Food prices, wages, and welfare in rural India.
Jacoby, Hanan G.
Food prices, wages, and welfare in rural India.
I. INTRODUCTION
Elevated food prices over the last half decade have provoked a rash
of government interventions in agricultural markets across the globe,
often in the name of protecting the poor. Of course, it is well
recognized that many poor households in developing countries, especially
in rural areas, are also food producers and hence net beneficiaries of
higher prices. (1) Even so, there is another price-shock transmission
channel, potentially more important to the poor, which has received far
less attention in the literature: rural wages. (2) To what extent do
higher agricultural commodity prices translate into higher wages? For
rural India, home to roughly a quarter of the world's poor (those
living on less than $1.25/day), the answer to this question can have
momentous ramifications. After all, the vast majority of India's
rural population relies on the earnings from their manual labor, most of
which is devoted to agriculture. (3) Any thorough accounting of the
global poverty impacts of improved terms of trade for agriculture must,
therefore, confront rural wage responses in India.
Textbook partial equilibrium analysis (e.g., Deaton 1989; Singh et
al. 1986) considers only the direct income effect of a price change on
household welfare, which, to a first order, is proportional to the
household's production of the good net of consumption. While this
approach is useful for understanding the very short-run welfare impacts
of price shocks, it ignores the inevitable labor market repercussions of
persistent price changes. Insofar as higher agricultural prices lead to
higher wages, then, there are three channels of general equilibrium
welfare effects: (1) higher labor income; (2) lower capital (land)
income due to higher labor costs; and (3) higher prices for
nontradables. To quantify these effects and obtain the full welfare
impact of changes in agriculture's terms of trade, one needs, first
and foremost, an estimate of the relevant wage-price elasticity.
A few existing studies estimate wage-price elasticities using long
aggregate time series data from countries that were effectively autarkic
in the main food staple (pre-1980s Bangladesh in Boyce and Ravallion
1991; the Philippines in Lasco, Myers, and Bernsten 2008), thus raising
serious endogeneity issues. Alternatively, Porto (2006) estimates the
wage impacts of changes in traded goods prices using several years of
repeated cross-sectional household survey data from Argentina. In the
case of agricultural goods, which must somehow be aggregated, Porto
creates a price index using household expenditure shares as weights (as
does Nicita 2009). To appreciate the issue involved with this strategy,
consider an extreme example. Suppose that a country is a net exporter of
cotton and net importer of wheat, its sole consumption item. Since the
cotton industry is a major demander of labor, a rise in the cotton price
should lead to higher wages (and, ultimately, higher welfare);
conversely, a rise in the wheat price should have little impact on wages
(i.e., only through an income effect on labor supply). Hence, in this
scenario, the correlation between changes in wages and changes in the
expenditure share weighted agricultural price index may well be close to
zero. Clearly, however, this is not the relevant wage-price elasticity
for our purposes. Indeed, as I show in the context of a formal general
equilibrium trade model, the relevant elasticity is one based on a
production share weighted agricultural price index. (4)
Even with the correct wage-price elasticity estimate in hand, one
must still wrestle with what to do about non-traded goods. One option is
to simply ignore them; that is, by assuming either that they constitute
a negligible share of the budget or that their prices are fixed.
Unfortunately, the first assumption is counterfactual, at least in the
case of India, and the second assumption is inconsistent with theory. As
I will show, in a multisector general equilibrium model, in which one of
the sectors is nontradable, the price of the nontraded good is
increasing in the agricultural price index. Recognizing this
possibility, Porto (2006) provides one of the few, if only, econometric
estimates of the elasticity of nontraded goods prices with respect to
traded goods prices. In India, however, as in most developing countries,
reliable data on prices of services and other nontradables are
unavailable. One contribution of this paper, therefore, is to quantify
the nontradable price elasticity without actually estimating it
econometrically.
To evaluate the distributional impacts of changes in
agriculture's terms of trade, I integrate a three-sector, specific
factors, general equilibrium trade model (e.g., Jones 1975) into a
first-order welfare analysis. (5) Appealing to the widely noted
geographical immobility of labor across rural India (e.g., Topalova
2007, 2010), (6) I apply this general equilibrium framework at the
district level, treating each of these several hundred administrative
units as a separate country with its own labor force but with open
commodity trade across its borders. (7) This district-level perspective
has two implications for empirical implementation of my approach. First,
since each district produces a different basket of agricultural
commodities, differences in the magnitude of wholesale price changes
across crops (even if common across districts), generate cross-district
variation in agricultural price (index) changes. Second, following the
logic of the model, the wage-price elasticity itself is specific to a
district, varying with characteristics of the local labor market.
While my estimation strategy is related to the "differential
exposure approach" (Goldberg and Pavcnik 2007) employed in studies
of the local wage impacts of tariff reform (most recently in Topalova
2010; McCaig 2011; and Kovak 2010, 2013), there are several novel
elements. Kovak, for example, uses the same type of theoretical model to
motivate his empirical specification, but he has many industrial
sectors; there is no distinctive treatment of agriculture. Moreover,
Kovak ignores intermediate inputs, whereas in this paper intermediates
play a quantitatively important role in transmitting food price shocks.
Finally, Kovak does not consider the welfare or distributional
implications of trade shocks, or of food price shocks more particularly,
which is a point of departure for this paper. Topalova (2010) finds that
tariff reductions during India's trade liberalization led to a fall
in wages, including agricultural wages, and to a rise in rural poverty.
Although Topalova's analysis is reduced-form and ex-post, (8) she
interprets her findings through the lens of a specific-factors trade
model with sectorally immobile labor (and mobile capital). Such a model,
however, implies that nonagricultural wages would fall with higher food
prices and, hence, that households would be affected very differently by
rising food prices according to the sector in which their members are
employed. My evidence will show the contrary, that the wage benefits of
higher food prices are similar across employment sectors. More broadly,
Topalova's results do not speak directly to the impact of shifts in
agriculture's terms of trade. (9) This study is thus the first to
adapt the differential exposure approach specifically to the
agricultural sector and to the question of food-price crises.
My empirical analysis finds that nominal wages for manual labor
across rural India respond elastically to higher (instrumented)
agricultural prices. (10) In particular, wages rose faster in the
districts growing relatively more of the crops that experienced
comparatively large run-ups in price over the 2004-2005 to 2009-2010
period. Importantly, the magnitude of these wage responses is broadly
consistent with the quantitative predictions of the specific-factors
model. These results have striking distributional implications. Improved
terms of trade for agriculture, rather than reducing the welfare of the
rural poor as indicated by the conventional approach (which ignores wage
impacts), would actually benefit both rich and poor alike, even though
the latter are typically not net sellers of food. (11)
In the next section, I sketch the theoretical framework and develop
my empirical testing strategy. Section III discusses the econometric
issues and the estimates. Section IV presents the distributional
analysis of food price shocks, comparing the general to partial
equilibrium scenarios. I conclude, in Section V, with a discussion of
the Government of India's responses to the 2007-2008 food price
spike, notably its export ban on major foodgrains.
II. GENERAL EQUILIBRIUM FRAMEWORK
A. Model Assumptions
Consider each district as a separate economy with three sectors:
agriculture (A) and manufacturing (M), both of which produce tradable
goods, and services (S), which produces a nontradable. The reason it is
necessary to distinguish services from manufacturing is simple.
Combining the two into one nontradable nonagricultural sector is
tantamount to allowing changes in agricultural prices to affect the
prices of both manufactured goods and services. Since manufactured goods
are, in fact, tradable, this approach would overstate the welfare impact
of changes in agriculture's terms of trade.
