Final- Econ470

A VAR with five variables, 4 lags and constant terms for each equation will have a total of Select one: A. 84 coefficients. B. 21 coefficients. C. 105 coefficients. D. 100 coefficients.

105 coefficients.

To choose the number of lags in either an autoregression or in a time series regression model with multiple predictors, you can use any of the following test statistics with the exception of the Select one: A. Bayes Information Criterion. B. F-statistic. C. Augmented Dickey-Fuller test. D. Akaike Information Criterion.

Augmented Dickey-Fuller test.

The formulae for the AIC and the BIC are different. The Select one: A. AIC will typically underestimate p with non-zero probability B. BIC is preferred because it is a consistent estimator of the lag length C. difference is irrelevant in practice since both information criteria lead to the same conclusion D. AIC is preferred because it is easier to calculate

BIC is preferred because it is a consistent estimator of the lag length

This is the output of a VAR(4,4) between inflation and unemployment: VAR system, lag order 4 OLS estimates, observations 1960:2-1999:4 (T = 159) Log-likelihood = 688.07245 Determinant of covariance matrix = 5.9735546e-07 AIC = -8.4286 BIC = -8.0812 HQC = -8.2875 Portmanteau test: LB(39) = 141.403, df = 140 [0.4509] Equation 1: d_LHUR coefficient std. error t-ratio p-value -------------------------------------------------------------- const −0.116196 0.0378731 −3.068 0.0026 *** d_LHUR_1 0.620263 0.0788278 7.869 6.58e-13 *** d_LHUR_2 −0.000728463 0.0976435 −0.007460 0.9941 d_LHUR_3 −0.0547470 0.0974852 −0.5616 0.5752 d_LHUR_4 −0.134874 0.0754216 −1.788 0.0758 * ld_PUNEW_1 17.1756 5.60628 3.064 0.0026 *** ld_PUNEW_2 −13.8426 6.46331 −2.142 0.0338 ** ld_PUNEW_3 5.50424 6.30396 0.8731 0.3840 ld_PUNEW_4 1.55057 5.68203 0.2729 0.7853 Mean dependent var −0.006499 S.D. dependent var 0.332118 Sum squared resid 8.781049 S.E. of regression 0.241951 R-squared 0.496145 Adjusted R-squared 0.469273 F(8, 150) 18.46308 P-value(F) 4.56e-19 rho 0.047451 Durbin-Watson 1.881521 F-tests of zero restrictions: All lags of d_LHUR F(4, 150) = 22.755 [0.0000] All lags of ld_PUNEW F(4, 150) = 5.7776 [0.0002] All vars, lag 4 F(2, 150) = 1.5990 [0.2055] Equation 2: ld_PUNEW coefficient std. error t-ratio p-value ------------------------------------------------------------ const 0.000177139 0.000531998 0.3330 0.7396 d_LHUR_1 −0.00632881 0.00110728 −5.716 5.71e-08 *** d_LHUR_2 0.00283530 0.00137159 2.067 0.0404 ** d_LHUR_3 0.000898540 0.00136936 0.6562 0.5127 d_LHUR_4 −0.00307946 0.00105944 −2.907 0.0042 *** ld_PUNEW_1 0.641591 0.0787507 8.147 1.35e-13 *** ld_PUNEW_2 0.115388 0.0907893 1.271 0.2057 ld_PUNEW_3 0.305335 0.0885509 3.448 0.0007 *** ld_PUNEW_4 −0.0795958 0.0798147 −0.9973 0.3202 Mean dependent var 0.010983 S.D. dependent var 0.007751 Sum squared resid 0.001733 S.E. of regression 0.003399 R-squared 0.817493 Adjusted R-squared 0.807759 F(8, 150) 83.98565 P-value(F) 1.65e-51 rho −0.000260 Durbin-Watson 1.993884 F-tests of zero restrictions: All lags of d_LHUR F(4, 150) = 9.8933 [0.0000] All lags of ld_PUNEW F(4, 150) = 163.42 [0.0000] All vars, lag 4 F(2, 150) = 5.2729 [0.0061] For the system as a whole: Null hypothesis: the longest lag is 3 Alternative hypothesis: the longest lag is 4 Likelihood ratio test: Chi-square(4) = 14.9531 [0.0048] Comparison of information criteria: Lag order 4: AIC = -8.42858, BIC = -8.08116, HQC = -8.28750 Lag order 3: AIC = -8.38485, BIC = -8.11464, HQC = -8.27512 Select one: A. Both variables Granger cause each-other B. None of the variables Granger causes the other C. An Engle-Granger causality test shows that Inflation Granger causes Unemployment but not viceversa D. An Engle-Granger causality test shows that Unemployment Granger causes Inflation but not viceversa

