metadata: authors: 0: author: Selod,Harris
1: author: Tobin,Lara
count: World
docna: 0: docna: The informal city
docty: Policy Research Working Paper
abstracts: cdata!: This paper proposes a theory of urban
            land use with endogenous property rights. Socially
            heterogeneous households compete for where to live in the
            city and choose the type of property rights they purchase
            from a land administration which collects fees in
            inequitable ways. The model generates predictions regarding
            sorting and spatial patterns of informality consistent with
            developing country cities. It also highlights non-trivial
            effects of land administration reforms in the presence of
            pecuniary externalities, possibly explaining why elites may
            have an interest in maintaining inequitable land
            administrations that insulate them from competition for land
            from the rest of the population.
repnme: repnme: The informal city
display_title: The informal city
listing_relative_url: /research/2018/06/30169469/informal-city
publishtoextweb_dt: 2018-06-20T00:00:00Z
no_of_pages: 57
author_keys: 0: author_key: 750638
1: author_key: 1202464
model_extractions: WPS8482 Policy Research Working Paper 8482 The Informal City _Harris Selod Lara Tobin_ Development Economics Development Research Group June 2018
Policy Research Working Paper 8482

# **Abstract**

This paper proposes a theory of urban land use with endogenous property rights. Socially heterogeneous households compete for where to live in the city and choose the type of property rights they purchase from a land administration which collects fees in inequitable ways. The model generates predictions regarding sorting and spatial patterns of informality consistent with developing country cities. It also highlights non-trivial effects of land administration reforms in the presence of pecuniary externalities, possibly explaining why elites may have an interest in maintaining inequitable land administrations that insulate them from competition for land from the rest of the population.

This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/research. The authors may be contacted at hselod@worldbank.org and lara.tobin@m4x.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# The Informal City<sup>_∗_</sup>

Harris Selod<sup>_†_</sup> and Lara Tobin<sup>_‡_</sup>

**JEL classification** : R14, R52 and P48

**Keywords** : Land markets; Property rights; Land administration; Tenure security; Multiple sales

> _∗_ We are grateful to Asao Ando, Jan Brueckner, Denis Cogneau, Ma ̈ylis Durand-Lasserve, Gilles Duranton, Karen Macours, Stephen Sheppard, Jacques-Fran ̧cois Thisse, Thierry Verdier, and the participants to seminars and conferences where this paper was presented for useful discussions. We acknowledge funding from the World Bank’s Knowledge for Change Program and the Multi Donor Trust Fund for Sustainable Urban Development. The views expressed in this paper are those of the authors and do not necessarily reflect those of the World Bank, its Board of Directors or the countries they represent.

> _†_ Harris Selod: Energy and Environment Team, Development Research Group, The World Bank. Email: hselod@worldbank.org.

> _‡_ Lara Tobin: _Minist`ere de la coh ́esion des territoires_ , France. Email: lara.tobin@m4x.org.

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# **1 Introduction**

The main forces that shape the spatial structure of cities have long been identified by urban economic theory. In the standard land-use model of urban economics (Alonso, 1964; Muth, 1969; Mills, 1972), heterogeneous households compete for where to live in the city while trading-off accessibility for land consumption under endogenously determined land prices. This spatial equilibrium representation of cities accounts for universal regularities such as decreasing population densities, a negative land price gradient moving away from city centers, and residential stratification by income (Fujita, 1989; Anas et al., 1998). This canonical model, however, implicitly assumes costless and clearly defined property rights. Its validity is thus challenged in many developing country cities where land tenure informality and insecurity is more often the norm than the exception (Marx et al., 2013; UN-Habitat, 2010).

The objective of our paper is to fill this gap and build an urban land use theory which can account for informal property rights and associated tenure insecurity. Our framework has three important ingredients observed in many developing countries: a multiplicity of tenure options ranging from very insecure to very secure (UN-Habitat, 2012), a risk of conflict in the presence of multiple sales of a same plot (Durand-Lasserve et al., 2015), and costly access to secure tenure (Wehrmann, 2008), which is often blamed for driving households into informality (Udry, 2011; Collier and Venables, 2013). We focus on the trade-off households face between establishing costly property rights and facing the risk of dispossession in a context where unclear property rights may result in multiple sales.

While most models so far have focused on a binary vision of residential informality (i.e., formal versus informal), it is important to acknowledge that there is in fact a wide range of tenure situations in the cities of developing countries, depending on legal documentation held by the “owner” of a plot (Bruce, 1998; Becker, 2013; Durand-Lasserve et al., 2013). Taken together, these situations constitute a “continuum” of options for holding land under various levels of tenure security (UN-Habitat, 2012). The existence of this continuum also implies that different 2
tenure situations often coexist within a same city, an issue which has largely remained unexplored and requires systemic analyses land markets, such as the one we are proposing here.

Secondly, the model needs to specify the exact mechanisms whereby the lack of property rights or lack of enforcement of property rights results in tenure insecurity. So far, the literature has exclusively focused on the risk of eviction of squatters who occupy someone else’s land (Jimenez, 1984; Turnbull, 2008; Brueckner and Selod, 2009). Although squatting is an important topic, it only concerns a particular form of tenure insecurity. In many cities, the main source of tenure insecurity that affects the poor as well as a large fraction of the middle class is of a different nature as it often stems from the multiplicity of claims (either because of multiple sales to different buyers, or because multiple claimants each managed to obtain a property right for the same plot) (Wehrmann, 2008; Durand-Lasserve et al., 2015). We retain multiple sales as the source of insecurity in our model, resulting in households paying for urban land before knowing whether or not they will be able to exercise their rights.<sup>1</sup> Lastly, the theory should account for the costly processes faced by households to obtain property rights from the land administration.<sup>2</sup> We thus allow the land administration to be clientelistic, possibly collecting fees in inequitable ways that favor some households and harm others. The legal and illegal fees 1A recent study on land markets in Ghana ranked “double sales of land by traditional owners” as the number one problem in Accra (Omirin and Antwi, 2004). In Benin, it was estimated that 20 percent of urban plots were subject to a conflict (OCS, 2006). The problem of multiple sales is so pervasive in that country that a specific provision has been inserted in the recent land code to punish authors of multiple sales with a heavy fine and a jail sentence of up 5 years. In Mali, in the sole district of Bamako, at least 12,000 cases of double allocations of use rights or of superimposition of property titles have been identified (Coulibaly, 2009). Multiple sales are actually clogging tribunals as an estimated 80% of cases in Mali are related to land (Camara, 2012). In Togo, land-related conflicts represent 70% of tribunal cases (Kakpo, 2018).

