The political economy of rural property rights and the persistence of the dual economy

Journal of Development Economics 103 (2013) 167–181

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The political economy of rural property rights and the persistence of the dual economy Leopoldo Fergusson ⁎ Universidad de los Andes, Facultad de Economía, Calle 19A No. 1-37 Este Bloque W, Of W-812, Bogotá, Colombia

a r t i c l e

i n f o

Article history: Received 1 July 2010 Received in revised form 1 November 2012 Accepted 7 February 2013 JEL classification: H2 N10 O1 O10 P16

a b s t r a c t Rural areas often have more than one regime of property rights and production. Large, private-property farms owned by powerful landowners coexist with subsistence peasants who farm small plots with limited property rights. At the same time, there is broad consensus that individual, well-specified and secure property rights over land improve economic outcomes. If property rights in land are so beneficial, why are they not adopted more widely? I put forward a theory according to which politically powerful landowners choose weak property rights to impoverish peasants and force them to work for low wages. Moreover, because weak property rights force peasants to stay in the rural sector protecting their property, the incentives to establish poor property rights are especially salient when peasants can migrate to an alternative sector, such as when urban wages increase with industrialization. © 2013 Elsevier B.V. All rights reserved.

Keywords: Political economy Institutions Economic development Taxation Property rights Land Dualism

The fact that the wage level in the capitalist sector depends upon earnings in the subsistence sector is sometimes of immense political importance, since its effect is that capitalists have a direct interest in holding down the productivity of the subsistence workers (…) In actual fact the record of every imperial power in Africa in modern times is one of impoverishing the subsistence economy, either by taking away the people's land, or by demanding forced labour in the capitalist sector, or by imposing taxes to drive people to work for capitalist employers. Sir W. Arthur Lewis, 1954

1. Introduction In many less-developed countries, property rights over land are poorly specified and weakly enforced. More specifically, rural areas in developing countries throughout history, and even today, often have ⁎ Tel.: +57 1 339 4949x2439; fax: +57 1 332 4492. E-mail address: [email protected]. 0304-3878/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jdeveco.2013.02.009

more than one regime of property rights and production. A more “modern” group of “capitalist” landowners, with large, private-property farms, coexists with a more “traditional” or “subsistence” group of peasants, who farm small plots with limited property rights. At the same time, there is broad consensus that individual, wellspecified and secure property rights over productive assets, and land in particular, improve economic outcomes. Thus the “dual” structure of the agricultural sector may reduce productivity, and raises some key questions: Why aren't strong, private property rights adopted more widely? Why did this structure emerge and persist? In this paper, I examine these questions and put forward a theory of endogenous rural property rights. The main message is that politically powerful landowners may choose weak property rights to impoverish peasants and force them to work for low wages. Moreover, I show that the incentives to do this are especially salient when peasants can migrate to an alternative sector, such as when urban wages increase with industrialization. In the model economy, the elite owns land and holds political power and uses this power to tax peasants and establish property rights institutions governing peasant farms. Peasants, on the other hand, are the only source of labor. They can work on their own farms, for the rural elite, or migrate to an alternative sector. While

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L. Fergusson / Journal of Development Economics 103 (2013) 167–181

this sector may be any other that competes with landowners for labor and requires peasants' outmigration, it is natural to think of it as the “urban sector” and to associate an increase in the urban wage with “modernization”. When choosing property rights, the elite faces the following trade off. On the one hand, weak property rights on peasant plots may increase landowner profits either by forcing peasants to remain in the agricultural sector to protect their property – “tying” peasants to the land – or by reducing productivity in peasant plots, thus reducing peasant income. These two effects increase peasants' willingness to work for the elite, reducing wages and increasing elite profits. On the other hand, since weak property rights reduce agricultural productivity, they also reduce the elite's tax revenues. Maximizing tax revenues thus compels the elite to establish strong property rights, but maximizing farm profits creates incentives to establish weak property rights. The model's key predictions concern the conditions under which the elite establishes weak property rights. The key parameters influencing this decision are urban wages, peasant plot size, and the elite's fiscal capacity (ability to raise taxes). The model predicts that when urban wages are low, strong property rights prevail as long as landowners can effectively tax peasants. Intuitively, setting weak property rights destroys economic surplus. It is preferable not to create this inefficiency, and instead promote efficient production and tax the returns. Moreover, when the elite taxes peasants, this not only creates direct benefits from tax revenues, it also reduces the income peasants receive from working their own plot. Peasants become more willing to work the landowner's plot for lower wages thus increasing landowner profits. The implications of high urban wages are markedly different. High wages provide peasants with an alternative option in the urban sector. With the effective threat of migration, imposing taxes on peasant's income no longer induces them to work for landowners at low wages. Instead, it reduces the attractiveness of rural areas and the ensuing migration decreases labor input for landowners. Thus, when hoping to avoid labor force migration, the elite chooses minimal taxation and tax revenues account for a lesser portion of total landowner income, muting incentives to adopt strong property rights. To avoid migration and extract more labor from peasants, the elite selects weak property rights institutions. This logic prevails when peasants own little land. If peasants own sufficient land, however, taxable income from peasant farms is high enough that the elite assigns greater importance to resources from taxation. Thus, to increase tax revenues, the elite promotes strong property rights for peasants. This logic also implies a non-monotonic, U-shaped relationship between the quality of rural property rights and peasant land. Recall that if peasants own little land, the elite selects poor property rights and no taxation to stop peasant migration to the cities. Notice also that if peasants' landholdings increase, they work more on their own plots and less for landowners. This initially strengthens the rural elite's incentives to weaken property rights in order to extract labor. However, if peasant landholdings continue to increase, at some point peasant income is large enough that the elite prefers to tax part of it, even if this creates some migration. At this point, the elite is better off promoting strong property rights institutions to increase tax revenues. This paper is related to several strands of literature. By proposing a specific mechanism for the endogenous persistence of “bad” rural institutions as development unfolds, it contrasts with other theories of the dual economy in which the disappearance of the peasant subsistence sector is a natural consequence of capital accumulation. In this sense, my paper relates to underdevelopment theories of the “dependency” tradition, most notably applied to Africa1. As Clarke (1975) puts it, in these theories: “the ‘traditional’ social forms are not simply relics of the past but have been necessary and integral to the development,

1

See Phimister (1979) for a historiographical essay.

maintenance and reproduction of peripheral capitalism (…). The state, continues to support such ‘traditional’ structures [which] have been made thoroughly modern, poor, and dependent” (p. 75). I argue that weak property rights are a particularly relevant way of impoverishing the ‘traditional’ peasant economy. The underlying reason why weak property rights may be preferred by the elite is the fact that they ‘tie’ peasants to the land. The importance of deterring rural–urban migration in order to lower rural wages is explicitly illustrated by the direct restrictions on peasant migration (vagrancy laws, labor passes, etc.) used by elites in China, Latin America and many parts of Africa. Yet the role of weak property rights has received comparatively little attention2. The idea that weak, informal property rights may tie households to their property and affect labor market decisions is studied in a different context by Field (2007). More generally, De Soto (1989, 2000) famously emphasized barriers to legal property ownership of assets in developing countries as a major obstacle to prosperity. However, these papers are vaguer about the causes of such extralegality. This paper, while emphasizing the factor market consequences of imperfect property rights, focuses on their political economy determinants and argues that property rights are intentionally precarious. A few papers have provided formal models in which poor property rights may be intentionally encouraged by elites. However, the arguments I put forward are distinct. Besley and Ghatak (2010a), for example, explore the consequences of creating and improving property rights so that fixed assets can be used as collateral. Imperfect property rights may in effect protect borrowers from lenders who force them to put up more of their wealth as collateral. Hence, borrowers may oppose improving property rights. Diaz (2000) argues that rural elites grant land with poorly defined rights and low productivity in order to “destroy” this land. This strategy profits landowners under sufficiently strong complementarity of land and labor and sufficient land abundance. However, many other distortions imposed on granted land have similar consequences. In contrast, the attractiveness of poor property rights in the theory I propose depends on a characteristic that distinguishes this distortion from others: it simultaneously affects the productivity of the sector and the cost of migration to other sectors. Sonin (2003) offers a theory more focused on property rights, though his emphasis is not on the rural sector or land. He uses the Russian case to argue that the rich have a comparative advantage in the private provision of property rights. Hence, poor definition of property rights for a wide cross section of the population allows them to use this comparative advantage to predate from the poor. On a more general level, the paper is related to the literature on endogenous institutions and institutional persistence. It concurs with the political economy or “social conflict” view which contends that inefficient institutions arise and persist because powerful political groups support them (Acemoglu et al., 2005). The paper is closely related, both in following this approach and in the formal analysis, to Acemoglu (2006). The paper proceeds as follows. In Section 2, I lay out the basic setup of the model. Section 3 describes the economic equilibrium for a given set of institutions. Next, Section 4 characterizes the equilibrium institutions by finding the political equilibrium and describes the main results. Section 5 discusses a simple but important extension to the baseline model. Section 6 offers an historical discussion on the relevance of some of the model's assumptions and predictions, using the case of Rhodesia. Section 7 concludes with some final thoughts.

2 For instance, it is not part of the list suggested by Binswanger et al. (1995) (or Binswanger and Deininger (1993) for the specific case of South Africa). But the mechanism has not been completely neglected, and Binswanger and Deininger (1993) recognize its relevance when they note: “A further distortion against black African farming was the excessively restrictive ‘traditional’ communal tenure system imposed by successive land laws [in South Africa], the first and most important of which was the Glen Grey Act of 1894” (p. 1461).

