Question 1 carries a weight of 25%; Question 2 carries 20%; Question 3 carries 20%; Question 4 carries 35%.

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1 UNIVERSITY OF EAST ANGLIA School of Economics Main Series PGT Examination ECONOMETRIC METHODS ECO-7000A Time allowed: hours Answer ALL FOUR Questions. Question 1 carries a weight of 5%; Question carries 0%; Question 3 carries 0%; Question 4 carries 35%. Marks awarded for individual parts are shown in square brackets. A formula sheet, t-tables, F-tables, and chi-squared tables are attached to the examination paper. Notes are not permitted in this examination. Do not turn over until you are told to do so by the Invigilator. ECO-7000A Module Contact: Dr Susan Long, ECO Copyright of the University of East Anglia Version

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3 Page 3 QUESTION 1 [5 Marks] ALL WORKING MUST BE SHOWN IN YOUR ANSWER TO THIS QUESTION The following table contains data on weekly income (X) and weekly expenditure on restaurant meals (Y) for a sample of six households. Both variables are measured in pounds. Household X Y A B C D E F (a) Obtain ordinary least squares estimates of β1 and β in the model: Yi = β1+ βxi + ui i = 1, L, 6 [10 marks] (b) (c) (d) Place a precise economic interpretation on each of the two parameter estimates, ˆ β 1 and ˆ β. In particular, does it make any economic sense that your estimate of the intercept is negative? [6 marks] Find the residuals. Which of the six households has the highest positive residual associated with it? What conclusion can you draw about this household? [3 marks] Test the null hypothesis that β = 0 against the alternative that β > 0. What is the economic interpretation of your result (i.e. what term would an economist use to describe restaurant meals)? [6 marks] TURN OVER

4 Page 4 QUESTION [0 MARKS] Data on 900 properties sold in four postcode areas of Norwich during 017 are collected. The variables are: price: sqft: beds: nr1: nr: nr3: nr4: Price of property in thousands of pounds Internal area of property in square feet Number of bedrooms in property 1 if property is in NR1 (Central Norwich); 0 otherwise 1 if property is in NR (West Central Norwich); 0 otherwise 1 if property is in NR3 (North Central Norwich); 0 otherwise 1 if property is in NR4 (South-West Norwich); 0 otherwise Two models are estimated, with the following results:. * MODEL 1. regress price sqft beds Source SS df MS Number of obs = F(, 897) = Model Prob > F = Residual R-squared = Adj R-squared = 0.45 Total Root MSE = price Coef. Std. Err. t P> t [95% Conf. Interval] sqft beds _cons * MODEL. regress price sqft beds nr nr3 nr4 Source SS df MS Number of obs = F(5, 894) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = price Coef. Std. Err. t P> t [95% Conf. Interval] sqft beds nr nr nr _cons (a) Interpret the estimate of the intercept parameter in Model 1. Do the same for Model. [5 marks]

5 Page 5 (b) Explain why only three of the four postcode dummies have been included in Model. What would happen if you attempted to include all four? [5marks] (c) (d) Using an F-test, test Model 1 as a restricted version of Model. Interpret the result of the test. [5 marks] Interpret the coefficients on the three included postcode dummies. Which area has the highest prices, and which lowest? Why is the ceteris paribus concept important here? [5 marks] TURN OVER

6 Page 6 QUESTION 3 [0 marks] We have data on 53 countries in 017. Let p_locali be the price of a Big Mac (the McDonald s hamburger) in country i in local currency in 017. Let ei be the exchange rate for country i against the US dollar in 017 (that is, ei is the number of units of local currency that can be exchanged for one US dollar in 017). (a) Data on three of the 53 countries is shown in the following table. Country Currency p_local e Indonesia Rupiah Norway Kroner Japan Yen Compute the price of a Big Mac in each of the three countries in US dollars. On this basis, which of the three currencies appears under-valued in 017, and which appears over-valued? [7 marks] The following regression model is estimated using data from all 53 countries in 017 (p_usa is the price of a Big Mac in the USA in 017): _ log p locali = β + 1 βlog e + i ui ; i = 1, L,53 (1) p _ usa Following the regression, two tests are performed. The results are as follows:. regress log_p_ratio log_e Source SS df MS Number of obs = F(1, 51) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = log_p_ratio Coef. Std. Err. t P> t [95% Conf. Interval] log_e _cons test (_b[_cons]=0) (_b[log_e]=1) ( 1) _cons = 0 ( ) log_e = 1 F(, 51) = 56.4 Prob > F = test (_b[log_e]=1) ( 1) log_e = 1 F( 1, 51) = Prob > F =

