W_PS_ I 2
POLICY RESEARCH WORKING PAPER 2028
Access to Markets and the Improving road access to
agricultural markets in Nepal
Benefits of Rural Roads would confer substantial
economic benefits on
Hanan G. Jacob), average, much of them going
to poor households. But rural
road construction is more like
a tide that lifts all boats than a
highly effective means of
reducing income inequality.
The World Bank
Development Research Group
Rural Development
December 1998
l POLICY RESEARCH WORKING PAPER 2028
Summary findings
Transport infrastructure plays a central role in rural benefits from hypothetical road projects are calculated
development, yet little is known about the size - or, from the predicted appreciation in value of the
especially, the distribution - of benefits from road household's farmland. These predicted benefits are then
investments. Among other benefits, rural roads provide related to household per-capita expenditures to assess
cheaper access to both markets for agricultural output their distributional consequences.
and for modern inputs. The empirical analysis, using data from Nepal, shows
Jacoby develops and implements a method for large benefits from extending roads into remote rural
nonparametrically estimating the benefits from road areas, much of these gains going to poorer households.
projects at the household level. The idea is that since But rural road construction is not the magic bullet for
these benefits get capitalized in land values, they can be poverty alleviation. The benefits are neither large enough
estimated by examining how the value of farmland falls nor targeted well enough to reduce income inequality
with distance from agricultural markets. Household-level appreciably.
This paper-a product of Rural Development, Development Research Group-is part of a larger effort in the group to
study the impact of rural roads and other forms of infrastructure on household welfare and economic growth. Copies of
the paper are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Maria
Fernandez, roomMC3-542, telephone 202-473-3766, fax 202-522-1151, Internetaddress mfernandez2@worldbank.org.
The author may be contacted at hjacoby@worldbank.org. December 1998. (32 pages)
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about
development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The
papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this
paper are entirely those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors, or the
countries they represent.
Produced by the Policy Research Dissemination Center
Access to Markets and the Benefits of Rural Roads
Hanan G. Jacoby*
Keywords: Rural Roads, Income Distribution, Nonparametric Regression
JEL Classification: 012, D31, C14
*Development Research Group, The World Bank, 1818 H Street N.W., Washington DC
20433.
I. Introduction
Rural infrastructure is a major development priority (World Bank, 1994), yet little
is known about the size and especially the distribution of benefits from such investments in
LDCs. The distribution issue is salient, not only in the formulation of policy, but also in
understanding the political constraints on the allocation of infrastructure investment.
Rural roads are an. important form of public infrastructure, providing cheap access to both
markets for agricultural output and for modem inputs. Given limited policy instruments
for reaching the remote rural poor, road-building would seem desirable on distributional
grounds. On the other hand, the benefits of infrastructure projects accrue mainly to
landowners, who are generally not among the very poor. Thus, the extent to which rural
road construction ameliorates income inequality is ultimately an empirical question.'
In this paper, I examine the distributional consequences of rural roads using data
from Nepal, a country with a largely agrarian economy, a sparse highway network, and
extremely difficult terrain. To this end, I develop an empirical methodology for
nonparametrically estimating the household-specific benefits from alternative road projects
using information on the value of farmland and distance to agricultural markets. If land
behaves like a standard asset, which is a testable assumption, then its value equals the
discounted stream of maximal profits from cultivation. Hence, the income gains from
lower transport costs should be capitalized in land values. With an estimate of the land
value-distance relationship in hand, it is possible to describe the joint distribution of
hypothetical road project benefits anrd household income.
'Howe and Richards (1984) discuss some distributional aspects of rural roads and present case studies.
Also, van de Walle (1996) uses mnicro-data and a profit function approach to examine the distribution of
benefits from irrigation in Viet Nam.
1
In principle, road benefits could also be estimated from the relationship between
farm profits and distance to markets. However, there are several difficulties with this
approach, the most nettlesome of which is that survey data rarely, if ever, provide accurate
information on an essential component of profit, the cost of transporting goods and
agricultural inputs to and from markets. Another difficulty is that profit (or production)
functions assume a fixed technology and thus cannot easily account for potential
adaptations of farmers to greater remoteness from markets, such as substitution of
traditional for modern inputs or away from transport-intensive crops. The relationship
between land value and distance to market is immune from such difficulties.
To be sure, the idea of using land values to estimate the average benefits of
infrastructure investments in a population is hardly new, though it has not to my
knowledge been applied to rural transport. In any case, such estimates do not address the
primary question of this paper, which is a distributional one. The innovation here is to link
a household-level benefit estimate with a measure of household income. In doing so, I
take a nonparametric approach. While it is true that economic theory is largely silent on
the parametric form of hedonic price functions (see Stock, 1991), in practice, relaxing
parametric assumptions in hedonic models is much more likely to matter for distributional
questions than for questions about average benefits.
Theoretically, my analysis is based on the Ellet-Walters model of rural transport
(see Walters, 1968; Gersovitz, 1989), in which land rents decline with distance to markets
through the influence of distance on effective prices. The model, laid out in the next
section, provides a simple characterization of the potentially conflicting distributional
consequences of road projects.