L. Fergusson / Journal of Development Economics 103 (2013) 167–181

2. A model of (poor) property rights in the (dual) rural economy Consider a society with three sectors. The urban sector (denoted by U) and two rural or agricultural subsectors: the elite sector (E) and the peasant sector (P). The rural sector as a whole is denoted by R. I now describe these sectors and set the basic notation. 2.1. The rural sector In the rural sector R there are two types of producers. Landowners controlling the elite subsector E are politically powerful and own most of the land in society, but have no labor of their own. Subsistence farmers in the peasant sector P face the opposite situation: while their political power and ownership of land is limited, they are the sole suppliers of labor in society. The political power of the elite translates into the ability to select two key variables: taxation and property rights protection in the rural peasant sector. There are L peasant households in the economy, each possessing a unit of labor, and the size of the elite is normalized to 1. Peasants may remain in the rural areas or migrate to the urban sector. I denote the number of migrating households with m. Each household i in the rural areas allocates a share ei of its labor input to the peasant sector and the rest to the landowner sector. Total labor input in the rural sector is defined as LR = L − m, and in the peasant subsector as LP = ∑i ∈ Rei. Since landowners own no labor, the labor input in their farms amounts to total peasant input, LE = LR − LP. Landowners hire labor and pay a wage rate wE, which they take as given. Total land amounts to T hectares. Out of these, t hectares are controlled by peasants and the rest by the elite. For simplicity, I assume each peasant household has the same initial endowment of t/L units of land. 2.1.1. The elite subsector The elite agricultural sector consists of a representative landowner with the following production function: F ðT−t; LE Þ ¼

1 1−α α ðT−t Þ LE ; α

where α ∈ (0,1). The consumption of a representative member of the elite is the sum of farm profits (πE) and a lump-sum transfer G: cE ¼ π E þ G; ¼ ½F ðT−t; LE Þ−wE LE  þ G: Notice that in the expression for cE there are no taxes imposed on the elite's farm income, as elite members would never tax themselves. 2.1.2. The peasant subsector The rural subsistence sector has potentially weaker property rights institutions than the elite sector. Thus, a key assumption concerns the impact of property rights. In the model, I assume that a weakening of “property rights” produces two effects present in various definitions of the term. First, it increases the cost of migration. Weakened property rights (less security against expropriation, absence of selling or renting rights, or land use rights contingent on staying on the land as in many communal systems) create additional migration costs. Second, it reduces peasant productivity. Previous work justifying this assumption is summarized by Besley and Ghatak (2010b).3 3 Besley and Ghatak (2010b) divide these arguments into two broad categories: First, secure property rights limit expropriation, incentivizing investment and effort and reducing resources diverted for protection. Second, well-defined individual rights facilitate market transactions, improving the ability to collateralize assets (which may ease credit constraints that hinder investments) and generating gains from trade (by making sure land is held by the most productive owner).

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Property rightsh in the i peasant sector are therefore captured by a positive scalar μ∈ μ ; 1 , with μ small (i.e. μ ≈0). A larger μ increases the productivity of the subsector and the cost of migration. To capture the impact on productivity, I consider a reduced-form formulation and assume that each household's output in the peasant sector is given by   1  P 1−α α P x Aðμ Þf xi ; ei ¼ Aðμ Þ ei ; α i where xiP is the land input (with ∑i ∈ RxiP = t). Also, I assume A(μ) = μ. Adopting this functional form simplifies the analysis and satisfies two key properties: First, that property rights increase productivity (A′(μ) > 0); and second, that the elite and peasant sectors are equally productive under full property rights (A(1) = 1). To capture the impact of property rights on migration costs, I assume that a migrating peasant household can rent its land, but poorly defined property rights facilitate expropriation of this land upon migration. Hence, if r is the prevailing rental rate of peasant land, the migrating household will only get μ Lt r as rental income. The remaining fraction (1 − μ) may be expropriated and shared among all nonmigrating peasants. The rental rate of land in the peasant sector is taken as given by individual peasants. Peasants cannot rent land from landowners nor to them. Note also that vacant land is shared by peasants, not landlords 4. Consumption of non-migrating peasants is the sum of farm profits and wages (πiS) and any potential land rents expropriated from migrating households. Unlike elite farmers, peasants may face positive taxes τ on farm revenue, and they receive no redistribution (the elite will rationally transfer no tax revenues to peasants). Therefore, consumption for a member of the LR peasants is:

m t ciP ¼ πiS þ ð1−μ Þr L L R       t m t ¼ ð1−τÞAðμ Þf xPi ; ei − xPi − r þ ð1−ei ÞwE þ ð1−μ Þr : L LR L

Notice that peasants receive farm revenue, pay out any net land use at the rental rate r, and receive wage payments from landowners. These are the three components in πiS. The last term in ciP is the share 1 − μ of land rents expropriated from the m migrating households and shared by the LR non-migrating households. The maximized value of ciP is the value of remaining in the rural areas, VR, and is thus crucial in determining the migration decision. 2.2. The urban sector In the urban sector, workers are paid an exogenous wage wU. It is useful to think of this sector as the urban or industrial sector, but it could represent any additional sector that competes with the landowner for labor. The crucial assumption is that peasants must migrate to the U sector and cannot work in the agricultural sector simultaneously (i.e., a peasant leaves with his entire unit of labor). The urban wage is assumed exogenous for simplicity. A more realistic formulation would recognize that urban wages fall with rural– urban migration. In Section 5, I briefly discuss the effects of extending the model in this direction. The most important results, however, do not depend crucially on this assumption.

4 This assumption stacks the deck against the results of the model, as landlords would clearly have a direct interest in poor property rights if they were also allowed to appropriate vacant land.

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These assumptions, together with the fact that a share 1 − μ of land rents are lost upon migration, imply that the value of going to the urban sector, VU, is given by t V U ¼ wU þ μ r: L

ð1Þ

  t m V R ¼ wE þ r 1 þ ð1−μ Þ : L LR

2.3. The game The government's budget constraint, which states that total tax revenues from taxation of peasant income equals transfers to the elite, completes the description of the environment. It is given by: G ¼ τAðμ Þf ðt; LP Þ:

ð2Þ

I assume an upper bound τ on taxation, with τ≤1, for example, because producers can hide each dollar of income at a cost of τ. Consider the following simple game: 1. A representative agent of the landowning elite chooses tax policies τ and a level of property rights protection μ, with G given by the government budget constraint. 2. Peasants compare the value of moving to the urban sector VU with the value of staying in rural areas VR, and decide whether or not to migrate to the city. 3. Producers in rural areas maximize their consumption. Non-migrating peasants choose labor and land inputs in the peasant sector (ei and xi) to maximize consumption ciP. Landowners hire labor LE to maximize consumption cE. Labor markets are competitive and all agents take the wage rate wE as given. Stages 2 and 3 determine the economic equilibrium of the model for a given set of policies. This is the focus of Section 3. The elite's incentives to alter this economic equilibrium via their choice of policies in Stage 1 give us the political equilibrium, which is analyzed in Section 4. 3. Economic equilibrium To characterize the economic equilibrium, consider the landowners' problem in the third stage. They choose optimal labor demand LE to maximize consumption cE. The first-order condition for this problem equates marginal productivity to the wage: F 2 ðT−t; LE Þ ¼ wE :

ð3Þ

Each of the LR non-migrating peasants, in turn, chooses land and labor inputs (xiP and ei) in the peasant sector to maximize consumption ciP. The optimal choice satisfies the usual pair of first-order conditions specifying equality between each factor's marginal productivity and its price for all i ∈ R. These conditions can be expressed as those of a representative peasant with access to t units of land, hiring Lp = L − m − LE units of labor: ð1−τÞAðμ Þf 1 ðt; L−m−LE Þ ¼ r;

ð4Þ

ð1−τÞAðμ Þf 2 ðt; L−m−LE Þ ¼ wE :

ð5Þ

For a given migration m, Eqs. (3) and (5) determine the amount of rural labor peasants allocate to landowner and peasant farms (LE and LP). More precisely LE(m) satisfies: F 2 ðT−t; LE ðmÞÞ ¼ ð1−τÞAðμ Þf 2 ðt; L−m−LE ðmÞÞ≡wðmÞ:

ð6Þ

where the last term defines the resulting equilibrium rural wage, a monotonic and increasing function of migration 5. 5

Similarly, r(m) ≡ (1 − τ)A(μ)f1(t,L − m − LE(m))

To complete the description of the economic equilibrium, only the level of migration remains to be established. In the second stage, peasants continue to migrate as long as VU > VR, otherwise they remain in rural areas. Recall VR is the optimal value of ciP. This can be written using the homogeneity of degree zero of f and competitive markets (Eqs. (4) and (5)) as the sum of labor and land rents: ð7Þ

In the last term of Eq. (7), there are two components of rural land rent income: rents from the initial endowment and land left behind by migrant households. Of course, if either no one migrates (m = 0), or there are perfect property rights for migrating households (μ = 1), the second component of land rents vanishes. Starting with a situation in which VU = VR, migration will continue until VU = VR, or   t m t wE þ r 1 þ ð1−μ Þ ¼ wU þ μ r: L LR L   Grouping terms, this can be written as: wE −wU ¼ Lt r ð1−μ Þ 1 þ LmR : Finally, recalling that LR + m = L we rewrite the last term as L/LR and simplify: wU −wE ¼ ð1−μ Þ

t r: LR

ð8Þ

This equation states that at the optimal level of migration, the wage gain from moving to the city wU − wE equals the loss in land rents ð1−μ Þ LtR r. This loss arises due to imperfect property rights in the sense that migrating households do not get the full value of the rent from their land. Clearly, with μ = 1 there is no such loss; the no-migration condition simplifies to wU − wE. Of course, it is possible that VU b VR at m = 0. In this case, there are no incentives to migrate. In general, therefore, the migration decision can be summarized in complementary-slackness form: mðV R −V U Þ ¼ 0; m≥0; V R −V U ≥0:

