Using 352 observations on 44 rice farmers in the Tarlac region of the Phillipines for 8 years

Question:

Using 352 observations on 44 rice farmers in the Tarlac region of the Phillipines for 8 years from 1990 to 1997, we estimated the relationship between tonnes of freshly threshed rice produced (PROD), hectares planted (AREA), person-days of hired and family labor (LABOR), and kilograms of fertilizer (FERT). The log-log specification of the model, including the unobserved heterogeneity term, is

\[\ln \left(P R O D_{i t}\right)=\beta_{1}+\beta_{2} \ln \left(\text { AREA }_{i t}\right)+\beta_{3} \ln \left(L A B O R_{i t}\right)+\beta_{4} \ln \left(F E R T_{i t}\right)+u_{i}+e_{i t}\]

Table 15.14 contains various estimates of the model. Model (1) contains OLS estimates. Model (2) contains OLS estimates of the model including year dummy variables, which are not shown, such as \(D 91\) = 1 for year \(1991, D 91=0\) otherwise. Model (3) contains fixed effects estimates. Model (4) contains fixed effects estimates of the model including year dummy variables. In each case, conventional standard errors are reported, (se), and for Model (4), we also report cluster-robust standard errors (robust). For each model, we report the sum of squared residuals and the number of model parameters, apart from the intercept. The \(p\)-values are reported for the \(t\)-statistics computed using the conventional standard errors.

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a. Comment on the sensitivity of the estimates of the input elasticities to the various models.

b. Which of the estimated models do you prefer? Perform a series of hypothesis tests to help you make your decision.

c. For Model (4), find 95\% interval estimates for the input elasticities using (i) conventional standard errors and (ii) cluster-robust standard errors. Comment on any differences.

d. Calculate the \(p\)-value for the coefficient of \(\ln (F E R T)\) using the robust standard error.

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