There are some challenges in estimating this model, primarily the inability to take into account how farmers’ incomes may drive both rice yields and urea use. Estimating the relationship presents a potential endogeneity problem. This is because urea used will most likely be correlated with the error term in the yields equation because of omitted variable bias.<sup>10</sup> Those omitted variables that have an impact on yields, but were not included in the regression, either observable or unobservable effects, will be captured in the error term. Farmers’ incomes will most likely impact yields, but in the absence of a measure of wealth in the survey, it cannot be captured in the yields equation (1) explained below. Thus, income is a driver of yields if richer farmers have different production levels than poorer farmers as a result of being less credit constrained, risk averse, or having access to better farming techniques. On the other hand, income will determine how much urea farmers can buy and, for poorer farmers, spending on inputs accounts for a much higher share of their resources. Therefore, omitted variable bias can drive the relationship between urea usage and the error term when income is not accounted for in the yields equation. Other omitted variables that can impact yields include: the quality of irrigation, private capital, and effort or ability to grow rice.

To address this endogeneity problem, the model is estimated using an instrumental variable (IV) through a two-stage least square regression (2SLS).<sup>11</sup> The 2SLS estimator calculates the fitted values of the urea regression (2) and the fitted values of urea used squared (3) to use as IV’s and indirectly capture the impact on the yields regression (1). In the first stage regression, it breaks urea used (and urea used squared) into 2 components, a “problematic one” correlated with the error term and a “nonproblematic” exogenous component. Then, it takes the exogenous parts of urea used (and urea used squared) to capture the effect on the rice yields. There are two conditions to meet in order for this estimator to be valid: (i) instrument relevance, where the correlation between urea fitted and urea used is different from 0; and (ii) instrument exogeneity, where the correlation between urea fitted and the error term (e) is 0. Both these conditions are met by the model in this section.<sup>12</sup> The model looks at the relationship across the overall sample and also within each quintile of land size, given that urea usage and yields vary significantly according to plot size. The overall model captures better the relationship as a whole, is estimated over a wider sample, and allows for geographical differences with a dummy for Java-Bali. However, estimating the relationship at the quintile level shows interesting differences that illustrate smaller farmers having higher yields and on average using more urea than recommended. Interestingly, by grouping individuals according to the size of their rice paddies also captures farming variations across provinces because farms tend to be much smaller in Java-Bali (and are planted more intensively). Table 4.1 below suggests that larger farmers (quintile 5) can be predominantly found off-Java, while the composition of quintiles 1-4 is two thirds either Javanese or Balinese. Therefore, breaking the sample into land groups allows for the production functions to vary by land size and by geographical location.

> 10 The results of the Durbin-Wu-Hausman test for endogeneity confirm that urea used is correlated with the error term in the yields equation (1), (Stock and Watson 2003).

> 11 See Annex VII for a comparison between 2SLS and OLS estimators.

> 12 Instrument exogeneity in the model was tested with the overidentifying restrictions test and failed to reject the null hypothesis of exogeneity. The instruments used and results presented in this section meet the condition of  exogeneity and are statistically valid. (Stock and Watson, 2003).

**13**