WorksheetsRegression with Time-Series Data [2]
Total questions: 20
Worksheet time: 2hrs 40mins
If you are estimating y = β1 + β2x + e and realize x and y are both random variables, what condition must be true for simple regression estimators to be BLUE?
The data have been collected via random sampling.
The data are time series data.
e is normally distributed.
x is normally distributed.
Which assumption must be true when E(e|x) = 0?
E(e) = 0 and var(e) = σ2
e = 0
E(e) = 0 and cov(x,e) = 0
E(e) = e|x if x≠0
If the assumption E(e) = 0 and cov(x,e) = 0 holds, what are the implications of least squares estimators?
Unbiased, but not BLUE for small samples
Still BLUE for all sample sizes
Inconsistent; parameter estimates do not converge to true values regardless of sample size
Consistent and normally distributed in very large sample sizes
If the assumption that cov(x,e) = 0 is not true, what are the implications of least squares estimators?
Unbiased, but not BLUE for small samples
Still BLUE for all sample sizes
Inconsistent; parameter estimates do not converge to true values regardless of sample size
Consistent and normally distributed in very large sample sizes
Which of the following is not a common cause of endogeneity?
Measurement error
Simultaneous equations
Omitted variables
Continuous variables
When an exogenous instrument is used, IV estimators are
Consistent and approximately normally distributed in large samples
Unbiased and BLUE in all sample sizes
Consistent if z is normally distributed
Normally distributed in all sample sizes and consistent in large sample sizes
If you reject the null hypothesis when performing a Hausman test, what should you conclude?
At least one of the explanatory variables is endogenous.
There are no endogenous variables.
The 2SLS estimation has corrected the endogeneity in the initial model.
The 2SLS second stage equation still has endogenous variables.
A stochastic process is best described as _____.
deterministic
theoretical
random
mean reverting
Which non-stationary time series has a constant mean but non-constant variance?
Random walk
AR(1) with linear trend
Random walk with drift
Deterministic trend
What is a spurious regression?
Statistically significant but meaningless results generated by regression analysis of non-stationary data
The results generated by regression analysis of a station variable dependent on a non-stationary series
Regression analysis where endogenous and exogenous variables are reversed
Regression analysis that is impossible due to lack of identification
What is the alternative hypothesis of the Dickey-Fuller Test for testing with a constant and a trend?
yt=yt−1+vt
yt=ρyt−1+vt
yt=α+ρyt−1+vt
yt=α+ρyt−1+vt+λt
Why should augmented Dickey-Fuller tests always be used when performing econometric analysis?
To confirm that error terms are not autocorrelated.
The augmented tests allow for more degrees of freedom.
So that we can test hypotheses using a t-distribution.
Because no assumptions about the sign of ρ are needed to perform a one- tailed test.
What does it mean for a series to have a unit root?
It has a constant mean equal to 1.
It has a constant variance equal to 1.
It has a stochastic trend and is nonstationary.
It is integrated of order 1.
If series y and z have similar stochastic trends, but are otherwise unrelated, they are said to be _____.
cointegrated
jointly stationary
converging
cotrending
The minimum number of times a series must be differenced to generate a stationary series is the _____.
unit root
order of integration
spurious regression degree
trend coefficient
How do you check for cointegration of two series?
Estimate a regression of one as a function of the other and test the significance of the parameter estimates.
Test the significance of the covariance between the two series.
Subtract one series from the other and check for stationarity of the difference.
Estimate a regression of one series as a function of the other, then perform an augmented Dickey-Fuller test on estimated residuals.
Suppose you have two series that you have tested and have found them to be cointegrated. You are interested in explaining the dynamics of the relative short- run movements of the series. Which of the following estimation choices should you use?
An ARDL model in levels
A simple regression model with least squares
An error-correction model
An ARDL model in first-differences
Suppose you have two series that you have tested and have found to contain a stochastic trend but failed to find any evidence that they are cointegrated. Which of the following estimation choices should you use?
An ARDL model in levels
An ARDL model in first-differences
An error-correction model
A simple regression model with least squares
Which of the following is a common way to convert a series with a stochastic trend to a stationary series?
First differencing
Cointegrating
Running a spurious regression
Estimating distributed lags
An ARDL model with nonstationary variables is _____.
a variance decomposition
a VAR
a VEC
an error correction model
