伍德里奇计量经济学第六版答案Chapter-10

C10.3 Adding log(prgnp) to equation (10.38) gives

log(prepopt) = ?6.66 ? .212 log(mincovt) + .486 log(usgnpt) + .285 log(prgnpt) (1.26) (.040) (.222) (.080)

? .027 t (.005)

n = 38, R2 = .889, R2 = .876.

The coefficient on log(prgnpt) is very statistically significant (t statistic? 3.56). Because the dependent and independent variable are in logs, the estimated elasticity of prepop with respect to prgnp is .285. Including log(prgnp) actually increases the size of the minimum wage effect: the estimated elasticity of prepop with respect to mincov is now ?.212, as compared with ?.169 in equation (10.38).

C10.4 If we run the regression of gfrt on pet, (pet-1 – pet), (pet-2 – pet), ww2t, and pillt, the coefficient and standard error on pet are, rounded to four decimal places, .1007 and .0298,

respectively. When rounded to three decimal places we obtain .101 and .030, as reported in the text.

C10.5 (i) The coefficient on the time trend in the regression of log(uclms) on a linear time trend and 11 monthly dummy variables is about ?.0139 (se? .0012), which implies that monthly unemployment claims fell by about 1.4% per month on average. The trend is very significant. There is also very strong seasonality in unemployment claims, with 6 of the 11 monthly dummy variables having absolute t statistics above 2. The F statistic for joint significance of the 11 monthly dummies yields p-value? .0009.

(ii) When ez is added to the regression, its coefficient is about ?.508 (se? .146). Because this estimate is so large in magnitude, we use equation (7.10): unemployment claims are estimated to fall 100[1 – exp(?.508)] ? 39.8% after enterprise zone designation.

(iii) We must assume that around the time of EZ designation there were not other external factors that caused a shift down in the trend of log(uclms). We have controlled for a time trend and seasonality, but this may not be enough.

C10.6 (i) The regression of gfrt on a quadratic in time gives

? = 107.06 + .072 t - .0080 t2 gfrt (6.05) (.382) (.0051) n = 72, R2 = .314.

Although t and t2 are individually insignificant, they are jointly very significant (p-value? .0000).

122

(ii) Using gfrt as the dependent variable in (10.35) gives R2?.602, compared with about .727 if we do not initially detrend. Thus, the equation still explains a fair amount of variation in gfr even after we net out the trend in computing the total variation in gfr.

(iii) The coefficient and t statistic on t3 are about ?.00129 and .00019, respectively, which results in a very significant t statistic. It is difficult to know what to make of this. The cubic trend, like the quadratic, is not monotonic. So this almost becomes a curve-fitting exercise.

C10.7 (i) The estimated equation is gct = .0081 + .571 gyt (.0019) (.067) n = 36, R2 = .679.

This equation implies that if income growth increases by one percentage point, consumption growth increases by .571 percentage points. The coefficient on gyt is very statistically significant (t statistic? 8.5).

(ii) Adding gyt-1 to the equation gives gct = .0064 + .552 gyt + .096 gyt-1 (.0023) (.070) (.069) n = 35, R2 = .695.

The t statistic on gyt-1 is only about 1.39, so it is not significant at the usual significance levels. (It is significant at the 20% level against a two-sided alternative.) In addition, the coefficient is not especially large. At best there is weak evidence of adjustment lags in consumption.

(iii) If we add r3t to the model estimated in part (i) we obtain gct = .0082 + .578 gyt + .00021 r3t (.0020) (.072) (.00063) n = 36, R2 = .680.

The t statistic on r3t is very small. The estimated coefficient is also practically small: a one-point increase in r3t reduces consumption growth by about .021 percentage points.

123

C10.8 (i) The estimated equation is

gfrt = 92.05 + .089 pet ? .0040 pet-1 + .0074 pet-2 + .018 pet-3 + .014 pet-4 (3.33) (.126) (.1531) (.1651) (.154) (.105)

? 21.34 ww2t ? 31.08 pillt (11.54) (3.90)

n = 68, R2 = .537, R2 = .483.

The p-value for the F statistic of joint significance of pet-3 and pet-4 is about .94, which is very weak evidence against H0.

(ii) The LRP and its standard error can be obtained as the coefficient and standard error on pet in the regression

gfrt on pet, (pet-1 – pet), (pet-2 – pet), (pet-3 – pet), (pet-4 – pet), ww2t, pillt

We get LRP? .129 (se? .030), which is above the estimated LRP with only two lags (.101). The standard errors are the same rounded to three decimal places.

(iii) We estimate the PDL with the additional variables ww22 and pillt. To estimate ?0, ?1, and ?2, we define the variables z0t = pet + pet-1 + pet-2 + pet-3 + pet-4

z1t = pet-1 + 2pet-2 + 3pet-3 + 4pet-4

z2t = pet-1 + 4pet-2 + 9pet-3 + 16pet-4.