Both variables Granger cause each-other

Which measure assesses predictive accuracy? Select one: A. SBC (or BIC) B. AIC C. MAFE (Mean Absolute Forecast Error) D. Ljung-Box

MAFE (Mean Absolute Forecast Error)

Having learned in macroeconomics that consumption depends on disposable income, you want to determine whether or not disposable income helps predict future consumption. You collect data for the sample period 1962:I to 1995:IV and plot the two variables. (a) To determine whether or not past values of personal disposable income growth rates help to predict consumption growth rates, you estimate the following relationship. t = 1.695 + 0.126 △LnC t-1 + 0.153 △LnC t-2 , (0.484) (0.099) (0.103) + 0.294 △ LnC t-3 - 0.008 △ LnC t-4 (0.103) (0.102) + 0.088 △ LnY t-1 - 0.031 △ LnY t-2 - 0.050 △LnY t-3 - 0.091 △LnY t-4 (0.076) (0.078) (0.078) (0.074) The Granger causality test for the exclusion on all four lags of the GDP growth rate is 0.98. The critical values for F(4,∞) at the 1%, the 5%, and the 10% level are 3.32, 2.37, and 1.94, respectively. Make a decision on whether or not these additional variables Granger cause the change in the growth rate of consumption. Select one: A. You do not have sufficient information to answer the question. B. No, disposable income does not Granger cause consumption. C. Yes, disposable income Granger causes consumption. D. You should use instead the critical values from the t-distribution.

No, disposable income does not Granger cause consumption.

For Yi = ß0 + ß1Xi + ui, when the estimated slope coefficient in the simple regression model, ˆß1, is zero, then a. R2 =Y. b. 0 < R2 < 1. c. R2 = 0. d. R2 > (SSR/TSS).

R2 = 0.

The lag length in a VAR using the BIC proceeds as follows: Among a set of candidate values of p, the estimated lag length xxxis the value of p Select one: A. That maximizes BIC(p) B. Cannot be determined here since a VAR is a system of equations, not a single one C. For which the BIC exceeds the AIC D. That minimizes BIC(p)

That minimizes BIC(p)

The ADL(p,q) model is represented by the following equation

Yt = β0 + β1Yt-1 + β2Yt-2 + ... + βpYt-p + δ1Xt-1 + δ2Xt-2 + ... + δqXt-q + ut.

The time interval between observations can be all of the following with the exception of data collected Select one: A. bi-weekly. B. across firms. C. by decade. D. daily.

across firms.

In multiple regression, the R2 increases whenever a regressor is a. added unless the coefficient on the added regressor is exactly zero. b. added. c. added unless there is heterosckedasticity. d. greater than 1.96 in absolute value

added unless the coefficient on the added regressor is exactly zero.

Negative autocorrelation in the change of a variable implies that Select one: A. the series is not stable. B. an increase in the variable in one period is, on average, associated with a decrease in the next. C. the variable contains only negative values. D. the data is negatively trended.

an increase in the variable in one period is, on average, associated with a decrease in the next.

