Suppose that you were hired as a consultant by the Niagara School Board to assess the effectiveness of learning programs in five school districts in the region. The programs were active during the past ten years, and in no district was the program changed in any way throughout this time. The aim of these programs has been to increase the students’ test scores. You’re presented with the following data: Yit – average test score (in %) in district i during year t of the program. (4) X2it – amount of money (in millions of dollars) spent in district i during year t. (5) X3it – student population (in thousands) in district i during year t. (6) (a) (4 points) Do these data represent a balanced or unbalanced, short or long panel? Please explain why. (b) (7 points) Suppose that you estimated a linear regression where you simply regressed Yit on a constant, X2it and X3it using OLS, essentially ignoring panel nature of these data and treating them as a cross section. In addition to the usual CLRM assumptions, which other assumptions are required in order for your estimates to be unbiased and efficient? In other words – what needs to be true with respect to differences in order for such pooled OLS estimation to be unbiased and efficient? (c) (10 points) Suppose that you instead estimate the following LSDV model using these data: Yit = β1 + α1D1it + α2D2it + α4D4it + α5D5it + β2X2it + β3X3it + uit, (7) where Djit represents a dummy variable corresponding to j’th school district in the sample. Describe in detail how you would use your model estimates to jointly test the hypotheses that conditional on the same level of program funding (X2it) and the same student population (X3it), (i) average scores in school district #5 are 5% higher than in district #3, and that (ii) average scores in district #2 are 7% lower than in district #1. Hint: dummy for District 3 here is missing. This is on purpose. (d) (10 points) Suppose that currently district #4 and district #5 have the same number of students (X3it) and receive the same program funding (X2it). By how much (in millions of dollars) would you need to increase the funding, and for which district, so that to make average scores in both districts the same? For this question, suppose that coefficient estimates for the model in (7) are as follows: Coefficient β1 β2 β3 α1 α2 α4 α5 Estimate 70 5 -2 -1 -3 4 8 Table 2: Coefficient estimatse from Model (7). (e) (5 points) Is Moneyball (2011) the only major hollywood movie about Econometrics?
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