Continuing with the assumptions, output T, in each sector i = A, M,
S is produced with a specific (i.e., immobile) type of capital
[K.sub.i], along with manual labor [L.sub.i] and a tradable intermediate
input [I.sub.i], using sector-specific production function [Y.sub.i] =
[F.sub.i]([L.sub.i], [I.sub.i], [K.sub.i]). In the case of agriculture,
[K.sub.A] is land and [I.sub.A] is, for example, fertilizer.
Intermediate inputs do not play an essential role, except insofar as the
model provides quantitative predictions, in which case (as we will see)
they make a big difference.
In India, as in most developing countries, agricultural production
largely takes place on household-farms using family and hired labor.
Moreover, in a given year, these farms typically produce several crops
on the same land (contemporaneously via multicropping and/or
sequentially in multiple cropping seasons) with largely the same workers
and intermediate inputs. Hence, following, for example, Strauss (1984),
I treat the representative farm as a multiproduct firm that chooses
among a fixed set of c crops {[Y.sub.1], ..., [Y.sub.c]] to grow,
transforming between them according to the function [Y.sub.A] =
G([Y.sub.1], ..., [Y.sub.c]), where G is assumed to be homogeneous of
degree one. To account for the huge agroclimatic variation across India,
one should think of the set of feasible crops as varying across
districts.
Farmers then choose the particular quantities to grow, the
[Y.sub.j], to maximize total revenue, [[summation].sup.c.sub.j=1]
[P.sub.j][Y.sub.j], where [P.sub.j] is the price of crop j, subject to
the constraint that G([Y.sub.1], ..., [Y.sub.c]) = [Y.sub.A] for any
given [Y.sub.A]. Thus, in this set-up, production value shares [s.sub.k]
= [P.sub.k][Y.sub.k]/[[summation].sup.c.sub.j=1] [P.sub.j][Y.sub.j] are
determined by both agroclimatic conditions and by relative crop prices.
Given the homogeneity of G, there exists a price index [P.sub.A] such
that [P.sub.A] [Y.sub.A] =
[[summation].sup.c.sub.j=1][P.sub.j][Y.sub.j], which upon
differentiation yields
(1) [[??].sub.A] = [summation over j][s.sub.j][[??].sub.P]
where "hats" denote proportional changes; that is, [??] =
d log x. This establishes our production value share-weighted
agricultural price index.
Now, we may write profit per acre in agriculture as [[PI].sub.A] =
[[P.sub.A][F.sub.A]([L.sub.A],[I.sub.A],[K.sub.A]) - [P.sub.I][I.sub.A]
- W[L.sub.A]/ [K.sub.A], with analogous expressions for average profit
per unit capital in manufacturing, WM and in services [[PI].sub.S],
given respective output prices in these sectors, [P.sub.M] and
[P.sub.S]. I assume that manual labor is perfectly mobile across the
three sectors but its overall supply is fixed at L = [L.sub.A] +
[L.sub.M] + [L.sub.s] within each district. Thus, in each district
economy, there is one type of labor with a single nominal wage, W, and a
unique wage-price elasticity
(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
that must be solved for.
Because this is a general equilibrium framework, income effects of
changes in factor prices are fully accounted for. Thus, total income y
consists of the sum of value-added (revenue net input expenditures)
across sectors i = A, M, S
(3) y = [summation over i][P.sub.i][Y.sub.i] - [P.sub.1][I.sub.i] +
E
with an additional exogenous component, E. Although a technical
nuisance, the presence of E suits an important empirical purpose: A
significant portion of household income in rural India comes from
(salaried) nonmanual labor; for example, teachers, police/army, and
other civil servants. The exogeneity assumption on this income can be
motivated by thinking about entry into these professions as requiring an
advanced level of education (relative to unskilled labor), which cannot
be acquired in the short-run. (12)
B. Solution and Intuition
We are interested in what happens to the equilibrium wage in this
model when the agricultural price index changes, holding other tradable
prices constant; that is, [[??].sub.m] = [[??].sub.I] = 0. Given that
farmers are price-takers in all markets, we have (from price equals unit
cost)
(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where, under constant returns to scale, the input cost shares in
agriculture, the [[alpha].sub.l], l = K, L, I, are such that
[[alpha].sub.K] + [[alpha].sub.L] + [[alpha].sub.1] = 1. Similar
equations hold for the other sectors, each with its own set of input
cost shares. In the interest of clarity and because it will make no
appreciable difference empirically (see below), I assume equal input
cost shares across sectors from now on.
As I show in the Appendix,
(5) [psi] = ([[beta].sub.A] +
[delta][[beta].sub.S])/([[alpha].sub.L] + [[alpha].sub.K])
where the [[beta].sub.i] = [L.sub.i]/L are the sectoral labor
shares and [delta] = [[??].sub.S]/[[??].sub.A]. Note that [delta], the
elasticity of the nontradables price with respect to the price of
agriculture, is endogenous and needs to be solved out. (13)
Before doing so, however, we can gain some intuition for the
mechanics of the model by considering the special case [[alpha].sub.I] =
[[beta].sub.s] = 0; a two-input, two-sector economy (without
nontradables). According to Equation (5), in this case [psi] =
[[beta].sub.A], where [[beta].sub.A] is the share of the rural labor
force in agriculture. Referring to Figure 1, compare equilibrium A, with
a high share of labor in agriculture to equilibrium B with a low
agricultural share. At A the value of marginal product curve in
manufacturing (the supply curve of labor to agriculture) is necessarily
very steep; at B it is very flat. Thus, in moving from A to A , a 50%
increase in the agricultural price translates into an almost 50%
increase in the wage, whereas, in moving from B to B , the same price
increase leads to virtually no wage increase whatsoever (in proportional
terms).
If we now let [[alpha].sub.I] > 0, then we have [psi] =
[[beta].sub.A]/[[alpha].sub.L] + [[alpha].sub.K]) > [[beta].sub.A].
So, while the qualitative prediction is the same, the magnitude of the
wage-price elasticity can increase quite a lot after accounting for the
cost share of intermediate inputs. The source of this amplification
effect is the increase in intermediate input use induced by higher
agricultural prices, which boosts the marginal product of labor in
agriculture. Because of a greater exodus of labor from manufacturing in
response to agriculture's improved terms of trade, there must be an
even larger wage increase than was the case in the absence of
intermediates.
Finally, let us return to [delta] in Equation (5). To solve out
this parameter, we must equate the demand and supply of services, which
I discuss in the Appendix. For purposes of exposition, set
[[alpha].sub.I] = 0 again and consider the special case E = 0, in which
there is no exogenous source of income outside of the three sectors. As
shown in the Appendix, [psi] = [delta] = [[beta].sub.A]/(1 -
[[beta].sub.S]) > [[beta].sub.A] in this case. Thus, the introduction
of a nontradable sector also amplifies the wage-price elasticity. In
this economy, a rise in the wage induced by higher agricultural prices
reduces the supply of services; it also increases the demand for
services due to an income effect. Both forces put upward pressure on the
price of services, so that [delta] > 0. With the expansion of the
service sector as agricultural prices rise, the supply curve of labor to
agriculture becomes even more inelastic, making the rural wage even more
sensitive to these price changes.
C. Empirical Validation
The advantage of the above machinery is twofold: First, the model
tells us what the relevant wage-price elasticities are and, second, it
delivers explicit expressions for these elasticities in terms of input
cost shares, sectoral labor shares, and other parameters, all of which
can be computed from nationally representative data collected by
India's National Sample Survey (NSS) Organization. (14) I thus
calculate district (d) specific wage-price elasticities, [[psi].sub.d],
assuming equal input cost shares across sectors, (15) for 472 districts
in the 18 major states of India (see Table A2 for descriptive
statistics). (16) Generally speaking, the estimated elasticities are
high ([[bar.psi] = 1.15), reflecting large values of [[beta].sub.A].
