Econometrics Using Stata

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We need to regress log wheat yield on location, temperature, precipitation, and cultivar dummy variable on stata. Specifically, we consider the following multiple regression model with fixed effects to estimate the weather effect on wheat quantity:

y_ijt =γ_i + τ_j + α₁t + α₂t² + f(X_jtβ) + E_ijt ———————————— (1)

where y_ijt denotes the log wheat yield for variety i at trial location j in year t; γ_i is a vector of cultivar intercepts to control; τ_j denotes a vector of location intercepts to control; α₁t + α₂t² captures the time trend, and f(·) represents the weather function while X_jt is a vector of weather related variables and the β are the slope parameters for X_jt; E_ijt is the error term.

Precisely, we add intercepts γ_i to control for genetic differences in yield and τ_j to control for spatially-invariant unobserved effects such as soil quality. The time trend is included in this model as a quadratic form to capture the genetic improvements at a diminishing rate over time . Since only elite lines are likely tested and developed in the trial area, this property needs to be reflected. Next, we cluster standard errors by year, which takes account of random correlation among unobservables within the same period.

We presumes the nonlinear relationship between temperature and quantity rather than linearity. In other words, we assume that when the climate is below or above a certain threshold, two dependent variables – quantity and quality – may decline dramatically. From this point of view, we use the function for capturing weather effects as follows:

f(Xjt;β) = β1lowjt + β2medjt + β3highjt + β4Pjt + β5Pjt2 ——————– (2)

where β₁low_jt measures degree days from 0 to the lower threshold, 10 Celsius degree, β₂med_jt measures degree days between 11 and the upper threshold, 26 Celsius degree, and β₃high_jt measures degree days above the upper threshold, 27 Celsius degree, β₄P_jt and β₅P_jt² indicates a quadratic effect of precipitation during the growing season on wheat yield.

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