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FINAL EXAMINATION INTRODUCTION TO ECONOMETRICS (ECON 4500-01)  FALL SEMESTER 2021   Name:                                                                                                                                                                                                            Answer all questions

Economics

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FINAL EXAMINATION

INTRODUCTION TO ECONOMETRICS (ECON 4500-01)

 FALL SEMESTER 2021

 

Name:                                                                                                                                                                                           

               

 

ALL DATA SETS ARE FOUND ON BLACKBOARD.

 

1. (16 points) Suppose that a marketing executive has asked you to forecast monthly US retail sales. In order to be able to do so, you collected monthly data for US retail sales (in millions of dollars) from January 2002 to October 2019.
   1. Given the data found in “Retail Sales.xlsx”, generate the best possible forecast for US retail sales for December 2019 and January 2020.  Explain the rationale for the forecasting technique you used. 
   2. Generate a confidence interval for each forecast at the five percent level. Explain in words what each interval means. 
   3. Are your forecasts reasonable? Explain. 

 

 

2. (12 points) This exercise is about the US demand for fish from 1990 to 2014. The “Fish.xlsx” file contains data on the following variables:

  Ft   = average pounds of fish consumed per capita in year t   PFt = price index for fish in year t

             PBt = price index for beef in year t

              YDt = real per capita disposable income in year t

               

1. 1. Estimate the following equation using OLS: F_t = β₀+ β₁ PF_t + β₂ PB_t + β₃ log(Yd_t) +  ε_t.
   2. Examine the estimated regression equation results in part (a). Is there an underlying problem with the regression equation? If yes, what is it? Explain. 
   3. You decide to replace the individual price variables with a relative price variable: RP_t =PF_t/PB_t.

What is the expected sign of the coefficient of RP? Explain.

1. 4. Estimate the following equation using OLS: F_t = δ₀+ δ₁ RP_t + δ₂ log(Yd_t) + ε_t.
   5. Which equation do you prefer, the one from part (a) or part (d)? Explain your reasoning.
   6. Using your estimates from part (d), is fish a normal good in the US? Explain.

 

               

3. (12 points) Suppose that you specified the regression model below because you are interested in investigating what determines the price of a house in a small town. 

 

              Pi = β0+ β1 Si + β2 Ni + β3 Ai + β4 Ai2 + β5 CAi + εi              (I)

 

where P_i = the price of the ith house (in thousands of dollars);

S_i = the size pf the ith house (in square feet);

N_i = the quality of the neighborhood of the ith house (1=best, 4=worst);

A_i = the age of the ith house in years; and

CA_i = a dummy variable equal to 1 if the ith house has central air-conditioning, 0 otherwise.

 

1. Given the data found in “HOUSE.xlsx”, estimate equation (I) using OLS and interpret the coefficient estimate for each independent variable. 
2. Test whether the age of a house influences the price of a house.
3. Predict the selling price of an air-conditioned 40-year-old house located in the best neighborhood and whose size is 1800 square feet. 
4. Construct a confidence interval for your prediction in part (c) and explain what it means.
5. Is your estimated regression equation from part (a) a good one? Explain. If no, what modifications would you make to the regression equation? Explain.

 

4. (12 points) Suppose that you believe that the standard of living (Y) of a country, measured by real GDP per capita, is influenced by its real capital stock per worker (X).  In order to test your theory, you collected crosssection data for those two variables for 94 countries. Both variables are measured in US dollars.  
   1. Given the data found in “Standard of Living.xlsx, estimate the following regression equation:  log(Y_i) = β₀+ β₁ log(X_i) + ε_i.  
   2. What is the meaning of the coefficient estimate for β₁? Explain.
   3. Test for possible econometric problems given that you are working with cross-sectional data. What’s your conclusion?
   4. Assuming that any econometric problems you found in part (c) are not a result of a wrong functional form or an important variable missing, test whether the impact of capital stock per worker on the standard of living is positive.
   5. Calculate the confidence interval for the coefficient of capital stock per worker at the 5% level. Explain its meaning.

 

5. (12 points) Suppose you specified the regression equation below because you are interested in studying what influences a woman’s decision to enter the labor force. 

 

L: Pr(LF=1) = β₀+ β₁ S_i + β₂ M_i + β₃ A_i + β₄ A_i² + ε_i

 

where  LF = 1 if woman is in the labor force (employed or unemployed) and 0 otherwise;

               S = years of schooling; 

               M = 1 if woman is married and 0 otherwise; A = a woman’s age.

 

5. 1. What sign do you expect for each slope coefficient in the above equation? Explain.
   2. Given the data found in “Labor Force.xlsx”, estimate the above equation using LOGIT. 
   3. What is the economic meaning of the estimates for β₁ and β₂? Explain. 
   4. What is the predicted value for LF for a 50-year-old married woman with 12 years of education? What does the number you calculated mean? Explain.
6. (12 points) Suppose that you specified the regression equation below because you are interested in investigating what influences the stock price of the World Disney Company. 

 

                             SP_t  = β₀ + β₁ EARN_t + ε_t                          (I)

               

where  SP = stock price for the Walt Disney Company (in dollars per share), and                EARN = earnings for the Walt Disney Company (in dollars per share).

 

1. 1. Given the data found in “World Disnney.xlsx”, estimate equation (I) using OLS and test for first-order serial correlation at the 5% level. 
   2. What is the generalized difference equation for regression equation (I)? If you estimate the generalized difference equation using GLS, what is the main advantage and main disadvantage of such an estimation technique? Explain.
   3. Assuming your model above (equation I) is correctly specified (i.e. all important independent variables are included and the correct functional form is used), explain how one should deal with serial correlation and show your new estimates for equation I.
   4. Compare your regression estimates from parts (a) and (c). Which one of the two estimated versions of regression equation (I) do you prefer and why?

 

7. (12 points) Suppose that you are interested in how real US disposable personal income (DI) influences real US personal consumption expenditures (CE). You collected data for the two variables from 1953 to 2018. 

Both variables are measured in billions of US dollars. You also specified the following regression equation:

                                           CE_t = β₀ + β₁ DI_t + β₂ CE_t-1 + ε_t

1. Given the data found in “CE and DI.xlsx”, estimate the above regression equation using OLS.  Interpret each slope coefficient estimate.  
2. Forecast consumption expenditures for 2019 using your estimated equation from part (a). And generate a confidence interval for your forecast at the one percent level. Explain in words what the interval means. Is your forecast reasonable? Explain. 
3. Calculate the impact of DI_t-1 on CE_t. Explain what the number you calculated means.  
4. Is there evidence of first-order serial correlation at the 5% significance level in the regression equation you estimated in part (a)? If yes, why is it important to deal with serial correlation in such a regression model? Explain.

 

8. (12 points) Suppose that a fad for oats (resulting from an announcement of the health benefits of oat bran) has made you toy with the idea of becoming a broker in the oat market. Before spending your money, you decide to build a simple model of supply and demand of the market for oats:

                                             Demand: Q_t  = β₀ + β₁P_t + β₂PW_t + ε_t

                                           Supply: Q_t  = α0 +  α1 P_t + α2W_t + α3 S_t + u_t 

where Q is both the quantity of oats demanded or supplied in time period t, P_t  is the price of oats, PW_t is the price of wheat, W_t is the average oat-farmer wages, and S_t is the price of oat seeds.

1. Given the hypothetical data found in “OATS.xlsx”, use the appropriate estimation technique to estimate both equations. Explain what each slope coefficient estimate for your demand equation means.
2. Explain why you chose the estimation technique you did. Be specific and, if necessary, perform appropriate test.