2
Section IiI discusses the nonparametric or, more precisely, semi-nonparametric
estimation of the land value equation. Section IV describes the data, analyzes how farrner
behavior is influenced by distance to market, and tests the appropriateness of a standard
asset-pricing model for land. Section V presents the main empirical results, the analysis of
land values and of the distribution of benefits from hypothetical road projects. Section VI
concludes the paper.
II . Theoretical Framework
Basic Model
Farmers are assumed to cultivate a single crop using x kg per hectare of a modern
input, say chemical fertilizer, and / hours per hectare of labor. Crop yield y (kg per
hectare) is produced with a fixed technology represented by the neoclassical production
function y = f(x, 1). Let w be wage rate and v~ and p be the "effective" or farm gate
prices of output and fertilizer, respectively, discussed below. Per hectare land rent, p, is
defined as the maximal profit that can be earned on a hectare of land,
p(w,v,p)- max{py-wI-vx} (1)
I.x
and can be thought of as a long-run average.
Effective prices are determined by the economic geography, which is illustrated in
Figure 1. A highway of arbitrary length through the countryside runs through a large city
where all fertilizer is produced and output is purchased. The highway transects a series of
otherwise isolated mountain valleys along which all farms are located. This is a
convenient fiction, but not unlike the geography of Nepal. The total cost of transporting
3
goods between farms and the city has two components: a relatively large cost of
headloading goods (i.e., using human porters) between the farm and the road and a
relatively small cost of trucking goods along the road. All farmers trade agricultural
output and fertilizer in a competitive market center located at the road juncture with their
valley (markets at intermediate points up the valley are an inessential complication since
goods must still be headloaded from the main highway). From a given farm, it takes h
hours to walk to the market center and the portage cost of goods is b Rupees/(kg hours),
where b is proportional to the wage. If the money prices of fertilizer and output at a
particular market center are v and p, respectively, then the effective purchase price of
fertilizer is v = v + bh Rupees/kg and the effective selling price of output is p = p - bh
Rupees/kg. All labor can be obtained locally with zero transport costs.
Unprofitable land will not be cultivated, so the limit of cultivation in terms of
walking time to the market center, h , is implicitly defined by p(h ;w, p, v) = 0 . As
figure 1 illustrates, h declines across valleys as one moves away from the city, because
p declines and v increases; ultimately, h = 0 and all cultivation ends.
As to the relationship between land rent and travel time, by the envelope theorem
-b(y + x) for h < h- (2)
So, the negative rent gradient is just equal in magnitude to the total transport costs per
hour per hectare. Furthermore, by the convexity of the profit function in prices,
> 0 for h < h (3)
Thus, along any given valley, the rent function is convex.
4
Notice that convexity of the rent function does not require that farmers both
purchase fertilizer and sell output at the same time (though nonparticipation in the latter
market means that rents depend upon the endogenous shadow price of output). However,
if one moves far enough away from a market center, farmers may stop selling output and
buying fertilizer altogether, and the rent gradient would be zero beyond this point (and
thus the rent function not strictly convex). Convexity is also robust to the assumption of a
single crop or production technology. Figure 2 shows how the rent function along one of
the valleys in Figure 1 reflects the profit maximizing choice of available crops or
technologies; as travel time rises, farmers may switch away from bulkier crops or from
agricultural practices that are intensive in modem inputs.
Roads and Welfare
Using the above framework, consider the welfare implications of building a road of
given length off of the main highway into a particular valley. The local scale of the project
ensures that it has no general equilibrium effects on wages or prices. To avoid specifying
the source of public finance, assume that the project is funded by earmarked foreign aid.
Let A denote the length of the road in foot-travel (hours walking time) equivalents. By
enabling truck transport, the road effectively cuts portage costs by some fraction ,u. The
new rent function, suppressing its dependence on prices and on ',u2 iS
2The parameter u reflects road quality. I do not consider the welfare cffects of variation in p because, as
a practical matter, the cost of upgrading road surface (from earth to gravel or asphalt) far outweighs the
small reduction in vehicle operating cost, once truck transport is feasible (Beenhakker and Lago, 1983).
Although improvements in road conditions, given surface type, can substantially reeuce vehicle operating
cost, these cost-savings are likely to be small compared to those of a new road. Of course, in the extreme
case where an existing road is impassible to trucks, a road improvement is tantamount to a new road.
5
a(A,h) = p(u) forh < (4)
=p(h-2(l-,u)) forhˇ> (
Figure 3 illustrates the rise in land rents as a result of the project, along with the expansion
in the limit of cultivation h'.
