br>(0.83)</td><td>0.34<br>(0.78)</td><td>1.05<br>(0.84)</td></tr><tr><td>Summer Temperature Squared</td><td>0.02<br>(0.02)</td><td>0.02<br>(0.02)</td><td>0.02<br>(0.02)</td><td>0.01<br>(0.02)</td><td>-0.01<br>(0.03)</td><td>0.00<br>(0.03)</td><td>0.00<br>(0.02)</td><td>-0.01<br>(0.02)</td></tr><tr><td>Autumn Temperature</td><td>-2.25 ***<br>(0.98)</td><td>-1.79 ***<br>(0.99)</td><td>-2.11 ***<br>(0.95)</td><td>-1.40<br>(0.98)</td><td>-3.95 ***<br>(1.29)</td><td>-4.46 ***<br>(1.31)</td><td>-3.97 ***<br>(1.35)</td><td>-4.62 ***<br>(1.40)</td></tr><tr><td>Autumn Temperature Squared</td><td>0.13 ***<br>(0.04)</td><td>0.11 ***<br>(0.04)</td><td>0.12 ***<br>(0.04)</td><td>0.09 **<br>(0.04)</td><td>0.15 ***<br>(0.06)</td><td>0.15 ***<br>(0.05)</td><td>0.15 ***<br>(0.06)</td><td>0.15 ***<br>(0.06)</td></tr><tr><td>Winter Temperature</td><td>0.42 *<br>(0.26)</td><td>0.34<br>(0.27)</td><td>0.45 *<br>(0.26)</td><td>0.48 *<br>(0.29)</td><td>1.07 **<br>(0.35)</td><td>1.37 ***<br>(0.37)</td><td>1.11 **<br>(0.38)</td><td>1.62 ***<br>(0.43)</td></tr><tr><td>Winter Temperature Squared</td><td>-0.11 ***<br>(0.03)</td><td>-0.10 ***<br>(0.03)</td><td>-0.12 ***<br>(0.03)</td><td>-0.10 ***<br>(0.03)</td><td>-0.08 **<br>(0.04)</td><td>-0.07 *<br>(0.04)</td><td>-0.09 **<br>(0.04)</td><td>-0.08 **<br>(0.04)</td></tr><tr><td>Spring Precipitation</td><td>-0.97 ***<br>(0.20)</td><td>-1.04 ***<br>(0.20)</td><td>-0.89 ***<br>(0.23)</td><td>-0.86 ***<br>(0.22)</td><td>-0.93 ***<br>(0.26)</td><td>-1.08 ***<br>(0.27)</td><td>-0.74 ***<br>(0.27)</td><td>-0.78 ***<br>(0.27)</td></tr><tr><td>Spring Precipitation Squared</td><td>0.04 ***<br>(0.01)</td><td>0.04 ***<br>(0.01)</td><td>0.03 ***<br>(0.01)</td><td>0.03 ***<br>(0.01)</td><td>0.05 **<br>(0.02)</td><td>0.05 **<br>(0.02)</td><td>0.03 *<br>(0.02)</td><td>0.04 **<br>(0.02)</td></tr><tr><td>Summer Precipitation</td><td>0.01<br>(0.17)</td><td>0.05<br>(0.16)</td><td>0.05<br>(0.16)</td><td>0.01<br>(0.15)</td><td>0.28<br>(0.22)</td><td>0.41 *<br>(0.23)</td><td>0.43 **<br>(0.22)</td><td>0.53 **<br>(0.21)</td></tr><tr><td>Summer Precipitation Squared</td><td>0.01<br>(0.01)</td><td>0.01<br>(0.01)</td><td>0.01<br>(0.01)</td><td>0.01<br>(0.01)</td><td>-0.01 *<br>(0.01)</td><td>-0.01 *<br>(0.01)</td><td>-0.02 **<br>(0.01)</td><td>-0.02 **<br>(0.01)</td></tr><tr><td>Autumn Precipitation</td><td>0.31 ***<br>(0.12)</td><td>0.21 *<br>(0.12)</td><td>0.16<br>(0.13)</td><td>0.13<br>(0.12)</td><td>0.67 ***<br>(0.17)</td><td>0.66 ***<br>(0.18)</td><td>0.30 *<br>(0.16)</td><td>0.40 **<br>(0.16)</td></tr><tr><td>Autumn Precipitation Squared</td><td>-0.01<br>(0.01)</td><td>-0.01<br>(0.01)</td><td>0.00<br>(0.01)</td><td>0.00<br>(0.01)</td><td>-0.02 **<br>(0.01)</td><td>-0.02 **<br>(0.01)</td><td>-0.01<br>(0.01)</td><td>-0.01 *<br>(0.01)</td></tr><tr><td>Winter Precipitation</td><td>-0.12<br>(0.13)</td><td>-0.06<br>(0.13)</td><td>0.00<br>(0.13)</td><td>-0.02<br>(0.13)</td><td>-0.06<br>(0.18)</td><td>0.05<br>(0.18)</td><td>0.24<br>(0.17)</td><td>0.24<br>(0.17)</td></tr><tr><td>Winter Precipitation Squared</td><td>0.01<br>(0.01)</td><td>0.01<br>(0.01)</td><td>0.00<br>(0.01)</td><td>0.01<br>(0.01)</td><td>0.00<br>(0.01)</td><td>-0.01<br>(0.01)</td><td>-0.01<br>(0.01)</td><td>-0.02 *<br>(0.01)</td></tr><tr><td>Number of observations</td><td>344</td><td>344</td><td>344</td><td>344</td><td>344</td><td>344</td><td>344</td><td>344</td></tr><tr><td>Controls</td><td>No</td><td>No</td><td>Yes</td><td>Yes</td><td>No</td><td>No</td><td>Yes</td><td>Yes</td></tr><tr><td>Year fixed effects</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td></tr><tr><td>Adjusted R<sup>2</sup></td><td>0.45</td><td>0.50</td><td>0.49</td><td>0.54</td><td>0.17</td><td>0.21</td><td>0.34</td><td>0.38</td></tr></tbody></table>

NOTE. The figures report the estimates seasonal climate variables on forestland price in columns (1) to (4), in the spirit of the standard Ricardian approach, and on the multiplication of forestland area by forestland price in columns (5) to (8), in line with the land-adjusted Ricardian approach. Climate variables are computed using 30-year averages. Controls include population, average altitude and soil conditions. Standard errors adjusted for spatial dependence and computed using the delta method are displayed in brackets.