APPLIED FINANCIAL ECONOMETRICS, Financial Econometrics

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Question 1

Suppose that you have 150 observations on production (yt) and investment (it), and you have estimated the following ADL(3,2) model:

(1 – 0.5L – 0.1L2 – 0.05L3)yt = 0.7 + (0.2 + 0.1L +0.05L2)it (1)

a. Use this model to describe the dynamic effects of investment on production. Your answer should include a calculation of the impact multiplier and the long-run multiplier.

b. Suppose that you can obtain other output associated with the above regression (eg., the residuals et, the R2, the sum of squared residuals, etc.). Carefully explain how you would test each of the null hypotheses given below.

[Hints: In each case your answer should state the extra output you would need from regression of equation (1), the extra regression(s) that you would need to run, an explanation of how you would construct the test statistic, a statement on the distribution of the test statistic under the null hypothesis, and a brief description of your critical region.]

i. H0: investment has no long run effect on production.

ii. H0: there is no third order serial correlation in the errors.

Question 2

Consider the following equations which respectively describe demand, advertising and supply in the market for cigarettes:

qtyt = a1 + a2 adt + a3 prt + a4 inct + e1t

adt = b1 + b2 qtyt + b3 prt + b4 qtyt-1 + e2t

qtyt = c1 + c2 prt + c3 adt-1 + e3t

where qty is quantity, ad is advertising expenditure, pr is price of cigarettes, inc is income.

a. Briefly explain why economists should be concerned about using OLS to estimate these equations. (Give the gist of the argument – a formal proof is not necessary here)

b. Derive explicit expressions for the reduced form equations for this model.

c. Consider the order conditions for determining the identification status of each equation. Can you solve uniquely for the structural parameters? (Don’t try, just explain why or why not, for each of the three cases).

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