An interesting policy question concerns the length of the road, specifically whether
it makes sense to build a lot of short roads or fewer long ones, given a fixed construction
budget. A key input into this decision is the marginal social benefit of road length, where
"society" in this case refers to the farmers in the typical valley. Suppose that household
income z is determined by farm profit (land rent) and labor earnings, the latter which is
assumed fixed across households for expository purposes; i.e., z = o(A, h)A + e, where A
is total landholdings and e is earnings. Let G(h, A) denote the joint cumulative
distribution function for distance from market center and landholdings. Finally, let y/(z)
be the increasing, strictly concave, indirect utility function. Assuming it is additive, the
social welfare function is
W(2) f j (o-(Af(2, h)A + e)dG(h, A) (5)
A
Notice that households already on a road do not benefit from its extension further up the
valley (i.e., o-A = 0 for h < A), so that differentiating (5) with respect to A yields
W'(2) = J fV'adAdG(h, A) (6)
A
To illuminate the distributional issues, it is instructive to fix land area for the
moment and to decompose marginal social benefit as follows
W'(2,A) = 11 - G(A1A)]{E[4 A,h > A]E[cIA, h> A] +Cov[|V,aAIA,h> A]}A (7)
6
The first term in (7) is simply the fraction of households living off the road. The first term
in the curly brackets is the average marginal value of the road extension for these
beneficiaries, assuming their marginal utilities of income and appreciations in plot value are
uncorrelated. The second term in curly brackets accounts for this correlation, which must
be negative because V"ohA > 0 and o,Ih <0 . In other words, farther up the valley,
where land rents are low and thus households are poorer, rents rise by less due to the road
extension. The size of this "targeting inefficiency" depends crucially on the shape of the
rent ianction; indeed the covariance is zero if the rent function is linear in travel time. In
sum, the marginal social benefit of a road extension is higher when: (i) the fraction of the
population living off-road is higher; (ii) the average off-road household is poorer (i.e., has
a higher yV' ); (iii) the off-road rent gradient is steeper; and (iv) the targeting inefficiency
(the covariance term) is smaller.
With land area variable the distributional issue becomes cloudier. First, for any
given h, both the benefit from the road extension and household income are increasing in
landholdings.3 W'hile this effect exacerbates inequality, there is also an effect working in
the opposite direction. It is often the case in developing countries, and Nepal is no
exception, that poorer households are found in more remote areas, perhaps because poor
migrants settle on the frinees of cultivation Tf A and h are neeativelv correlated. then the
beneficiaries of a road extension (those off the original road) tend to be poorer, resulting
in a greater marginai social benefit than if A and h are uncorrelated. Allowing earnings, e,
to vary in the population complicates matters further, but the basic point remains, namely
3 Note that in this model renters do not benefit from road construction; their higher rent payments just
offset the greater profitability of the land.
7
that road construction has ambiguous distributional effects. The goal of the empirical
work is to resolve this ambiguity in the case of Nepal.
IH. Econometric Specification
The theoretical analysis is framed in terms of rents, but my data are on land values
at the plot level. According to the standard asset-pricing model
loa(V) = 1og(p(h;w,p,v))- log(r) (8)
whe. - V is the present market value of a plot of land and r is the constant discount rate.
Assume that this formula is valid, at least until it is tested in Section IV.
Besides negativity and convexity in h, economic theory imposes no restrictions on
the form of p. It is therefore desirable to estimate the rent function nonparametrically,
but this is not feasible when it includes many other variables besides h. For example, any
plot characteristic, such as soil quality, that shifts the production function f should also
shift the rent function p. Additionally, in the absence of accurate data on input and
output prices, geographic price variation can be swept out of the rent function by
including market center (regional) dummy variables.5 A within-market analysis also
ameliorates the problem of endogenous placement of roads and/or markets; in particular,
If farmers are risk neutral, then V = E to , where Eo is the expectations operator conditional
on today's information set. if it is further assumed that profits per hectare follow a random walk so that
Eo[pt+l ] = Pt, then the formula simplifies to V = p/r, where p = p0 (see Clark et. al, 1993).
Strictly speaking, this procedure is only an approximation. Since h enters effective prices linearly,
log(p) cannot be additively separable in money prices. Even with accurate price data, it would be difficult
to impose the full structure of the theoretical model in the estimation of the rent function. On the other
hand, given the relatively low cost of trucking, it is unlikely that price variation along the main highway
is sufficiently great to render this approximation inaccurate.
8
market centers may be located closer to more fertile land, where rents are higher. Given
these considerations, I take a semi-nonparametric approach by assuming that
log(p) = log 0(h) + r' X +6' M, where a is a nonparametric function, X is a vector of
plot characteristics, and M is a vector of regional dummy variables.
As to the dependent variable in (8), Colwell and Munneke (1997) warn against
using land value per-hectare because plot values may be nonlinear in area. If so, and if
parcel size is correlated with distance to market, then such a specification will lead to a
spurious correlation between land value and distance. Including the log of plot area, A,
to account for this nonlinearity in the empirical specification of (8) gives
log(V) = logO(h) +,l1og(A) + y'X + 6'M + u (9)
which nests the value per-hectare specification when / = 1. Note, log O(h) absorbs
log(r), and the error term, u, reflects unobserved attributes of the plot.
Following Robinson (1988) and Stock (1991), equation (9) can be estimated by
first using bivariate kernel regressions to "partial out" h from both sides. Since the
number of kernell regressions required equals one plus the dimensionality of ( A, X, M),
this method is computationally very expensive, especially given the large sample. A much
cheaper approach uses the fact that h is a discrete valued regressor in the data with k
distinct values. In the first stage, I include a k - I vector of dummy variables D in (9) for
each value of h; i.e., I replace logO with co = kJDJ. Applying ordinary least squares
(OLS) to this regression yields a consistent estimate of (A, ry 8, O . In the second stage, I
calculate t for each observation and run a nonparametric regression of this variable
against h to get a smoothed estimate of 9.
