UNIVERSITY OF EAST ANGLIA School of Economcs Man Seres PG Examnaton 2016-17 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
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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 400 30 B 500 0 C 600 40 D 800 40 E 900 100 F 1000 150 (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
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 = 300 -------------+------------------------------ F( 2, 297) = 130.30 Model 1021801.81 2 510900.905 Prob > F = 0.0000 Resdual 1164483.29 297 3920.81917 R-squared = 0.4674 -------------+------------------------------ Adj R-squared = 0.4638 Total 2186285.1 299 7311.99032 Root MSE = 62.616 rent Coef. Std. Err. t P> t [95% Conf. Interval] beds 51.7737 7.549298 6.86 0.000 36.91681 66.6306 beds2-3.601668 1.449289-2.49 0.014-6.453845 -.7494909 _cons 214.0019 8.0258 26.66 0.000 198.2072 229.7965 * MODEL 2:. regress rent beds beds2 nr2-nr4 Source SS df MS Number of obs = 300 -------------+------------------------------ F( 5, 294) = 228.55 Model 1738915.49 5 347783.099 Prob > F = 0.0000 Resdual 447369.61 294 1521.66534 R-squared = 0.7954 -------------+------------------------------ Adj R-squared = 0.7919 Total 2186285.1 299 7311.99032 Root MSE = 39.009 rent Coef. Std. Err. t P> t [95% Conf. Interval] beds 54.07607 4.750374 11.38 0.000 44.72702 63.42512 beds2-3.568954.9142577-3.90 0.000-5.368274-1.769635 nr2 55.13062 7.168803 7.69 0.000 41.02195 69.2393 nr3-58.46662 7.236588-8.08 0.000-72.7087-44.22454 nr4 29.12927 8.460637 3.44 0.001 12.47818 45.78036 _cons 203.6306 7.284335 27.95 0.000 189.2945 217.9666 ECO-7014A Verson 1
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
QUESTION 3 [20 marks] Page 6 We have data on 53 countres n 2016. Let p_local be the prce of a Bg Mac (the McDonald s hamburger) n country n local currency n 2016. 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 30500 13947.5 Norway Kroner 46.8 8.97 Sngapore Dollar 4.7 1.44 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 = 53 -------------+---------------------------------- F(1, 51) = 2935.98 Model 321.724259 1 321.724259 Prob > F = 0.0000 Resdual 5.58856532 51.109579712 R-squared = 0.9829 -------------+---------------------------------- Adj R-squared = 0.9826 Total 327.312824 52 6.29447738 Root MSE =.33103 log_p_rato Coef. Std. Err. t P> t [95% Conf. Interval] log_e.9328301.0172157 54.18 0.000.898268.9673921 _cons -.2810821.0610954-4.60 0.000 -.4037363 -.1584279. test (_b[_cons]=0) (_b[log_e]=1) ( 1) _cons = 0 ( 2) log_e = 1 F( 2, 51) = 54.49 Prob > F = 0.0000. test (_b[log_e]=1) ( 1) log_e = 1 F( 1, 51) = 15.22 Prob > F = 0.0003 ECO-7014A Verson 1
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 = 53 -------------+---------------------------------- F(2, 50) = 2053.75 Model 323.376414 2 161.688207 Prob > F = 0.0000 Resdual 3.93641025 50.078728205 R-squared = 0.9880 -------------+---------------------------------- Adj R-squared = 0.9875 Total 327.312824 52 6.29447738 Root MSE =.28059 log_p_rato Coef. Std. Err. t P> t [95% Conf. Interval] log_e.9796333.0178135 54.99 0.000.9438538 1.015413 gdp_rato.5294401.1155731 4.58 0.000.2973048.7615754 _cons -.662664.098082-6.76 0.000 -.8596675 -.4656605 (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
