Question 1

If $X _ { t } \text { and } Y _ { t }$ are cointegrated, then the OLS estimator of the coefficient in the cointegrating regression is

Accepted Answer

A)  BLUE 
B)  unbiased when using HAC standard errors. 
C)  unbiased even in small samples. 
D)  consistent. 
A)  BLUE 
B)  unbiased when using HAC standard errors. 
C)  unbiased even in small samples. 
D)  consistent. D

Question 2

Consider the GARCH  (1,1)  model $\sigma _ { t } ^ { 2 } = \alpha _ { 0 } + \alpha _ { 1 } u _ { t - 1 } ^ { 2 } + \phi _ { 1 } \sigma _ { t - 1 } ^ { 2 }$ Show that this model can be
rewritten as $\sigma _ { t } ^ { 2 } = \frac { \alpha _ { 0 } } { 1 - \phi _ { 1 } } + \alpha _ { 1 } \left( u _ { t - 1 } ^ { 2 } + \phi _ { 1 } u _ { t - 2 } ^ { 2 } + \phi _ { 1 } ^ { 2 } u _ { t - 3 } ^ { 2 } + \phi _ { 1 } ^ { 3 } u _ { t - 4 } ^ { 2 } + \ldots \right)$  (Hint: use the GARCH(1,1) model but specify it for $\sigma _ { t - 1 } ^ { 2 }$; substitute this expression into the original specification, and so on.) Explain intuitively the meaning of the resulting formulation.

Accepted Answer

$$\begin{aligned}
\sigma _ { t } ^ { 2 } & = \alpha _ { 0 } + \alpha _ { 1 } u _ { t - 1 } ^ { 2 } + \phi _ { 1 } \sigma _ { t - 1 } ^ { 2 } = \alpha _ { 0 } + \alpha _ { 1 } u _ { t - 1 } ^ { 2 } + \phi _ { 1 } \left( \alpha _ { 0 } + \alpha _ { 1 } u _ { t - 2 } ^ { 2 } + \phi _ { 1 } \sigma _ { t - 2 } ^ { 2 } \right) \
& = \alpha _ { 0 } \left( 1 + \phi _ { 1 } \right) + \alpha _ { 1 } \left( u _ { t - 1 } ^ { 2 } + \phi _ { 1 } u _ { t - 2 } ^ { 2 } \right) + \phi _ { 1 } ^ { 2 } \sigma _ { t - 2 } ^ { 2 } \
& = \alpha _ { 0 } \left( 1 + \phi _ { 1 } + \phi _ { 1 } ^ { 2 } \right) + \alpha _ { 1 } \left( u _ { t - 1 } ^ { 2 } + \phi _ { 1 } u _ { t - 2 } ^ { 2 } + \phi _ { 1 } ^ { 2 } u _ { t - 3 } ^ { 2 } \right) + \phi _ { 1 } ^ { 3 } \sigma _ { t - 3 } ^ { 2 } \text {. Continuing with the }
\end{aligned}$$
substitutions infinitely and noting that the sum of the geometric series is $1 + \phi _ { 1 } + \phi _ { 1 } ^ { 2 } + \phi _ { 1 } ^ { 3 } + \ldots = \frac { 1 } { 1 - \phi _ { 1 } }$ you finally arrive at $\sigma _ { t } ^ { 2 } = \frac { \alpha _ { 0 } } { 1 - \phi _ { 1 } } + \alpha _ { 1 } \left( u _ { t - 1 } ^ { 2 } + \phi _ { 1 } u _ { t - 2 } ^ { 2 } + \phi _ { 1 } ^ { 2 } u _ { t - 3 } ^ { 2 } + \phi _ { 1 } ^ { 3 } u _ { t - 4 } ^ { 2 } + \ldots \right)$. This expression states that the variances depend on a weighted average of past squared residuals, where the distant past receives a smaller weight than more recently observed squared residuals.

Question 3

The following is not an appropriate way to tell whether two variables are cointegrated

Accepted Answer

A) see if the two variables are integrated of the same order. 
B) graph the series and see whether they appear to have a common stochastic trend. 
C) perform statistical tests for cointegration. 
D) use expert knowledge and economic theory. 
A) see if the two variables are integrated of the same order. 
B) graph the series and see whether they appear to have a common stochastic trend. 
C) perform statistical tests for cointegration. 
D) use expert knowledge and economic theory. A

Question 4

A VAR allows you to test joint hypothesis that involve restrictions across multiple equations by

Accepted Answer

A) computing a z-statistic. 
B) computing the BIC but not the AIC. 
C) using a stability test. 
D) computing an F-statistic. 
A) computing a z-statistic. 
B) computing the BIC but not the AIC. 
C) using a stability test. 
D) computing an F-statistic.

