Fertilizer use, risk, and off-farm labor markets in the Semi-Arid Tropics of India.

The primary means of "getting agriculture moving" and raising rural incomes in developing countries has been the diffusion of new production techniques, especially high-yielding varieties of seeds, chemical fertilizers, and pesticides. A major impediment to the adoption of such modern inputs

A number of authors have documented the role of consumption smoothing and its effect on various aspects of rural household behavior. (2) Rosenzweig and Wolpin show that sales of farm assets, for example bullocks, are used to smooth consumption by farmers whose income is lowered by a negative production shock. Paxson shows that household-level consumption does not appear to track income seasonally, suggesting intra-year consumption smoothing and Townsend shows that household consumption comoves with village-level consumption and that contemporaneous income is not important in explaining contemporaneous consumption in India. Rosenzweig shows that inter-village transfers of wealth by family members are used to smooth consumption across villages.

To the extent that consumption risk is imperfectly insured, farmers' ex ante choices will be affected by risk aversion. For example, Rosenzweig and Stark show that inter-village transfers may help explain the prominence of patriarchal exogamy in India and the accompanying patterns of migration. Rosenzweig and Binswanger show that farmers in more risky areas deviate more from the optimal portfolio of assets, and that this deviation is worse among poorer farmers than wealthier ones. Indeed, risk aversion has been argued to play an important role in inhibiting the spread of modern inputs (Feder, Just, and Zilberman). Moreover, the risk-increasing role of modern inputs exacerbates the effect of risk aversion on production choices. Rosenzweig and Shaban show that farmers use share-tenancy contracts to spread the risk of new seeds when they are first introduced and their cultivation properties are still uncertain. To the extent that farmers choose traditional inputs over modern inputs in order to lower risk ex ante , any mechanism that allows farmers to smooth income ex post will raise the use of modern inputs and increase farmer productivity. Since poorer farmers are likely more risk averse than wealthy farmers, the effects of risk are likely even more important for them.

Another important mechanism for dealing with risk in developing countries is the use of off-farm labor supply in the daily wage labor market. Kochar finds that household earnings from day labor respond positively to negative idiosyncratic production shocks using the same dataset used here. Rose finds that second-period labor responds negatively to negative production shocks as well uses a different set of data on Indian households.

In this article, it is shown that farm households use off-farm labor supply to mitigate the effects of production shocks ex post in a dynamic production environment, and this leads to more efficient ex ante production choices in the presence of production risk, in particular greater use of chemical fertilizer. The organization of this article is as follows: First, the production environment and the structure of off-farm labor markets in the ICRISAT villages is described. Second, a two-period model of a risk-averse, expected-utility-maximizing farmer who chooses fertilizer in the first period and off-farm labor supply in the second period is developed. Third, estimates of fertilizer demand, which show that fertilizer demand increases as the off-farm labor market deepens, are presented. Finally, some concluding remarks are made.

Production in the Semi-Arid Tropics of India and the ICRISAT Panel

Previous research has found that the supply of harvest season labor in the off-farm labor market is an important method for smoothing income in the presence of negative shocks to farm production. If that is so, then the efficiency of ex ante choices will be improved, m particular, the degree of inefficiency arising because of risk aversion. A well-known dataset collected by the International Crop Research Institute for the Semi-Arid Tropics (ICRISAT) is used to study the effect of labor market structure on fertilizer demand by risk--averse farm households facing substantial, weather-related production risk.

Data were collected by ICRISAT from forty farmers, thirty of whom were cultivators and ten were landless laborers, in ten different Indian villages representing three distinct regions of India s semi-arid tropics (SAT) over the period 1975-84. Data are available from three of the study villages for ten years; three other villages have data available for only six years; data on the other four villages are available for two years. The focus here is on the three main study villages of Aurepalle, Shirapur, and Kanzara plus Boriya and Rampura, since data are available for these villages on both the structure of the off-farm labor market and the intensity of fertilizer use.

Agricultural production in the semi-arid tropics is characterized by two main growing seasons. The rainy (kharif) season begins with the onset of the monsoon when soils are water-rich and germination is easy. The post-rainy (rabi) season, which is somewhat less important in overall agriculture, begins after the monsoon, drawing on moisture stored in the soil after rainy season crops have been grown.

Kharif season production dominates in most of the ICRISAT villages; an exception is Shirapur, where the rabi season crops are more important. The interest in this article is on the interplay of risk aversion and off-farm labor markets. Since rabi production occurs after the uncertainty surrounding rainfall has been resolved, risk is unlikely to play a significant role in affecting fertilizer use for rabi season crops. Moreover, the model developed below more adequately describes kharif production. Therefore, rabi season fertilizer use is ignored in the estimation that follows.

Weather is a major source of the uncertainty surrounding the production environment and can be summarized by the timing and amount of rainfall. Crop yields are highly susceptible to variations in the timing and duration of the monsoon. Rosenzweig and Binswanger found that household profits from crop production are correlated with the monsoon onset date and Skoufias found total agricultural output to be strongly dependent on the monsoon onset as well. Moreover, Barah and Binswanger find that for unirrigated areas of the semi-arid tropics of India, yield variability contributed more than price variability to fluctuations in gross crop revenue, indicating the importance of weather-induced yield fluctuations in household income risk.

The extent of fertilizer use varies widely across the ICRISAT villages and across time. For both Aurepalle and Kanzara the extent of fertilizer use increased fairly substantially from the beginning of the ICRISAT study to the end. In the mid 1970s only 20% of the farmers in Aurepalle and 50% of the farmers in Kanzara used fertilizer on their fields. By 1984, almost 75% of the farmers in Aurepalle and over 90% of the farmers in Kanzara used some chemical fertilizer. Fertilizer use is much lower in Shirapur and did not increase appreciably during the study period.

