Stats Quizzes
a. a series of t-tests may or may not give you the same conclusion. b. the F-statistic must be negative. c. all of the hypotheses are always simultaneously rejected. d. the regression is always significant. A
If you reject a joint null hypothesis using the F-test in a multiple hypothesis setting, then
a. add and subtract 1.96 from the slope and check if that interval includes 1. b. see if the slope coefficient is between 0.95 and 1.05. c. subtract 1 from the estimated coefficient, divide the difference by the standard error, and check if the resulting ratio is larger than 1.96. d. check if the adjusted R2 is close to 1. C
If you wanted to test, using a 5% significance level, whether or not a specific slope coefficient is equal to one, then you should (assuming large sample)
a. is the difference between the coefficient on Xt-1 and Xt-r. b. is the coefficient on Xt-r in the standard formulation of the distributed lag model. c. cannot be calculated since in the long-run, we are all dead. d. is the sum of all individual dynamic multipliers. D
The long-run cumulative dynamic multiplier
a. allows you to analyze behavior across time but not across entities. b. allows you to look up critical values in the standard normal distribution. c. allows you to control for some types of omitted variables without actually observing them. d. gives you more observations. C
The main advantage of using panel data over cross sectional data is that it
a. is the same as the logit model. b. always gives the same fit for the predicted values as the linear probability model for values between 0.1 and 0.9. c. should not be used since it is too complicated. d. forces the predicted values to lie between 0 and 1. D
The probit model
a. internal and external validity b. the quality of your statistical software package c. internal but not external validity d. external but not internal validity A
The question of reliability/unreliability of a multiple regression depends on
a. stochastic trend model. b. deterministic trend model. c. binomial model. d. stationary model. A
The random walk model is an example of a
a. the goodness of fit of your regression line. b. whether or not ESS > TSS. c. whether or not X causes Y. d. the square of the determinant of R. A
The regression R2 is a measure of
a. the study is out of date b. of geographical differences c. of differences in characteristics of the population d. all of the above D
The true causal effect might not be the same in the population studied and the population of interest because
a. when there are more than 100 observations. b. if these omitted variables are constant across entities but not over time. c. if these omitted variables vary across entities and not over time. d. even if you only have a cross-section of data available. B
Time Fixed Effects regression are useful in dealing with omitted variables
a. the slope no longer indicates the effect of a unit change of X on Y in the log-linear model. b. the TSS are different c. ln(Y) may be negative for 0<Y<1. d. the regression R2 can be greater than one in the second model. B
To decide whether Yi = β0 + β1X + ui or ln(Yi) = β0 + β1X + ui fits the data better, you cannot consult the regression R2 because
a. can also be used with cross-sectional data. b. is sometimes referred to as ADL. c. gives estimates of dynamic causal effects. d. is also called AR(p). C
A distributed lag regression
a. use the square root of that variable since the error becomes smaller. b. choose different functional forms. c. mitigate the problem through instrumental variables regression. d. use log-log specifications. C
A possible solution to errors-in-variables bias is to
a. the OLS estimator is unbiased and consistent, and the standard errors are computed in a way that makes confidence intervals have the desired confidence level. b. you use a two-sided alternative hypothesis, and standard errors are calculated using the heteroskedasticity-robust formula. c. weighted least squares produces similar results, and the t-statistic is normally distributed in large samples. d. the errors are homoskedastic, and there are no more than two binary variables present among the regressors. A
