Consumption growth and spatial poverty traps : an analysis of the effect of social services and community infrastructures on living standards in rural Peru

We test the effect of local geographic endowment of capital on household growth in living standards in rural Peru, using a four years unbalanced panel data set. Our theoretical model of household consumption growth allows for the effect of community variables to modify the returns to augmented capital in the household production function. Three different sources of data are used: the ENAHO 1997-2000 household surveys, the population census of 1993 and the district infrastructure census of 1997. Altogether the addition of these different data sources makes an unusually rich data set, at least when considered with developing country standards. As in Jalan and Ravallion (2002), we use a quasi-differencing method to identify the impact of locally determined geographic and socioeconomic variables, while removing unobserved household and community level fixed effects. GMM are then used to estimate the model parameters. Several significant interesting results appear, confirming that private consumption growth depends on local geographic variables. JEL Classification : C33 H23 I18 I32 I38 012


Abstract:
Why are there areas with persistenly low levels of income or consumption?
This could result from the concentration of households with a low capital endowment or from variations in households' environment. Peru is a country with a very much fragmented topography and climate, that combines dry deserts, high mountains and rain forest. One important question is to assess the weight of the geographic endowment in the growth process. If differences in geographic endowment matter more than those in households' characteristics, then encouraging migration to better endowed regions might be a good development policy whereas, in the opposite, it might be better to invest in households' capital. Of course several factors, either geographic or not, can combine to explain persistent poverty in a given area. In this chapter we test the effect of local geographic endowment of capital on household growth in living standards in rural Peru, using a four years unbalanced panel data set. Our theoretical model of household consumption growth allows for the effect of community variables to modify the returns to augmented capital in the household production function. Three different sources of data are used: the ENAHO 1997-2000 households surveys, the population census of 1993 and the district infrastructure census of 1997. Altogether the addition of these different data sources makes an unusually rich data set, at least when considered with developing country standards. As in Jalan and Ravallion (2002), we use a quasi-differencing method to identify the impact of locally determined geographic and socioeconomic variables, while removing unobserved household and community level fixed effects. GMM are then used to estimate the model parameters. Several significant interesting results appear, showing that private consumption growth depends on local geographic variables, but more on local endowments of private and public assets than on pure geographic characteristics. This suggests to combine policies focused on private and public asset endowments that will reinforce local positive externalities, with infrastructure investments that will help poor households to take advantage of growth opportunities, offered by more dynamic markets across local communities.
As pointed by Ravaillion (1998) and more recently by Kanbur and Venables (2005), there are very few countries without large regional inequalities in living standards and with homogeneous spatial growth patterns. The spatial heterogeneity of growth can often be linked to persistenly poor areas, at least in relative terms. Such areas have been a concern in many countries, including those undergoing sustained aggregate economic growth. Examples include China, the eastern Outer Islands of Indonesia, parts of northeastern India, northwestern and southern rural areas of Bangladesh, much of northern Nigeria or the northeast of Brazil.
Peru is yet another example, as the prevalence of poverty varies considerably across regions: the sierra and selva have poverty rates that are nearly twice and extreme poverty rates that are about seven times that of the coast. 1,2 More than half of the extreme poor reside in the rural sierra, though it has less than a quarter of the national population. 3 Turning to growth, Escobal and Torero (2005) noted a high degree of disparity of the per capita expenditure growth rate between provinces. They also found that provinces with the highest, or the lowest, consumption growth rates tend to be clustered. Finally, regional heterogeneity in poverty and growth rates combines with an apparent high 3 degree of poverty persistence. According to Herrera (2001), three quarters of the poor in 1997 remained poor in 1998 and about 60% of them were still poor in 1999.
Why are there areas with persistenly low levels of income or consumption? One possibility is that households with identical characteristics tend to concentrate: poor areas would then be populated by households with low capital endowment and the particular location of these households would have nothing to do to explain their persistent poverty. However, Peru is a country with a very much fragmented topography and climate, that combines dry deserts, high mountains and rain forest. Throughout the country this results in large variations in the natural environment faced by households, that could help explain the observed variations in living standards and growth, particularly in rural areas. In terms of development policy, one important question is to assess the weight of the geographic endowment in the growth process. If growth in a given area is slow because altitude is too high then it might not be worthwhile to invest in the development of this area and preferable to help the migration of households. If, on the other hand, slow growth results from a low endowment in the human capital of households, then policy should be directed to investments in health and education. Of course several factors, either geographic or not, can combine to explain persistent poverty in a given area. Moreover, "pure" geographic endowments like ecological conditions, climate, altitude or latitude add to man made "geographic capital" that includes the supply of local public goods and 4 infrastructure, or the local endowments of private goods. All this can impact individual productivity and our purpose in this chapter is to determine whether and which components of "geographic capital" have a non zero impact on the marginal productivity of private capital, and thus help in determining growth in living standards in rural areas of Peru.
