Question 1

Including a lagged dependent variable in an OLS model when autocorrelation exists will:

Accepted Answer

A)  Will lead to unbiased coefficients. 
B)  Will lead to biased coefficients. 
C)  Will lead to larger standard errors. 
D)  Will lead to smaller standard errors. 
A)  Will lead to unbiased coefficients. 
B)  Will lead to biased coefficients. 
C)  Will lead to larger standard errors. 
D)  Will lead to smaller standard errors. B

Question 2

Please describe the steps involved in diagnosing autocorrelation when using the graphical method.

Accepted Answer

Run a standard OLS model that ignores autocorrelation, and generate the residuals. These residuals are calculated as e_t =Y_t-β₀hat - β₁hatX_t (include all independent variables in regression). Then we graph these residuals over time. If the errors move slowly, then they are positively correlated, while if they bounce around violently, then they are negatively correlated. On the other hand, if we can't tell, then chances are that the errors are not correlated.

Question 3

Using equations, describe/show the steps needed to be undertaken in order to p-transform data.

Accepted Answer

1. Write an equation for the lagged value of $Y _ { t }$, which simply requires replacing the $t$ subscripts with $t - 1$ subscripts in the original model:
$Y _ { t - 1 } = \beta _ { 0 } + \beta _ { 1 } X _ { t - 1 } + \epsilon _ { t - 1 }$ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $(13.5)
2. Multiply both sides of Equation 13.5 by $\rho$ :
$\rho Y _ { t - 1 } = \rho \beta _ { 0 } + \rho \beta _ { 1 } X _ { t - 1 } + \rho \epsilon _ { t - 1 }$ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $(13.6) 3. Subtract the equation for $\rho Y _ { t - 1 }$ (Equation 13.6) from Equation 13.4. That is, subtract the left side of Equation 13.6 from the left side of Equation 13.4 and subtract the right side of 13.6 from the right side of Equation 13.4.
$$Y _ { t } - \rho Y _ { t - 1 } = \beta _ { 0 } - \rho \beta _ { 0 } + \beta _ { 1 } X _ { t } - \rho \beta _ { 1 } X _ { t - 1 } + \epsilon _ { t } - \rho \epsilon _ { t - 1 }$$
4. Notice in Equation 13.2 that $\epsilon _ { t } - \rho \epsilon _ { t - 1 } = \nu _ { t }$ and rewrite:
$$Y _ { t } - \rho Y _ { t - 1 } = \beta _ { 0 } - \rho \beta _ { 0 } + \beta _ { 1 } X _ { t } - \rho \beta _ { 1 } X _ { t - 1 } + \nu _ { t }$$
5. Rearrange things a bit:
$$Y _ { t } - \rho Y _ { t - 1 } = \beta _ { 0 } ( 1 - \rho ) + \beta _ { 1 } \left( X _ { t } - \rho X _ { t - 1 } \right) + \nu _ { t }$$
6. Use squiggles to indicate the transformed variables (where $\tilde { Y } _ { t } = Y _ { t } - \rho Y _ { t - 1 } , \tilde { \beta } _ { 0 } = \beta _ { 0 } ( 1 - \rho$ ) and $\left. \tilde { X } _ { t } = X _ { t } - \rho X _ { t - 1 } \right)$
$$\tilde { Y } _ { t } = \tilde { \beta } _ { 0 } + \beta _ { 1 } \tilde { X } _ { t } + \nu _ { t }$$

Question 4

Explain the three ways in which a dynamic model differs from a standard OLS model.

Accepted Answer

A) The interpretation of the coefficient

Question 5

Which of the following correctly states concerns about stationarity for the following model:
Yt = $\gamma$Yt-1 + $\beta$0 + $\beta$1Xt + $\varepsilon$t

Accepted Answer

A)  If $\gamma$$\lt$1, the model is stationary and spurious regression results are likely. 
B)  If $\gamma$=1, the model will "blow up" as Y will get larger and larger in every period. 
C)  If $\gamma$$\gt$ 1, the model will "blow up" as Y will get larger and larger in every period. 
D)  If $\gamma$=1, the model is stationary and spurious regression results are likely. 
A)  If $\gamma$$\lt$1, the model is stationary and spurious regression results are likely. 
B)  If $\gamma$=1, the model will "blow up" as Y will get larger and larger in every period. 
C)  If $\gamma$$\gt$ 1, the model will "blow up" as Y will get larger and larger in every period. 
D)  If $\gamma$=1, the model is stationary and spurious regression results are likely.

Question 6

One of the methods of dealing with non-stationary data is:

Accepted Answer

A)  Using a $\rho$-transformed model. 
B)  Using a dynamic model. 
C)  Using a regular OLS model while keeping non-stationarity in mind. 
D)  Using a differenced model. 
A)  Using a $\rho$-transformed model. 
B)  Using a dynamic model. 
C)  Using a regular OLS model while keeping non-stationarity in mind. 
D)  Using a differenced model.