A study based on OLS regressions is internally valid if
a. simultaneous causality bias. b. errors-in-variables bias. c. companies that typically bargain with workers in 100s of dollars. d. sample selection bias. B
A survey of earnings contains an unusually high fraction of individuals who state their weekly earnings in 100s, such as 300, 400, 500, etc. This is an example of
a. 6. b. 21. c. 26. d. 28. C
Consider a panel regression of unemployment rates for the G7 countries (United States, Canada, France, Germany, Italy, United Kingdom, Japan) on a set of explanatory variables for the time period 1980-2000 (annual data). If you included entity and time fixed effects, you would need to specify the following number of binary variables:
a. a high R2 does not necessarily mean that you have the most appropriate set of regressors. b. a high R2 does not mean that the regressors are a true cause of the dependent variable. c. a high R2 always means that an added variable is statistically significant. d. a high R2 does not mean that there is no omitted variable bias. C
All of the following are true, with the exception of one condition:
a. Yi = β0 + β1X + β2X^2 + ui. b. Yi = β0 + β1X + β2Y^2 + ui. c. Yi = β0 + β1X + d. = β0 + β1X + ui. A
An example of a quadratic regression model is
a. Yi = β0 + β1X1i + β2X2i + β3(X1i × X2i) + ui. b. Yi = β0 + β1X1i + β2X2i + ui. c. Yi = β0 + β1D1i + β2D2i + β3 (D1i × D2i) + ui. d. Yi = β0 + β1Xi + β2Di + β3(Xi × Di) + ui. A
An example of the interaction term between two independent, continuous variables is (using the notation from Stock and Watson)
a. economic theory. b. use of HAC standard errors. c. expert judgment. d. institutional knowledge. B
Ascertaining whether or not a regressor is strictly exogenous or exogenous ultimately requires all of the following with the exception of
a. 3.85 b. 3.80 c. Cannot be calculated because the function is non-linear d. 2.96 D
Assume that you had estimated the following quadratic regression model: Happiness_hat = 607.3 + 3.85 Income - 0.0423 Income^2. If Income increased from 10 to 11 (income is measured in thousands), then the predicted change in Happiness would be (round to two decimals):
a. causes the usual OLS standard errors to be inconsistent. b. causes OLS to be no longer consistent. c. makes it impossible to calculate homoskedasticity only standard errors. d. results in OLS being biased. A
Autocorrelation of the error terms
a. current and lagged values of the residuals. b. lags of the dependent variable, and lagged values of an additional predictor variable. c. current and lagged values of the error term. d. lags and leads of the dependent variable. B
Autoregressive distributed lag models include
a. Reject the null hypothesis at the 5% level of significance. b. Do not reject the null hypothesis at the 5% level of significance. c. Uncertain---not enough information. B
Consider the estimated equation from a sample of 1000. Yi_hat= 5.25 - 3.75 * Xi (1.75) (2.50) R2 = 0.50, SER = 18.6 note: standard errors in parenthesis Perform the following hypothesis test: Ho: ß1 = 0 HA: ß1 does not equal 0
a. 0.25 b. 0.650 c. 0.586 d. 1.96 C
Consider the following regression output: Y_hati = 698.9 - 1.50 * X1,i - 0.75 * X2,i. You are told that STATA-generated t-statistic on X1's coefficient is -2.56. The standard error for X1's coefficient is approximately
30
Consider the following regression results: Yi_hat = 10 + 2.5 * X1,i+ -5.5 * X2,i + 15 * X3,i How much does Yi_hat change, holding all else equal, of increasing X3 by 2 units?
a. -2 b. 52 c. 8 d. -8 C
Consider the following regression results: Yi_hat = 10 + 2.5 * X1,i+ -5.5 * X2,i + 15 * X3,i What is the predicted value of Yi_hat when X1 =2, X2 =4, and X3 =1?
