Question: A negative income tax experiment was conducted in Seattle and Denver to see if a guaranteed annual income would cause people to work less. The experiment contained two sample groups. The "experimental group" was guaranteed a minimum income; the "control group" was not. One way to investigate the work-incentive effects of the guaranteed-income program is to com-pare the annual earnings (not counting the subsidy) of the two groups. The average earnings of the sample families are given in the table below, with the number in parenthesis representing the standard deviation of earnings within each group in each period (before and during the experiment).
a. Using a 5% significance level, test whether the mean earnings of the experimental group differed from the mean earnings of the control group in the period before the experiment began. What does this suggest about the way families were assigned into each group?
b. One estimator of the program's effect on earnings is the difference in average earnings be-tween the experimental and control families during the experiment. Using a 5% significance level, test whether this estimated difference is significantly different from zero. Would you want to use a one-tailed or two-tailed test? What is the probability that a sample difference as large as (or larger than) this one would occur if the true difference were zero?
c. Why is the above estimator of the program's effect likely to be biased? Suggest and compute an alternative estimator of the effect of the income guarantee on family earnings, and again test whether the program has zero average effect. (Use the fact that the sample covariance between earnings before and during the experiment is 6,771,923 for the experimental families and 6,757,797 for the control families.)