9
IV. Data and Preliminary Analysis
Nepal Living Standards Survey
The data for this study come from the 1995-96 Nepal Living Standards Survey
(NLSS), a nationwide multi-topic survey collected by the Central Bureau of Statistics
assisted by the World Bank (Central Bureau of Statistics, 1995). A stratified random
sample of around 3400 households was drawn from four zones: Mountains, urban Hills,
rural Hills, and Terai. Jn addition, a special sample of 1200 households was surveyed in
the Arun valley (rural Hills), which I include in my analysis.
The NLSS contains a detailed agricultural module including information on the use
of modern inputs, of which chemical fertilizer predominates, and on crop production and
saies- In addition, the survey provides a listing of all plots owned or leased in by the
household along with information on plot area, land quality, irrigation by season, net rent
received by season (if leased out), and, of course, value of owned plots. The question on
plot value reads as follows: "If you wanted to buy a plot exactly like this, how much
would it cost you?" One indication of farmers' awareness of land values, besides the fact
that it is by far their most productive asset, is the frequency of land transactions, which is
surprisingly high in the sample.6 Among the 3,621 landowning households, 5 percent
bought land the previous year and 9 percent either bought or sold land. Moreover,
although 85 percent of all plots are inherited, 28 percent of the landowning households
purchased at least one of their current plots. Note also that any nonsystematic
6Land transactions are sparse in most contexts. For this reason many hedonic studies use self-assessed
land values (see, in particular, Mendelsohn, et al., 1994 and the citations in Colwell and Munneke, 1997)
or housing values (see Bartik and Smith, 1987).
10
measurement error in plot values will not affect the coefficients of a regression in which
plot value is the dependent variable.
A unique feature of the NLSS questionnaire is that it collects information at the
household level on access to 14 different facilities. For each facility, the survey asks about
travel time (in minutes, hours, and days) and mode of transport; i.e., by foot (without
load), bicycle, motorcycle, car/bus, and mixed (foot+vehicle). Keep in mind that
collecting data on actual distance, even using satellite telemetry, would be of little value in
moun1tainous Nepal (except perhaps in the Terai). However, I do not use the household-
level travel time information directly. Instead, I take the median of travel times by
"wards" (in rural areas these are villages and environs) based on households that report
travel times by foot, which the great majority do. The advantage of this procedure is that
it standardizes travel times for mode of transport, which is potentially endogenous, and it
mitigates the measurement error that is likely to be present in household level travel times.
I focus on market centers and agricultural cooperatives, since these facilities are
the most likely to offer the opportunity to sell output and purchase modem inputs. In fact,
over two-thirds of the households who report using chemical fertilizers obtained them
from agricultural cooperatives, and most of the rest from private traders. My measure of
h is the minimum of ward- median travel times to the market center and agricultural
cooperative. Ideally, travel times to all relevant facilities should be considered separately,
but this would lead to mu!ticollinearity problems, not to mention making nonparametric
estimation practically impossible. Median travel time to a market center or a cooperative
in the sample of 3,724 cultivating households is 2 hours (mean=2.8 hrs.). Median travel
11
times are shorter on the plains of the Terai (1.25 hrs.) than in the Hills (2 hrs.) or
Mountains (3 hrs.).
Finally, it is necessary to define a market area within which money prices (i.e., p,
v, and w ) do not vary. I take each district to be a distinct market; 73 out of the 75
districts in the country are represented in the NLSS sample and there are on average about
4 wards in a district (except in the oversampled Arun valley where this number is much
higher). Though somewhat arbitrary, identifying a market by a district is consistent with
evid.-ice from the village questionnaires attached to the NLSS. These data show that very
few villages have either market centers or agricultural cooperatives located in the same
ward; households living in several different wards share these facilities.
Analysis of Fertilizer Use and Crop Sales
If proximitv to markets influences land values through the effective prices of
agricultural inputs and outputs, then purchases of modem inputs and sales of output
should decline with distance from the market center. According to the model, observed
fertilizer use per hectare, allowing for corner solutions, is x* = max{x(w, v,),0}. A
similar equation holds for observed total crop sales per hectare, s*, except that sales also
depend on household consumption decisions. Analyzing marketed surplus (s* minus
consumption) is problematic because transport costs drive a wedge between selling and
purchase prices and net sellers respond differently to variation in these transport costs than
do net buyers (see, e.g., Omamo, 1998). Examining crop sales alone focuses on the
selling decision, which is my primary interest. It is also probably reasonable to assume
12
that for net sellers consumption is relatively unresponsive to transport costs, given that
income and substitution effects work in opposite directions.
