The following OLS regressions were run by an applied economist investigating the determinants of US annual food consumption over the 25 year period 1989-2013:
economics
Description
The
following OLS regressions were run by an applied economist investigating the
determinants of US annual food consumption over the 25 year period 1989-2013:
Model A:
= -1.189 + 0.324
LGDPI + 0.729 LGPOPN R2 = 0.9790 ;
n=25
(1.861) (0.176)
(0.566) RSS. =0 .011096; TSS=0.528779
Model B:
= 1.201 + 0.549 LGDPI R2 = 0.9774 ;
n=25
(0.115) (0.017) RSS. =0 .011931; TSS=0.528779
(Figures
in brackets are the estimated standard errors of the coefficients, R2 is the coefficient of determination, n is the
sample size, RSS is the residual sum of squares and TSS is the total sum of
squares)
where LGFOOD is the logarithm of real food
expenditure in the USA
LGDPI is the
logarithm of real personal disposable income in the USA
LGPOPN is the
logarithm of the resident population of the USA.
(a)
Interpret precisely the estimated
regression coefficients in Model A
(ignoring the constant term) and explain how they correspond with your a priori beliefs.
(b)
Interpret the value of the R2 statistic for Model A.
Formally test whether the explanatory power of Model A is significant.
(c)
Both real food expenditure and
real personal disposable income exhibit strong upward trends over the sample
period. What features of these results
should lead the economist to suspect that the regression results are affected
by multicollinearity?
(d)
What are the consequences of
multicollinearity for the properties of the OLS estimators of the regression
coefficients?
(e)
Assuming Model A is correctly specified, evaluate the likely direction of
bias in the response coefficient on DPI in
Model B. State clearly any additional assumptions that
you have to make to arrive at you answer.
Do the results support your conclusion?