The kharif season is characterized by a high degree of uncertainty concerning the effectiveness of fertilizer application. While some field preparation for kharif production takes place before the monsoon onset, most planting activities are triggered with the beginning of rainfall in June or early July. As the monsoon unfolds, planting (and transplanting) occur, fertilizer is applied, fields are weeded, and other production tasks are completed. The vast majority of fertilizer applied to the kharif season crops occurs during the monsoon; little fertilization takes place after the end of the monsoon in most villages. In fact, in both Aurepalle and Kanzara over 95% of all fertilizer used during the kharif season is applied either before the monsoon onset or between the monsoon onset and end. Farmers must invest considerable resources in fertilizer application before it is clear whether fertilizer use will be effective or not.

The ICRISAT dataset is well suited to considering the effect of off-farm labor markets on ex ante decision making because it contains detailed information on the timing of production and labor market activities by the household, which allows an ex ante information set to be identified and the depth of the labor market in the planting period to be measured.

Most rural households in the semi-arid tropics engage in substantial labor activities off their own farms. Off-farm labor supply is an important source of household income and labor markets are well developed and complex. Although men and women contribute about equally to crop labor, women dominate in the off-farm labor market. Off-farm labor supply varies by gender across the crop production cycle, due to custom. While harvesting and threshing are undertaken by both men and women, most other tasks are gender-specific (Walker and Ryan, p. 110). Men concentrate on nine specific production tasks, four of which involve the use of bullock power, reflecting the fact that women are prevented by custom from touching the plow (Walker and Ryan, p. 125) (3) The result of this is substantial labor market segmentation by gender in the study villages. In turn, there is little correlation between male and female wages across production years in four of the six villages, and in none of the villages do male and female wages move together within the crop year (Walker and Ryan, p. 124).

Segmentation of labor market tasks shows up in the share of labor supply accounted for by pre-harvest and harvest labor, by gender. Preharvest labor accounts for between 50 and 75% of male (off-farm) labor supply during the year for the three villages (averaged across all years in the sample). In contrast, pre-harvest labor supply accounts for almost 50% of the total for females in Kanzara, but is closer to 25% in both Aurepalle and Shirapur. The dominance of second-period labor in female off-farm labor supply likely arises because of the dominance of harvest tasks in female agricultural work.

If the supply of harvest season labor in the off-farm labor market is an important tool for smoothing income, there should be significant interactions between fertilizer use and off-farm labor supply. A natural first step is to look at whether the availability of off farm employment opportunities raises fertilizer use. Since farmers must form expectations about the harvest season labor market at planting time, it is the planting period labor market conditions that should affect fertilizer use. Ignoring the role of off-farm labor in smoothing the effects of production shocks on household income, higher levels of involuntary unemployment would cause farmers to allocate more labor to own-farm production, since involuntary unemployment acts like a tax on the market wage. Since own-farm labor and fertilizer are widely viewed as complementary in production, this would boost fertilizer use. On the other hand, if off-farm labor markets are a tool for income smoothing then lower levels of involuntary unemployment in the off farm labor market would make it easier for farmers to smooth income expost in the face of a negative production shock. In this case, lower levels of unemployment in the labor market should raise fertilizer use.

In fact, there is a substantial negative correlation between the planting season unemployment rate (for both males and females) and the share of farmers using chemical fertilizers in the three villages (figure 1). A simple regression analysis shows that the relationship is in fact negative and significant (the t-statistic is -2.72), suggesting that farmers may use the off-farm labor market to smooth income in case of crop failure. Of course, the simple bivariate relationship shown in figure i could be spurious. If, for example, there are binding credit constraints that limit the use of fertilizer by poorer households, then off-farm work might be a way of relaxing those credit constraints. A more rigorous empirical analysis is needed to establish the role of off-farm labor markets in dealing with production choices in a risky environment.

Theoretical Model

A formal model is developed relating the depth of the off-farm labor market to fertilizer use. Consider an expected-utility-maximizing farmer who produces a single crop over a two-period (intra-year) crop cycle. Assume that the farmer's preferences are characterized by a strictly concave utility function U(I), where I is total income, U' >0, and U" <0. All consumption takes place in period 2.

The two distinct production periods are identified by a village-level random production shock [[theta].sub.k] where k indexes villages. The shock, which is fully known at the beginning of the second period, has mean [[theta].sub.k], and a purely random component, [[theta].sub.k], which the farmer cannot forecast using information available in the first period. The random shock [[theta].sub.k] is assumed to be i.i.d. across time with zero mean and finite variance, [[sigma].sup.2.sub.k]; rainfall uncertainty varies across villages. The production shock may be thought of as village-level weather patterns, which are critical in determining farm profits in the semi-arid tropics considered below. More specifically, while the monsoon onset is well known before most production activities get underway, information about the length of the monsoon, the total amount of rainfall, and the distribution of rainfall during the monsoon (frequency of rainfall days, etc.) is not known.

In the first period, the farmer chooses the quantity of the variable input, which may be fertilizer or pesticide, for example. In the second period the farmer allocates household labor between labor used in crop production (1) and off-farm labor supply (L). (4) Each household is endowed with a fixed quantity of labor resource, L, and the household's labor constraint is given by

(1) L+1 = L.

Let Q denote output. The production technology is given in (2),

(2) Q = [[[theta].sub.k] + (1 - [gamma])[[theta].sub.k]]f(X, L - L)

where X is variable input; [gamma] is a parameter that affects the farmer's ability to cope with rainfall uncertainty, which might measure the share of irrigated land; L - L is the labor used in crop production, substituting in the constraint in (1); f(X, L - L) has the properties of a neoclassical production function: [f.sub.x] > 0, [f.sub.1] > 0, [f.sub.ll] < 0, [f.sub.xx] < 0, [f.sub.xl] > 0, and [f.sub.ll] [f.sub.xx] - [f.sup.2.sub.xl] > 0. Equation (2) decomposes the effect of weather into its mean and random components. The effect of [[theta].sub.k], on output depends inversely on [gamma].