ð9Þ

This completes the basic description of the economic equilibrium, which I define as follows. Definition 1. (Economic equilibrium) The economic equilibrium is given by a tuple {m eq, LEeq, r eq, wEeq} such that: 1. Taking wE, r and m as given, landowners choose LE to maximize their consumption cE and each non-migrating peasant i ∈ R chooses ei and xiP to maximize his consumption ciP. In particular, {LEeq,r eq,wEeq} satisfy Eqs. (3)–(5), and 2. Migration (m eq) satisfies Eq. (9). Fig. 1 illustrates the economic equilibrium. Panel A depicts the equilibrium without migration. The horizontal axis measures, from left to right, total labor on landowner farms LE and, in the opposite direction, labor on peasant farms Lp. The marginal productivity of labor on landowner farms is the corresponding downward-sloping curve, F2(T − t, LE). As more labor is devoted to the elite subsector, labor on peasant farms falls, and the marginal productivity of labor in the peasant subsector increases. This is depicted with the upward-sloping curve, (1 − τ)A(μ) f2(t, Lp). The equilibrium wage rate wE is found at the intersection of these two curves: it equates the marginal product of labor in the elite and peasant subsectors. In Panel A, this resulting wage rate is such that wU is smaller than wE þ ð1−μ Þ Lt r. In other words, the urban wage is not large enough to compensate for the wage and relative land-rent benefit of the rural areas. Panel B, instead, shows positive migration. Again,

L. Fergusson / Journal of Development Economics 103 (2013) 167–181

Panel A

Panel B

Economic Equilibrium without migration wU < wE+(1-µ)(t/L)r

Economic Equilibrium with positive migration wU > wE+(1-µ)(t/L)r

(1- )A(µ)f 2(t,LP)

F2(T-t,LE)

171

F2(T-t,LE)

(1- )A(µ)f 2(t,LP)

wU (1-µ)(t/L R)r

wE+(1-µ)(t/L)r wE

wE wU

LE

LE

LR = L

LP

LR

LP

m

L

Fig. 1. Economic equilibrium.

the equilibrium rural wage rate is found as the intersection between the marginal productivity of labor in the peasant and elite subsectors. However, the urban wage is large enough that part of the rural population migrates to the cities. This migration is shown on the rightmost end of the horizontal axis as a decrease in total rural labor LR below L. Notice that migration, by decreasing available rural labor to be distributed in each rural subsector, increases the marginal product of agricultural labor and the equilibrium rural wage wE. Migration continues until wU −wE ¼ ð1−μ Þ LtR r, so that the urban wage exactly compensates the wage and relative land-rent benefit of the rural areas. Thus far, I largely ignored functional form assumptions. Given the Cobb–Douglas assumption for both subsectors, the only difference in technology results from A(μ). It is also useful to define the following “distortion adjusted” measure of land endowment in society: T~ ≡t ½ð1−τ Þμ 

1 1−α

þ ðT−t Þ:

enjoys if he decides to remain in the rural areas rather than migrate. Similarly, the function w ðτ; μ Þ, defined on the right hand side of Eq. (10), is the rural wage plus the relative advantage of land rents in rural areas when m = 0. It crucially determines whether or not there will be migration in equilibrium. This function is decreasing in τ, whereas the impact of property rights is more subtle. I summarize the features of w ðτ; μ Þ in the following remark. h i Remark 1. Consider the function w : ½0; τ   μ ; 1 →Rþ defined in Eq. (10). 1. w ðτ; μ Þ achieves a global maximum at (0,μ ∗), where (a) μ⁎ = 1 if α ∈ [1/2,1). h  (b) μ⁎ b 1 otherwise. Moreover, w ðτ; μ Þ is increasing for μ∈ μ ; μ  and decreasing for μ ∈ (μ ∗,1]  1−α     T~ T−t 1−α 2. w ðτ; 1Þ ¼ > ≈w τ; μ for small μ : L

In the absence of any policy distortion (when μ = 1 and τ = 0), then T~ ¼ T. Much of the analysis focuses on the elite's incentives to reduce μ or increase τ, which effectively reduce T~ below T. Along these lines, I define the “distortion-adjusted” share of land in the elite sector as γE ¼ T−t ; and similarly, for the peasant sector, γP = 1 − γE. Therefore, the T~ equations that satisfy the economic equilibrium indicate that the peasant and elite sectors absorb a share of rural labor proportional to the size of their (distortion-adjusted) landholdings: LE = γELR and LP = γPLR. Factor prices, in turn, are given by: r ¼ ½ð1−α Þ=α ½ð1−τÞμ 

1 1−α

 1−α  α LR =T~ and wE ¼ T~ =LR :

As for migration, Eq. (9) implies that T~ m ¼ 0 if wU b L

!1−α  1 þ ð1−μ Þ

 1−α γP ≡ w ðτ; μ Þ: α

ð10Þ

Otherwise, m satisfies wU ¼

!1−α   1−α T~ γP : 1 þ ð1−μ Þ α L−m

ð11Þ

The right hand side of Eq. (11) is the wage in rural areas plus an extra term capturing the relative advantage of land rents a peasant

L

Proof. See Section A.1. ■ The second part of this remark is straightforward, but let's take a look at the first part. Increased taxation increases the threat of migration (∂w=∂τ b 0). Indeed, an increase in τ reduces two terms in w:  1−α  T~ =L ; First, the rural equilibrium wage wE at zero migration and second, the distortion-adjusted share of land in the peasant sector γP. In other words, given more rural taxation, peasants earn less from both land and labor, so they are more willing to migrate. Property rights have a more complex effect. Weakened property rights in the peasant sector have two countervailing effects: (i) reducing productivity in the peasant sector and reducing the relative value of rural areas, similar to the way taxation does (by reducing wE and γP); (ii) while this productivity effect encourages migration, a lower μ also has a security effect as captured by (1 − μ) in the expression. This second effect encourages peasants to remain in the countryside to protect land rents, which would be (partially) lost upon migration to the cities. Now, recall that α is the coefficient of labor in the Cobb–Douglas production function. Thus, when α ≥ 1/2, income from land rents is smaller than wage income. Therefore, the productivity effect prevails and an increase in μ improves the relative value of rural areas and w. However, if land rents are large enough (if α b 1/2), with high μ the security effect prevails and the value of μ that maximizes w is less than 1.

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This remark is useful in establishing the following three regimes arising regardless of the value of α.    1. No migration  regime wU b w τ; μ . If the urban wage is lower than w τ ;μ , the global minimum of w ðτ; μ Þ, there will be no migration in equilibrium regardless adopted,  hof the  policies  i so LR = L. 2. Avoidable migration regime wU ∈ w τ ;μ ; w ð0; μ  Þ . If the urban wage is at an intermediate level, the elite can avoid migration with the right combination of policies. 3. Unavoidable migration regime ðwU > w ð0; μ  ÞÞ. With high wages, not even zero rural taxation and the level of property rights (μ ∗) that maximizes w ðτ; μ Þ can forestall migration. Fig. 2 depicts the functions w ðτ; μ Þ and w ð0; μ Þ. It also shows the values for wU corresponding to each regime. The avoidable migration regime is a transitional regime in which policies gradually transition from those of the no migration regime to those of the unavoidable migration regime. For this reason, and to reduce the number of cases to be analyzed, I study the unavoidable migration case in Appendix B. Also, I explain the intuition of the results in the main text, and present algebraic details in Sections A.2–A.4. 4. Political equilibrium Political equilibrium is defined as the level of property rights and taxation on the peasant sector that maximizes elite consumption:

where I stands for “interior” and LRI is found by solving L − m in Eq. (11): LR ¼ T~ I



  1 1−α γP 1 þ ð1−μ Þ : wU α 1 1−α

ð14Þ

The above discussion on the effects of limited property rights showed the conflicting effects of weakening property rights in peasant plots. To gain intuition and highlight these conflicting effects, I analyze problem (12), as in Acemoglu (2006), by dividing it into two separate problems: (i) the Factor Price Manipulation (henceforth FPM) problem, which arises when the elite receives no tax revenues and maximizes only the first term in Eq. (12); (ii) the Revenue Extraction (henceforth RE) problem, which focuses squarely on increasing tax revenues, the maximization of the second term in Eq. (12). I discuss each case, emphasizing the conditions under which a dual rural economy arises, or those in which μ b 1. 4.1. Factor price manipulation Consider first the pure FPM problem that arises when maximizing only elite agricultural profits, the first term in (12):   1 α 1−α max ð1−α Þ ðγE LR Þ ðT−t Þ : ð15Þ τ;μ α

A political equilibrium is defined as a tuple {τ POL, μ POL, G POL} such that

Ignoring constant terms, and substituting γE, this expression underlines the fact that to minimize the equilibrium rural wage, landowners choose taxation and property rights to maximize the ratio of   labor to distortion-adjusted land LR =T~ . The following proposition summarizes the solution:

   POL POL eq eq eq POL τ ;μ ∈arg max F T−t; LE −wE LE þ G

Proposition 1. Summary of FPM policies

Definition 2. (Political equilibrium)

τ;μ

where G POL satisfies Eq. (2), and migration, labour allocation, land rents, and wages, are given by {m eq,LEeq,r eq,wEeq} in Definition 1. The elite's problem in the previous definition can be written more explicitly by using the functional form assumptions and substituting our previous findings, namely that land in each subsector is proportional to its distortion-adjusted share of land (LE = γELR and LP =  1−α : γPLR) and that wE ¼ T~ =LR     1 1 α 1−α α 1−α max ð1−α Þ ðγE LR Þ ðT−t Þ þ τ μ ðγ P LR Þ t ; τ;μ α α

ð12Þ

with LR given by: n o I LR ¼ min L; LR ;

ð13Þ

Case

Suppose the elite maximizes the first term in Eq. (12). Then, with w ðτ; μ Þ as defined in (10) and μ⁎ from Remark 1, the unique political equilibrium features the following level of taxation (τ FPM) and property rights (μ FPM):   1. (No migration) If wU bw τ; μ , then τFPM ¼ τ and μ FPM ¼ μ . 2. (Unavoidable migration) If wU > w ð0; μ  Þ; then τ FPM = 0 and μ FPM ∈ (0, 1/(2 − α)). Moreover, ∂μ FPM/∂T > 0, ∂μ FPM/∂α > 0, and ∂μ FPM/∂t b 0. Finally, as T → ∞ or t → 0, μ FPM → 1/(2 − α) Proof. See Section A.2. ■ Consider the results of Proposition 1 for wU bw ðτ; μ Þ. In this no migration regime, regardless of the policies selected by the elite, LR = L. Without an effective threat of migration to another sector the only peasant

