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.

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

Question:

Write out a DD regression equation which would include all the years. Run this regression and explain the difference from Question 1. [Hint: create a dummy variable for pre- and post-TRA86]

Data for Analysis is below:

Group	Year	Insurance_Rate	Group_Dummy	Time_Dummy	Group_Time_Dummy
Self_emp	1982	68.9	1	0	0
Self_emp	1983	72	1	0	0
Self_emp	1984	68.9	1	0	0
Self_emp	1985	68.6	1	0	0
Self_emp	1986	70.1	1	0	0
Self_emp	1987	76.1	1	1	1
Self_emp	1988	73.2	1	1	1
Self_emp	1989	73.5	1	1	1
Employed	1982	88.6	0	0	0
Employed	1983	88.9	0	0	0
Employed	1984	88.1	0	0	0
Employed	1985	88	0	0	0
Employed	1986	88	0	0	0
Employed	1987	86.8	0	1	0
Employed	1988	86.1	0	1	0
Employed	1989	84.5	0	1	0

Answer 1

The DD regression equation is:

y = 91.9867 - 21.2867*x1 - 1.1867*x2 + 7.0867*x3 - 0.3333*t

The time variable is included in the model. The regression analysis is:

	R²	0.987
	Adjusted R²	0.983
	R	0.994
	Std. Error	1.120
	n	16
	k	4
	Dep. Var.	Insurance_Rate
ANOVA table
Source	SS	df	MS	F	p-value
Regression	1,072.8814	4	268.2203	213.67	2.40E-10
Residual	13.8080	11	1.2553
Total	1,086.6894	15
Regression output				confidence interval
variables	coefficients	std. error	t (df=11)	p-value	95% lower	95% upper
Intercept	91.9867
Group_Dummy	-21.2867	1.9620	-10.849	3.25E-07	-25.6050	-16.9683
Time_Dummy	-1.1867	1.2273	-0.967	.3544	-3.8880	1.5147
Group_Time_Dummy	7.0867	1.1571	6.124	.0001	4.5398	9.6335
t	-0.3333	0.2287	-1.458	.1729	-0.8367	0.1700