# Sectoral fiscal multipliers and technology in open economy

Olivier Cardi, Romain Restout

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## To cite this version:

Olivier Cardi, Romain Restout. Sectoral fiscal multipliers and technology in open economy. Journal of International Economics, 2023, 144, pp.103789. 10.1016/j.jinteco.2023.103789. hal-04522948

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# SECTORAL FISCAL MULTIPLIERS AND TECHNOLOGY IN OPEN ECONOMY*

Olivier CARDI†

Lancaster University Management School

Romain RESTOUT‡

Université de Lorraine BETA (CNRS UMR 7522)

## Abstract

Our evidence reveals that the rise in real GDP is uniformly distributed across sectors following a government spending shock while labor growth is concentrated in non-traded industries. A rationale behind these two findings lies in technology which responds endogenously to the government spending shock. While technology improvements are concentrated in traded industries, technological change is biased toward labor (capital) in non-traded (traded) industries. To account for our evidence, we consider a semi-small open economy model with tradables and non-tradables where both capital and technology can be used more intensively. While financial openness amplifies the biasedness of the demand shock toward non-traded goods, labor mobility costs, imperfect substitutability between home- and foreign-produced traded goods and endogenous capital utilization are necessary conditions for giving rise to traded technology improvement. The model can reproduce the size of fiscal multipliers once we let technology adjustment costs together with factor-biased technological change vary across sectors.

**Keywords:** Sector-biased government spending shocks; Endogenous technological change; Factor-augmenting efficiency; Open economy; Labor reallocation; CES production function; Labor income share.

**JEL Classification:** E25; E62; F11; F41; O33

<footnote>*We are grateful to Peter Jørgensen and Søren Ravn for insightful discussions at an early stage of the paper and Christoph Thoenissen, Mathias Klein, Pawel Krolikowski, William Tayler, for their suggestions and comments. We are also grateful to editor Kim Ruhl and two anonymous referees for very constructive and helpful comments which have permitted to significantly improve an earlier version of the manuscript. We thank participants at the Computing in Economics and Finance Conference, June 15-17 2021, the Asian Meeting of Econometric Society in Seoul, June 25-27 2021, the International Conference on Public Economic Theory at Marseille, June 8-10 2022, the conference of the Nordic Econometric Meeting at Sandbjerg, Denmark, September 10-13 2022, the North American Summer Meeting of the Econometric Society at Los Angeles, June 22-25 2023, for their valuable comments. Obviously, any remaining shortcomings are our own. Olivier Cardi thanks the Leverhulme Trust for its research support (RPG-2019-348 Grant). Romain Restout thanks the Region of Lorraine for its research support (AAP-009-020 Grant).</footnote>

<footnote>†Olivier Cardi. Correspondence address: Lancaster University Management School, Bailrigg, Lancaster LA1 4YX. E-mail: o.cardi@lancaster.ac.uk.</footnote>

<footnote>‡Romain Restout. Correspondence address: Université de Lorraine, BETA, CNRS, INRA, 54000, Nancy, France. E-mail: romain.restout@univ-lorraine.fr.</footnote>
# 1 Introduction

Until recently, fiscal policy was considered to be effective only through higher private consumption or greater labor supply or both. In their article, Delong and Summers [2012] set out the possibility of a persistent increase in productivity following a rise in government spending. The evidence recently documented by D'Alessandro et al. [2019] and Jørgensen and Ravn [2022] on quarterly U.S. data reveals that an exogenous and temporary shock to government consumption significantly increases aggregate total factor productivity (TFP), lending credence to Delong and Summers's hypothesis. If TFP increases, the aggregate fiscal multiplier is higher than initially thought. Because the ability of firms to increase efficiency in the use of capital and labor may vary across industries, we address the following questions: Does the positive effect of a rise in government consumption on technology vary across traded and non-traded sectors? How does the technology channel modify the distribution of government spending multipliers across sectors in open economy? We find that shocks to government consumption significantly increase traded TFP relative to non-traded TFP, thus pushing up the value added multiplier of tradables relative to non-tradables. While technology improvements are concentrated in the traded sector, non-traded industries bias technological change toward labor, which increases the labor multiplier of non-tradables relative to tradables.

As exemplified by D'Alessandro et al. [2019], Jørgensen and Ravn [2022], Antolin-Diaz and Surico [2022], Klein and Linnemann [2022], the literature highlighting the technology channel of fiscal policy remains distinct from a second strand emphasizing the role of the sector's intensity in the government spending shock and barriers to mobility in determining sectoral and aggregate fiscal multipliers, see e.g., Boehm [2020], Bouakez et al. [2022b], Cardi et al. [2020], Cox et al. [2020], Lambertini and Proebsting [2022], Proebsting [2022]. Our paper brings these two distinct threads in the existing literature together in an open economy setting. We show that the technology channel is a key driver of the distribution of government spending multipliers across sectors, and that both the multi-sector aspect and the (financial and trade) openness dimension play a critical role.

Investigating the link between technology and fiscal policy at a sectoral level is important as it has a major economy policy implication. Evidence documented by Hlatshwayo and Spence [2014], Mian and Sufi [2014], Aghion et al. [2021], Beraja and Wolf [2022] show that labor in non-exporting industries experiences the largest drop (relative to traded labor) during downturns while value added of sectors producing traded goods declines more than that of sectors producing non-traded goods.<fnref n="1" /> The fact that sectors are not symmetrically

<footnote n="1">¹In Online Appendix A, we document evidence for the eighteen OECD countries of our sample which shows that non-traded hours worked fall more than traded hours worked during downturns while the reverse is true for traded value added as its decline is more pronounced than non-traded value added. By keeping in mind that the variations in the value added of tradables are driven by Manufacturing which is made up of industries producing durable goods, our empirical facts square well with the evidence documented by</footnote>
affected by recessions raises the question of the capacity of fiscal policy to mitigate such a differential response of non-tradable versus tradable industries. Our work suggests that the technology channel of fiscal policy can accomplish this task as it encourages traded firms to improve technology and has an expansionary effect on non-traded labor through factor-biased technological change (FBTC henceforth).

To guide our quantitative analysis, we estimate the sectoral value added and sectoral hours effects of a shock to government consumption for eighteen OECD countries over the period running from 1970 to 2015, using Jordà's [2005] local projection method. We find empirically that the real GDP multiplier averages 1.4 during the first six years after the shock and importantly, 39% of the increase in real GDP is driven by TFP gains. Our estimates reveal that the aggregate multiplier is uniformly distributed across sectors, i.e., in accordance with the sectoral value added share. The muted response of the value added share of non-tradables to the government spending shock at any horizon is puzzling since according to the data taken from the World Input-Output Database, government purchases are concentrated in non-traded industries. A rationale behind this finding lies in the technology channel of fiscal transmission. We find that technology improvements are concentrated in the traded sector which offset the impact of the biasedness of the government spending shock, thus leaving the value added share of non-tradables unchanged.

The allocation of labor across sectors is quite distinct from the sectoral distribution of value added. While the labor multiplier averages 1.15 during the first six years after the shock, 88% of the rise in total hours worked is concentrated in non-traded industries. Our evidence suggests that the disproportionate increase in non-traded hours is driven by the biasedness of technological change toward labor in non-traded industries which amplifies the impact on non-traded hours of the biasedness of the demand shock toward non-tradables.

To account for the role of technology in determining the magnitude of government spending multipliers, we put forward a two-sector open economy model with tradables and non-tradables which is similar to the model version by Chodorow-Reich et al. [2021] except that we abstract from nominal and financial frictions and instead consider the specific elements detailed below.<fnref n="2" /> Building on Bianchi et al. [2019], we endogenize technological change at a sectoral level by allowing for endogenous utilization of technology. This modelling is based on our evidence which reveals that changes in capital-utilization-adjusted-TFP of tradables are not associated with an increase in the stock of R&D. By taking advantage of the panel data dimension of our sample, we conduct a split-sample analysis which reveals that effi-

<footnote>Beraja and Wolf [2022] who show that recessions are deeper and the recovery greater in U.S. States where the share of sectors producing durable goods is larger.</footnote>

<footnote n="2">²Like Kehoe and Ruhl [2009] and Bertinelli et al. [2022], we assume that the economy is small in world capital markets so that the world interest rate is given, but large enough in the world goods market to influence the relative price of its export good so that terms of trade are endogenous. Our model can also be viewed as a two-sector extension with endogenous technology and capital use of the open economy RBC model developed by Ferrara et al. [2021].</footnote>
ciency gains we estimate following a government spending shock are based on the internal
organization of firms which is a mediating factor through which demand conditions affect
technology adjustment. Building on our model’s predictions, we show that the variations
in technology are influenced by three sets of elements which includes the biasedness of the
demand shock, barriers to factors’ mobility and technology factors.

First, because the decision to improve technology is pro-cyclical and sectoral value
added is affected by the reallocation of productive resources, the biasedness of the govern-
ment spending shock towards non-traded goods impacts negatively the incentive to increase
efficiency in the traded sector. Financial openness amplifies the impact of the biasedness of
the demand shock towards non-traded goods. Because traded goods can be imported while
non-traded goods must be produced by domestic firms, the open economy finds it optimal to
borrow from abroad which further shifts productive resources away from traded industries.
The reallocation of capital and labor is hampered however by barriers to factors’ mobility
which include workers’ switching costs and imperfect substitutability between home-and
foreign-produced traded goods. As home- and foreign-produced tradables are more differ-
entiated, households are more reluctant to substitute imported for domestic goods which
dramatically reduces the current account deficit and thus the reallocation of resources to-
ward non-traded industries.

We find quantitatively that frictions into factors’ mobility are not sufficient on their own
to generate an increase in traded production efficiency. To give rise to an increase in overall
efficiency of tradables, we have to allow for either an endogenous capital utilization rate or
FBTC. To account for the magnitude of technology improvement in tradables relative to
non-tradables we estimate empirically, both elements are necessary. Intuitively, a higher
capital utilization rate in both sectors reduces the need to shift capital toward the non-
traded sector and increases capital services rented by traded firms which has a positive
impact on traded value added. Capital shifts toward tradable industries only once we
assume that sectoral goods are produced by means of CES production functions and we let
the mix of labor- and capital-augmenting efficiency vary along the technology frontier, along
the lines of Caselli [2016]. Intuitively, because technological change is biased toward labor
in the non-traded sector and biased toward capital in the traded sector, tradable industries
experience a large capital inflow giving rise to incentives for improving technology.

To assess quantitatively the contribution of technology in determining the magnitude
of aggregate and sectoral fiscal multipliers, we start with a simplified version of our model
which collapses to the semi-small open economy model developed by Kehoe and Ruhl [2009]
with capital adjustment costs and imperfect mobility of labor across sectors. In this re-
stricted version, we shut down endogenous capital and technology utilization in both sectors
and assume that sectoral goods are produced from Cobb-Douglas production functions. Un-
der these assumptions, the restricted model considerably understates both real GDP and labor multipliers that we estimate empirically. By assuming fixed sectoral TFPs, the model also predicts a fall in traded value added and a disproportionate increase in non-traded value added, in contradiction with our evidence while the shift of labor toward the non-traded sector falls short of our estimates.

Once we let capital-utilization-adjusted-technology respond endogenously to the rise in government spending and allow firms to change the mix of labor- and capital-augmenting efficiency over time, the model can account for both the aggregate and sectoral effects that we estimate empirically. By increasing real GDP directly and also indirectly through higher wages which provide more incentives to increase labor supply, the rise in aggregate TFP allows the model to generate government spending multipliers larger than one in line with our evidence. Although the government spending shock is biased toward non-tradables, technology improvements are concentrated in tradables because the cost of adjusting technology is lower in the traded than in the non-traded sector, conditionally on barriers to factors' mobility together with FBTC and increased capital utilization. The TFP differential leads the real GDP multiplier to be symmetrically distributed across sectors. Conversely, the bulk of the rise in total hours worked is concentrated in the non-traded sector which biases technological change toward labor.

**Literature.** Our paper fits into several different literature strands, as we bring several distinct threads in the existing literature together.

Recently, Jordà et al. [2020] and Baqaee et al. [2021] have documented evidence pointing at the presence of a technology channel brought about by monetary policy and proposed an interpretation of TFP gains based on the shifts in the allocation of resources across firms, respectively. In contrast, in our paper, variations in TFP are the result of changes in endogenous utilization of existing technologies, along the lines of Bianchi et al. [2019]. This modelling strategy has been already introduced in a New Keynesian model by Jørgensen and Ravn [2022]. Differently, to generate a rise in aggregate TFP following a government spending shock, D'Alessandro et al. [2019] endogenize technological progress by assuming skill accumulation through past work experience, echoing the learning-by-doing mechanism. In contrast to these two papers, we show that the technology channel determines the distribution of real GDP and labor multipliers across sectors and that the decision to improve technology depends on the biasedness of the demand shock, barriers to factors' mobility, and sector-specific FBTC.

In this regard, we also contribute to a growing literature investigating fiscal transmission at a sectoral level, both empirically and theoretically. Ramey and Shapiro [1998] find that a rise in military spending (which is intensive in traded goods) reallocates labor toward traded industries. Benetrix and Lane [2010] document evidence which reveals that a government
spending shock disproportionately increases non-traded value added. As shown by Cardi et al. [2020] and Lambertini and Proebsting [2022], to account for the fiscal transmission mechanism, the open economy model with tradables and non-tradables must allow for both a non-traded bias in government spending and imperfect mobility of labor across sectors. In contrast to both these aforementioned works, we highlight empirically the technology channel of government spending shocks and quantify its role in determining the size of sectoral government spending multipliers.

Third, our paper also relates to a growing literature which highlights the role of sub-categories of aggregate government spending. Like us, research works by Boehm [2020], Bouakez et al. [2022a] and Proebsting [2022] stress the role of labor mobility costs in a multi-sector model and place the emphasis on the composition of government spending. Differently, we show that abstracting from the technology channel leads to understate the actual magnitude of both output and labor multipliers. Our results also point out that shutting down technology at a sectoral level would lead to overstate the value added multiplier of non-tradables and understate its labor multiplier. Bouakez et al. [2022b] and Cox et al. [2020] use granular U.S. data and find that government spending shocks are concentrated towards a few industries. Like them, we emphasize that government purchases do not mimic private demand in OECD countries. These two papers have a different strategy as they seek to determine the aggregate effects of sector-specific government spending shocks. Instead, our main objective is to analyze the distribution of real GDP and labor multipliers across sectors and thus we have to let all components of government spending vary at the same time. When we adopt the same strategy as Bouakez et al. [2022b] and Cox et al. [2020], we find that the multiplier is maximized as long as government consumption is allocated to the sector with the highest labor compensation share when technology is shut down, and differently that government consumption must be allocated to the sector with the lowest technology adjustment cost once we allow for the technology channel. In contrast to Bouakez et al. [2022b] and Cox et al. [2020] who estimate the multipliers only numerically, we quantify the multipliers at an aggregate and sectoral level, both empirically and numerically, like Bouakez et al. [2022a] who estimate the sectoral effects of a shock to government consumption.

**Outline.** In section 2, we document evidence about the technology channel of fiscal policy at both aggregate and sectoral levels. In section 3, we develop a semi-small open economy model with tradables and non-tradables, endogenous technology choices and FBTC. In section 4, we uncover the factors giving rise to technology improvements in the traded sector and quantify the role of the technology channel in driving aggregate and sectoral spending multipliers. The Online Appendix contains more empirical results, conducts robustness checks, details the solution method, and shows extensions of the baseline model.
## 2 Sectoral Fiscal Multipliers and Technology: Evidence

In this section, we document evidence for eighteen OECD countries about the role of the technology channel in determining the allocation of government spending multipliers across sectors. Below, we denote the percentage deviation from initial steady-state (or the rate of change) with a hat.

### 2.1 Preliminaries

To discipline our empirical investigation, we first develop intuition about how technology affects government spending multipliers at a sectoral level. We consider a two-sector open economy and make a distinction between a traded (indexed by the superscript $H$) vs. a non-traded sector (indexed by the superscript $N$).

**Sectoral decomposition of the change in real GDP.** Real GDP denoted by $Y_R$ is the sum of value added at constant prices, i.e., $Y_{R,t} = P^H Y_t^H + P^N Y_t^N$ where $Y_t^j$ is the real value added of sector $j = H, N$ at time $t$ evaluated at the base year price $P^j$.<fnref n="3" /> Log-linearizing in the neighborhood of the initial steady-state shows that the deviation of real GDP relative to its initial steady-state in percentage, $\hat{Y}_{R,t}$, is the sum of percentage deviations of value added (at constant prices) relative to their initial steady-state:

$$ \hat{Y}_{R,t} = \nu^{Y,H} \hat{Y}_{t}^{H} + \nu^{Y,N} \hat{Y}_{t}^{N}, \quad (1) $$

where $\hat{Y}_t^j = \frac{Y_t^j - Y_j}{Y_j}$ and we denote the value added share of sector $j$ by $\nu^{Y,j}$. Note that $\nu^{Y,H} + \nu^{Y,N} = 1$.

