Program evaluation with two-period panel data I Suppose the local government in a small town is concerned about a growing obesity epidemic among the town's residents. To address this issue, government officials implemented a program that offered free diet pills to residents to help them lose weight. Government officials also collected a sample of residents, who did not take the pill, to act as a control group. Government officials then weighed all individuals in year 1, before any diet pills were given out, and then weighed the same group of individuals again in year 2 after the diet pills had been administered. Consider the following model to evaluate the effectiveness of the diet pill program on the weight of residents in the town:
weightit = β0 + yr2t + β1pillit + vit
where
weigh it = weight of individual i, in yeart, in pounds
yr2t = binary variable equal to 1 if the time period is year 2, and 0 otherwise
pillit = binary variable equal to 1 if individual i took the diet p in yeart, and 0 otherwise
vit composite error consisting of the unobserved, time-constant effect (a) and the idiosyncratic error (vit)
Suppose a researcher suggests simply pooling the cross sections from year 1 and year 2, and estimating the model by running an OLS regression on the pooled cross-sectional data set. Which of the following factors, captured by air would cause this pooled OLS strategy to yield biased and inconsistent estimates of β, the effect of the pill on the weight of the residents of the town.
A. Government officials randomly assign the diet pills to individuals independent of the un-observed heterogeneity among individuals.
B. Government officials systematically give the diet pills to individuals who are genetically pre-disposed to being underweight.
C. Government officials systematically give the diet pills to individuals who are genetically pre-disposed to being overweight.
Suppose, instead of taking the advice of the researcher, you difference the data and estimate the first-differenced equation so that the unobserved time-constant effects are differenced away. The regression results in the following estimates:
Δweight = 166 - 4 Δpilli
(49.0) - (1.0)
According to the estimated first-differenced equation, on average, taking the diet pillbody weight bypounds. The magnitude of the t-statistic on β1 implies the effect of the pillstatistically significant.
Out of curiosity, you take the researcher's initial advice and use pooled OLS to estimate the original model, without differencing the data. This yields an estimate of β1 - 0.2, (standard error 0.18). Which of the following most likely explains the differences between the pooled OLS estimate and the first-differenced estimates?
A. Government officials randomly assign the diet pills were randomly assigned to residents, independent of the unobserved heterogeneity among individuals.
B. Out of concern for the health of the citizens of the town, government officials systematically gave the diet pills to individuals who are genetically predisposed to being overweight.
C. In an attempt to make the diet pills appear more effective, government officials systematically gave the diet pills to individuals who are genetically predisposed to being underweight.