Indeed, for the average rural district, around three-quarters of manual
labor days (adjusted for efficiency units; see Sectoral Labor Shares
section in Appendix) are spent in agriculture. Note also that
intermediate inputs play a quantitatively important role in the
elasticity calculation; if I assume that [[alpha].sub.1] = 0, then
[[bar.psi] would drop to 0.85. In other words, the input amplification
effect on the wage-price elasticities, discussed in the previous
section, is substantial.
In principle, one could econometrically estimate separate
wage-price elasticities for each district and compare them to their
theoretically implied counterparts above. In practice, however, this
would require long time-series of wages and prices for each district
over a period of structural stasis. (1)7 In lieu of such data, I
estimate the regression analog to the identity given by Equation (2), or
(6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where c is an intercept, y is a slope parameter, and
[[epsilon].sub.d] is a disturbance term for each district d. Thus,
Equation (6) replaces [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN
ASCII] by their empirical counterparts; [DELTA][w.sub.d] is the
difference in log wages between years t - k and t and the
[DELTA][p.sub.j] are the corresponding time-differences in log prices of
crop j, which are weighted by production value shares [s.sub.d,j] as
already discussed.
Under the null hypothesis, which is that the model and all its
auxiliary assumptions holds true on average, we have [gamma] = 1. In
other words, under the null, the magnitude of observed wage responses to
actual changes in the agricultural price index corresponds (in an
average sense) to what the theory says it should be. Several econometric
issues arise in implementing Equation (6), including potential
endogeneity of price changes. These are left for Section III.D.
III. EMPIRICAL ANALYSIS
A. Domestic Agricultural Markets
Since at least the 1960s, Indian governments, both at the national
and state level, have intervened extensively in agricultural markets.
Interstate trade in foodstuffs is often severely circumscribed through
tariffs, taxes and licensing requirements (see Atkin 2010, for a review)
with some states (e.g., Andhra Pradesh) going so far recently as to
prohibit the exportation of rice to other states (Gulati 2012). The
Government of India also sets minimum support prices (MSPs) at which
major food crops are, or at least can be, procured for eventual release
into the nationwide public distribution system (PDS). In practice,
however, the level of procurement, and thus the extent to which the MSPs
are binding, varies greatly by crop and state, and even within states
(Parikh and Singh 2007). The principal foodgrains, rice and wheat, have,
in recent years, been the overwhelming focus of government procurement
efforts, concentrated in the states of Punjab and Haryana, often for
lack of storage capacity and marketing infrastructure elsewhere. By
contrast, procurement of pulses and oilseeds has been minimal, as market
prices have consistently exceeded MSPs. (18)
During and after the sharp run-up in international food prices in
2007-2008, the Government of India imposed export bans on rice, wheat,
and a few other agricultural commodities in an attempt to tamp down
domestic price increases. Meanwhile, over several consecutive years,
MSPs for rice and wheat (and most other major crops) were raised
substantially, partly in response to international prices; huge
stockpiles of foodgrains were subsequently accumulated through
government procurement (Ahmed and Jansen 2010; Himanshu and Sen 2011).
The upshot of these interventions is that output prices faced by
Indian agricultural producers do not always perfectly track those in
international markets. (19) Moreover, as domestic market integration is
somewhat limited (especially in the case of rice), there is considerable
variability across states in crop price movements. On the one hand, this
variation may reflect differential transmission of exogenous price
pressure (e.g., because of varying levels of state procurement or
exposure to trade, both with other countries and with other states); on
the other hand, it may reflect localized supply or demand shocks, which
can also drive rural wages directly.
B. Crop Prices
Wholesale crop price data averaged at the state level from
observations at several district markets per state (and weighted by
district production), are compiled by the Ministry of Agriculture, as
are production and area data at the district level. So as to focus on a
period of substantial price movement, as well as to match the NSS wage
data (see below), I consider state-level price changes between the
2004-2005 and 2009-2010 crop marketing seasons. Given the relative ease
of moving produce across district (as opposed to state) lines,
state-level wholesale prices appear the appropriate measure of farmer
production incentives. (20)
I base the crop value shares, the sdj in Equation (6), on
production data from the 2003- 2004 crop-year, which has the best
district/crop coverage for the pre-2004-2005 period. Value of production
is calculated at 2004- 2005 state-level prices. Note, however, that I do
not take the value-weighted sum of price changes across every single
agricultural product grown in India. Price data for many of the minor
field crops and the tree crops are incomplete or not reliable. Moreover,
the associated production data are often inaccurate (especially for
vegetables and tree products). I thus select major field crops according
to the criteria that they cover at least 1% of total cropped area
nationally or that at least five districts had no less than 10% of their
cropped area planted to them in 2003-2004. These 18 crops, listed in
Table 1 in descending order of planted area, comprise some 92% of area
devoted to field crops in 2003-2004 in the major states of India. Table
1 also reports national average log-price changes (weighted by the state
share of total production) relative to rice. Thus, in the first row, the
relative price change for rice is zero, quite negative for several
important crops (e.g., cotton, gram, groundnut, and mustard/rapeseed)
and highly positive for pulses (Urad, Moong, and Arhar).
C. Wages
Wage data are derived from the NSS Employment-Unemployment Survey
(EUS), normally conducted every 5 years. The most recent round, the
66th, collected in 2009-2010, is the first conducted in the wake of the
food price "crisis" of 2007-2008, whereas the 61 st round of
2004-2005 most closely preceded it. Once again, in the spirit of the
theoretical model, I focus on manual labor, which constitutes nearly 83%
of days of paid employment in rural areas. (21) The first-stage of the
estimation takes individual log daily wages in the last week and
regresses them on district fixed effects as well as a quadratic in age
interacted with gender. Thus, I estimate the respective log-wage
district fixed effects, [[bar.w].sub.d.09] and [[bar.w].,sub.d,04],
separately for each round, removing, via the constant terms, year
effects due to, for example, general inflation. Estimates of the
standard errors of the fixed effects [sigma]([[bar.w].sub.d,09]) and
[sigma]([[bar.w].sub.d,04]), which I use below to construct regression
weights, are obtained following the procedure of Haisken-DeNew and
Schmidt (1997).
D. Identification
Rewriting Equation (6) to reflect the price data discussed above, I
wish to estimate
(7) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
where [STATE.sub.d] denotes the state in which district d is
located. There are two endogeneity issues to contend with: measurement
error and simultaneity between wage and price changes.
As to the first issue, both the crop value shares, [s.sup.d,j], and
the crop-specific log-price changes, [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII], may be measured with error. Putting aside the
latter concern momentarily and assuming that measurement error is
confined solely to value shares, I could deploy the instrument
(8) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [a.sub.d,j] is the area share of crop j in district d. To be
sure, cropped areas may also be measured with error, but these errors
should not be correlated with those of crop production and prices.
Clearly, IV [1.sub.d] does not deal with measurement error in price
changes, which could arise if, for example, the marketed varieties or
grades of a certain crop in a certain state change over time. Another
concern is unobserved district-level shocks (or trends) correlated with
both wage and price changes. For instance, suppose that a particular
district has been industrializing relatively rapidly over the 2004-2009
period, or that it has experienced comparatively rapid technological
improvement in agriculture. Both types of shocks would tend to raise
district wages. And, they may influence crop prices as well insofar as
the state's agricultural markets are insulated from the rest of
India (and the world) and the district is important relative to that
market, or the shocks are strongly spatially correlated.
The next step, therefore, is to develop an instrument that is
uncorrelated both with districtlevel wage shocks and with measurement
error in price changes (and crop value shares). Consider, then,
(9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] the
production share weighted mean change in the log-price of crop j across
states excluding the state to which district d belongs. (22) In other
words, [IV2.sub.d] replaces the state price changes in [IV1.sub.d] with
a national average price change uncontaminated by state-specific shocks
or measurement error because no price data from that state or production
data from that district are used in its construction. The idea, then, is
that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] reflects
exogenous international price changes transmitted to other states of
India as well as shifts in demand and supply in the vast domestic market
outside of the particular state.