< 1/2

Case

wU

Unavoidable migration

1/2

wU

Unavoidable migration

Avoidable migration

Avoidable migration

0

µ*

1

No migration µ

0 Fig. 2. Three regimes.

No migration µ µ*=1

L. Fergusson / Journal of Development Economics 103 (2013) 167–181

outside option is income from their own plots. The FPM motive – namely, increasing elite agricultural profits – compels landowners to make this outside option as poor as possible by imposing the highest taxation and poorest property rights institutions on the peasant subsector, τ and μ . If urban wages increase enough, part 2 of Proposition 1 applies and the society is placed in an unavoidable migration regime. In this case, LR = LRI for any combination of policies, and landowners maximize LIR =T~ . It is straightforward to verify that LIR =T~ is monotonically decreasing in τ, and this has a simple intuition. Landowners receive no benefit from imposing taxation on the peasant sector because, while increasing the share of rural labor in their plots, γE, taxation encourages enough migration to the urban sector that overall labor input falls. Hence, the optimal τ is zero. Although optimal taxation is zero, not all distortions disappear when peasants can migrate. In particular, the peasant sector will not have perfect property rights, μ = 1. Instead, a similar basic trade-off between better rural productivity and protection of property rights (i.e., between the productivity and security effects discussed before), implies the optimal level of property rights is μ FPM b 1. The solution also shows that the equilibrium level of property rights is an increasing function of α and, in the empirically relevant case of T large and t small, it is almost wholly determined by α. Larger α means land plays a less important role in the production function and land rents have less influence in peasants' decision to stay. This increases property rights μ FPM because it weakens the security effect (the importance of losing land rents upon migration, which pushes μ FPM down) relative to the productivity effect (the impact on peasant sector productivity and effective land endowment, which persuades the elite to concede better property rights). The comparative static results also indicate that when peasants have more land it is important to reduce the security of their property rights, compelling them to remain un rural areas. Indeed, if t is very small, then remaining in rural areas to protect land rents is relatively unimportant. Instead, where peasants are able to control or obtain larger land concessions, the model predicts that landowners will try to partly compensate for this by reducing μ 6. The FPM case highlights in the simplest manner the main argument whereby, in tying peasants to the land, weak property rights act as a distinct persistent distortion. However, the case does so by eliminating any direct tax benefits for elite landowners. To understand the puzzle of persistently weak property rights, one must ask why elites choose them even when they benefit directly from taxation of the peasant sector. I address this issue in two steps. First, I solve the RE problem to show that tax revenues accruing to the elite are always increasing in property rights. Next, I show that despite this result, in the full solution to the model, landowners may choose weak property rights, especially when threatened by “modernization.” 4.2. Revenue extraction Consider now the problem of maximizing tax revenues only, the Revenue Extraction (RE) problem 7:  max τ τ;μ

 1 α 1−α μ ðγ P LR Þ t : α

ð16Þ

6 In the model, the implications of an increase in the amount of peasant land are similar to those of an increase in peasants' total factor productivity. Since such comparative static results would add few new elements, and to reduce the cases to be analyzed, I do not directly incorporate a parameter for peasant factor productivity (other than property rights, which directly influence it). 7 One might alternatively think of the RE problem as that which emerges when all the land controlled by the peasant sector, t = T. Indeed, when the elites are not involved in production, they inevitably do not compete for factors with the peasants, and focus merely on revenue extraction. The features of the solution to such a problem can be seen as a special case of problem (16). Thus I focus on the latter.

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Unlike Proposition 1, this section shows that policies in the RE solution are similar, regardless of urban wage levels: there is an intermediate level of taxation and the level of property rights is always maximal. I summarize the key features of the solution in the next Proposition. Proposition 2. Summary of RE policies Suppose the elite solves problem (16). Then, with w ðτ; μ Þ as defined in (10) and μ⁎ from Remark 1, the

 unique political equilibrium features μ RE = 1 and τRE ¼ min τ; τLaffer , where: 1. (No migration) If wU bw ðτ ; μ Þ, then τ Laffer ∈ (1 − α,1). Moreover, ∂τ Laffer/∂T b 0, ∂τ Laffer/∂α b 0, and ∂τ Laffer/∂t > 0. Finally, as T → ∞ or t → 0, τ Laffer → 1 − α. 2. (Unavoidable migration) If wU > w ð0; μ  Þ; then τ Laffer ∈ (1 − α). Proof. See Section A.3. ■ The intuition for this solution in the no migration regime (when LR = L) is simple. To maximize tax revenues, the landowning elite has a direct interest in raising productivity in the peasant sector to increase the tax base. On the other hand, as regards τ, standard Laffer-curve logic applies. Although there is no labor-leisure trade-off for workers and they supply a unit of labor inelastically, labor supply in the peasant sector responds to τ because there exists an alternative, untaxed sector on elite farms. Therefore, increasing the tax rate reduces the tax base by reducing the share of labor in the peasant sector. Unless the exogenous level of feasible taxation, τ, is binding, taxation will be set at the interior tax rate τLaffer ∈ (1 − α, 1) such that the marginal increase in revenue from raising the tax rate equals the marginal decrease in revenue from tax base erosion. In the other extreme, the unavoidable migration regime applies and LR = LRI for any combination of policies. To characterize the solution in this case, it can again be shown that although poor property rights may deter some migration, the maximand increases in μ for each τ. Therefore, the preferred level of μ remains equal to 1. Taking this as given, the optimal level of taxation, τ Laffer, can be easily calculated as τ Laffer = 1 − α. Again, the exogenous limit to taxation may become binding. Thus, the equilibrium level of taxation is given by τRE ¼ minfτ; 1−α g, as noted in the Proposition. Regarding comparative static results, the tax rate is higher when α is small. The reason is that with higher α taxation is less distortionary, as labor experiences a rise in diminishing returns and labor input declines little in response to taxes. In the no migration regime, the elite also sets a higher tax rate when t is larger or T is smaller. More land in the traditional sector amounts to an increase in the tax base. A decrease in T implies the alternative landowner sector is able to absorb less labor. Both these effects reduce the response of peasant labor supply to taxation, increasing the optimal tax rate. With unavoidable migration, taxation is instead independent of relative land endowments since the relevant outside option for peasants is now the urban sector, whose capacity to absorb workers is unrelated to rural land endowments. In sum, when the objective is maximizing tax revenues, increasing urban wages reduces taxation to some extent, but property rights remain at their maximum level. This contrasts with the FPM solution in which the elite maximizes only agricultural profits and weak property rights persist with “modernization.” The dual economy in the RE, as opposed to the FPM, solution, does not emerge endogenously as wU increases. Revenue extraction, in other words, poorly explains the dual rural economy. The RE economy is instead a single-sector economy with differential taxation of politically-weak producers. Thus, it is important to examine whether the argument about the persistence of weak property rights set forth in the FPM case is robust to inclusion of an RE concern. The next section tackles this issue.

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L. Fergusson / Journal of Development Economics 103 (2013) 167–181

4.3. The combined problem In this section I examine problem (12) in which the elite receives the full benefit of taxation of peasant income and also strives to obtain cheap labor to increase agricultural profits. The next Proposition summarizes the solution. To simplify the cases, I suppose that the exogenous limit to taxation τ is not binding (and note in the Corollary an important instance when τ≤τ is binding). Proposition 3. Summary of COM policies Suppose the elite solves problem (12). Also, assume that τ ¼ 1. Then, with w ðτ; μ Þ as defined in (10) and μ⁎ from Remark 1, the unique political equilibrium features the following level of taxation (τPCOM) and property rights (μ COM):   1. (No migration) If wU bw τ; μ , then μ COM = 1 and τ COM ∈ (τ Laffer,1), where τ Laffer is as in Proposition 2, part 1. 2. (Unavoidable migration) If wU > w ð0; μ  Þ, then thresholds t and t exist with 0b t bt b1 such that: a. if t∈ð0; t , then τ COM = 0 and μ COM = μ FPM; b. if t∈ t ; T , then τ COM = 1 − α, and μ COM = 1.   α ð1−αÞ Laffer , then μ COM ¼ μ and Corollary 1. If wU bw τ ;μ and τb1þα ð1−α Þbτ COM τ ¼ τ: Proof. See Section A.4. ■ To understand Proposition 3, it is useful to contrast it with Propositions 1 and 2. To ease this comparison, Table 1 summarizes the main theoretical predictions. To simplify the exposition, in the table we assume that the exogenous τ is not binding. Starting with the no migration regime, Part 1 of Proposition 3 and the first two columns in Table 1 show that RE-type policies prevail in the combined problem. Without migration, incentives to maximize tax revenues call for optimal property rights and positive but less than confiscatory taxation. On the other hand, to maximize agricultural profits, the elite must reduce wages as much as possible. This is achieved by setting high taxes and weak property rights to reduce peasant's income from their own plots. In short, good property rights are preferable when seeking to increase the tax base and extract revenue (RE), while bad property rights are better when seeking cheap labor (FPM). If this is the case, why do RE-type incentives dominate in the combined problem with no migration? Intuitively, setting bad property rights destroys economic surplus. It is better not to create this inefficiency and instead promote efficient production and tax the returns. Moreover, when the elite taxes peasants, it not only benefits directly from tax revenues, it also reduces peasants' outside income, creating a cheap labor force. A more detailed intuition stems directly from the proof in Section 4: while RE and FPM incentives push the elite in