. tab approve Page 8 approve Freq. Percent Cum. ------------+----------------------------------- 0 1,513 55.02 55.02 1 1,237 44.98 100.00 ------------+----------------------------------- Total 2,750 100.00. tab default default Freq. Percent Cum. ------------+----------------------------------- 0 1,069 86.42 86.42 1 168 13.58 100.00 ------------+----------------------------------- Total 1,237 100.00. * MODEL 1: LOGIT MODEL OF LOAN DEFAULT (WITHOUT MARITAL STATUS DUMMIES).. logt default age age2 male oth Iteraton 0: log lkelhood = -491.44578 Iteraton 1: log lkelhood = -456.5194 Iteraton 2: log lkelhood = -453.87615 Iteraton 3: log lkelhood = -453.86889 Iteraton 4: log lkelhood = -453.86889 Logstc regresson Number of obs = 1,237 LR ch2(4) = 75.15 Prob > ch2 = 0.0000 Log lkelhood = -453.86889 Pseudo R2 = 0.0765 default Coef. Std. Err. z P> z [95% Conf. Interval] age -.1149922.0429701-2.68 0.007 -.199212 -.0307724 age2.0009463.0004605 2.05 0.040.0000437.0018489 male.8270569.1756338 4.71 0.000.482821 1.171293 oth 1.001396.1902749 5.26 0.000.6284644 1.374328 _cons.1883769.9275886 0.20 0.839-1.629663 2.006417. * 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) = 92.21 Prob > ch2 = 0.0000 Log lkelhood = -445.34151 Pseudo R2 = 0.0938 default Coef. Std. Err. z P> z [95% Conf. Interval] age -.1202169.0434973-2.76 0.006 -.2054701 -.0349637 age2.0009977.0004651 2.15 0.032.0000862.0019093 male.8184828.1772511 4.62 0.000.471077 1.165889 oth.9656294.1917768 5.04 0.000.5897537 1.341505 mar2.9158093.2293636 3.99 0.000.4662649 1.365354 mar3.5970918.2386064 2.50 0.012.1294317 1.064752 mar4.3528362.250437 1.41 0.159 -.1380113.8436837 _cons -.0708133.9456729-0.07 0.940-1.924298 1.782672 ECO-7014A Verson 1
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) = 154.46 Prob > ch2 = 0.0000 Log lkelhood = -1815.0508 Pseudo R2 = 0.0408 approve Coef. Std. Err. z P> z [95% Conf. Interval] age.020065.0203201 0.99 0.323 -.0197617.0598916 age2.0000588.000218 0.27 0.787 -.0003686.0004862 male -.5019176.078964-6.36 0.000 -.6566841 -.347151 oth -.3704996.0803846-4.61 0.000 -.5280506 -.2129487 mar2 -.1608895.1090288-1.48 0.140 -.3745821.052803 mar3 -.1184889.1075361-1.10 0.271 -.3292559.092278 mar4 -.0994917.1078515-0.92 0.356 -.3108767.1118932 _cons -.709939.4471732-1.59 0.112-1.586382.1665043 (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
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 1 2 2 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
Page 11 Table 1: Crtcal values of the t-dstrbuton df = 0.10 = 0.05 = 0.025 = 0.01 = 0.005 1 3.08 6.31 12.71 31.82 63.66 2 1.89 2.92 4.30 6.97 9.93 3 1.64 2.35 3.18 4.54 5.84 4 1.53 2.13 2.78 3.75 4.60 5 1.48 2.02 2.57 3.37 4.03 6 1.44 1.94 2.45 3.14 3.71 7 1.42 1.90 2.37 3.00 3.50 8 1.40 1.86 2.31 2.90 3.36 9 1.38 1.83 2.26 2.82 3.25 10 1.37 1.81 2.23 2.76 3.17 11 1.36 1.80 2.20 2.72 3.11 12 1.36 1.78 2.18 2.68 3.06 13 1.35 1.77 2.16 2.65 3.01 14 1.35 1.76 2.15 2.62 2.98 15 1.34 1.75 2.13 2.60 2.95 16 1.34 1.75 2.12 2.58 2.92 17 1.33 1.74 2.11 2.57 2.90 18 1.33 1.73 2.10 2.55 2.88 19 1.33 1.73 2.09 2.54 2.86 20 1.33 1.73 2.09 2.53 2.85 21 1.32 1.72 2.08 2.52 2.83 22 1.32 1.72 2.07 2.51 2.82 23 1.32 1.71 2.07 2.50 2.81 24 1.32 1.71 2.06 2.49 2.80 25 1.32 1.71 2.06 2.49 2.79 26 1.32 1.70 2.06 2.48 2.78 27 1.31 1.70 2.05 2.47 2.77 28 1.31 1.70 2.05 2.47 2.76 29 1.31 1.70 2.04 2.46 2.76 30 1.31 1.70 2.04 2.46 2.75 40 1.30 1.68 2.02 2.42 2.70 50 1.30 1.68 2.01 2.40 2.68 60 1.30 1.67 2.00 2.39 2.66 70 1.29 1.67 1.99 2.38 2.65 80 1.29 1.66 1.99 2.37 2.64 90 1.29 1.66 1.99 2.37 2.63 100 1.29 1.66 1.98 2.36 2.63 125 1.29 1.66 1.98 2.36 2.62 150 1.29 1.65 1.98 2.35 2.61 200 1.29 1.65 1.97 2.35 2.60 1.28 1.64 1.96 2.33 2.58 ECO-7014A Verson 1