Figures 4 and 5 plot nonparametric regression estimates of fertilizer use per
hectare and crop sales per hectare, respectively, against travel time. The econometric
specification is similar to equation (9) and the sample consists of 3,712 cultivating
households.7 Since both fertilizer use and crop sales are heavily censored at zero, I
estimate the first-.stage models by tobit, in addition to OLS.8 For the tobits, I drop
obsc.vations with perfect classification; i.e., where all cases of a given value of h or of a
given district are censored (167 observations for fertilizer, 6 for crop sales).9 The second-
stage nonparamel:ric regressions are estimated using the LOWESS smoother with
bandwidth=0.8. The choice of smoother is dictated by its robustness to outliers and by the
fact that the 60 successive values of h are not equally spaced, which can lead to biases in
kernel regressions (Fan, 1992).
The figures show that fertilizer purchases and crop sales per hectare decline
steadily beyond travel times of about one hour. It is unclear why the curves are increasing
for travel times of less than an hour, but one reason might be that cultivation is typically
less intensive near urban areas. Also, comparing the curves based on OLS and tobit first-
stage regressions indicates that accounting for censoring makes little substantive
7Twelve households are dropped because they are uniquely identified by their district and their value of h.
s The first-stage parnmeter estimates are suppressed for brevity. To summarize, education of the head and
the set of district durnmies are jointly significant in all regressions, and the demographic variables
(number of adult males and females and male and female children), included only in the crop sales
equation to capture consumption variation, are also jointly significant.
9The high rate of ce:nsoring within certain districts precludes the use of semiparametric methods that are
robust to deviations from normality. In particular, the censored LAD estimator fails to converge when
13
difference. In sum, this analysis supports the notion that transport costs influence farm
profits through input use and crop marketing decisions. The fertilizer result, in particular,
confirms the importance of the intensive margin of cultivation, implying that the farm
profit function, and hence the rent function, should be convex.
Analysis of Plot Values and Rents
Underlying the asset-pricing formula given by equation (8) are several strong
assun.r.tions about land and credit markets,'0 which may not hold in Nepal. To test
equation (8), along with the validity of self-reported plot values, I compare values with
rents received on plots that are leased out (mainly sharecropped). My analysis is based on
a sample of 381 plots that were either rented out during both agricultural seasons, or were
rented out in the wet (the main growing season) and left fallow in the dry. It should be
noted, however, that about twice this many plots (around six percent of all those owned)
were rented out during at least one season. Net rents are summed across both seasons,
and include the value of in-kind payments while netting out the cost of inputs provided to
tenants. The median rent to value ratio (p/V) is 0.055, which can be viewed as an
estimate of the discount rate r. Formally, I run the regression
log(V)= 7o + 77q109og(p)+4 (9)
and test whether r7, = 1.
district dummies are included in the specifications. The overall rates of censoring in the samples are 43
percent for fertilizer and 49 percent for sales.
10 For example, where land is the sole form of collateral for loans, its price may reflect its collateral value
in addition to the capitalized value of the stream of rents (see Chalamwong and Feder, 1988).
14
Table 1 reports a series of estimators of q, that make progressively less restrictive
assumptions about the form of correlation between log(p) and the error term 4. The
OLS estimate in columnn (1) assumes that log(p) and ; are uncorrelated, and it falls well
short of unity. However, one reason for this low estimate could be attenuation bias due to
random measurement error in rents. Specification (2) thus instruments rents with plot
area, which does indeed raise the estimate of 71, though it remains marginally below unity.
Specification (3) corrects for the possibility that credit market conditions (i.e., log(r)) and
rents might covary across markets by including district fixed effects (using only districts
that contribute more than one plot to the sample); i7j is still precisely estimated, but it is
no longer statistically different from unity. Finally, specification (4) includes household
fixed effects, using the 90 households that contribute more than one plot to the sample.
This estimator correcr:s for the possibility that household-specific interest rates and rents
are correlated, as wet[ as for any selection bias induced by restricting the sample to those
households that rent out land. This last estimate of q, is again indistinguishable from
unity, so that the maintained assumptions of the asset- pricing model and of no systematic
reporting bias in plot values cannot be rejected.
V. Main Results
Plot Values and Distance to Market
Information is available on a total of 13,672 plots owned by 3,621 households.
Plot characteristics include suitability for rice cultivation (khet land), whether irrigated,
and if so whether seasonally or year round, mode of irrigation (tubewell, canal, other),
system of irrigation (self-managed, agency managed, community managed), and the
"quality" of the plot based on a four grade classification used by the land revenue
department for tax assessments. Land value is missing for 13 plots and quality for 98
plots, so the plot value regressions are based on 13,651 observations. However, when
predicting plot values based on the regression results, these missing observations can be
recovered by imputing plot quality with its modal value.
Table 2 reports two specifications of the plot value regression. The first assumes
that O(h) = h and the second performs the first-stage in the semi-nonparametric
estimation described in Section HI. In both specifications, the plot characteristics have
significant and sensible coefficients; for example, plots that are suitable for rice, plots with
year round irrigation," high quality plots, and, of course, larger plots are more valuable.
However, the value per-hectare specification (,/ = 1 in equation (9)) is resoundingly
rejected, which is important because plot size turns out to be negatively correlated with
distance to markets. Thus, restricting /3 to one would have led to an underestimate of the
rate of decline of land values with travel time (Colwell and Munneke, 1997). As it is,
travel time is strongly negatively associated with land values.