Identifying the factors that explain spatial poverty traps requires extensive data and rigorous econometric methods. We use a 4 years households panel, from 1997 to 2000 (ENAHO survey), the population census of 1993 and the district infrastructure census of 1997. Altogether the addition of these different data sources makes an unusually rich data set, at least when considered with developing country standards. In particular, the panel dimension of the data allows to purge the estimation from any household and community unobservables that could bias our results.
In section 2 the various models that can explain spatial poverty traps and several identification problems are discussed. In section 3, a model of consumption growth that allows for the effect of community variables to modify the returns to augmented capital in the household income generating function is presented. The way to control for latent heterogeneity is also exposed. The model is very similar to that of Jalan and Ravallion (2002). Detailed presentation of the data is given in section 4. Econometric estimation results are analysed in section 5. They show that private consumption growth depends 5 on local geographic variables, but more on local endowments of private and public assets than on pure geographic characteristics. This suggests to combine policies focused on private and public asset endowments that will reinforce local positive externalities, with infrastructure investments that will help poor households to take advantage of growth opportunities, offered by more dynamic markets across local communities.
2 How to explain and identify spatial poverty traps?
Schematically two models compete to explain spatial poverty traps. With free household mobility the spatial concentration of poverty can arise because people with similar characteristics concentrate. If these people were to move to other areas they would experience the same growth in their living standards, holding everything else equal (this is what Ravallion, 1998, terms the individualistic model ). The alternative explanation is that, with no mobility, spatial poverty traps occur because in some areas the "geographic capital" is lower or less efficient than in others, and because such capital has a positive impact on the marginal productivity of private inputs. In this case, otherwise identical households do not experience the same growth in their living standards, if they live in areas with different endowments of geographic capital (this is called the geographic model). Free mobility, that is mobility without any cost, is an ideal situation that one is unlikely to find in a low-income country. In Bangladesh for instance, Ravallion and Wodon (1999) find that "sizable geographic differences in living standards persist when one takes account of the spatial concentration of households with readily observable non geographic characteristics conducive to poverty. The same, observationally equivalent, household is poor in one place but not in another." What is remarkable in this example is that this occurs even though there are no administrative restriction to migration, and very few physical ones, and the vast majority of the country population shares the same ethnicity, language and religion. Just the direct costs of migration -small in absolute terms but prohibitively high relatively to their ressources -prevent poor people from migrating to areas in which they would enjoy higher living standards. In Peru, like in Bangladesh, migration is "free" but, unlike that of Bangladesh, the geography raises physical barriers to the mobility of households.
Thus, high transportation costs, lack of information on opportunities outside the area of residence, ethnic fragmentation, ill-functioning markets for land and so on are as many impediments to the migration of poor households.
From an empirical point of view, making the distinction between the individualistic and the geographic models is not easy, because with free mobility of people or households, it is not difficult to imagine cases where an apparent effect of geographic capital in fact results from the concentration of households 7 with similar characteristics. Suppose for instance that people with high endowments of private capital concentrate in areas with a given range of average temperature. One would then observe that people living under temperate climatic conditions have higher living standards than others, but it would be wrong to attribute this difference to the climate. The issue is the potential endogenous location of individuals and households. It turns out to be particularly accute in static models of living standard levels. As noted by Ravallion (1998), one way of dealing with this is to estimate a switching regression which determines which region the household is located in. But such regression would likely be plagued by endogeneity and identification problems of its own. In other words this might be asking too much to the data. Another strategy is to use an estimation method that permits to control for the effects of unobserved household characteristics and that could bias the coefficients of the geographic variables. This can be done provided that panel data are available. This is the approach followed in this chapter and that is developed in the next section.
3 A simple model of consumption growth. 3.1 Theoretical model. Jalan and Ravallion (2002), we extend the Ramsey model of consumption planning to the case of a household facing geographic externalities in its income generating process. The household, h, finances its consumption entirely from its current income, which is produced according to a production function that admits as arguments the level of productive capital, K, and a vector G of community level variables that might have a positive or a negative effect on the returns to capital:

As in
(1) We depart from Jalan and Ravallion in assuming that K is the level of "augmented capital" in the sense that it includes physical as well as human capital. The reason for this choice will become clear when we will turn to the specification of the capital marginal productivity in the econometric application. Thus y ht is Becker's full income or, in other words, the potential income of the household. It is the income that the household could obtain if it were using entirely both physical and human capital to produce income. The household is assumed to have no access to the credit market for capital, an assumption that seems reasonable given the particular context of rural Peru.