**Definition of government spending multipliers.** We denote government final consumption expenditure by $G_t$. We calculate the government spending multiplier over a $t$-year horizon as the ratio of the present value of the cumulative change in value added to the present value of the cumulative change in $G_t$ over $t$ years. Denoting the world interest rate by $r^*$, pre-multiplying both sides of (1) by the discount factor, integrating over $(0, t)$ and denoting the multiplier by a superscript $G$ leads to:

$$ \hat{Y}_{R,t}^{G} = \nu^{Y,H} \hat{Y}_{t}^{H,G} + \nu^{Y,N} \hat{Y}_{t}^{N,G}, \quad (2) $$

where $\hat{X}_t^G = \frac{\int_0^t \hat{X}_\tau e^{-r^*\tau} d\tau}{\omega_G \int_0^t \hat{G}_\tau e^{-r^*\tau} d\tau}$ for $X = Y_R, L$, and $\hat{X}_t^{j,G} = \frac{\int_0^t \hat{X}_\tau^j e^{-r^*\tau} d\tau}{\omega_G \int_0^t \hat{G}_\tau e^{-r^*\tau} d\tau}$ for $X^j = Y^j, L^j$ with $\omega_G = G/Y$. Because the shock to $G_t$ is normalized to 1% of GDP at time $t = 0$, impact effects collapse to impact multipliers, i.e., $\hat{X}_0 = \hat{X}_0^G$. We do not refer exclusively to the concept of spending multiplier below and also employ interchangeably the terms of growth or cumulative change over a $t$-year horizon (implicitly conditional on a shock to $G_t$) because the concept of multiplier is less meaningful for prices, wages, labor income shares, hours worked shares or value added shares.

<footnote n="3">³We consider an initial steady-state where prices are those at the base year so that real GDP, $Y_R$, collapses to nominal GDP, $Y$, initially.</footnote>
**Value added share at constant prices and its determinants.** A sufficient statistic determining the degree of asymmetry in the distribution of real GDP growth across sectors is the change in the value added share at constant prices $\nu_t^{Y,j}$ in sector $j = H, N$; the change in $\nu_t^{Y,j}$ is defined as the excess (measured in ppt of GDP) of real value added growth in sector $j$ over real GDP growth, i.e., $d\nu_t^{Y,j} = \nu^{Y,j}(\hat{Y}_t^j - \hat{Y}_{R,t})$. Rearranging the latter equality as follows $\nu^{Y,j}\hat{Y}_t^j = \nu^{Y,j}\hat{Y}_{R,t} + d\nu_t^{Y,j}$ reveals that when $d\nu_t^{Y,j} = 0$, we have $\nu^{Y,j}\hat{Y}_t^j = \nu^{Y,j}\hat{Y}_{R,t}$, so that the cumulative change in real GDP caused by a shock to $G_t$ is uniformly distributed across sectors, i.e., in accordance with their value added share. Conversely, value added of sector $j$ increases disproportionately when $d\nu_t^{Y,j} > 0$.

The change in the value added share of sector $j$ is determined by the reallocation of productive resources across sectors and the TFP growth differential caused by a government spending shock, see Online Appendix B.1 for a formal derivation. Using data from the World Input-Output Database (WIOD) [2013], [2016], we constructed time series for sectoral government consumption and find empirically that the non-traded sector receives on average 80% of government consumption (see column 4 of Table 1).<fnref n="4" /> As demonstrated in Online Appendix R.1, see also Cardi et al. [2020], Proebsting [2022], when the intensity of the non-traded sector in the government spending shock, denoted by $\omega_{GN}$, is higher than the share of non-tradables in GDP (which averages 64%, see column 1 of Table 1), the demand shock moves productive resources toward the non-traded sector, as long as technology is kept fixed. The impact of the biasedness of the demand shock toward non-tradables can be neutralized however if the rise in $G_t$ leads to endogenous TFP gains which vary across sectors.

**Sectoral decomposition of the change in hours.** While changes in sectoral TFPs influence the distribution of real GDP growth across sectors, technology adjustment also shapes the responses of sectoral hours worked as a result of factor-biased technological change (FBTC henceforth). To shed some light on the impact of FBTC on the responses of sectoral hours worked, we start with the sectoral decomposition of the percentage deviation of total hours worked relative to its initial steady-state:

$$ \hat{L}_t = \alpha_L^H \hat{L}_t^H + \alpha_L^N \hat{L}_t^N, \qquad (3) $$

where $L$ and $L^j$ are total and sectoral hours worked, respectively, $\alpha_L^j$ is the labor compensation share in sector $j$ and $\alpha_L^H + \alpha_L^N = 1$. Note that $\alpha_L^j$ collapses to $L^j/L$ when we impose perfect mobility of labor across sectors.

**Determinants of the change in the labor share of non-tradables.** Like the value added share, the change in the labor share of sector $j$ computed as $d\nu_t^{L,N} = \alpha_L^N (\hat{L}_t^N - \hat{L}_t)$, see Online Appendix B.2, indicates whether the rise in $L_t$ is uniformly distributed across sectors. Because a shock to $G_t$ is biased toward non-tradables, as evidence suggests, labor

<footnote n="4">⁴Bussière et al. [2013] also find that government spending mostly includes non-tradables.</footnote>
shifts toward the non-traded sector, i.e., $d\nu_t^{L,N} > 0$, which has a positive impact on the labor multiplier of non-tradables measured by $\alpha_L^N \hat{L}_t^N = \alpha_L^N \hat{L}_t + d\nu_t^{L,N}$. Both barriers to mobility and factor-augmenting technology influence the magnitude of $d\nu_t^{L,N} > 0$.

Frictions in the movement of labor between sectors, caused by imperfect substitutability between traded and non-traded hours worked and between home- and foreign-produced traded goods, mitigate the rise in $\nu_t^{L,N}$ while FBTC may amplify it. We derive below a formal expression for $L_t^N/L_t$ when labor market clears. Denoting the elasticity of labor supply across sectors by $\epsilon$, the share of hours worked supplied to sector $j$ is increasing in the wage differential, i.e., $\frac{L_t^j}{L_t} = \vartheta^j \left(\frac{W_t^j}{W_t}\right)^\epsilon$ where $\vartheta^j$ stands for the weight attached to labor supply in sector $j = H, N$, $W_t^j$ and $W_t$ are sectoral and aggregate wage rates, respectively. We assume perfectly competitive markets and constant returns to scale in production. Under these assumptions, labor is paid its marginal product. Denoting the labor income share by $s_L^j$, the marginal revenue product of labor, $s_{L,t}^j \frac{P_t^j Y_t^j}{L_t^j}$, must equate the wage rate $W_t^j$. The same logic applies at an aggregate level, i.e., $s_{L,t} \frac{Y_t}{L_t} = W_t$ where $s_{L,t}$ is the aggregate labor income share (LIS henceforth) and $Y_t$ is GDP at current prices. Dividing $W_t^N$ by $W_t$ and making use of labor supply to sector $j$ to eliminate $W_t^N/W_t$ leads to a formal expression for the equilibrium non-traded-goods-share of total hours worked (see Online Appendix B.2):

$$L_t^N/L_t = (1 - \vartheta)^{\frac{1}{1+\epsilon}} (s_{L,t}^N/s_{L,t})^{\frac{\epsilon}{1+\epsilon}} (\omega_t^{Y,N})^{\frac{\epsilon}{1+\epsilon}}, \quad (4)$$

where $\omega_t^{Y,N}$ is the value added share of non-tradables at current prices. In a model where production functions are Cobb-Douglas, LISs remain fixed. Eq. (4) states that by pushing up $\omega_t^{Y,N}$, a demand shock biased toward non-tradables increases $L_t^N/L_t$. The rise in $\omega_t^{Y,N}$ is curbed however by imperfect substitutability between home- and foreign-produced traded goods as households are reluctant to substitute imported for domestic goods; this gives rise to a terms of trade appreciation that raises the return on capital and labor in the traded sector. For a given change in $\omega_t^{Y,N}$, a lower labor mobility (i.e., $\epsilon$ takes lower values) mitigates the rise in $L_t^N/L_t$.

When sectoral goods are produced by means of CES production functions, the technology of production can become more labor (capital) intensive if technological change is biased toward labor (capital). If non-traded firms decide to bias technological change toward labor and traded firms to bias technological change toward capital, the non-traded LIS, $s_{L,t}^N$, increases relative to the aggregate LIS, $s_{L,t}$, which tilts the demand for labor toward the non-traded sector as shown on the RHS of (4). As shall be useful later, we draw on Caselli and Coleman [2006] and Caselli [2016] to construct time series for FBTC which must be adjusted with the capital utilization rate, as explained in section 2.3. Denoting the elasticity of substitution between capital and labor by $\sigma^j$, capital- and labor-augmenting efficiency by $B_t^j$ and $A_t^j$, respectively, our measure of capital-utilization-adjusted-FBTC,
denoted by FTBC<sub>t,adjK</sub><sup>j</sup>, reads (see Online Appendix G for a formal derivation):

$$
\mathrm{FBTC}_{t, \mathrm{adj} K}^{j} = \left( \frac{\mathrm{B}_{t}^{j} / \bar{\mathrm{B}}^{j}}{\mathrm{A}_{t}^{j} / \bar{\mathrm{A}}^{j}} \right)^{\frac{1-\sigma^{j}}{\sigma^{j}}} = \frac{\mathrm{S}_{t}^{j}}{\mathrm{S}^{j}} \left( \frac{\mathrm{k}_{t}^{j}}{\bar{\mathrm{k}}^{j}} \right)^{-\frac{1-\sigma^{j}}{\sigma^{j}}} \left( \frac{\mathrm{u}_{t}^{K, j}}{\bar{\mathrm{u}}^{K, j}} \right)^{-\frac{1-\sigma^{j}}{\sigma^{j}}}, \quad (5)
$$

where a bar refers to averaged values of the corresponding variable over 1970-2015. To construct time series for FTBC<sub>t,adjK</sub><sup>j</sup>, we plug time series for the ratio of the labor to the capital income share, S<sub>t</sub><sup>j</sup> = s<sub>L,t</sub><sup>j</sup> / (1 - s<sub>L,t</sub><sup>j</sup>), the capital-labor ratio, k<sub>t</sub><sup>j</sup>, the capital utilization rate defined later, u<sub>t</sub><sup>K,j</sup>. We also plug values for σ<sup>j</sup> we have estimated for each country of our sample (see columns 14 and 15 of Table 1). We find values for σ<sup>j</sup> smaller than one for the whole sample (and most of countries/sectors), thus corroborating the gross complementarity between capital and labor documented by Klump et al. [2007], Herrendorf et al. [2015], Oberfield and Raval [2021], Chirinko and Mallick [2017]. When FBTC<sub>t,adjK</sub><sup>j</sup> increases, technological change is biased toward labor while a fall indicates that technological change is biased toward capital.

2.2 VAR Model and Identification

To conduct our empirical study, we follow Corsetti et al. [2012] and compute the responses of selected variables by using a two-step estimation procedure. Like Bernardini et al. [2020] and Liu [2022], we first identify shocks to government consumption by considering a baseline VAR model where government spending is ordered before the other variables which amounts to adopting the standard Cholesky decomposition pioneered by Blanchard and Perotti [2002]. In the second step, we trace out the dynamic effects of the identified shock to government consumption by using Jordà's [2005] local projections.

**First step.** In the first step, we identify the government spending shocks by estimating
the reduced-form VAR model in panel format on annual data:

$$
Z_{i,t} = \alpha_i + \alpha_t + \beta_i t + \sum_{k=1}^{2} A^{-1} B_k Z_{i,t-k} + A^{-1} \epsilon_{i,t}, \quad (6)
$$

where subscripts *i* and *t* denote the country and the year, *k* is the number of lags and *Z*<sub>*i*,t</sub> is the vector of endogenous variables; the specification includes country fixed effects, *α*<sub>*i*</sub>, which control for time-invariant countries’ characteristics, time dummies, *α*<sub>*t*</sub>, which account for macroeconomic shocks common to OECD countries, and country-specific linear time trends; *A* is a matrix that describes the contemporaneous relation among the variables collected in vector *Z*<sub>*i*,t</sub>, *B*<sub>*k*</sub> is a matrix of lag-specific own- and cross-effects of variables on current observations, and the vector *ε*<sub>*i*,t</sub> contains the structural disturbances which are uncorrelated with each other. In line with current practice, we include two lags in the regression model and use a panel OLS regression to estimate the coefficients *A*<sup>-1</sup>*B*<sub>*k*</sub> and the reduced-form innovations *A*<sup>-1</sup>*ε*<sub>*i*,t</sub>. The VAR model we estimate in the first step includes government final consumption expenditure, real GDP, total hours worked, the real consumption wage,
and aggregate total factor productivity, where all variables are logged, while all quantities are expressed in real terms and scaled by the working-age population. Like Blanchard and Perotti [2002], we base the identification scheme on the assumption that there are some delays inherent to the legislative system which prevents government spending from responding endogenously to contemporaneous output developments.

**Second step.** Once we have identified government spending shocks, $\epsilon_{i,t}^G$, from (6), in the second step, we estimate the effects on selected variables (detailed later) by using Jordà's [2005] single-equation method. The local projection method amounts to running a series of regressions of each variable of interest on a structural identified shock for each horizon $h = 0, 1, 2, ...$:

$$x_{i,t+h} = \alpha_{i,h} + \alpha_{t,h} + \beta_{i,h}t + \psi_h(L) z_{i,t-1} + \gamma_h \epsilon_{i,t}^G + \eta_{i,t+h}, \quad (7)$$

where $\alpha_{i,h}$ are country fixed effects, $\alpha_{t,h}$ are time dummies, and we include country-specific linear time trends; $x$ is the logarithm of the variable of interest, $z$ is a vector of control variables (i.e., past values of government spending and of the variable of interest), $\psi_h(L)$ is a polynomial (of order two) in the lag operator. The coefficient $\gamma_h$ gives the response of $x$ at time $t+h$ to the government spending shock at time $t$. We compute heteroskedasticity and autocorrelation robust standard errors based on Newey-West.

**Robustness checks.** We have conducted a series of robustness checks related to several aspects of our VAR identification of government spending shocks and measures of technology which are detailed in Online Appendices P and Q. First, because using annual data makes the Blanchard-Perotti identification less natural, we have alternatively identified fiscal shocks by using quarterly data or by using military expenditure to instrument government consumption and find that our results are robust to our identification assumption and data frequency (see Online Appendices P.1, P.2, P.3). Second, instead of adopting a two-step approach where generated residuals are used as regressors, we alternatively considered the one-step method of Ramey and Zubairy [2018] and find that our results are unchanged (see Online Appendix P.6). Third, Online Appendix P.4 shows that the concern related to the potential presence of anticipation effects is substantially mitigated. Fourth, in Online Appendix P.5, we find that controlling for monetary policy does not affect our estimates. Fifth, the evidence documented in Online Appendices Q.1 and Q.3 reveals that the technology channel of fiscal transmission we highlight is robust to alternative measures of technology such as Fernald's [2014] or Basu's [1996] time series for utilization-adjusted-TFP.

## 2.3 Data Construction

Before presenting evidence on fiscal transmission across sectors, we briefly discuss the dataset we use. We take data from EU KLEMS [2011],[2017] and OECD STAN [2011],
[2017]. Our sample contains annual observations and consists of a panel of 18 OECD countries. The period runs from 1970 to 2015. In Online Appendix D, we detail the source and the construction of time series for value added at constant prices, $Y_{it}^j$, hours worked, $L_{it}^j$, the hours worked share, $\nu_{it}^{L,j}$, the value added share at constant prices, $\nu_{it}^{Y,j}$, the labor income share, $s_{L,it}^j$, of sector $j = H, N$.

