Prof. Bryan Caplan

Name:_______________________

Economics 637 Final

Prof. Bryan Caplan

Spring, 1998

Instructions:

You have 2 hours, 30 minutes to complete this exam.
You may use any books, notes, or other materials that you wish, but avoid spending too much time on any one question.

Partial credit may be awarded on all questions.

The maximum possible number of points is 200.
Spend 6-7 minutes on each T/F/Explain question, and about 13 minutes on each short answer question.
You should have ten pages, counting this one.

Part 1: True, False, and Explain

(10 points each - 3 for the right answer, and 7 for the explanation)

State whether each of the following twelve propositions is true or false. Using 2-3 sentences AND/OR equations, explain your answer.

1. True, False, and Explain: If a regression of Y on X (without a constant) yields: Y=3X, then a regression of X on Y necessarily yields X=(1/3)Y.

2. Suppose that in reality, a person's income I=$20,000+$200*IQ+$500*PIQ, where PIQ is a measure of a person's "practical intelligence." PIQ tries to measure "practical" cognitive abilities not captured in IQ tests.

True, False, and Explain:

If an econometric researcher unfamiliar with PIQ uses OLS to estimate I=a+b*IQ, it is possible that he will still find that b=$200.

3. A multiple regression of income (in $'s) on years of education and years spent in prison yields:

I=15,000+1000*Education-1500*Prison

The variance-covariance matrix of the coefficients is:

	Education	Prison
Education	40,000	-50,000
Prison	-50,000	90,000

True, False, and Explain: You can reject the hypothesis (at the 5% level) that the summed effect on your earnings of doing prison time AND attending the prison school is zero.

4. OLS on the following data yields:

Y	X	Y_i=1.500 + .700*X_i (.245) (.100) R²=.942
4	3
4	4
3	2
2	1
1.5	0

True, False, and Explain: The matrix s ^2W (used to calculate the HCSE's) can be estimated to be:

5. If the correlation between e_t and e_t-1 is -.3, then the DW statistic will approximately equal 3.4.

6. True, False, and Explain: The following ARMA process for Y_t is difference stationary: (1-L)Y_t=(1-L-L²)e _t. (e _t is iid).

7. Consider the VAR: Y_t=AY_t-1+e _t, where Y_t=[GDP_t M_t]' and A=.

True, False, and Explain: The impulse-response function for the impulse

e ₀=[0 1]' looks like:

t	GDP_t	M_t
0	0	1
1	.5	.9
2	.3	.4

Questions 8 and 9 refer to the following system:

Dosage_t=b1*Sickness_t+b2*Wealth_t+b3*Medicare

Sickness_t=c1*Dosage_t+c2*Wealth_t+c3*Parents_t

Medicare_t is a dummy variable that equals 1 if a subject is eligible for Medicare, and Parents_t is the number of living natural parents of the subject.

8. True, False, and Explain: The system is overidentified.

9. True, False, and Explain: The second stage of 2SLS of the complete system would require a regression of Dosage_t on Sickness_t*, Medicare_t, Wealth_t, and Parents_t*, AND a regression of Sickness_t on Dosage_t*, Wealth_t, Parents_t, and Medicare_t*.

10. You are performing SUR on a system with 5 equations and 50 observations. You need to estimate S .

True, False, and Explain: The dimensionality of S is 5x5.

11. A logit of P(below the poverty line) on a constant, IQ, socio-economic status, and age yields the following coefficients. (Note that as in Herrnstein and Murray, all variables are normalized to have a mean of 0 and a SD of 1):

Constant	IQ	SES	Age
-2.649	-.838	-.330	-.024

True, False, and Explain: If a man has an IQ 2 SD's below average, SES 1 SD below average, and Age 3 SD above average, then his predicted P(below the poverty line) is about 33%.

12. You are given the following data for two dichotomous variables:

	x
y	0	1	Total
0	75	15	90
1	50	60	110
Total	125	75	200

True, False, and Explain: The linear probability model y_i=a+bx_i+e _i estimated from this data yields a=.4 and b=.4.

Part 2: Short Answer

(20 points each)

In 4-6 sentences AND/OR equations, answer all three of the following questions.

1. Consider a simple VAR: Y_t=a+bY_t-1, where Y_t=[M_t G_t]. Prove that OLS is the best linear unbiased estimator of the parameters in this equation. (Hint: Remember SUR).

2. Suppose you are trying to estimate the following model on demeaned data:

Dosage_t=b1*Sickness_t+b2*Wealth_t+b3*Medicare

Sickness_t=c1*Dosage_t+c2*Wealth_t+c3*Parents_t

You are given the following matrix of second moments:

	Dosage	Sickness	Wealth	Medicare	Parents
Dosage	10	5	8	4	-5
Sickness	5	5	-5	0	-5
Wealth	8	-5	1	4	1
Medicare	4	0	4	2	0
Parents	-5	-5	1	0	1

Set up a matrix equation for the 2SLS estimates of c1, c2, and c3; then simplify it by substituting the correct numerical values into it. Once you have substituted in for all of the variables, you do not have to (and should not!) actually solve the equation. In particular, you do not have to calculate any inverses or multiply any matrices.

3. The graph below shows the results from one of the logits performed in The Bell Curve. What two aspects of this graph indicate that Herrnstein and Murray used a logit rather than a linear probability model? Could either of these aspects have been reproduced in a re-specified linear probability model?

4. Caplan's "War as a Natural Macro Experiment" tries to investigate the causal link between macro policy and macro performance. Many critics of econometrics (discussed in both Week 1 and Week 14) doubt that this is really possible. Explain TWO of the econometric technique Caplan uses to separate causation from correlation. What are the best criticisms of the validity of these techniques?