Figure'6(a) plots the 9(h) derived from the two specifications in Table 2
(normalized by taking deviations from means). In the first case, O(h) = h0222, which is
obviously convex. The nonparametric estimate of O(h) (LOWESS; bandwidth=0.8) is
also roughly convex, except that the function is increasing above travel times of 12 hours,
l Since irrigation is an investment, which may be responsive to distance to market, I also ran the plot
value regressions unconditional on the irrigation variables. In this case, the coefficient on log travel time
is -0.225 (0.0217), which is almost identical to its value of -0.222 in specification (1) of Table 2.
16
though only 5 percent of plots are located this far from markets. 12 To formally compare
the parametric and nonparametric models, I use the bootstrap, drawing 100 percent
random samples in two stages, first by sampling plots within households and then by
sampling households. On each replication, the two models are run and the difference in
the slope of 9(h) is calculated at each value of h. As a test of whether the actual slope
differences in Figure 6(a) are significantly different from zero, Figure 6(b) plots, at each h,
the ratio of the actual slope difference to the standard deviation over the 100 bootstrap
replications. When the absolute value of this ratio exceeds 1.96, the equality of slopes can
be rejected at the 5 percent level. That this hypothesis is rejected near the endpoints is
perhaps not too surprising. However, the nonparametric estimate is also significantly
steeper (more negatively sloped) than the parametric estimate in much of the one to three
hour travel time range, where the data are most dense. Although other parametric models
might fit the data better, this test shows that there is sufficient power to reject a reasonable
parametric alternative, thus supporting a nonparametric approach.
Benefits and Distributional Consequences of Road Projects
The expected appreciation in value of a given plot as travel time falls from an
initial value of h( to a value of h, is
[b(hl) - 6(ho)] exp[6log(A) + fX + SM]E[exp(u)] (10)
The last term in this expression takes into account unobserved heterogeneity in plot
values, and can be estimated nonparametrically as the average exponentiated residual from
12 Bandwidth choice is subjective, but the main features of the nonparametric fit are robust to bandwidth.
17
(9). Although nonparainetric regression only provides an estimate of 0 at actual values of
h, 0(hl) can be estimated by linear interpolation between known values of 0. To
simulate the benefits from the road project discussed in Section II, let h, = ,uho for
ho < A and h1 = ho - A(I-v) for ho 2 A . I set the value of , at 0.1 to reflect the fact
that the cost per ton-km of headloading in Nepal is roughly ten times the cost of
trucking."3 Total household (capitalized) benefit from the project is simply the sum of the
appreciations in value of each of the household's plots. 14
Following standard practice, I use total household consumption expenditures as a
measure of income and per-capita expenditures, adjusted for regional price differences, as
a measure of welfare. Let us say that a road project is progressively (regressively)
targeted if the ratio of benefit to total household expenditures, the benefit ratio, is
decreasing (increasing) in per-capita expenditures. Figure 9 plots nonparametric
regression curves (LOWESS; bandwidth=0.8) of benefit ratios against log per-capita
expenditures for three road projects, corresponding to three values of A. The estimates
are based on the full sample of 4,573 households, which includes both households who do
not cultivate and those who do not own land. 15
13 This number is based on information in Walters (1968), but it is still approximately valid according to
World Bank transport economists familiar with Nepal.
in the few cases dihere duc ioii i Laaei iiic uceurs on uIe icitesirfg pol-auiu of 9I, bI eEl iSSCt
to zero. Note that it is not possible to calculate benefits from the additional land brought under cultivation
as h increases. However, as long as one considers a marginal road extension, these benefits are an
envelope phenomenon and hence are zero.
All statistics reported for this sample (e.g., the expenditure deciles in Figure 7) are calculated using
population weights to insure that they are nationally representative. Ninety-three percent of the
households (on weighted basis) live in rural areas.
18
Figure 7 shows that as the road is extended farther up the "representative>' valley,
benefits are targeted more progressively. Indeed, the distribution of benefits from a short
road, one that extends a mere 1.5 hours walking time up the valley, is slightly regressive.
Sixty percent of the sample would lie along such a road, whereas 85 percent would lie
along the 3-hour rioad and 98 percent would lie along the 8-hour road. The key factor
behind the increasing progressivity is the strong tendency for poorer households to live
farther away from markets, as confirmed by the nonparametric regression curve in Figure
8. E idently, this factor dominates the opposing tendency of poorer households to have
less valuable landholdings, also illustrated in Figure 8.
While suggestive, Figure 7 does not address the question of whether the benefits of
a hypothetical road project are sufficiently large and distributed sufficiently progressively
to reduce overall income inequality. To tackle this question first requires converting the
capitalized benefits into a permanent income flow, which in tum requires an assumption
about the discount rate, r. Suppose that current household expenditures equal permanent
income. For a pure farm household, with no off-farm employment and which leases in no
land, permanent income equals rVrOT,L, where VrOTAL is the sum of the value of all plots
owned; more generally, income comes from other sources as well. Thus, in a regression
of total household expenditures on VTOTALL, the coefficient on VTOT,J should equal the
discount rate r, with other sources of income consigned to the residual. A slight
refinement of this regression, which includes ward (village) fixed effects and which
instruments VTOT4L for measurement error using total land area owned, gives r = 0.058
19
with a standard error of 0.010.116 This estimate of the discount rate is remarkably close to
that derived earlier from the rent to value ratio (i.e., 0.055). In the calculations that
follow, I set r = 0.06.