Then, run the regression gfrtt on z0t, z1t, z2t, ww2t, pillt. Using the data in FERTIL3.RAW gives (to three decimal places) ??0= .069, ??1= –.057, ??2= .012. So ??0= ??0 = .069, ??1= .069 - .057 + .012 = .024, ??= .069 – 2(.057) + 4(.012) = .003, ??= .069 – 3(.057) + 9(.012) = .006,

23??4= .069 – 4(.057) + 16(.012) = .033. Therefore, the LRP is .135. This is slightly above

the .129 obtained from the unrestricted model, but not much.

Incidentally, the F statistic for testing the restrictions imposed by the PDL is about [(.537 - .536)/(1 ? .537)](60/2) ? .065, which is very insignificant. Therefore, the restrictions are not rejected by the data. Anyway, the only parameter we can estimate with any precision, the LRP, is not very different in the two models.

C10.9 (i) The sign of ?2 is fairly clear-cut: as interest rates rise, stock returns fall, so ?2< 0. Higher interest rates imply that T-bill and bond investments are more attractive, and also signal a future slowdown in economic activity. The sign of ?1 is less clear. While economic growth can

124

be a good thing for the stock market, it can also signal inflation, which tends to depress stock prices.

(ii) The estimated equation is

rsp500t = 18.84 + .036 pcipt ? 1.36 i3t (3.27) (.129) (0.54)

n = 557, R2 = .012.

A one percentage point increase in industrial production growth is predicted to increase the stock market return by .036 percentage points (a very small effect). On the other hand, a one

percentage point increase in interest rates decreases the stock market return by an estimated 1.36 percentage points.

(iii) Only i3 is statistically significant with t statistic? ?2.52.

(iv) The regression in part (i) has nothing directly to say about predicting stock returns

because the explanatory variables are dated contemporaneously with rsp500. In other words, we do not know i3t before we know rsp500t. What the regression in part (i) says is that a change in i3 is associated with a contemporaneous change in rsp500.

C10.10 (i) The sample correlation between inf and def is only about .098, which is pretty small. Perhaps surprisingly, inflation and the deficit rate are practically uncorrelated over this period. Of course, this is a good thing for estimating the effects of each variable on i3, as it implies almost no multicollinearity.

(ii) The equation with the lags is

i3t = 1.61 + .343 inft + .382 inft-1 ? .190 deft + .569 deft-1

(0.40) (.125) (.134) (.221) (.197) n = 55, R2 = .685, R2 = .660.

(iii) The estimated LRP of i3 with respect to inf is .343 + .382 = .725, which is somewhat larger than .606, which we obtain from the static model in (10.15). But the estimates are fairly close considering the size and significance of the coefficient on inft-1.

(iv) The F statistic for significance of inft-1 and deft-1 is about 5.22, with p-value? .009. So they are jointly significant at the 1% level. It seems that both lags belong in the model.

C10.11 (i) The variable beltlaw becomes one at t = 61, which corresponds to January, 1986. The variable spdlaw goes from zero to one at t = 77, which corresponds to May, 1987.

(ii) The OLS regression gives

125

log(totacc) = 10.469 + .00275 t ? .0427 feb + .0798 mar + .0185 apr (.019) (.00016) (.0244) (.0244) (.0245) + .0321 may + .0202 jun + .0376 jul + .0540 aug (.0245) (.0245) (.0245) (.0245) + .0424 sep + .0821 oct + .0713 nov + .0962 dec (.0245) (.0245) (.0245) (.0245)

2

n = 108, R = .797

When multiplied by 100, the coefficient on t gives roughly the average monthly percentage growth in totacc, ignoring seasonal factors. In other words, once seasonality is eliminated, totacc grew by about .275% per month over this period, or, 12(.275) = 3.3% at an annual rate.

There is pretty clear evidence of seasonality. Only February has a lower number of total accidents than the base month, January. The peak is in December: roughly, there are 9.6% accidents more in December over January in the average year. The F statistic for joint significance of the monthly dummies is F = 5.15. With 11 and 95 df, this give a p-value essentially equal to zero.

(iii) I will report only the coefficients on the new variables: log(totacc) = 10.640 + … + .00333 wkends ? .0212 unem (.063) (.00378) (.0034) ? .0538 spdlaw + .0954 beltlaw (.0126) (.0142)

2

n = 108, R = .910

The negative coefficient on unem makes sense if we view unem as a measure of economic activity. As economic activity increases – unem decreases – we expect more driving, and therefore more accidents. The estimate that a one percentage point increase in the

unemployment rate reduces total accidents by about 2.1%. A better economy does have costs in terms of traffic accidents. (iv) At least initially, the coefficients on spdlaw and beltlaw are not what we might expect. The coefficient on spdlaw implies that accidents dropped by about 5.4% after the

highway speed limit was increased from 55 to 65 miles per hour. There are at least a couple of possible explanations. One is that people because safer drivers after the increased speed limiting, recognizing that the must be more cautious. It could also be that some other change – other than the increased speed limit or the relatively new seat belt law – caused lower total number of accidents, and we have not properly accounted for this change.

126