2In the case of Mali for instance, Djir ́e (2007) reports an example in a locality at the outskirts of the Bamako district where the average cost of obtaining a property title is 725 _,_ 000 CFA Francs (about $1 _,_ 500). This includes the payment for the topographical survey, the permit fees (valid for five years), the fees for demarcation, registration, notice of public inquiry, the signature of the sub-prefect and the village chief, and the Land Office registration stamp... In comparison, the price of land in that locality is on average 225 _,_ 000 CFA Francs per hectare (about USD 450) (Djir ́e, 2007; Bouju, 2009).

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necessary to establish property rights are documented in a few descriptive studies, which also insist on the role of social connections and corruption in the land administration, which can be determining factors in obtaining a plot, regularizing tenure and speeding up the process of obtaining a property right (Bertrand, 1995, 2006, 1998; Djir ́e, 2007). In our model we allow the “cost of tenure” (the fee paid to the land administration to obtain a property right) to increase with the level of tenure security provided by the purchased right and to decrease with household’s social connexion to the land administration.

Our setting is the first to account for the continuum of property rights, multiple sales and a dysfunctional land administration in a unified land-market equilibrium which applies to cities in developing countries. It makes it possible to understand the non-trivial interactions between land administration practices, household tenure choices, and exposure to multiple sales in a context where land prices and city structure are endogenously determined, and thus to understand the general equilibrium effects of urban land tenure policies. Section 2 presents relevant insights from the literature on the urban land market models. Section 3 presents the model while section 4 studies how changes in the parameters of the model affect city structure. Section 5 concludes.

# **2 Insights from urban land market models**

The theoretical literature on the coexistence of formal and informal types of land use was initiated by Jimenez (1985) and Hoy and Jimenez (1991) who analyzed squatting in a partial equilibrium perspective. These papers present a framework of tenure choice under uncertainty, where in the case of an eviction from a squat, households have to relocate in the formal market. In these “eviction – models”, the probability of eviction a direct measure of tenure insecurity – is endogenous but the price of housing in the formal market is exogenous and not affected by the informal sector. This is a strong assumption, especially considering that a large fraction of the population usually occupies land informally.

Relaxing the assumption of a fixed formal land price, Turnbull (2008) considers 4
a stochastic (but still exogenous) formal land price on which the probability of eviction depends. Brueckner and Selod (2009) are the first to adopt a general equilibrium perspective by modeling the effect of squatter settlements on formal land prices in a context of fixed land supply. In their setting, inflation of the squatter settlement “squeezes” the formal market, leading to an increase in the price of land in the formal sector up to the point where landowners would find it profitable to evict squatters. Subsequent work considers the case of squatting on public land instead of private land (Shah, 2014) and introduce competition among squatter organizers (Brueckner, 2013). Other general equilibrium models (Alves, 2016; Cavalcanti et al., 2018) study the formation of slums and study the role of barriers to formalization and regularization policies on informality. None of these models, however, offer an explicit representation of the urban space within a city. An exception is Henderson et al. (2016) who propose a spatial model where developers may switch from informal to formal development over time as a response to rising land values but they do not account for insecurity of property rights. These drawbacks are somehow addressed in Cai et al. (2018) who study the dynamics of property rights in a city. Their representation of the urban space, however, is simplified as they do not account for the direct capitalization of tenure insecurity in land rents.<sup>3</sup> In a nutshell, the above contributions focus on specific and sometimes simplified definitions of informality, and, with the exception of (Cai et al., 2018), none adopt the continuous spatial framework of urban economics.<sup>4</sup> Our model fills these two important gaps as it determines an equilibrium land use with an endogenous choice of tenure among a continuum of options.

> 3In their dynamic stochastic setting, they model each sub-period as an instantaneous land market equilibrium where land is held with certainty.

> 4There are empirical papers on the measurement of the tenure security and tradability premia which allow for more diverse tenure situations (Jimenez, 1982, 1984; Friedman et al., 1998; Lanjouw and Levy, 2002; Kim, 2004) as well as papers on the impacts of land tenure formalization in an urban context (Field, 2007; Di Tella et al., 2007; Galiani and Schargrodsky, 2010). Very few papers have analyzed the causes of residential informality (Hidalgo et al., 2010).

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# **3 The model**

## **3.1 The setup**

The economy has a city and a rural area and an overall population of mass _N_ . The city is linear and represented by a segment with a Central Business District (CBD) located at one origin. The rural area encompasses all non-urban locations and does not have an explicit spatial representation. The city is open, meaning that the equilibrium number of households in the city is endogenously determined by migration to the urban area. We assume that there is one unit of land in each point and that each urban household consumes a fixed quantity of land, normalized to one. Within a distance _x_ from the CBD, there are thus exactly _x_ units of land and _x_ households. The model also has absentee landlords who extract rents from households who are competing on the land market.<sup>5</sup> A household located at a distance _x_ from the CBD (i.e. in location _x_ ) pays an endogenous rent _R_ ( _x_ ) to an absentee landlord. It also has one member who commutes to the CBD to work at a cost _xt_ , where _t_ is the unit transport cost. All workers in the economy earn the same exogenous urban wage _yu_ when residing in the city. We assume that the urban wage is significantly higher than the income _yr_ of households residing in the rural area who can only engage in low-productivity agricultural activities. When residing in the rural area, households incur a cost _Ra_ to access land but do not pay any commuting cost since they derive all their income from on-farm activities and do not need to travel to the city in order to work.

Our model departs from standard urban land use models as it allows a same plot of land to be sold to more than one household, generating conflicts and tenure insecurity. Buyers reduce tenure insecurity by purchasing property rights from a land administration offering a menu of options that are more or less efficient in deterring multiple sales. This continuum reflects the different steps along the formalization process towards a fully-fledged ownership right. It can 5Landlords are defined in a broad sense and refer to all individuals, groups or institutions that make land available for housing. They can be the primary owners of the land, private developers, or public authorities, and, in practice, are often a combination of these different stakeholders.

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include situations where a plot is held with a simple sales certificate, different levels of administrative documents which do not provide a statutory right but instead confer a “presumption of right”, various types of revocable temporary permits to occupy, and, at the end of the spectrum, a registered ownership title. If a buyer obtains a registered property right, the nature and number of checks that are made before the right can be delivered makes it unlikely–although not impossible–that multiple sales will happen. Formally, we assume that there exists a continuum of tenure situations, each characterized by a level of tenure security measured by the probability _π ∈_ [ _πmin, πmax_ ] that a right holder can successfully discourage multiple sales. When _π_ = _πmin_ , the probability of keeping the purchased plot is lowest, corresponding to a situation in which the household has no recognized right and the probability of occurrence of multiple sales is highest. _π_ = _πmax_ corresponds to the most secure form of tenure for which multiple sales are scarcest. Intermediate values of _π_ correspond to property rights with moderate levels of tenure security.