different directions regarding property rights institutions, the elite prefers to tax peasants heavily, both for the tax revenue and the increased labor this provides. For this reason, as noted in the proposition, the desired level of taxation in the combined problem (maximizing tax revenues and elite agricultural profits) exceeds the desired taxation in the RE model (maximizing tax revenues alone). A high tax rate, in turn, resolves the ambivalence over property rights: it compels the elite to focus on collecting revenue through taxing peasants thus creating a direct interest in increasing peasants' productivity by selecting good property rights institutions. The intuition in the preceding paragraph also has an interesting corollary: If the exogenous limit to taxation τ is low enough, the elite's FPM incentives will again prevail, because tax revenues account for a lesser portion of their income. In other words, without an effective threat of migration, the case for bad property rights in the peasant sector is only compelling if the elite's ability to tax the sector is limited (low τ). Proposition 3 and the last two columns in Table 1 show that when urban wages are high and the threat of migration effective, RE incentives do not necessarily prevail. The reason for this is also apparent in the discussion above. Recall that when considering a reduction of rural wages (FPM), an effective threat of migration renders an increase in taxation of peasant income useless. As Proposition 1 established, increasing taxes reduces the attractiveness of rural areas and the ensuing migration decreases landowners' labor input and profits. Thus, we can no longer conclude, as in the no migration case, that a high level of taxation is preferable. In fact, if sufficiently concerned with avoiding labor force migration, the elite chooses minimal taxation. Proposition 3 establishes that the elite will be “sufficiently” concerned with migration if peasants own little land ðtb t Þ. Since less land for peasants means more land for the elite, this not only reduces revenues from taxation of peasant production, but also increases profits from landowners' farms. Thus, factor price manipulation incentives dominate and the desired tax rate is zero. A zero tax rate obviously implies zero tax revenues and no incentives to adopt good property rights institutions to increase taxable income. In the resulting equilibrium, to avoid migration and extract more labor from peasants, the elite selects poor property rights institutions. However, if peasants own enough land, the elite faces the reverse situation. Due to sufficiently large peasant income and sufficiently small landowner profit from their own farms, the elite focuses on increasing taxation, not on reducing wages. In this case, peasant property rights are optimal and taxation is positive. Turning to comparative static results, over the range t∈ð0; t  there is zero taxation τ COM = 0. Thus RE incentives to increase the tax base have no bearing on the desired level of property rights. Hence, μ COM coincides with μ FPM from FPM Proposition 1, and satisfies the same comparative static results. Similarly, over the range t∈ t ; T the fact that μ COM = 1 implies that τ COM coincides exactly with tau RE =

Table 1 Summary of main predictions. Low urban wages (no migration) Taxation (τ)

High urban wages (unavoidable migration) Property rights (μ)

  τ > τ Laffer T ; t ; α − þ −

1

Taxation (τ) tb t :0

Property rights (μ)   t b t : μ T;t;α b1

t > t : τ Laffer ¼ 1−α

t>t :1

−

−

þ − þ

Notes: Each cell displays the theoretical prediction for taxation (τ) or property rights (μ). To simplify the exposition, results in the table assume that the exogenous limit on taxation (τ ) is not binding. Factor price manipulation refers to the maximization of elite agricultural profits as in Proposition 1, Revenue Extraction to the maximization of tax revenues as in Proposition 2, and Combined to the maximization of both components as in Proposition 3. Where applicable, comparative static results with respect to total agricultural land (T), land in the peasant subsector (t), and the coefficient of labour in the Cobb–Douglas production function (α),are summarized with a minus (−) or plus sign (+) under each parameter. Hence, for instance, τLaffer(T,t,α) means that ∂τLaffer/∂T > 0, and so on.

L. Fergusson / Journal of Development Economics 103 (2013) 167–181

1 − α of Proposition 2. Indeed, with perfect property rights and positive migration the rural wage wE will be identical to the exogenous urban wage wU, eliminating any scope for factor price manipulation. Nonetheless, there are additional comparative static results in the combined problem because variation in the model's parameters may move the economy from a situation with t∈ð0; t  to one in which t∈ t ; T . More specifically, they predict a non-monotonic relationship between the quality of rural property rights and the amount of land in the hands of peasants. When peasants hold relatively little land (t∈ð0; t ), obtaining more land increases the rural elite's incentives to reduce property rights in order to obtain cheap labor. However, if enough land is allocated to the peasants such that t∈ t; T , the elite promotes optimal property rights institutions to increasetax revenues. This prediction is interesting given its implications for the much-debated impact of inequality on development (for reviews, see Bénabou (1996) and Aghion et al. (1999)). In particular, this result highlights that if the relatively poor (here, the peasants) are sufficiently wealthy, then elites may have weaker incentives to impose distortions affecting productivity, as they may move from further impoverishing the poor in order to exploit their labor to promoting prosperity in order to tax proceeds. This particular political economy link between equality and better institutions for development can plausibly arise in other contexts too. 5. Extension: Endogenous urban wages and the industrial elite Thus far the role of the urban-industrial elite has been ignored, adopting the simplified assumption that all political power lies in the hands of the rural elite. In this section, I discuss whether urban and rural elites converge or diverge on the subject of property rights. To do so, I adopt a plausibly more realistic formulation in which urban wages fall with migration to the cities. The urban wage is now given by the following function, wU(m) = wU − κm, for some constant κ. The main change in the analysis comes when expressing the value of urban areas, now given by: t V U ¼ wU −κm þ μ r: L Other expressions of the economic equilibrium, including the value of the rural areas, remain the same. The key change concerns the equation for migration. As above, there is positive migration until VU = VR, which now corresponds to: t r þ κm: wU −wE ¼ ð1−μ Þ L−m Hence, m is (implicitly) given by the equation above (remember wE is also a function of m), and exactly as before migration is equal to zero if wU is less than wE + (1 − μ)(t/L)r at m = 0. Using the functional form assumptions, equilibrium migration is thus, T~ m ¼ 0 if wU b L

!1−α "

# 1 1−α t ½ð1−τ P Þμ 1−α ≡ w ðτ; μ Þ; 1 þ ð1−μ Þ α T~

ð17Þ

otherwise, m satisfies wU ¼

!1−α " # T~ 1−α t ½ð1−τP Þμ  1 þ ð1−μ Þ þ κm: L−m α T~ 1 1−α

ð18Þ

Eq. (17), determining the conditions under which there would be positive migration, is exactly as before (Eq. (10)). Eq. (18), on the other hand, which describes equilibrium positive migration, is identical to the original equation (Eq. (11)) except for the term κm. This has two implications: first, the same regimes of unavoidable migration,

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avoidable migration and no migration arise as in the baseline model; second, since migration now reduces urban wages, a lower level of migration equates the value of urban and rural wages. However, aside from this implication, Eq. (18) otherwise has the same comparative static implications for migration m and hence rural labor LR as in the original model. In short, in this more realistic formulation there is less migration in the equilibrium, but no further implications for the main conclusions drawn from the analysis of rural elite incentives. It is reasonable to suppose that the welfare of the urban-industrial elite decreases with an increase in urban wages. If so, the urban elite will oppose institutions that reduce migration and increase urban wages. A conflict of interest between rural and urban elites would then arise: the rural elite supports weak property rights to tie peasants to the land, and the urban elite opposes them for exactly the same reason. An alternative possibility is that, as weak property rights reduce peasant productivity, they also help provide industry with cheap labor. For this to be the case, urban wages would have to be closely linked to rural wages, such that the effect of a decrease in rural wages generated by lower peasant productivity dominates the effect of a fall in migration. The exact details of the urban labor market and its integration with the rural labor market will determine which effect dominates. In the next section, I discuss the Rhodesian case and the empirical relevance of my theoretical analysis, including its effects on the industrial elite. I show that urban-industrial elites opposed weak property rights institutions in the rural peasant sector because they discouraged permanent rural–urban migration. Interestingly, however, in cases such as South Africa, where the industrial and rural labor markets are more closely integrated, the opinions of certain industrial and rural elites seem to converge on the subject of rural institutions. While otherwise very similar to Rhodesian society and economy, a key difference in South Africa was the competition from the mines that agricultural elites faced when seeking cheap labor. The mines, however, adopted a system of short-term migrant workers and were able to survive based on this system alone. They might, in fact, have benefited from limited outside options for peasants but these implied huge obstacles for industry, which required a more stable and better educated labor force (see Feinstein, 2005, p. 130). 6. The Rhodesian case History and the developing world provide many examples of dual rural economies in which the property rights and political influence of peasants are more limited than those of landowners. Arguably, there is no better illustration of this situation than the settler colonies of Southern Africa, where the rural dual economy has been institutionally codified and land has been geographically segregated along racial lines. Large private estates owned by white farmers have coexisted with overcrowded African reserves. Similar to the ancient customs of African societies, land in the black reserves is typically owned by the community, not the individual. While individuals may enjoy secure (and often inheritable) land rights, the communal structure often means they lack permanent property rights over a specific plot, or that these rights are forfeited in cases of extended absence. Also important, transfer rights (if any) such as sales or rental rights are limited to the community. Needless to say, white agricultural interests also historically held far greater political power than the excluded black majority. A full test of the model's assumptions and predictions goes beyond the scope of this paper. However, this section examines the case of Rhodesia (formerly Southern Rhodesia, or current-day Zimbabwe) as particularly representative of other settler colonies in Africa where exploitation of the black peasant economy by white agricultural interests played a prominent role. Admittedly, a case study is only a limited test

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of the model. But it should be noted that these theoretical mechanisms may also be relevant in many other poor countries where large landowners often have more political power and better-defined rights than smallholders. 8In many instances, landowners use their political power to generate distortions in various markets to discriminate against peasants and support their own estates. Binswanger et al. (1995) offer a review, noting, as assumed in this paper, that a key objective of discrimination is securing cheap labor for large estates by “lowering expected utility of profits in the free peasant sector in order to reduce peasants' reservation utility (…) or shift their labor supply curve to the right” (p. 15). The following discussion of the Rhodesian case is divided in two parts. First, I demonstrate the historical relevance of the main theoretical assumptions. Next, I discuss the usefulness of the theoretical predictions and mechanisms in interpreting Rhodesian agricultural history.