Potential income can be used by the household either to increase its capital stock (by accumulating physical assets or by investing in the human capital of its members) or to consume: with δ the rate of depreciation of augmented capital. The household is assumed to have perfect foresight and to maximize the present value of its utility flows at date 0 under the budget constraint: (3) max This yields the following set of first order conditions: They show that an increase into the marginal productivity of capital induces an increase into consumption, if the marginal utility of consumption is decreasing.
The particular feature of this model is that geographic externalities can influence consumption growth rates through effects on the marginal productivity of capital.
In order to get an estimable form of this equation we follow Jalan and Ravallion in assuming that the instantaneous utility function is of the isoelastic form: where x ht and z h are vectors of specific household-community time dependent and independent variables that modify the marginal productivity of capital. 4 Note that the marginal productivity of capital does not depend on the level of capital, that is constant returns to scale are assumed. But recall that K is, in our case, augmented capital, in the sense that it includes the human capital stock of the household members, so that imposing constant returns to scale is not as restrictive as it might seem.
In order to allow for unobserved heterogeneity we complete equation (4) by adding to the deterministic part a stochastically determined error term: v ht . In this chapter we are particularly interested in determining the effect of community specific variables on the marginal productivity of capital. In order to do so, we have to precisely control for the effect of community and household unobserved specific effects that our model cannot account for and that one cannot hope to fully capture in the available data. As these unobserved variables are likely to be correlated with our included explanatory variables, lack of control of their effects will result in biased OLS estimates of the β and γ coefficients vectors. The usual cure for such unobserved effects is to work with the first differenced version of the base model. But, in our case, this would result into the dropping of the time invariant variables, a most undesirable consequence given our purposes. However, as noted in Jalan and Ravallion (2002), the existence of economy-wide factors suggests that the impact of observed and unobserved heterogeneity on the marginal productivity of capital is not necessarily constant over time. For instance a well maintained irrigation network is likely to increase the productivity of farmers in the corresponding area, but this could matter more in bad (dry) years than in good (rainy) ones.
In other words, economy-wide shocks do not necessarily have the same impact on all households and it is a reasonable assumption to allow the effect of these shocks to vary with unobserved household heterogeneity. We thus follow Holtz-Eakin, Newey and Rosen (1988), Ahn, Lee and Schmidt (2000) and Jalan and Ravallion (2002) and decompose the error term as follows: Equation (4) is written as: where µ ht is assumed to be an i.i.d. variable with zero mean and ω h is a household specific effect (also with zero mean) which is not assumed orthogonal to the regressors and that modifies the impact of external shocks, θ t , on consumption growth. Now, lagging equation (6) by one period, multiplying the resulting equation by r t = θ t /θ t−1 , and substracting it from (6) we get: The determining advantage of this modelling strategy is that in the preceding equation the coefficients of the time invariant variables are identified, provided 13 r t is not found equal to one.
This specification is tested in Jalan and Ravallion (2002) for China. However it assumes that external shocks are identical for every household of the economy.
But in a country like Peru, that presents a wide disparity of ecological conditions this does not seem a very reasonable assumption, particularly in rural areas. Thus we choose to relax this hypothesis and to give more flexibility to the error term decomposition, by allowing inter-regional variation of the r t ratio. We experimented with several regional classifications. The best results are obtained with a six natural regions classification, defined according to altitude and the localization relative to the Cordillera de los Andes. 5 We also allow the constant term to change with the year of observation. The resulting estimates are then used to construct a starting value of the weighting matrix of the GMM criterion. With this matrix we compute the one step GMM estimator. In the final step, the residuals of this estimation are employed to obtain a White-heteroscedastic consistent weighting matrix on which the two step GMM estimator is based. 14 3.3 Determining the instrumental set of variables.
In equation (7) one of our regressors, namely ∆ ln c ht−1 , is correlated with the error term µ ht − r t µ ht−1 , so that instrumentation of this variable is required. A natural choice of instrument is the growth or level of log-consumption with an appropriate lag. As measurement error on consumption growth is a possibility that we cannot reasonably exclude, the year t-2 consumption level cannot be retained as an instrument for ∆ ln c ht−1 , and we have to rely on year t-3 observations, so that a minimum of four years of observations are a priori necessary in order to properly identify our model if lagged consumption is the only available instrument. 6 However, one can imagine to use the log-income level observed in year t-2 as an instrument, if one is willing to assume that measurement errors on income are independent from those on consumption.