Different households face different costs to obtain property rights. This is because social status and personal acquaintances are crucial in determining the level of bribes households may have to disburse to obtain land documentation.<sup>6</sup> We model this by having each household characterized by its ability to interact with the land administration, as measured by its “social distance” _e_ from the administration, with _e_ uniformly distributed over [0 _,_ 1] across the population. To purchase a property right providing a level _π_ of tenure security, a type- _e_ household incurs a cost _C_ ( _π, e_ ). This “tenure cost function” is increasing in _π_ as more secure property rights come at higher fees, and in _e_ as more socially distant households face higher fees to acquire a given level of tenure security.<sup>7</sup> We further assume that the marginal cost of tenure security is increasing with distance to the administration, implying _∂π∂e∂_<sup>2</sup> _<u>C</u>_<sup>_>_0,andthatthecostoftenuresecurityisconvexin</sup><sup>_π_.</sup>

> 6See Van der Molen and Tuladhar (2007) for a description of corruption in land administrations in a selection of Asian, African, and Central and Eastern European countries.

> 7 _C_ ( _π, e_ ) could be regarded as a tenure security premium captured by the land administration. This is consistent with bureaucrats designing complex systems to induce agents to transfer some of the rents to them (Antwi and Adams, 2003).

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The tenure cost function is represented on Figure 1 below for two different agents.<sup>8</sup> <!-- Start of picture text --> C�Π,e�<br>Π<br>Πmin Πmax<br><!-- End of picture text -->

**Figure 1:** Tenure cost functions of well-connected ( _e_ =.1) and poorly-connected ( _e_ =.9) households

We can now present the timing of the model. In a first stage, households decide whether to purchase land in the city and the type of property rights (if any at all) they purchase from the land administration. Because of multiple sales, conflicts emerge over land. In a second stage, each plot of land is adjudicated to one buyer only. Households who bought land in the first stage remain in the city if they are able to enforce their property right and stay in the rural area otherwise.

A type- _e_ household who bought a plot in location _x_ with tenure security _π_ in the first stage has a probability _π_ of retaining its plot during the second stage. If so, the household then faces the second-stage budget constraint given by Equation (1), in which _zu_ is the consumption of a composite good taken as the numeraire.

With probability 1 _− π_ , the household loses the plot it purchased and remain in the rural area. It faces the second-stage budget constraint given by Equation (2) in which _zr_ is the consumption of the composite good. The amount initially paid 8Figure 1 and all the other figures in this section are drawn for the specifications and parameter values used in our base case simulation (see Section 4 below).

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to buy the plot and the property right are both lost.

Under the assumption that the consumption of land is fixed, the only endogenous argument in the household’s utility function is its consumption of the composite good _z_ . We assume without loss of generality that _u_ ( _z_ ) = _z_ . The expected utility of a household purchasing land in the city (at location _x_ ) is therefore: In this setting, a type- _e_ household purchasing land in a given location _x_ , chooses its level of tenure security _π_ and its anticipated consumption levels _zu_ and _zr_ in each state of the nature so as to maximize its expected utility function (3) subject to budget constraints (1) and (2). Recognizing that budget constraints must be saturated at the optimum, the household’s optimization program conditional on _x_ and _R_ ( _x_ ) simplifies to the choice of _π_ which maximizes the objective function: Solving the model requires identifying, in equilibrium, which households purchase land in the city, where, and with which level of tenure security. It also requires determining the expected utilities of all households, and the profile of land rents prevailing in the city. Note that our equilibrium definition may have several households choose a same location _ex-ante_ due to the possibility of multiple sales but, _ex-post_ , after the conflicts arising from multiple claims are resolved, only a fraction of the initial buyers will effectively reside in the city. The equilibrium is determined _ex-ante_ as all decisions are made in the first stage, anticipating outcomes in the second stage.

We solve the model in two steps. In a first step, we parametrize by _x_ and determine, for a given household of type _e_ , the optimal choice of _π_ as function of _x_ and _R_ ( _x_ ). In a second step, we account for competition for land in a context of multiple sales and determine the equilibrium mapping between household types and land 9
purchase locations (including multiple purchases of a same plot). We then derive all the endogenous variables of the model. These two steps are presented sequentially in the two subsections below.

# **3.2 Tenure choice**

Let us denote _π_<sup>_∗_</sup> ( _x, e_ ) the optimal level of tenure security chosen by a type- _e_ household in location _x_ . _π_<sup>_∗_</sup> ( _x, e_ ) is a solution to the maximization problem: Since the tenure cost function is convex in _π_ , the expected utility function (4) is concave in _π_ and therefore has a unique maximum reached in _π_ = _π_<sup>_∗_</sup> ( _x, e_ ) _∈_ [ _πmin, πmax_ ]. If _π_<sup>_∗_</sup> ( _x, e_ ), is an interior solution to the maximization problem, it must verify the first order condition obtained from differentiating Equation (4): The above equation simply states that the optimal level of tenure security must equate the marginal cost of tenure security with the marginal gain from tenure security improvement. Because the tenure cost and the land rent are paid in both states of nature, the gain associated with a marginal increase in tenure security is simply the difference between the urban wage net of commuting costs and the rural wage net of the agricultural land rent as expressed by Equation (6). If the marginal gain and the marginal cost of tenure security do not intersect over [ _πmin, πmax_ ] then _π_<sup>_∗_</sup> ( _x, e_ ) is a corner solution. If the marginal gain is greater (respectively smaller) than the marginal cost of tenure security over [ _πmin, πmax_ ], then the optimal level of tenure security is _π_<sup>_∗_</sup> ( _x, e_ ) = _πmax_ (respectively _π_<sup>_∗_</sup> ( _x, e_ ) = _πmin_ ). Differentiating Equation (6) with respect to _x_ and _e_ , we derive proposition 1 (proof in Appendix A).

**Proposition 1.** _The demand for tenure security is non-increasing with physical distance to the CBD and social distance to the land administration. Where π_<sup>_∗_</sup>

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_is differentiable, we have:_ The intuition for these results is straightforward: Consider first a household of given type _e_ . Inspection of Equation (6) shows that the relative gain from residing in the city as opposed to the rural area, _yu − xt − yr_ + _Ra_ , increases with proximity to the CBD. The closer the location to the CBD, the greater the saving on commuting costs and thus the stronger the incentive to seek secure tenure so as to be able to stay in the city. Now consider a location _x_ , because the marginal cost of tenure security is increasing in _e_ ( _∂e∂π_<sup>_<u>∂</u>_2</sup><sup>_<u>C</u>>_0),ahouseholdwhich</sup> is socially more distant from the land administration will choose to purchase property rights that are less secure than a household which has better connections.

