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Suppose we want to investigate the money spending behavior in the US, by using the following model..

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Question;See attachment for questions:Suppose we want to investigate the money spending behavior in the US, by using the following model;M2t = fio + PiGDPt + fcFFRt + fijnflationt + st;C P l t ? C P l t? 4 where?2: money supply, GDP;Gross Domestic Product, FFR: interest rate, lnflation= ? ? * 100;and CPI: Consumer Price Index.;We expect thatf)i >0, 0;We want to test the seasonality effect to see if the US;money supply is larger during the Thanksgiving and Christmas;holidays (last quarter of the year).;The quarterly dummy variables are defined as;51 = 1 for Quarter 1, = 0 otherwise S3 =1 for Quarter 3;= 0 otherwise;52 = 1 for Quarter 2, = 0 otherwise S4 =1 for Quarter 4;= 0 otherwise;After regressing without the dummy variables we get the;following results;Dependent Variable:?2;Method: Least Squares;Date: 09/05/14 Time: 14:06;Sample (adjusted): 1991Q1 2008Q4;Included observations: 72 after adjustments;Question 1 (25%);Variable Coefficient Std. Error t-Statistic Prob.;? 17.35961 104.2171 0.166572 0.8682;GDP 0.533719 0.007350 72.61667 0.0000;FFR -106.6752 11.36128 -9.389367 0.0000;INFLATION 92.00183 20.81161 4.420698 0.0000;R-squared 0.990164 Mean dependent var 5015.053;Adjusted R-squared 0.989730 S.D. dependent var 1455.821;S.E. of regression 147.5375 Akaike info criterion 12.87999;Sum squared resid 1480178. Schwarz criterion 13.00648;Log likelihood -459.6798 Hannan-Quinn criter. 12.93035;F-statistic 2281.682 Durbin-Watson stat 0.525617;Prob(F-statistic) 0.000000;A. Analyze the sign of the coefficients. Are they;consistent with what we expect? Analyze the effect of;each coefficient to the dependent variable.;We now apply the seasonal effects (by adding dummy;variables) to our model and we get the following outputs in;each case;Dependent Variable: M2;Method: Least Squares;Date: 09/05/14 Time: 14:07;Sample (adjusted): 1991Q1 2008Q4;Included observations: 72 after adjustments;Variable Coe fficient Std. Error t-Statistic Prob.;C 45.63989 107.8607 0.423137 0.6736;GDP 0.533536 0.007399 72.10652 0.0000;FFR -106.5331 11.42487 -9.324662 0.0000;INFLATION 95.61539 21.09593 4.532409 0.0000;S1 -24.45142 49.73021 -0.491681 0.6246;S2 -63.74150 49.83238 -1.279118 0.2054;S3 -60.87846 49.74099 -1.223909 0.2254;R-squared 0.9 90495 Mean dependent var 501 5.053;Adjusted R-squared 0.989618 S.D. dependent var 1455.821;S.E. of regression 148.3399 Akaike info criterion 12.92905;Sum squared resid 1430307. Schwarz criterion 13.15040;Log likelihood -458.4460 Hannan-Quinn criter. 13.01717;F-statistic 1128.911 Durbin-Watson stat 0.492410;Prob(F-statistic) 0.000000;Dependent Variable: M2;Method: Least Squares;Date: 09/05/14 Time: 14:07;Sample (adjusted): 1991Q1 2008Q4;Included observations: 72 after adjustments;Variable Coe fficient Std. Error t-Statistic Prob.;C -1.372527 104.9418 -0.013079 0.9896;GDP 0.533376 0.007328 72.78867 0.0000;FFR -106.5102 11.31972 -9.409262 0.0000;INFLATION 95.18970 20.89570 4.555468 0.0000;S4 49.62241 40.38395 1.228766 0.2235;R-squared 0.9 90380 Mean dependent var 501 5.053;Adjusted R-squared 0.989806 S.D. dependent var 1455.821;S.E. of regression 146.9875 Akaike info criterion 12.88549;Sum squared resid 1447556. Schwarz criterion 13.04359;Log likelihood -458.8775 Hannan-Quinn criter. 