Assignment #2 (1 point)
Given a sample of 50 observations and 4 explanatory variables, what can you say about autocorrelation if (a) d=1.05, (b) d= 1.40, (c) d=2.50, (d) d=3.97.
Show your work.
For
n=50 and k=4, and
,
the critical d values are:
dL = 1,38 4 - dL = 2,62
dU = 1,72 4 - dU = 2,28
(a) positive autocorrelation; (b) inconclusive; (c) inconclusive; (d) negative autocorrelation
When
the errors in the regression model have AR (1) serial correlation,
why do the OLS standard errors tend to underestimate the sampling
variation in the
?
Is it always true that the OLS standard errors are too small?
We can reason this from equation 1 (12.4 Wooldridge):
because
the usual OLS standard error is an estimate of
.
When the dependent and independent variables are in level (or log)
form, the AR(1) parameter, ρ, tends to be positive in time series
regression models. Further, the independent variables tend to be
positive correlated, so
– which is what generally appears in eq. 1 when the {xt}
do not have zero sample average – tends to be positive for most t
and
j.
With multiple explanatory variables the formulas are more complicated
but have similar features.
If
ρ < 0, or if the {xt}
is negatively autocorrelated, the second term in the last line of eq.
1 could be negative, in which case the true standard deviation of
is actually less than
.
Assignment #3 (2 points)
In studying the movement in the production workers’ share in the value added, the following models were considered:
Where Y=labor’s share and t=time. Based on annual data for 1949-1964, the following results were obtained for the primary metal industry:
Is there a serial correlation in Model A? In Model B?
There is a serial correlation in Model A, but not in Model B.
What accounts for the serial correlation?
The autocorrelation may be due to misspecification of Model A because it excludes the quadratic trend term.
How would you distinguish between “pure” autocorrelation and specification bias?
I would need prior knowledge of the probable functional form.
Assignment #4 (2 points)
In a regression of average wages (W) on the number of employees (N) for a random sample of 30 firms, the following regression results were obtained:
How do you interpret the two regressions?
As equation1 shows, as N increases by a unit, on average, wages increases by about 0,009 dollars. If we multiply the second equation through by N, we will see that results re quite similar to Eq. (1).
What is the author assuming going from Eq. (1) to Eq. (2)? Was he worried about heteroscedasticity? How do you know?
Apparently, the author was concerned about heteroscedasticity, since he divided the original equation by N. This amounts to assuming that the error variance is proportional to the square of N. Thus the author is using weighted least-squares in estimating Eq. (2).
Can you relate the slopes and intercepts of the two models?
The intercept coefficient in Eq. (1) is the slope coefficient in Eq. (2) and the slope coefficient in Eq. (1) is the intercept in Eq. (2).
Can you compare the R2 values of the two models? Why or why not?
No. The dependent variables in the models are not the same.