Pseudo out of sample forecasting can be used for the following reasons with the exception of A. evaluating the relative forecasting performance of two or more forecasting models. B. estimating the RMSFE. C. analyzing whether or not a time series contains a unit root. D. giving the forecaster a sense of how well the model forecasts at the end of the sample.

analyzing whether or not a time series contains a unit root.

The first difference of the logarithm of Y t equals Select one: A. approximately the growth rate of Y when the growth rate is small. B. the first difference of Y. C. the difference between the lead and the lag of Y. D. the growth rate of Y exactly.

approximately the growth rate of Y when the growth rate is small.

A multiperiod regression forecast h periods into the future based on an AR(p) is computed Select one: A. by estimating the multiperiod regression Yt = δ 0 + δ 1 Yt -h + ut , then using the estimate coefficients to compute the forecast h period in advance. B. the same way as the iterated AR forecast. C. by first computing the one-period ahead forecast, next using that to compute the two-period ahead forecast, and so forth. D. by estimating the multiperiod regression Yt = δ 0 + δ 1 Yt -h + ... + δpYt -p-h+1 + ut , then using the estimated coefficients to compute the forecast h periods in advance.

by estimating the multiperiod regression Yt = δ 0 + δ 1 Yt -h + ... + δpYt -p-h+1 + ut , then using the estimated coefficients to compute the forecast h periods in advance.

You can determine the lag lengths in a VAR Select one: A. with the help from economic theory and institutional knowledge. B. by using either F-tests or information criteria. C. by using confidence intervals. D. by using critical values from the standard normal table.

by using either F-tests or information criteria.

Multiperiod forecasting with multiple predictors Select one: A. can use the iterated VAR forecast method. B. will yield superior results when using the multiperiod regression forecast h periods into the future based on p lags of each Yt , rather than the iterated VAR forecast method. C. will always yield superior results using the iterated VAR since it takes all equations into account. D. is the same as the iterated AR forecast method.

can use the iterated VAR forecast method.

Unit root tests Select one: A. use the standard normal distribution since they are based on the t-statistic. B. can use the standard normal distribution only when testing that the level variable is stationary, but not the difference variable. C. cannot use the standard normal distribution for statistical inference. As a result the ADF statistic has its own special table of critical values. D. can use the standard normal distribution but only if HAC standard errors were computed.

cannot use the standard normal distribution for statistical inference. As a result the ADF statistic has its own special table of critical values.

The j th autocorrelation coefficient is defined as

cov(Yt, Ty-j) / √var(Yt)var(Yt-j)

The OLS estimator is derived by a. connecting the Yi corresponding to the lowest Xi observation with the Yi corresponding to the highest Xi observation. b. making sure that the standard error of the regression equals the standard error of the slope estimator. c. minimizing the sum of absolute residuals. d. minimizing the sum of squared residuals.

d. minimizing the sum of squared residuals.

The coefficients of the VAR are estimated by Select one: A. estimating each of the equations by OLS. B. using a simultaneous estimation method such as TSLS. C. panel methods. D. maximum likelihood.

estimating each of the equations by OLS.

The following is not a consequence of Xt and Yt being cointegrated: Select one: A. Xt and Yt have the same stochastic trend. B. in the expression Yt - θ Xt , θ is called the cointegrating coefficient. C. if Xt and Yt are cointegrated then integrating one of the variables gives you the same result as integrating the other. D. if Xt and Yt are both I(1), then for some θ, Yt - θ Xt is I(0).

if Xt and Yt are cointegrated then integrating one of the variables gives you the same result as integrating the other.

If a "break" occurs in the population regression function, then Select one: A. this suggests the presence of a deterministic trend in addition to a stochastic trend. B. forecasting, but not inference, is unaffected, if the break occurs during the first half of the sample period. C. an Augmented Dickey Fuller test, rather than the Dickey Fuller test, should be used to test for stationarity. D. inference and forecasting are compromised when neglecting it.

inference and forecasting are compromised when neglecting it.