**Classification of industries as tradables or non-tradables.** Since our primary objective is to quantify the role of the technology channel in determining the sectoral effects of a government spending shock, we describe below how we construct time series at a sectoral level. Our sample covers eleven 1-digit ISIC-rev.3 industries. Following De Gregorio et al. [1994], we define the tradability of an industry by constructing its openness to international trade given by the ratio of total trade (imports plus exports) to gross output, see Online Appendix O.1 for more details. Data for trade and output are taken from WIOD [2013], [2016]. “Agriculture, Hunting, Forestry and Fishing”, “Mining and Quarrying”, “Total Manufacturing” and “Transport, Storage and Communication” exhibit high openness ratios and are thus classified as tradables. At the other end of the scale, “Electricity, Gas and Water Supply”, “Construction”, “Wholesale and Retail Trade” and “Community Social and Personal Services” are considered as non-tradables since the openness ratio in this group of industries is low (i.e., less than 10% for most of the countries in our sample). For the three remaining industries “Hotels and Restaurants”, “Financial Intermediation”, “Real Estate, Renting and Business Services” the results are less clearcut since the openness ratio averages (across countries) 14% for the former and 20% for the last two sectors. In the benchmark classification, we adopt the standard classification of De Gregorio et al. [1994] by treating “Real Estate, Renting and Business Services” and “Hotels and Restaurants” as non-traded industries. Given the dramatic increase in financial openness that OECD countries have experienced since the end of the eighties, we allocate “Financial Intermediation” to the traded sector. This choice is also consistent with the classification of Jensen and Kletzer [2006] who categorize “Financial Intermediation” as tradable.<fnref n="5" />

**Utilization-adjusted sectoral TFPs.** Sectoral TFPs are Solow residuals calculated from constant-price (domestic currency) series of value added, $Y_{it}^j$, capital stock, $K_{it}^j$, and hours worked, $L_{it}^j$, i.e., $\text{TFP}_{it}^j = \hat{Y}_{it}^j - s_{L,i}^j \hat{L}_{it}^j - (1 - s_{L,i}^j) \hat{K}_{it}^j$ where $s_{L,i}^j$ is the LIS in sector $j$ averaged over the period 1970-2015. To obtain series for the capital stock in sector $j$, we first compute the overall capital stock by adopting the perpetual inventory approach, using constant-price investment series taken from the OECD's Annual National Accounts. Following Garofalo and Yamarik [2002], we split the gross capital stock into traded and non-traded industries by using sectoral valued added shares.<fnref n="6" /> Once we have constructed

<footnote n="5">⁵Evidence documented in Online Appendix O.1 shows that treating “Financial Intermediation” as non-tradables or classifying “Hotels and Restaurants” or “Real Estate, Renting and Business Services” as tradables does not affect our main results.</footnote>

<footnote n="6">⁶In Online Appendix O.5, we use EU KLEMS [2011], [2017] which provide disaggregated capital stock</footnote>
the Solow residual for the traded and the non-traded sectors, we construct a measure for technological change by adjusting the Solow residual with the capital utilization rate, denoted by $u_{it}^{K,j}$:

$$ \hat{Z}_{it}^{j} = \text{TFP}_{it}^{j} - (1 - s_{L,i}^{j}) \hat{u}_{it}^{K,j}, \qquad (8) $$

where we follow Imbs [1999] in constructing time series for $u_{it}^{K,j}$ because time series for utilization-adjusted TFP are not available at a sectoral level for most of the OECD countries of our sample; see Online Appendix E where we detail the adaptation of Imbs's [1999] method to our case where sectoral goods are produced from CES production functions.

## 2.4 Sectoral Effects of Government Spending Shocks: VAR Evidence

We generated impulse response functions by means of local projections. The dynamic adjustment of variables to an exogenous increase in $G_{it}$ by 1 percentage point of GDP is displayed by the solid blue line in Fig. 1. The shaded areas indicate 90% confidence bounds. The horizontal axis of each panel measures the time after the shock in years and the vertical axis measures deviations from trend. Responses of sectoral value added and sectoral hours worked are re-scaled by the sample average of sectoral value added to GDP and sectoral labor compensation share, respectively. As such, on impact, the responses of sectoral value added at constant prices and sectoral hours worked can be interpreted as value added and labor multipliers as they are expressed in percentage points of GDP and total hours worked, respectively. We also compute the government spending multipliers over a six-year horizon by setting the interest rate to 3% in accordance with the value shown in column 20 of Table 1 in section 4.1.

**Aggregate effects.** The first row of Fig. 1 displays the aggregate effects of a shock to government consumption. As shown in Fig. 1(a), government consumption, $G_{it}$, follows a hump-shaped response and displays a high level of persistence. Fig. 1(b) and Fig. 1(c) reveal that a rise in $G_{it}$ has a strong expansionary effect on $L_{it}$ and real GDP. Total hours worked increase by 0.9% on impact, while real GDP increases by 1.2%. The real GDP and labor multipliers over a six-year horizon average 1.4 and 1.15, respectively, the responses of $L_{it}$ and $Y_{R,it}$ being statistically significant over this period. One key driver of a real GDP multiplier larger than one is technology, since 39% of real GDP growth is driven by TFP gains (see Fig. 1(d)) over a six-year horizon. To further check the importance of technology improvement in driving real GDP growth, we have adapted the methodology proposed by Sims and Zha [2006] to estimate empirically the government spending multiplier if the technology channel were shut down. As detailed in Online Appendix J, we find that the fiscal multiplier is reduced by 42% when the response of TFP to a shock to $G_{it}$ is shut

<footnote>data (at constant prices) at the 1-digit ISIC-rev.3 level for thirteen countries of our sample over the period 1970-2015. Our estimates show that our empirical findings are robust and unsensitive to the way the sectoral capital stocks are constructed in the data.</footnote>
down.<fnref n="7" />

**Sectoral labor multipliers and LISs.** The second row of Fig. 1 displays the dynamic adjustment of sectoral hours worked. Fig. 1(e) and 1(f) reveal that a shock to $G_{it}$ by 1 ppt of GDP increases both traded and non-traded hours but only the latter is statistically significant. More specifically, the six-year-horizon labor multipliers of non-tradables and tradables average 1.02 ppt and 0.13 ppt of total hours worked, respectively. Therefore, the rise in $L_{it}^N$ contributes 88% to the increase in $L_{it}$. As displayed by Fig. 1(g), the non-traded goods-sector-share of total hours worked increases by 0.3 ppt of total hours worked on average over the first six years, which implies that the reallocation of labor toward the non-traded sector contributes 29% to the rise in $L^N$. The expansionary effect of the biasedness of the demand shock toward non-tradables on $\nu_{it}^{L,N}$ is amplified by the increased labor intensity of non-traded production, as reflected in a non-traded LIS which builds up relative to the traded LIS, see Fig. 1(h). When we apply the Sims and Zha [2006] methodology and assume that the ratio of the non-traded to the traded LIS is unresponsive to the government spending shock, the rise in $\nu_{it}^{L,N}$ is found to be almost twice smaller. Our evidence shown below reveals that the rise in $s_L^N/s_L^H$ is brought about by technological change biased toward labor.<fnref n="8" />

**Sectoral value added multipliers and TFPs.** The third row of Fig. 1 shows that a rise in $G_{it}$ increases both traded and non-traded value added at constant prices. Both responses are statistically significant. Over the first six years, the value added multipliers of tradables and non-tradables average 0.52 ppt and 0.89 ppt of GDP, respectively. In contrast to labor, the non-traded sector contributes 64% only to the cumulative change in real GDP, a value which collapses to its share in GDP. In accordance with this observation, Fig. 1(k) reveals that $\nu_{it}^{Y,N}$ remains unresponsive to the shock which is puzzling because the government spending shock is strongly biased toward non-tradables. As shown in Fig. 1(l), the solution to this puzzle lies in the technology channel. On average, over the first six years, the TFP differential between tradables and non-tradables amounts to 1.5% per year. The technology gap between sectors is large enough to neutralize the impact of the reallocation of productive resources toward the non-traded sector, thus leaving $\nu_{it}^{Y,N}$ unaffected. The Sims and Zha [2006] approach corroborates the role of technology as we find empirically that $\nu_{it}^{Y,N}$ increases by 0.26 ppt per year over a six-year horizon when the ratio of traded to non-traded TFP is kept fixed but rises by only 0.09 ppt once we allow for the technology channel.

**Utilization-adjusted TFP.** The last row of Fig. 1 displays the dynamic adjustment

<footnote n="7">⁷We estimate a VAR model with three variables, government consumption, aggregate TFP and real GDP. We find a six-year-horizon-government spending multiplier of 1.25. When we shut down technological change, the real GDP multiplier averages 0.73 only.</footnote>

<footnote n="8">⁸We compute the LIS like Gollin [2002], i.e., labor compensation is defined as the sum of compensation of employees plus compensation of the self-employed. We find that our results are robust to alternative constructions of the LIS, see Online Appendix O.2.</footnote>
<figure><img src="image_3.png" /><figcaption>(a) Government Consumption</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>(b) Total Hours Worked</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>(c) Real GDP</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>(d) Aggregate TFP</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>(e) Traded Hours Worked</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>(f) Non-Traded Hours Worked</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>(g) Labor Share of Non-Tradables</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>(h) Non-Traded to Traded LIS</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>(i) Traded Value Added</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>(j) Non-Traded Value Added</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>(k) Value Added Share of Non-Tradables</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>(l) Traded to Non-Traded TFP</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>(m) Utilization-Adjusted Traded TFP</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>(n) Utilization-Adjusted Non-Traded TFP</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>(o) Utilization-Adjusted Traded FBTC</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>(p) Utilization-Adjusted Non-Traded FBTC</figcaption></figure>

<caption>**Figure 1: Sectoral Effects of a Shock to Government Consumption.** Notes: The solid blue line shows the response of aggregate and sectoral variables to an exogenous increase in government final consumption expenditure by 1% of GDP. Shaded areas indicate the 90 percent confidence bounds based on Newey-West standard errors. To estimate the dynamic responses to a shock to government consumption, we adopt a two-step method. In the first step, the government spending shock is identified by estimating a VAR model that includes real government final consumption expenditure, real GDP, total hours worked, the real consumption wage, and aggregate TFP. In the second step, we estimate the effects by using Jordà's [2005] single-equation method. Horizontal axes indicate years. Vertical axes measure percentage deviation from trend in GDP units (sectoral value added, sectoral value added share, labor income share), percentage deviation from trend in total hours worked units (sectoral hours worked, labor share), percentage deviation from trend (sectoral TFPs, sectoral FBTCs). Sample: 18 OECD countries, 1970-2015, annual data.</caption>
of TFP and FBTC for tradables and non-tradables, which are both adjusted with capital utilization to reflect the true variations of technological change. After correcting for capital utilization, Fig. 1(m) and Fig. 1(n) reveal that technology improves in the traded sector and is essentially unchanged in the non-traded sector, respectively. Because the capital utilization rate increases in the traded relative to the non-traded sector, these findings indicate that the rise in the relative TFP of tradables shown in Fig. 1(l) is driven by both a higher utilization of capital and a technology improvement in the traded sector, thus explaining the muted response of $\nu_{it}^{Y,N}$.

**Utilization-adjusted FBTC.** The last two panels of the last row of Fig. 1 show the responses of utilization-adjusted FBTC. Because higher values for $FBTC_{adjK}^j$ imply that production turns out to be more labor intensive, evidence displayed by Fig. 1(o) and Fig. 1(p) reveal that technological change is biased toward labor in the non-traded sector and biased toward capital in the traded sector. These findings are consistent with the rise in the non-traded LIS relative to the traded LIS shown in Fig. 1(h).

Since $FBTC_{t,adjK}^j = \left( \frac{B_t^j / \bar{B}^j}{A_t^j / \bar{A}^j} \right)^{\frac{1-\sigma^j}{\sigma^j}}$ (see eq. (5)) where both $\sigma^H < 1$ and $\sigma^N < 1$ for the whole sample, the traded sector lowers $B^H/A^H$ and non-traded firms increase capital- relative to labor-augmenting productivity $B^N/A^N$. In Online Appendix I, we document evidence which rationalizes the decision to bias technological change toward one factor of production. Because the non-traded sector must pay higher wages to encourage workers to shift, non-traded firms increase labor-augmenting productivity to mitigate the rise in the labor cost. Since our estimates show that labor- and capital-augmenting productivity are strong complements along the technology frontier, capital-augmenting efficiency dispropor- tionately increases, thus generating a rise in $B^N/A^N$. The other way around is true in the traded sector.

**Technology channel at a disaggregated level.** Our dataset covers eleven industries and in Online Appendix O.3, we conduct the same empirical analysis as in the main text, except that we consider a more disaggregated industry level. We find that the five industries classified as tradables increase their TFP, which confirms that the rise in traded TFP is driven by a technology improvement within each industry. Conversely, the responses of TFP in non-traded industries are more heterogeneous and clustered around the horizontal axis.

**Technology improvements are driven by a cost-minimization strategy.** The evidence documented above raises two important questions: does the technology channel vary across countries and which factors cause such international differences? Our evidence relegated to Online Appendix K shows that technology tends to increase more in the traded than in the non-traded sector but the responses of utilization-adjusted TFP to a government spending shock display a wide cross-country dispersion. We also find empirically that
technology improvements are driven by a cost-minimization strategy, as sector $j = H, N$
increases utilization-adjusted-TFP in countries where the unit cost for producing rises fol-
lowing a government spending shock. In accordance with this observation, we model the
decision to increase the utilization of available technology as a trade-off between the rise in
output generated by enhanced productivity and the cost associated with a higher utilization
rate of technology within each sector $j = H, N$.

**Potential determinants of technology adjustment costs.** Before discussing fac-
tors that could potentially influence the variations in technology following a government
spending shock, it is important to clarify the concept of technology utilization rate. Vari-
ations in utilization-adjusted TFP in sector $j$, $Z_{it}^j$, can be driven by a change in the stock
of knowledge, $\bar{Z}_{it}^j$, or by a change in the rate of utilization of the stock of ideas, $u_{it}^{Z,j}$, or
both. Using data from Stehrer et al. [2019] (EU KLEMS database) we construct time
series for both gross fixed capital formation and capital stock in R&D in the traded and
non-traded sectors. Data are available for twelve countries over 1995-2015. As detailed in
Online Appendix Q.4, our estimates reveal that neither investment in R&D nor the stock
of knowledge respond to the government spending shock. These evidence thus suggest that
the variations in the utilization-adjusted TFP reflect a better firm's organization leading
to efficiency gains necessary to curb upward pressure on production costs instead of pure
innovation that would be reflected into a rise in the stock of knowledge. In our model,
higher production efficiency is thus captured by a rise in the use of existing technology.

Since we interpret the technology utilization rate as the capacity of firms to increase
overall production efficiency to meet higher demand, firms' characteristics such as the inten-
sity of production in capital and/or skilled labor and/or R&D are likely to influence their
ability to adjust efficiency. In this regard, the literature on institutions and international
trade provides an insightful link between production/goods' characteristics and efficiency.
The complexity of a good is captured by its intensity in relationship-specific efforts or in-
vestment and according to the evidence documented by Nunn [2007], goods' complexity is
strongly and positively correlated with skill intensity but negatively correlated with capital
intensity. In the same vein, Costinot [2009] shows that more complex goods involve a more
fragmented chain of production with a higher number of tasks, all of them being essential.
Because transaction and coordination costs become larger as the chain of production be-
comes more fragmented, we expect capital intensive industries to be more prone to improve
efficiency to meet higher demand while industries which are more intensive in skilled labor
or in R&D should experience a larger cost of adjusting technology. These predictions also
echo evidence documented by Adão et al. [2022] who find that skills' specificity tend to
slow productivity gains.

To test our hypothesis, we perform a split-sample based on the median of the intensity
of value added in tangible assets, skilled labor, and intangible assets, see Online Appendix Q.4 which details the source and construction of data. For each group of countries, we plot the technology multiplier against time. The technology multiplier is calculated as the cumulative response of utilization-adjusted aggregate TFP divided by the cumulative response of government consumption. In line with our assumptions, we find that the long-run technology multiplier is significantly positive in the group of countries where traded and non-traded industries are relatively more intensive in physical capital and relatively less intensive in skilled labor or in R&D. More specifically, the technology multiplier is significantly larger than one after six years for industries relatively more intensive in capital, or relatively less intensive in skilled labor or in the stock of knowledge. Conversely, in the second group of countries where the intensity in capital is lower and the intensity in skilled labor or R&D is larger, the technology multiplier is not statistically different from zero in the long-run.