Under this assumption, the model can be estimated using two consecutive periods and the use of GMM estimation techniques allows each equation to be instrumented with a different set of instruments. Moreover, one can extend the list of potential instruments and include capital stock variables as measured at the beginning of the observation period and the household and community variables, either fixed or measured at the beginning of the corresponding observation period. For instance, in estimating the determinants of consumption growth between year t-1 and year t, households characteristics as observed in years t-1, t-2 and t-3 are potential valid instruments. However, even 15 though extending the set of instruments never lessens efficiency in infinite samples, in finite samples this could result in very poor estimator properties (Wooldridge 2002). For this reason we tried to restrict the set of instrumental variables to a minimum.
In order to test our specification, we follow Arellano and Bond (1991)   From the ENAHO household surveys it is also possible to calculate geographic level variables.
The list of explanatory variables includes, 11 at the household level, a set of dummies controlling for the sex, age and employment status of the head at the beginning of year t, together with the proportion of children less than five years 18 of age and the proportion of adults more than 65. As one of our assumptions is that there are constant returns to scale to augmented capital in the household production function, we choose not to include the household size, neither the proportion of children of working age, nor the proportion of other adults as explanatory variables, since these variables are proxies for the level of productive human capital in the household. This assumption will be checked by testing the significance of these variables, together with other proxies for productive capital, such as household owned assets, the household's head education level and the connection of the household to electricity, public water and public sewage. The proportion of children less than five years old is included in order to account for eventual opportunity costs borned by active adults when caring for these children. The proportion of adults more than 65 is added in the regression as a way to control for potential opportunity costs of caring for the elderly but also, and mainly, because as one of our geographic explanatory variable is the proportion of old people in 1993 at the district level, we think it is important to control for that proportion at the household level, in order to exclude the possibility that the geographic-level variable captures the effect of the corresponding omitted household level variable.

Model identification.
The validity of our instrumentation procedure bears upon the value of the Sargan statistic. 16 In all three cases this value is found well below the critical value at the 5%, or even the 1%, level. This means that we can be confident that, first, the quasi-differentiation of our model indeed has removed any household or community unobserved specific effect and that, second, instrumentation of the lagged-consumption growth is correct. This conclusion is reinforced by the fact that, in all three regressions, controls for the household's head professional activity, sex and age are included, together with the proportion of children less than 5 and the proportion of adults more than 65 in the household and that none of these variables have coefficients statistically different from zero (results not shown). Had the model quasi-differentiation not removed all unobserved household specific effects, one would expect such effects to be correlated with one or more of these variables and their coefficients to be, spuriously, found different from zero. This is not what we find.
Turning now to the identification issue remember that coefficients of the geographic time-invariant variables are identified provided that the r t ratios are found different from one. We find that this is always the case in the Chala, Distance to equator is positively related to consumption growth. As this variable is expressed in thousand kilometers, its coefficient means that, ceteris paribus, moving south by one thousand kilometers adds 11 percentage points to consumption growth. This could be expected given that, in Peru, the degree of humidity diminishes with increasing latitudes and is consistent with the "geographic" point of view advocated by Gallup and Sachs (1999), Gallup et alli. (2000a), Gallup and Sachs (2000b). However, altitude is not found to have a direct impact, in opposition to what has been found by Escobal and Torero (2000), but this could result, first, from our control for community and household unobserved specific effects and, second, from the fact that observations from the "Suni+Puna" region do not contribute to the identification of time-invariant variables, since the r t ratio is never found different from one for this region (see supra). As it lies entirely above 3500 meters of altitude, this could explain why we do not find any significant impact of this variable. These results are similar with those found in China where infant mortality rate and medical personnel per capita have a significant impact on farm-household productivity, and those found by Murrugarra et al. (1999) and Cortez (1999) on wages and productivities in rural and urban areas in Peru.
The aim of this chapter was to test the effect of local geographic capital endowments on consumption growth in Peru, using a micro model of household behavior that allows for the effect of community variables to modify the returns to augmented capital in the household income generating function. Estimation results depend crucially on the control for community and household unobserved specific effects and tend to be consistent with the hypothesis that local geographic endowments have a non zero effect on consumption growth, a prediction of the geographic model. Somewhat unexpectedly, given the heterogeneity of the Peruvian geography and the obvious difficulty to live in some areas, it appears that most socio-economic variables have significant coefficients, but not all pure geographic characteristics.
