Jim XanderECO6416 SPR ‘96
ECO 6416 TEST II SPRING '96
NAME______
I. MULTIPLE CHOICE(select single best answer and enter in underlined space at start of question, 3 points per question)
_____ 1. To determine whether or not to pool a time series data set and estimate a single regression equation or to estimate two or more regression equations for subsets of the time period requires the following test
a. Goldfeld-Quandt Test
b. Joint F-Test
c. Durbin-Watson Test
d. Chow Test
_____ 2. If the appropriate model to estimate the demand for Pentium processor chips is
QI = 0 + 1 PI + 2PC +
where
QI = the quantity demanded of Intel Pentium chips
Pi = the price of an Intel Pentium chip
PC = the price of a Cyrix Pentium Chip (a substitute for Intel Chips)
the stochastic error term
and the following model is erroneously estimated
QI = 0 + 1 PC +
economic theory would suggest that the estimate of 1
a. will be biased in a positive direction
b. will be biased in a negative direction
c. will not be biased
d. will be inefficient
_____ 3. A large F-stat combined with small t-stats is a strong indication that we have a problem with
a. serial correlation
b. positive serial correlation
c. multicollinearity
d. discrete heteroskedasticity
_____ 4. If the appropriate model to estimate the consumption of chicken is
C = 0 + 1 PC + 3LYD +
and the following model is erroneously estimated
C = 0 + 1 PC + 2PB + 3LYD + *
economic theory would suggest that the estimate of 1
a. will be biased in a positive direction
b. will be biased in a negative direction
c. will be inconsistent.
d. will be inefficient
_____ 5. For the estimated regression equation: = 15 + 4X1 - 6X2 + 2X1X2 , X2 is a dummy equal to 1 for senior citizens and equal to 0 otherwise. The rate of change in Y with respect to X1 (same as slope or derivative), for senior citizens is equal to
a. -2
b. +6
c. +4
d. -6
_____ 6. The elasticity of demand with respect to disposable income (note LQ is the logarithm of Q or demand) for the following function
LQ = 0 + 1 PC + 2PB + 3YD
would be determined by solving which of the following formulas?
a. 3
b. 3(Q/PC)
c. 3(YD)
d. 3/Q
_____ 7. Given the following implicit regression model, Y = f(X1,X2,X3) , the elasticity of Y with respect to X1 is defined as
a. the percentage change in X1 / the percentage change in Y
b. the percentage change in Y / the percentage change in X1
c. the change in X1 / the change in Y
d. the change in Y / the change in X1
_____ 8. According to the text, model specification should be strongly rooted in
a. data mining
b. stepwise regression procedures
c. theory
- long specification searches, where numerous models are tried
_____ 9. Which of the following is not a consequence of multicollinearity?
a. the variances of the estimates will decrease
b. the computed t-scores will fall
c. estimates will remain unbiased
d. the overall fit of the equation will be largely unaffected
_____ 10. Multicollinearity can be detected (suggested) by all of the following except
a. a high adjusted coefficient of determination coupled with low t-scores
b. high simple coefficients of correlation between independent variables
c. large variance inflation factors(VIFs)
d. A high Durbin-Watson statistic
_____ 11. Which of the following statements is inconsistent with the existence of serial correlation?
a. the variances of the coefficients are underestimated
b. the variances of the sampling distributions of B (distribution of B-hat) are inflated
c. bias in the the coefficient estimates
d. overestimate of the t-scores
_____ 12. Which of the following is not a shortcoming of the Durbin-Watson d statistic?
a. it only measures first-order serial correlation
b. it is an inappropriate if the eqaution contains a lagged value of Y as an independent variable
c. the regression model must not contain an intercept term
d. it has an indeterminate region in the test
_____ 13. A Durbin-Watson d statistic of 2 would suggest
a. extreme positive serial correlation
b. no serial correlation
c. extreme negative serial correlation
d. rho equal zero
_____ 14. Which of the following regression models would provide a valid opportunity to use the Durbin-Watson Test?
a. Yt = B0 + B1 X1 + B2 Yt-1 + t where t = t-1 + t
b. Yt = B1 X1 + B2 X2 + t where t = t-2 + t
c. Yt = B0 + B1 X1 + B2 X2 + t where t = t-1 + t
d. Yt = B0 + B1 X1 + B2 Yt-1 + t where t = t-2 + t
_____ 15. A Variance Inflation Factor, VIF, of 2 for independent variable #3 in a four independent variable regression model, would mean that independent variables #1,#2, and #4 'explain' what percent of the variability in #3?
a. 0
b. 50
c. 80
d. 20
II.Your text identifies three methods for specification searches: data mining, stepwise regression, and sequential searches.
Briefly discuss each method (10).
