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1 UNIVERSITY OF EAST ANGLIA School of Economcs Man Seres PG Examnaton ECONOMETRIC METHODS ECO-7000A Tme allowed: hours Answer ALL FOUR Questons. Queston 1 carres a weght of 5%; Queston carres 0%; Queston 3 carres 0%; Queston 4 carres 35%. Marks awarded for ndvdual parts are shown n square brackets. A formula sheet, t-tables, F-tables, and chsquared tables, are attached to the examnaton paper. Notes are not permtted n ths examnaton. Do not turn over untl you are told to do so by the Invglator. ECO-7000A Module Contact: Dr Susan Long, ECO Copyrght of the Unversty of East Angla Verson 1

3 QUESTION 1 [5 Marks] Page 3 ALL WORKING MUST BE SHOWN IN YOUR ANSWER TO THIS QUESTION The followng table contans data on advertsng expendture (X) and profts (Y) for a sample of sx small frms. Both varables are measured n thousands of pounds. Frm X Y A 0 5 B 3 3 C 4 8 D 7 13 E 10 9 F 1 16 (a) Fnd OLS estmates, ˆ 1 and ˆ of the parameters of the model: Y X u 1, 6. [8] 1, (b) Interpret the two parameter estmates. [4] (c) Fnd the resduals. Whch of the sx frms has the hghest postve resdual assocated wth t? What can you conclude about ths frm? [3] (d) Fnd the estmated standard error, se ( ˆ ), of ˆ. Then conduct a test of the hypothess H0: = 0 aganst H1 : > 0. Interpret the test result. [7] (e) Brefly explan why we chose to conduct a one-taled test n (d) rather than a two-taled test. [3] TURN OVER

4 QUESTION [0 Marks] Page 4 Data was collected on 300 rental propertes n Norwch. All propertes are n one of the four postcodes NR1-NR4. The varables are: rent: beds: nr1: nr: nr3: nr4: rent n pounds per month number of bedrooms 1 f located n NR1 (South Central Norwch); 0 otherwse 1 f located n NR (West Central Norwch); 0 otherwse 1 f located n NR3 (North Central Norwch); 0 otherwse 1 f located n NR4 (South-West Norwch); 0 otherwse The followng STATA results are obtaned:. gen beds=beds^ * MODEL 1:. regress rent beds beds Source SS df MS Number of obs = F(, 97) = Model Prob > F = Resdual R-squared = Adj R-squared = Total Root MSE = rent Coef. Std. Err. t P> t [95% Conf. Interval] beds beds _cons * MODEL :. regress rent beds beds nr-nr4 Source SS df MS Number of obs = F( 5, 94) = 8.55 Model Prob > F = Resdual R-squared = Adj R-squared = Total Root MSE = rent Coef. Std. Err. t P> t [95% Conf. Interval] beds beds nr nr nr _cons

5 Page 5 (a) (b) (c) (d) What s the estmate of the ntercept parameter n model 1? What s the nterpretaton of ths estmate? [5] Explan the economc prncple(s) underlyng the ncluson of the varable beds n model 1. Does the assocated t-statstc confrm that these prncples are at work? [5] Explan why only three of the four locaton dummes have been ncluded n model. What would happen f you tred to nclude all four? [5] Carry out an F-test to test model 1 as a restrcted verson of model, n order to test the mportance of locaton n rent determnaton. Interpret your result. [5] TURN OVER

6 QUESTION 3 [0 marks] Page 6 We have data on 53 countres n 016. Let p_local be the prce of a Bg Mac (the McDonald s hamburger) n country n local currency n 016. Let e be the exchange rate for country aganst the US dollar n 016 (that s, e s the number of unts of local currency that can be exchanged for one US dollar n 016). (a) Data on three of the 53 countres s shown n the followng table. Country Currency p_local e Inda Rupee Swtzerland Franc Brazl Real Compute the prce of a Bg Mac n each of the three countres n US dollars. On ths bass, whch of the three currences appears under-valued n 016, and whch appears over-valued? [7] The followng regresson model s estmated usng data from all 53 countres n 016 (p_usa s the prce of a Bg Mac n the USA n 016): _ log p local 1 log e u ; 1,,53 p_ usa Followng the regresson, two tests are performed. The results are as follows:. regress log_p_rato log_e Source SS df MS Number of obs = F(1, 51) = Model Prob > F = Resdual R-squared = Adj R-squared = Total Root MSE = log_p_rato 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) = Prob > F = test (_b[log_e]=1) ( 1) log_e = 1 F( 1, 51) = 15. Prob > F =