7 Page 7 (b) (c) Consider the two tests performed following the regression above. The first test is a test of the Law of One Price (LOP). Explain the concept of the LOP. Is it rejected by the 017 Big Mac data? Which theory is being tested by the second test? Is it rejected? [7 marks] Explain the Balassa-Samuelson effect, and explain why you might expect it to hold. How would you extend the regression model (1) in order to carry out a test of the Balassa-Samuelson effect? [6 marks] TURN OVER

8 QUESTION 4 [35 Marks] Page 8 A sample of 1,000 high school graduates in the US is drawn and the following data is collected on each: Y: = 1 if the student goes to college, = 0 otherwise Grades: Average grade in Maths, English and Social Studies on a 13 point grading scale, with 13 for the highest grade and 1 for the lowest grade Income: Gross family income in thousands of dollars Famsize: Number of family members Parcoll: = 1 if the most educated parent graduated from college, = 0 otherwise Gender: = 1 if male, = 0 if female White: = 1 if the student is white, = 0 if non-white Two logit models are estimated, with Y as the dependent variable. The results are shown in the following table. The numbers in brackets are the asymptotic standard errors. Model 1 Model Constant -.60 (0.41) -.40 (0.4) Grades 0.60 (0.07) 0.65 (0.06) Income 0.01 (0.004) 0.01 (0.005) Famsize (0.73) (0.74) Parcoll 0.53 (0.5) 0.40 (0.18) Gender (0.19) White 0.0 (0.15) LogL (a) (b) (c) (d) A colleague been asked to estimate the probability of a high school graduate going to college. They would like to estimate a linear probability model but are unsure whether this model is suitable. What would you advise? [4 marks] Using Model 1, interpret the results and test for the individual significance of the four explanatory variables. [10 marks] Using Model, predict the probability of a white female from a family with four members, whose average grade is 9, whose family income is $60,000 and whose most educated family member is a college graduate, going to college. [6 marks] Conduct a likelihood ratio (LR) test of the joint significance of the Gender and White dummy variables. [3 marks]

9 (e) (f) Page 9 Explain how you would extend Model to investigate whether the effect of grades on the probability of going to college differs between males and females. [4 marks] Suppose now that the high school graduate has three options; their choices are: 1. Do not go to college. A two-year college course 3. A four-year college course Which model could be used to estimate the probability of the high school graduate choosing each of these options? [4 marks] (g) Do you think that the assumption of Independence of Irrelevant Alternatives (IIA) might be violated in this situation? Explain your answer. [4 marks] END OF PAPER

10 The simple regression model Consider the model: Y = β + β X + u i,...,n. i 1 i i = 1 Page 10 Econometric Methods Formula Sheet The ordinary least squares estimators of β and β1 are: ( X i X )Y i ˆ i β = ( X i X ) i ˆ β = Y ˆ 1 β The fitted values of Y are given by: ˆ Ŷi = β 1 + β X i The residuals are: û i i ˆ = Y Ŷ i X The standard error of the regression is given by: = ûi ˆ σ n The estimated standard errors of $ β and $ β 1 are given by: se( ˆ β ) = ˆ σ se( ˆ β ) = ˆ σ 1 ( X i 1 X ) 1 X + n ( X i X ) Testing joint restrictions in the multiple regression model Let n be the sample size, let r be the number of restrictions under test, let k be the number of parameters in the unrestricted model, let R U be the R in the unrestricted model and let R R be the R in the restricted model. Under the null hypothesis that the r restrictions are true, the F-statistic (R U R R ) / r F = ( 1 R U ) /(n k ) has an Fr,n-k distribution, that is, an F distribution with r, n-k degrees of freedom. The Logit Model exp( xi ' β ) P(Yi = 1) = 1+ exp( x ' β ) i

11 Page 11 Table 1: Critical values of the t-distribution df α = 0.10 α = 0.05 α = 0.05 α = 0.01 α =

12 Page 1 Table : Critical values of the F- distribution (α=0.05) df1= df=

13 Page 13 Table 4: Critical values of the χ -distribution df α = 0.10 α = 0.05 α = 0.05 α = 0.01 α = END OF MATERIALS