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Econometrics Exam Questions Johns Hopkins

Johns Hopkins. Final Exams for “Econometrics”. Christ and Harberger, 1951-1952

 If you have ever wondered why the journal Econometrica has always published much content with next to no “econometrics” (in the sense of mathematical statistics with special application to economics), the final exams for the Johns Hopkins graduate course “Econometrics” taught by Carl Christ and Arnold Harberger in 1951-52 provide us with a ready explanation. We can see that their course offered a combination of mathematical modeling and econometrics, narrowly defined. At mid-20th century economists regarded “econometrics” as the union of mathematical economics and mathematical statistics rather than as the intersection of the two fields.

Fun fact: Marc Nerlove, who entered the Johns Hopkins graduate program in economics in 1952, was in Carl Christ’s econometrics course. This fact and the photo of Christ and Harberger come from Nerlove’s note included on the In Memoriam page for Carl Christ (1923-2017).

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EXAMINATION
ECONOMETRICS

Friday, January 25, 1952 — 2-5 p.m.

Dr. Christ
Dr. Harberger

  1. A monopolist produces Z goods, X1 and X2, under constant unit costs C1 and C2 respectively. The demands for his products are

x1 = x10 – a11 (P1 – C1) – a12 (P2 – C2)
x2 = x20 – a21 (P1 – C1) – a22 (P2 – C2)

Find the Outputs of X1 and X2 which the monopolist will produce in order to maximize profits. What condition on the a’s must be satisfied if your solution is to reflect a true maximum?

  1. Prove Euler’s theorem for homogeneous functions of the first degree.
  2. Consider the utility functions

(1) U1 = ху
(2) U2 = logex + logey

For each function state:

      1. whether the marginal utility of each good is increasing, decreasing, or constant.
      2. whether the marginal utility of one good is independent of the amount of the other good consumed.
      3. the demand functions of a person having a fixed income.

What conclusions do your results suggest?

  1. Two countries. A and B, produce export commodities XA and XB at constant cost in local currency. Income in each country is stabilized by government policy, and the demand for imports depends solely on the local-currency price of imports. The exchange rate is normally fixed, but is subject to change by policy action. Assume Country A, in an initial equilibrium of the system, does not receive as much foreign currency as it has to pay for the imports its citizens demand. What are the conditions under which the gap between its receipts and expenditures of foreign currency can be decreased by devaluation? Do these same conditions apply to the gap between receipts and expenditures expressed in its own currency?
  2. Factor A is the only factor used by a monopolist, who produces good X. The suppliers of factor A always demand a constant percentage of the product price p as their unit price. At, this price they are willing to supply unlimited amounts of A.
      1. Assume returns to scale are constant. What output will the monopolist produce? Is thin output any different from that he would produce if A were free good.
      2. Assume returns to scale are decreasing. What output will the monopolist produce? Compare your present result with your answer to (a).

*  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *

ECONOMETRICS 633-34
Final Examination

Thursday, May 22, 1952
  1. Define
      1. exogenous variable
      2. overidentified equation
      3. consistency
      4. likelihood function
      5. condensed likelihood function
  2. Suppose the actual supply and demand equations for 2 goods X1 and X2 are as follows (where p1 and p2 are their respective prices, and income Y and wage rate w are exogenous):

S1:           X1 = 3p1 – 6w + 1

D1:           X1 = 2p1 – 5p2 + Y + 2

S2:           X2 = 7p2 – 8w +3

D2:           X2 = 4p1 – 4p2 + 2Y +4

State whether each equation is identified.

  1. Given that y = ax + b + u, where a is an independent variable, u is a random normal disturbance with mean 0 and constant variance σ2, and a and b are parameters. Derive the maximum likelihood estimates of a, b, and σ2 based on N observations on the pair of variables x and y.
  2. What assumptions must you make and what data do you need in order to obtain limited-information maximum-likelihood estimates of the following equation:

C= α Y + β C-1 + γ

where C and Y are real consumption and disposable income, respectively.

  1. The output of each of n industries (excluding households) is produced by a given process requiring fixed proportions of inputs of the other n-1 commodities. If these proportions are known and if a final-demand bill of goods is specified, how are the total outputs of the n industries determined?
  2. It has been asserted that the materials restrictions imposed on durable goods manufactures after Korea, while limiting the output of durable goods well below the level of 1950, did not reduce the quantities sold to a point below what they would have been in the absence of the restrictions. This assertion is supported by empirical evidence is the form of the observed accumulation of manufacturers’ and dealers’ inventories and of some price-cutting in 1951-52. Can you think of any way whereby back in 1950 you could have anticipated these developments? To answer this question, what empirical data would you seek and how would you use it, with respect to consumer durables generally or to any particular durable good?

Source: Johns Hopkins University. Eisenhower Library, Ferdinand hamburger, Jr. Archives. Department of Political Economy, Series 6, Series 7, Subseries 1, Box 3/1, Folder “Department of Political Economy, Graduate Exams 1933-1965.”

Image Source: Department of Economics, Johns Hopkins University. Webpage “In Memoriam – Carl Christ (1923-2017).” Carl Christ and Arnold Harberger at the Johns Hopkins conference in honor of Marc Nerlove, 2014.