Purchase Areas). The property rights regime in these native areas was the most complete since land, unlike in reserves, was owned individually and not by the tribe. Even so, “there were many limitations to its transferability, such as maximum size of holdings and sales to Europeans. Among other things, this meant that the extension of credit (…) to African farmers was hampered and therefore a constant lack of financing was bound to hold back their development” (Arrighi, 1973, p. 347). Finally, while not an assumption, a key parameter in the theoretical analysis shaping the direction of comparative static results is the size of the peasant sector. There is little doubt that the expropriation of African land and the movement of Africans onto the reserves, described by Palmer (1977b) as a “squeezing-out process” (p. 80), implies that the empirically relevant case corresponds to a small peasant sector (t in the model). 6.2. Interpreting Rhodesian agricultural history

6.1. Key assumptions in practice My theoretical analysis is based on three important assumptions: the first is that political power (the ability to shape key institutions and policies) is largely in the hands of private landowners; the second and third assumptions concern the double-impact of poor property rights on the peasant sector – lowering productivity and increasing the cost of rural–urban migration. In Rhodesia, there is ample support for each of these assumptions. In Southern Africa in general (and Rhodesia in particular), the elite and peasant sectors are easily identifiable, having been segregated along racial lines. Undoubtedly, the white capitalist minority held political power and shaped policies in detriment to the native minority. Palmer (1977a) puts it bluntly: in Rhodesian agricultural history, the dominant theme “is surely the triumph of European over African farmers” (p. 221). This triumph includes a history of war and dispossession that followed European colonization and highlights the political power of the white minority. Soon after Cecil Rhodes' British South Africa Company (BSAC) obtained a Royal Charter in 1889 to administer the territory as a protectorate, the two main indigenous peoples (the Ndebele or Matabele, and the Shona) experienced large-scale dispossession of their land through violent and illegal means and found themselves under the political domination of settlers (see Palmer (1977b, p. 27)). The dual rural economy was codified when the Natives were confined in reserves, some of which were considered “cemeteries, not Homes” (Palmer, 1977b, p. 33) even by the Colonial Office. And around 1907, when BSAC Directors convinced themselves that the gold they had been longing for did not exist in Rhodesia, they established the “White Agricultural Policy”, which marked the beginning of differential support for European farmers via government bureaucracy, banks, and research, none of which were available to Africans. Moreover, the political power of white agricultural interests persisted when, in 1922, the era of Company rule came to an end and political power formally passed to white settlers after a referendum in which the (small and mostly European) electorate rejected joining the Union of South Africa. Moving to the second and third key assumptions, it is also clear that limited property rights on African reserves both hindered rural–urban migration and limited productivity. (Arrighi (1970, p. 223) notes that the Rhodesian tribal social system made black peasants unwilling to permanently migrate to industrial urban centers. If indeed they migrated, they did so only temporarily, “so as to retain [their] cultivation rights and to be able to claim support and succour when necessary” (Arrighi, 1970, p. 223). As for the limited productivity that arose out of limited property rights, nothing is more telling than the NPA experience (Native 8 See, for example, Binswanger and Deininger (1997), Deininger and Binswanger (1999), Deininger and Feder (2001), and World Bank (2008).

The theoretical sections' most important predictions concern the conditions under which weak property rights emerge. These conditions crucially depend on the development of the modern industrial or urban sector. I now examine whether or not Rhodesian history fits the theoretical implications at low and high levels of modernization. I begin with the case of high urban wages, since my theoretical predictions contrast many theories of the dual economy, where the disappearance of the peasant subsistence sector is a direct consequence of the modernization process. 9My theory predicts instead that with modernization, parametrized by a wage increase in the urban-industrial sector, a rural dual economy in which limited property rights persist in rural peasant areas is in fact more likely. The Rhodesian case provides clear validation of this prediction and the mechanisms involved. It also falls in line with the expected effects on the industrial elite discussed in Section 5. In particular, the industrial-urban sector took on an important role around the 1950s. The industrial elite pushed for a reform after suffering from the persistence of traditional forms of tenure in the countryside which discouraged permanent migration and created a stagnant agricultural sector. But landowners resisted the change and, given their political power, were largely successful. In 1951, the Native Land Husbandry Act (NLHA) was adopted. This key piece of legislation sought, firstly, to replace the traditional system of native land tenure under the control of native chiefs with a system of individual tenure under government control and, secondly, to promote “good” husbandry. The traditional scheme harmed industries, especially those requiring a stable labor source (Arrighi, 1970, p. 223). As the official discourse noted: “Grave problems flow from crowded and stagnant communities scraping a bare existence from the exhausted countryside, and spilling as an inefficient migrant labor force into industrial centers many miles from their homes and families” (cited in (Floyd (1959, p. 114)).“The time has come when all indigenous natives can no longer continue to maintain a dual existence as part-time employment in the European areas and part-time farming in the Native reserves for, apart from its impossibility, it does not conduce to efficiency in either area” (cited in (Alexander (2006, pg.46)). It was thus expected that by introducing individual rights, those excluded from land would provide industry with a stable source of labor, and that security of tenure in the reserves would improve productivity. This, however, is exactly the opposite of what the rural elite looks for in

9 For instance, in Lewis (1954), capital accumulation or productivity gains in the modern sector pull “unlimited supplies of labor” out of the subsistence sector. Models of the dual economy and growth with structural change overcome some of the limitations of the Lewis model, but share the idea that accumulation of capital and knowledge in the modern economy gradually reduces the size of the subsistence sector.

L. Fergusson / Journal of Development Economics 103 (2013) 167–181

my model economy. According to the results of Proposition 3, the rural elite opposes these aims for the same reason that the industrial sector supports them. Ultimately, policies to introduce private property on the traditional African sector turned out to be partial and timid. While the NLHA was supposedly revolutionary, “directly repudiat[ing] ‘customary’ and communal rights to land in favor of individual land right holders and ‘secular state power’, [it] was to be tempered by a host of restrictions” (Alexander, 2006): only those who farmed and owned stock at the time the Act was implemented were eligible for rights; land rights could not be used as collateral for loans; and the size of the arable allocations and number of stock rights were limited. Hence, the NLHA which in theory might have been a triumph of manufacturing interests, was at best a compromise between settler farmers and secondary industries (Duggan (1980, p. 230), Arrighi (1973) and Phimister (1993)). Underlying this result was the political power of white farmers. A senior official of the Native Affairs Department recognized the impossibility of truly revolutionary policy changes. He remarked at the time, referring to an increase in the minimum wage that would stabilize labor in the urban areas: “if a minimum wage [is] introduced in the towns you are bound to have repercussions amongst the farming community and today the farming community rules the country, so that flattens out the minimum wage straight away” (Arrighi, 1973, p. 362, emphasis added). Also in the 1950s, liberals failed to repeal the Land Apportionment Act which had created Native Purchase Areas and forbidden Africans from buying land in European areas. White farmers reaffirmed their political power, however, when the United Federal Party lost the 1962 elections to the Rhodesian Front Party (Mosley (1983, p. 29) and (Duggan (1980, p. 232)) and the Land Apportionment Act was confirmed by the 1969 Land Tenure Act. Duggan (1980) interprets these measures in the following way: “The Rhodesian state had thus come full circle. Its first coherent agricultural policy, in the decade before World War I, was to eliminate the commercial production of Africans and encourage that of settlers. Industrialization after 1940 produced an ambivalent government policy; protection of settler farmers was costly to the growing manufacturing sector (…). During the 1960s, with the Rhodesian Front in power, ambivalence towards African commercial agriculture disappeared” (p. 237). The persistence of a rural dual economy in Rhodesia following the rise of the industrial sector can therefore be interpreted in terms of the theoretical analysis. However, when focusing on a context of low urban wages, the theoretical predictions are puzzling. In particular, without a relevant industrial sector, the model predicts that landowner elites will support strong property rights institutions. When there is no threat of peasants migrating from rural to urban areas, promoting efficiency-enhancing reforms in the peasant sector and taxing the returns is, in theory, a better strategy. Why didn't white Rhodesian farmers introduce more complete property rights institutions in the native areas early on? I conclude by suggesting an answer tothis riddle: the limited ability of landowners to tax the peasant sector, especially early on. The weakness of the African state is well-established and lies at the center of many academic debates (see e.g. Herbst (2000)). While the relatively high proportion of white settlers in Rhodesia, and Southern Africa in general, made thesecountries special in comparison with other nations on the continent, state capacity was undoubtedly limited. Alexander (2006) clearly states, referring to the process leading to power over Africans and their land: “This was in part a story of dispossession and repression, but it was also a story of contradiction and compromise in which the state's goals were far from easily realised” (p. 17). State-making, she argues, was constantly challenged by Africans, who “spread out from hilltop fortifications;

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they fled from landlords; they sought to evade tax” (p. 20, emphasis added). As shown in the Corollary to Proposition 3, when its ability to raise taxes is limited, the rural elite's attention shifts from increasing peasant sector productivity in order to increase tax revenues, to lowering such productivity in order to produce cheap labor. The rural elites competing for labor had reason to resent native prosperity and impose the maximum possible distortions on natives. Historical records show that white colonists did in fact impoverish the traditional economy as much as possible to force peasants into the labor market. Contemporary observers were aware of the impact of native prosperity on labor supply; a native Commissioner candidly admitted in 1906 that “[Locusts are] not an unmitigated evil, for a really abundant harvest of kaffir corn and mwalies would probably have the effect of reducing the number of Native laborers 50 per cent” (see Palmer (1977b, p. 78–79) for other similar testimonies). Impoverishing peasant agriculture meant increasing taxes, and allocating the worst tracts of lands to black reserves. 10It also meant no incentives to introduce innovations in property rights institutions. Finally, an interesting piece of evidence highlighting the importance of the theoretical mechanisms is the fact that a clear record of native prosperity exists for the very early years of white settlement: “A substantial amount of productive investment was nonetheless carried out by the African peasantry during the first two decades of the present century. Africans bought wagons and carts for the transport to the towns and mining centers, some invested in corn crushers and in water boreholes (…) by far the most prominent forms of productive investment were cattle and plows. In the period 1905–21 the number of African-owned cattle increased from 114,560 to 854,000 head (…) the number of plows in use by Africans increasing from 440 in 1905 to 16,900 in 1921” (Arrighi, 1970, p. 214). Palmer (1977b, p. 72) concurs, noting early Shona prosperity. Peasants, living within access to the main markets and the railroad and facing growing demand from mines, took advantage of new market opportunities and grew new crops. This early prosperity fits my theory in that, during these years, whites had limited direct involvement in agricultural production. Hence, competition for production factors such as labor was not as fierce as it would become soon afterwards. Indeed, initial land grabbing was mostly by companies, absentee landowners and speculators who were not actively involved in farming (see Palmer (1977b, p. 33) and Mosley (1983, p. 20)). These early years may be thought of as mirroringthe equilibrium of Proposition 2 describing an RE solution. 11Without strong, direct involvement in agricultural production, politically powerful groups had few reasons to resent this early prosperity. 7. Final remarks This paper suggests a political economy explanation for the persistence of poor property rights. Often, the rural sector in developing countries has a dual structure of politically powerful producers or elites alongside traditional peasants with little voice in the political 10 In 1914, a Chief Native Commissioner, referring to reserves “defended their extent on the ground[s] that much of the land selected was ‘interspersed with granite and was otherwise unfit for cultivation’” (Floyd, 1959, p. 72). Likewise, the Land Settlement Department Director, F.W. Inskipp said: “As the area in question, which is practically a conglomeration of kopjes with very small cultivable valleys in between, is infested with baboons and is only transversable by pack animals, I see no objection [to making it a native reserve]” (Palmer, 1977b, p. 104). 11 Recall as noted in footnote 2 that only RE incentives exist for the rural elite when peasants are the only ones who work the land.