A problem with [IV2.sub.d], however, is that it does not meet the
exclusion restriction if [[epsilon].sub.d] are correlated across state
boundaries. In other words, if industrialization or agricultural
innovation (or even weather) in, say, southern Andhra Pradesh and
northern Tamil Nadu move together, then the [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII] for a district in Andhra Pradesh may reflect
these shocks inasmuch as price changes from Tamil Nadu contribute to the
weighted average. To deal with this concern, I first establish some
notation: Let [BSTATE.sup.r.sub.d] be the set of states within a radius
of r kilometers around district d; of course, [STATE.sub.d] [subset or
equal to] [BSTATE.sub.r.sub.d]. Thus, [BSTATE.sup.r.sub.d] for the
district in southern Andhra Pradesh, depending on r, may include
Karnataka and Tamil Nadu (in addition to AP itself), whereas, if d were
instead in northern AP, [BSTATE.sup.r.sub.d] might include Maharashtra
and Chhattisgarh. With this definition, my instrument becomes
(10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the
production share weighted mean change in the log-price of crop j across
states excluding those in [BSTATE.sup.r.sub.d]. Here, again, the logic
is that the price instrument should not directly, or, in this case, even
indirectly, be driven by local shocks that also determine differential
wage growth across districts (and states).
The choice of r, the radius of "influence" of local wage
shocks on prices in bordering states may seem arbitrary. As, on average,
districts are 57 kilometers apart (centroid-to-centroid), at r - 100
kilometers, the sets [BSTATE.sup.r.sub.d] and [STATE.sub.d] differ only
for districts relatively close to their state's border with another
Indian state. Indeed, [IV3.sup.100.sub.d] = [IV2.sub.d] for half of the
462 districts in my estimation sample (those in the deep interior of
states or along the coasts or international borders). By contrast,
[IV3.sup.200.sub.d] = [IV2.sub.d] for fewer than 10% of sample
districts. This suggests a strategy of comparing alternative estimates
of y from Equation (7) based on [IV3.sup.r.sub.d] with successively
higher values of r to determine at what point increasing the radius of
influence ceases to matter.
Finally, as Equation (10) makes evident, differences in price
trends across crops is key to identification; if the [MATHEMATICAL
EXPRESSION NOT REPRODUCIBLE IN ASCII] are the same for all j, then
[IV3.sup.r.sub.d] collapses to [DELTA][PBSTATE.sub.r.sup.d], essentially
a constant. Given the inclusion o/ the constant term c, [tamma] is
virtually nonidentified in this scenario. Equally as important is
variation in crop composition across districts (see Table 2). If
[a.sub.d,j] = [a.sub.j] for all d, then even if the [MATHEMATICAL
EXPRESSION NOT REPRODUCIBLE IN ASCII] are not all equal,
[IV3.sup.r.sub.d] again essentially collapses to a constant. The
adjusted [R.sup.2]s of the first-stage regressions using [IV1.sub.d],
[IV2.sub.d, [IV3.sup.100.sub.d]. and [IV3.sup.200] are, respectively,
0.788, 0.121, 0.103, and 0.091.
E. Inference
As already alluded to, the error term [[epsilon].sub.d] is likely
to be correlated across neighboring districts, if only because
geographically proximate regions experience similar productivity shocks
over time. I use a nonparametric covariance matrix estimator or spatial
HAC (Conley 1999) to account for heteroskedasticity and spatial
dependence. A familiar alternative to the spatial HAC is the clustered
covariance estimator. But clustering standard errors by state or region
assumes independence of errors across state or regional boundaries, a
serious lacuna given the large fraction of districts bordering an
adjacent state. (23)
Bester et al. (2014) show that the asymptotic normal distribution,
typically used to obtain critical values for inference in HAC
estimation, is a poor approximation in finite samples. I thus follow
their suggestion of bootstrapping the distribution of the relevant
test-statistics. For this reason, inference should be guided by p-values
rather than by standard errors, although I will follow convention and
report both. In particular, bootstrapped p-values are much less
sensitive than standard errors to choice of the tuning or bandwidth
parameter (i.e., the degree of kernel smoothing). (24)
Both numerator, [DELTA][w.sub.d] = [[bar.w].sub.d,09] -
[[bar.w].su.d,04], and denominator, of the dependent variable in
Equation (7) are district-level summary statistics derived from
micro-data. This gives rise to a particular form of heteroskedasticity
and renders least-squares estimation inefficient. The standard solution
is to use weighted least-squares, taking the inverse of the estimated
sampling variances as weights. While the sampling variance of
[[DELTA][w.sub.d] is [[sigma].sup.2] ([[bar].sub.d,09]) +
[[sigma].sup.2] ([[bar.w].sub.d,04]) (see above), there is no equally
straightforward "plug-in" estimate of the sampling variance of
[[psi].sub.d]. I, therefore, bootstrap this variance as well by drawing
1000 random samples of individuals from each district's original
sample and computing [[psi].sub.d] repeatedly. From these two
components, then, I obtain the sampling variance of
[DELTA][w.sub.d]/[[psi].sub.d] using the delta-method. (25)
F. Estimation Results
Estimates of [gamma] based on Equation (7) are reported in Table
2A, in which identifying assumptions become progressively less
restrictive across columns. Thus, column 1 estimates are by ordinary
(weighted) least squares, column 2 uses [IV1.sub.d] as an instrument,
column 3 uses [IV2.sub.d], column 4 uses [IV3.sup.100.sub.d], and column
5 uses [IV3.sup.200.sub.d]. Instrument diagnostics are problematic given
the spatial error structure discussed above. However, for lack of a
better alternative, I report Cragg-Donald F-stats, which assume i.i.d.
errors, in Table 2 for all IV regressions. The critical value for the
associated weak instrument test, based on 10% maximal size for a 5% Wald
test, is 16.4 in all cases (Stock and Yogo 2002). Hence, subject to the
caveat already noted, I can strongly reject weak identification, even
using [IV3.sup.200.sub.d].
While a comparison of the first two columns suggests that
measurement error in crop shares leads to a modicum of attenuation bias,
even the column 2 estimate is well below unity as indicated by the
p-values from the bootstrapped-based t-test of [H.sub.0]: [gamma] = 1.
(26) Relaxing the assumption of no measurement error or simultaneity
bias in price changes in columns 3-5 delivers a [??] much closer to
unity, albeit one much less precisely estimated. The specifications in
columns 4 and 5, however, which allow shocks to be correlated across
state borders, do not give much different results from that of column 3,
which ignores such correlation. The pattern of coefficients across
columns suggests a rough balance between measurement error in prices
(attenuation bias) and simultaneity bias.
None of the p-values for [H.sub.0]: [gamma] = 1 in columns 3-5 are
anywhere near rejection levels, evidence in favor of the
specific-factors model. To assess power, I use the bootstrapped
t-distribution to answer the question: How likely would I have been to
reject [H.sub.0]: [gamma] = 1 had the true [gamma] been at or very near
zero? Based on this empirical power functions, at a true [gamma] of
zero, [H.sub.0] : [gamma] = 1 would be rejected with 95% certainty in
the column 3 specification, and with closer to 90% certainty in the
column 5 specification. In this sense, then, power is reasonably good:
The evidence does not support the view that rural wages are unresponsive
to agricultural price changes over a half-decade period.
G. Robustness: NREGA
India's National Employment Rural Guarantee Act (NREGA) is
meant to provide every rural household with 100 days of manual labor at
a state-level minimum wage, which is typically above the market wage.