Denote household benefits per capita from a road of length A by B(2). Per capita
expenditures (permanent income) as a function of road length is thus -(2) = ZO + rB(2),
where zo is baseline per capita expenditures. Assuming that y/(z) = z', e> 0, the
social welfare function (see (5)) can be written as W(2) = [Y(A)(I - I(2))11c, where z is
mean per capita expenditures and I E [0,1] is Atkinson's measure of inequality. 17
Differentiating with respect to A gives
W'(2) Z-(2) I'(i) (10)
W(A) z-(A) I1- I(A)
In other words, the rate of increase in social welfare as the road is extended can be
decomposed into the rate of increase in mean income and the rate of increase in income
equality, I - I. An assessment of whether road building has important distributional
consequences can be made by comparing the magnitudes of these two components at
reasonable values of the inequality aversion parameter c. Specifically, define
I(R-n In /(A y 7(i ) - Zn 1 i) n)
1-10 / I-IO
16 7.1- nT cZ Pzimat 5 5' i dent. ^nlr--int fn-r -nmeSrm.mPnt F-rTre it sihctnntii1, smaller at
0.0076 (0.0007). These regressions are based on the sample of 3,621 households that own land.
Recall that I 1- - I(z)i for S lwhere N is the number of individuals. When
= 1, W(A) = log[F(A)(1 - I())], where I = 1- i (4 u-
20
where the zero sulbscript denotes values prior to the road project. S2(A; e) represents the
contribution of reduced income inequality to the increase in social welfare from the
building of a road of length 2.
Figure 9 plots n(A;e) using the Nepal data for A 's ranging from 0.5 to 10 hours,
beyond which value practically every household is on the road so that W'(2) - 0. Note
that putting all households in the sample on a road would raise 5 by ten percent, quite a
substantial gain in permanent income.'8 Interestingly, at high values of inequality aversion
( = 4 ), building a short road actually increases income inequality ( Q < 0). For any value
of , the contribution of inequality reduction to the increase in social welfare rises with
the length of the road, again because of the strong tendency for the poor to live in more
remote areas. However, unless one chooses a value of e above 2 or so, which is usually
considered rather large, the increase in social welfare is due overwhelmingly to higher
mean income. Rural road construction thus appears to be like a tide that lifts all boats
rather than a highly effective means of reducing income inequality.
VI. Conclusion
Transport infrastructure plays a central role in rural development, but the
distributional consequences of rural roads have not received adequate theoretical or
empirical attentiorn. This paper develops and implements a method for nonparametrically
estimating the benefits from road projects at the househoid ievei and for examining the
distribution of these benefits across income classes. The findings for Nepal suggest that
18 Keep in mind that because I have weighted the sample to represent the population of Nepal, all of these
calculations take proper account of the fact that population is less dense in more remote areas.
21
providing extensive road access to markets would confer substantial benefits on average,
much of these going to poor households. However, the benefits would not be large
enough or targeted efficiently enough to appreciably reduce income inequality in the
population (unless there is an exceptionally high degree of inequality aversion). Thus,
while my analysis may paint a more optimistic picture than the World Bank's (1994, p. 80)
general assessment that infrastructure is "a blunt instrument for intervening directly on
behalf of the poor," rural road construction is certainly not the magic bullet for poverty
allev ation.
Another lesson of this research is that data on land values and characteristics,
particularly at the plot level, can be extremely useful in measuring the benefits of
infrastructure investments in LDCs, and not just of rural roads. To be sure, land may not
always behave like a typical asset, so that benefit capitalization may be imperfect, but the
asset-pricing model can be tested to determine whether the methodology developed in this
paper is appropriate in a particular context.
Finally, it is important to mention.the other benefits of rural roads besides cheaper
transport to and from agricultural markets, such as better access to schools and health
facilities and, more generally, to a greater variety of consumer goods. Insofar as farmers
prefer to live near their farms, at least some of these gains are likely to be capitalized in
farmland values. Separating out these distinct benefits of rural roads is left as a topic for
future research.
22
References
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Chapt. 31 in Handbook of Regional and Urban Economics, Vol. I, ed. by Edwin
Mills. Amsterdam: North Holland.
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Roads. World Bank Staff Working Papers No. 610. Washington: The World
Bank.
Central Bureau of Statistics. 1995. Nepal Living Standards Survey: Interviewers
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Land Values, Land Rents, and Capitalization Formulas," American Journal of
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Journal of Urban Economics, 41:321-36.
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American Statistical Association, 87:998-1004.
Gersovitz, Mark. 1989. "Transportation, State Marketing, and the Taxation of the
Agricultura.l Hinterland," Journal of Political Economy, 97(5): 1113-37.