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L. Fergusson / Journal of Development Economics 103 (2013) 167–181

process. In this context, rural elites curb agricultural productivity in the traditional sector to obtain cheap peasant labor. However, this objective runs into trouble when peasants enjoy alternative employment opportunities in the urban (or other) sector. In general, the emergence of new outside options for peasants limits the elite's ability to manipulate factor prices. Distorting the traditional economy fails to increase elite profits, instead increasing outmigration. This is true for a number of potential distortions in the subsistence sector, which I have specifically captured in my theoretical model using taxation on peasant income. But limited property rights in the peasant sector constitute a distinct distortion. Like other distortions, they reduce the income peasants receive from their plots, but achieve something more: they force peasants to remain in the agricultural sector to protect their property. Thus, rural elites have little incentive to promote a transition to private property institutions in the peasant subsistence economy. This suggests a specific mechanism for the endogenous persistence of weak rural institutions as development unfolds. While other theories of dualism predict development will erode the traditional economy, in this theory the rise of an alternative modern or urban sector shifts the attention of the rural elite away from taxation to prevent migration. As a result, tax revenues fall and rural elites have no direct interest in peasant sector productivity or incentives to promote efficiency-enhancing innovations in property rights institutions. A noteworthy aspect of the analysis is that poor property rights are preferred for precisely the same reason they harm overall economic development: they simultaneously reduce the supply of labor to industry (tie peasants to land) and the surplus of food in society (reduce peasants' productivity in their plots). This theory thus provides a link between political institutions that give large landowners disproportionate power and barriers to the structural transformations required for development. Other theories share this viewpoint but emphasize the landed elite's interest in raising direct barriers to industrialization or under investing in necessary public goods in order to protect their income (see, for example, Adamopoulos (2008) and Galor et al. (2009)). Acknowledgments I thank Daron Acemoglu, Abhijit Banerjee and James Robinson for their advice and many useful discussions. I also thank Ximena Cadena, Sarah Hamilton, Ana María Ibáñez, Samuel Pienknagura, Sally Station and Juan Fernando Vargas for their comments. The two anonymous referees, the seminar participants at the MIT political economy breakfast, the MIT development lunch and the 2010 Midwestern Political Science Association, and members of the Political Economy and the Economic History/Historical Development (EHHD) groups at Harvard-MIT also provided useful suggestions. I especially thank Dave Donaldson, Esther Duflo, Rachel Glennerster, Gina M.S. Lambright, Carl Levan and Benjamin Olken and gratefully acknowledge the financial support provided by the Central Bank of Colombia. Appendix A. Proofs A.1. Characterization of w ðτ; μ Þ An inspection of (10) or simple differentiation shows that the relative attractiveness of the rural areas at m = 0, w ðτ; μ Þ, is decreasing in τ is straightforward. To characterize the behavior of w ðτ; μ Þ as μ changes, rewrite it as follows: ∂w ðτ; μ Þ ¼ B  kðμ Þ  lðμ Þ; ∂μ

where:  1−α 1 1 B≡ t ½ð1−τP Þ > 0; L α μ α ; kðμ Þ≡  1 t ½ð1−τ Þμ  þ T−t 1−α

1−α

1−α

1

lðμ Þ≡1−

1−α 1−μ t ½ð1−τÞμ  μþ −ð1−μ Þ : 1 α α t ½ð1−τÞμ  þ T−t 1−α

1−α

h i Now note the following properties 12: (1) k(μ) > 0 for all μ∈ μ ; 1 ;   (2) l μ ≈1 þ 1=α > 0; (3) lð1Þ ¼ 2α−1 α ≶0 if α ≶ 1/2, and (4) l′(μ) b 0. If h i α > 1/2, these properties imply that ∂w ðτ; μ Þ=∂μ > 0 for all μ∈ μ ; 1 and thus μ⁎ = 1. If instead α > 1/2, from properties 1 and 3 

∂w ðτ; 1Þ=∂μb0. Properties 1 and 2 imply in turn that

∂w τ μ; ∂μ



> 0. These

observations, together with properties 1 and 4, imply that there exists   a unique μ  ∈ μ ; 1 such that ∂w ð∂μτ;μ Þ ¼ B  kðμ  Þ  lðμ  Þ ¼ 0 which maximizes w ðτ; μ Þ. Since k(μ ∗) > 0, μ⁎ is defined by l(μ ∗) = 0, or (also using 

τ = 0) by:

1¼

 t μ 1−α  1−μ    μ − þ 1−μ  : α α t μ þ T−t 1 1−α

1 1−α

A.2. Characterization of the FPM problem A.2.1. Equilibrium policies in the no migration regime The elite maximizes ~L which is monotonically increasing in τ and T monotonically decreasing in μ. A.2.2. Equilibrium policies in the unavoidable migration regime The main text observed that the optimal property tax rate for the elite is τ = 0. Taking this as given, one can take a monotone transformation and note that maximizing LIR =T~ with respect to μ is equivalent   1 1−α to maximizing zðμ Þ ¼ log ð1−μ Þ tμ T~ . The first order condition can be written as, z′(μ) = − 1/(1 − μ) + γE/[(1 − α)μ] = 0. Since z′(μ) is monotonically decreasing in μ, z′(0) = ∞, and z′(1) = − ∞, there   exists a unique μ FPM ∈ μ; 1 such that z′(μ FPM) = 0. Hence, LIR =T~ achieves a unique maximum at μ FPM. Straightforward differentiation then yields the following comparative static results: ∂ μ FPM/∂ T > 0, ∂ μ FPM/∂ α > 0, ∂μ FPM/∂t b 0. Moreover, note from inspection of the first order condition that z′(1/(2 − α)) b 0, and since z′(μ) is decreasing in μ, μ FPM b 1/(2 − α). Also from the first order condition, 1 . as T → ∞ or t → 0, γE approaches 1 and thus μ FPM →2−α A.3. Characterization of the RE problem A.3.1. Equilibrium policies in the no migration regime The main text observed that in the no migration regime the optimal property rights level for the elite in the RE problem is μ = 1. Taking this as given, taking logs on the maximand, and ignoring constant terms, one can find the optimal level of taxation by maximizing

1 1−α

12

To see Propertyi4, write l′(μ) = (α − 2)/α + a(μ) ∗ b(μ) with aðμ Þ≡t ½ð1−τ Þμ  = t ½ð1−τ Þμ  þ T−t and b(μ) ≡ 1 − (1 − μ)(1 − a(μ))/(μ(1 − α)). Note the following: (α − 2)/α is negative and independent of μ; α(μ) is increasing in μ and positive for all μ; b(μ) approaches minus infinity at μ = 0, equals 1 at μ = 1hand iis also increasing in μ. Thus a sufficient condition for l′(μ) to be negative for all μ∈ μ; 1 is that it is negative at μ = 1. But this always holds because (2 − α)/α > 1 > a(1) h

1 1−α

L. Fergusson / Journal of Development Economics 103 (2013) 167–181

  z~ðτP Þ ¼ log τ

1 1−α

ð1−τ Þ

t ð1−τ Þ

1 1−α

þ ðT−t Þ

α  ′ . The first order condition is z˜ ðτÞ ¼

′ 1=τ−αγE =ðð1−α Þð1−τÞÞ ¼ 0: Since z˜ ðτÞ is monotonically decreasing in μ z′(0) = ∞, and z′(1) = − ∞, there exists a unique τ ∈ [0,1] denoted ′ τLaffer such that z~ ðτÞ ¼ 0. Hence, there exists a unique τ ∈ (0,1) that satisfies the first order condition and maximizes tax revenues13. Inspection of this condition or straightforward differentiation then yields the following comparative static results: ∂τLaffer/∂T b 0, ∂τLaffer/ ∂α b 0 ∂τLaffer/∂t b 0 Moreover, τ > 1 − α but as T → ∞ or t → 0, τ → 1 - α.

A.3.2. Equilibrium policies in the unavoidable migration regime Taking logs and ignoring constant terms, the maximization problem in this case is equivalent to maximizing

z ðτ; μ Þ ¼ log τ þ þ

1 log μ 1−α

α 1−α t ½ð1−τ P Þμ  log ð1−τ Þ 1 þ ð1−μ Þ 1−α α T~

1 1−α

!!