Question 7

A stationary variable has:

Accepted Answer

A)  The same distribution over the entire time series. 
B)  The same distribution over each unit. 
C)  A different distribution over the entire time series. 
D)  A different distribution over each unit. 
A)  The same distribution over the entire time series. 
B)  The same distribution over each unit. 
C)  A different distribution over the entire time series. 
D)  A different distribution over each unit.

Question 8

The interpretation of the coefficient in a $\rho$ transformed model is the same as in a regular OLS model.

Accepted Answer

A) True 
 B)False

Question 9

Describe how you interpret the coefficient results in a dynamic model.

Accepted Answer

Independent variables have sho

Question 10

One way to detect autocorrelation is to graph the residuals from a standard OLS model over time.

Accepted Answer

A) True 
 B)False

Question 11

We face the largest risk of getting a spurious result when:

Accepted Answer

A)  Regressing a variable with a unit root against a variable without a unit root. 
B)  Regressing a variable with a unit root against a variable with a unit root. 
C)  Regressing a variable with $\gamma$$\lt$1 
D)  When errors are autocorrelated. 
A)  Regressing a variable with a unit root against a variable without a unit root. 
B)  Regressing a variable with a unit root against a variable with a unit root. 
C)  Regressing a variable with $\gamma$$\lt$1 
D)  When errors are autocorrelated.

Question 12

In time series data, if errors are correlated over time, than B1hat is biased.

Accepted Answer

A) True 
 B)False

Question 13

In autoregressive models, the dependent variable depends directly on the value of the dependent variable in the previous period.

Accepted Answer

A) True 
 B)False

Question 14

Which of the following is one way to detect autocorrelation?

Accepted Answer

A)  Estimate a standard OLS model and look at sign of coefficient. 
B)  Graph the residuals over time. 
C)  Estimate an auxiliary regression where the value of X is the dependent variable and the lagged value of X is the independent variable. 
D)  Estimate an auxiliary regression where the value of e (the residual) is the dependent variable and the lagged value of X is the independent variable. 
A)  Estimate a standard OLS model and look at sign of coefficient. 
B)  Graph the residuals over time. 
C)  Estimate an auxiliary regression where the value of X is the dependent variable and the lagged value of X is the independent variable. 
D)  Estimate an auxiliary regression where the value of e (the residual) is the dependent variable and the lagged value of X is the independent variable.

Question 15

Which of the following is the correct final equation for a p transformed model?

Accepted Answer

A)  Yt = B0(1-$\rho$) +B1(Xt-$\rho$Xt-1) + vt 
B)  Yt-$\rho$Yt-1 = B0(1-p) +B1(Xt-$\rho$Xt-1) + vt 
C)  Yt-$\rho$Yt-1 = B0 + B1(Xt-$\rho$ Xt-1) + vt 
D)  Yt-$\rho$Yt-1 = B0(1-$\rho$) + B1Xt + vt 
A)  Yt = B0(1-$\rho$) +B1(Xt-$\rho$Xt-1) + vt 
B)  Yt-$\rho$Yt-1 = B0(1-p) +B1(Xt-$\rho$Xt-1) + vt 
C)  Yt-$\rho$Yt-1 = B0 + B1(Xt-$\rho$ Xt-1) + vt 
D)  Yt-$\rho$Yt-1 = B0(1-$\rho$) + B1Xt + vt

Question 16

Which of the following is the most serious problem that can arise when dealing with non-stationary data with a unit-root?

Accepted Answer

A)  The estimates for the variance of the coefficient are wrong. 
B)  Regression could give us spurious results. 
C)  Heteroscedastic errors 
D)  A low R2. 
A)  The estimates for the variance of the coefficient are wrong. 
B)  Regression could give us spurious results. 
C)  Heteroscedastic errors 
D)  A low R2.

Question 17

Which of the following is a consequence of failing to use a $\rho$-transformed model when errors are correlated?

Accepted Answer

A)  Produces biased coefficient estimates. 
B)  Produces incorrect standard errors. 
C)  Produces coefficient estimates that cannot be interpreted. 
D)  Produces consistent coefficient estimates. 
A)  Produces biased coefficient estimates. 
B)  Produces incorrect standard errors. 
C)  Produces coefficient estimates that cannot be interpreted. 
D)  Produces consistent coefficient estimates.

Question 18

The interpretation of the coefficient in a dynamic model is the same as in a regular OLS model.

Accepted Answer

A) True 
 B)False

Question 19

Which of the following is not a way in which dynamic models differ from OLS?

Accepted Answer

A)  Different interpretation of the coefficient. 
B)  Correlated errors cause bias in dynamic models. 
C)  Will have smaller standard errors than OLS. 
D)  Coefficients can be biased if an irrelevant lagged variable is included. 
A)  Different interpretation of the coefficient. 
B)  Correlated errors cause bias in dynamic models. 
C)  Will have smaller standard errors than OLS. 
D)  Coefficients can be biased if an irrelevant lagged variable is included.

