December 4 In-Class Review Problems
Based on Question 10.1 in the text:
A researcher estimates the effect of inflation on interest rates as
intt = + inft –.15inft-1 + inft-2 + u
This model implies an impact propensity of .48 and:
a) a long-run propensity of .95
b) a long-run propensity of .65
c) a long-run propensity of .17
d) a long-run propensity of -.15
Based on Question 10.4 in the text:
Consider the following model of the fertility rate (gfr is births per 1000 women), where pe is the dollar value of the personal tax exemption:
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gfr | Coef. Std. Err. t P>|t| [95% Conf. Interval]
------+------
pe | .186662 .0346265 5.39 0.000 .1175841 .2557399
t |-.9051881 .1089923 -8.31 0.000 -1.122622 -.6877543
_cons | 109.9302 3.47526 31.63 0.000 102.9972 116.8631
------
We can infer the following:
a) When the personal exemption increases $1, fertility increases 18%
b) This model cannot apply for all future time periods
c) Fertility decreased by about 91% per year over this time period
d) all of the above
Based on Examples 10.3 and 10.9 in the text:
A researcher is trying to determine the effect of increased coverage in PR by the minimum wage and regresses ln(employment rate) on ln(coverage) and ln(GNP) and is surprised to find that the coefficient on ln(GNP) is insignificant and negative. A trend is added to the regression, and while the elasticity of employment with respect to coverage changes very little, the elasticity with respect to GNP is now 1 and significantly different from zero. We can infer the following:
a) When GNP increases 1% above its long-run trend, employment increases by about 1%.
b) That GNP and employment were trending down together
c) That GNP and employment were trending up together
d) none of the above
Based (very loosely) Problem 12.15 in the text:
After using daily price data to estimate fish prices as a function of day of the week, a trend and the weather, a researcher obtains the residual, uhat, and its lag, uhat_1 and obtains the following regression results:
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lavgprc | Coef. Std. Err. t P>|t| [95% Conf. Interval]
------+------
mon | .0461405 .0894371 0.52 0.607 -.1316254 .2239065
tues | -.034506 .0864821 -0.40 0.691 -.2063985 .1373865
wed | .0455634 .0861483 0.53 0.598 -.1256656 .2167925
thurs | .1112257 .0855505 1.30 0.197 -.0588152 .2812666
t |-.0009613 .0010765 -0.89 0.374 -.003101 .0011783
wave2 | .075572 .0169039 4.47 0.000 .0419736 .1091704
wave3 | .0724065 .0165095 4.39 0.000 .0395922 .1052209
uhat_1 | .6442224 .0842293 7.65 0.000 .4768076 .8116372
_cons |-.9709482 .1468677 -6.61 0.000 -1.262864 -.6790326
------From this we can definitely conclude the following:
a) Endogeneity is not a problem in the original regression
b) Serial correlation is not a problem in the original regression
c) We could replace lavgprc with uhat and do the exact same test
d) all of the above
Based on Example 18.2 in the text:
Suppose we do a Dickey-Fuller test in Stata and obtain the following:
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D.r3 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
------+------
r3 |
L1 |-.0907106 .0366782 -2.47 0.015 -.1633247 -.0180965
_cons | .6253371 .2608254 2.40 0.018 .1089645 1.14171
------
Assuming that r3 is the real 3-month T-bill rate:
a) we cannot reject that 3-month T-bill rates have a unit root
b) we have estimated that the AR(1) parameter = .91
c) r3t – r3t-1 is an I(0) process
d) all of the above
Based on Problem 18.20 in the text:
The logs of industrial production (lip) and the S&P 500 index (lsp500) are both random walks with drift. A researcher is interested in whether there is a long-run relationship between the two, and estimates that
lsp500 = 1.87 + .34lip + .004t
(.383) (.12) (.0004)R2 = .92
From this, we should conclude that:
a) the elasticity of the S&P index with respect to industrial production is .34 and significant at the 5% level
b) the elasticity of the S&P index with respect to industrial production is .34 and is not significant at the 5% level
c) the elasticity of the S&P index with respect to industrial production is .34 and may or may not be significant at the 5% level
d) the S&P index and industrial production are cointegrated
Suppose we saved the residual from the above regression, do an augmented Dickey-Fuller test with a trend, and find that the coefficient (std error) on the lagged residual is -.013 (.005). We can:
a) reject serial correlation in the errors of the original regression
b) not reject serial correlation in the errors of the original regression
c) reject that lsp500 and lip are cointegrated
d) not reject that lsp500 and lip are cointegrated