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1 STOCKHOLM UNIVERSITY Department of Economics Course name: Empirical Methods Course code: EC40 Examiner: Lena Nekby Number of credits: 7,5 credits Date of exam: Friday, June 5, 009 Examination time: 3 hours Write your name, Swedish personal number and the number of the question on every cover sheet. Do not write answers for more than one question in the same cover sheet. Explain notions/concepts and symbols. Only legible exams will be marked. No aids are allowed with the exception of calculators provided by exam administrators The exam consists of two parts. Part consists of 0 multiple choice questions worth 40 points in total ( points each). All students must answer this part of the exam. Part consists of two discussion questions worth 60 points in total (30 points each). Discussion question is worth 30 points for those that successfully acquired credit on the first credit assignment. Discussion question is worth 30 points for those that successfully acquired credit on the second credit assignment. If you have received credit you do not need to answer the respective discussion question on the exam. The exam is worth 00 points in total. For the grade E 40 points are required, for D 50 points, C 60 points, B 75 points and A 90 points If you think that a question is vaguely formulated: specify the conditions used for solving it Results will be posted on the notice board, House A, floor 3, June 6, 009 at the latest Good luck!

2 Part : Multiple Choice Questions (40 points). Circle the right answer. Only one answer per question. No credit will be given for multiple answers or additional explanations. Two points per question for correct answers.. The reason why estimators have a sampling distribution is that a. economics is not a precise science. b. individuals respond differently to incentives. c. in real life you typically get to sample many times. d. the values of the explanatory variable and the error term differ across samples.. The following are all least squares assumptions with the exception of: a. The conditional distribution of u i given X i has a mean of zero. b. The explanatory variable in regression model is normally distributed. c. ( X i, Yi ), i =,..., n are independently and identically distributed. d. Large outliers are unlikely. 3. To decide whether Yi = β0 + βx + ui or ln( Y i ) = β0 + βx + u i fits the data better, you cannot consult the regression R because a. ln(y) may be negative for 0<Y<. b. the TSS are not measured in the same units between the two models. c. the slope no longer indicates the effect of a unit change of X on Y in the log-linear model. d. the regression R can be greater than one in the second model. 4. The slope estimator, β, has a smaller standard error, other things equal, if a. there is more variation in the explanatory variable, X. b. there is a large variance of the error term, u. c. the sample size is smaller. d. the intercept, β 0, is small. 5. The sample average of the OLS residuals is a. some positive number since OLS uses squares. b. zero. c. unobservable since the population regression function is unknown. d. dependent on whether the explanatory variable is mostly positive or negative.

3 6. The t-statistic is calculated by dividing a. the OLS estimator by its standard error. b. the slope by the standard deviation of the explanatory variable. c. the estimator minus its hypothesized value by the standard error of the estimator. d. the slope by In the log-log model, the slope coefficient indicates a. the effect that a unit change in X has on Y. b. the elasticity of Y with respect to X. c. Y / X. Y Y d. X X. 8. Correlation of the regression error across observations a. results in incorrect OLS standard errors. b. makes the OLS estimator inconsistent, but not unbiased. c. results in correct OLS standard errors if heteroskedasticity-robust standard errors are used. d. is not a problem in cross-sections since the data can always be reshuffled. 9. Two Stage Least Squares is calculated as follows; in the first stage a. Y is regressed on the exogenous variables only. The predicted value of Y is then regressed on the instrumental variables. b. the unknown coefficients in the reduced form equation are estimated by OLS, and the predicted values are calculated. In the second stage, Y is regressed on these predicted values and the other exogenous variables. c. the exogenous variables are regressed on the instruments. The predicted value of the exogenous variables is then used in the second stage, together with the instruments, to predict the dependent variable. d. the unknown coefficients in the reduced form equation are estimated by weighted least squares, and the predicted values are calculated. In the second stage, Y is regressed on these predicted values and the other exogenous variables. 0. If you included both time and entity fixed effects in the regression model which includes a constant, then a. one of the explanatory variables needs to be excluded to avoid perfect multicollinearity. b. you can use the before and after specification even for T >. c. you must exclude one of the entity binary variables and one of the time binary variables for the OLS estimator to exist. d. the OLS estimator no longer exists.