# 3 A Semi-Small Open Economy Model with Tradables and Non-Tradables

We consider a semi-small open economy that is populated by a constant number of identical households and firms that have perfect foresight and live forever. Like Kehoe and Ruhl [2009], Chodorow-Reich et al. [2021], the country is assumed to be semi-small in the sense that it is a price-taker in international capital markets, and thus faces a given world interest rate, r*, but is large enough on world good markets to influence the price of its export goods. The open economy produces a traded good which can be exported, consumed or invested and imports consumption and investment goods. While the home-produced traded good, denoted by the superscript H, faces both a domestic and a foreign demand, a non-traded sector produces a good, denoted by the superscript N, for domestic absorption only. Households supply labor and capital services to firms and must decide about the intensity in the use of tangible and intangible assets. We add a tilde below when the variable is augmented with the rate of utilization of (tangible or intangible) assets. Firms rent capital and labor services and choose a mix of capital- and labor- along the technology frontier. The foreign good is chosen as the numeraire. Time is continuous and indexed by t.

## 3.1 Households

At each instant the representative household consumes traded and non-traded goods denoted by $C^T(t)$ and $C^N(t)$, respectively, which are aggregated by means of a CES function:

$$C(t) = \left[ \varphi^{\frac{1}{\phi}} (C^T(t))^{\frac{\phi-1}{\phi}} + (1-\varphi)^{\frac{1}{\phi}} (C^N(t))^{\frac{\phi-1}{\phi}} \right]^{\frac{\phi}{\phi-1}}, \quad (9)$$

where $0 < \varphi < 1$ is the weight of the traded good in the overall consumption bundle and $\phi$ corresponds to the elasticity of substitution between traded goods and non-traded goods.
The traded consumption index $C^T(t)$ is defined as a CES aggregator of home-produced traded goods, $C^H(t)$, and foreign-produced traded goods, $C^F(t)$:

$$C^T(t) = \left[ \left(\varphi^H\right)^{\frac{1}{\rho}} (C^H(t))^{\frac{\rho-1}{\rho}} + \left(1-\varphi^H\right)^{\frac{1}{\rho}} (C^F(t))^{\frac{\rho-1}{\rho}} \right]^{\frac{\rho}{\rho-1}}, \quad (10)$$

where $0 < \varphi^H < 1$ is the weight of the home-produced traded good and $\rho$ corresponds to the elasticity of substitution between home- and foreign-produced traded goods.

The representative household supplies labor to the traded and non-traded sectors, denoted by $L^H(t)$ and $L^N(t)$, respectively. To put frictions into the movement of labor across sectors, we build on Horvath [2000] and assume that sectoral hours worked are imperfect substitutes:

$$L(t) = \left[ \vartheta^{-1/\epsilon} (L^H(t))^{\frac{\epsilon+1}{\epsilon}} + (1-\vartheta)^{-1/\epsilon} (L^N(t))^{\frac{\epsilon+1}{\epsilon}} \right]^{\frac{\epsilon}{\epsilon+1}}, \quad (11)$$

where $0 < \vartheta < 1$ parametrizes the weight attached to the supply of hours worked in the traded sector and $\epsilon$ is the elasticity of substitution between sectoral hours worked.

The representative agent is endowed with one unit of time, supplies a fraction $L(t)$ as labor, and consumes the remainder $1 - L(t)$ as leisure. At any instant of time, households derive utility from their consumption and experience disutility from working. Assuming that the felicity function is additively separable in consumption and labor, the representative household maximizes the following objective function:

$$U = \int_{0}^{\infty} \left\{ \frac{1}{1 - \frac{1}{\sigma_C}} C(t)^{1 - \frac{1}{\sigma_C}} - \frac{1}{1 + \frac{1}{\sigma_L}} L(t)^{1 + \frac{1}{\sigma_L}} \right\} e^{-\beta t} dt, \quad (12)$$

where $\beta > 0$ is the discount rate, $\sigma_C > 0$ the intertemporal elasticity of substitution for consumption, and $\sigma_L > 0$ the Frisch elasticity of (aggregate) labor supply.

Households receive a wage rate $\tilde{W}(t)$ and a capital rental rate $\tilde{R}(t)$, in exchange for labor $L(t)$ and capital services $K(t)$. We assume that households choose the level of capital utilization $u^{K,j}(t)$ in sector $j$. They also own the stock of intangible capital $\bar{Z}^j$ and decide about the level of utilization $u^{Z,j}(t)$ of existing technology in sector $j$. In the sequel, we normalize the stock of knowledge, $\bar{Z}^j$, to one as we abstract from endogenous choices on the stock of knowledge.<fnref n="9" /> Because households may decide to use more intensively the stock of knowledge in sector $j$ which increases the efficiency in the use of inputs, the counterpart is a rise in factor prices, since factors are paid their marginal product. In accordance with the Euler Theorem, we have $P^j(t)u^{Z,j}(t)Y^j(t) = \tilde{W}^j(t)L^j(t) + \tilde{R}^j(t)u^{K,j}(t)K^j(t)$ where $\tilde{R}^j(t) = u^{Z,j}(t)R(t)$ is the capital rental rate, $\tilde{W}^j(t) = u^{Z,j}(t)W^j(t)$ is the wage rate, $P^j(t)$ is the value added deflator and $Y^j$ stands for technology-utilization-adjusted real value added in sector $j$. Both the capital $u^{K,j}(t)$ and the technology utilization rate $u^{Z,j}(t)$

<footnote n="9">⁹Bianchi et al. [2019] assume that firms can choose both the technology utilization rate and the stock of knowledge. In accordance with the evidence documented in Online Appendix Q.4 which reveals that capital stocks in R&D in both sectors are unresponsive to a government spending shock, we assume that the stocks of knowledge are constant over time. In addition, our estimates show that utilization-adjusted-sectoral TFP is restored back toward its initial steady-state level in both sectors which is consistent with a time-varying technology utilization rate at a sectoral level.</footnote>
collapse to one at the steady-state. We let the functions $C^{K,j}(t)$ and $C^{Z,j}(t)$ denote the adjustment costs associated with the choice of capital and technology utilization rates, which are increasing and convex functions of utilization rates:

$$C^{K,j}(t) = \xi_1^j (u^{K,j}(t) - 1) + \frac{\xi_2^j}{2} (u^{K,j}(t) - 1)^2, \quad (13a)$$

$$C^{Z,j}(t) = \chi_1^j (u^{Z,j}(t) - 1) + \frac{\chi_2^j}{2} (u^{Z,j}(t) - 1)^2, \quad (13b)$$

where $\xi_2^j > 0$, $\chi_2^j > 0$ are free parameters; as $\xi_2^j \to \infty$, $\chi_2^j \to \infty$, utilization is fixed at unity. It is worth mentioning that while the technology utilization rate is assumed to be Hicks-neutral and factor-biased technological change is recovered by using a wedge analysis as detailed later, we could alternatively assume that households choose the utilization rate of factor-augmenting technology. We have considered this possibility both theoretically and numerically. The model fails to reproduce our evidence however as it can account for neither the technology improvement in the traded sector nor the magnitude of technological change biased toward labor which is necessary to generate a rise in the non-traded LIS.

Households can accumulate internationally traded bonds (expressed in foreign good units), $N(t)$, that yield net interest rate earnings of $r^*N(t)$. Denoting lump-sum taxes by $T(t)$, and the aggregate consumption and investment price index by $P_C(t)$ and $P_J(t)$, respectively, the household's flow budget constraint states that real disposable income can be saved by accumulating traded bonds, $\dot{N}(t)$, consumed, $P_C(t)C(t)$, invested, $P_J(t)J(t)$, or can cover (capital and technology) utilization adjustment costs:

$$\begin{aligned} \dot{N}(t) + P_C(t)C(t) + P_J(t)J(t) + P^H(t)C^{K,H}(t)\alpha_K(t)K(t) + P^N(t)C^{K,N}(t)(1-\alpha_K(t))K(t) \\ + P^H(t)C^{Z,H}(t) + P^N(t)C^{Z,N}(t) = [\alpha_L(t)u^{Z,H}(t) + (1-\alpha_L(t))u^{Z,N}(t)]W(t)L(t) \\ + [\alpha_K(t)u^{K,H}(t)u^{Z,H}(t) + (1-\alpha_K(t))u^{K,N}(t)u^{Z,N}(t)]R(t)K(t) + r^*N(t) - T(t), \quad (14) \end{aligned}$$

where $P^H$ is the price of home-produced traded goods or the terms of trade and $P^N$ is the price of non-traded goods; we denote the share of traded capital in the aggregate capital stock by $\alpha_K(t) = K^H(t)/K(t)$ and the labor compensation share of tradables by $\alpha_L(t) = W^H(t)L^H(t)/W(t)L(t)$.

The investment good is (costlessly) produced using inputs of the traded good and the non-traded good by means of a CES technology:

$$J(t) = \left[ \varphi_J^{\frac{1}{\phi_J}} (J^T(t))^{\frac{\phi_J-1}{\phi_J}} + (1-\varphi_J)^{\frac{1}{\phi_J}} (J^N(t))^{\frac{\phi_J-1}{\phi_J}} \right]^{\frac{\phi_J}{\phi_J-1}}, \quad (15)$$

where $0 < \varphi_J < 1$ is the weight of the investment traded input and $\phi_J$ corresponds to the elasticity of substitution between investment traded goods and investment non-traded goods. The index $J^T(t)$ is defined as a CES aggregator of home-produced traded inputs, $J^H(t)$, and foreign-produced traded inputs, $J^F(t)$:

$$J^T(t) = \left[ (\iota^H)^{\frac{1}{\rho_J}} (J^H(t))^{\frac{\rho_J-1}{\rho_J}} + (1-\iota^H)^{\frac{1}{\rho_J}} (J^F(t))^{\frac{\rho_J-1}{\rho_J}} \right]^{\frac{\rho_J}{\rho_J-1}}, \quad (16)$$
where $0 < \iota^H < 1$ is the weight of the home-produced traded input and $\rho_J$ corresponds to the elasticity of substitution between home- and foreign-produced traded inputs.

Installation of new investment goods involves convex costs, assumed to be quadratic. Thus, total investment $J(t)$ differs from effectively installed new capital:

$$J(t) = I(t) + \frac{\kappa}{2} \left( \frac{I(t)}{K(t)} - \delta_K \right)^2 K(t), \quad (17)$$

where the parameter $\kappa > 0$ governs the magnitude of adjustment costs to capital accumulation. Denoting the fixed capital depreciation rate by $0 \le \delta_K < 1$, aggregate investment, $I(t)$, gives rise to capital accumulation according to the dynamic equation:

$$\dot{K}(t) = I(t) - \delta_K K(t). \quad (18)$$

Households choose consumption, hours, capital and technology utilization rates, investment in capital and traded bonds by maximizing lifetime utility (12) subject to (14) and (18) together with (17). Denoting by $\lambda$ and $Q'$ the co-state variables associated with (14) and (18), the first-order conditions characterizing the representative household's optimal plans are:

$$(C(t))^{-\frac{1}{\sigma_C}} = P_C(t)\lambda(t), \quad (19a)$$

$$\gamma (L(t))^{\frac{1}{\sigma_L}} = \lambda(t) \tilde{W}(t), \quad (19b)$$

$$Q(t) = P_J(t) \left[ 1 + \kappa \left( \frac{I(t)}{K(t)} - \delta_K \right) \right], \quad (19c)$$

$$\dot{\lambda}(t) = \lambda(\beta - r^*), \quad (19d)$$

$$\dot{Q}(t) = (r^* + \delta_K) Q(t) - \left\{ \begin{aligned} & [\alpha_K(t)u^{K,H}(t)u^{Z,H}(t) + (1 - \alpha_K(t))u^{K,N}(t)u^{Z,N}(t)] R(t) \\ & - P^H(t)C^{K,H}(t)\alpha_K(t) - P^N(t)C^{K,N}(t)(1 - \alpha_K(t)) - P_J(t)\frac{\partial J(t)}{\partial K(t)} \end{aligned} \right\}, \quad (19e)$$

$$R(t)u^{Z,j}(t) = P^j(t) \left[ \xi_1^j + \xi_2^j (u^{K,j}(t) - 1) \right], \quad j = H, N, \quad (19f)$$

$$Y^j(t) = \chi_1^j + \chi_2^j (u^{Z,j}(t) - 1), \quad j = H, N, \quad (19g)$$

and the transversality conditions $\lim_{t \to \infty} \bar{\lambda}N(t)e^{-\beta t} = 0$ and $\lim_{t \to \infty} Q(t)K(t)e^{-\beta t} = 0$; to derive (19c) and (19e), we used the fact that $Q(t) = Q'(t)/\lambda(t)$. To determine (19g), we made use of the fact that value added is exhausted by factor payments $P^j(t)Y^j(t) = R(t)\tilde{K}^j(t) + W^j(t)L^j(t)$ where $\tilde{K}^j(t) = u^{K,j}(t)K^j(t)$.

The technology channel of fiscal policy is captured by eq. (19g) which states that the decision to improve technology in sector $j$ is pro-cyclical. As detailed later in sections 4.2 and 4.3, the adjustment in $Y^j(t)$ depends on the intensity (measured by $\omega_{Gj}$) of the sector in the government spending shock, the degree of labor mobility across sectors (measured by $\epsilon$), the substitutability between home- and foreign-produced traded goods (measured by $\rho$ and $\rho_J$), the intensity in the use of tangible assets, $u^{K,j}(t)$, and FBTC (presented later).
In an open economy model with a representative agent having perfect foresight, a constant rate of time preference and perfect access to world capital markets, we impose $\beta = r^*$ in order to generate an interior solution. Setting $\beta = r^*$ into (19d) implies that the shadow value of wealth is constant over time, i.e., $\lambda(t) = \bar{\lambda}$. When new information about the fiscal shock arrives, $\bar{\lambda}$ jumps to fulfill the intertemporal solvency condition and remains constant afterwards. While the rise in taxes to balance the government budget puts upward pressure on $\bar{\lambda}$, the technology channel lowers it.

Once aggregate consumption and investment have been chosen, the allocation of expenditure across goods, i.e., $C^g$ and $I^g$ (with $g = F, H, N$), is determined by applying Shephard's lemma. The same logic applies to labor, i.e., $L^H(t) = \vartheta (\tilde{W}^H(t)/\tilde{W}(t))^\epsilon L(t)$ and $L^N(t) = (1 - \vartheta) (\tilde{W}^N(t)/\tilde{W}(t))^\epsilon L(t)$. As the elasticity of labor supply across sectors, $\epsilon$, takes higher values, workers experience lower mobility costs and thus more labor shifts from one sector to another.

## 3.2 Firms

We denote by $\tilde{Y}^j(t)$ the value added of sector $j$ inclusive of technology utilization, i.e., $\tilde{Y}^j(t) = u^Z(t)Y^j(t)$. Both the traded and non-traded sectors use physical capital (inclusive of capital utilization), denoted by $\tilde{K}^j(t) = u^{K,j}(t)K^j(t)$, and labor, $L^j$, according to a constant returns-to-scale technology described by a CES production function:

$$ \tilde{Y}^j(t) = \left[ \gamma^j \left( \tilde{A}^j(t)L^j(t) \right)^{\frac{\sigma^j-1}{\sigma^j}} + (1-\gamma^j) \left( \tilde{B}^j(t)\tilde{K}^j(t) \right)^{\frac{\sigma^j-1}{\sigma^j}} \right]^{\frac{\sigma^j}{\sigma^j-1}}, \quad (20) $$

where $0 < \gamma^j < 1$ and $0 < 1 - \gamma^j < 1$ are the weight of labor and capital in the production technology, respectively, $\sigma^j$ is the elasticity of substitution between capital and labor in sector $j = H, N$. We allow for labor- and capital-augmenting efficiency denoted by $\tilde{A}^j(t)$ and $\tilde{B}^j(t)$. We assume that factor-augmenting productivity has a symmetric time-varying component which collapses to $u^{Z,j}(t)$, such that $\tilde{A}^j(t) = u^{Z,j}(t)A^j(t)$ and $\tilde{B}^j(t) = u^{Z,j}(t)B^j(t)$. For given Hicks-neutral technology improvement, the mix of labor and capital-augmenting efficiency can change at each point of time along the technology frontier described later.

