Suppose you are employed by the Central Bank and given the task to analyze saving behavior of the country. A researcher obtained the following regression results by using time series data with 92 observations. S= total savings, YD= disposable income, IR= interest rate Model 1: S =-2.5 + 0.15YD R²=? (-3.7) (75.2) Model 2: S= -3.2 +0.15YD+ 1.2IR R²=0.987 (-4.8) (59.5) (7.53) Model 3: S= -1.91 + 0.08YD - 0.081 Ŝ ² +0.0006 § ³ - 0.00002 § 4 R²=0.996 SSR = 47.54 (-6.1) (44.5) (-9.5) (8.11) (-0.7) Model 4: S= -2.44 + 0.11YD -0.042 § 2 R²=0.914 SSR = 57.54 (-2.1) (33.3) (1.7) a) Can you compute the R2 of Model 1? If YES, provide the answer. If NO, explain what additional information you would need? b) Discuss the economic intuition for the choice of independent variables in Model 2. Is the sign of estimated coefficients consistent with economic theory? Are the estimated relationships statistically meaningful? c) Can you test the hypothesis that sum of slope coefficients in Model 2 is equal to 2 at 10% significance level? If YES, provide the answer. If NO, explain what additional information you would need? d) Why do you think the researcher estimated multiple models? Which model should the researcher choose to work with? Explain your answer.
Suppose you are employed by the Central Bank and given the task to analyze saving behavior of the country. A researcher obtained the following regression results by using time series data with 92 observations. S= total savings, YD= disposable income, IR= interest rate Model 1: S =-2.5 + 0.15YD R²=? (-3.7) (75.2) Model 2: S= -3.2 +0.15YD+ 1.2IR R²=0.987 (-4.8) (59.5) (7.53) Model 3: S= -1.91 + 0.08YD - 0.081 Ŝ ² +0.0006 § ³ - 0.00002 § 4 R²=0.996 SSR = 47.54 (-6.1) (44.5) (-9.5) (8.11) (-0.7) Model 4: S= -2.44 + 0.11YD -0.042 § 2 R²=0.914 SSR = 57.54 (-2.1) (33.3) (1.7) a) Can you compute the R2 of Model 1? If YES, provide the answer. If NO, explain what additional information you would need? b) Discuss the economic intuition for the choice of independent variables in Model 2. Is the sign of estimated coefficients consistent with economic theory? Are the estimated relationships statistically meaningful? c) Can you test the hypothesis that sum of slope coefficients in Model 2 is equal to 2 at 10% significance level? If YES, provide the answer. If NO, explain what additional information you would need? d) Why do you think the researcher estimated multiple models? Which model should the researcher choose to work with? Explain your answer.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Suppose you are employed by the Central Bank and given the task to analyze saving behavior of the country.
A researcher obtained the following regression results by using time series data with 92 observations. S= total
savings, YD= disposable income, IR= interest rate
Model 1: S = -2.5 + 0.15YD R²=?
(-3.7)
(75.2)
Model 2: S= -3.2 + 0.15YD+ 1.2IR R²=0.987
(-4.8) (59.5)
(7.53)
Model 3: S= -1.91 + 0.08YD - 0.081 §² +0.0006 § 3 - 0.00002 § 4 R²=0.996 SSR = 47.54
(-6.1)
(44.5)
(-9.5)
(8.11)
(-0.7)
Model 4: S= -2.44 + 0.11YD -0.042 § ² R²=0.914 SSR = 57.54
(-2.1)
(33.3)
(1.7)
a) Can you compute the R? of Model 1? If YES, provide the answer. If NO, explain what additional
information you would need?
b) Discuss the economic intuition for the choice of independent variables in Model 2. Is the sign of estimated
coefficients consistent with economic theory? Are the estimated relationships statistically meaningful?
c) Can you test the hypothesis that sum of slope coefficients in Model 2 is equal to 2 at 10% significance
level? If YES, provide the answer. If NO, explain what additional information you would need?
d) Why do you think the researcher estimated multiple models? Which model should the researcher choose to
work with? Explain your answer.
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