4 . A pattern in the coefficients of the time fixed effects binary variables may reveal the following in a study of the determinants of state unemployment rates using panel data:. The J-statistic a. macroeconomic effects, which affect all states equally in a given year. b. attitude differences towards unemployment between states. c. there is no economic information that can be retrieved from these coefficients. d. regional effects, which affect all states equally, as long as they are a member of that region. a. tells you if the instruments are exogenous. b. provides you with a test of the hypothesis that the instruments are exogenous for the case of exact identification. c. is distributed χ where m-k is the degree of overidentification. d. Is distributed regressors. m k χm k where m-k is the number of instruments minus the number of 3. The distinction between endogenous and exogenous variables is a. that exogenous variables are determined inside the model and endogenous variables are determined outside the model. b. dependent on the sample size: for n > 00, endogenous variables become exogenous. c. depends on the distribution of the variables: when they are normally distributed, they are exogenous, otherwise they are endogenous. d. whether or not the variables are correlated with the error term. 4. If the instruments are not exogenous, a. you cannot perform the first stage of TSLS. b. then, in order to conduct proper inference, it is essential that you use heteroskedasticityrobust standard errors. c. your model becomes overidentified. d. then TSLS is inconsistent. 5. In the context of a controlled experiment, consider the simple linear regression formulation Yi = β0 + βx i + ui. Let the Y i be the outcome, X i the treatment level, and u i contain all the additional determinants of the outcome. Then e. the OLS estimator of the slope will be inconsistent in the case of a randomly assigned X i since there are omitted variables present. b. X i and u i will be independently distributed if the X i be are randomly assigned. c. β 0 represents the causal effect of X on Y when X is zero. d. E( Y X = 0) is the expected value for the treatment group.

5 6. In the linear probability model, the interpretation of the slope coefficient is a. the change in odds associated with a unit change in X, holding other regressors constant. b. not all that meaningful since the dependent variable is either 0 or. c. the change in probability that Y= associated with a unit change in X, holding others regressors constant. d. the response in the dependent variable to a percentage change in the regressor. 7. In the case of heterogeneous causal effects, the following is not true: a. in the circumstances in which OLS would normally be consistent (when E( ui X i ) = 0 ), the OLS estimator continues to be consistent. b. OLS estimation using heteroskedasticity-robust standard errors is identical to TSLS. c. the OLS estimator is properly interpreted as a consistent estimator of the average causal effect in the population being studied. d. the TSLS estimator in general is not a consistent estimator of the average causal effect if an individual s decision to receive treatment depends on the effectiveness of the treatment for that individual. 8. When the fifth assumption in the Fixed Effects regression (cov ( uit, uis X it, X is ) = 0 for t s ) is violated, then f. using heteroskedastic-robust standard errors is not sufficient for correct statistical inference when using OLS. b. the OLS estimator does not exist. c. you can use the simple homoskedasticity-only standard errors calculated in your regression package. d. you cannot use fixed time effects in your estimation. 9. The rule-of-thumb for checking for weak instruments is as follows: for the case of a single endogenous regressor, a. a first stage F must be statistically significant to indicate a strong instrument. b. a first stage F >.96 indicates that the instruments are weak. c. the t-statistic on each of the instruments must exceed at least.64. d. a first stage F < 0 indicates that the instruments are weak. 0. To test for randomization when X i is binary, e. you regress X i, on all W s and compute the F-statistic for testing that all the coefficients on the W s are zero. (The W s measure characteristics of individuals, and these are not affected by the treatment.) f. is not possible, since binary variables can only be regressors. g. requires reordering the observations randomly and re-estimating the model. If the coefficients remain the same, then this is evidence of randomization. h. requires seeking external validity for your study.

