Question

For this assignment, we will replicate the DD study by Gruber & Poterba (1994) [`a la Donald & Lang, 2007]. In their study, they estimate the impact of TRA86 on health insurance take-up of ‘self-employed’ workers. The policy intervention they use is a tax subsidy on health insurance purchase for the self-employed introduced in the Tax Reform Act of 1986. There treatment group are the self-employed workers and their control group are the other workers who are employed. In particular, they look at the aggregate insurance rates of these two groups.

Question:

First, find the difference in employment between self-employed and employed for all years. Now, find the DD estimate relative to the previous year [i.e. the difference, relative to last year, of the difference you just calculated]. Think of this as if there was a policy every year starting with 1983. We are finding a placebo-DD for all years. How do these compare with the real effect (i.e. for the year 1986-87)? Using the standard errors from Question 1, test the significance for the estimates for each year at 5%? What is an issue with our findings?

Table 1: Aggregate Insurance Rates

Year Self-Employed Employed

1982 68.9 88.6

1983 72.0 88.9

1984 68.9 88.1

1985 68.6 88.0

1986 70.1 88.0

1987 76.1 86.8

1988 73.2 86.1

1989 73.5 84.5

Source: Table IV of GP1994

Answer 1

Year	Self-Employed	Employed	Difference
1982	68.9	88.6	19.7
1983	72	88.9	16.9
1984	68.9	88.1	19.2
1985	68.6	88	19.4
1986	70.1	88	17.9
1987	76.1	86.8	10.7
1988	73.2	86.1	12.9
1989	73.5	84.5	11
		87.3750	mean Employed
		71.4125	mean Self-Employed
		15.9625	mean difference (Employed - Self-Employed)
		3.8284	std. dev.
		1.3536	std. error
		8	n
		7	df

11.793	t
7.15E-06	p-value (two-tailed)

There is a significant difference in employment between self-employed and employed for all years.