Imbert and Papp (2012), using NSS-EUS data and exploiting the gradual
phase-in of the program since 2006, find that NREGA increased overall
public works employment while (modestly) raising private-sector wages in
rural India. As these labor market changes were contemporaneous with
rising food prices, they are worth taking seriously as possible
confounding factors. Given my estimation strategy, however, NREGA will
only affect the results insofar as the local expansion of the program
was systematically related to the (instrumented) change in the
agricultural price index.
Based on 7-day employment recall information in the NSS-EUS, I
compute the population weighted district average days spent in public
works employment (both NREGA and other) for rounds 61 and 66. (27)
Including the 2004-2009 change in this public works employment variable
([DELTA]PW) in regression (Equation (7)) results in no appreciable
changes in my estimates of [gamma] (compare columns 5 and 6 of Table 2).
Of course, the coefficient on [DELTA]PW does not necessarily reflect the
causal impact of NREGA or any other public works employment program in
India on rural wages; this specification merely serves as a robustness
check.
H. Sectoral Labor Mobility
My framework assumes perfect mobility of labor across production
sectors over the relevant horizon. However, as noted above, Topalova
(2010) proposes an alternative specific-factors model to rationalize her
empirical results for India in which labor is perfectly immobile, but
capital moves freely, across sectors. It is easy to see that, in this
set-up, agricultural wages respond positively to an increase in food
prices but nonagricultural wages respond negatively, as capital is
reallocated away from the sector whose terms of trade have deteriorated
and toward agriculture.
To test perfect intersectoral mobility of labor, I use the same
procedure just employed to construct log-wage district fixed effects for
the 2004-2005 and 2009-2010 NSS-EUS rounds, except in this case using
only wage data for nonagricultural jobs. The dependent variable is again
the time difference of these district fixed effects scaled by
[[psi].sub.d]. Relative to the previous analysis, 17 districts are
dropped for lack of data on nonagricultural wage jobs. The estimates, in
panel (B) of Table 2, differ little from their counterparts in panel
(A), nor can I reject [H.sub.0] : [gamma] = 1 in the specifications with
the least restrictive identifying assumptions. Hence, it appears that
nonagricultural wages, contra Topalova's implication, respond as
positively to higher food prices as do wages overall. Consequently, the
resulting welfare gains accruing to manual laborers (through wages)
should not depend on the sector in which they happen to be employed.
IV. FOOD PRICES AND WELFARE
A. Welfare Elasticities
Now consider a rural household embedded within the economy sketched
out in Section II. Its contribution to aggregate income consists of
value-added from its enterprises, both farm and nonfarm, its net
earnings from manual labor, and its exogenous income E. The second of
these components, which I will denote by W([L.sup.S] - [L.sup.D]), is
not present in Equation (3) because manual labor supply ([L.sup.S]) and
demand ([L.sup.D]) are equal in the aggregate.
Household indirect utility is a function of income and prices,
[P.sub.M], [P.sub.S], and [P.sub.j] = 1, ..., c. Following the
conventional derivation, the proportional change in money-metric utility
m is
(11)[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [OMEGA] = [[lambda].sub.A] + ([[lambda].sub.S] -
[[upsilon].sub.S])[delta] + [[lambda].sub.L][psi], [[upsilon].sub.j] is
the expenditure share of good j (S in the case of services),
[[lambda].sub.A] = [P.sub.A] [Y.sub.A]/y is the ratio of gross farm
revenue to income, [[lambda].sub.S] = [P.sub.S][Y.sub.S]/y is the ratio
of gross revenue from service enterprises to income, and
[[lambda].sub.L] = [W([L.sup.S] - [L.sup.D])]/y is the ratio of the net
earnings of manual labor to income. The term [OMEGA][S.sub.j] -
[[upsilon].sub.j] is reminiscent of Deaton's (1989) well-known net
consumption ratio (revenue minus expenditures on crop j divided by total
consumption expenditures) except that, unlike Deaton's partial
equilibrium result, it fully accounts for the changes in factor income
induced by a given price change, as well as for changes in the price of
nontradables. There are also several differences between Equation (11)
and the compensating variation formula used by Porto (2006), and earlier
by Ravallion (1990). First, [OMEGA] allows not just for changes in labor
earnings but for changes in capital (land) income, which is obviously
critical in my setting. Second, whereas the [lambda]s vary by household,
as in Porto's application, the elasticities [delta] and [psi] vary
in my case by the sectoral composition of the district labor market.
Moreover, rather than plugging in reduced-form econometric estimates of
these elasticities (which are infeasible for reasons already discussed),
I compute them based on an empirically validated theoretical model.
In what follows, 1 consider the distributional consequences of a
uniform percentage increase in all agricultural commodity prices
relative to the price of manufactures, the numeraire. According to
Equation (11), the corresponding household welfare elasticity is simply
[epsilon] = [OMEGA] - [[upsilon].sub.A], where [[upsolon].sub.A] is the
expenditure share of food crops.
B. Distributional Analysis
The India Human Development Survey (IHDS) of 2005 is a nationally
representative household survey of both rural and urban India (Desai,
Vanneman, and National Council of Applied Research 2008). Within the 18
major states already discussed, the IHDS covers nearly 24 thousand rural
households spread over 254 districts, collecting information on
consumption expenditures and income, including revenues and costs from
household enterprises, both agricultural and nonagricultural. Figure 2
shows the patterns of [[lambda].sub.A] and [[lambda].sub.S] smoothed
across percentiles of per-capita expenditures, as represented by the
IHDS rural sample. Relative to total household income, gross revenues
from both farming and service enterprises increase by percentile, though
the former increases much faster. By contrast, because the demand for
hired labor across household enterprises increases with wealth,
[[lambda].sub.L] decreases and essentially goes to zero for the highest
percentile. On the consumption side (Figure 3), the behavior of the food
share is familiar, falling steadily and quite rapidly by percentile,
whereas the share of expenditures on nontraded goods has the opposite,
though a less steep, distributional gradient. (28)
Turn now to the main results in Figure 4, showing the relationship
between the welfare elasticity with respect to food prices, [epsilon],
and per capita expenditure percentile. Observe that e is positive across
the income spectrum, never falling below 0.4. Thus, higher food prices
confer substantial and broad-based benefits to the rural population of
India, although the pattern of proportional welfare gains is mildly
hump-shaped, with the poorest and richest households gaining least. This
latter feature is driven by changes in non-traded goods prices and the
relatively large share of expenditures devoted to these goods by the
rich. In other words, if [delta] is artificially set to zero, then
[epsilon] would be essentially flat across the top per capita
expenditure quintile.29
Finally, let us compare the general equilibrium welfare analysis to
a more conventional partial equilibrium one. Of course, the latter
assumes that [psi] = [delta] = 0 so that, from Equation (11), [OMEGA] =
[[lambda].sub.A]. The distribution of partial equilibrium welfare
elasticities looks dramatically different than that of [epsilon] (Figure
4). Without the large and beneficial adjustment in rural wages, the
poorest rural households in India would experience a welfare loss of
around 0.2% for a 1% uniform increase in agricultural prices. However,
the relative advantage of the general equilibrium scenario erodes
rapidly with income as manual labor earnings become progressively less
important in the higher percentiles. Indeed, because in partial
equilibrium, the richest households do not have to pay higher prices for
services or higher wages to hired labor, they would benefit even more
than in general equilibrium from higher food prices.
V. CONCLUSIONS
In reaction to the food price spike of 2007-2008, the Government of
India imposed export bans on certain major crops. Such efforts to
restrain consumer prices can have the unfortunate side-effect of
restraining producer prices as well. My analysis shows that, in the face
of higher agricultural commodity prices, a stand-alone export ban, or
any policy that mimics its effects, would reduce welfare for the vast
bulk of India's population. Moreover, it is precisely the poorest
rural households (and, hence, the poorest in India as a whole) that are
most harmed by forestalling, or at least delaying, the substantial
trickle-down effects of higher crop prices via rural wages.
