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Danish M.
UC Berkeley BA Economics, BA Statistics
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Econometrics
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Question:

A simple macroeconomic consumption function relates consumption to income: Ci = B_0 +B_one*Ii, where B_one is the marginal propensity to consume. The Bureau of Labor Statistics attempts to collect data on household purchases and income by randomly sampling U.S. households, but it is known that high-income households tend to under-report their purchases (so as to not appear materialistic) while low-income households tend to over-state their purchases (to mask their lack of means). In that case, the ordinary least squares assumptions—for both the classical and robust regressions—are violated and as a result, the OLSE of the marginal propensity to consume that is biased toward zero.

Danish M.
Answer:

TRUE. The pattern described will violate the assumption that E(ui | X) = 0 which is an assumption made by both the classical and robust regressions models. As a consequence the properties of OLSE slope estimate no longer hold; in particular it is no longer unbiased. In fact, assuming that the marginal propensity to consume is positive, the OLSE of the slope is biased toward zero.

Corporate Finance
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Question:

Identify the Arbitrage Opportunity: (State, Asset 1 payoff, Asset 2 payoff): (1, 1, 5), (2, -.6,-3) Price of Asset 1: 0.5 Price of Asset 2: 4

Danish M.
Answer:

Notice that 5 shares of asset 1 and one share of asset 2 have the same payoffs, yet 5 shares of asset 1 cost only 2.5. Since 5 shares of asset 1 and one share of asset 2 have the same payoffs but different prices, the Law of One Price is violated in this situation. This violation of LOOP is the source of the arbitrage opportunity. To exploit it, short sell 1 share of asset 2 for every 5 shares of asset 1 bought. For each share of asset 2 shorted, you will pocket 1.5 today and pay nothing tomorrow.

Statistics
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Question:

For a simple random sample of size 5 from a population of 100 subjects, let I(1), I(2), ..., I(5) be the indices of the first, second, third, fourth, and fifth subjects sampled. Compute the following and show your work.

Danish M.
Answer:

(a) P(I(1) = 100) P(I(1) = 100) =1/100 (b) P(I(1) = 100 and I(2) = 2) P(I(1) = 100 and I(2) = 2) =(1/100) · (1/99) (c) P(I(1) = 10, I(2) = 20, I(3) = 30, I(4) = 40, and I(5) = 50) P(I(1) = 10, I(2) = 20, I(3) = 30, I(4) = 40, and I(5) = 50) =(1/100) · (1/99) · (1/98) · (1/97) · (1/96) (d) P(the 10th, 20th, 30th, 40th, and 50th subjects are in the sample) P(the 10th, 20th, 30th, 40th, and 50th subjects are in the sample) = 5! · (1/100) · (1/99) · (1/98) · (1/97) · (1/96)

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