ECN 522 Final2023Fall

ECONOMICS 522 Final Exam Yulong Wang Fall 2023 Instructions: ° You have 24 hours to do the following 5 problems. ° The total number of points is 165. ° The problems have not been ordered in terms of di¢ culty. There is huge variability in the di¢ culty of questions. ° Note that most of the questions within each problem can be answered independently of each other. ° To obtain full credit, write out numerical answers in decimal form. In the calculations please keep at least three signi°cant °gures. ° The test is open-book. ° Please make sure your answer is readable and send it to Yichi by email to yzhan424 @syr.edu, no later than Wednesday 13th 3:30PM . In the title of the email, please write " ECN522-Final-Your Name ." 1

Problem 1 (40 points) A researcher wants to study the e/ect of income on spending. She uses a dataset that contains information on spending by those who won a lottery last year. The dataset contains the following variables for each individual: S : (annual) spending (in thousands of dollars); Lott : lottery winnings (in thousands of dollars); Inc : (annual) income (in thousands of dollars, does not include Lott); TotInc : = Lott + Inc . The researcher estimates the following regressions (assuming homoskedasticity): Dependent Variable: S S S S log ( S ) log ( S ) Regressors (1) (2) (3) (4) (5) (6) TotInc 0.728*** 0.698*** 0.693*** 0.0192*** (0.0580) (0.0618) (0.209) (0.00260) Lott 0.202 x1 (0.146) Inc x2 TotInc 2 0.00226 (0.0129) log ( TotInc ) 1.200*** (0.164) constant 1.282 -2.096 x3 2.424 2.323*** -1.312* (4.232) (4.874) (7.777) (0.190) (0.678) Observations 120 120 120 120 120 120 R 2 0.572 0.578 0.572 0.315 0.311 The dependent variable in regressions (1)-(4) is S , and it is log ( S ) in regressions (5) and (6). Standard errors in parentheses; *** p < 0.01, ** p < 0.05, * p < 0.1. Answer the following questions: 1. (6 points) Interpret the coe¢ cients on TotInc in regressions (1) and (5), and the coe¢ cient on log ( TotInc ) in regression (6). 2. (4 points) Interpret the coe¢ cient on Lott in regression (2). (Hint: Remember the de°nition of TotInc.) 3. (4 points) Describe how you test the null hypothesis "neither lottery winnings nor other income has an e/ect on spending" using regression (2). 4. (6 points) Consider an individual with TotInc = 50 . Compute the e/ect (in thousands of dollars) of increasing TotInc by 10% (other things being the same) according to the estimates of regressions (4) and (6). 5. (10 points) Find x1, x2, x3 for regression (3). (Hint: Use regression (2) and the relation TotInc = Lott + Inc: ) 6. (10 points) What do you think is the advantage of using the data on individuals who won a lottery to estimate the e/ect of income on spending? (Answer in 150 words or less, but please be precise). Problem 2 (20 points) The table below presents the results of estimating a Linear Regression (LR) model, a Logit model, and a Probit model for a binary dependent variable, y , using the explanatory variables x; m; m ± x , and a constant. Here m is a dummy (binary) variable, and x is continuously distributed. 2

Problem 4 (15 points) Suppose that Y t follows the stationary AR (2) model, Y t = ² 2 + 0 : 75 Y t ± 1 ² 0 : 125 Y t ± 2 + u t where u t has E [ u t ] = 0 and V [ u t ] = 9 and is independent of ( Y t ± 1 ; Y t ± 2 ; Y t ± 3 ; ::: ) (and of ( u t ± 1 ; u t ± 2 ; u t ± 3 ; ::: ) ). Note that the coe¢ cients -2, 0.75, -0.125 and 9 above are assumed to be known rather than estimated. 1. (5 points) Suppose that you observe Y t = 1 and Y t ± 1 = ² 1 , what are your forecasts of Y t +1 and Y t +2 ? 2. (5 points) Assume that this process is stationary. Compute the mean of Y t . (Hint: consider the mean on both side of the equation and use stationarity.) 3. (5 points) What is the root mean squared forecast errors of the forecasts in (a)? (Hint: it should use the value of V [ u t +1 ] and V [ u t +2 ] ) Problem 5 (50 points) During the 1880s, a cartel known as the Joint Executive Committee (JEC) controlled the rail transport of grain from the Midwest to eastern cities in the United States. The cartel preceded the Sherman Antitrust Act of 1890, and it legally operated to increase the price of grain above what would have been the competitive price. From time to time, cheating by members of the cartel brought about a temporary collapse of the collusive pricesetting agreement. In this exercise, you will use variations in supply associated with the cartel±s collapses to estimate the elasticity of demand for rail transport of grain. The data °le JEC contains weekly observations on the rail shipping price and other factors from 1880 to 1886.1 A detailed description of the data is contained in JEC_Description . Suppose that the demand curve for rail transport of grain is speci°ed as ln ( Q i ) = ° 0 + ° 1 ln( P i ) + ° 2 Ice i + 12 X j =1 ° 2+ j Seas j;i + u i , where Q i is the total tonnage of grain shipped in week i , P i is the price of shipping a ton of grain by rail, Ice i is a binary variable that is equal to 1 if the Great Lakes are not navigable because of ice, and Sea j is a binary variable that captures seasonal (monthly) variation in demand (in total 12 of them). Ice is included because grain could also be transported by ship when the Great Lakes were navigable. Answer the following questions by running appropriate regressions and explaining the results. Be sure to attach your STATA output table in questions 1, 4, 5, which contains the code already. (If you use some other software, please attach the code.) 1. (10 points) Estimate the demand equation by OLS. What is the estimated value of the demand elasticity and its standard error? 2. (10 points) Is the OLS estimator of the elasticity biased? If yes, why? 3. (10 points) Consider using the variable cartel as instrumental variable for ln( P ) . Use economic reasoning to argue whether cartel plausibly satis°es the two conditions for a valid instrument. 4. (10 points) Estimate the °rst-stage regression. Is cartel a weak instrument? 5. (10 points) Estimate the demand equation by instrumental variable regression. What is the estimated demand elasticity and its standard error? 6. (Bonus question, 10 points) Does the evidence suggest that the cartel was charging the pro°t- maximizing monopoly price? Explain. ( Hint : What should a monopolist do if the price elasticity is less than 1?) 4