Show transcribed image text Problem 5. Consider the following panel data regression model. Suppose there are two time periods (T-2), and there is a large number of cross-section units (n). Suppose that there is only one covariate Xit and in the first time period its value is zero for all i, i.e., Xi1 – 0 for all i. In the second time period the covariate takes only two values. O and 1, ie., Xi26 {0, 1). Consider the panel data regression model (a) Let m-Σ=1 Xi2. Explain why that the standard differences estimator in this model can be written simply as β differences where Σ:xi,-, AY, is the sum oAY; only for observations i with = 1. (b) In Iowa 250 farms grew corn in years 1980 and 1981. In January 1981 a new fertilizer has been introduced and in the Spring of 1981 it has been adopted by 100 of the farms. For the 100 farms that have adopted the fertilizer the average yields (bushels per acre) were 101.1 and 107.3 in years 1980 and 1981 respectively. For the 150 farms that have not adopted the fertilizer the yields were 93.2 and 96.1 respectively. Use this information together with the result of part (a) to estimate the effect of the fertilizer on the yield.
Problem 5. Consider the following panel data regression model. Suppose there are two time periods (T-2), and there is a large number of cross-section units (n). Suppose that there is only one covariate Xit and in the first time period its value is zero for all i, i.e., Xi1 – 0 for all i. In the second time period the covariate takes only two values. O and 1, ie., Xi26 {0, 1). Consider the panel data regression model (a) Let m-Σ=1 Xi2. Explain why that the standard differences estimator in this model can be written simply as β differences where Σ:xi,-, AY, is the sum oAY; only for observations i with = 1. (b) In Iowa 250 farms grew corn in years 1980 and 1981. In January 1981 a new fertilizer has been introduced and in the Spring of 1981 it has been adopted by 100 of the farms. For the 100 farms that have adopted the fertilizer the average yields (bushels per acre) were 101.1 and 107.3 in years 1980 and 1981 respectively. For the 150 farms that have not adopted the fertilizer the yields were 93.2 and 96.1 respectively. Use this information together with the result of part (a) to estimate the effect of the fertilizer on the yield.