For example, weather uncertainty is less important for output the greater the level of irrigation.

Farmers may also sell their labor in the off-farm labor market at a wage rate [w.sub.k] where k refers to the farmer's village. The weather shock affects the wage paid in the off-farm labor market, [w.sub.k] = [w.sub.k] + (1 - [d.sub.k])[[theta].sub.k]. For a given level of d in the local labor market, positive (negative) weather shocks increase (decrease) the demand for labor and thus the wage. The expected wage in village k is [w.sub.k], and the variance of the village wage is given by [[sigma].sup.2.sub.k][(1 - [d.sub.k]).sup.2], so that the effect of the weather shock on the variance of the village wage depends inversely on the depth of the village labor market, [d.sub.k]. One interpretation of the parameter d is d = (1-UR) where UR is the village-level unemployment rate. However, the unemployment rate is not a fully adequate measure of depth in the labor market, so the empirical analysis also uses an alternative measure, the share of nonagricultural employment in the labor market, for comparison.

The farmer's total profits from own-farm production and off-farm labor supply are

(3) [pi] = [[[theta].sub.k] + (1 - [gamma])[[theta].sub.k]] f(X, L - L) - qX

+ ([w.sub.k] + (1 - [d.sub.k])[[theta].sub.k])L

where input price is denoted by q and output price is normalized to one.

The farmer uses the standard dynamic programming algorithm to solve the maximization problem (Intrilligator). He first solves the second-period problem by choosing the optimal allocation of labor between farm production and off-farm labor supply in the second period, conditional on his choice of fertilizer in the first period, and the realization of production shock. Since there is no uncertainty, the farmer's problem is to maximize profits. The first-order condition for the second-period maximization problem is given in (4),

(4) [[w.sub.k] + (1 - d)[[theta].sup.*.sub.k]]

- [[[theta].sub.k] + (1 - [gamma])[[theta].sup.*.sub.k]][f.sub.1]([X.sup.*], L - L) = 0

where [X.sup.*] is the optimal level of fertilizer from the first-period maximization problem and [[theta].sup.*.sub.k] is the realization of the random shock. The second-order condition for maximization requires ([[theta].sub.k] + (1 - [gamma])[[theta].sup.*.sub.k])[f.sub.ll] < 0, which holds if and only if ([[theta].sub.k] + (1 - [gamma])[[theta].sup.*.sub.k]) > 0; this is a regularity condition ensuring that the total output is positive.

Totally differentiating the first-order condition, we can derive the comparative statics for the second-period labor supply. Increases in the average wage increase off-farm labor supply, ceteris paribus (conditional on the actual [[theta].sup.*] and [X.sup.*])

(5) [partial]L/[partial][w.sub.k] = -1/[[[theta].sub.k] + (1 - [gamma])[[theta].sup.*.sub.k]][f.sub.ll] > 0

by the second-order conditions. Evaluated at the mean of the weather shock, [[theta].sub.k] = 0, the weather uncertainty has no effect on the slope of the labor supply curve.

The effect of the production shock on second-period labor supply is

(6) [partial]L/[partial][[theta].sup.*.sub.k] = [(1 - [gamma]) [f.sub.1] - (1 - [d.sub.k])]/[[[theta].sub.k] + (1 - [gamma])[[theta].sup.*.sub.k]][f.sub.ll]

If better rainfall raises the marginal productivity of labor by more than it raises the off-farm wage, for example, (1 - [gamma])[f.sub.l] > (1 - [d.sub.k]), then [partial]L/[partial][[theta].sup.*] < 0 holds, and farmers supply less labor off-farm the greater the production shock. In the extreme case in which [d.sub.k] = 1, for example, the village labor market is fully diversified, then better weather always lowers off-farm labor supply since the wage is independent of the weather shock, for example, [partial]L/[partial][[theta].sup.*.sub.k] < 0. The key relationship is that between the effect of the random weather shock on the marginal productivity of farm production labor (through [gamma]) and its effect on the wage in the village labor market (through [d.sub.k]). There are good reasons to think that the weather shock affects own-farm production labor more than the wage in the village market. Even in the village economies, labor has uses outside agriculture. Moreover, labor is portable, so the impact on t he wage in the village should be limited by the costs of moving labor to another village.

Off-farm labor also responds to the quantity of fertilizer used by the farmer in the first period, for example, [partial]L/[partial][X.sup.*] = [f.sub.lx]/[f.sub.ll]. If fertilizer use raises the marginal productivity of labor, then [partial]L/[partial][X.sup.*] < 0. In the case of negative production shocks, off-farm labor supply is higher the greater the depth of the local labor market, [d.sub.k] is

(7) [partial]L/[partial][d.sub.k] = [[theta].sup.*.sub.k]/[[[theta].sub.k] + (1 - [gamma])[[theta].sub.k]] [f.sub.ll] > 0

for [[theta].sup.*.sub.k] < 0.

Likewise, in the presence of negative production shocks, the labor supplied off-farm is lower the higher the share of irrigated land,

(8) [partial]L/[partial][gamma] = -[[theta].sup.*.sub.k] [f.sub.l]/[[[theta].sub.k] + (1 - [gamma])[[theta].sub.k]] [f.sub.ll] < 0.