a. perfect multicollinearity b. dummy variable trap c. omitted variable bias d. heteroskedasticity C
Consider the multiple regression model with two regressors X1 and X2, where both variables are determinants of the dependent variable. You first regress Y on X1 only and find no relationship. However when regressing Y on X1 and X2, the slope coefficient ß1 changes by a large amount. This suggests that your first regression suffers from
a. you cannot use time fixed effects and include beer tax since beer taxes are the same at a point in time across states. b. it would not make sense to use state fixed effect. c. you can test state fixed effects using homoskedastic-only standard errors. d. all OLS coefficient estimates will be biased in the model. A
Consider the regression example from your textbook, which estimates the effect of beer taxes on fatality rates across the 48 contiguous U.S. states. If beer taxes were set yearly by the national government rather than by the states, then
a. then this often provides evidence that the original specification had omitted variable bias. b. then you should change the scale of the variables to make the changes appear to be smaller. c. then choose the specification for which your coefficient of interest is most significant. d. then this can be expected from sample variation. A
If the estimates of the coefficients of interest change substantially across specifications,
a. the sample mean of the Xs is much larger than the sample mean of the errors. b. the sample regression function residuals are related to the explanatory variable. c. dividing the error by the explanatory variable results in a zero (on average). d. the conditional distribution of the error given the explanatory variable has a zero mean. D
E(ui|Xi) = 0 says that
a. implies that the t-statistic is less than 1.96. b. indicates evidence against the null hypothesis. c. will only happen roughly one in twenty samples. d. indicates evidence in favor of the null hypothesis. B
Finding a small value of the p-value (e.g. less than 5%)
a. you need new estimation techniques since the OLS assumptions do not apply any longer. b. the techniques for estimation and inference developed for multiple regression can be applied. c. the critical values from the normal distribution have to be changed to 1.96^2, 1.96^3, etc. d. you can still use OLS estimation techniques, but the t-statistics do not have an asymptotic normal distribution. B
For the polynomial regression model,
a. clustered standard errors are the square root of HAC standard errors b. they are the same c. they are the same if the data is differenced d. clustered standard errors are one type of HAC standard error D
HAC standard errors and clustered standard errors are related as follows:
a. are calculated when using the Cochrane-Orcutt iterative procedure. b. require an estimation strategy different than OLS c. have the same formula as the heteroskedasticity robust standard errors in cross-sections. d. should be used when errors are autocorrelated. D
Heteroskedasticity- and autocorrelation-consistent standard errors
a. reject the assumption that the error terms are homoskedastic. b. conclude that most of the actual values are very close to the regression line. c. safely assume that your regression results are significant. d. reject the null hypothesis. D
If the absolute value of your calculated t-statistic exceeds the critical value from the standard normal distribution you can
a. safely assume that your regression results are insignificant. b. reject the null hypothesis. c. reject the assumption that the error terms are homoskedastic. d. conclude that most of the actual values are very close to the regression line. B
If the absolute value of your calculated t-statistic exceeds the critical value from the standard normal distribution, you can
a. the model makes little sense, since the dependent variable can only be 0 or 1. b. given the values for the explanatory variables, there is a 40 percent probability that the dependent variable will equal one. c. the most likely value the dependent variable will take on is 60 percent. d. given the values for the explanatory variables, there is a 60 percent probability that the dependent variable will equal one. D
In a linear probability model, a predicted value of 0.6 means that
a. it is no longer reasonable to assume that the errors are heteroskedastic. b. you are no longer controlling for the influence of the omitted variable. c. the remaining coefficient is certainly biased d. the OLS estimator no longer exists. B
In a two regressor regression model, if both are determinants of Y and you exclude one then
a. added unless there is heterosckedasticity. b. greater than 1.96 in absolute value. c. added unless there is multicolinearity. d. added. D
In multiple regression, the R2 can increase whenever a regressor is
