econometrics final yang

" (Requires Appendix material) The relationship between the TSLS slope and the corresponding population parameter is: A. (β ̂_1 TSLS - β_1) = (1/n∑(zi-z ̅ )μi)/(1/n∑(z_i-z ̅)(x_i-x ̅)) B. (β ̂_1 TSLS - β_1) = (1/n∑(zi-z ̅ ))/(1/n∑(z_i-z ̅)(x_i-x ̅)) C. (β ̂_1 TSLS - β_1) = (1/n∑(zi-z ̅ ) ui )/(1/n∑(z_i-z ̅)^2 ) D. (β_1 TSLS - β_1) = (1/n∑(x_i-x̅)ui)/(1/n∑(z_i-z ̅)(x_i-x ̅))"

A

" (Requires Appendix material) When the fifth assumption in the Fixed Effects regression (cov (uit, uis Xit, Xis) = 0 for t ≠ s ) is violated, then: A. using heteroskedastic-robust standard errors is not sufficient for correct statistical inference when using OLS. B. the OLS estimator does not exist. C. you can use the simple homoskedasticity-only standard errors calculated in your regression package. D. you cannot use fixed time effects in your estimation."

A

" Assume that you wanted to investigate whether or not females and males are affected differently by marriage in earnings functions. Let Y be the log of average hourly earnings, and DF and DM being binary variables for females (DF = 1 if female, DF = 1 if male) and marital status (DM = 1 if married, DM = 0 if single). The following specification will allow for marriage/gender effects to be different for the four possible marriage-gender combinations:. The following specification will allow for marriage/gender effects to be different for the four possible marriage-gender combinations: A. ln() = + D + D + (D × D) + B. ln() = + D + D + C. ln() = + (D × D) + D. ln() = + D + (D × D) +"

A

" Consider the following least squares specification between test scores and the student-teacher ratio: = 557.8 + 36.42 ln (Income). According to this equation, a 1% increase income is associated with an increase in test scores of: A. 0.36 points. B. 36.42 points. C. 557.8 points. D. cannot be determined from the information given here."

A

" Endogenous variables: A. are correlated with the error term. B. always appear on the LHS of regression functions. C. cannot be regressors. D. are uncorrelated with the error term."

A

" In the expression Pr(Y = 1 Φ(β0 + β1X): A. (β0 + β1X) plays the role of z in the cumulative standard normal distribution function. B. β1 cannot be negative since probabilities have to lie between 0 and 1. C. β0 cannot be negative since probabilities have to lie between 0 and 1. D. min (β0 + β1X) > 0 since probabilities have to lie between 0 and 1."

A

" Nonlinear least squares: A. solves the minimization of the sum of squared predictive mistakes through sophisticated mathematical routines, essentially by trial and error methods. B. should always be used when you have nonlinear equations. C. gives you the same results as maximum likelihood estimation. D. is another name for sophisticated least squares."

A

" One of the sources of error in the RMSFE in the AR(1) model is: A. the error in estimating the coefficients β0 and β1. B. due to measuring variables in logarithms. C. that the value of the explanatory variable is not known with certainty when making a forecast. D. the model only looks at the previous period's value of Y when the entire history should be taken into account."

A

" The logic of control variables in IV regressions: A. parallels the logic of control variables in OLS. B. only applies in the case of homoskedastic errors in the first stage of two stage least squares estimation. C. is different in a substantial way from the logic of control variables in OLS since there are two stages in estimation. D. implies that the TSLS is efficient."

A

" To calculate the MSFE, we square the forecast error because: A. a single very large forecast error can call the entire forecasting activity into question. B. Forecast errors are typically small and we need to amplify them to make them meaningful. C. we want positive forecast errors to cancel negative ones. D. squared units are easier to interpret in least squares estimation."

