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. $$h = \left( 1 - \frac { d } { 2 } \right) \sqrt { \frac { n } { 1 - n \left( \operatorname { var } \left( \hat { \beta } ^ { } \right) \right) } }$$

Accepted Answer

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?

Accepted Answer

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. $$\begin{array}{l}
\begin{array} { l l l l } 
\text { ADF Test Statistic } & - 0.615077 & 1 \% \text { Critical Value* } & - 3.7667 \
&& 5 \% \text { Critical Value } & - 3.0038 \
&& 10 \% \text { Critical Value } & - 2.6417 \
\hline \hline
\end{array}\
\text { Unit root test on FDM1. }
\end{array}$$

Accepted Answer

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.

Accepted Answer

The answer of A) List the three conditions for a...

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.

Accepted Answer

The answer of A) What is a correlogram (autocorrelation function)?
B)...

Question 6

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

Accepted Answer

The answer of A) What is cointegration? B) Given Y_t =...

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?

Accepted Answer

The answer of A) For the regression given in question...

Question 8

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

Accepted Answer

Serial correlation in the error terms of an autoregressive model violates the assumption of no autocorrelation in the residuals, leading to biased estimates of the structural parameters.

Question 9

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

Accepted Answer

SSR_R refers to the sum of squares due to regression for a specific model, and SSR refers to the sum of squares due to regression in general. The number of explanatory variables in each regression depends on the specific models being compared, not on the notation used to describe the sum of squares.

Question 10

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

Accepted Answer

If both the Granger and reverse Granger tests result in not rejecting the null hypothesis, it means there is no evidence of causality in either direction, making the test inconclusive regarding causality between the two variables.

Question 11

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

Accepted Answer

Nelson and Plosser's 1982 paper "Trends and Random Walks in Macroeconomic Time Series" was influential in demonstrating that many macroeconomic variables follow a nonstationary process, challenging the prevailing assumption of stationarity and sparking significant debate and further research in the field of econometrics.

Question 12

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

Accepted Answer

Two cross-sectional variables can be spuriously correlated if they have a common cause or are influenced by a third variable, leading to a correlation that does not imply a direct causal relationship between them.

Question 13

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

Accepted Answer

A cross-sectional variable is a variable that is measured at a single point in time. Nonstationarity refers to a situation where the mean or variance of a variable changes over time. Since a cross-sectional variable is measured at a single point in time, it cannot 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.

Accepted Answer

If the dependent variable Granger-causes the independent variables, it implies reverse causality, which can lead to endogeneity and biased regression estimates.

Question 15

The Lagrange multiplier test is only for autoregressive models.

Accepted Answer

The Lagrange multiplier test is a general statistical test used for hypothesis testing, not limited to autoregressive models. It can be applied in various contexts to test for the presence of a constraint in a model.

Question 16

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

Accepted Answer

The Lagrange multiplier test uses an auxiliary regression that is autoregressive in order to test for the presence of autocorrelation in the residuals of a regression model.

Question 17

C. W.J. Granger is deceased.

Accepted Answer

C. W.J. Granger, a renowned British econometrician, passed away on May 27, 2009.

Quiz 6: Alternate Functional Forms

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.

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.

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

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?