We now derive the household’s demand for tenure security throughout the city which, due to possible corner solutions in the optimization program, may be characterized by a piecewise function (proof in Appendix A).

**Proposition 2.** _The household tenure choice function x �→ π_<sup>_∗_</sup> ( _x, e_ ) _can be defined by parts over at most three zones in the city:_

- _a central zone defined by x ≤_ _<u>x</u>_ <u>(</u> _e_ ) _where a type-e household chooses π_<sup>_∗_</sup> ( _x, e_ ) = _πmax,_

- _an intermediate zone defined by_ _<u>x</u>_ ( _e_ ) _< x <_ _<u>x</u>_ <u>(</u> _e_ ) _where a type-e household chooses π_<sup>_∗_</sup> ( _x, e_ ) _∈_ ] _πmin, πmax_ [ _, given by Equation_ (6) _,_

- _a peripheral zone defined by_ _<u>x</u>_ <u>(</u> _e_ ) _≤ x where a type-e household chooses π_<sup>_∗_</sup> ( _x, e_ ) = _πmin._

Proposition 2 states that there are threshold locations, _<u>x</u>_ ( _e_ ) and _<u>x</u>_ <u>(</u> _e_ ), below and beyond which a household’s optimal tenure choice is a corner solution. In locations up to _<u>x</u>_ <u>(</u> _e_ ), transport costs are small and the relative gains to residing in the city area high, so that the household chooses the highest level of tenure security. In locations beyond _<u>x</u>_ <u>(</u> _e_ ) transport costs are high and relative gains to being in the 11
urban area low, the household therefore chooses the lowest level of tenure security. Between these two thresholds, the household chooses intermediate values of tenure security. The optimal tenure choice _π_<sup>_∗_</sup> ( _x, e_ ) is represented on Figure 2a below as a function of distance to the CBD for a given value of _e_ .

<!-- Start of picture text --> Π � �x,e� x<br>Πmax x �e�<br>x �e�<br>Πmin<br>x e<br>x �e� x �e� Π � �Πmax Πmin�Π � �Πmax Π � �Πmin<br>(a) Demand for tenure security as a (b) Tenure threshold locations x ( e ) and<br>function of location ( e = 0 . 2) x ( e ) as functions of e<br><!-- End of picture text -->

**Figure 2:** Household demand for tenure security

Appendix A explicits how these functions are derived from the maximization of Equation (5) and shows that _<u>x</u>_ <u>(</u> _e_ ) and _<u>x</u>_ <u>(</u> _e_ ) are decreasing in _e_ . Observe that the three zones may not necessarily exist for all values of _e_ . For some sufficiently high _e_ for instance, the central and intermediate zones may not exist if for all values _x ≥_ 0, _π_<sup>_∗_</sup> ( _x, e_ ) = _πmin_ . Figure 2b graphs tenure threshold locations as functions of household type. For each location _x_ plotted on the vertical axis, it shows which household type _e_ plotted on the horizontal axis would choose the minimum, intermediate, and maximum tenure security options.

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# **3.3 The Land Market Equilibrium**

Now that we have determined how tenure choice is affected by location and type, we solve the land market equilibrium. We proceed in four steps. We first determine how much each household is willing to pay for a plot in all possible locations. Taking into account competition on the land market, we then derive the overall city structure (i.e. household locations and tenure zones), the city fringe beyond which no plots are purchased, and finally land prices and household utilities.

## **3.3.1 Bid Rents**

The bid rent of a type- _e_ household is defined as the maximum payment that the household would be willing to make to purchase a plot in location _x_ in order to be indifferent between all locations and achieve a given level of expected utility _ν_ ( _e_ ). Inverting the indirect utility function (4), we obtain the bid rent as a function of _π_<sup>_∗_</sup> ( _x, e_ ), presented in the previous subsection. The bid rent function expresses the maximum land rent that an individual of type _e_ would be willing to pay to reside in location _x_ so as to achieve utility _ν_ ( _e_ ) and taking into account its optimization of tenure security. It is expressed as Equation (7).

Differentiating the bid-rent function with respect to _x_ results in Proposition 3.

**Proposition 3.** _Bid-rent functions are downward sloping and convex_

Proposition 3 states that a household located in _x_ is willing to pay more for a location marginally closer to the CBD because of the _expected_ marginal saving in commuting costs under the household’s optimal level of tenure security. This is a modified version of the Alonso-Muth-Mills condition which states that, under complete tenure security, savings in land consumption should exactly compensate 13
for transport costs (Fujita, 1989).<sup>9</sup> In our setting, introducing tenure insecurity, makes bid-rents flatter compared to the standard monocentric model without tenure insecurity,<sup>10</sup> which will have a dampening effect on equilibrium land prices.

As a result of Proposition 2, the bid rent Ψ _e_ can be defined piecewise over at most three zones in the city:

- In the central zone defined by _x ≤_ _<u>x</u>_ <u>(</u> _e_ ), the type- _e_ household chooses _π_<sup>_∗_</sup> ( _x, e_ ) = _πmax_ , the slope of the bid rent is _−πmaxt_ and the bid rent is a linear function of _x_ .

- In the peripheral zone defined by _<u>x</u>_ <u>(</u> _e_ ) _≤ x_ , the household chooses _π_<sup>_∗_</sup> = _πmin_ , the slope of the bid rent is _−πmint_ and the bid rent is a linear function of _x_ .

- For _<u>x</u>_ <u>(</u> _e_ ) _< x <_ _<u>x</u>_ <u>(</u> _e_ ), the bid rent is strictly convex.<sup>11</sup>

Over the portion of the city where the household would choose intermediate levels of tenure security, the convexity of the bid-rent function reflects the willingness to pay a higher land price for a plot marginally closer to the CBD, with the increment compensating for the marginal increase in tenure security in addition to the marginal saving in transport costs. This is represented on Figure 3 below. To continue our demonstration, we now establish the following Lemma by differentiating Equation (8) with respect to _e_ , and using the fact that _π_<sup>_∗_</sup> is a non-increasing function of _e_ (see Proposition 1). The intuition is that lower-type households demand higher levels of tenure security due to their advantage in terms of land administration fees. They thus have an incentive to bid more for a location marginally closer to the CBD.

> 9In the standard urban economics model, the Alonso-Muth-Mills condition strictly speaking actually equates the marginal transport cost increment with the marginal saving in land consumption. Our result in Equation (8) follows from the assumption that land consumption is constant and normalized to unity and accounts for the likelihood of keeping the plot (and having to commute to the city center). The standard urban economics model can thus be viewed as a specific case of our broader model under which tenure security is certain.