a. the response in the dependent variable to a percentage change in the regressor. b. the change in odds associated with a unit change in X, holding other regressors constant. c. the change in probability that Y=1 associated with a unit change in X, holding others regressors constant. d. not all that meaningful since the dependent variable is either 0 or 1. C
In the linear probability model, the interpretation of the slope coefficient is
a. ΔY / ΔX. b. Y x X c. the elasticity of Y with respect to X. d. the effect that a unit change in X has on Y. C
In the log-log model, the slope coefficient indicates
a. the β's do not have a simple interpretation. b. β0 is the probability of observing Y when all X's are 0 c. β0 cannot be negative since probabilities have to lie between 0 and 1. d. the slopes tell you the effect of a unit increase in X on the probability of Y. A
In the probit model Pr(Y = 1 |X1, X2,..., Xk) = Φ(β0 + β1X1 + βxX2 + ... + βkXk),
a. the change in the z- value associated with a unit change in X b. the change in the probability of Y = 1 given a percent change in X c. the change in the probability of Y = 1 given a unit change in X d. none of the above A
In the probit regression, the coefficient β1 indicates
a. is the difference in means in Y between the two categories. b. indicates the difference in the intercepts of the two regressions. c. indicates the difference in the slopes of the two regressions. d. is usually positive. B
In the regression model Yi = β0 + β1Xi + β2Di + β3(Xi × Di) + ui, where X is a continuous variable and D is a binary variable, β2
a. indicates by how many units Y changes, given a one unit increase in X. b. indicates by how many percent Y changes, given a one percent increase in X. c. when multiplied with the explanatory variable will give you the predicted Y. d. represents the elasticity of Y on X. A
In the simple linear regression model, the regression slope
a. consisting of the same subject being given different treatments at different points in time b. as being non-existent (this is a time series after all, and there are no real "parallel universes") c. consisting of different subjects being given the same treatment at the same point in time d. consisting of the at least two subjects being given different treatments at the same point in time A
In time series data, it is useful to think of a randomized controlled experiment
a. results in a type of omitted variable bias. b. is more serious in the case of homoskedasticity-only standard error. c. is overcome by adding the squares of all explanatory variables. d. requires alternative estimation methods such as maximum likelihood. A
Misspecification of functional form of the regression function
a. OLS estimate of the slope the same. b. OLS estimate of the intercept the same. c. regression R-squared the same. d. variance of the OLS estimators the same. C
Multiplying the dependent variable by 100 and the explanatory variable by 100,000 leaves the
a. longitudinal data. b. time series data. c. cross-sectional data. d. experimental data. A
Panel data is also called
a. data are collected from a population by simple random sampling. b. samples are chosen to be small rather than large. c. the choice between two samples is made by the researcher. d. the availability of the data is influenced by a selection process that is related to the value of the dependent variable. D
Sample selection bias occurs when
a. means you must run a second regression of X on Y. b. cannot be established since regression analysis only detects correlation between variables. c. means that a third variable affects both Y and X. d. leads to correlation between the regressor and the error term. D
Simultaneous causality
a. is also called sample selection bias. b. arises in a regression of Y on X when, in addition to the causal link of interest from X to Y, there is a causal link from Y to X. c. results in biased estimators if there is heteroskedasticity in the error term. d. happens in complicated systems of equations called block recursive systems. B
Simultaneous causality bias
a. forecasts remain within 1.96 standard deviation outside the sample period. b. probability distribution of the time series variable does not change over time. c. time series has a unit root. d. error terms are not correlated. B
Stationarity means that the
a. can be represented as follows: Yt = β0 + β1Xt + βpYt-p + ut. b. is defined as Yt = β0 + βpYt-p + ut. c. represents Yt as a linear function of p of its lagged values. d. can be written as Yt = β0 + β1Yt-1 + ut-p. C
The AR(p) model
a. has a normal distribution in large samples. b. is a two-sided test. c. is an extension of the Dickey-Fuller test when the underlying model is AR(p) rather than AR(1). d. has the identical distribution whether or not a trend is included or not. C
The Augmented Dickey Fuller (ADF) t-statistic
a. only used in cross-sectional analysis b. developed by the Bank of England in its river of blood analysis c. commonly used to test for serial correlation d. used to help the researcher choose the number of lags in an autoregression D
The BIC is a statistic