Question 5

The following is not a consequence of  Xt  and  Yt  being cointegrated:

Accepted Answer

A)  if  $X _ { t }$  and  Yt  are both  I(1) , then for some $\theta , Y _ { t } - \theta X _ { t } \text { is } I ( 0 )$ 
B)  $X _ { t } \text { and } Y _ { t }$ have the same stochastic trend. 
C)  in the expression $Y _ { t } - \theta X _ { t } , \theta$ is called the cointegrating coefficient. 
D)  if $X _ { t } \text { and } Y _ { t }$ are cointegrated then integrating one of the variables gives you the same result as integrating the other. 
A)  if  $X _ { t }$  and  Yt  are both  I(1) , then for some $\theta , Y _ { t } - \theta X _ { t } \text { is } I ( 0 )$ 
B)  $X _ { t } \text { and } Y _ { t }$ have the same stochastic trend. 
C)  in the expression $Y _ { t } - \theta X _ { t } , \theta$ is called the cointegrating coefficient. 
D)  if $X _ { t } \text { and } Y _ { t }$ are cointegrated then integrating one of the variables gives you the same result as integrating the other.

Question 6

Using the ADL  (1,1)  regression $Y _ { t } = \beta _ { 0 } + \beta _ { 1 } Y _ { t - 1 } + \gamma _ { 1 } X _ { t - 1 } + u _ { t }$
the ARCH model for the regression error assumes that  ut  is normally distributed with mean zero and variance $\sigma _ { t } ^ { 2 }$ where

Accepted Answer

A)  $\sigma _ { t } ^ { 2 } = \alpha _ { 0 } + \alpha _ { 1 } u _ { t - 1 } ^ { 2 } + \alpha _ { 2 } u _ { t - 2 } ^ { 2 } + \ldots + \alpha _ { p } u _ { t - p } ^ { 2 }$ 
B)  $\sigma _ { t } ^ { 2 } = u _ { t - 1 } ^ { 2 } + \ldots + u _ { t - p } ^ { 2 } + \phi _ { 1 } \sigma _ { t - 1 } ^ { 2 } + \ldots + \phi _ { q } \sigma _ { t - q } ^ { 2 }$ 
C)  $\sigma _ { t } ^ { 2 } = \phi _ { 1 } \sigma _ { t - 1 } ^ { 2 } + \ldots + \phi _ { q } \sigma _ { t - q } ^ { 2 }$ 
D)  $\sigma _ { t } ^ { 2 } = \alpha _ { 0 } + \alpha _ { 1 } u _ { t - 1 } ^ { 2 } + \ldots + \alpha _ { p } u _ { t - p } ^ { 2 } + \phi _ { 1 } \sigma _ { t - 1 } ^ { 2 } + \ldots + \phi _ { q } \sigma _ { t - q } ^ { 2 }$ 
A)  $\sigma _ { t } ^ { 2 } = \alpha _ { 0 } + \alpha _ { 1 } u _ { t - 1 } ^ { 2 } + \alpha _ { 2 } u _ { t - 2 } ^ { 2 } + \ldots + \alpha _ { p } u _ { t - p } ^ { 2 }$ 
B)  $\sigma _ { t } ^ { 2 } = u _ { t - 1 } ^ { 2 } + \ldots + u _ { t - p } ^ { 2 } + \phi _ { 1 } \sigma _ { t - 1 } ^ { 2 } + \ldots + \phi _ { q } \sigma _ { t - q } ^ { 2 }$ 
C)  $\sigma _ { t } ^ { 2 } = \phi _ { 1 } \sigma _ { t - 1 } ^ { 2 } + \ldots + \phi _ { q } \sigma _ { t - q } ^ { 2 }$ 
D)  $\sigma _ { t } ^ { 2 } = \alpha _ { 0 } + \alpha _ { 1 } u _ { t - 1 } ^ { 2 } + \ldots + \alpha _ { p } u _ { t - p } ^ { 2 } + \phi _ { 1 } \sigma _ { t - 1 } ^ { 2 } + \ldots + \phi _ { q } \sigma _ { t - q } ^ { 2 }$

Question 7

The error term in a multiperiod regression

Accepted Answer

A) is serially correlated. 
B) causes OLS to be inconsistent. 
C) is serially correlated, but less so the longer the forecast horizon. 
D) is serially uncorrelated. 
A) is serially correlated. 
B) causes OLS to be inconsistent. 
C) is serially correlated, but less so the longer the forecast horizon. 
D) is serially uncorrelated.