Question 20

Time series data is data for many units at a given point in time.

Accepted Answer

A) True 
 B)False

Including a lagged dependent variable in an OLS model when autocorrelation exists will:

Please describe the steps involved in diagnosing autocorrelation when using the graphical method.

Using equations, describe/show the steps needed to be undertaken in order to p-transform data.

Explain the three ways in which a dynamic model differs from a standard OLS model.

Which of the following correctly states concerns about stationarity for the following model: Y_t = $\gamma$ Y_t-1+ $\beta$ ₀+ $\beta$ ₁X_t+ $\varepsilon$ _t

One of the methods of dealing with non-stationary data is:

A stationary variable has:

The interpretation of the coefficient in a $\rho$ transformed model is the same as in a regular OLS model.

Describe how you interpret the coefficient results in a dynamic model.

One way to detect autocorrelation is to graph the residuals from a standard OLS model over time.

We face the largest risk of getting a spurious result when:

In time series data, if errors are correlated over time, than B1hat is biased.

In autoregressive models, the dependent variable depends directly on the value of the dependent variable in the previous period.

Which of the following is one way to detect autocorrelation?

Which of the following is the correct final equation for a p transformed model?

Which of the following is the most serious problem that can arise when dealing with non-stationary data with a unit-root?

Which of the following is a consequence of failing to use a $\rho$ -transformed model when errors are correlated?

The interpretation of the coefficient in a dynamic model is the same as in a regular OLS model.

Which of the following is not a way in which dynamic models differ from OLS?

Time series data is data for many units at a given point in time.

The Quest for Causality

Stats in the Wild: Good Data Practices

Bivariate Ols: the Foundation of Econometric Analysis

Hypothesis Testing and Interval Estimation: Answering Research Questions

Multivariate Ols: Where the Action Is

Dummy Variables: Smarter Than You Think

Specifying Models

Using Fixed Effects to Fight Endogeneity in Panel Data and Difference-In-Difference Models

Instrumental Variables: Using Exogenous Variation to Fight Endogeneity

Experiments: Dealing With Real-World Challenges

Regression Discontinuity: Looking for Jumps in Data

Dummy Dependent Variables

Advanced Ols

Advanced Panel Data

Filters

Exam 13: Time Series: Dealing With Stickiness Over Time

Including a lagged dependent variable in an OLS model when autocorrelation exists will:

Please describe the steps involved in diagnosing autocorrelation when using the graphical method.

Using equations, describe/show the steps needed to be undertaken in order to p-transform data.

Explain the three ways in which a dynamic model differs from a standard OLS model.

Which of the following correctly states concerns about stationarity for the following model: Yt = γ\gammaγ Yt-1 + β\betaβ 0 + β\betaβ 1Xt + ε\varepsilonε t

One of the methods of dealing with non-stationary data is:

A stationary variable has:

The interpretation of the coefficient in a ρ\rhoρ transformed model is the same as in a regular OLS model.

Describe how you interpret the coefficient results in a dynamic model.

One way to detect autocorrelation is to graph the residuals from a standard OLS model over time.

We face the largest risk of getting a spurious result when:

In time series data, if errors are correlated over time, than B1hat is biased.

In autoregressive models, the dependent variable depends directly on the value of the dependent variable in the previous period.

Which of the following is one way to detect autocorrelation?

Which of the following is the correct final equation for a p transformed model?

Which of the following is the most serious problem that can arise when dealing with non-stationary data with a unit-root?

Which of the following is a consequence of failing to use a ρ\rhoρ -transformed model when errors are correlated?

The interpretation of the coefficient in a dynamic model is the same as in a regular OLS model.

Which of the following is not a way in which dynamic models differ from OLS?

Time series data is data for many units at a given point in time.

The Quest for Causality

Stats in the Wild: Good Data Practices

Bivariate Ols: the Foundation of Econometric Analysis

Hypothesis Testing and Interval Estimation: Answering Research Questions

Multivariate Ols: Where the Action Is

Dummy Variables: Smarter Than You Think

Specifying Models

Using Fixed Effects to Fight Endogeneity in Panel Data and Difference-In-Difference Models

Instrumental Variables: Using Exogenous Variation to Fight Endogeneity

Experiments: Dealing With Real-World Challenges

Regression Discontinuity: Looking for Jumps in Data

Dummy Dependent Variables

Advanced Ols

Advanced Panel Data

Filters

Which of the following correctly states concerns about stationarity for the following model: Y_t = $\gamma$ Y_t-1+ $\beta$ ₀+ $\beta$ ₁X_t+ $\varepsilon$ _t

The interpretation of the coefficient in a $\rho$ transformed model is the same as in a regular OLS model.

Which of the following is a consequence of failing to use a $\rho$ -transformed model when errors are correlated?