Partial equilibrium analysis, which assumes fixed wages, provides a
highly misleading picture of the distributional impacts of food price
shocks among India's vast rural population. To be sure, the story
may be quite different in metropolitan India, where the poor, arguably,
benefit little from rising rural wages. (30) Even though not much more
than a quarter of India's population resides in cities, urban
constituencies are obviously more concentrated than rural ones and,
hence, from a political-economy standpoint, are likely to be more
pivotal in shaping government policy on such matters as food security.
Finally, this study speaks to the broader debate on the link
between trade and poverty. Consistent with the WTO's Doha agenda,
my results imply that lowering barriers to trade in agricultural goods
on the part of developed countries, if only by improving the lot of the
rural poor in India, can make a significant dent in global poverty.
APPENDIX
MODEL SOLUTION
I assume Cobb-Douglas production functions with input cost shares
[[alpha].sub.Li] + [[alpha].sub.Ii] + [[alpha].sub.Ki] = 1 in each
sector i=A,M,S. The first step is to solve the following system of four
equations:
(A1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
for [??] and [[??].sub.i], (recall, [[??].sub.M] = [[??].sub.I] = 0
by assumption). The first three equations are the sectoral
price-equals-unit-cost conditions, whereas the last equation is derived
from the labor constraint (which implies [[summation over
(i)][[beta].sub.i][[??].sub.i] = 0) and the fact that [[??].sub.i] =
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in the
Cobb-Douglas case.
The solution for the wage-price elasticity is given as follows:
(A2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
where D = 1 + [[summation].sub.i][[beta].sub.i][[alpha].sub.Li]/[[alpha].sub.Ki]. In the case of equal input cost shares across sectors, D
= 1 + [[alpha].sub.L]/[[alpha].sub.K] and Equation (A2) reduces to
Equation (5) in the text.
Solving for the elasticity of the services sector price with
respect to the agricultural sector price, [delta], involves equating
changes in service sector supply [[??].sub.S] and demand [[??].sub.S].
If the Marshallian demand function for services takes the form [X.sub.S]
= [eta]y/[P.sub.S] (i.e., Cobb-Douglas preferences), where [eta] is a
share parameter, then
(A3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [[omega].sub.j] = (1 +
[[alpha].sub.Kj]/[[alpha].sub.Lj])[[beta].sub.j]/(1 +
[[summation].sub.i][[beta].sub.i][[alpha].sub.Ki]/[[alpha].sub.Li]).
On the supply side, from the services production function and the
specificity of capital, we have:
(A4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Meanwhile, the condition that input prices equal respective
marginal value products delivers [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII], where the second equality in each case follows
from the total differentiation of the marginal product functions
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Solving these two
equations, after first substituting out [[??].sub.S] from the second
using Equation (A4), yields
(A5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Substituting Equation (A2) into Equation (A5), equating the result
to Equation (A3), and solving gives:
(A6) [delta] = [[alpha].sub.KS](1 -
E/y)[[omega].sub.A]D+[[alpha].sub.LS][[beta].sub.A]/[[alpha].sub.KA]/D(1
- [[alpha].sub.KS] (1 - E/y)[[omega].sub.S) -
[[alpha].sub.LS][[beta].sub.S]/[[alpha].sub.KS].
With equal input cost shares, Equation (A6) simplifies to [delta] =
R[[beta].sub.A]/([[alpha].sub.K] + [[alpha].sub.L] - R[[beta].sub.S])
where R = [[alpha].sub.L] + [[alpha].sub.K]([[alpha].sub.K] +
[[alpha].sub.L])(1 - E/y). Finally, as mentioned in the text, E = 0 and
[[alpha].sub.I] = 0 [??] R = 1 [??] [delta] = [[beta].sub.A]/(1 -
[[beta].sub.S]).
PARAMETERS COMPUTED FROM NSS DATA
Input Cost Shares in Agriculture
The 59th round of the National Sample Survey (NSS59) collected
nationally representative farm household data in 2002-2003, including
information on agricultural inputs and outputs for over 40,000 farms.
The labor cost share is [[alpha].sub.L] = W([l.sub.h] +
[l.sub.f])/[[summation].sub.j][P.sub.j][Y.sub.j], where [l.sub.h] and
[l.sub.f] are, respectively, hired and family labor in agriculture and
the denominator is the value of crop production. We may write the
numerator as [Wl.sub.h](1 + f), where f = [l.sub.f]/[l.sub.h] is the
ratio of family to hired labor. For a labor market in equilibrium, /
should equal the ratio of the number of agricultural laborers working on
their own farm to the number working for wages on other farms. Thus, we
can calculate f for each of the five regions (north, northwest, center,
east, and south) from individual employment data in NSS61-EUS.
Comparable data on hired labor expenses (for regular and casual farm
workers), [Wl.sub.h], and on total value of crop production are
available at the farm-level by season from NSS59. Summing up [Wl.sub.h]
across seasons and households within each region (using sampling
weights) multiplying by (1 + f) and dividing by a similarly computed sum
of production value gives the regional labor shares. I use the same
approach for the intermediate input shares [[alpha].sub.I] =
[P.sub.I][A.sub.I]/[[summation].sub.j][P.sub.j][Y.sub.j], where the
numerator is the total expenditures on non-labor variable inputs as
reported in NSS59 (seed, fertilizer, pesticide, and irrigation). The
results of these calculations are as follows:
TABLE A1
Estimated Input Shares
North Northwest Center East South
[[alpha].sub.L] 0.331 0.304 0.258 0.317 0.260
[[alpha].sub.I] 0.264 0.325 0.258 0.250 0.238
TABLE A2
Summary Statistics for Major States of India
Annual [[beta].
PC Expend. [psi] sub.A]
North
Haryana 4.559 1.177 0.785
(0.817) (0.136) (0.138)
Himachal Pradesh 4.094 1.161 0.772
(0.551) (0.112) (0.120)
Punjab 4.535 1.145 0.731
(0.891) (1.145) (0.160)
Uttaranchal 3.296 1.177 0.761
(0.474) (0.163) (0.180)
Uttar Pradesh 3.108 1.182 0.781
(0.596) (0.127) (0.124)
Northwest
Gujarat 3.136 1.316 0.835
(0.579) (0.169) (0.136)
Rajasthan 3.317 1.266 0.758
(0.503) (0.103) (0.091)
Center
Chhattisgarh 2.244 1.253 0.870
(0.481) (0.085) (0.1 13)
Madhya Pradesh 2.489 1.249 0.860
(0.608) (0.092) (0.117)
Maharashtra 2.752 1.204 0.825
(0.558) (0.137) (0.120)
Orissa 1.964 1.131 0.759
(0.557) (0.135) (0.137)
East
Bihar 2.408 1.183 0.802
(0.391) (0.155) (0.167)
Jharkhand 2.257 1.040 0.697
(0.441) (0.282) (0.243)
West Bengal 2.667 0.951 0.603
(0.363) (0.189) (0.139)
South
Andhra Pradesh 2.486 1.073 0.717
(0.308) (0.081) (0.090)
Karnataka 2.595 1.159 0.828
(0.593) (0.208) (0.176)
Kerala 4.355 0.686 0.370
(0.877) (0.289) (0.223)
Tamil Nadu 2.386 0.891 0.588
(0.369) (0.228) (0.174)
[[beta]. [[beta]. No. of
sub.S] sub.M] Districts
North
Haryana 0.142 0.073 19
(0.111) (0.081)
Himachal Pradesh 0.165 0.063 12
(0.095) (0.049)
Punjab 0.203 0.067 17
(0.135) (0.041)
Uttaranchal 0.187 0.052 13
(0.147) (0.058)
Uttar Pradesh 0.149 0.070 70
(0.090) (0.068)
Northwest
Gujarat 0.088 0.078 25
(0.084) (0.093)
Rajasthan 0.168 0.075 31
(0.073) (0.057)
Center
Chhattisgarh 0.092 0.038 13
(0.093) (0.041)
Madhya Pradesh 0.104 0.035 45
(0.103) (0.050)
Maharashtra 0.118 0.057 33
(0.071) (0.058)
Orissa 0.151 0.090 30
(0.114) (0.076)
East
Bihar 0.142 0.055 37
(0.126) (0.068)
Jharkhand 0.210 0.093 18
(0.210) (0.073)
West Bengal 0.223 0.174 17
(0.075) (0.113)
South
Andhra Pradesh 0.174 0.109 22
(0.099) (0.052)
Karnataka 0.094 0.078 27
(0.081) (0.117)
Kerala 0.458 0.172 14
(0.172) (0.096)
Tamil Nadu 0.225 0.187 29
(0.114) (0.139)
Notes: Means (standard deviations) of district-level data.