A vector autoregression Select one: A. involves errors that are autocorrelated but can be written in vector format. B. is the ADL model with an AR process in the error term. C. is the same as a univariate autoregression. D. is a set of k time series regressions, in which the regressors are lagged values of all k series.

is a set of k time series regressions, in which the regressors are lagged values of all k series.

The Augmented Dickey Fuller (ADF) t-statistic Select one: A. is a two-sided test. B. has the identical distribution whether or not a trend is included or not. C. has a normal distribution in large samples. D. is an extension of the Dickey-Fuller test when the underlying model is AR(p) rather than AR(1).

is an extension of the Dickey-Fuller test when the underlying model is AR(p) rather than AR(1).

The error term in a multiperiod regression Select one: A. is serially uncorrelated. B. causes OLS to be inconsistent. C. is serially correlated, but less so the longer the forecast horizon. D. is serially correlated.

is serially correlated.

The order of integration Select one: A. is the number of times that the series needs to be differenced for it to be stationary. B. depends on the number of lags in the VAR specification. C. is the value of φ 1 in the quasi difference(ΔYt - φ 1 Yt -1). D. can never be zero.

is the number of times that the series needs to be differenced for it to be stationary.

The Times Series Regression with Multiple Predictors Select one: A. requires that the k regressors and the dependent variable have nonzero, finite eighth moments. B. gives you more than one prediction. C. cannot be estimated by OLS due to the presence of multiple lags. D. is the same as the ADL(p,q) with additional predictors and their lags present.

is the same as the ADL(p,q) with additional predictors and their lags present.

One advantage of forecasts based on a VAR rather than separately forecasting the variables involved is Select one: A. it can help to make the forecasts mutually consistent. B. that VAR forecasts are easier to calculate. C. you typically have knowledge of future values of at least one of the variables involved. D. that VAR involves panel data.

it can help to make the forecasts mutually consistent.

Departures from stationarity Select one: A. cannot be fixed. B. jeopardize forecasts and inference based on time series regression. C. occur often in cross-sectional data. D. can be made to have less severe consequences by using log-log specifications.

jeopardize forecasts and inference based on time series regression.

A VAR with k time series variables consists of Select one: A. a single equation, where the regressors are lagged values of all the variables B. k equations, one for each of the variables, where the regressors in all equations are never more than one lag of all the variables C. k equations, one for each of the variables, where the regressors in all equations are current values of all the variables D. k equations, one for each of the variables, where the regressors in all equations are lagged values of all the variables

k equations, one for each of the variables, where the regressors in all equations are lagged values of all the variables

The forecast is Select one: A. another word for the OLS predicted value. B. equal to the residual plus the OLS predicted value. C. made for some date beyond the data set used to estimate the regression. D. close to 1.96 times the standard deviation of Y during the sample.

made for some date beyond the data set used to estimate the regression.

An autoregression is a regression A. that allows for the errors to be correlated. B. of a dependent variable on lags of regressors. C. to predict sales in a certain industry. D. model that relates a time series variable to its past values.

model that relates a time series variable to its past values.

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

non-normal distribution which requires EG-ADF critical values for inference.

In a VECM, Select one: A. errors are corrected for serial correlation using the Cochrane-Orcutt method. B. VAR techniques, such as information criteria, no longer apply. C. past values of Yt - θ Xt help to predict future values of ΔYt and/or ΔXt . D. current values of Yt - θ Xt help to predict future values of ΔYt and/or ΔXt .

past values of Yt - θ Xt help to predict future values of ΔYt and/or ΔXt .

Stationarity means that the Select one: A. error terms are not correlated. B. forecasts remain within 1.96 standard deviation outside the sample period. C. time series has a unit root. D. probability distribution of the time series variable does not change over time.

probability distribution of the time series variable does not change over time.

The AR(p) model Select one: A. can be written as Yt = β 0 + β 1 Yt -1 + ut -p . B. is defined as Yt = β 0 + βpYt -p + ut . C. represents Yt as a linear function of p of its lagged values. D. can be represented as follows: Yt = β 0 + β 1 Xt + βpYt -p + ut .

represents Yt as a linear function of p of its lagged values.