Irrigation is an important tool available to help farmers mitigate the effects of negative rainfall shocks. The effect of [gamma] on the response of the second-period labor supply to the rainfall shock is given by

(9) [[partial].sup.2]L/[partial][[theta].sup.*.sub.k][partial][gamma] = -[f.sub.l][[[theta].sub.k] + (1 - [gamma])[[theta].sup.*.sub.k]][f.sub.ll] + [(1 - [gamma])[f.sub.l] - (1 - [d.sub.k])][[[theta].sup.*.sub.k][f.sub.ll]]/[[[[theta].sub.k] + (1 - [gamma])[[theta].sup.*.sub.k]].sup.2][f.sup.2.sub.ll]

which is always positive for negative production shocks, [[partial].sup.2]L/[partial][[theta].sup.*.sub.k][partial][gamma] > 0 if [[theta].sub.k] < 0, suggesting that irrigation mitigates the effect of the production shock in the model.

In the first period, the farmer chooses the quantity of the variable input X to maximize the expected utility of profits, [E.sub.0](U([pi])}. The farmer's choice of X is conditioned on the response of the second-period labor to fertilizer use. So that now the farmer's maximization problem is given by

(10) Max [E.sub.[theta]]{U(([[theta].sub.k] + (1 - [gamma])[[theta].sub.k]) x f(X, L - L(X)) - qX + ([w.sub.k] + (1 - [d.sub.k])[[theta].sub.k])L(X)}.

The first-order condition for the first period problem is (5)

(11) [E.sub.[theta]]U'[([theta] + (1 - [gamma])[theta]) x [f.sub.x](X, L - L(X)) - q] = 0.

Denote [Z.sub.x] = ([[theta].sub.k] + (1 - [gamma])[[theta].sub.k])[f.sub.x](X, L - L(X)) - q. Since the covariance between U' and [Z.sub.x] is negative, the farmer under utilizes fertilizer, in the sense that the expected marginal product of fertilizer is greater than its price. Thus, the expected profits could be raised by increasing fertilizer use. Second-order conditions require that the total differential of (11) be negative, for example,

(12) [DELTA] = [E.sub.[theta]]U"[Z.sup.2.sub.x] + EU'([[theta].sub.k] + (1 - [gamma])[[theta].sub.k]) x ([f.sub.xx] - [f.sub.xl][partial]L/[partial]X) < 0.

Note that the first term is negative since U" < 0 everywhere. Substituting for [partial]L/[partial]X from above, the second term becomes [E.sub.[theta]]U'([theta] + (1 - [gamma])[theta])([f.sub.xx] - [f.sup.2.sub.xl]/[f.sub.ll]). By assumption U' > 0 and [[theta].sub.k] + (1 - [gamma])[[theta].sub.k] > 0 everywhere. By concavity of the production function the term ([f.sub.xx] - [f.sup.2.sub.xl]/[f.sub.ll]) is negative, so that the second term above is negative, and the second-order conditions are satisfied.

It was shown above that as the labor markets deepened, as represented by a falling unemployment rate, fertilizer use in the ICRISAT sample rose, especially in Aurepalle and Shirapur. The response of fertilizer demand to d, which measures the depth of the local labor market, captures this effect in the model. Totally differentiating (11) and rearranging yields

(13) [partial]X/[partial][d.sub.k] = [[E.sub.[theta]]U"{(-[[theta].sub.k]L)[[([[theta].sub.k] + (1 - [gamma])[theta]).sub.k][f.sub.x] - q]} - [E.sub.[theta]]U'([[[theta].sub.k] + (1 - [gamma])[[theta].sub.k]][f.sub.xl][partial]L/[partial][d.sub.k]}]/-[D ELTA].

Substituting for [partial]L/[partial][d.sub.k] from above yields (14):

(14) [partial]X/[partial][d.sub.k] = [E.sub.[theta]]U"{-[[theta].sub.k]L}[[[theta].sub.k] + (1 - [gamma])[[theta].sub.k]][f.sub.x] - q} - [E.sub.[theta]]U'[[theta].sub.k][f.sub.xl]/[f.sub.ll]/-[DELTA].

The denominator is positive by the second-order conditions. Under the assumption of nonincreasing absolute risk aversion, the first term in the numerator is positive, since [E.sub.[theta]]U"[theta][[theta] + (1 - [gamma])[theta]][f.sub.x] - q} = [E.sub.[theta]]U"[theta][Z.sub.x] which is negative (Feder, 1977, p. 508). The second term is negative, since [f.sub.ll] < 0 and cov(U', [theta]) < 0. Therefore, [partial]X/[partial][d.sub.k] > 0 holds if the first term is greater (in absolute value) than the second term. The sign of [partial]X/[partial]d ultimately depends on the trade-off between the agent's risk aversion (captured by U" in the first term in (14)) and the "cost" of labor market participation in terms of lost farm output, captured by the second term through [f.sub.xl]. While a deeper labor market, as measured by [d.sub.k], offers insurance and makes the household more willing to use fertilizer, participation in the off-farm labor market involves a cost. The farmer knows that participation in the off- farm market ex post will further lower the return to first-period fertilizer use, as measured by the term [f.sub.xl] in the second term. If [f.sub.xl] = 0, then of course, [partial]X/[partial]d is unambiguously positive; there is no effect on the marginal product of fertilizer from working in the off-farm labor market and so no cost in terms of lost own-farm output.

Likewise, the response of fertilizer demand to the expected wage, [partial]X/[partial][w.sub.k], can be derived utilizing [partial]L/[partial][w.sub.k] from above:

(15) [partial]X/[partial][w.sub.k] = [L.sup.*] [E.sub.[theta]]U"[Z.sub.x] - [E.sub.[theta]] U' [f.sub.xl]/[f.sub.ll]/- [DELTA].

This effect is unambiguously positive. The first term is positive (Feder, 1977, p. 508) and the second term is positive as long as fertilizer and production labor are complements.

