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(ECON233)[2008](f)final~2047^_10245.pdf
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Econ 233 (L1) Final Exam
Fall 2008
Time Allowed: 2 hours



Part I. Short Questions (8 points each)

1. To decide whether or fits the data better, you cannot compare the regressions. T/F (Explain briefly). 01iiYXu.....
01ln()iiYXu.....
2R

Ans: True [Because the dependent variables and hence TSS are not measured in the same units.]
2. You try to explain the number of IBM shares traded in the stock market per day in 2005. As an independent variable you choose the closing price of the share. This is an example of sample selection bias. T/F (Explain briefly).
Ans: False [This is an example of simultaneous equation bias, since stock price and transaction volumes are jointly determined by demand and supply for the stock.]
3. The presence of (imperfect) multicollinearity jeopardizes regression analysis because it violates the OLS assumptions needed. T/F (Explain briefly).


Ans: False [Multicollinearity is a data problem and does not concern the error term, so as long as the error term is random and uncorrelated to the regressors, the OLS estimates are still BLUE.]
4. What kind of nonlinear regression model(s) cannot be estimated by OLS?


Ans: Those that are not linear in parameters. Eg. Negative exponential growth model in the lecture notes.
5. What kind of model(s) can be used to specify a dependent variable which measures a sample of respondents that contain both smokers and non-smokers?


Ans: Probit or Logit models.

Part II. Long Questions (15 points each)

1. Consider the relationship between the expenditure on travel (Et) and total income (Yt)given by: Et=0+1Yt+ut

(a) You suspect that the error term ut is heteroskedastic. Describe in details how you can use the Park Test to verify if this is indeed the case.

(b) Suppose you suspect that the heteroskedasticity have the form Var ut =Yt1/3. Write down the weighted least square model you should estimate and show that the transformed regression is homoskedastic. In what way are the



slope coefficients of the two models (the original and the transformed) comparable?



Ans: (a)
. Run the regression model Et=0+1Yt+ut and obtain u t

. Take log of u t2 and run lnu t2=0+1Yt+t

. Do a t-test on the null of 1=0.

. If can reject the null, there is evidence of heteroskedasticity.


(b)
. Use the weight Yt1/6

. Regress EtYt1/6=01Yt1/6+1Yt5/6+utYt1/6

. ut.=utYt1/6Var ut. =Var utYt16 =1Yt13Var ut =1Yt13Yt13=

. The slope coefficients of both models are 1 but the interpretation of them are different as the variables are not measured in the same units.

2. Using annual data for the U.S. for years 1948 through 1997, the relationship between inflation rate and unemployment rate is: infl t=1.42+0.468unemt.

(a) After calculating the residuals et for the above regression, you regress et on et.1 and an error term. The OLS estimate of the slope coefficient of et.1 is =0.573 w