12.94843;F-statistic 1724.470 Durbin-Watson stat 0.514963;Prob(F-statistic) 0.000000;B. Analyze the signs of the dummy coefficients. Do you;think that they are consistent with what we;might expect?;C. Suppose now that you multiply the S4 dummy with the;independent variables and you get the;following output. Analyze the signs of the dummy;coefficients. Do you think that they are consistent;with what we might expect?;Dependent Variable: M2;Method: Least Squares;Date: 10/14/14 Time: 14:07;Sample (adjusted): 1991Q1 2008Q4;Included observations: 72 after adjustments;Variable Coe fficient Std. Error t-Statistic Prob.;C -5.457339 116.7781 -0.046733 0.9629;GDP 0.526958 0.008244 63.92108 0.0000;FFR -100.8604 12.86390 -7.840581 0.0000;INFLATION 110.0289 22.34296 4.924546 0.0000;S4 65.68057 236.3460 0.277900 0.7820;S4*GDP 0.025358 0.016431 1.543338 0.1277;S4*FFR -15.35441 25.13758 -0.610815 0.5435;S4*INFLATION -76.12432 54.16507 -1.405413 0.1647;R-squared 0.991298 Mean dependent var 501 5.053;Adjusted R-squared 0.990346 S.D. dependent var 1455.821;S.E. of regression 143.0427 Akaike info criterion 12.86860;Sum squared resid 1309517. Schwarz criterion 13.12156;Log likelihood -455.2697 Hannan-Quinn criter. 12.96931;F-statistic 1041.476 Durbin-Watson stat 0.585303;Prob(F-statistic) 0.000000;Suppose we want to test whether there is any structural;break (or change) after the year of 1980;Ho: There was no structural break (or change) after 1980;H1: There was a structural break (or change) after 1980;You get the following three outputs by doing Chow Test.;Dependent Variable: Y;Method: Least Squares;Date: 03/10/14 Time: 13:48;Sample: 1960 1999;Included observations: 40;Question 2 (25%);Variable Coefficient Std. Error t-S tatistic P rob.;C 27.59394 1.584458 17.41539 0. 0000;PC -0.607160 0.157120 -3.864300 0.0004;PB 0.092188 0.039883 2.311452 0.0266;YD 0.244860 0.011095 22.06862 0.0000;R-squared 0.990391 Mean dependent var 50.5 6725;Adjusted R-squared 0.989590 S.D. dependent var 19.53879;S.E. of regression 1.993549 Akaike info criterion 4.312350;Sum squared resid 143.0726 Schwarz criterion 4.481238;Log likelihood -82.24700 Hannan-Quinn criter. 4.373414;F-statistic 1236.776 Durbin-Watson stat 0.897776;Prob(F-statistic) 0.000000;Dependent Variable: Y;Method: Least Squares;Date: 03/10/14 Time: 13:50;Sample: 1960 1979;Included observations: 20;Variable Coefficient Std. Error t-S tatistic P rob.;C 27.59882 2.433883 11. 33942 0. 0000;PC -0.899693 0.297873 -3.020394 0.0081;PB 0.181932 0.098121 1.854171 0.0822;YD 0.265328 0.058970 4.499342 0.0004;R-squared 0.913357 Mean dependent var 34.2 8700;Adjusted R-squared 0.897112 S.D. dependent var 6.199594;S.E. of regression 1.988596 Akaike info criterion 4.389592;Sum squared resid 63.27225 Schwarz criterion 4.588738;Log likelihood -39.89592 Hannan-Quinn criter. 4.428467;F-statistic 56.22198 Durbin-Watson stat 1.116410;Prob(F-statistic) 0.000000;Dependent Variable: Y;Method: Least Squares;Date: 03/10/14 Time: 13:51;Sample: 1980 1999;Included observations: 20;Variable Coefficient Std. Error t-S tatistic P rob.;C 16.18376 3.8 74379 4.1 77124 0. 