> 10Constraining _π⋆_ ( _x, e_ ) to be equal to 1 would lead the standard condition that _<u>∂∂x</u>_ <u>Ψ</u> _<u>e</u>_<sup>=</sup><sup>_−t_</sup> 11 _<u>∂</u>_<sup>2</sup> <u>Ψ</u> _<u>e</u>_ Since _∂x_<sup>2(</sup><sup>_x, ν_(</sup><sup>_e_)) =</sup><sup>_−t_</sup><sup>_<u>∂π</u>_</sup> _∂x_<sup>_∗>_0with</sup><sup>_<u>∂π</u>_</sup> _∂x_<sup>_∗<_0followingProposition1.</sup>

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<!-- Start of picture text --> �<br>�� x �e��<br>�� x �e��<br>x<br>x �e� x �e�<br><!-- End of picture text -->

**Figure 3:** The bid rent function for household _e_ = 0 _._ 2

**Lemma 1.** _Wherever they may intersect, the bid rent of a lower type-e household has a steeper or same slope than that of a higher type-e household._

We can now characterize the land market equilibrium. The requirement in competitive land use models that land gets allocated to the highest bid also holds in the presence of multiple sales.<sup>12</sup> When comparing purchase location choices, we use the standard result that, in equilibrium, agents are ranked by order of bid-rent steepness: agents with steeper bid-rents bid away other agents to more remote locations (Fujita, 1989). Under Lemma 1, households purchase plots in order of increasing type. Although this is indeed true in our model, the determination of the spatial equilibrium is more complex than in the standard case and requires addressing three specific issues.

First, we are dealing with a continuum of households instead of a discrete number of agents, and must compare a continuum of bid rents. Building on an assignment problem first analyzed by Beckmann (1969), several papers in the urban economics literature have developed methods to ensure that the hypothesized mapping between types and space results from competition in the land market (Brueckner et al., 2002; Selod and Zenou, 2003; Brueckner and Selod, 2006; Behrens et al., 2014). We resort to a similar approach. Second, the model has multiple sales, 12In the model, multiples sales occur at identical prices to ensure profit maximization of sellers.

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which means that there are more transactions than plots available in the city (there are more buyers than sellers). In order to define the equilibrium mapping between households purchases and locations, we will need to account for the way the risk of multiple sales is attenuated by the purchase of property rights and how these choices translate into land use. Third, the unambiguous ranking of households according to type is valid only for bid rents that intersect over isolated points. In our model bid rents may overlap over a whole interval. This happens in zones of the city where the optimal tenure choice of households yields a common corner solution. Over such zones, the bid rents all have the same slope (see Equation (8) and Figure 3) irrespective of household type. It is possible to determine which households purchase a plot in that zone but not their exact location within the zone. This indeterminacy means that there can be an infinity of spatial configurations in equilibrium. Fortunately, this will not affect the model in any significant way since these equilibria share the same general spatial structure of the city and all the other endogenous variables of the model will take the exact same value.

# **3.3.2 City structure**

We now identify the spatial distribution of tenure situations throughout the city as well as the mapping between households and locations of purchased land. Confronting the piecewise bid rents of households described in Proposition 2 and the condition that households must be ranked in decreasing order of their bid rents’ steepness, we obtain Proposition 4 (proof in Appendix B).

**Proposition 4.** _In equilibrium, the city is divided into at most three different “tenure zones”_ :

- **_A “secure tenure zone” in the central section of the city_** _(x ∈_ [0 _, x_ ] _) where households with the strongest social ties to the land administration (e ≤_ _<u>e)</u> reside and purchase the most secure type of property rights (π_<sup>_∗_</sup> = _πmax)_ .

- **_A “precarious tenure zone” in the intermediate section of the city_**<sup>13</sup> _(x ∈_ _<u>x, x</u>_ <u>[</u> _) where households with intermediate values of e (e ∈_ ] _<u>e, e</u>_ [ _)_

- 13The term “precarious” is used in a country like Mali for instance to designate a range of

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_reside and purchase property rights with intermediate levels of tenure security π_<sup>_∗_</sup> ( _x, e_ ).

- **_An “insecure tenure zone” in the peripheral section of the city_** _(for x_ = _<u>x</u> to the city fringe) where the households with the weakest ties to the administration (e ≥_ _<u>e)</u> reside and purchase the lowest level of tenure security from the administration (π_<sup>_∗_</sup> = _πmin)_ .

A city may exhibit either one, two or three zones depending on the model’s parameters and the exact location of households within the secure zone and the insecure zone (if they exist) are undetermined. Without loss of generality, we consider only the equilibrium in which households are ordered by increasing _e_ . With this ordering, and accounting for multiple sales, we derive Proposition 5.

**Proposition 5.** _The equilibrium mapping x_ ( _e_ ) _between types and locations verifies the differential equation and initial conditions described by Equation_ (10) _._

Proposition 5 maps types and purchase locations considering that _Nde_ buyers, with type between _e_ and _e_ + _de_ , purchase land _dx_ located between between _x_ ( _e_ ) and _x_ ( _e_ ) + _dx_ . For an infinitesimal _de_ , each plot is bought with tenure security _π_<sup>_∗_</sup> ( _x_ ( _e_ ) _, e_ ). Equating the quantity of available land with the number of “successful buyers” results in _dx_ = _π_<sup>_∗_</sup> ( _x_ ( _e_ ) _, e_ ) _Nde_ . Solving this differential equation requires an initial condition given by _x_ (0) = 0 since we consider the case in which households are ordered by type.

We now determine the thresholds _<u>e</u>_ <u>,</u> _<u>x</u>_ <u>,</u> _<u>e</u>_ and _<u>x</u>_ which characterize city structure. The resolution is presented graphically on Figure 4 which superimposes the mapping _x_ ( _e_ ) and the tenure threshold functions represented on Figure 2b. The intersection between _<u>x</u>_ ( _e_ ) and _x_ ( _e_ ) gives _<u>e</u>_ and _<u>x</u>_ <u>.</u> Figure 4 shows that for any household with _e <_ _<u>e</u>_ <u>,</u> we have _x_ ( _e_ ) _<_ _<u>x</u>_ <u>(</u> _e_ ) and _π_<sup>_∗_</sup> ( _x, e_ ) = _πmax_ . Therefore, _x_ ( _e_ ) = _πmaxNe_ for _e <_ _<u>e</u>_ <u>.The</u> intersection of _x_ ( _e_ ) with _<u>x</u>_ ( _e_ ) gives _<u>e</u>_ and _<u>x</u>_ <u>.</u> For a revocable permits to occupy (known as “precarious titles”), which stand in between the absence of any statutory right (very insecure tenure) and the registered ownership title (very secure tenure).