Empirical Estimates of Fertilizer Demand

The optimization problem described above gives rise to highly nonlinear relationships for fertilizer demand which depends on the parameters of production technology and utility function. Estimating the structural parameters of these demand relationships is beyond the scope of this article. Rather, the linear approximations to the underlying fertilizer demand functions arising from equation (11) are estimated. The optimization problem results in a notional demand for fertilizer of the form

(16) [X.sup.*.sub.it] = [alpha] + [Z.sub.it]B + [u.sub.it]

where I refers to household "I" at time t. [Z.sub.it] is a vector of regressors and B is a coefficient vector to be estimated; [u.sub.it] is a random error term. While [X.sup.*.sub.it] may well be negative, we observe in practice [X.sub.it], which is zero if [X.sup.*.sub.it] [less than or equal to] 0 and equal to [X.sup.*.sub.it] otherwise. This is the classical tobit regression model.

A further complication arises in the empirical model because we observe the same households over time. If the disturbance term in (16) is written as [u.sub.it] = [[delta].sub.i] + [[epsilon].sub.it], where [[epsilon].sub.it] is a white noise error term, with zero mean, finite variance, and E{[[epsilon].sub.it] [[epsilon].sub.jt]} = 0 for all i [not equal to] j and E {[[epsilon].sub.it] [[epsilon].sub.is]} = 0 for all s [not equal to] t then the appropriate estimation technique depends on the nature of [[delta].sub.i]. In the presence of household-level fixed effects, the classical fixed-effects estimator yields unbiased parameter estimates. On the other hand, if [[delta].sub.i] is a random variable which represents an additional source of error in the regression, then correcting the estimates for household random effects will allow for more efficient estimates of the parameters of B. Whether random effects or fixed effects are appropriate is, of course, an empirical question. Fertilizer demand is estimated using both methods below and tested for appropriateness by using the method suggested by Hausman. While evidence is found that there are fixed effects in the model, both fixed and random effects are reported for comparison.

The key relationship in the above model is that between the depth of the off-farm labor market, d, and the household's demand for fertilizer, which must be made in advance of the resolution of production risk related to weather. Measuring the depth of the local labor market is a complicated question. One approach would be to utilize the degree of involuntary unemployment that exists in the local labor market as a measure of how well the labor market works. To the extent that some workers are unable to obtain employment at the prevailing wage, the labor market is less useful as a hedge against negative production shocks.

A more direct measure of depth in the context of the semi-arid tropics is the share of total employment in the local labor market that is not dependent on agriculture. If labor markets offer opportunities for farm laborers to participate in nonagricultural activities then wage levels and access to employment will be less dependent on shocks to agricultural production. In fact, the government of Maharashtra instituted a work guarantee scheme to provide nonagricultural employment for farm laborers (Walker and Ryan, p. 62).

In this article, an empirical approach is taken to choosing an appropriate measure of the depth of the village labor market. Measures of both involuntary unemployment and the share of nonagricultural employment at the village level are constructed and estimate fertilizer demand conditional on both measures. Since there are well-known and rigid gender differences in agricultural production tasks, both measures are constructed by gender.

Detailed information contained in Schedule K of the ICRISAT data on the labor market activities of sample households is used to construct both gender-specific unemployment rates and shares of nonagricultural employment. From 1979 to 1984 information was collected on the number of days individual members of the households worked own-farm and off-farm in both agricultural production, and on a number of types of nonagricultural activities. In addition, information on the number of days in the sample period during which workers looked for work, but were unable to obtain it, was also collected. Total labor supply is calculated by adding up days worked in all activities except own-farm production work, and the unemployment rates for both planting period and harvest period activities by village, where the numerator is days unemployed and the denominator is days in the labor market (excluding own-farm work days), both summed across all households in the village. Since this detailed information is only available from 1979 onward, the sample period used in estimation is somewhat restrictive. The unemployment rate is a measure of (1 - d), or more generally, is negatively related to the depth of the labor market.

As an alternative measure of the depth of the village labor market, the share of total labor market activities that took place in the nonagricultural sector is calculated, again by gender and during the planting period only. The greater the share of labor market activities that are in the nonagricultural sector, the deeper the village labor market, and the more immune are village wages to agricultural production shocks. Again, own-farm work is excluded from the calculation, and the variables are created at the village level.

An important question that must be addressed in the empirical analysis is the amount of information about the village labor market available to the household at the time it must choose its fertilizer level. Obviously, since the monsoon has not run its course, households have less than perfect information about village wages in the post-harvest period and, also, about their access to the labor market in the case of a negative production shock. Therefore, estimates of fertilizer demand are conditioned only on information available to the household during the first period of the above model; for example, before rainfall uncertainty is completely resolved. (6)

Table 1 contains a summary of variables used in estimation. Activities that occurred before the end of the monsoon, period 1 in the model, are distinguished from activities occurring in period 2 (after the end of the monsoon) using Rosenzweig and Binswanger's (1993) definition of the monsoon onset and end dates. Period-specific wages were defined using information on time and type of task. (7) The village average wage in agriculture is divided by the village consumer price index (Walker and Ryan, p. 28) to create the real village-level wage by gender for the first period. The real price of chemical fertilizer in the village is calculated as the price of urea adjusted for inflation. (8) The share of cropped area that is irrigated is an important measure of the household's ability to deal with risk; for example, it corresponds to [gamma] in the above model. In addition, the real level of household wealth is used as a proxy for whether the household faces binding credit constraints or not. If what is happening i s simply that off-farm work is used to finance fertilizer purchases, then the household's level of real wealth should soak up the explanatory power of the variables measuring village labor market depth. (9)