Annual per capita expenditures are in thousands of 2004 Rupees.
Sectoral Labor Shares
Despite being a so-called "thin" round, NSS64, collected
in 2007-2008, fielded the standard Employment-Unemployment Survey
questionnaire on a "thick"-round sample of nearly 80,000 rural
households. I use these data to compute district-level sectoral labor
shares at roughly the mid-point between 2004-2005 and 2009-2010. As the
survey was carried out throughout the whole year in most districts,
agricultural labor seasonality is not a major issue at the district
level. For each individual. I compute the total manual labor days in the
last week in both agricultural and nonagricultural jobs, apportioning
the latter (based on industry codes) between services and manufacturing
sectors. I then take a population-weighted sum of days across
individuals in each district to get total district labor days (per week)
by sector, [D.sub.d,m], m = MA (manual ag. labor), MNA (manual nonag.
labor), and MNAS (manual nonag. labor in services).
There is a persistent daily wage gap between agriculture and
nonagriculture, present across all NSS-EUS rounds, which suggests that
days spent in agriculture are substantially less productive than those
spent in nonagriculture. In particular, an agricultural sector dummy
included in a log-wage regression using the NSS64 rural sample attracts
a coefficient of -0.243, after controlling flexibly for gender, age,
education, and district. Thus, labor productivity is around 24% lower
per day in agriculture. To account for this productivity difference, I
incorporate an efficiency units assumption into the model. In other
words, the labor constraint becomes L = [L'.sub.A] + [L.sub.M] +
[L.sub.S], where [L'.sub.A] = [L.sub.A] [e.sup.- 0.243]. The
district-level sectoral labor shares, in efficiency units, can hence be
calculated using
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Descriptive statistics for sectoral labor shares and other key
variables are shown in Table A2.
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doi: 10.1111/ecin.12237
HANAN G. JACOBY *
* I am grateful to David Atkin, Madhur Gautam, Denis Medvedev,
Rinku Murgai, Maros Ivanic, and Will Martin for useful suggestions and
to Maria Mini Jos for assistance in processing the data. The findings,
interpretations, and conclusions of this paper are mine and do not
necessarily reflect the opinions of the World Bank, its executive
directors, or the countries they represent.
Jacoby: Lead Economist, Development Research Group, The World Bank,
Washington, DC 20433, Phone (202)-458-2940, Fax (202J-522-1151, E-mail
hjacoby@ worldbank.org
(1.) Ivanic, Martin, and Zaman (2012), Wodon et al. (2008), and
World Bank (2010) provide recent multi-country assessments of the
welfare impacts of food price increases accounting for such producer
gains. See also the study by de Janvry and Sadoulet (2009) for an
analysis along these lines using Indian data.
(2.) Ravallion (1990) surveys the debate in development on the
nexus between the intersectoral terms of trade and poverty. Sah and
Stiglitz (1987) provide an early theoretical treatment. In their
cross-country study, Ivanic and Martin (2008) incorporate price-induced
changes in wages for unskilled labor derived from nation-level versions
of the GTAP computable general equilibrium model.
(3.) Indeed, rising wages are seen as the major driver of rural
poverty reduction in recent decades (Datt and Ravallion 1998; Eswaran et
al. 2007; Lanjouw and Murgai 2009).
(4.) A related issue is that prices or unit values obtained from
household expenditure surveys (as in Marchand 2012; Porto 2006) may not
reflect the wholesale prices faced by farmers in a particular region,
especially where government intervention is heavy (as in India).
(5.) Another strand of the literature incorporates second-order
(substitution) effects of price increases on the consumption side based
on demand-system estimation (most recently, Attanasio et al. 2013).
Banks, Blundell, and Lewbel (1996), however, provide evidence that
first-order approximations do reasonably well (relative error of around
10%) for price changes on the order of 20%.
(6.) Kovak (2010) finds no evidence that labor migration matters
for local wage responses to trade reform in Brazil, a country with much
higher inter-regional labor mobility than India.
(7.) Capital (land, in agriculture) is also assumed immobile across
both districts and production sectors. Longer-run Stolper-Samuelson
effects are not of paramount concern in policy discussion of food price
shocks.
(8.) In other words, rather than predicting distributional impacts
from a model based on estimated elasticities, it looks at changes in
poverty rates directly. By contrast, Marchand (2012) uses an ex-ante
simulation of household consumption along the former lines to find that
the fall in India's trade barriers during the 1990s would have
reduced rural poverty in India.
(9.) In particular, as high nontariff barriers on agricultural
products remained in force well after India's initial trade
liberalization (Anderson 2009), it is not clear what actually happened
to the relative price of agriculture in Topalova's post-reform
period.
(10.) In rural India, manual labor by far predominates over
nonmanual labor in terms of annual days worked, and much of the latter
is in the public (i.e., nonmarket) sector. Thus, unlike, e.g., Porto
(2006) or Nicita (2009), I do not attempt to estimate separate
wage-price elasticities for skilled and unskilled workers.
(11.) To be sure, the increase in rural wages may lag the increase
in consumer prices, and so the conventional analysis may be more
appropriate for the very short run. This article does not speak to the
timing issue.
(12.) We can also think of rural nonmanual labor as paid for out of
a central government budget financed by urban taxpayers and not
contributing directly to output in any rural sector.
(13.) Combining (4) and (5) also gives [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII]. So the elasticity of the return on land with
respect to the agricultural price index incorporates the direct
(positive) effect of price changes on farm profits as well as the
indirect (negative) effect of price induced wage changes.
(14.) An exception is the share of aggregate income from exogenous
sources, or Ely (cf., Appendix), which is computed at the state-level
from IHDS data described below.
(15.) While it is straightforward to allow for sector-specific
input cost shares using the results in Appendix, it is somewhat messy.
Fortunately, it hardly matters, because they yield virtually identical
elasticity results as in the equal shares case. Cost shares of
value-added for Indian manufacturing and ser vice sectors based on
national accounts are available from Narayanan, Aguiar, and McDougall
(2012). As it turns out, however, the ratio of capital to labor shares
is what is most relevant to our calculations, and these are quite
similar across sectors.
(16.) Excluded are the peripheral states of Jammu/Kashmir in the
far north and Assam and its smaller neighbors to the north and east of
Bangladesh. Included states, organized into five regions, are
North'. Harayana, Himachal Pradesh, Punjab, Uttar Pradesh, and
Uttaranchal; Northwest'. Gujarat and Rajastan; Center'.
Chhattisgarh, Madhya Pradesh, Maharashtra, and Orissa; East'.
Bihar, Jharkhand, and West Bengal; South: Andhra Pradesh, Karnataka,
Kerala, and Tamil Nadu.
