Notes are not permitted in this examination. Do not turn over until you are told to do so by the Invigilator.

Transcription

1 UNIVERSITY OF EAST ANGLIA School of Economcs Man Seres PG Examnaton BANKING ECONOMETRICS ECO-7014A Tme allowed: 2 HOURS Answer ALL FOUR questons. Queston 1 carres a weght of 30%; queston 2 carres 20%; queston 3 carres 20%; queston 4 carres 30%. Marks awarded for ndvdual parts are shown n square brackets. A formula sheet, t-tables, F-tables, and 2 -tables are ncluded at the end of the exam paper. Notes are not permtted n ths examnaton. Do not turn over untl you are told to do so by the Invglator. ECO-7014A Module Contact: Prof Peter Moffatt, ECO Copyrght of the Unversty of East Angla Verson 1

2 Page 2 THIS PAGE IS DELIBERATELY LEFT BLANK ECO-7014A Verson 1

3 QUESTION 1 [30 MARKS] Page 3 ALL WORKING MUST BE SHOWN IN YOUR ANSWER TO THIS QUESTION. The followng table contans data on weekly ncome (X) and weekly expendture on restaurant meals (Y) for a sample of sx households. Both varables are measured n pounds. Household X Y A B C D E F (a) Obtan ordnary least squares estmates of 1 and 2 n the model: Y 1 2X u 1,,6 [10] (b) (c) (d) (e) Place a precse economc nterpretaton on each of the two parameter estmates, ˆ 1 and ˆ 2. In partcular, does t make any economc sense that your estmate of the ntercept s negatve? [6] Fnd the resduals. Whch of the sx households has the hghest postve resdual assocated wth t? What concluson can you draw about ths household? [4] Test the null hypothess that 2=0 aganst the alternatve that 2 >0. What s the economc nterpretaton of your result (.e. what term would an economst use to descrbe restaurant meals)? [7] Brefly explan why we chose to conduct a one-taled test n (d) rather than a two-taled test. [3] TURN OVER ECO-7014A Verson 1

4 QUESTION 2 [20 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: nr2: nr3: nr4: rent n pounds per month number of bedrooms 1 f located n NR1 (South Central Norwch); 0 otherwse 1 f located n NR2 (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 beds2=beds^2 * MODEL 1:. regress rent beds beds2 Source SS df MS Number of obs = F( 2, 297) = 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 2:. regress rent beds beds2 nr2-nr4 Source SS df MS Number of obs = F( 5, 294) = 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 ECO-7014A Verson 1

5 Page 5 (a) (b) (c) (d) Explan the economc prncple(s) underlyng the ncluson of the varable beds2 n model 1. Does the assocated t-statstc confrm that these prncples are at work? [5] Carry out an F-test to test model 1 as a restrcted verson of model 2, n order to test the mportance of locaton n rent determnaton. Interpret your result. [5] Interpret the coeffcents of the locaton dummes. Create a rankng of the four locatons by rent levels. [5] Why mght you expect the problem of heteroscedastcty to arse n ths model, and what mpact would t have on the results nterpreted above? How would you correct for the problem of heteroscedastcty? [5] TURN OVER ECO-7014A Verson 1

6 QUESTION 3 [20 marks] Page 6 We have data on 53 countres n Let p_local be the prce of a Bg Mac (the McDonald s hamburger) n country n local currency n Let e be the exchange rate for country aganst the US dollar n 2016 (that s, e s the number of unts of local currency that can be exchanged for one US dollar n 2016). (a) Data on three of the 53 countres s shown n the followng table. Country Currency p_local e Indonesa Rupah Norway Kroner Sngapore Dollar 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 2016, and whch appears over-valued? [7] The followng regresson model s estmated usng data from all 53 countres n 2016 (p_usa s the prce of a Bg Mac n the USA n 2016): _ log p local 1 2log 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 ( 2) log_e = 1 F( 2, 51) = Prob > F = test (_b[log_e]=1) ( 1) log_e = 1 F( 1, 51) = Prob > F = ECO-7014A Verson 1