7 (b) Page 7 Consder the two tests performed followng the regresson above. The frst test s a test of the Law of One Prce (LOP). Explan the concept of LOP. Is t rejected by the 016 Bg Mac data? Whch theory s beng tested by the second test? Is t rejected? [7] A further varable, gdp_rato, s generated, defned as GDP per head n the local country n US dollars dvded by GDP per head n the USA. Ths varable s added to the regresson, wth the results:. regress log_p_rato log_e gdp_rato Source SS df MS Number of obs = F(, 50) = Model Prob > F = Resdual R-squared = Adj R-squared = Total Root MSE =.8059 log_p_rato Coef. Std. Err. t P> t [95% Conf. Interval] log_e gdp_rato _cons (c) Does gdp-rato have a sgnfcant effect on log_p_rato? What s the name of the theory that s beng confrmed by ths test? Does the test result provde an explanaton for the results of the tests carred out n (b)? Explan your answer. [6] TURN OVER

8 QUESTION 4 [35 Marks] Page 8 A sample of 753 marred women (aged years) s drawn, and the followng characterstcs are recorded: Y: One f the woman s workng; zero f out of the labour market Cty: One f the famly lves s a large cty; zero otherwse Age: Age n years Chldren6: Number of chldren aged less than 6 years Chldren18: Number of chldren aged between 6 and 18 years old Educaton: Years of educaton Husbandhours: Husband s usual hours of work Husbandage Husband s age Husbandeduc Husband s years of educaton Two logt models are estmated, wth Y as the dependent varable. The results are shown n the followng table. The numbers n parentheses are the asymptotc standard errors. Model 1 Model Constant (0.771).364 (0.884) Cty (0.169) (0.174) Age (0.013) (0.0) Chldren (0.195) (0.199) Chldren (0.067) (0.067) Educaton 0.04 (0.038) 0.68 (0.047) Husbandhours (0.0014) Husbandage (0.0) Husbandeduc (0.035) LogL (a) (b) (c) (d) A researcher was asked to estmate the probablty of a marred woman (aged years) workng. He/she estmated a logt model, but was not sure whether a probt or lnear probablty model should have been estmated nstead. What advce can you offer? [5] Usng Model 1, consder the sgns of the coeffcents for the fve explanatory varables. Are they what you would expect? Explan your answers. [4] Usng Model 1: Test for the ndvdual sgnfcance of the fve explanatory varables. Are marred women who lve n large ctes more lkely to work than those who do not? [6] Conduct a lkelhood rato (LR) test of the jont sgnfcance of Husbandhours, Husbandage and Husbandeduc. Do these varables affect the marred woman s workng decson? [4]

9 (e) (f) Page 9 Usng Model, predct the probablty of workng for a 40 year-old marred woman who does not lve n a large cty, who has1 years of educaton, who has chldren age less than 6, who has no chldren aged between 6 and 18, whose 45 year-old husband works 40 hours per week and has 17 years of educaton. [8] Now assume that the marred woman has four optons; her choces are: 1. Work full-tme. Work part-tme 3. Self-employed (work for herself) 4. Do not work Whch model could be used to estmate the probablty of the marred woman choosng one of these optons? How would you nterpret the effect of age n such a model? [4] (g) Explan why the assumpton of Independence of Irrelevant Alternatves (IIA) mght be volated n ths stuaton. [4] END OF PAPER

10 The smple regresson model Consder the model: Y X u,...,n. 1 1 Page 10 Econometrc Methods Formula Sheet The ordnary least squares estmators of and 1 are: ( X X )Y ˆ ( X X ) ˆ Y ˆ 1 The ftted values of Y are gven by: ˆ ˆ X Ŷ 1 X The resduals are: û Y Ŷ The standard error of the regresson s gven by: û ˆ n The estmated standard errors of and 1 are gven by: se( ˆ ) ˆ se( ˆ ) ˆ 1 1 ( X X ) 1 X n ( X X ) Testng jont restrctons n the multple regresson model Let n be the sample sze, let r be the number of restrctons under test, let k be the number of parameters n the unrestrcted model, let R U be the R n the unrestrcted model and let R R be the R n the restrcted model. Under the null hypothess that the r restrctons are true, the F-statstc (R U R F ( 1 R U R ) /(n ) / r k ) has an Fr,n-k dstrbuton, that s, an F dstrbuton wth r, n-k degrees of freedom. The Logt Model exp( x' ) P(Y 1) 1 exp( x ' )

11 Page 11 Table 1: Crtcal values of the t-dstrbuton df = 0.10 = 0.05 = 0.05 = 0.01 =

12 Page 1 Table : Crtcal values of the F- dstrbuton ( =0.05) df1= df=

13 Page 13 Table 4: Crtcal values of the -dstrbuton df = 0.10 = 0.05 = 0.05 = 0.01 = END OF MATERIALS

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