Question #52

, Smith uses a dummy variable that equals 1 whenever the Federal government intervened with a fiscal policy stimulus package that exceeded 2% of the annual Gross Domestic Product. Smith sets the dummy variable equal to 1 for four quarters starting with the quarter in which the policy is enacted and extending through the following 3 quarters. Otherwise, the dummy variable equals zero. Smith uses quarterly data over the past 5 years to derive her regression. Smith's regression equation is provided in Exhibit 1: Exhibit 1: Foreclosure Share Regression Equation foreclosure share = b0 + b1(ΔINT) + b2(STIM) + b3(CRISIS) + ε where: Foreclosure share = the percentage of all outstanding mortgages foreclosed upon during the quarter ΔINT = the quarterly change in the 1-year Treasury bill rate (e.g., ΔINT = 2 for a two percentage point increase in interest rates) STIM = 1 for quarters in which a Federal fiscal stimulus package was in place CRISIS = 1 for quarters in which the median house price is one standard deviation below its 5-year moving average The results of Smith's regression are provided in Exhibit 2: Exhibit 2: Foreclosure Share Regression Results Variable Coefficient t-statistic Intercept 3.00 2.40 ΔINT 1.00 2.22 STIM -2.50 -2.10 CRISIS 4.00 2.35 The ANOVA results from Smith's regression are provided in Exhibit 3: Exhibit 3: Foreclosure Share Regression Equation ANOVA Table Source Degrees of Freedom Sum of Squares Mean Sum of Squares Regression 3 15 5.0000 Error 16 5 0.3125 Total 19 20 Smith expresses the following concerns about the test statistics derived in her regression: Concern 1: If my regression errors exhibit conditional heteroskedasticity, my t- statistics will be underestimated. Concern 2: If my independent variables are correlated with each other, my F-statistic will be overestimated. Before completing her analysis, Smith runs a regression of the changes in foreclosure share on its lagged value. The following regression results and autocorrelations were derived using quarterly data over the past 5 years ( Exhibit 4 and Exhibit 5, respectively): Exhibit 4. Lagged Regression Results Δ foreclosure sharet = 0.05 + 0.25(Δ foreclosure sharet– 1) Exhibit 5. Autocorrelation Analysis Lag Autocorrelation t-statistic 1 0.05 0.22 2 -0.35 -1.53 3 0.25 1.09 4 0.10 0.44 Exhibit 6 provides critical values for the Student's t-Distribution Exhibit 6: Critical Values for Student's t-Distribution Area in Both Tails Combined Degrees of Freedom 20% 10% 5% 1% 16 1.337 1.746 2.120 2.921 17 1.333 1.740 2.110 2.898 18 1.330 1.734 2.101 2.878 19 1.328 1.729 2.093 2.861 20 1.325 1.725 2.086 2.845