140_problems5

# 140_problems5 - ECON 140 Fall 2008 10/23 Alex Rothenberg...

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ECON 140, Fall 2008 - 10/23 Alex Rothenberg Practice Problems: Omitted Variables, Errors in Variables, Randomized Experiments Problem 1 Suppose you were interested in understanding how corruption aﬀects the provision of driver’s licenses in India. There are two competing hypotheses that we’d like to distinguish empirically: Hypothesis I : Paying bribes might help to eliminate red tape and “grease the wheels” of a slow, ineﬃcient bureaucracy. Bribes represent a transfer between good drivers who are willing to pay for a license and bureaucrats. There is no social loss. Hypothesis II : Corruption has damaging eﬀects to society. Those who pay bribes to obtain a license are typically less likely to be good drivers. As a result, corruption makes the streets unsafe for everyone who drives. How might we test these hypotheses? Suppose we collected data on a random sample of people who tried to obtain drivers licenses in India. Let D i be an indicator equal to 1 if individual i got a license, 0 otherwise. Let B i denote the amount of bribes paid by individual i in trying to obtain the license. Let A i denote the driving ability of individual i , measured by their score on an objective driving exam. 1. Suppose we were trying to decide between estimating two possible linear probability models: D i = α 0 + α 1 B i + ε i (1) D i = β 0 + β 1 B i + β 2 A i + ε i (2) Which of these models would be most interesting to estimate for the purpose of determining which of our hypotheses is more plausible? 2. Suppose the true model is (2) but we estimate (1) with ordinary least squares. Derive an expression for the omitted variable bias. 3. (Optional) Explain the diﬀerences between estimating model (2) and the following model: D i = γ 0 + γ 1 B i + γ 2 A i + γ 3 ( B i × A i ) + ε i How do we interpret γ 3 , the coeﬃcient on the interaction term? 1

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ECON 140, Fall 2008 - 10/23 Alex Rothenberg 4. Suppose we tried to estimate (1) but we mis-measure B i . Our true model is the following: D i = α 0 + α 1 B i + ε i But instead, we have a noisy measure of B i : e B i = B i + υ i So, the regression we actually run takes the following form: D i = α 0 + α 1 e B i + ε i Here, we assume that the υ i ’s are iid , with E [ υ i ] = - 1000. That is, on average, individuals under-report the bribes they pay by Rs 1000. Assuming that υ i ε i , work
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140_problems5 - ECON 140 Fall 2008 10/23 Alex Rothenberg...

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