Firms lease the capital from households and hire workers. They face two cost components: a capital rental cost equal to $R(t)$, and a labor cost equal to the wage rate $W^j(t)$. Both sectors are assumed to be perfectly competitive and thus choose capital services and labor by taking prices as given. While capital can move freely between the two sectors, costly labor mobility implies a wage differential across sectors:<fnref n="10" />

$$ P^j(t)\gamma^j(A^j(t))^{\frac{\sigma^j-1}{\sigma^j}}(y^j(t))^{\frac{1}{\sigma^j}} = W^j(t), \quad (21a) $$

$$ P^j(t)(1-\gamma^j)(B^j(t))^{\frac{\sigma^j-1}{\sigma^j}}(u^{K,j}(t)k^j(t))^{-\frac{1}{\sigma^j}}(y^j(t))^{\frac{1}{\sigma^j}} = R(t), \quad (21b) $$

<footnote n="10">¹⁰Since the profit function is a linear function of the technology utilization rate, i.e., $\tilde{\Pi}^j(t) = u^{Z,j}(t)\Pi^j(t)$, $u^{Z,j}(t)$ does not show up in the first-order conditions shown in (21).</footnote>
where we denote by $k^j(t) \equiv K^j(t)/L^j(t)$ the capital-labor ratio for sector $j = H, N$, and $y^j(t) \equiv Y^j(t)/L^j(t)$ refers to value added per hours worked.

Demand for inputs can be rewritten in terms of their respective cost in value added; for labor, we have $s_L^j(t) = \gamma^j (A^j(t)/y^j(t))^{\frac{\sigma^j-1}{\sigma^j}}$. Applying the same logic for capital and denoting the ratio of labor to capital income share by $S^j(t) \equiv s_L^j(t)/(1-s_L^j(t))$, we have:

$$S^j(t) = \frac{s_L^j(t)}{1-s_L^j(t)} = \frac{\gamma^j}{1-\gamma^j} \left( \frac{B^j(t)u^{K,j}(t)K^j(t)}{A^j(t)L^j(t)} \right)^{\frac{1-\sigma^j}{\sigma^j}}. \quad (22)$$

When technological change is assumed to be Hicks-neutral, productivity increases uniformly across inputs, i.e., $\hat{A}^j(t) = \hat{B}^j(t)$. Sectoral LISs are thus affected only through changes in $u^{K,j}(t)k^j(t)$. By contrast, when technological change is factor-biased, higher values for capital relative to labor efficiency (i.e., a rise in $B^j(t)/A^j(t)$) increases capital-utilization-adjusted-FBTC in sector $j$, i.e., $(B^j(t)/A^j(t))^{\frac{1-\sigma^j}{\sigma^j}}$, because $\sigma^j < 1$ as evidence suggests. Higher values of capital-utilization-adjusted-FBTC has an expansionary effect on the demand for labor and thus generates a rise in the sectoral LIS, $s_L^j(t)$. By encouraging firms to increase the intensity of production either in labor or in capital, FBTC influences the reallocation of factors across sectors. Because $u^{Z,j}(t)$ is pro-cyclical and $Y^j(t)$ is affected by the shift of inputs, FBTC impinges on $u^{Z,j}(t)$.

Finally, aggregating over the two sectors gives us the resource constraint for capital:

$$K^H(t) + K^N(t) = K(t). \quad (23)$$

## 3.3 Technology Frontier

While households choose capital and technology utilization rates, firms within each sector $j = H, N$ decide about the split of capital-utilization-adjusted-TFP, denoted by $Z^j(t) = u^{Z,j}(t)\bar{Z}^j$ where $\bar{Z}^j$ is normalized to one, between labor- and capital-augmenting efficiency $\tilde{A}^j(t)$ and $\tilde{B}^j(t)$. Following Caselli and Coleman [2006] and Caselli [2016], we assume that firms choose a mix of $\tilde{A}^j(t)$ and $\tilde{B}^j(t)$ along a CES technology frontier:

$$\left[ \gamma_Z^j \left( \tilde{A}^j(t) \right)^{\frac{\sigma_Z^j-1}{\sigma_Z^j}} + (1-\gamma_Z^j) \left( \tilde{B}^j(t) \right)^{\frac{\sigma_Z^j-1}{\sigma_Z^j}} \right]^{\frac{\sigma_Z^j}{\sigma_Z^j-1}} \leq Z^j(t), \quad (24)$$

where $Z^j(t) > 0$ is the height of the technology frontier, $0 < \gamma_Z^j < 1$ is the weight of labor efficiency in utilization-adjusted-TFP and $\sigma_Z^j > 0$ corresponds to the elasticity of substitution between labor- and capital-augmenting productivity. Firms choose $\tilde{A}^j$ and $\tilde{B}^j$ along the technology frontier described by eq. (24) that minimizes the unit cost function. The unit cost minimization requires that (see Online Appendix I):

$$\frac{\gamma_Z^j}{1-\gamma_Z^j} \left( \frac{\tilde{A}^j(t)}{\tilde{B}^j(t)} \right)^{\frac{\sigma_Z^j-1}{\sigma_Z^j}} = \frac{s_L^j(t)}{1-s_L^j(t)} \equiv S^j(t). \quad (25)$$
Solving (25) for the LIS in sector j leads to $s_L^j = \gamma_Z^j (\tilde{A}^j/Z^j)^{\frac{\sigma_Z^j-1}{\sigma_Z^j}}$. Inserting this equality into the log-linearized version of the technology frontier (24) shows that technological change in sector j is a factor-income-share-weighted sum of changes in factor-augmenting efficiency:

$$ \hat{Z}^j(t) = s_L^j \hat{A}^j(t) + (1 - s_L^j) \hat{B}^j(t). \qquad (26) $$

As shown in eq. (26), while we assume that technology improvement is Hicks-neutral within each sector j, i.e., $Z^j(t) = u^{Z,j}(t)$, the stock of knowledge is made up of a mix of labor- and capital-augmenting productivity which can be modified at each point in time, thus leading technological change to be factor-biased.

## 3.4 Government

The final agent in the economy is the government. Government spending includes expenditure on non-traded goods, $G^N$, home- and foreign-produced traded goods, $G^H$ and $G^F$, respectively. The government finances public spending, $G$, by raising lump-sum taxes, $T$. As a result, Ricardian equivalence obtains and the time path of taxes is irrelevant for the real allocation. We may thus assume without loss of generality that government budget is balanced at each instant:

$$ G(t) \equiv P^N(t)G^N(t) + P^H(t)G^H(t) + G^F(t) = T(t). \qquad (27) $$

In Online Appendix V, we allow for distortionary labor and consumption taxation and consider a rise in $G(t)$ which is debt-financed. Quantitative results displayed in Online Appendix V.7 show that results are similar to those obtained when assuming a balanced-budget government spending shock.

## 3.5 Model Closure and Equilibrium

Denoting exports of home-produced goods by $X^H$, the goods market clearing conditions for non-traded and home-produced traded goods read:

$$ Y^N(t) = C^N(t) + J^N(t) + G^N(t) + C^{K,N}(t)K^N(t) + C^{Z,N}(t), \qquad (28a) $$

$$ Y^H(t) = C^H(t) + J^H(t) + G^H(t) + X^H(t) + C^{K,H}(t)K^H(t) + C^{Z,H}(t), \qquad (28b) $$

where exports are assumed to be decreasing in the terms of trade, $P^H$:

$$ X^H(t) = \varphi_X (P^H(t))^{-\phi_X}, \qquad (29) $$

where $\varphi_X > 0$ is a scaling parameter, and $\phi_X$ is the elasticity of exports w.r.t. $P^H$. Using the properties of constant returns to scale in production, identities $P_C(t)C(t) = \sum_g P^g(t)C^g(t)$ and $P_J(t)J(t) = \sum_g P^g(t)J^g(t)$ (with $g = F, H, N$) along with market clearing conditions (28), the current account equation (14) can be rewritten as a function of the trade balance:

$$ \dot{N}(t) = r^* N(t) + P^H(t)X^H(t) - M^F(t), \qquad (30) $$
where $M^F(t) = C^F(t) + G^F(t) + J^F(t)$ stands for imports of foreign-produced consumption and investment goods.

We drop the time index below to denote steady-state values. In order to account for the dynamic adjustment of $G(t)$ (see Fig. 1(a)), we assume that the deviation of government spending relative to its initial value, i.e., $dG(t) = G(t) - G$, as a percentage of initial GDP is governed by the law of motion:

$$dG(t)/Y = e^{-\xi t} - (1 - g) e^{-\chi t}, \qquad (31)$$

where $g > 0$ parametrizes the magnitude of the exogenous fiscal shock, $\xi > 0$ and $\chi > 0$ are (positive) parameters which are set in order to capture the hump-shaped endogenous response of $G(t)$. We assume that the rise in $G(t)$ is split into non-traded, $\omega_{GN}$, and home-produced traded goods, $\omega_{GH} = P^H G^H / G$, and foreign-produced traded goods, $\omega_{GF}$. Formally, we have $dG(t)/Y = \sum_{g=F,H,N} \omega_{Gg} dG(t)/Y$. In line with the evidence we document in Appendix F, $\omega_{GN}$ refers to the non-tradable content of government consumption, as well as the intensity of the government spending shock in non-traded goods.

To recover the dynamics of factor-augmenting productivity, we adopt a wedge analysis. As detailed in subsection 4.2, we estimate the shifts of $A^j(t)$ and $B^j(t)$ along the technology frontier (24), which are consistent with the demand for labor relative to the demand for capital described by (22). Denoting $X^j = A^j, B^j$, to achieve a perfect match with the data, we specify the law of motion for labor- and capital-augmenting efficiency expressed as a percentage deviation relative to the initial steady-state:

$$\hat{X}^j(t) = e^{-\xi_x^j t} - (1 - x^j) e^{-\chi_x^j t}, \qquad (32)$$

and choose $x^j$ to reproduce the impact response of factor-augmenting technological change while $\xi_x^j > 0$ and $\chi_x^j > 0$ are chosen to reproduce the shape of factor-augmenting productivity together with their cumulative change following a shock to government consumption that we infer from (22) and (26).

The adjustment of the open economy toward the steady-state is described by a dynamic system which comprises two equations. The first dynamic equation corresponds to the non-traded goods market clearing condition (28a) and the second dynamic equation corresponds to (19e) which is a no-arbitrage condition. To solve the model, we adopt the solution method by Buiter [1984] for continuous time models. See Online Appendix U which details the solution method.

# 4 Quantitative Analysis

In this section, we take the model to the data. For this purpose we solve the model numerically. Therefore, first we discuss parameter values before turning to the effects of an exogenous temporary increase in government consumption.
## 4.1 Calibration

**Calibration strategy.** At the steady-state, utilization rates for technology, $u^{Z,j}$, and capital, $u^{K,j}$, collapse to one so that $\tilde{Y}^j = Y^j$ and $\tilde{K}^j = K^j$. We consider an initial steady-state with Hicks-neutral technological change and normalize $A^j = B^j = Z^j$ to 1. To ensure that the initial steady-state with CES production functions is invariant when $\sigma^j$ is changed, we normalize CES production functions by choosing the initial steady-state in a model with Cobb-Douglas production functions as the normalization point. Once we have calibrated the initial steady-state with Cobb-Douglas production functions, we assign values to $\sigma^j$ in accordance with our estimates and the CES economy is endogenously calibrated to reproduce the ratios of the Cobb-Douglas economy, including the sectoral LISs.

To calibrate the reference model that we use to normalize the CES economy, we have estimated a set of ratios and parameters for the eighteen OECD economies in our dataset, see Table 7 relegated to Online Appendix L.1. Our reference period for the calibration corresponds to the period 1970-2015. Because we calibrate the reference model to a representative OECD economy, we take unweighted average values of ratios and parameters which are summarized in Table 1. Among the 26 parameters that the model contains, 12 have empirical counterparts while the remaining 14 parameters must be endogenously calibrated to match ratios.

**Fourteen parameters must be set to target ratios.** Out of fourteen parameters, $\varphi, \varphi^H, \iota, \iota^H, \vartheta, \delta_K, G, G^N, G^H$ and initial conditions ($N_0$ and $K_0$), must be set to target a non-tradable content of consumption and investment expenditure of $1 - \alpha_C = 56\%$ and $1 - \alpha_J = 69\%$, respectively, a home content of consumption and investment expenditure in tradables of $\alpha^H = 66\%$ and $\alpha^H_J = 43\%$, respectively, a weight of labor supply to the non-traded sector of $L^N/L = 62\%$, an investment-to-GDP ratio of $\omega_J = 24\%$, a ratio of government spending to GDP of $\omega_G = 19\% (= G/Y)$, a non-tradable and home-tradable share of government spending of $\omega_{GN} = 80\% (= P^N G^N / G)$, and $\omega_{GH} = 18\% (= P^H G^H / G)$, and we choose initial conditions so as trade is balanced, i.e., $v_{NX} = \frac{NX}{P^H Y^H} = 0$ with $NX = P^H X^H - C^F - I^F - G^F$. Because $u^{K,j} = u^{Z,j} = 1$ at the steady-state, four parameters related to capital $\xi_1^H, \xi_1^N$, and technology, $\chi_1^H, \chi_1^N$, adjustment cost functions are set to be equal to $R/P^H, R/P^N, Y^H, Y^N$, respectively.

**Five parameters are assigned values which are taken directly or estimated from our own data.** We choose the model period to be one year. In accordance with the column 20 of Table 1, the world interest rate, $r^*$, which is equal to the subjective time discount rate, $\beta$, is set to 3%. In line with mean values shown in columns 10 and 11 of Table 1, the shares of labor income in traded and non-traded value added, $\theta^H$ and $\theta^N$, are set to 0.63 and 0.69, respectively, which leads to an aggregate LIS of 66% (see column 17 of Table 1).
<table><caption>Table 1: Data to Calibrate the Two Open Economy Sector Model</caption><thead><tr><th colspan="5">Non-tradable share</th><th colspan="4">Home share</th><th colspan="2">Labor Share</th></tr><tr><th>GDP</th><th>Cons.</th><th>Inv.</th><th>Gov.</th><th>Labor</th><th>X<sup>H</sup></th><th>C<sup>H</sup></th><th>I<sup>H</sup></th><th>G<sup>H</sup></th><th>LIS<sup>H</sup></th><th>LIS<sup>N</sup></th></tr></thead><tbody><tr><td>(1)</td><td>(2)</td><td>(3)</td><td>(4)</td><td>(5)</td><td>(6)</td><td>(7)</td><td>(8)</td><td>(9)</td><td>(10)</td><td>(11)</td></tr><tr><td>0.64</td><td>0.56</td><td>0.69</td><td>0.80</td><td>0.62</td><td>0.13</td><td>0.66</td><td>0.43</td><td>0.18</td><td>0.63</td><td>0.69</td></tr></tbody><tbody><tr><th colspan="5">Elasticities</th><th colspan="4">Aggregate ratios</th></tr><tr><th>φ</th><th>ε</th><th>σ<sup>H</sup></th><th>σ<sup>N</sup></th><th>φ<sub>X</sub></th><th>LIS</th><th>I/Y</th><th>G/Y</th><th>r</th></tr><tr><td>(12)</td><td>(13)</td><td>(14)</td><td>(15)</td><td>(16)</td><td>(17)</td><td>(18)</td><td>(19)</td><td>(20)</td></tr><tr><td>0.77</td><td>0.83</td><td>0.64</td><td>0.80</td><td>1.70</td><td>0.66</td><td>0.24</td><td>0.19</td><td>0.030</td></tr></tbody></table>

Notes: Columns 1-5 show the GDP share of non-tradables, the non-tradable content of consumption, investment and government expenditure, the share of non-tradables in labor. Column 6 gives the ratio of exports of final goods and services to GDP; columns 7 and 8 show the home share of consumption and investment expenditure in tradables and column 9 shows the content of government spending in home-produced traded goods; φ is the elasticity of substitution between traded and non-traded goods in consumption; ε is the elasticity of labor supply across sectors; σ<sup>J</sup> is the elasticity of substitution between capital and labor in sector j = H, N; estimates of the elasticity of exports w.r.t. terms of trade, φ<sub>X</sub>, are taken from Imbs and Mejean [2015]. LIS<sup>J</sup> stands for the labor income share in sector j = H, N while LIS refers to the aggregate LIS; I/Y is the investment-to-GDP ratio and G/Y is government spending as a share of GDP. The real interest rate is the real long-term interest rate calculated as the nominal interest rate on 10 years government bonds minus the rate of inflation which is the rate of change of the Consumption Price Index.

Because barriers to labor mobility play a key role in our model and estimates for OECD countries are not available, we have estimated empirically the elasticity of labor supply across sectors, ε, for each OECD economy. As shown in Online Appendix L.2, we pin down ε from a testable equation obtained by combining labor supply and labor demand and run the regression in panel format on annual data of the percentage change in the labor share of sector j on the percentage change in the relative share of value added paid to workers in sector j over 1970-2015. Building on our estimates, the degree of labor mobility across sectors is set to 0.83, in line with the average of our estimates (see column 13 of Table 1). Note that this value is close to the value of 1 estimated by Horvath [2000] on US data over 1948-1985 and commonly chosen in the literature allowing for imperfect mobility of labor.