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<!-- Start of picture text --> x<br>x �e�<br>x �e�<br>x<br>x<br>x�e�<br>e<br>e e<br><!-- End of picture text -->

**Figure 4:** Determination of tenure category zones in the city

household with _e >_ _<u>e</u>_ , we have _<u>x</u>_ <u>(</u> _e_ ) _< x_ ( _e_ ), such that they purchase land in the insecure portion of the city and have tenure security _πmin_ . For _e >_ _<u>e</u>_ , _x_ ( _e_ ) is a linear function of slope _Nπmin_ . Finally, for households with _<u>e</u> < e <_ _<u>e</u>_ , we have _<u>x</u>_ <u>(</u> _e_ ) _< x_ ( _e_ ) _<_ _<u>x</u>_ <u>(</u> _e_ ), implying that they reside in the precarious portion of the city and demand intermediate levels of tenure security.

# **3.3.3 City composition and urban fringe**

Figure 4 represents the type/location mapping as if all households in the economy purchased a plot in the city. There is no reason for this to be the case in equilibrium and we need to determine which households purchase land and the spatial extent of the corresponding market (which will define the true domain of definition for the mapping function). There are two conditions that characterize the city fringe. First, by definition of the land market equilibrium, there is no discontinuity in rural and urban land prices at the city fringe _xf_ . The second condition is the open city assumption, requiring that household of type _ep_ located at the urban fringe at the equilibrium (or the “last” household purchasing land in the city) is indifferent between purchasing a plot at the urban fringe and not attempting migration. These conditions are given by Equation (11).

To show the existence of _ep_ , we write the indirect utility of a household _e_ purchasing 18
a plot at the city fringe, using Equation (11) and the mapping function _x_ ( _e_ ).

We then differentiate this expression with respect to _e_ . Using the envelope theorem, we obtain Equation (12) which is is always negative given that<sup>_<u>dx</u>_</sup> _de_<sup>(</sup><sup>_e_)</sup><sup>_>_0.</sup> The unique value _ep_ is such that all households with a smaller _e_ purchase land in the urban area, whereas all others do not attempt migration.<sup>14</sup> Depending on the value of _ep_ relative to _<u>e</u>_ and _<u>e</u>_ as previously defined, the sections of the city described in Proposition 4 may or may not exist. _ep_ determines the city fringe _xf_ through Equation (13).<sup>15</sup> The urban fringe is represented on Figure 5. It is not possible to come up with an analytical expression for the city fringe except in the particular case when the cost of buying minimal tenure security is the same for all households ( _C_ ( _πmin, e_ ) = _C_ ( _πmin_ )) and the three tenure zones exist <u>(</u> _<u>e</u> < ep_ ). In this case we can derive an explicit value for _xf_ by solving Equation (11) considering that _R_ ( _xf_ ) can be written as Ψ _e_ ( _x, ν_ ( _e_ )) (as given by Equation (7) with _x_ = _xf_ , _π_<sup>_∗_</sup> = _πmin_ and _ν_ ( _e_ ) = _yr − Ra_ ).<sup>16</sup>

# **3.3.4 Land prices and utilities**

We determine the utilities _ν_ ( _e_ ) and the land-rent curve _R_ ( _x_ ) (which is defined as the upper envelope of bid rents in equilibrium). The utilities of a continuum of households are determined using an equilibrium condition which states that the

> 14 _ep_ is equal to 1 if for all values of _e_ , _ν_ ( _e_ ) _|R_ ( _x_ ( _e_ ))= _Ra > yu − Ra_ .

> 15Because of unit land consumption, _xf_ is also the number of “successful buyers”.

> 16We obtain _xf_ =<sup>_<u>y</u>_</sup> _<u>u</u>_<sup>_−_</sup> _t_<sup>_<u>y</u>_</sup> _<u>r</u> −_<sup>_Ra_</sup><sup><u>(1</u></sup><sup>_−πmin_</sup> _tπmin_<sup><u>)+</u></sup><sup>_C_</sup><sup><u>(</u></sup><sup>_πmin_</sup><sup><u>)</u></sup> , where the second term is negative. In this particular case, urban extent is thus smaller than in the standard model with complete tenure security where it can be shown that the city extends up to _xf_ =<sup>_<u>yr−</u>_</sup> _t_<sup>_<u>yu</u>_</sup> . This property bears no generality as simulations outside this particular case exhibit situations in which the urban extent is larger in our model.

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<!-- Start of picture text --> x<br>x f<br>x<br>x<br>e<br>e e e p<br><!-- End of picture text -->

**Figure 5:** Determination of the city fringe

mapping _x_ ( _e_ ) is consistent with land being allocated in equilibrium to highest bids: This reflects competition for land and trivially holds on the secure and insecure portions of the city since households which purchase land in those zones have the same bid-rents. In what follows, we assume that all three zones exist<sup>17</sup> <u>(</u> _<u>e</u> < ep_ ) and consider each zone sequentially, starting with the most remote, and apply land-rent and expected utility continuity at the thresholds identified in Proposition 4.

# **The insecure tenure zone**

In the insecure zone [ _<u>x, xf</u>_ ], households of type _e ∈_ [ _<u>e, ep</u>_ ] purchase land with the lowest level of tenure security _πmin_ . Equation (15) gives their bid-rent.

Since all households have the same bid rent over <u>[</u> _<u>x, xf</u>_ ], Equation (15) is also the analytical expression for _R_ ( _x_ ) on this portion of the city. The border condition equates the urban and rural rents at the fringe, such that rent and utility are given

> 17A similar approach can be applied in the other configurations with less than three zones.

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by Equation (16) with _K_ 1 = _πmin_ ( _yu − xf t_ ) + (1 _− πmin_ )( _yr − Ra_ ) _− Ra_ .

# **The precarious tenure zone**

Households of type _e ∈_ [ _<u>e, e</u>_ <u>] purchase land in the precarious section of the city [</u> _<u>x, x</u>_ <u>]</u> and choose intermediate values for _π_<sup>_∗_</sup> . Each household’s location is given by the mapping _x_ ( _e_ ) and must satisfy Equation (14). We derive the first order condition of Equation (14) by considering Equation (7) for _x_ = _x_ ( _e_ ) and differentiating the resulting expression with respect to _e_ .<sup>18</sup> Using the envelope theorem, we find that the first order condition of Equation (14) is equivalent to Equation (17).