Question 8

Some macroeconomic theories suggest that there is a short-run relationship between the
inflation rate and the unemployment rate.How would you go about forecasting these two
variables? Suggest various alternatives and discuss their advantages and disadvantages.

Accepted Answer

There are various methods available for

Question 9

Assume that you have used the OLS estimator in the cointegrating regression and test the residual for a unit root using an ADF test.The resulting ADF test statistic has a

Accepted Answer

A) normal distribution in large samples. 
B) non-normal distribution which require ADF critical values for inference. 
C) non-normal distribution which require EG-ADF critical values for inference. 
D) normal distribution when HAC standard errors are used. 
A) normal distribution in large samples. 
B) non-normal distribution which require ADF critical values for inference. 
C) non-normal distribution which require EG-ADF critical values for inference. 
D) normal distribution when HAC standard errors are used.

Question 10

The biggest conceptual difference between using VARs for forecasting and using them for structural modeling is that

Accepted Answer

A) you need to use the Granger causality test for structural modeling. 
B) structural modeling requires very specific assumptions derived from economic theory and institutional knowledge, of what is exogenous and what is not. 
C) you can no longer use the information criteria to decide on the lag length. 
D) structural modeling only allows a maximum of three equations in the VAR. 
A) you need to use the Granger causality test for structural modeling. 
B) structural modeling requires very specific assumptions derived from economic theory and institutional knowledge, of what is exogenous and what is not. 
C) you can no longer use the information criteria to decide on the lag length. 
D) structural modeling only allows a maximum of three equations in the VAR.

Question 11

Multiperiod forecasting with multiple predictors a. is the same as the iterated AR forecast method.
b. can use the iterated VAR forecast method.
c. will yield superior results when using the multiperiod regression forecast $h$ periods into the future based on $p$ lags of each $Y _ { t }$, rather than the iterated VAR forecast method.
d. will always yield superior results using the interated VAR since it takes all equations into account.

Accepted Answer

The answer of Multiperiod forecasting with multiple predictors a. is...

Question 12

Your textbook states that there "are three ways to decide if two variables can plausibly be
modeled as cointegrated: use expert knowledge and economic theory, graph the series
and see whether they appear to have a common stochastic trend, and perform statistical
tests for cointegration.All three ways should be used in practice." Accordingly you set
out to check whether (the log of)consumption and (the log of)personal disposable
income are cointegrated.You collect data for the sample period 1962:I to 1995:IV and
plot the two variables.   (a)Using the first two methods to examine the series for cointegration, what do you think the
likely answer is?

Accepted Answer

The t-statistic on the null hy

Question 13

The order of integration a. can never be zero.
b. is the number of times that the series needs to be differenced for it to be stationary.
c. is the value of $\phi _ { 1 }$ in the quasi difference $\left( \Delta Y _ { t } - \phi _ { 1 } Y _ { t - 1 } \right)$.
d. depends on the number of lags in the VAR specification.

Accepted Answer

The answer of The order of integration a. can never...

Question 14

The DOLS estimator has the following property if $X _ { t } \text { and } Y _ { t }$
are cointegrated:

Accepted Answer

A)  it is BLUE even in small samples. 
B)  it is efficient in large samples. 
C)  it has a standard normal distribution when homoskedasticity-only standard errors are used. 
D)  it has a non-normal distribution in large samples when HAC standard errors are used. 
A)  it is BLUE even in small samples. 
B)  it is efficient in large samples. 
C)  it has a standard normal distribution when homoskedasticity-only standard errors are used. 
D)  it has a non-normal distribution in large samples when HAC standard errors are used.