While there is a consensus in the open-economy macroeconomics literature that C<sup>T</sup> and C<sup>N</sup> are gross complements and thus φ should take a value lower than one, precise estimates for OECD countries are still lacking. In the same spirit as Mendoza [1992], we use the first-order condition for C<sup>N</sup> and run the regression of the logged share of non-tradables 1 − α<sub>C</sub>(t) on logged P<sup>N</sup>(t)/P<sub>C</sub>(t). Time series for 1 − α<sub>C</sub>(t) are constructed by using the market clearing condition for non-tradables. Building on our panel data estimates, the elasticity of substitution φ between traded and non-traded goods is set to 0.77, since this value corresponds to the average of estimates (see column 12 of Table 1). It is worth mentioning that our value is close to the estimated elasticity by Mendoza [1992] who reports an estimate of 0.74 for thirteen OECD countries by using cross-section data for the year 1975.

Seven parameters are taken from external research works. As pointed out recently by Best et al. [2020], there exists no consensus on a reasonable value for the intertemporal elasticity of substitution for consumption as estimates in the literature range between 0 and 2. We choose a value of one for σ<sub>C</sub>. Estimates reported by empirical studies for the Frisch elasticity of labor supply range from 0 to 3, see Peterman [2016] for a survey. We set σ<sub>L</sub> to 1. These values for σ<sub>C</sub> and σ<sub>L</sub> are a typical choice in the business cycle
literature and have the advantage of making our quantitative results directly comparable
with other macroeconomic studies. We choose the value of parameter $\kappa$ which captures
the magnitude of capital adjustment costs so that the elasticity of $I/K$ with respect to
Tobin's q, i.e., $Q/P_J$, is equal to the value implied by estimates in Eberly et al. [2008]. The
resulting value of $\kappa$ is equal to 17.

In line with the empirical findings documented by Bems [2008] who finds that the
non-tradable content of investment expenditure is stable in OECD countries, we set the
elasticity of substitution, $\phi_J$, between $J^T$ and $J^N$ to 1. Following Backus et al. [1994],
we set the elasticity of substitution in consumption (investment), $\rho$ ($\rho_J$), between home-
and foreign-produced traded goods (inputs) to 1.5 which fits estimates by Bertinelli et al.
[2022] who find a vale of 1.48 for $\rho$ from a panel of seventeen OECD countries. Building on
structural estimates of the price elasticities of aggregate exports documented by Imbs and
Mejean [2015], we set the export price elasticity, $\phi_X$, to 1.7 in the baseline calibration (see
column 16 of Table 1).

**Calibrating the CES economy.** To calibrate the CES economy, we proceed as
follows. First, we choose the same values for the twelve parameters which have empirical
counterparts as above, except for the labor income shares which are now endogenously
calibrated. Thus in addition to $\sigma_C$, $\sigma_L$, $\kappa$, $\phi_J$, $\rho$, $\rho_J$, $\phi_X$, $r^*$, $\epsilon$, $\phi$, we have to choose values
for the elasticity of substitution between capital and labor for tradables and non-tradables,
$\sigma^H$ and $\sigma^N$. We estimate $\sigma^H$ and $\sigma^N$ over 1970-2015 on panel data so as to have consistent
estimates in accordance with our classification of industries as tradables and non-tradables
and sample composition. Drawing on Antràs [2004], we run the regression of value added
per hours worked on the real wage in sector $j$ by adopting cointegration methods, see Online
Appendix L.3 which details the empirical strategy. In line with our panel data estimates,
we choose $\sigma^H = 0.64$ and $\sigma^N = 0.80$ (see columns 14 and 15 of Table 1).

Given the set of elasticities above, the remaining parameters are set so as to maintain the
steady-state of the CES economy equal to the normalization point. Therefore, we calibrate
the model with CES production functions so that fifteen parameters $\phi$, $\iota$, $\phi^H$, $\iota^H$, $\vartheta$, $\delta_K$,
$G$, $G^N$, $G^H$, $N_0$, $K_0$, $Z^H$, $Z^N$, $\gamma^H$, $\gamma^N$ are endogenously set to target $1 - \bar{\alpha}_C$, $1 - \bar{\alpha}_J$, $\bar{\alpha}^H$,
$\bar{\alpha}_J^H$, $\bar{L}^N/\bar{L}$, $\bar{\omega}_J$, $\bar{\omega}_G$, $\bar{\omega}_{GN}$, $\bar{\omega}_{GH}$, $\bar{v}_{NX}$, $\bar{K}$, $\bar{y}^H$, $\bar{y}^N$, $\bar{s}_L^H = \theta^H$, $\bar{s}_L^N = \theta^N$, respectively, where a
bar indicates that the ratio is obtained from the Cobb-Douglas economy. In addition, four
parameters, including $\xi_1^H$, $\xi_1^N$, $\chi_1^H$, $\chi_1^N$, are endogenously set to target $R/P^H$, $R/P^N$, $Y^H$,
$Y^N$.

## 4.2 Government Spending Shock and Technology: Calibration

In this subsection, we detail how we calibrate the endogenous responses of $G(t)$, $u^{K,j}(t)$,
$u^{Z,j}(t)$ to the exogenous fiscal shock, and factor-biased technological adjustment.
**Endogenous response of G(t) to exogenous fiscal shock.** In order to capture the endogenous response of government consumption to the exogenous fiscal shock we have identified, we assume that the dynamic adjustment of G(t) is governed by eq. (31). In the quantitative analysis, we set g = 0.01 so that G(t) increases by 1 ppt of initial GDP. To calibrate ξ and χ which parametrize the shape of the dynamic adjustment of G(t) along with its persistence, we proceed as follows. Because G(t) peaks after one year, we have $\dot{G}(1)/Y = -[\xi e^{-\xi} - \chi(1-g)e^{-\chi}] = 0$. In addition, the cumulative response of G(t) over a ten-year horizon is $\int_{0}^{9} [dG(\tau)/Y] e^{-r^*\tau} d\tau = g'$ with g' = 6.56 ppt of GDP. We choose ξ = 0.430 and χ = 0.439. Left-multiplying eq. (31) by $\omega_{Gg}$ (with g = F, H, N) gives the dynamic adjustment of sectoral government consumption to the exogenous fiscal shock:

$$ \omega_{Gg} (dG(t)/Y) = \omega_{Gg} \left[ e^{-\xi t} - (1-g) e^{-\chi t} \right], \quad (33) $$

where $\omega_{Gg}$ is the share of government final consumption expenditure in good g. To determine (33), we assume that the parameters that govern the persistence and shape of the response of sectoral government consumption are identical across sectors, while the sectoral intensity of the government spending shock is constant over time and thus collapses to $\omega_{Gj}$.<fnref n="11" />

**Capital utilization adjustment costs.** Log-linearizing (19f) shows that it is profitable to increase $u^{K,j}(t)$ when the real capital rental rate goes up

$$ \hat{u}^{K,j}(t) = \frac{\xi_1^j}{\xi_2^j} \left( \hat{R}^j(t) - \hat{P}^j(t) \right). \quad (34) $$

The parameter $\xi_2^j$ determines the magnitude of the adjustment in $u^{K,j}(t)$. We set $\xi_2^H = 0.27$ and $\xi_2^N = 0.03$ so as to account for empirical responses of $u^{K,j}(t)$ conditional on the government spending shock.<fnref n="12" />

**Technology utilization adjustment costs.** Log-linearizing (19g) shows that the intensity in the use of existing technologies is pro-cyclical:

$$ \hat{u}^{Z,j}(t) = \frac{\chi_1^j}{\chi_2^j} \hat{Y}^j(t). \quad (35) $$

Intuitively, since $Y^j(t) = \frac{W^j(t)L^j(t)+R(t)\tilde{K}^j(t)}{P^j(t)}$, it is profitable to increase the technology rate when the real cost of producing goes up. The parameter $\chi_2^j$ determines the magnitude of the response of the technology utilization rate $u^{Z,j}(t)$. We choose 0.8 and 2.85 for $\chi_2^H$ and $\chi_2^N$, respectively, in order to reproduce the empirical responses of the capital-utilization-adjusted TFP, $Z^j(t)$, see Fig. 2(a) and Fig. 2(d). The model produces a cumulative change in $Z^H(t)$ and $Z^N(t)$ over a 10-year horizon of 5.84% and 2.12%, respectively, close to what we estimate in the data, i.e., 6.12% and 2.15%.

<footnote n="11">¹¹Assuming that the intensity of the non-traded sector in the government spending shock collapses to the non-tradable content of G(t) is in line with the evidence documented in Online Appendix F. In particular, Fig. 7 shows that a shock to government consumption by 1% of GDP is associated with a rise in $G^N$ by 0.8% of GDP on impact.</footnote>

<footnote n="12">¹²For reasons of space, the responses of $u^{K,j}$ are relegated to the Online Appendix E, see Fig. 6.</footnote>
**Building intuition on the determinants of the technology channel.** Using the fact that $Y^j(t) - \chi_1^j = dY^j(t)$ (since $\chi_1^j = Y^j$) and making use of the expression for the capital income share which implies that $Y^j(t)$ co-moves with $\frac{R(t)}{P^j(t)} \frac{\tilde{K}^j(t)}{1-s_L^j(t)}$, we derive a simple expression which links the change in the technology utilization rate and the variation in the real cost of capital services (instead of the real cost of producing):

$$du^{Z,j}(t) = \frac{1}{\chi_2} d \left( \frac{R(t)}{P^j(t)} u^{K,j}(t) \alpha_K^j(t) \frac{K(t)}{1-s_L^j(t)} \right), \quad (36)$$

where $\alpha_K^j(t) \equiv \frac{K^j(t)}{K(t)}$. When terms of trade are exogenous (i.e., $P^H(t) = P^H = 1$), production functions are Cobb-Douglas (i.e., $s_L^j(t) = \theta^j$ is fixed), and the capital utilization rate is shut down (i.e., $u^{K,j}(t) = 1$), the change in the technology utilization rate in the traded sector on impact, i.e., $du^{Z,H}(0)$, depends only on the response of the capital rental rate $dR(0)$ and the reallocation of capital across sectors captured by $d\alpha_K^H(0)$ because the aggregate capital stock is predetermined (i.e., $K(0) = K_0$). A one-sector model ignores capital reallocation so that $\alpha_K^j$ collapses to one. Under this assumption, since a government spending shock leads households to supply more labor which lowers the capital-labor ratio, the capital cost increases and thus firms improve technology. In a two-sector model, technology decisions are influenced by the reallocation of factors. A rise in $G(t)$ which is biased toward non-traded goods produces a dramatic shift of capital away from traded industries (i.e., $\alpha_K^H(t)$ falls). Because workers do not experience labor mobility costs (i.e., $\epsilon \to \infty$), the traded sector also experiences a dramatic labor outflow that increases its capital-labor ratio $k^H$ and thus lowers the capital rental rate $R(t)$. Since the capital cost $R(t)K^H(t)$ declines, traded firms reduce $u^{Z,H}(t)$. By mitigating the shift of labor toward non-traded industries, labor mobility costs (i.e., $0 < \epsilon < \infty$) lead $k^H(t)$ to fall. Because $k^H(t)$ declines, $R(t)$ increases. However, the traded sector experiences a dramatic capital outflow that lowers $R(t)K^H(t)$ because capital can move freely across sectors.

When we assume that home- and foreign-produced traded goods are imperfect substitutes (i.e., $0 < \rho < \infty$ and $0 < \rho_J < \infty$), the terms of trade $P^H(t)$ appreciate as households are less inclined to substitute imported for home-produced traded goods. While the appreciation in $P^H(t)$ mitigates the shift of capital toward non-traded industries, numerical results in the next subsection show that the real cost of capital services increases only once we let tangible assets to be used more intensively in both sectors. FBTC also matters. When we allow for CES production functions, technological change biased toward capital in the traded sector amplifies the rise in the capital cost which leads traded firms to improve technology by a magnitude that squares well with our evidence.

**Factor-augmenting efficiency.** To set the adjustment of factor-augmenting efficiency, we first recover their dynamics in the data. Using the fact that factor-augmenting productivity has a symmetric time-varying component denoted by $u^{Z,j}(t)$ such that $\tilde{A}^j(t) = u^{Z,j}(t)A^j(t)$ and $\tilde{B}^j(t) = u^{Z,j}(t)B^j(t)$, log-linearizing the demand for labor relative to the
demand for capital (22) and using the log-linearized version of the technology frontier (26), we can solve for deviations of $A^j(t)$ and $B^j(t)$ relative to their initial values:

$$ \hat{A}^j(t) = -(1 - s_L^j) \left[ \left( \frac{\sigma^j}{1 - \sigma^j} \right) \hat{S}^j(t) - \hat{k}^j(t) - \hat{u}^{K,j}(t) \right], \quad (37a) $$

$$ \hat{B}^j(t) = s_L^j \left[ \left( \frac{\sigma^j}{1 - \sigma^j} \right) \hat{S}^j(t) - \hat{k}^j(t) - \hat{u}^{K,j}(t) \right]. \quad (37b) $$

Plugging estimated values for $\sigma^j$ and empirically estimated responses for $s_L^j(t)$, $k^j(t)$, $u^{K,j}(t)$ into above equations enables us to recover the dynamics for $A^j(t)$ and $B^j(t)$ consistent with the demand for factors of production (22) and the technology frontier (26). Then we choose values for exogenous parameters $x^j$ (for $x = a, b$), $\xi_X^j$ and $\chi_X^j$ (for $X = A, B$) of the continuous time paths (32) within sector $j = H, N$, which are consistent with the estimated paths (37a)-(37b) for $A^j(t)$ and $B^j(t)$.

## 4.3 Drivers of the Technology Channel

As suggested by our empirical evidence and corroborated by our numerical results in the next subsection, the technology channel of fiscal transmission plays a key role in determining the size of aggregate and sectoral fiscal multipliers. In this subsection, we highlight the factors driving the technology decisions following a government spending shock. We show that both the two-sector dimension and the open economy aspect of our model matter in determining the adjustment in the technology utilization rate.

Our baseline model includes three sets of elements. The first set is related to the biasedness of the demand shock toward non-traded goods. The second set of elements is related to barriers to factors' mobility which include labor mobility costs and imperfect substitutability between home- and foreign-produced traded goods. The third set of elements is related to sector-specific capital utilization rates together with factor-biased technological change. To understand (and quantify) the role of each element, we first consider the simplest model and add one ingredient at a time. Table 2 reports the cumulative change of selected variables, including value added, $\tilde{Y}^j(t)$, the value added share of non-tradables, $\nu^{Y,N}(t)$, the technology utilization rate $u^{Z,j}(t)$, and the current account $CA(t)$, over a six-year horizon.

**Perfect mobility of labor across sectors.** In columns 1-4 of Table 2, we consider a model with perfect mobility of labor (PML) across sectors (i.e., we let $\epsilon \to \infty$), assume that home- and foreign-produced traded goods are perfect substitutes (i.e., we let $\rho, \rho_J$ and $\phi_X$ tend toward infinity) so that terms of trade (TOT) are exogenous and fixed, and allow for Cobb-Douglas (CD) production functions (so that FBTC is shut down). In column 1, we abstract from capital adjustment costs (i.e., we set $\kappa = 0$) and shut down the technology channel. As shown in panel A, a rise in $G(t)$ has a negative impact on traded value added. Intuitively, productive resources shift toward the non-traded sector because this sector is highly intensive in the government spending shock. Financial openness and the tradability
of goods further bias the demand shock toward non-tradables. Intuitively, when home- and foreign-produced traded goods are perfect substitutes, it is optimal for the open economy to import traded goods and reallocate capital and labor to produce additional units of non-traded goods. The open economy thus runs a large current account deficit (see panel C). Because workers are not subject to switching costs, the labor inflow experienced by the non-traded sector is such that it keeps non-traded prices and thus factor prices unchanged.<fnref n="13" />

When we allow for capital adjustment costs (CAC), as considered in column 2, the (slight) appreciation in the relative price of non-tradables produces stronger incentives to shift productive resources toward the non-traded sector which in turn amplifies the expansionary effect of the government spending shock on the non-traded sector at the expense of traded industries. As shown in column 3, when we allow for an endogenous intensity in the use of existing technologies, the dramatic decline in traded value added produces a fall in $u^{Z,H}(t)$. As highlighted in the previous section, the fall in $\tilde{Y}^H$ mimics the decline in the real capital cost which leads traded firms to reduce their efforts to improve production efficiency. As shown in column 4, the decline in the technology utilization rate $u^{Z,H}$ is still large but mitigated once we allow for endogenous capital utilization. Intuitively, in face of a higher real capital rental rate (driven by the rise in $u^{Z,N}(t)$), non-traded firms increase $u^{K,N}(t)$, while the other way around is true for traded firms which lower $u^{K,H}(t)$. Because non-traded firms use more intensively the physical capital stock while traded firms reduce $u^{K,H}(t)$, less capital shifts away from traded industries which softens the fall in $\tilde{Y}^H(t)$ and thereby in $u^{Z,H}(t)$.