Howe, John and Peter Richards. 1984. Rural Roads and Poverty Alleviation. London:
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Global Warming on Agriculture: A Ricardian Analysis," American Economic
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Omamo, Steven Were. 1998. "Transport Costs and Smallholder Cropping Choices: An
Application to Siaya District, Kenya," American Journal ofAgricultural
Economics, forthcoming.
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56(4):931-54.
23
Stock, James H. 1991. "Nonparametric Policy Analysis: An Application to Estimating
Hazardous Waste Cleanup Benefits," in William A. Barnett, James Powell, and
George Tauchen, eds., Nonparametric and Semiparametric Methods in
Econometrics and Statistics. Cambridge: Cambridge University Press.
Walters, Alan A. 1968. T7he Economics of Road User Charges. World Bank Staff
Occasional Papers No. 5. Washington: The World Bank.
World Bank. 1994. World Development Report 1994: Infrastnrct2re for Development.
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Working Paper, No. 21. Washington: The World Bank.
24
Table 1
Plot Values and Rents
(1) (2) (3) (4)
OLS IV, IVb IVb
,i 0.658 0.825 1.047 1.034
StandardError 0.064a 0.108a 0.091 0.115
Ho0 ill= 1 (p-value) 0.000 0.105 0.606 0.767
Fixed Effects none none district household
N 381 381 373 278
aRobust standard error accounts for district-level clustering.
bLog of plot area is the excluded instrunent.
25
Table 2
Plot Value Regressions
Means (1) (2)
Log(hours travel time) 3.47 -0.222
b (4.01)a (10.3)
Hzo: S= 0 (p-value) --- 0.0000
Log(area in hectares) 0.298 0.558 0.547
(1. 16)' (37.8) (37.4)
Suitable for rice (khet) 0.434 0.149 0.144
(3.89) (3.84)
Irrigation:
seasonal 0.175 0.341 0.325
(4.55) (4.47)
year-round 0.138 0.497 0.450
(6.29) (5.88)
canal 0.239 0.060 0.052
(1.0) (0.88)
tubewell 0.030 -0.034 -0.061
(0.41) (0.74)
self-managed 0.189 -0.082 -0.051
(1.664) (1.09)
agency managed 0.018 -0.219 -0.209
(1.663) (1.67)
OQualitv:
dwaim 0.240 -0.250 -0.226
(5.27) (5.02)
sim 0.304 -0.499 -0.465
(9.04) (8.84)
chahar 0.365 -0.833 -0.792
(13.9) (13. 9)
District dummies (p-value) 0.0000 0.0000
R2 0.546 0.568
Notes: Robust t-values accounting for household-level clustering in parentheses. Omitted categories:
pakho/bari (dry) for khet; non-irrigated for irrigation; other for irrigation mode; community managed for
irrigation management; and awal (highest grade) for quality. Sample size is 13,561 plots belonging to
3,586 households.
aStatistics are for levels. Standard deviations are in parentheses.
bJoint significance of the dummy variables for each of the 60 values of h.
26
Limits of CulCivation Farms
, > ~ ~ ~ ~~I I I
Aft Afi,
Market Centers ! Main Highway
Figure 1: Economic Geography
rent, profit
rent function
--------------~ ~ ~~~~ ~ ~ ~~~~~~~~ - -- ------- ----------
hours travel time
Figure 2: Rent Function Along a Valley with Technology Switching
p h h A hours walkcing time
rent, prOFit 3
Fiur 3: 4c rfaRod oad ofn lengthion
OLS first-stage Tobitfirst-stage
.2 -
o~~ ~ ~ 0
0)
z .2
-.4 -
0 5 10 15 20
hours travel time
Figure 4: Fertilizer Use vs. Travel Time
OLS first-stage Tobit first-stage
.4 -
.2 -
0
c
0)
0) -.2
-.4
0 5 10 15 20
hours travel time
Figure 5: Crop Sales vs. Travel Time
parametric nonparametric
1.5
1
0
(0
0
-.5
0 5 10 15 20 25
hours travel time
Figure 6(a): Estimates of theta(h)
(nonparametric slope - parametric slope)
I-19
0 5 10~~~i' 1f5 210 25
hours travel time
Figure 6(b): Pointwise Bootstrap Test of Slope Difference
road length = 1 1/2 hourwalk + road length = 3 hour walk
road length = 8 hour walk
6
5
4-
CL
0
.0
0 1
7 8 9 10
log per-capita expenditures (gridlines=deciles)
Figure 7: Distribution of Benefit from Road Projects
o value of land (Rupees) travel time (hours)
600000 7.02205
0. 400000
0
0~~~~~~~~~~~~~~~~~~~
-°,200000j 2
o -:X 0\r.00287
7 8 9 1 0
log per-capita expenditures (gridlines=deciles)
Figure 8: Land Value and Travel Time vs. Income
g = 4
.4
.3-e =2 ,
.1
0
-- 1!1
-.2
-.3
-.4
I I I lI I I I I I I
0 1 2 3 4 5 6 7 8 9 10
road length (hours walking time)
Figure 9: Effect of Road Extension on Inequality (Q)
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