Solving this differential equation determines _ν_ ( _e_ ) for all _e ∈_ [ _<u>e, e</u>_ <u>]</u> and enables us to determine _R_ ( _x_ ), which is continuous in _<u>x</u>_ due to the continuity of _ν_ in _<u>e</u>_ .

The function _ν_ ( _._ ), defined in Equation (18), is continuous such that _K_ 2 = _−C_ ( _πmin,_ _<u>e</u>_ ) + _K_ 1. The mapping is an invertible function over <u>[</u> _<u>e, e</u>_ <u>]</u> and its inverse is _e_ ( _x_ ), such that the bid-rent over <u>[</u> _<u>x, x</u>_ <u>]</u> is given by Equation (19).

_R_ ( _x_ ) = _π_<sup>_∗_</sup> ( _x, e_ ( _x_ ))[ _yu−xt_ ]+[1 _−π_<sup>_∗_</sup> ( _x, e_ ( _x_ ))][ _yr−Ra_ ] _−C_ ( _π_<sup>_∗_</sup> ( _x, e_ ( _x_ )) _, e_ ( _x_ )) _−ν_ ( _e_ ( _x_ )) (19)

# **The secure tenure zone**

Households of type _e ∈_ [0 _, e_ <u>] purchase land over [0</u> _, x_ <u>] and choose</u> _π_<sup>_∗_</sup> = _πmax_ . Their bid rents are given by Equation (20).

Since their bid rents are confounded in the secure zone, we equate Ψ( _<u>x, ν</u>_ ( _e_ )) 18 Differentiating a second time with respect to _e_ , rearranging the terms, and using (10), we can show that the second order condition always holds.

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and Ψ( _<u>x, ν</u>_ <u>(</u> _<u>e</u>_ <u>)).</u> This yields _ν_ ( _e_ ) + _C_ ( _πmax, e_ ) = _ν_ <u>(</u> _<u>e</u>_ <u>)</u> + _C_ ( _πmax, e_ ) where _ν_ <u>(</u> _<u>e</u>_ <u>)</u> is provided by the limit when _e →_ _<u>e</u>_ +<sup>ofthefunction</sup><sup>_ν_over</sup><sup><u>[</u></sup><sup>_<u>e</u>_</sup> _,_ _<u>e</u>_ ]. Plugging _ν_ <u>(</u> _<u>e</u>_ ) + _C_ ( _πmax, e_ <u>)</u> back into Equation (20) and using Equation (18) to express _ν_ <u>(</u> _<u>e</u>_ ), we obtain Equation (21) with _K_ 3 = _C_ ( _πmax, e_ <u>) +</u> � _<u>ee ∂C∂e</u>_<sup>[</sup><sup>_π∗_(</sup><sup>_x_(</sup><sup>_e_)</sup><sup>_, e_)</sup><sup>_, e_] +</sup><sup>_K_2.</sup> _R_ ( _x_ ) = _πmax_ ( _yu−xt_ )+(1 _−πmax_ )( _yr−Ra_ ) _−K_ 3 and _ν_ ( _e_ ) = _−C_ ( _πmax, e_ )+ _K_ 3 (21) The land market equilibrium is represented in Figure 6 below.<sup>19</sup> Other aggregates from the model such as the utilities, the land administration’s revenue and the total income of landowners are presented in Appendix C.

<!-- Start of picture text --> R�x�<br>x<br>Secure x Precarious x Insecure x f<br><!-- End of picture text -->

**Figure 6:** The equilibrium land rent _R_ ( _x_ ) and the threshold values _<u>x</u>_ <u>,</u> _<u>x</u>_ <u>,</u> and _xf_

> 19The predictions of our model that more secure forms of tenure are located closer to the city center and that the price gradient is steeper for secure forms than for insecure forms of tenure are confirmed by an empirical study of land transfers in Bamako, Mali (Durand-Lasserve et al., 2015). To our knowledge, it is the only study so far which has documented the spatial patterns of the continuum of tenure rights at the scale of a single city.

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# **4 Comparative statics**

## **4.1 Population, transport costs and wage differentials**

We discuss here the effects on city patterns of marginal changes in the parameters of the model (see the demonstrations in Appendix D). We consider a growing population ( _dN >_ 0), decreasing unit transport cost ( _dt <_ 0) and a rising urban income relative to the rural income ( _d_ ( _yu − yr_ ) _>_ 0), which effects are presented in Table 1 below. We are able to determine how changes in the values of these parameters affect the size and the composition of the secure zone of the city but the effects on the precarious and insecure zones are in several instances ambiguous.

We find that an increase in the overall population leads to an increase in the size _<u>x</u>_ of the secure section of the city but to a decrease in the share _<u>e</u>_ of households purchasing secure property rights. This is because an increase in _N_ increases the number of well-connected households purchasing land close to the city center, pushing away other households towards the periphery of the city where they choose lower levels of tenure security. If transport costs are reduced, or the urban rural wage differential is increased, the size of the formal section of the city will also increase but the share of households in the secure section of the city will in this case increase rather than decrease. This is because these variations in transport costs or wages increase the gains a household can expect from purchasing land in the city, providing households with an incentive to purchase higher levels of tenure security for any given location, which inflates both the zone over which households purchase secure rights and the share of households doing so.

In the specific case where the city has three zones, we show that city size _xf_ increases with the urban rural wage differential and as the unit transport cost decreases (as the city becomes more attractive). On the other hand, the share _ep_ of households purchasing land in the city decreases as _N_ or _yu − yr_ increase, or when _t_ decreases, reflecting the fact that households with a smaller _e_ are taking up more space (either because they are more numerous or because they demand more secure tenure).

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**Table 1:** Comparative statics

||**Population**<br>_dN >_0|**Transport costs**<br>_dt <_0|**Wage diferential**<br>_d_(_yu −yr_)_>_0|
|---|---|---|---|
|**dx**|+|+|+|
|**de**|_−_|+|+|
|**d**<br>**x**|+|+|+|
|**d**<br>**e**|_−_|?|?|
|**dxf**|0|+|+|
|**dep**|_−_|_−_|_−_|

General case for _<u>x, e, x</u>_ and _<u>e</u>_ <u>;</u> city with three zones for _xf_ and _ep_ .

# **4.2 Land administration policies**

The key parameter in the model which affects city patterns is _C_ ( _π, e_ ), which describes the cost paid by a household _e_ to establish a property right ensuring security _π_ over a plot of land. This parameter is a function such that it is difficult to say anything about how variations of _C_ affect the city structure and the land market in the general case. To get some grip on this question, we parameterize _C_ and resort to simulations to illustrate the predictions of our model and the likely _general equilibrium effects_ of policies.

We specify the cost function _C_ ( _e, π_ ) as a function of two parameters _K_ and _θ_ which affect the “level” and “equity” of the cost function. The details of the simulations are given in Appendix E.