Page 12 Table 2: Crtcal values of the F- dstrbuton (=0.05) df1=1 2 3 4 5 6 7 8 10 15 df2=1 161.4 199.5 215.7 224.6 230.2 234.0 237.0 238.9 241.9 245.9 2 18.51 19.00 19.16 19.25 19.30 19.33 19.4 19.37 19.40 19.43 3 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.79 8.70 4 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 5.96 5.86 5 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.74 4.62 6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.06 3.94 7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.64 3.51 8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.35 3.22 9 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.14 3.01 10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 2.98 2.85 11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.85 2.72 12 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.75 2.62 13 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.67 2.53 14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.60 2.46 15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.54 2.40 16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.49 2.35 17 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.45 2.31 18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.41 2.27 19 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.38 2.23 20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.35 2.20 21 4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2.32 2.18 22 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.30 2.15 23 4.28 3.42 3.03 2.80 2.64 2.53 2.44 2.37 2.27 2.13 24 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.25 2.11 25 4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2.24 2.09 26 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.22 2.07 27 4.21 3.35 2.96 2.73 2.57 2.46 2.37 2.31 2.20 2.06 28 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.19 2.04 29 4.18 3.33 2.93 2.70 2.55 2.43 2.35 2.28 2.18 2.03 30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.16 2.01 40 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.08 1.92 50 4.03 3.18 2.79 2.56 2.40 2.29 2.20 2.13 2.03 1.87 60 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 1.99 1.84 70 3.98 3.13 2.74 2.50 2.35 2.23 2.14 2.07 1.97 1.81 80 3.96 3.11 2.72 2.49 2.33 2.21 2.13 2.06 1.95 1.79 90 3.95 3.10 2.71 2.47 2.32 2.20 2.11 2.04 1.94 1.78 100 3.94 3.09 2.70 2.46 2.31 2.19 2.10 2.03 1.93 1.77 125 3.92 3.07 2.68 2.44 2.29 2.17 2.09 2.01 1.91 1.75 150 3.90 3.06 2.66 2.43 2.27 2.16 2.08 2.00 1.89 1.73 200 3.89 3.04 2.65 2.42 2.26 2.14 2.06 1.98 1.88 1.72 3.84 3.00 2.60 2.37 2.21 2.10 2.01 1.94 1.83 1.67 ECO-7014A Verson 1
Page 13 Table 3: Crtcal values of the 2 -dstrbuton df = 0.10 = 0.05 = 0.025 = 0.01 = 0.005 1 2.71 3.84 5.02 6.64 7.88 2 4.61 5.99 7.38 9.21 10.60 3 6.25 7.82 9.35 11.34 12.84 4 7.78 9.49 11.14 13.28 14.86 5 9.24 11.07 12.83 15.09 16.75 6 10.64 12.59 14.45 16.81 18.55 7 12.02 14.07 16.01 18.48 20.28 8 13.36 15.51 17.53 20.09 21.95 9 14.68 16.92 19.02 21.67 23.59 10 15.99 18.31 20.48 23.21 25.19 11 17.28 19.68 21.92 24.72 26.76 12 18.55 21.03 23.34 26.22 28.30 13 19.81 22.36 24.74 27.69 29.82 14 21.06 23.68 26.12 29.14 31.32 15 22.31 25.00 27.49 30.58 32.80 ECO-7014A Verson 1