Taking the derivative with respect to μ, it is clear that z ðτ; μ Þ is increasing in μ for each τ. To see this, taking the derivative and simplifying:

179

A.4. Characterization of the Combined Problem A.4.1. Equilibrium Policies in the No Migration Regime −α Rewrite (12) as max c E = max π FPM + π RE where πFPM ¼ kT~ , RE L π ¼ ktμ τP ð1−τÞ , and k ¼ AE α . That the optimal τ must be larger than τ Laffer, follows by taking the derivative of c E with respect to τ, ∂c E/∂τ = ∂π FPM/∂τ + ∂π RE/∂τ, and noting from the analysis of the previous cases that while the first term is positive, the second is zero for τ = τLaffer (and positive for lower values and negative for larger ones). Thus, τCOM such that ∂cE/∂τ = 0 must satisfy τPCOM ≥ τLaffer ≥ 1 − α. Also, since limτ → 1 ∂ πRE/∂ τ = − ∞ while limτ → 1 ∂ πFPM/∂ τ is finite, τ COM b 1. On the other hand, ∂c∂μ ¼ kð⋅ÞhðτÞ, where kð⋅Þ ¼ μ g~ t ð1−τÞ is always positive, while h(τ) = − α(1 − γP) + τP(1 − αγP)/[(1 − τ) (1 − α)] may be positive or negative. However, one can verify that h′(τ) > 0 for τP > 1 − α. This, together with the fact that h(1 − α) > 0 implies that h(τ) > 0 for any τP > 1 − α. This completes the proof that ∂cE/∂μ > 0 for τ ≥ 1 − α, and since τ COM ≥ 1 − α, that μ COM = 1. Finally, note that for small τ the second term in h(τ) approaches 0, thus rendering h(τ) b 0. Thus, a sufficient condition for μCOM to be equal to zero is that τ is sufficiently small that h(τ) b 0 at μ = 0, or since γP = 0 at μ = 0, that τbα ð1−α Þ=ð1 þ α ð1−α ÞÞ. α 1−α

1 1−α

α

1 1−α

α 1−α

E

A.4.2. Equilibrium policies in the unavoidable migration regime h i FPM RE Rewrite maxcE ¼ maxK ωFPM ðt Þπ~ ðμ; τÞ þ ωRE ðt Þπ~ ðμ; τ P Þ where   A K ¼ α1 Eα , ωFPM(t) = (1 − α)(T − t), ωRE ðt Þ ¼ t ð1þ wU   1−α FPM RE ð1−μ Þ1−α , π~ ¼ 1 þ ð1−μ Þ γP , π~ ¼ μ τP ð1−τÞ . α γP Þ 1 1−α

z 2 ðτ; μ Þ ¼

 1 1 αt ½ð1−τ Þμ  þ 1−α μ α T~ þ ð1−μ Þð1−α Þt ½ð1−τÞμ    1−μ T−t  −ð1−α Þ þ μ T~ 1 1−α

α 1−α

1 1−α

it can be no smaller than -(1 - α). Thus, to verify that the expression is positive, it is sufficient to show that

1 1−α

α T~ þ ð1−μ Þð1−α Þt ½ð1−τÞμ 

1 1−α

1 1−α

α 1−α

ðμ; τÞ; is monoNow we can observe that ω FPM(t), the weight on π~ tonically decreasing in t, and zero at t = T. Also, ω RE(t), the weight RE on π~ ðμ; τ Þ; is monotonically increasing in t, and zero at t = 0. Thus for any t sufficiently close to 0, the optimal is equivalent to that of maxFPM imizing π~ ; which from the preceding cases has a maximum at μ = FPM μ , τ = 0 and for any t sufficiently close to T, the optimum coincides RE with that of π~ , which has a maximum at μ = 1, τ = 1 − α This establishes the result in the Proposition. FPM

  T−t is decreasing in μ and Now note that 1μ > 1; and −ð1−α Þ þ 1−μ μ T~

αt ½ð1−τÞμ 

α 1−α

α

1 : 1−α

b

Appendix B. The Avoidable Migration Regime After some algebra, it can be shown that this is equivalent to verifying that α ðT−t Þ −1 þ ðμ þ α Þð1−α Þ b t ½ð1−τÞμ 

1 1−α

:

But since μ b 1 substituting (1 + α) for (μ + α) in the left hand side of the inequality, 2

−1 þ ðα þ μ Þð1−α Þb−1 þ ð1 þ α Þð1−α Þ ¼ −α b0b

α ðT−t Þ t ½ð1−τÞμ 

1 1−α

:

Therefore z 2 ðτ; μ Þ > 0 and the preferred level of μ is 1. Taking this as given, one can find z 1 ðτ; 1Þ ¼ 1=τ−α=½ð1−α Þð1−τ Þ ¼ 0 and solve for the optimal τS, τ = 1 − α.This is indeed a maximum since z 11 ðτ; 1Þb0:

13 Alternatively, straightforward differentiation shows that the maximand is everywhere concave in τ, so this solution is indeed a global maximum.

B.1. FPM Policies As perhaps expected, when urban wages increase and society transitions from the “no migration” to the “unavoidable migration” regime, increases in the urban wage force the elite to grant policy concessions (in the form of lower taxation or better property rights in the peasant areas) to try to prevent migration. The elite gradually reduces τ and increases μ from τ and μ ; their levels in the no migration regime. Over a range of values for wU, these concessions imply there is no migration when in fact the threat of migration exists. However, once the elite reaches zero taxation and achieves the same property rights as in the unavoidable migration regime, it will choose to grant no further policy concessions. From this point forward, further increases in the urban wage generate positive migration. The next proposition summarizes the solution more precisely. Proposition 4. (Summary of FPM policies in the avoidable migration regime) Suppose the elite maximizes the first term in (12) and wU ∈½w ðτ ; μ Þ; w ð0; μ  Þ. Also, let μ⁎⁎ be the level of property rights in the unavoidable migration regime with FPM policies as described in Proposition 1. Then, with w ðτ; μ Þ as defined in (10) and μ⁎ from

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L. Fergusson / Journal of Development Economics 103 (2013) 167–181

Remark 1, the unique political equilibrium features the following level of taxation (τ FPM) and property rights (μ FPM): FPM 1. if wU bw ð0; μ  Þ; then τFPM ∈½ μ ; μ  ; and as wU inP ∈½0; τ ; μ FPM FPM creases, τ falls, or μ increases, or both. 2. if wU ≥w ð0; μ  Þ; then τPFPM = 0 and μ FPM = μ ∗∗.

n o Proof. The problem is to maxmin LIR =T~ ; L=T~ subject to wU ∈ ½w ðτ ; μ Þ; w ð0; μ  Þ: Since L ≥ LRI, it is preferable, if unconstrained, to maximize L=T~ than to maximize LI =T~ . However, since the elite's probR

lem is to maximize the minimum of the two expressions, the unconstrained maximum of L=T~ will in fact, over the relevant range of wages of the avoidable migration regime, be above LIR =T~ . This means that the elite will have to content itself with the “best” combi    nation of policies (that maximizes L~) such that L=T~ ≤ LI =T~ (equivT

R

alently, wU ≤w ðτ; μ Þ). Hence, for a range of values of wU, one can think of the elite as solving the problem: max L=T~ subject to wU ≤w ðτ; μ Þ:

ð19Þ

τ;μ

However, this reasoning fails when wU is large enough that (τ,μ) = (0,μ ∗∗) and LIR =T~ is smaller than L=T~ (that is, wU > w ð0; μ  Þ). Since (τ,μ) = (0,μ ∗∗) maximizes LIR =T~ , there can be no other combination  of ~ ≤ policies that yields a higher utility for the elite and satisfies L= T   LIR =T~ . Therefore, only for wU ≤w ð0; μ  Þ the results are based on the solution to (19), and for wU > w ð0; μ  Þ the solution is (τ,μ) = (0,μ∗∗). As for the characteristics of the solution to (19), note the following. First, recall that w ðτ; μ Þ is increasing in μ for μ b μ⁎, is maximized at μ⁎, and is decreasing thereafter. Note also that μ⁎⁎ maximizes LIR ~T , but since LIR =T~ ¼ w ðτ;wμ Þ L~T and L~T is monotonically decreasing in μ, it must be the case that μ⁎⁎ b μ⁎. From Remark 1, this implies that w ðτ; μ Þ in the constraint of (19) is increasing in μ. We also know that w ðτ; μ Þ is decreasing in τ. Second, the objective function, L=T~ , is decreasing in μ and increasing in τ. These two observations imply that the constraint will always bind and, regardless of the exact combination of policies (τ, μ) that solve (19), an increase in wU will necessarily imply a decrease in τ, and increase in μ, or both to satisfy such constraint. ■ 1 1−α

u

B.2. RE policies Since μ = 1 is optimal in either extreme regime, it is optimal in the avoidable migration regime, where LR in the maximand is either L or LRI. Fixing μ = 1, this is then a simple maximization problem in one variable. In particular, when feasible the elite will set τ such that LRI = L. Intuitively, this equilibrium level of taxation decreases as urban areas become more attractive and the elite tries to prevent migration. When migration becomes unavoidable, as noted above, the desired level of taxation reaches 1 - α. Of course, if the exogenous limit on taxation τ is binding, then τRE ¼ τ. Proposition 5. (Summary of RE policies in the avoidable migration regime) Suppose the elite solves problem (16) and wU ∈½w ðτ ; μ Þ; w ð0; μ  Þ. Then, with w ðτ; μ Þ as defined in (10) and μ⁎ from Remark 1, the unique political equilibrium features μ RE = 1 and τRE ¼ min

Laffer ~ ~ and is decreasing in wU. fτ ; τ g; where τ ∈ 1−α; τ Proof. Fixing μ = 1 this is a standard maximization of Leontiefftype preferences on one variable, τ. The elite will set τ such that h  i1−α LRI = L, or wU ¼ AE ð1=LÞ t ð1−τ Þ þ T−t . Solving for τ, this is   1−α which is decreasing in wU. τ ¼ 1− ð1=t Þ LðwU =AE Þ −ðT−t Þ 1 1−α

1 1−α

B.3. COM policies A general characterization of equilibrium policies for the combined problem is more complicated. However, from the preceding analysis some of its key features are easily established. Proposition 6. (Summary of COM policies in the avoidable migration regime) Suppose the elite solves problem (12) and wU ∈½w ðτ ; μ Þ; w ð0; μ  Þ. Then, with w ðτ; μ Þ as defined in (10), (τ FPM,μ FPM) and (τ RE,μ RE) given by Propositions 4 and 5, respectively, and μ⁎ from Remark 1, the unique political equilibrium features the following level of taxation (τ COM) and property rights (μ COM): (i) if t∈ð0; t ; then τPCOM = τ FPM, μ COM = μ FPM; if t∈ t ; T ; then τ COM = τ RE, μ COM = μ RE = 1. Proof. Follows from the proof for COM policies in the unavoidable regime case.

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