Deck 6: Alternate Functional Forms

Question 1

Given: WHY_t = 2.00 - 0.15 EX_t + 0.70 WHY_t-1 + e_t
(0.10) (0.35) (0.10) $\leftarrow$ standard errors
R² = .9 DW = 2.10 n = 26

A) What is the short run impact of EX on WHY
B) What is the long run impact of EX on WHY?
C) Does this regression suffer from serial correlation according to Durbin's h-test? Show the 5-step procedure.
$$h = \left( 1 - \frac { d } { 2 } \right) \sqrt { \frac { n } { 1 - n \left( \operatorname { var } \left( \hat { \beta } ^ { } \right) \right) } }$$

Answer 1

A) -0.15
B) -.15/(1-.70) = -.5
C) 1)Ho: no autocorrelation Ha: auto present
2)5%
3)If $\text{\textbar}$ h $\text{\textbar}$ > t^c, then reject Ho (d.f. = n-k)
4)h = -0.3 ; t^c = 2.069 (d.f. = 26 - 3 = 23)
5)Do not reject Ho; no auto present $$h = \left( 1 - \frac { d } { 2 } \right) \sqrt { \frac { n } { 1 - n ( \operatorname { var } ( \hat { \beta } ) ) } } \quad h = \left( 1 - \frac { 2.10 } { 2 } \right) \sqrt { \frac { 26 } { 1 - 26 \left( 0.1 ^ { 2 } \right) } } = - .05 ( 5.93 ) = - 0.3$$

Question 2

A) Using lags of two periods on both independent variables, write the Granger equation to test if the chicken came before the egg.
B) Staying with the CHICK/EGG example, write the regression that would be used to obtain SSR_R in the following equation? $$F = \frac { \left( S S R _ { R } - \operatorname { SSR } \right) / R } { \operatorname { SSR } / ( n - k ) }$$
C) Write the regression that would be used to obtain SSR in the same equation?

Answer 2

A) EGG_t = $\hat { \beta } _ { 0 }$ + $\hat { \beta } _ { 1 }$ EGG_t-1 + $\hat { \beta } _ { 2 }$ EGG_t-2 + $\hat { \beta } _ { 3 }$ CHICK_t-1 + $\hat { \beta } _ { 4 }$ CHICK_t-2 + e_t
B) EGG_t = $\hat { \beta} _ { 0 }$ + $\hat { \beta } _ { 1 }$ EGG_t-1 + $\hat { \beta } _ { 2 }$ EGG_t-2 + e_t
C) EGG_t = $\hat { \beta } _ { 0 }$ + $\hat { \beta } _ { 1 }$ EGG_t-1 + $\hat { \beta } _ { 2 }$ EGG_t-2 + $\hat { \beta } _ { 3 }$ CHICK_t-1 + $\hat { \beta } _ { 4 }$ CHICK_t-2 + e_t

Question 3

A) Given the Eviews printout below, did the chicken come before the egg? Explain how you know.
Pairwise Granger Causality Tests
Sample: 19511994
Lags: 2
$\begin{array}{lccc}\hline \hline \text { Nul1 Hypothesis: } & \text { Obs } & \text { F-Statistic } & \text { Probability } \\\hline \hline \text { CHICK does not Granger Cause EGG } & 42 & 12.55461 & 0.17900 \\\text { EGG does not Granger Cause CHICK } & & 0.09849 & 0.04644 \\\hline\end{array}$
B) Are the first differences of M1 (FDM1) stationary? Using the Eviews printout below, show the 5-step procedure. $$\begin{array}{l}\begin{array} { l l l l } \text { ADF Test Statistic } & - 0.615077 & 1 \% \text { Critical Value* } & - 3.7667 \\&& 5 \% \text { Critical Value } & - 3.0038 \\&& 10 \% \text { Critical Value } & - 2.6417 \\\hline \hline\end{array}\\\text { Unit root test on FDM1. }\end{array}$$

Answer 3

A) We do not reject the first hypothesis given its P-value, so CHICK does not cause EGG. We reject the second hypothesis, so EGG Granger-causes CHICK. Therefore, the egg came before the chicken, unequivocally.
B) 1) Ho: B1 = 0 (FDM1 is nonstationary) Ha: B1 < 0 (FDM1 is stationary)
2) 5%
3) If t-ratio < -tc*, reject Ho
4) -.615077 > -3.0038
5) Do not reject Ho: FDM1 is nonstationary

Question 4

A) List the three conditions for a variable to be stationary.
B) What is spurious correlation? A strong relationship between variables that is the result
C) Explain why two nonstationary time series are likely to be spuriously correlated.

Question 5

A) What is a correlogram (autocorrelation function)?
B) Draw the correlogram of a stationary variable. (Be sure to label the axes of your drawing.)
C) Draw the correlogram (autocorrelation function) of a nonstationary variable.

Question 6

A) What is cointegration?
B) Given Y_t = Bo + B1 X_t + e_t describe how to determine if Y and X are cointegrated. Spell out the augmented Dickey-Fuller regression involved.

Question 7

A) For the regression given in question 1., write the auxilliary regression for the Lagrange multiplier test.
B) What are the degrees of freedom for the Lagrange multiplier test in this particular case?

Question 8

The structural parameters are biased in an autoregressive model suffering from serial correlation.

Question 9

The regression to find the SSR_R has more explanatory variables than the regression to find SSR.

Question 10

If the Granger and the reverse Granger test both result in not rejecting the null hypothesis, then the test is inconclusive.

Question 11

Nelson and Plosser's paper caused a major controversy when they showed that many macroeconomic variables are nonstationary.

Question 12

It is impossible for two cross-sectional variables to be spuriously correlated.

Question 13

It is impossible for a cross-sectional variable to be nonstationary.

Question 14

If the dependent variable in a regression "Granger-causes" one or more independent
variables, then the regression results are likely to be biased.

Question 15

The Lagrange multiplier test is only for autoregressive models.

Question 16

The auxilliary regression used in the Lagrange multiplier test is autoregressive.

Question 17

C. W.J. Granger is deceased.