0007;PC -0.345689 0.136746 -2.527964 0.0224;PB 0.151866 0.046860 3.240840 0.0051;YD 0.272712 0.008611 31.67100 0.0000;R-squared 0.993168 Mean dependent var 66.8 4750;Adjusted R-squared 0.991887 S.D. dependent var 13.68186;S.E. of regression 1.232329 Akaike info criterion 3.432546;Sum squared resid 24.29817 Schwarz criterion 3.631692;Log likelihood -30.32546 Hannan-Quinn criter. 3.471421;F-statistic 775.3400 Durbin-Watson stat 1.665783;Prob(F-statistic) 0.000000;A. Explain the procedure of the Chow Tests, i.e the steps;you have to take in order to make conclusion;about the structural stability.;B. Calculate the Chow F-Statistic. According to the F;statistic you just calculated do you reject or fail to;reject the Null Hypothesis? What does that mean for your;data?;You are given that Fcriticai(0.05,4,32)=2.6896.;A. One of the ways to detect multicollinearity is the;Variance Inflation Factor (VIF). Define and;analyze as much as you can.;Question 3 (25%);B. Suppose we used Condition Index (CI) in our model to;detect multicollinearity and we found;CI=42. What is the formula of the Condition Index and what;this number means for our;model?;Suppose we have the following regression model;PCONi = po + piREG + P2TAX + ut;wherePCONi = petroleum consumption in the ith;state (millions of BTUs);REGi = motor vehicles registration in the ith state;(thousands);TAXi = the gasoline tax rate in the ith state (cents per;gallon);The expected sign of the coefficients are P1 >;0 and P2 < 0;We ran the regression in Eviews and we obtained the;following output.;Question 4 (25%);Dependent Variable: PCON;Method: Least Squares;Date: 03/15/14 Time: 12:08;Sample: 1 50;Included observations: 50;Variable Coefficient Std. Error t-S tatistic P rob.;C 551.6880 186.2709 2.961750 0. 0048;REG 0.186132 0.011719 15.88302 0.0000;TAX -53.59101 16.85588 -3.179365 0.0026;R-squared 0.866368 Mean dependent var 603. 7000;Adjusted R-squared 0.860682 S.D. dependent var 677.8267;S.E. of regression 253.0010 Akaike info criterion 13.96279;Sum squared resid 3008447. Schwarz criterion 14.07751;Log likelihood -346.0697 Hannan-Quinn criter. 14.00648;F-statistic 152.3567 Durbin-Watson stat 2.197170;Prob(F-statistic) 0.000000;A. Discuss the sign of the coefficients and the;t-Statistics results. Do they seem fine to you?;B. We want to check if there exists Heteroscedasticity in;our model. One of the ways to do it is to;use the Park Test. Suppose we created our auxiliary;regression model and we ran it and we;obtained the following output below.;Test if there is Heteroscedasticity or not. Hint: You can;use either the t-Statistic outputs or use;the LM test to define the existence or not of;Heteroscedasticity. You do not have to use both;tests. For the use of LM test, use as critical value;of Chisquared(0.05,1)=3.841.;Dependent Variable: L0G(RESID01A2);Method: Least Squares;Date: 03/15/14 Time;Sample: 1 50;Included observations;12:13;50;Variable Coefficient Std. Error t-S tatistic P rob.;C;L0G(REG);1.650293;0.951916;2.3 74469 0.6 95016;0.308304 3.087594;0. 4904;0.0033;R-squared;Adjusted R-squared;S.E. of regression;Sum squared resid;Log likelihood;F-statistic;Prob(F-statistic);0.165700;0.148318;2.075513;206.7723;-106.4368;9.533234;0.003349;Mean dependent var;S.D. dependent var;Akaike info criterion;Schwarz criterion;Hannan-Quinn criter.;Durbin-Watson stat;8.92 5457;2.248987;4.337472;4.413953;4.366596;1.759930

 

Paper#55404 | Written in 18-Jul-2015

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