(17.) India's quinquennial labor force survey, available since
1983, would yield, at best, five first-differenced wage observations per
district. Alternatively, Jayachandran (2006) examines a 30-year
agricultural wage series for Indian districts. Although these data fall
entirely within the pre-reform (largely autarkic) trade regime,
Jayachandran estimates a national-level wage elasticity with respect to
agricultural TFP, instrumented with rainfall shocks. One of the
difficulties with interpreting this as an estimate of tg, however, is
that the year-to-year TFP shocks induced by annual rainfall deviations
are unanticipated and thus are unlikely to give rise to the sectoral
labor reallocations underlying the general equilibrium model of this
paper.
(18.) See the reports by the Commission for Agricultural Costs and
Prices on http://cacp.dacnet.nic.in/ for more details.
(19.) This is true for the principal intermediate input in
agriculture as well. Despite a substantial upsurge in the international
prices of chemical fertilizers beginning in 2007, retail prices in
India, which are set by the central government, remained uniform and
unchanged over the 2004-2009 period (Sharma 2012).
(20.) As sugarcane is sold mostly to mills and not in wholesale
markets, I use the national MSP or, when relevant, "State Advised
Prices," which tend to be much higher and, hence, closer to
international cane pricing standards (see Gulati 2012).
(21.) The NSS-EUS categorizes jobs in terms of manual and
non-manual labor only for rural, not urban, workers. Based on the 61st
round sample of nearly 39,000 individuals, the population-weighted
proportions in each category are as follows: 58% in manual-agricultural;
24% in manual nonagricultural; and 18% in nonmanual (virtually all in
nonagriculture). For the 66th round sample of some 30,000 individuals,
the corresponding proportions are 51%, 30%, and 19%, respectively.
(22.) To be precise, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN
ASCII] where [STATE.sup.C.sub.d] is the set of states excluding
[STATE.sub.d] and [[omega].sub.kj] is state Ac's share of total
production of crop j among all states in [STATE.sup.C.sub.d].
(23.) Also note that with only a single (5-year difference)
observation per district, serial correlation is not an issue in my
set-up.
(24.) Bandwidth here is the distance cutoff, in degrees of
lat/long, beyond which spatial dependence is assumed to die out. Based
on simulation evidence from Bester et al. (2014), I choose a bandwidth
of 16; i.e., given the area of my "sampling region" (the 18
major states of India), this choice should yield minimal test-size
distortion across a range of possible spatial correlations. I find these
p-values to be highly robust to bandwidth deviations of at least [+ or
-] 4.
(25.) Although this procedure ignores correlation between numerator
and denominator arising from the fact that these two statistics are
calculated from partially overlapping samples of the same underlying
micro-data, it should serve adequately as a first approximation.
(26.) The p-value is the proportion of times the boot strapped,
re-centered, t-statistic of Bester et al. (2014) exceeds the
conventional t-statistic for the null in question computed for the
original sample. I use 10,000 bootstrap replications.
(27.) This is essentially the same variable considered by Imbert
and Papp (2012). In 2004-2005, public-works employment accounted for
just 0.22% of a day of work on average, increasing to a still minuscule
1.44% of a day in 2009-2010. Note, however, that NREGA employment is
concentrated in the agricultural off-season.
(28.) Nontraded goods expenditure categories include: firewood,
entertainment, conveyance, house rental, repair and maintenance, medical
care, education, and other services.
(29.) In Jacoby (2013), I further account for India's vast
Public Distribution System (PDS), under which eligible households
(generally, those below the poverty line) can purchase fixed rations of
either rice, wheat, or sugar in "Fair Price Shops" at
below-market prices. If I assume that PDS prices remain stable even as
market prices rise, I obtain modestly better welfare outcomes for all
but the top two deciles.
(30.) A full analysis of rural-urban labor market linkages is
beyond the scope of this study, but is an important topic for future
research.
TABLE 1
Summary Statistics for Major Crops
[DELTA]
[p.sub.j] -
Area Value No. of [DELTA]
Share Share Districts [p.sub.rice]
Rice 0.380 0.408 447 0.000
(0.320) (0.328)
Wheat 0.225 0.199 390 -0.032
(0.183) (0.165)
Soyabean 0.092 0.099 153 0.056
(0.151) (0.159)
Bajra 0.076 0.037 287 -0.064
(0.146) (0.091)
Cotton 0.076 0.128 206 -0.130
(0.112) (0.175)
Maize 0.067 0.054 410 -0.011
(0.112) (0.103)
Jowar 0.065 0.024 317 -0.041
(0.110) (0.040)
Ragi 0.052 0.030 192 0.052
(0.123) (0.092)
Groundnut 0.046 0.050 349 -0.112
(0.115) (0.115)
Gram 0.043 0.045 385 -0.195
(0.072) (0.087)
Sugarcane 0.035 0.090 386 0.001
(0.082) (0.164)
Rapeseed/Mustard 0.034 0.038 367 -0.199
(0.073) (0.090)
Urad 0.028 0.012 409 0.364
(0.042) (0.018)
Moong 0.025 0.014 424 0.586
(0.041) (0.030)
Arhar 0.021 0.019 428 0.253
(0.033) (0.033)
Potato 0.019 0.053 312 -0.146
(0.061) (0.105)
Sunflower 0.014 0.009 271 -0.083
(0.048) (0.032)
Sesamum 0.012 0.008 387 0.053
(0.022) (0.022)
Notes: Means (standard deviations) of district-level data
and number of districts growing each crop in 2003-2004.
Log-price changes for 2004-2009 are averages across the 18 major
states of India weighted by state production shares.
TABLE 2
Rural Wage Impacts of Crop Price Changes: 2004-2009
(1) (2) (3)
(A) Wages for all manual
labor (N = 462)
[gamma] 0.429 0.547 0.864
[DELTA]PW (a) (0.100) (0.105) (0.305)
p-values
[H.sub.0]: [gamma] = l 0.000 0.014 0.672
[H.sub.0]: [gamma] = 0 0.000 0.001 0.006
Cragg-Donald F-stat (weak 1384.1 61.0
identification test)
(B) Wages for nonagricultural
manual labor (N = 445)
[gamma] 0.672 0.779 0.988
(0.109) (0.104) (0.263)
[DELTA]PW (a)
p-values
[H.sub.0]: Y = 1 0.010 0.461 0.969
[H.sub.0]: Y = 0 0.000 0.000 0.004
Cragg-Donald F-stat (weak 1522.6 73.1
identification test)
Instrument -- [IV1.sub.d] [IV2.sub.d]
(4) (5) (6)
(A) Wages for all manual
labor (N = 462)
[gamma] 0.822 0.847 0.846
[DELTA]PW (a) (0.302) (0.318) (0.320)
0.042
p-values (0.215)
[H.sub.0]: [gamma] = l 0.579 0.660 0.663
[H.sub.0]: [gamma] = 0 0.009 0.014 0.018
Cragg-Donald F-stat (weak 50.0 39.0 38.5
identification test)
(B) Wages for nonagricultural
manual labor (N = 445)
[gamma] 0.844 0.900 0.851
(0.245) (0.249) (0.250)
[DELTA]PW (a) -0.228
p-values (0.242)
[H.sub.0]: Y = 1 0.585 0.733 0.613
[H.sub.0]: Y = 0 0.008 0.006 0.010
Cragg-Donald F-stat (weak 59.0 48.2 49.8
identification test)
Instrument [IV2.sup. [IV2.sup. [IV2.sup.
100.sub.d] 100.sub.d] 200.sub.d]
Notes: Standard errors robust to spatial dependence in
parentheses. All p-values based on Bester et al. (2014)
bootstrapped critical values (R= 10000). Dependent variable
is the change in log wage district fixed effect between 2004
and 2009 scaled by the district wage-price elasticity. All
regressions include a constant term and are weighted by the
inverse estimated sampling variance of the dependent
variable. See text for definition of instruments.
(a) Difference in average days of public works employment
per week in district between 2004 and 2009.
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