Estimates of the fertilizer demand equation conditional on labor market depth, measures of village-level risk, irrigation and household wealth, and prices and wages, and are reported in table 2. Random effects tobit model estimates are reported in column (1), using the share of nonagricultural employment as a measure of labor market depth and in column (3), using the unemployment rate to measure labor market depth. (10) The most important finding here is that the level of fertilizer demand is positively related to the depth of the village labor market, whether measured using the unemployment rate or the share of nonagricultural employment. Both male and female shares of nonagricultural employment in period 1 are statistically significant at the 5% level and positive, as predicted in the above model. The level of real wealth is significant and positive. While the positive coefficient on the wealth variable may reflect lower levels of risk aversion or greater access to ex post consumption smoothing through asse t sales, it is consistent with the presence of binding credit constraints which limit poorer farmers' access to fertilizer. The share of irrigated land, which measures the household's ability to cope with rainfall variability, is also significant and positive. The variables measuring risk, including the standard deviation in four measures of timing and extent of the monsoon and their interactions with the female share of nonagricultural employment in the village labor market are jointly statistically significant at the 1% level. Among the price and wage variables, the real price of fertilizer and the real wage for female laborers are both negative and statistically significant at the 1% level, as one would expect if fertilizer use and production labor are complements.

Random effects tobit estimates conditional on the first-period unemployment rate for male and female laborers (column (3) of table 2) are quite similar, although somewhat weaker than results conditional on the share of nonagricultural employment. The male unemployment rate is statistically significant at the l% level and negative as expected, but the female unemployment rate is not significant at even the 10% level. Real wealth is positive and significant and the share of the household's cropped area that is irrigated raises fertilizer use. The variables measuring risk effects are jointly significant here as well. The four variables measuring the dispersion of rainfall in the villages are significant at the 1% level and their interactions with the female unemployment rate are significant at the 10% level, suggesting important interaction between the household's exposure to risk and the off-farm labor market. The real fertilizer price is significant at the 1% level, but male and female wages are not jointly s ignificant at even the 10% level.

For estimates conditional on either unemployment or nonagricultural employment, the null hypothesis of no fixed effects is rejected at the 5% level. Therefore, parameter estimates of fertilizer demand using a fixed-effects tobit estimator are also reported for comparison. Including a household dummy variable and then running the standard tobit estimation routine yields results which are not consistent as the number of individuals increases and the number of time periods is constant. Therefore, a fixed-effects estimator that is consistent and works well with short panels like the one here is used. Consider the case of fertilizer demand [X.sup.*.sub.it] from equation (16). Honore (1992) shows that if [u.sub.it] and [u.sub.it+1] are independent and identically distributed conditional on the regressors [Z.sub.it], [Z.sub.it+1], then the distribution of the latent dependent variables [X.sup.*.sub.it] and [X.sup.*.sub.it+1] is distributed symmetrically around the 45[degrees] line that passes through ([DELTA]Z[beta], 0), where [DELTA]Z = [X.sub.it+1] - [X.sub.it]. Because the symmetry is not affected by censoring, the observed fertilizer demands are also distributed symmetrically. Symmetry suggests orthogonality conditions which must hold at the true parameter values, and these orthogonality conditions form the basis for the estimator. The Honore estimator takes the squared value of all the trimmed deviations ([X.sub.it+j] - [X.sub.it]) across all households and all possible time pairs contained in the data. The objective function is minimized using numerical methods implemented in Gauss. (11) Honore shows that the trimmed estimator is consistent and asymptotically normal when the underlying model is accurately described by fixed effects. Since the estimator does not estimate the fixed effects directly, it is consistent as the number of individuals goes to infinity, but the number of time periods is fixed. This appro ach is ideally suited for the case of short panels, such as the ICRISAT data.

Results for fertilizer demand using Honore's fixed-effects tobit estimator are reported in columns (2) and (4) of table 2. The dependent variable is fertilizer use per acre of total cropped area. The coefficient estimates in this model reflect the within-household variation only, and therefore exhibit higher standard errors. For estimates conditional on the share of nonagricultural employment in the off-farm labor market, column 2, the coefficients on labor market depth are not significant at even the 10% level. However, the estimated coefficients are quite close to those obtained from random effects, and the low t-ratios largely reflect higher standard errors arising from fixed-effects estimation. Among variables measuring risk mitigation, the coefficient on the share of irrigated land is positive and significant at the 1% level while household wealth levels are not significant. Neither fertilizer price nor wages are statistically significant at even the 10% level. The variables measuring the interaction of the shares with the standard deviation of the rainfall shock are jointly statistically significant at the 1% level.

Fixed-effects estimates of the fertilizer demand model conditional on unemployment rates are reported in column 4 of table 2. The first-period male unemployment rate is statistically significant and negative at the 10% level, and the unemployment rates are jointly significant at the 10% level as well. The share of irrigated land is significant and positive, while the real wealth variable is not significant. The variables measuring the interaction of unemployment rates with the variance of rainfall measures are jointly significant at the 10% level as well. This suggests that there is an important interaction between the riskiness of the production environment and the household's access to off-farm labor markets. The wage and price variables are not statistically significant.

That the fixed-effects results are less forceful than the random-effects results is not surprising. By sweeping out all the factors that are constant across time within a household, including characteristics of the distribution of village-level shocks that are not measured directly and the household's own appetite for risk taking, the fixed-effects model leaves less variation for the data to explain, and hence, the much larger standard errors in the fixed-effects model. The fact that the variables measuring the depth of the village labor market continue to be important in explaining the residual variation in fertilizer demand suggests that there is an important relationship between the household's access to off-farm employment as a hedge and its willingness to use fertilizer.