Question 15

If Yt is I(2), then a. $\Delta ^ { 2 } Y _ { t }$ is stationary.
b. $Y _ { t }$ has a unit autoregressive root.
c. $\Delta Y _ { t }$ is stationary.
d. $Y _ { t }$ is stationary.

Accepted Answer

The answer of If Yt is I(2), then a. \(\Delta...

Question 16

Consider the following model $Y _ { t } = \beta _ { 0 } + \beta _ { 1 } X _ { t } + \beta _ { 2 } X _ { t - 1 } + \beta _ { 3 } Y _ { t - 1 } + u _ { t } \text {, where } X _ { t }$ is strictly
exogenous. Show that by imposing the restriction $\sum _ { i = 1 } ^ { 3 } \beta _ { i } = 1$ you can derive the following so-called Error Correction Mechanism (ECM) model
$\Delta Y _ { t } = \beta _ { 0 } + \beta _ { 1 } \Delta X _ { t } - \theta ( Y - X ) _ { t - 1 } + u _ { t }$
where $\theta = \beta _ { 1 } + \beta _ { 2 }$
What is the short-run (impact) response of a unit increase in  X ?  What is the long-run solution? Why do you think the term in parenthesis in the above expression is called ECM?

Accepted Answer

Starting with 11ec79e8_5240_bb2f_8839_c9

Question 17

Think of at least five examples from economics where theory suggests that the variables
involved are cointegrated.For one of these cases, explain how you would test for
cointegration between the variables involved and how you could use this information to
improve forecasting.

Accepted Answer

Answers will vary by student, but given

Question 18

In a VECM, a. past values of $Y _ { t } - \theta X _ { t }$ help to predict future values of $\Delta Y _ { t }$ and/or $\Delta X _ { t }$.
b. errors are corrected for serial correlation using the Cochrane-Orcutt method.
c. current values of $Y _ { t } - \theta X _ { t }$ help to predict future values of $\Delta Y _ { t }$ and/or $\Delta X _ { t }$.
d. VAR techniques, such as information criteria, no longer apply.

Accepted Answer

The answer of In a VECM, a. past values of...

Question 19

A multiperiod regression forecast h periods into the future based on an AR(p)is computed a. the same way as the iterated AR forecast.
b. by estimating the multiperiod regression $Y _ { t } = \delta _ { 0 } + \delta _ { 1 } Y _ { t - h } + \ldots + \delta _ { p } Y _ { t - p - h + 1 } + u _ { t }$, then using the estimated coefficients to compute the forecast $h$ periods in advance.
c. by estimating the multiperiod regression $Y _ { t } = \delta _ { 0 } + \delta _ { 1 } Y _ { t - h } + u _ { t }$, then using the estimate coefficients to comput the forecast h period in advance.
d. by first computing the one-period ahead forecast, next using that to compute the two-period ahead forecast, and so forth.

Accepted Answer

The answer of A multiperiod regression forecast h periods into...

Question 20

Purchasing power parity (PPP), postulates that the exchange rate between two countries equals the ratio of the respective price indexes or ExchRate $= \frac { P ^ { f } } { P }$ (where ExchRate is the foreign exchange rate between the two countries, and $P$ represents the price index, with $f$ indicating the foreign country). The long-run version of PPP implies that that the exchange rate and the price ratio share a common trend. (a) You collect monthly foreign exchange rate data from 1974:1 to 2002:4 for the U.S./U.K. exchange rate $( \$ / £ )$ and you collect data on the Consumer Price Index for both countries. Explain how you would used the Engle-Granger test statistic to investigate the long-run PPP hypothesis.

Accepted Answer

The answer of Purchasing power parity (PPP), postulates that the...

If $X _ { t } \text { and } Y _ { t }$ are cointegrated, then the OLS estimator of the coefficient in the cointegrating regression is

The following is not an appropriate way to tell whether two variables are cointegrated

A VAR allows you to test joint hypothesis that involve restrictions across multiple equations by

The following is not a consequence of X_t and Y_t being cointegrated:

Using the ADL (1,1) regression $Y _ { t } = \beta _ { 0 } + \beta _ { 1 } Y _ { t - 1 } + \gamma _ { 1 } X _ { t - 1 } + u _ { t }$ the ARCH model for the regression error assumes that u_t is normally distributed with mean zero and variance $\sigma _ { t } ^ { 2 }$ where

The error term in a multiperiod regression

Some macroeconomic theories suggest that there is a short-run relationship between the inflation rate and the unemployment rate.How would you go about forecasting these two variables? Suggest various alternatives and discuss their advantages and disadvantages.

