We are interested in the relationship between rice production, inputs of labor and fertilizer, and the area planted using data on \(N=44\) farms.

a. We observe the least squares residuals, \(\hat{e}_{i}\), increase in magnitude when plotted against ACRES. We regress \(\hat{e}_{i}^{2}\) on ACRES and obtain a regression with \(R^{2}=0.2068\). The estimated coefficient of ACRES is 2.024 with the standard error of 0.612. What can we conclude about heteroskedasticity based on these results? Explain your reasoning.

b. We instead estimate the model

What is the implicit assumption about the heteroskedasticity pattern?

c. Many economists would omit \(\left(1 / A C R E S_{i}\right)\) from the equation. What argument can you propose that would make this defensible?

d. Following the estimation of the model in (b) or (c), the squared residuals, \(\tilde{e}_{i}^{2}\), are regressed on ACRES. The estimated coefficient is negative and significant at the \(10 \%\) level. The regression

\(R^{2}=0.0767\). What might you conclude about the models in (b) or (c)? That is, what could have led to such results?

e. In a further step, we estimate \(\ln \left(\hat{e}_{i}^{2}\right)=-1.30+1.11 \ln (A C R E S)\) and \(\ln \left(\tilde{e}_{i}^{2}\right)=-1.20-\) \(1.21 \ln (A C R E S)\). What evidence does this provide about the question in part (d)?

f. If we estimate the model in (c), omitting (1/ACRES \(\left.S_{i}\right)\), would you advise using White heteroskedasticity robust standard errors? Explain why or why not.

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RICE, B+BLABOR, +FERT, + ACRES; + e;