The following is not an appropriate way to tell whether two variables are cointegrated: Select one: A. perform statistical tests for cointegration. B. use expert knowledge and economic theory. C. graph the series and see whether they appear to have a common stochastic trend. D. see if the two variables are integrated of the same order.

see if the two variables are integrated of the same order.

The random walk model is an example of a Select one: A. binomial model. B. deterministic trend model. C. stationary model. D. stochastic trend model.

stochastic trend model.

The biggest conceptual difference between using VARs for forecasting and using them for structural modeling is that Select one: A. structural modeling requires very specific assumptions derived from economic theory and institutional knowledge of what is exogenous and what is not. B. structural modeling only allows a maximum of three equations in the VAR. C. you can no longer use the information criteria to decide on the lag length. D. you need to use the Granger causality test for structural modeling.

structural modeling requires very specific assumptions derived from economic theory and institutional knowledge of what is exogenous and what is not.

E(ui|X) = 0 says that a. dividing the error by the explanatory variable results in a zero (on average). b. the sample regression function residuals are unrelated to the explanatory variable. c. the sample mean of the Xs is much larger than the sample mean of the errors. d. the conditional distribution of the error given the explanatory variable has a zero mean.

the conditional distribution of the error given the explanatory variable has a zero mean.

One of the sources of error in the RMSFE in the AR(1) model is Select one: A. due to measuring variables in logarithms. B. the error in estimating the coefficients β 0 and β 1. C. the model only looks at the previous period's value of Y when the entire history should be taken into account. D. that the value of the explanatory variable is not known with certainty when making a forecast.

the error in estimating the coefficients β 0 and β 1.

Problems caused by stochastic trends include all of the following with the exception of Select one: A. the model can no longer be estimated by OLS. B. t-statistics on regression coefficients can have a nonnormal distribution, even in large samples. C. the presence of spurious regression.. D. the estimator of an AR(1) is biased towards zero if its true value is one.

the model can no longer be estimated by OLS.

Time series variables fail to be stationary when Select one: A. there is strong seasonal variation in the data. B. the population regression has breaks. C. the economy experiences severe fluctuations. D. there are no trends.

the population regression has breaks.

In order to make reliable forecasts with time series data, all of the following conditions are needed with the exception of Select one: A. coefficients having been estimated precisely. B. the regression having high explanatory power. C. the presence of omitted variable bias. D. the regression being stable.

the presence of omitted variable bias.

You should use the QLR test for breaks in the regression coefficients, when Select one: A. the suspected break data is known. B. the Chow F-test has a p value of between 0.05 and 0.10. C. the suspected break data is not known. D. there are breaks in only some, but not all, of the regression coefficients.

the suspected break data is not known.

One reason for computing the logarithms (ln), or changes in logarithms, of economic time series is that Select one: A. natural logarithms are easier to work with than base 10 logarithms. B. they often exhibit growth that is approximately exponential. C. economic variables are hardly ever negative. D. numbers often get very large.

they often exhibit growth that is approximately exponential.

To test the null hypothesis of a unit root, the ADF test Select one: A. cannot be calculated if the variable is integrated of order two or higher. B. has higher power than the so-called DF-GLS test. C. uses complicated interative techniques. D. uses a t-statistic and a special critical value.

uses a t-statistic and a special critical value.

The Granger Causality Test Select one: A. uses the F-statistic to test the hypothesis that certain regressors have no predictive content for the dependent variable beyond that contained in the other regressors. B. establishes the direction of causality (as used in common parlance) between X and Y in addition to correlation. C. is a special case of the Augmented Dickey-Fuller test. D. is a rather complicated test for statistical independence.

uses the F-statistic to test the hypothesis that certain regressors have no predictive content for the dependent variable beyond that contained in the other regressors.

The root mean squared forecast error (RMSFE) is defined as

√E[YT+1-Y(hat)T+1 I T)^2]