Data mining
Stepwise regression
Sequential searches
III. The following EViews - estimated models are for the consumption spending (variable CS). Perform a test of structural change (Chow Test) based on the output provided. The time series is of quarterly data for the period 1947:1 - 1994:4 (48 full years).. The hypothesized structural change is to have occurred at time of the OPEC oil embargo(1973:2). . Thus, the data has been divided into a pre-embargo period, 1947:1 to 1973:2 (observations 1-106) and a post-embargo period, 1973:3 to 1994:4 (observations 107-192) and the question is whether the relationship has been altered by the OPEC oil embargo and whether the data shoud be pooled. Be complete in your analysis. (10 points[JX1])
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Jim XanderECO6416 SPR ‘96
Dependent Variable: CSMethod: Least Squares
Date: 06/02/99 Time: 12:22
Sample: 1947:1 1994:4
Included observations: 192
Variable / Coefficient / Std. Error / t-Statistic / Prob.
C / -90.10527 / 8.965506 / -10.05022 / 0.0000
GDP / 0.623155 / 0.006859 / 90.84975 / 0.0000
P_GDP / 2.519035 / 0.337925 / 7.454424 / 0.0000
GOV_NET / -0.216905 / 0.078647 / -2.757957 / 0.0064
R-squared / 0.998768 / Mean dependent var / 1947.873
Adjusted R-squared / 0.998749 / S.D. dependent var / 850.4167
S.E. of regression / 30.08160 / Akaike info criterion / 9.666318
Sum squared resid / 170121.8 / Schwarz criterion / 9.734183
Log likelihood / -923.9665 / F-statistic / 50820.45
Durbin-Watson stat / 0.206962 / Prob(F-statistic) / 0.000000
Dependent Variable: CS
Method: Least Squares
Date: 06/02/99 Time: 12:25
Sample: 1947:1 1973:2
Included observations: 106
Variable / Coefficient / Std. Error / t-Statistic / Prob.
C / -222.9177 / 16.30310 / -13.67333 / 0.0000
GDP / 0.423003 / 0.017704 / 23.89337 / 0.0000
P_GDP / 23.20436 / 1.858297 / 12.48689 / 0.0000
GOV_NET / 0.791736 / 0.301522 / 2.625795 / 0.0100
R-squared / 0.996610 / Mean dependent var / 1282.326
Adjusted R-squared / 0.996510 / S.D. dependent var / 369.5865
S.E. of regression / 21.83318 / Akaike info criterion / 9.041744
Sum squared resid / 48622.16 / Schwarz criterion / 9.142251
Log likelihood / -475.2124 / F-statistic / 9995.198
Durbin-Watson stat / 0.239582 / Prob(F-statistic) / 0.000000
Dependent Variable: CS
Method: Least Squares
Date: 06/02/99 Time: 12:27
Sample: 1973:3 1994:4
Included observations: 86
Variable / Coefficient / Std. Error / t-Statistic / Prob.
C / -97.97543 / 37.35864 / -2.622564 / 0.0104
GDP / 0.657458 / 0.019132 / 34.36389 / 0.0000
P_GDP / 0.763353 / 0.583095 / 1.309141 / 0.1941
GOV_NET / -0.393875 / 0.066190 / -5.950687 / 0.0000
R-squared / 0.998003 / Mean dependent var / 2778.288
Adjusted R-squared / 0.997931 / S.D. dependent var / 478.9437
S.E. of regression / 21.78447 / Akaike info criterion / 9.045158
Sum squared resid / 39388.75 / Schwarz criterion / 9.158534
Log likelihood / -389.4644 / F-statistic / 13828.79
Durbin-Watson stat / 0.676551 / Prob(F-statistic) / 0.000000
IV. Suppose a time plot of your residuals looks like the following. What does this suggest to you? (10 points)
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Jim XanderECO6416 SPR ‘96
V. The Research Department in your organization has estimated the relationship between the firm’s sales and its community service(CS) using 50 time series observations. The following results[standard errors of each partial slope are in parentheses below the equation, eg. .03 is the SE(B's) ] are brought to you for review.
SALES = 45 + .36CS - .05(CS)2
(.03) (.10)
Based on the regression results and the residual plot, do you think the quadratic model estimated provides the best specification? Explain. (10 points)
VI. Using the last 30 years of data, on investment spending(I), the rate of interest(r), consumption exenditures(C), and the capacity utilization rate(u) you estimate an OLS regression model(I is dependent variable, others are independent variables) and find that the estimated serial correlation(autocorrelation) coefficient, -hat, equals +0.80.
a.Based on the estimated serial correlation (autocorrelation) coefficient, calculate the value of “d” the Durbin-Watson test statistic. (5 points)
b.Even before estimating the model, you expect that the errors are positively correlated. Using the value of d found in Part a.[1] test your expectation with respect to serial correlation. (10 points)
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[1] If you could not do Part a., assume a value of 1.3 for d.
[JX1]1
Chow Breakpoint Test: 1973:2F-statistic / 44.55533 / Probability / 0.000000
Log likelihood ratio / 130.2087 / Probability / 0.000000