Conclusion

A two-period model is developed to show that farmers may use more fertilizer the deeper the off-farm labor market is. A well-known dataset on a sample of farmers in the semi-arid tropics of India is used to test the model. Farmers use more fertilizer as the depth of the off-farm labor market increases, where depth is measured by using both the unemployment rate and the share of employment in nonagricultural activities. Moreover, the interaction between the depth of the labor market and the degree of riskiness is important in explaining fertilizer use. This suggests that the labor market is important in smoothing income in the face of shocks to agricultural production. In fact, if the labor market were acting to eliminate credit constraints, then not only should the interaction between risk and the labor market not be important, but the level of real wealth should take up most of the explanatory power of the labor market variables, which is not the case. In fact, in fixed-effects estimates real wealth is not s ignificant explaining fertilizer use at all.

These results have important implications for development policy. While it is tempting to view off-farm work and farm production as substitutes, so that policies designed to raise the one must come at the expense of the other, the results here suggest that there are important complementarities between farm production and off-farm work. These complementarities suggest that policies that deepen the off-farm labor market may promote more intensive own-farm production and higher profits as well, particularly where such policies focus on the role off-farm labor may play in income smoothing ex post. For example, the policy is designed to help rural households deal with the risk inherent to production agriculture. These results suggest that a program designed to help rural households deal with the risk inherent to production agriculture (The Employment Guarantee Scheme in India) should weigh carefully the trade-off between higher wages and greater access to off-farm employment in the case of crop failure. To the ext ent that it is access to off-farm employment, and the incomesmoothing opportunities it provides, that matters to households, some higher wages should be sacrificed for greater access to off-farm employment.

The results also provide further evidence on the variety of activities available to low-income rural households in smoothing the effects of production risk in agriculture. As Morduch notes, one cannot simply look at measured consumption and determine what mechanism is at work, nor the cost of such a mechanism in terms of lost income or profits. As he notes (p. 105), "Mitigating risk through production choices can be costly, since typically expected profits must be sacrificed for lower risk." Costly smoothing has implications for income distribution over time, as poorer households undertake less risky activities with lower returns, and become relatively worse off over time. For researchers, further evidence that income is smoothed suggests that regressions of measured consumption against, say, household's transitory income may underestimate the costs of risk to low-income rural households. To the extent that income is already smoothed, such regressions give too much weight to the role of credit and insurance markets in smoothing consumption, and thus understate the real costs of risk in terms of lower average incomes.

[FIGURE 1 OMITTED]

Table 1

Means for Variables Used in ICRISAT Models


Fertilizer use per acre (kg)                  9.82
Real fertilizer price (rupees/kg)             2.44
First-period real wage, male (rupees/hour)    0.86
First-period real wage, female (rupees/hour)  0.54
First-period unemployment rate, males         0.15
First-period unemployment rate, females       0.15
Share of nonagricultural employment, males    0.59
Share of nonagricultural employment,          0.36
 females
Share of crop area irrigated                  0.11
Household's real assets (1000 rupees)         21.7
Standard deviation, monsoon onset (days)      15.4
Standard deviation, total rainfall             205
Standard deviation, rain per day              1.72
Standard deviation, frequency of rainfall     0.10
 days

Note: Based on 560 observations used in estimates of fertilizer demand,
drawn from five of the ICRISAT study villages. Values for the whole
ICRISAT sample may differ.

Table 2

Tobit Estimates for Fertilizer Demand Dependent Variable: Fertilizer
Demand Per Acre

                                       (1)          (2)
                                      Random       Fixed
                                     Effects      Effects

Labor market depth
 Share of nonagricultural labor    4347.9 **    3069.
  in female labor, planting          (2.17)       (1.29)
  period
 Share of nonagricultural labor      44.02 **     33.69
  in male labor, planting            (2.75)       (1.41)
  period
 Unemployment rate, female,
  planting period
 Unemployment rate,
  males planting period

Risk mitigation variables
 Share of irrigated land             52.23 ***    67.17 ***
                                     (9.13)       (3.46)
 Real value of household assets      20.5 ***     -2.42
                                     (3.76)      (-0.37)
Shock and risk measures
 Monsoon onset date (deviation       -2.47        -0.23
  from village mean)                (-0.17)      (-0.92)
 Standard deviation--monsoon         -3.27
  onset                             (-0.86)
 Standard deviation--total           17.38 *
  rainfall                           (1.84)
 Standard deviation--rain          -1351 *
 per day                            (-1.62)
 Standard deviation--frequency of    23.8 *
 days with rain (x1000)              (1.89)
 SD monsoon onset x share of         -4.46       -14.89
  nonagricultural,                  (-0.85)      (-1.45)
  female planting period
 SD total rainfall x share          -21.18 *      11.27
  of nonagricultural,               (-1.93)      (-0.76)
  female planting period
 SD rainfall per day x share          1.55 *     595.7
  of nonagricultural,                (1.60)       (0.45)
  female planting period
 SD frequency of rain days          -25.65 *      -1.48
  x share of nonagricultural,       (-1.75)      (-0.80)
  female planting period
 SD monsoon onset x
  planting period, female UR
 SD total rainfall x planting
  period, female UR
 SD rain per day x planting
  period, female UR
 SD frequency of rain days
  x planting period, female UR

Price/wage variables
 Real fertilizer price              -16.43 **     -5.85
                                    (-2.39)      (-0.56)
 Real wage for male                   5.88       -13.97
  labor, planting period             (0.30)      (-0.58)
 Real wage for female               -79.87 **    -28.07
  labor, planting period            (-2.32)      (-0.36)

Joint hypothesis tests
 chi-square test for                  5.54 *       2.11
  significance of wages (a)          (0.06)       (0.35)
 chi-square test for                 30.01 **
  significance of rainfall SD        (0.00)
 chi-square test significance of     24.2 **      14.5 ***
  interaction SD in rainfall and     (0.00)       (0.01)
  labor market depth
 chi-square test for                  8.44 **      2.1
  significance of labor              (0.01)       (0.36)
  market depth
 chi-square test for null            27.09 **
 hypothesis of no fixed effects      (0.01)