Assume that you have used the OLS estimator in the cointegrating regression and test the residual for a unit root using an ADF test.The resulting ADF test statistic has a

The biggest conceptual difference between using VARs for forecasting and using them for structural modeling is that

The DOLS estimator has the following property if $X _ { t } \text { and } Y _ { t }$ are cointegrated:

If Yt is I(2), then a. $\Delta ^ { 2 } Y _ { t }$ is stationary. b. $Y _ { t }$ has a unit autoregressive root. c. $\Delta Y _ { t }$ is stationary. d. $Y _ { t }$ is stationary.

Think of at least five examples from economics where theory suggests that the variables involved are cointegrated.For one of these cases, explain how you would test for cointegration between the variables involved and how you could use this information to improve forecasting.

Economic Questions and Data

Review of Probability

Review of Statistics

Linear Regression With One Regressor

Regression With a Single Regressor: Hypothesis Tests and Confidence Intervals

Linear Regression With Multiple Regressors

Hypothesis Tests and Confidence Intervals in Multiple Regression

Nonlinear Regression Functions

Assessing Studies Based on Multiple Regression

Regression With Panel Data

Regression With a Binary Dependent Variable

Instrumental Variables Regression

Experiments and Quasi-Experiments

Introduction to Time Series Regression and Forecasting

Estimation of Dynamic Causal Effects

The Theory of Linear Regression With One Regressor

The Theory of Multiple Regression

Filters

Exam 16: Additional Topics in Time Series Regression

If Xt and YtX _ { t } \text { and } Y _ { t }Xt​ and Yt​ are cointegrated, then the OLS estimator of the coefficient in the cointegrating regression is

The following is not an appropriate way to tell whether two variables are cointegrated

A VAR allows you to test joint hypothesis that involve restrictions across multiple equations by

The following is not a consequence of Xt and Yt being cointegrated:

The error term in a multiperiod regression

Some macroeconomic theories suggest that there is a short-run relationship between the inflation rate and the unemployment rate.How would you go about forecasting these two variables? Suggest various alternatives and discuss their advantages and disadvantages.

Assume that you have used the OLS estimator in the cointegrating regression and test the residual for a unit root using an ADF test.The resulting ADF test statistic has a

The biggest conceptual difference between using VARs for forecasting and using them for structural modeling is that

The DOLS estimator has the following property if Xt and YtX _ { t } \text { and } Y _ { t }Xt​ and Yt​ are cointegrated:

If Yt is I(2), then a. Δ2Yt\Delta ^ { 2 } Y _ { t }Δ2Yt​ is stationary. b. YtY _ { t }Yt​ has a unit autoregressive root. c. ΔYt\Delta Y _ { t }ΔYt​ is stationary. d. YtY _ { t }Yt​ is stationary.

Think of at least five examples from economics where theory suggests that the variables involved are cointegrated.For one of these cases, explain how you would test for cointegration between the variables involved and how you could use this information to improve forecasting.

Economic Questions and Data

Review of Probability

Review of Statistics

Linear Regression With One Regressor

Regression With a Single Regressor: Hypothesis Tests and Confidence Intervals

Linear Regression With Multiple Regressors

Hypothesis Tests and Confidence Intervals in Multiple Regression

Nonlinear Regression Functions

Assessing Studies Based on Multiple Regression

Regression With Panel Data

Regression With a Binary Dependent Variable

Instrumental Variables Regression

Experiments and Quasi-Experiments

Introduction to Time Series Regression and Forecasting

Estimation of Dynamic Causal Effects

The Theory of Linear Regression With One Regressor

The Theory of Multiple Regression

Filters

If $X _ { t } \text { and } Y _ { t }$ are cointegrated, then the OLS estimator of the coefficient in the cointegrating regression is

The following is not a consequence of X_t and Y_t being cointegrated:

The DOLS estimator has the following property if $X _ { t } \text { and } Y _ { t }$ are cointegrated:

If Yt is I(2), then a. $\Delta ^ { 2 } Y _ { t }$ is stationary. b. $Y _ { t }$ has a unit autoregressive root. c. $\Delta Y _ { t }$ is stationary. d. $Y _ { t }$ is stationary.