**Imperfect mobility of labor across sectors and technology.** In column 5, we consider the same model as in column 4 except that we now assume that traded and non-traded hours worked are imperfect substitutes. When workers experience costs of switching sectors, less labor shifts away from traded industries. Therefore both $\tilde{Y}^H(t)$ and the use of existing technologies $u^{Z,H}(t)$ decline by a lower magnitude.

**Imperfect mobility of labor across sectors, endogenous terms of trade and technology.** In columns 6-9, we assume that home- and foreign-produced traded goods are imperfect substitutes. This assumption leads to a significant reduction in the magnitude of the current account deficit (see panel C) because households are reluctant to substitute imported for home-produced traded goods. Higher demand for domestic goods appreciates $P^H(t)$ which increases the return on factors. The real capital rental rate increases in the traded sector which makes it more profitable to raise $u^{K,H}(t)$. The combined effect of labor mobility costs, imperfect substitutability between home- and foreign-produced traded goods

<footnote n="13">¹³Because factor prices remain fixed as the result of the immediate reallocation of inputs, as pointed out by Baqaee [2018] and Bouakez et al. [2022a], the absence of frictions in a multi-sector model implies that the allocation of government spending across sectors does not impact the aggregate outcome, i.e., the magnitude of aggregate fiscal multipliers. This is true in a closed economy but not in an open economy because a demand shock biased toward non-traded goods produces a current account deficit which impinges on the equilibrium value of the marginal utility of wealth and thus on aggregate labor supply.</footnote>
<table><caption>Table 2: Cumulative Effects on Technology of a Government Spending Shock</caption><thead><tr><th rowspan="3"></th><th colspan="4">CD: PML</th><th colspan="2">CD: IML</th><th colspan="2">CES: FBTC &amp; IML &amp; TOT</th></tr><tr><th>No CAC</th><th>CAC</th><th>u<sup>Z,j</sup></th><th>u<sup>K,j</sup></th><th>exo TOT</th><th>endo TOT</th><th>No u<sup>K,j</sup></th><th>No u<sup>K,j</sup></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><th>(9)</th></tr></thead><tbody><tr><td><strong>A.Sectoral Value Added</strong></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>T VA, dY<sup>H</sup>(t)</td><td>-3.52</td><td>-3.45</td><td>-8.26</td><td>-4.86</td><td>-1.40</td><td>1.10</td><td>-0.84</td><td>1.61</td><td>3.12</td></tr><tr><td>NT VA, dY<sup>N</sup>(t)</td><td>4.04</td><td>4.15</td><td>5.75</td><td>7.89</td><td>5.35</td><td>6.08</td><td>3.85</td><td>3.54</td><td>4.24</td></tr><tr><td>VA share of NT, dv<sup>Y,N</sup>(t)</td><td>3.73</td><td>3.75</td><td>8.06</td><td>6.94</td><td>2.97</td><td>1.48</td><td>1.96</td><td>0.24</td><td>-0.41</td></tr><tr><td><strong>B.Technology</strong></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>T technology, dv<sup>Z,H</sup>(t)</td><td>0.00</td><td>0.00</td><td>-12.14</td><td>-7.55</td><td>-2.57</td><td>1.50</td><td>-1.27</td><td>2.26</td><td>4.35</td></tr><tr><td>NT technology, dv<sup>Z,N</sup>(t)</td><td>0.00</td><td>0.00</td><td>2.71</td><td>3.60</td><td>2.17</td><td>2.79</td><td>1.81</td><td>1.62</td><td>1.97</td></tr><tr><td><strong>C.Current Account</strong></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Current Account, dCA(t)</td><td>-4.80</td><td>-4.80</td><td>-5.82</td><td>-4.18</td><td>-1.96</td><td>-0.19</td><td>-0.42</td><td>-0.09</td><td>-0.02</td></tr></tbody></table>

Notes: This table shows cumulative effects over a six-year horizon of a 1% temporary increase in government consumption in the baseline model (column 9) and in restricted versions of the model (columns 1-8). Impact and cumulative effects for additional variables are relegated to Online Appendix N for reasons of space. 'T' refers to traded industries while 'NT' refers to non-tradables. Panel A shows the cumulative effects for traded and non-traded value added, panel B displays the cumulative effects for traded and non-traded technology, panel C reports the cumulative change in the current account (in percentage point of GDP). Across all scenarios, we consider a 1% increase in government consumption on impact which gives rise to a (present discounted value of) cumulative change of G(t) by 5.46 ppt of GDP over a six-year horizon. In columns 1-5, we consider a small open economy model where home-produced and foreign-produced traded goods are perfect substitutes so that terms of trade are exogenous. In columns 1-4 we consider four variants of a model with perfect mobility of labor while in column 5 we assume imperfect mobility of labor across sectors. In column 1, we abstract from capital installation costs and shut down the technology channel. In column 2, we allow for capital installation costs and switch off the technology channel. In column 3, we allow for capital installation costs and endogenous technology utilization rate. In column 4, we allow for capital installation costs, endogenous technology and capital utilization rates. In column 5, we assume imperfect mobility of labor across sectors and allow for the technology channel. In columns 6-7, we allow for capital installation costs, imperfect substitutability between home- and foreign- produced traded goods and assume Cobb-Douglas production functions. In column 6, we allow for endogenous technology and capital utilization rates while in column 7, we shut down capital utilization rates. In column 8, we consider the baseline model with CES production functions, factor-biased technological change, and endogenous technology utilization rates except that we shut down the capital utilization rate.

together with higher $u^{K,H}(t)$ pushes $\tilde{Y}^H(t)$ up and encourages traded firms to increase production efficiency (see panel B).

Endogenous capital utilization is key to giving rise to technology improvement in the traded sector. As shown in column 7, when we consider the same setup as in column 6 whilst shutting down $u^{K,j}(t)$ (i.e., $\chi_2^j \to \infty$), the model fails to account for the rise in $u^{Z,H}(t)$ because the capital outflow experienced by the traded sector is too large.

**Imperfect mobility of labor across sectors, endogenous terms of trade, FBTC and technology.** In column 8, we keep the same model as in column 7 (i.e., $\chi_2^j \to \infty$), except that we allow for CES production functions and FBTC. These two elements result in changes in the intensity of production technology in capital and labor in both sectors. Because technological change is biased toward capital in the traded sector and biased toward labor in the non-traded sector, traded industries experience a capital inflow instead of a capital outflow. Since capital is not subject to mobility costs across sectors, the capital inflow more than offsets the greater labor outflow experienced by traded industries, thus raising $\tilde{Y}^H(t)$ and encouraging traded firms to increase $u^{Z,H}(t)$.

**Taking stock.** In column 9 of Table 2, we consider our baseline model. As displayed by panel B, allowing for endogenous capital utilization (column 6) or FBTC (column 8) in addition to labor mobility costs and endogenous terms of trade are necessary elements to give rise to technology improvements in the traded sector. However, our empirical evidence over a six-year horizon shows that overall efficiency gains are 2.8 larger in traded than in non-traded industries. As shown in column 9, it is only once we allow for both endogenous
$u^{K,j}(t)$ and FBTC in addition to $\epsilon < \infty$, $\rho < \infty$, $\rho_J < \infty$, that the model can account for the concentration of technology improvements in the traded (relative to the non-traded) sector we estimate.

## 4.4 Government Spending Shock and Technology: Model Performance

Our objective is now to isolate quantitatively the role of the technology channel in determining the size of fiscal multipliers in an open economy. In our baseline calibration, we assume that capital and technology utilization rates (i.e., $u^{K,j}(t)$ and $u^{Z,j}(t)$) respond endogenously to the government spending shock, and allow for time-varying FBTC in sector $j$ driven by the dynamic adjustment of labor- and capital-augmenting efficiency, while sectoral goods are produced from CES production functions. To gauge the quantitative implications of technology for fiscal transmission, we contrast our results with those obtained in a restricted model with Cobb-Douglas production functions (i.e., $\sigma^j = 1$) where we shut down the endogenous response of capital and technology utilization by letting $\xi_2^j$ and $\chi_2^j$ tend towards infinity and impose $\xi_A^j = \xi_B^j = \chi_A^j = \chi_B^j = 0$ so that $u^{K,j}(t) = u^{Z,j}(t) = A^j(t) = B^j(t) = 1$.<fnref n="14" />

In Table 3, we report the simulated impact (i.e., at $t=0$) and six-year cumulative (i.e., at $t=0, \dots, 5$) effects following an exogenous temporary increase in $G(t)$ by 1 ppt of GDP. Cumulative effects are expressed in present discounted value terms. The six-year horizon fiscal multiplier is obtained by dividing the cumulative change in value added (or labor) by the cumulative change in $G(t)$.

While columns 1 and 4 show impact and cumulative responses from local projection for comparison purposes, columns 2 and 5 show results for the baseline model. We contrast the benchmark results with those shown in columns 3 and 6 for impact and cumulative effects, respectively, which are obtained in the restricted model where technology is shut down. While in Table 3, we focus on value added and hours worked, numerical results for sectoral TFPs, utilization-adjusted-TFPs, and sectoral LISs are relegated to Online Appendix M for reasons of space.

**Adjustment in $G(t)$**. As can be seen in the first row of panel A of Table 3, the baseline (and the restricted) model generates a cumulative change in $G(t)$ of 5.46 ppt of GDP (see columns 5-6), close to our estimation of 5.51 ppt (see column 4). As shown in Fig. 3(a), the endogenous response of $G(t)/Y$ to an exogenous fiscal shock that we generate theoretically (black line with squares) by specifying the law of motion (31) reproduces well the dynamic adjustment we estimate empirically (blue line).

**Restricted model.** Results for the restricted model where technology is shut down are

<footnote n="14">¹⁴While in the main text we assume MaCurdy [1981] preferences, perfect mobility of capital across sectors and flexible prices, in Online Appendices W and X we allow for non-separability in utility between consumption and leisure in the lines of Shimer [2009], imperfect mobility of capital, and nominal price rigidities on non-traded goods. We contrast the predictions of the baseline model with those of its variants in Online Appendix Y.</footnote>
reported in columns 3 and 6 of Table 3. Because the capital and technology utilization rates remain fixed, sectoral TFPs are unchanged, see the first two columns of Fig. 2. Because the elasticity of value added w.r.t. inputs is fixed (i.e., $s_L^j = \theta^j$) the labor income shares are constant, see the last column of Fig. 2.

We start with the aggregate effects. By producing a negative wealth effect, a balanced-budget government spending shock leads agents to supply more labor, which in turn increases real GDP. As shown in panel A of Table 3, a rise in $G(t)$ by 1% of GDP generates an increase in $L(t)$ by 0.63% and a rise in real GDP by 0.42% on impact, the latter value being almost three times smaller what we estimate empirically (i.e., 1.18%, see column 1).

Panel B of Table 3 shows that non-traded and traded hours increase by 0.54 ppt and 0.09 ppt of total hours worked, respectively. Formally, the rise in non-traded hours worked, i.e., $\alpha_L^N \hat{L}^N(t) = \alpha_L^N \hat{L}(t) + d\nu^{L,N}(t)$ (see section 2.1), is driven by higher labor supply $\hat{L}(t)$ and the reallocation of hours across sectors, as captured by $d\nu^{L,N}(t)$. In the model and the data, the labor multiplier of non-tradables is larger than that of tradables because the non-traded sector accounts for almost two-third (i.e., $\alpha_L^N = 63\%$) of total labor and also experiences a labor inflow (i.e., $d\nu^{L,N}(t) > 0$) as a result of the biasedness of the government spending shock towards non-tradables which is reinforced by the current account deficit.

Although the demand boom for non-traded goods is amplified by financial openness as discussed in the previous subsection, the restricted model substantially understates the cumulative change in $L^N(t)$ (2.87 ppt of total hours vs. 5.64 ppt in the data, see the first row of panel B). The reason is twofold. By shutting down technology, the restricted model produces a labor multiplier over a six-year horizon of 0.6 (= 3.34/5.46) only which is two times smaller what we estimate because the rise in $W(t)$ is not large enough to encourage households to supply more labor. The restricted model also substantially understates the reallocation of labor toward the non-traded sector (0.71 ppt against 1.68 ppt of total hours worked, see the third row of panel B).

Turning to value added, the model shutting down technology and capital utilization rates generates a real GDP multiplier of 0.4 over a six-year horizon (= 2.14/5.46), which is more than three times smaller its estimated value 1.4 (= 7.74/5.51). As a matter of consequence, the restricted model predicts a value added multiplier of non-tradables which is twice smaller what we estimate empirically at any horizon. By overestimating the shift of capital toward the non-traded sector, the restricted model also generates a decline in traded value added both on impact and over a six-year horizon (see the first row of panel C) which is at odds with our empirical findings.

**Baseline model.** The performance of the model increases when the capital and the technology utilization rates are allowed to respond endogenously to the government spending shock and firms bias technological change toward production factors. Quantitative
<table><caption>Table 3: Impact and Cumulative Effects of an Increase in $G(t)$ by 1% of GDP</caption><thead><tr><th rowspan="3"></th><th colspan="1">LP t = 0</th><th colspan="2">Impact Responses</th><th colspan="1">LP t = 0...5</th><th colspan="2">Cumulative Responses</th></tr><tr><th>Data</th><th>CES-TECH</th><th>CD</th><th>Data</th><th>CES-TECH</th><th>CD</th></tr><tr><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th></tr></thead><tbody><tr><td><strong>A. Aggregate Multipliers</strong></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Gov. spending, dG(t)</td><td>1.00</td><td>1.00</td><td>1.00</td><td>5.51</td><td>5.46</td><td>5.46</td></tr><tr><td>Total hours worked, dL(t)</td><td>0.91</td><td>0.97</td><td>0.63</td><td>6.37</td><td>5.61</td><td>3.34</td></tr><tr><td>Real GDP, dY<sub>R</sub>(t)</td><td>1.18</td><td>1.07</td><td>0.42</td><td>7.74</td><td>7.36</td><td>2.14</td></tr><tr><td><strong>B. Sectoral Labor</strong></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Traded labor, dL<sup>H</sup>(t)</td><td>0.21</td><td>0.18</td><td>0.09</td><td>0.73</td><td>0.69</td><td>0.47</td></tr><tr><td>Non-traded labor, dL<sup>N</sup>(t)</td><td>0.71</td><td>0.78</td><td>0.54</td><td>5.64</td><td>4.92</td><td>2.87</td></tr><tr><td>Labor share of non-tradables, dν<sup>L,N</sup>(t)</td><td>0.13</td><td>0.16</td><td>0.14</td><td>1.68</td><td>1.26</td><td>0.71</td></tr><tr><td>Decomposition</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Caused by dω<sup>Y,N</sup>(t)</td><td></td><td>0.14</td><td>0.14</td><td></td><td>0.31</td><td>0.71</td></tr><tr><td>Caused by cap. deep. differential</td><td></td><td>0.01</td><td>0.00</td><td></td><td>-0.24</td><td>0.00</td></tr><tr><td>Caused by FBTC differential</td><td></td><td>0.01</td><td>0.00</td><td></td><td>1.20</td><td>0.00</td></tr><tr><td><strong>C. Sectoral Value Added</strong></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Traded VA, dY<sup>H</sup>(t)</td><td>0.33</td><td>0.20</td><td>-0.04</td><td>2.86</td><td>3.12</td><td>-0.28</td></tr><tr><td>Non-traded VA, dY<sup>N</sup>(t)</td><td>0.85</td><td>0.88</td><td>0.46</td><td>4.88</td><td>4.24</td><td>2.41</td></tr><tr><td>Non-traded VA share, dν<sup>Y,N</sup>(t)</td><td>0.16</td><td>0.20</td><td>0.20</td><td>-0.01</td><td>-0.41</td><td>1.07</td></tr><tr><td>Decomposition</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Caused by TFP differential</td><td></td><td>0.03</td><td>0.00</td><td></td><td>-0.47</td><td>0.00</td></tr><tr><td>Caused by labor reallocation</td><td></td><td>0.16</td><td>0.14</td><td></td><td>1.30</td><td>0.72</td></tr><tr><td>Caused by capital reallocation</td><td></td><td>0.01</td><td>0.06</td><td></td><td>-1.23</td><td>0.35</td></tr></tbody></table>

Notes: Impact ($t=0$) and cumulative ($t=0...5$) effects of an exogenous temporary increase in government consumption by 1% of GDP. Panels A,B,C show the deviation in percentage relative to the steady-state for aggregate and sectoral variables. Sectoral value added and the value added share are both expressed as a percentage of initial GDP, while sectoral labor and the labor share are both expressed as a percentage of initial total hours worked. Columns 2 and 5, labelled 'CES-TECH', show predictions of the baseline model while columns 3 and 6, labelled 'CD', shows predictions of the restricted version of the model. In the restricted model, we impose $\sigma^j = 1$ so that production functions are Cobb-Douglas, let $\xi_1^j, \chi_1^j$ tend toward infinity so that the capital and technology utilization rate collapses to one, and set $\xi_4^j, \chi_4^j, \xi_5^j, \chi_5^j$ to zero so that the labor- and capital-augmenting technological rate remain fixed. In columns 1 and 4, we report point estimates from local projections. Since there is a (slight) discrepancy between the response of aggregate real GDP (total hours worked) and the sum of the responses of traded and non-traded value added (hours worked), columns 1 and 4 report the sum of responses of $Y^H$ and $Y^N$ ($L^H$ and $L^N$, resp.) to ensure consistency between aggregate and sectoral responses.

results are shown in column 2 for impact effects and in column 5 for the cumulative effects.