                                        (3)         (4)
                                      Random        Fixed
                                     Effects       Effects

Labor market depth
 Share of nonagricultural labor
  in female labor, planting
  period
 Share of nonagricultural labor
  in male labor, planting
  period
 Unemployment rate, female,        -2589.9       -795.3
  planting period                    (-1.28)      (-0.37)
 Unemployment rate,                 -128.06 **   -105.6 *
  males planting period              (-2.29)      (-1.73)

Risk mitigation variables
 Share of irrigated land              49.42 ***    60.59 ***
                                      (8.66)       (4.42)
 Real value of household assets       21.89 ***     0.56
                                      (3.99)       (0.06)
Shock and risk measures
 Monsoon onset date (deviation        -9.04        -0.17
  from village mean)                 (-0.68)      (-0.83)
 Standard deviation--monsoon           0.40
  onset                               (0.51)
 Standard deviation--total            -0.35
  rainfall                           (-0.55)
 Standard deviation--rain             30.8
 per day                              (0.54)
 Standard deviation--frequency of     60.53
 days with rain (x1000)               (0.74)
 SD monsoon onset x share of
  nonagricultural,
  female planting period
 SD total rainfall x share
  of nonagricultural,
  female planting period
 SD rainfall per day x share
  of nonagricultural,
  female planting period
 SD frequency of rain days
  x share of nonagricultural,
  female planting period
 SD monsoon onset x                  -10.38        -7.80
  planting period, female UR         (-1.44)       (0.83)
 SD total rainfall x planting         14.62         5.30
  period, female UR                   (1.28)       (0.42)
 SD rain per day x planting         1093.8       -319.0
  period, female UR                  (-1.09)      (-0.29)
 SD frequency of rain days            16.91      4272
  x planting period, female UR        (1.14)       (0.27)

Price/wage variables
 Real fertilizer price               -12.63 **     -1.53
                                     (-2.40)      (-0.21)
 Real wage for male                   -6.44       -38.69
  labor, planting period             (-0.28)      (-1.09)
 Real wage for female                -49.4          7.05
  labor, planting period             (-1.40)       (0.14)

Joint hypothesis tests
 chi-square test for                   2.92         1.7
  significance of wages (a)           (0.23)       (0.43)
 chi-square test for                  49.24 **
  significance of rainfall SD         (0.00)
 chi-square test significance of       8.19 **      8.1 *
  interaction SD in rainfall and      (0.08)       (0.09)
  labor market depth
 chi-square test for                   5.29 *       4.8 *
  significance of labor               (0.07)       (0.09)
  market depth
 chi-square test for null             24.02 **
 hypothesis of no fixed effects       (0.02)

Note: t-statistic are shown in parentheses.

(a)For chi-quare tests, p-values are shown in parentheses.

[Received June 2001; final revision received September 2002.]

(1.) Ex ante refers to the period before the realization of the weather shock, and ex post refers to the period after the shock is realized.

(2.) For an excellent survey of these issues see Morduch.

(3.) Nursery-bed raising, planting, transplanting, thinning, and weeding are gender-specific to women.

(4.) There is a labor allocation decision in the first period as well. Including the first-period labor allocation decision greatly complicates the analytics of the model, since it increases the dimension to three inputs. To the extent that labor use is proportional to fertilizer use in the first period, then omitting the labor choice from the first period will not bias the results.

(5.) Note that the term [E.sub.[theta]]U' * {([w.sub.k] + (1 - [d.sub.k])[[theta].sub.k] - ([[theta].sub.k] + (1 - [gamma])[[theta].sub.k][f.sub.l])[partial]L/[partial]X is zero by the first-order condition in (4). Nonetheless, the fact that L is a function of X will affect the comparative statics of X.

(6.) A referee suggested that a better predictor of ex post labor market conditions might be the lagged value of the ex post labor market variables, for example, the unemployment rate and share of nonagricultural employment the previous year. However, these variables proved less satisfactory in the empirical application. In particular, while the coefficient estimates were similar between the two, the standard errors were sharply higher using the previous year's ex post variables.

(7.) The structure of the ICRISAT questionnaire changed in 1979; from 1975 to 1978 respondents were asked how many hours they worked the previous day in various activities. After 1978 households were asked how many hours they had worked since the last interview.

(8.) In fact, by the end of the sample period farmers use a wide variety of complex fertilizers on their crops. However, urea is a common fertilizer used in all the ICRISAT villages in every year. The price of chemical fertilizers should move together, sousing the price of urea should not bias results.

(9.) In fact, the potential role of credit constraints in the empirical results is quite important. In a related article, which came to the author's attention after this article was completed, Chaudhuri and Osborne test for the potential role of credit constraints using the ICRISAT data. They find that credit constraints cannot explain the limited use of fertilizer in the ICRISAT study villages. They argue (p.25),"... a lack of credit may be a less important impediment to fertilizer use than incomplete markets for risk."

(10.) Estimation of the random-effects tobit model is achieved using maximum likelihood techniques in Stata, Release 7. For a fuller discussion of the methodology, including the likelihood function, see the Stata Reference Manual, Release 7, Vol. 4, pp. 446-50.

(11.) I am grateful to Professor Bo Honore of Princeton University for making available the Gauss code to implement the estimator. The software may be downloaded from the web at http://web.princeton.edu/sites/econometrics/programs/pantob/.

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Russell L. Lamb is assistant professor, Department of Agricultural and Resource Economics, North Carolina State University.

The author thanks Jere Behrman, Andrew Foster, Mark Rosenzweig, Spiro Stefanou, wally Thurman, two anonymous referees, and seminar participants at North Carolina State University and the University of Pennsylvania for useful comments on the paper. All remaining errors are the responsibility of the author.