7 Page 7 (b) 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 2016 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(2, 50) = 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 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] QUESTION 4 [30 MARKS] From a bank, we obtan nformaton on a sample of customers who appled for a partcular type of loan. The varables are: approve: default: age: age2: male: oth: mar: 1 f the bank approved the customer s applcaton; 0 f declned 1 f customer defaulted on loan; 0 f pad on tme Age of customer n years Age-squared 1 f customer s male; 0 f female 1 f customer has other loans; 0 otherwse Martal status of customer: 1 f lvng wth parents 2 f sngle 3 f marred 4 f separated, dvorced or wdowed Analyss of the sample s carred out n STATA, wth the followng results: TURN OVER ECO-7014A Verson 1

8 . tab approve Page 8 approve Freq. Percent Cum , , Total 2, tab default default Freq. Percent Cum , Total 1, * MODEL 1: LOGIT MODEL OF LOAN DEFAULT (WITHOUT MARITAL STATUS DUMMIES).. logt default age age2 male oth Iteraton 0: log lkelhood = Iteraton 1: log lkelhood = Iteraton 2: log lkelhood = Iteraton 3: log lkelhood = Iteraton 4: log lkelhood = Logstc regresson Number of obs = 1,237 LR ch2(4) = Prob > ch2 = Log lkelhood = Pseudo R2 = default Coef. Std. Err. z P> z [95% Conf. Interval] age age male oth _cons * MODEL 2: LOGIT MODEL OF LOAN DEFAULT (WITH MARITAL STATUS DUMMIES).. logt default age age2 male oth mar2 mar3 mar4 Logstc regresson Number of obs = 1,237 LR ch2(7) = Prob > ch2 = Log lkelhood = Pseudo R2 = default Coef. Std. Err. z P> z [95% Conf. Interval] age age male oth mar mar mar _cons ECO-7014A Verson 1

9 Page 9.. * MODEL 3: LOGIT MODEL OF LOAN APPROVAL.. logt approve age age2 male oth mar2 mar3 mar4 Logstc regresson Number of obs = 2,750 LR ch2(7) = Prob > ch2 = Log lkelhood = Pseudo R2 = approve Coef. Std. Err. z P> z [95% Conf. Interval] age age male oth mar mar mar _cons (a) (b) (c) (d) (e) (f) How many customers are n the sample? How many had loans approved? Of these, what proporton of these defaulted on ther loan? [5] Test the sgnfcance of the effect of the varable male n Model 1. Interpret the result. [5] Usng the coeffcents of age and age2 n Model 1, fnd the age of customer at whch the probablty of loan default s maxmsed or mnmsed. Have you located a maxmum or a mnmum? How do you know ths? [5] Usng an LR of Model 1 as a restrcted verson of Model 2, test the sgnfcance of martal status n explanng loan defaults. Whch martal status s most lkely to default, and whch least? [5] Usng Model 2, predct the probablty of default for a 35-year-old marred female, wth other loans. [5] By comparng the results of Model 3 to those of Model 2, consder whether the bank s strategy for approvng loans s sensble. On the bass of the two sets of results, what advce would you gve to the bank n order to brng about an mprovement n ther strategy? [5] END OF PAPER ECO-7014A Verson 1

10 Page 10 Bankng Econometrcs - Formula Sheet The smple regresson model Consder the model: Y 1 2X u 1,, n. The ordnary least squares estmators of 2 and 1 are: ˆ 2 2 X X X Y X The ftted values of Y are gven by: Yˆ ˆ ˆ X 1 2 ˆ Y ˆ X 1 2 The resduals are: u Y Yˆ ˆ The standard error of the regresson s gven by: ˆ uˆ2 n 2 The estmated standard errors of ˆ 2 and ˆ 1 are gven by: se ˆ ˆ X X se ˆ ˆ 2 1 X n X X 1 2 Testng jont restrctons n the multple regresson model 2 2 RU RR / r 2 1 RU / n k F ~ F r, n k under H 0: the r restrctons are true The logt Model exp ' Py 1 1 exp x ' x ECO-7014A Verson 1

11 Page 11 Table 1: Crtcal values of the t-dstrbuton df = 0.10 = 0.05 = = 0.01 = ECO-7014A Verson 1

12 Page 12 Table 2: Crtcal values of the F- dstrbuton (=0.05) df1= df2= ECO-7014A Verson 1

13 Page 13 Table 3: Crtcal values of the 2 -dstrbuton df = 0.10 = 0.05 = = 0.01 = ECO-7014A Verson 1