As can be seen in panel A of Table 3, the baseline model does a good job in reproducing the aggregate effects of a shock to $G(t)$. More specifically, along the transitional path, the baseline model produces a cumulative change in $L(t)$ and in real GDP of 5.61% and 7.36% (vs. 6.37% and 7.74% in the data), respectively, thus generating spending multipliers of 1.03 for labor and 1.35 for real GDP on average over the first six years close to the multipliers that we estimate empirically (i.e., 1.15 and 1.40). Three factors give rise to government spending multipliers above one like in the data. First, in the face of a higher real capital rental rate, both sectors, especially traded firms, increase the capital utilization rate, $u^{K,j}(t)$. By raising the demand for labor and the use of the capital input, higher capital utilization amplifies the rise in $L(t)$ and $\tilde{Y}_R(t)$. Second, because the rise in $G(t)$ puts upward pressure on the unit cost for producing, it is optimal to increase the technology utilization rate in both sectors. Efficiency gains increase real GDP directly and also through higher labor supply by putting upward pressure on $\tilde{W}(t)$. Third, as discussed below, the rise in $L(t)$ is amplified because the production technology becomes more labor intensive in the non-traded sector.

Panel B of Table 3 reveals that the baseline model reproduces well the cumulative rise in traded and non-traded hours worked which amounts to 0.69 ppt (vs. 0.73 ppt in the data)
and 4.92 ppt (vs. 5.64 ppt in the data) of total hours worked, respectively. The reason is twofold. First, the model allowing for technological change can account for the increase in $L(t)$, each sector receiving a share (which collapses to their labor compensation share) of $\hat{L}(t)$. Second, because non-traded firms bias technological change toward labor and traded firms bias technological change toward capital, technology further tilts the demand of labor toward non-tradables which amplifies the shift of labor away from traded industries, as detailed below.

As shown in the third row of panel B, we have $d\nu^{L,N}(t) > 0$. The non-traded sector thus experiences a labor inflow which in turn increases disproportionately $L^N(t)$. The last three rows of panel B of Table 3 breaks down the change in $\nu^{L,N}(t)$ into three components, see Online Appendix C for a formal derivation. Focusing on cumulative changes, the decomposition shown in column 6 of panel B for the restricted model reveals that the rise in $\nu^{L,N}(t)$ by 0.71 ppt of total hours worked is only driven by the biasedness of the demand shock toward non-tradables. When we turn to the decomposition of $d\nu^{L,N}(t)$ for the baseline model shown in column 5, our findings show that the bulk of $d\nu^{L,N}(t)$ is driven by the FBTC differential between non-tradables and tradables. The combined effect of technological change biased toward labor in the non-traded sector and biased toward capital in the traded sector generates on its own a cumulative reallocation of labor of 1.2 ppt of total hours worked toward the non-traded sector. The biasedness of the demand shock toward non-tradables further increases $\nu^{L,N}(t)$ by 0.31 ppt of total hours worked. Conversely, capital deepening in the traded sector increases labor demand in this sector, which lowers $\nu^{L,N}(t)$ by -0.24 ppt of total hours worked. The sum of these three effects results in a cumulative increase in the labor share of non-tradables by 1.26 ppt of total hours worked (1.68 ppt in the data). Importantly, FBTC contributes 69% on its own to the change in $\nu^{L,N}(t)$ over a six-year horizon.

We turn to the adjustment in sectoral value added at constant prices, shown in panel C of Table 3. The baseline model generates a multiplier of 0.57 (= 3.12/5.46) for tradables and 0.78 (= 4.24/5.46) for non-tradables, respectively while we estimate empirically a government spending multiplier of 0.52 (= 2.86/5.51) for tradables and 0.89 (= 4.88/5.51) for non-tradables over a six-year horizon. The performance of the baseline model in reproducing the size of the government spending multiplier, i.e., $\hat{Y}_R^G(t)$, along with its distribution across sectors, as captured by $d\nu^{Y,N}(t)$, lies in the technology channel which varies across sectors as discussed below.

As shown in the third row of column 4, $\nu^{Y,N}(t)$ remains almost unchanged and thus the cumulative change in real GDP is distributed across sectors in accordance with their value added share. The last three rows of panel C of Table 3 provide a quantitative decomposition of the cumulative change in the value added share of non-tradables, see Online Appendix
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<figure><img src="image_24.png" /><figcaption>Figure 2: Theoretical vs. Empirical Responses Following Unanticipated Government Spending Shock: Technology Effects. Notes: ‘LP (data)’ refers to the solid blue line which displays point estimate from local projections with shaded areas indicating 90% confidence bounds except for Fig. 2(d) and 2(e) where we have reconstructed empirical responses of TFP$^N(t)$ and $Z^N(t)$ because we found a substantial discrepancy between the empirically estimated (dotted blue line) and reconstructed (solid blue line) responses. In the latter case, we use empirical responses of aggregate and traded TFP, which are both statistically significant, to reconstruct the dynamic responses of TFP$^N(t)$ by using the fact that aggregate TFP growth is equal to the sum of traded and non-traded TFP growth weighted by the value added share of the corresponding sector, and once we have recovered TFP$^N(t)$, we recover $\hat{Z}^N(t)$ by subtracting the response of $\hat{u}^{K,N}(t)$ weighted by $1-s_L^N$, see eq. (8). The thick solid black line with squares displays model predictions in the baseline scenario with capital and technology utilization together with FBTC, while the dashed red line shows predictions of a model with Cobb-Douglas production functions and abstracting from capital and technology utilization.</figcaption></figure>

C for a formal derivation. As can be seen in column 6, when technological change is shut down, both labor and capital shift toward the non-traded sector, increasing $\nu^{Y,N}(t)$ by 1.07 ppt of GDP which in turn gives rise to a fall in traded value added, in contradiction with our evidence. In contrast, in the baseline scenario displayed by column 5, the labor inflow amplified by technological change biased toward labor in the non-traded sector is offset by the capital outflow caused by technological change biased toward capital in the traded sector. Because TFP gains are concentrated in the traded sector, $\nu^{Y,N}(t)$ slightly declines by 0.41 ppt, which in turn prevents traded value added from decreasing, in line with our evidence.

The ability of the model to account for the muted response of $\nu^{Y,N}(t)$ lies in the technology adjustment cost which is lower in the traded than in the non-traded sector. If instead we had set $\chi_2^H = \chi_2^N$ (and $\xi_2^H = \xi_2^N$), the cumulative change in $u^{Z,N}(t)$ would have been twice larger than that of $u^{Z,H}(t)$, thus producing a rise in $\nu^{Y,N}(t)$ by 2.7 ppt of GDP, in contradiction with our evidence.

**Dynamics: Empirical vs. theoretical responses.** In Fig. 2 and Fig. 3, we contrast theoretical predictions (displayed by solid black lines with squares) with empirical responses from local projections (displayed by solid blue lines). The shaded area indicates the 90%
<figure><img src="image_25.png" /></figure>

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<figure><img src="image_36.png" /><figcaption>Figure 3: Theoretical vs. Empirical Responses Following Unanticipated Government Spending Shock: Hours and Value Added Effects. Notes: 'LP (data)' refers to the solid blue line which displays point estimate from local projections with shaded areas indicating 90% confidence bounds; the thick solid black line with squares displays model predictions in the baseline scenario with capital and technology utilization together with FBTC, while the dashed red line shows predictions of a model with Cobb-Douglas production functions and abstracting from capital and technology utilization. The relative wage of non-tradables is constructed as the ratio of the non-traded wage to the aggregate wage, the relative price of non-tradables is computed as the ratio of the non-traded value added deflator to the traded value added deflator, and the terms of trade are constructed as the ratio of the traded value added deflator of the home country i to the geometric average of the traded value added deflator of the seventeen trade partners of the corresponding country i, the weight being equal to the share of imports from the trade partner k (averaged over 1970-2015).</figcaption></figure>
confidence bounds. For comparison purposes and to assess the role of the technology channel in driving the effects, the dashed red lines show the predictions of the restricted model where technology is shutdown.

We start with the adjustment of technology displayed by Fig. 2. Because higher $G(t)$ increases the demand for traded and non-traded goods, both sectors find it profitable to raise their efficiency in the use of inputs to meet higher demand for sectoral goods. While the demand shock is biased toward non-traded goods, Fig. 2(a) and Fig. 2(d) show that technology improvements along the transitional path (i.e., $\hat{Z}^j(t) > 0$) are much more pronounced in the traded than in the non-traded sector because the former sector experiences a lower adjustment cost of technology. Since the demand for capital rises in both sectors, which puts upward pressure on the real capital rental rate, it is profitable to use the stock of capital more intensively (i.e., $u^{K,j}(t)$ rises) which results in higher sectoral TFPs as displayed by Fig. 2(b) and Fig. 2(e). Besides technology improvements, firms change the mix of labor- and capital-augmenting efficiency. Because traded firms bias technological change toward capital, the traded LIS falls below trend, as shown in Fig. 2(c). Conversely, non-traded firms bias technological change toward labor which increases the non-traded LIS, as displayed by Fig. 2(f).

As shown in Fig. 3, both the shift in the technology frontier and the change in the mix of labor- and capital-augmenting efficiency along the technology frontier increase the ability of the two-sector open economy model to account for the empirical evidence. As can be seen in Fig. 3(b) and Fig. 3(c), the model reproduces well the dynamics of $L(t)$ and real GDP once we allow for the technology channel. Intuitively, technology improvements and a higher labor intensity of production result in a higher wage rate which encourages agents to supply more labor. The combined effect of TFP gains and higher labor supply amplifies the increase in real GDP.

As displayed by Fig. 3(f), more labor shifts toward the non-traded sector in the baseline than in the restricted model because non-traded (traded) firms use labor (capital) more intensively. By further increasing labor supply and generating a labor inflow in the non-traded sector, the model can account for the dynamics of traded and non-traded hours worked (see Fig. 3(d) and 3(e)) we estimate empirically. As displayed by the dashed red line in Fig. 3(i), by producing a shift of capital toward non-traded industries the restricted model generates an increase in $\nu^{Y,N}(t)$, thus leading to a decline in $\tilde{Y}^H(t)$ in contradiction with our evidence, see Fig. 3(g). Conversely, by letting both capital and technology utilization rates increase endogenously, the baseline model can account for the hump-shaped dynamics of traded value added.

To gain a better understanding of fiscal transmission, in the fourth row of Fig. 3, we assess the ability of our model to account for the behavior of relative wages $\tilde{W}^j(t)/\tilde{W}(t)$
and relative prices. As shown in Fig. 3(j), non-traded firms increase wages above the aggregate wage to encourage workers (who experience mobility costs) to shift toward the non-traded sector. The fact that sectoral wages move away from the aggregate wage reveals the presence of switching costs. Because technological change is biased toward capital in the traded sector and biased toward labor in the non-traded sector, the adjustment in relative wages is more pronounced in the baseline model, in line with the evidence. As can be seen in Fig. 3(l), because the demand shock is biased toward non-tradables, the relative price of non-tradables appreciates. If home- and foreign-produced traded were perfect substitutes, the terms of trade would be unchanged. Instead, because households are reluctant to substitute imported for domestic goods and since $G^H(t)$ increases, the terms of trade slightly appreciate on impact and then depreciate as a result of technology improvements concentrated in the traded sector, see Fig. 3(k).

**Distortionary labor and consumption taxation.** While the dynamics of the baseline model shown in Fig. 2 and Fig. 3 can account for the empirical evidence until $t = 6$, it cannot account for the persistent decline in value added and in hours worked below trend after $t = 7$. As shown in Online Appendix V.7, the model can generate the adjustment in $L(t)$ and real GDP (and their sectoral counterparts) after $t = 7$ we estimate empirically once we relax the assumption of lump-sum taxes and allow for distortionary (labor and consumption) taxation.

**Shocks to Sectoral government consumption.** So far, we have investigated the dynamic effects of a shock to $G(t)$, assuming that 80% of $dG(t)/Y$ is spent on non-traded goods and 20% is spent on traded goods. Instead of highlighting the role of the technology channel in determining the allocation of spending multipliers across sectors, we could ask: which sector should be allocated government purchases so as to maximize the real GDP and total hours effects? Numerical results detailed in Online Appendix R.3 show that both labor (i.e., 0.62) and real GDP multipliers (i.e., 0.40) after a shock to $G^N$ are larger than those after a shock to $G^T$. This conclusion is reversed (1.54 and 2.19 for labor and real GDP multipliers) once we allow for the technology channel because the cost of adjusting technology is smaller in the traded than in the non-traded sector.

# 5 Conclusion

This paper highlights the role of the technology channel in determining the size of the government spending multiplier and its sectoral decomposition. First, we find empirically that the government spending multiplier is higher than one and 39% of the cumulative change in real GDP over a six-year horizon is driven by TFP gains. Second, while the demand shock is biased toward non-traded goods, the concentration of technology improvements in traded industries implies that the government spending multiplier is distributed uniformly across
sectors at any horizon. Conversely, 88% of the cumulative change in total hours worked is concentrated in the non-traded sector as non-traded (traded) production becomes more intensive in labor (capital).

To rationalize our evidence, we consider a semi-small open economy with tradables and non-tradables in the lines of Kehoe and Ruhl [2009]. Drawing on Bianchi et al. [2019], we assume that capital and technology can be used more intensively while the mix of labor- and capital-augmenting efficiency also vary, like Caselli and Coleman [2006]. We show that in a multi-sector open economy, the concentration of technology improvements in the traded sector following a rise in government consumption is conditional on barriers to factors' mobility and technological factors. Because the technology decision is pro-cyclical, the high intensity of non-traded industries in the government spending shock which is amplified by increased foreign borrowing produces a strong negative impact on traded overall efficiency. While both imperfect substitutability between traded and non-traded hours, and between home- and foreign-produced traded goods mitigate the shift of resources toward the non-traded sector, these two elements are not sufficient to generate a technology improvement in the traded sector. It is only once we allow capital to be used more intensively in both sectors and technological change to be biased toward labor in non-traded industries and to be biased toward capital in traded industries, that the model can account for the magnitude of the rise in overall efficiency in the traded relative to the non-traded sector.

To quantify the role of technology in determining the size of government spending multipliers and their distribution across sectors, we contrast the predictions of the baseline model with those of a restricted model where technological change is shut down and sectoral goods are produced from Cobb-Douglas production functions. Our quantitative analysis shows that a model abstracting from technological change cannot generate the rise in real GDP and in total hours worked that we estimate empirically, generates a disproportionate increase in non-traded relative to traded value added in contradiction with our evidence, understates the rise in non-traded hours worked, and cannot account for the dynamics of sectoral LISs. Conversely, the two-sector open economy model can account for the value added and labor effects of a government spending shock once we let the decision on technology improvement and factor intensity of production vary across sectors and time.

What are the determinants of technology adjustment costs at a sectoral level? While we document evidence which reveals that productivity gains (conditional on a government spending shock) are larger in industries which are relatively more intensive in tangible assets or less intensive in skilled labor or in intangible assets, we see these estimates as a first attempt to unravel the relationship between technology improvements and firm production structure. More work should be done to understand what is the optimal form of firm organization to adjust production along the business cycle in open economy.
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