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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} + * α_{1}t + α_{2}t^{2}* +

*f*(

*X*) + E

_{jt}β_{ijt}———————————— (1)

where *y _{ijt }*denotes the log wheat yield for variety i at trial location j in year t;

*γ*is a vector of cultivar intercepts to control;

_{i }*τ*denotes a vector of location intercepts to control;

_{j }*α*

_{1}

*t*+

*α*

_{2}

*t*

^{2 }captures the time trend, and

*f*(·) represents the weather function while

*X*is a vector of weather related variables and the

_{jt }*β*are the slope parameters for

*X*; E

_{jt}_{ijt}is the error term.

Precisely, we add intercepts *γ _{i }*to control for genetic differences in yield and

*τ*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.

_{j }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*) = *β*1*lowjt *+ *β*2*medjt *+ *β*3*highjt *+ *β*4*Pjt *+ *β*5*Pjt*2 ——————– (2)

where *β*_{1}*low _{jt }*measures degree days from 0 to the lower threshold, 10 Celsius degree,

*β*

_{2}

*med*measures degree days between 11 and the upper threshold, 26 Celsius degree, and

_{jt }*β*

_{3}

*high*measures degree days above the upper threshold, 27 Celsius degree,

_{jt }*β*

_{4}

*P*and

_{jt }*β*

_{5}

*P*

_{jt}^{2 }indicates a quadratic effect of precipitation during the growing season on wheat yield.

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