a. a method to compute HAC standard errors. b. a special case of GLS estimation. c. a grid search for the autoregressive parameters on the error process. d. a special case of maximum likelihood estimation. B
The Cochrane-Orcutt iterative method is
a. is a special case of the Augmented Dickey-Fuller test. b. is a rather complicated test for statistical independence. c. establishes the direction of causality (as used in common parlance) between X and Y in addition to correlation. d. 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. D
The Granger Causality Test
a. minimizing the sum of squared residuals. b. minimizing the sum of absolute residuals. c. connecting the Yi corresponding to the lowest Xi observation with the Yi corresponding to the highest Xi observation. d. making sure that the standard error of the regression equals the standard error of the slope estimator A
The OLS estimator is derived by
a. only if the omitted variable is not normally distributed. b. if an omitted variable is correlated with at least one of the regressors, even though it is not a determinant of the dependent variable. c. if an omitted determinant of Yi is correlated with at least one of the regressors. d. only if an omitted determinant of Yi is a continuous variable. C
The OLS estimators of the coefficients in multiple regression will have omitted variable bias
a. can be calculated using the errors from the regression function. b. are unknown since we do not know the population regression function. c. can be calculated by subtracting the fitted values from the actual values. d. should not be used in practice since they indicate that your regression does not run through all your observations. C
The OLS residuals
a. can be calculated by subtracting the fitted values from the actual values. b. are zero because the predicted values are another name for forecasted values. c. are typically the same as the population regression function errors. d. cannot be calculated because there is more than one explanatory variable. A
The OLS residuals in the multiple regression model
a. is the same as the ADL(p,q) with additional predictors and their lags present. b. requires that the k regressors and the dependent variable have nonzero, finite eighth moments. c. cannot be estimated by OLS due to the presence of multiple lags. d. gives you more than one prediction. A
The Times Series Regression with Multiple Predictors
a. its inferences and conclusions can be generalized from the population and setting studied to other populations and settings. b. some committee outside the author's department has validated the findings. c. the study has passed a double blind refereeing process for a journal. d. the statistical inferences about causal effects are valid for the population being studied. A
The analysis is externally valid if
a. under strict exogeneity, OLS may not be efficient as an estimator of dynamic causal effects. b. maximum likelihood estimation is no longer valid. c. it clarifies whether or not the variable is determined inside or outside your model. d. endogenous variables are not stationary, but exogenous variables are. C
The concept of exogeneity is important because
a. can be used to compare the value of the slope relative to that of the intercept. b. can be used to conduct a test about a hypothesized population regression function slope. c. allows you to make statements about the economic importance of your estimate. d. adds and subtracts 1.96 from the slope. B
The confidence interval for the sample regression function slope
a. uses ±1.96 for the two-sided test, but only +1.96 for the one-sided test. b. depends on the critical value from the appropriate distribution. c. is the same. d. is different since the critical value must be 1.645 for the one-sided hypothesis, but 1.96 for the two-sided hypothesis (using a 5% probability for the Type I error). C
The construction of the t-statistic for a one- and a two-sided hypothesis
a. an unbalanced panel contains missing observations for at least one time period or one entity. b. you cannot have both fixed time effects and fixed entity effects regressions. c. in the former you may not include drivers who have been drinking in the fatality rate/beer tax study. d. the impact of different regressors are roughly the same for balanced but not for unbalanced panels. A
The difference between an unbalanced and a balanced panel is that
a. There is no perfect multicollinearity. b. The random variables Xt and Yt have a stationary distribution. c. E(ut | Xt, Xt-1, Xt-2) = 0 d. Xt is strictly exogenous. D
The distributed lag model assumptions include all of the following with the exception of:
a. imperfect multicollinearity b. something that is of theoretical interest only c. perfect multicollinearity d. something that does not happen to university or college students C
The dummy variable trap is an example of
a. Xi is normally distributed. b. there are no outliers. c. var[ui|Xi] is constant for all i=1, 2,..., n d. var[ui|Xi] depends on Xi C