6 Part : Discussion Questions (60 points) On separate sheets of paper, answer the following discussion questions. Write your name, personal number (personnummer) and the question number on each sheet. Answer each question clearly and concisely. Only legible answers will be considered, others will be disregarded. If you think that a question is vaguely formulated, specify the conditions used for solving it. Each question is worth 30 points. Discussion Question : NOTE: Those with credit on credit assignment receive 30 points for this question and do not have to answer discussion question A study, published in 993, used U.S. state panel data to investigate the relationship between minimum wages and employment of teenagers. The sample period was 977 to 989 for all 50 states. The author estimated a model of the following type: ln(e it )= β 0 + β ln(m it /W it ) + γ D i γ n D50 i + δ B t δ T B3 t + u it, where E is the employment to population ratio of teenagers, M is the nominal minimum wage, and W is average hourly earnings in manufacturing. In addition, other explanatory variables, such as the adult unemployment rate, the teenage population share, and the teenage enrollment rate in school, were included. (a) Explain what types of factors might be picked up by time and state fixed effects and give examples. (b) The author decided to use eight regional dummy variables instead of the 49 state dummy variables. What is the implicit assumption made by the author? Could you test for its validity? How? (c) The results, using time and region fixed effects only, were as follows: NO ln E it = 0.8 ln(m it /W it ) +...; (0.036) R = 0.77 Interpret the result fully. (d) State minimum wages do not exceed federal minimum wages often. As a result, the author decided to choose the federal minimum wage in his specification above. How does this change your interpretation? How is the original equation

7 ln(e it )= β 0 + β ln(m it /W it ) + γ D i γ n D8 i + δ B t δ T B3 t + u it, affected by this? (e) Your textbook modifies the four assumptions for the multiple regression model by adding a new assumption. This represents an extension of the cross-sectional data case, where errors are uncorrelated across entities. The new assumption requires the errors to be uncorrelated across time, conditional on the regressors as well (cov(u it, u is X it, X is ) = 0 for t s.). Discuss why there might be correlation over time in the errors when you use U.S. state panel data. Does this mean that you should not use OLS as an estimator? Why or why not? How is inference affected and what can be done to correct for correlated standard errors?

8 Discussion Question : NOTE: Those with credit on credit assignment receive 30 points for this question and do not have to answer discussion question. To analyze the effect of a minimum wage increase, a famous study used a quasi-experiment for two adjacent states: New Jersey and (Eastern) Pennsylvania. A ˆβ was calculated by comparing average employment changes per restaurant between the treatment group (New Jersey) and the control group (Pennsylvania). In addition, the authors provide data on the employment changes between low wage restaurants and high wage restaurants in New Jersey only. A restaurant was classified as low wage, if the starting wage in the first wave of surveys was at the then prevailing minimum wage of $4.5. A high wage restaurant was a place with a starting wage close to or above the $5.5 minimum wage after the increase. (a) Explain why employment changes of the high wage and low wage restaurants might constitute a quasi-experiment. Which is the treatment group and which the control group? (b) The following information is provided FTE Employment before FTE Employment after Low wage High wage Where FTE is full time equivalent and the numbers are average employment per restaurant. Calculate the change in the treatment group, the change in the control group, and finally ˆβ. Since minimum wages represent a price floor, did you expect ˆβ to be positive or negative? Explain. (c) The standard error for ˆβ is.48. Test whether or not this is statistically significant, given that there are 74 observations (critical value at the five percent level (two sided) is.96). (d) Let the vertical axis of a figure indicate the average employment fast food restaurants. There are two time periods, t = and t =, where time period is measured on the horizontal axis. Enter the treatment, before treatment, after control, before control, after four points in the figure and label them Y, Y, Y, and Y. Connect the points. Finally show in the figure the value for ˆβ. What is the main assumption behind difference and difference estimation?

9 (e) Specify the multiple regression model that contains the difference-in-difference estimator. Explain your model fully. Why might you want to include additional regressors in the model? (f) Discuss how the differences-in-differences estimator can be extended to multiple time periods. In particular, assume that there are n individuals and T time periods. What do the individual and time effects control for?

Write your identification number on each paper and cover sheet (the number stated in the upper right hand corner on your exam cover).

Write your identification number on each paper and cover sheet (the number stated in the upper right hand corner on your exam cover). STOCKHOLM UNIVERSITY Department of Economics Course name: Empirical Methods in Economics 2 Course code: EC2402 Examiner: Peter Skogman Thoursie Number of credits: 7,5 credits (hp) Date of exam: Saturday,