These results have several important analytical and policy implications. First, it pinpoints the weakness of models that only consider income dynamics purely in terms of individual household characteristics. Income dynamics are also explained by "geographic" endowments. Second, the way in which geographic capital affects consumption is complex. Spatial poverty traps are linked more strongly to socio-economic features of villages and provision of public goods 29 rather than to purely geographic attributes. Lower endowments have negative externalities adversely affecting the returns to households assets and therefore their consumption growth.
This adverse impact of spatial factors bears also crucial policy implications. It leads to stress the need to combine policies focused on income transfers and assets reinforcement (particularly human capital) with policies that favour mobility across regional markets. In this sense, reduction of transaction costs plays an important role (access to markets, information on market opportunities etc.). Households in poverty trap areas will then more easily take advantage of growth opportunities offered by more dynamic markets across local communities.
Targeting is the other aspect of anti-poverty policies that may be affected when the dynamic and spatial dimensions are taken into account. The existence of poverty traps implies that chronic and transient poverty may be distinguished and have different determinants which in turn implies specific policy contents.
Dynamic targeting also implies identifying factors associated with vulnerability in order to prevent households to fall into poverty (transient or permanent) after a shock. Since externalities are mostly linked to provision of public goods and agglomeration effects, medium-term anti-poverty policy will necessarily have a public investment component. Besides, anti-poverty policies may not necessarily target poor households or villages but may also focus on bridging poor villages with more dynamic regional markets.

30
Although we have considered regional fixed effects and taken into account unobservable individual effects, an explicit and more complete treatment of covariant shocks is needed. In the same vein, we have made the hypothesis that  3 More generally, poverty rates are significantly higher in rural than in urban areas: 78.4% of households are poor in rural areas, against "only" 42% in urban areas. For extreme poverty these rates are 51.3% and 9.9% respectively.
4 Reporting the marginal utilities in the first order equation yields: Taking the logarithm on both sides and assuming that F 0 K < 1 This can be tested provided that at least five years of observations are available.
Unfortunately only four years are available in the present case.
8 This is also the case for urban households. There are 1809 observations over the first three years, but only 716 over the complete period. 9 We thank an anonymous referee for pointing this problem and for suggesting the appropriate method to run the check on the model's residuals. questions on the targeting efficiency of anti-poverty programmes (Paxon, Schady, 33 2003, INEI, 2000a, 2000b, Schady, 2002, Alderman and Stifel, 2003 13 Specifically we follow Maddala (1983) and suppose that under programme participation, the household consumption growth rate is written y i = y i1 = α 1 + Household participation is commanded by the following latent variable I * i = z 0 i γ + ε i and we allow the correlation between ε i and u i1 and u i2 to differ. Under 14 The concentration of people -with or without specific characteristics -may improve individual productivity because agglomeration encourages information spillovers or because a high level of activity brings efficiency (Romer, 1986, Durlauf, 1994. 15 Unfortunately, the ethnic origin of the population is not available in the 1993 census population, nor in the 1997-2000 ENAHO households surveys. 16 The set of non included instruments is as follows : number of years since administrative creation of the district, longitude, nine housing quality variables in 1997, household log-income in 1997 (for growth periods 1998-1999 and 1999-2000) and household log-consumption in 1997 (for growth period 1999-2000 only).
17 A positive value of this coefficient means that households with unobservable 34 characteristics that increase the likelihood of their enrollment in a given programme, also get higher benefits from this programme than other households, holding everything else equal.
18 The impact of some education oriented social programmes on educational outcomes has been analysed by Paxson and Schady (2003). For instance, they show that in districts which received FONCODES support, education expenditure increased school attendance for young children, but no evidence that these programmes affect the probability of being at the right school level, and weak evidence that it decreased the average time it takes children to go to school. Alderman and Stifel (2003) evaluate the "Vaso de Leche" (glass of milk) feeding programme. They find that the programme is relatively well targeted to the poor, but no econometric evidence that its nutritional objectives are achieved.   Distributions of fixed effect model estimation residuals in: -3 years and 4 years panels are equal 0.887        Model 1: Heckman's type correction terms not included Model 2: Heckman's type correction terms included Model 3: Model 2 with proxies for household owned assets included *, **, ***: significant at the 10%, 5% and 1% level, respectively s: different from 1 at the 1% level; t: different from 1 at the 10% level. In all regressions, controls for the household head's professional activity, sex and age are included, together with the proportion of children less than 5 and the proportion of adults more than 65 in the household. None of these variables have coefficients statistically different from zero. Other unreported results are the values of the intercept coefficients for years 1998 to 2000 and, in model 3, the coefficients of the household's proxies for productive capital (all unsignificant).