The error term is homoskedastic if
a. the first difference of Y. b. the growth rate of Y exactly. c. approximately the growth rate of Y when the growth rate is small. d. the difference between the lead and the lag of Y. C
The first difference of the logarithm of Yt equals
a. Large outliers are unlikely. b. The explanatory variable in regression model is normally distributed. c. (Xi, Yi), i = 1,..., n are independently and identically distributed. d. The conditional distribution of ui given Xi has a mean of zero. B
The following are all least squares assumptions with the exception of
a. 95% confidence interval using ± 1.96 times the standard error. b. Joint hypothesis testing c. regression R2. d. significance test using the t-statistic. C
The following tools from multiple regression analysis carry over in a meaningful manner to the linear probability model, with the exception of the
a. using GLS rather than OLS b. the assumption that X is exogenous c. not having more than four lags when using quarterly data d. the use of monthly rather than annual data B
The interpretation of the coefficients in a distributed lag regression as causal dynamic effects hinges on
a. a 1% change in X is associated with a change in Y of 0.01 β1. b. a 1% change in X is associated with a β1 % change in Y. c. a change in X by one unit is associated with a β1 100% change in Y. d. a change in X by one unit is associated with a β1 change in Y. A
The interpretation of the slope coefficient in the model Yi = β0 + β1 ln(Xi) + ui is as follows:
Select one: a. the application of the multiple regression model with a continuous left-hand side variable and a binary variable as at least one of the regressors. b. another word for logit estimation. c. an example of probit estimation. d. the application of the linear multiple regression model to a binary dependent variable. D
The linear probability model is
a. maximum likelihood estimation. b. OLS estimation. c. differences in means between those individuals with a dependent variable equal to one and those with a dependent variable equal to zero. d. the linear probability model. A
The logit model can be estimated and yields consistent estimates if you are using
a. the error terms are highly, but not perfectly, correlated. b. two or more of the regressors are highly correlated. c. the OLS estimator cannot be computed. d. the OLS estimator is biased even in samples of n > 100. B
Under imperfect multicollinearity
a. use the homoskedasticity only formula because the t-statistic becomes larger b. make a decision depending on how much different the estimate of the slope is under the two procedures c. first test for homoskedasticity of the errors and then make a decision d. use the heteroskedasticity robust formula D
Using the textbook example of 420 California school districts and the regression of testscores on the student-teacher ratio, you find that the standard error on the slope coefficient is 0.51 when using the heteroskedasticity robust formula, while it is 0.48 when employing the homoskedasticity only formula. When calculating the t-statistic, the recommended procedure is to
a. use t-statistics for each hypothesis and reject the null hypothesis once the statistic exceeds the critical value for a single hypothesis. b. use the F-statistic and reject all the underlying hypothesis if the statistic exceeds the critical value. c. use the F-statistics and reject at least one of the underlying hypothesis if the statistic exceeds the critical value. d. use t-statistics for each hypothesis and reject the null hypothesis is all of the restrictions fail. C (but this question had errors apparently)
When testing joint hypothesis, you should
a. the included explanatory variables, other than the state fixed effects, are unimportant. b. time fixed effects are unimportant. c. state fixed effects account for a large amount of the variation in the data. d. the coefficients on the other included explanatory variables will not change. C
When you add state fixed effects to a simple regression model for U.S. states over a certain time period, and the regression R2 increases significantly, then it is safe to assume that
a. [-0.25, -0.05] b. [-0.63, -0.40] c. cannot be determined given the information provided d. [-0.53, -0.37] D
You extract approximately 5,000 observations from the Current Population Survey (CPS) and estimate the following regression function: ahei_hat = 3.32 — 0.45 *Agei, (1.00) (0.04) R2= 0.02, SER = 8.66 note: standard errors in parenthesis where ahe is average hourly earnings, and Age is the individual's age. Given the specification, your 95% confidence interval for ß1:
a. the suspected break date is known. b. there are breaks in only some, but not all, of the regression coefficients. c. the suspected break date is not known. d. the Chow F-test has a p value of between 0.05 and 0.10. C
You should use the QLR test for breaks in the regression coefficients, when