The base case scenario is constructed assuming that the administration serves the interests of a small elite. Examples of such clientelism abound in many different countries (Van der Molen and Tuladhar, 2007; Deininger and Feder, 2009) and it makes sense to make this situation the initial stage or benchmark from which we will explore the desirability and feasibility of policies. The base case is obtained by maximizing the expected welfare of the best-connected household _e_ = 0. We find 24
that _the well-connected households benefit from a land administration that treats households as unequally as possible_ . This is due to a pecuniary externality: the more expensive tenure security is made for higher types, the smaller their demand for tenure security and the more depressed their bid rents (because of the negative tenure insecurity premium which materializes in the form of a flatter bid-rent). In this context, it is thus easier for lower types to bid away higher types to the periphery of the city without having to bid too much for central locations (prices are depressed throughout the city and _in fine_ the land rent in _x_ = 0 is low). In a sense, the land administration makes land available under advantageous conditions for the elite while protecting them from the competition of others on the formal segment of the market.

# **4.2.1 More affordable property rights**

It is often argued that excessive land administration fees push people into informality. To explore this argument within the framework or our model, we simulate a policy that makes fees smaller without making them less inequitable. There are three interesting impacts we can highlight from those simulations (see Appendix E for the details). Making land administration fees more affordable results in:

1. _An increase in (and displacement of) the spatial extent of the secure and precarious sections_ at the expense of the insecure zone.

2. _An increase in land rents associated with tenure security improvement_ . This comes from the shrinking of the insecure portion of the city, which pushes all prices up, and the capitalization in land prices of more secure tenures over the precarious and secure portions of the city.

3. _A disparate effect on the expected utility_ . The expected utility of households in the “social vicinity” of the land administration decreases because of the higher land rents they now face. The expected utility of households residing in the secure and precarious sections of the city increases, as the decrease in the cost of acquiring secure property rights outweighs increase in land rent they face.

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# **4.2.2 More equitable property rights**

It is often advocated to increase transparency in the land administration in order to avoid bribes and discretionary treatment. We simulate such a policy by making the land administration more equitable, without making them less expensive for the median household, but increasing them for the low _e_ households and decreasing them for the high _e_ households (see Appendix E for the details). Making land administration fees more equitable results in:

1. _A larger precarious section of the city_ at the expense of both the spatial extent of the secure and insecure sections of the city.

2. _A nuanced effect on rent curves_ . At the periphery of the city, locations held under insecure tenure under the base case are now held under precarious tenure, which raises the price of land for these plots and exerts an upward pressure on land rents in more central locations. But because of increased fees, households who formerly had secure tenure now demand lower tenure security. There is thus a countervailing force towards the decrease in land prices for central locations.

3. _A nuanced effect on expected utility_ . Households who have switched from insecure to precarious tenure (in the middle of the distribution) experience an increase in expected utility, whereas household with lower types face a decrease in their expected utility due to an increase in tenure costs (which may result in the choice of a lower level of tenure security) which is not completely compensated by the decrease in land rents in more central locations.

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# **5 Conclusion**

In this paper, we introduced an endogenous choice of property rights in the standard urban land use model. To our knowledge, this is the first attempt to build a theory of residential informality that allows for a continuous spatial representation of the urban space under endogenously determined land prices. The result is an augmented monocentric land use model which generates the standard urban economics model as a particular case under the assumption of costless and fully secure property rights. Considering the more general case where property rights are costly and provide only limited tenure security, we proposed a suitable framework to analyze urban land markets and land tenure patterns in developing countries. Our approach makes the following four contributions: First, analyzing land tenure from a systemic perspective shifts the focus from an analysis of informal land markets in isolation from formal land markets to one where the formal and the informal sectors interact: In our model, although households may hold land under a continuum of tenure situations (from very insecure to very secure), they compete for land over the same city. A previous theoretical paper to have explored such interactions was Brueckner and Selod (2009) who argued, in a context of inelastic land supply, that the greater the informal squatting sector in a city, the greater the prices in the formal sector because of a “squeezing effect” (due to squatters settlements using up scarce land in the city). The assumptions in the present model, however, are different as land supply is not restricted and because informal dwellers are not squatters but actually pay a competitive price to use land under a chosen level of tenure security. Interestingly, holding city size constant, the predictions of our spatial model differ from Brueckner and Selod (2009): Because of competition for land and the lower value put by the market on insecure tenure, informal tenure in peripheral locations contributes to depressing rather than increasing land prices in central locations where formal housing locates.<sup>20</sup>

> 20Cai et al. (2018) also model the interaction between formal and informal land use in a spatial equilibrium but this is done in a simplified framework that does not account for the direct capitalization of tenure insecurity in land prices.

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A second lesson to be derived from the model is the central role of land administration fees in shaping cities. In line with recent research measuring the elasticity of demand for property rights with respect to regularization or registration fees (Monkkonen, 2012; Ali et al., 2013), our model suggests that land administration fees, which can reach the same order of magnitude as land prices, can significantly alter the tenure choices and location decisions of households within a city. The systemic approach also highlighted that land policies may entail responses from land markets that affect households beyond the targeted populations, with possible trade-offs regarding who benefits from the policy. An important implication for policy makers should thus be whether pricing by the land administration is compatible with urban planning objectives. Further studies on the willingness to pay of households for property rights, and on the impact of land administration fees on land markets will certainly be needed.

A third lesson is that clientelism in the land administration may determine _who_ has access to secure land in the city. In our model, a political elite benefits from imposing costly fees to others in order to weaken competition for land in the formal sector. This result is in line with the theoretical finding of Sonin (2003) who, in a different context, argues that the rich and the poor have different preferences for property rights institutions. Although political scientists and urban economists have long studied how cities serve political clienteles (Ades and Glaeser, 1995), discrimination in the land administration and how it affects city patterns and composition has been little studied. More generally, empirical studies that identify the losers and winners from the complex processes and barriers to obtain secure land in the cities of developing countries would be very useful. In this respect, Durand-Lasserve et al. (2015) highlight the disproportionate role of expatriates, (rich) merchants and (well-connected) civil servants in land purchases in Bamako, Mali, but further studies are needed.

Finally, linked to the previous comments, our analysis suggests that if governments want to improve access to secure land, improving the land institutions themselves should be a prerequisite. Whereas efforts to improve transparency in land administrations have been successful in some countries, they have failed or faced lack of 28
political will in other countries, especially in sub-Saharan Africa. Further thinking on the conditions that make a transition towards transparent and affordable land administrations possible is needed. More generally, studies on the political economy of the urban land sector are warranted. We leave these important issues for further research.

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