A

" When there is a single instrument and single regressor, the TSLS estimator for the slope can be calculated as follows: A. β̂ TSLS= S_zy/S_zx B. β̂ TSLS= S_xy/S2_x C. β̂ TSLS= S_xy/S_zy D. β̂ TSLS= S_zy/S2_z"

A

" You have estimated the following equation: = 607.3 + 3.85 Income - 0.0423 Income2 , where TestScore is the average of the reading and math scores on the Stanford 9 standardized test administered to 5th grade students in 420 California school districts in 1998 and 1999. Income is the average annual per capita income in the school district, measured in thousands of 1998 dollars. The equation: A. suggests a positive relationship between test scores and income for most of the sample. B. is positive until a value of Income of 610.81. C. does not make much sense since the square of income is entered. D. suggests a positive relationship between test scores and income for all of the sample."

A

" Your textbook plots the estimated regression function produced by the probit regression of deny on P/I ratio. The estimated probit regression function has a stretched ""S"" shape given that the coefficient on the P/I ratio is positive. Consider a probit regression function with a negative coefficient. The shape would: A. resemble an inverted ""S"" shape (for low values of X, the predicted probability of y would approach 1). B. not exist since probabilities cannot be negative. C. remain the ""S"" shape as with a positive slope coefficient. D. would have to be estimated with a logit function."

A

" Consider a model with one endogenous regressor and two instruments. Then the J-statistic will be large: A. if the number of observations are very large. B. if the coefficients are very different when estimating the coefficients using one instrument at a time. C. if the TSLS estimates are very different from the OLS estimates. D. when you use homoskedasticity-only standard errors."

B

" Consider the special panel case where T = 2. If some of the omitted variables, which you hope to capture in the changes analysis, in fact change over time, then the estimator on the included change regressor: A. will be unbiased only when allowing for heteroskedastic-robust standard errors. B. may still be unbiased. C. will only be unbiased in large samples. D. will always be unbiased."

B

" For the polynomial regression model: 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. you can still use OLS estimation techniques, but the t-statistics do not have an asymptotic normal distribution. D. the critical values from the normal distribution have to be changed to 1.962, 1.963, etc."

B

" HAR standard errors and clustered standard errors are related as follows: A. they are the same. B. clustered standard errors are one type of HAR standard error. C. they are the same if the data is differenced. D. clustered standard errors are the square root of HAR standard errors."

B

" Having more relevant instruments: A. is a problem because instead of being just identified, the regression now becomes overidentified. B. is like having a larger sample size in that the more information is available for use in the IV regressions. C. typically results in larger standard errors for the TSLS estimator. D. is not as important for inference as having the same number of endogenous variables as instruments."

B

" In the binary dependent variable model, a predicted value of 0.6 means that: A. the most likely value the dependent variable will take on is 60 percent. B. given the values for the explanatory variables, there is a 60 percent probability that the dependent variable will equal one. C. the model makes little sense, since the dependent variable can only be 0 or 1. D. given the values for the explanatory variables, there is a 40 percent probability that the dependent variable will equal one."

B

" In the expression Pr(deny = 1 P/I Ratio, black) = Φ(-2.26 + 2.74P/I ratio + 0.71black), the effect of increasing the P/I ratio from 0.3 to 0.4 for a white person: A. is 0.274 percentage points. B. is 6.1 percentage points. C. should not be interpreted without knowledge of the regression R2. D. is 2.74 percentage points."

B

" In the log-log model, the slope coefficient indicates: A. the effect that a unit change in X has on Y. B. the elasticity of Y with respect to X. C. ΔY / ΔX. D. × ."

B

" In the panel regression analysis of beer taxes on traffic deaths, the estimation period is 1982-1988 for the 48 contiguous U.S. states. To test for the significance of time fixed effects, you should calculate the F-statistic and compare it to the critical value from your Fq,∞ distribution, which equals (at the 5% level): A. 2.01. B. 2.10. C. 2.80. D. 2.64."

B

" Indicate for which of the following examples you cannot use Entity and Time Fixed Effects: a regression of: A. OECD unemployment rates on unemployment insurance generosity for the period 1980-2006 (annual data). B. the (log of) earnings on the number of years of education, using the Current Population Survey of 60,000 households for March 2006. C. the per capita income level in Canadian Provinces on provincial population growth rates, using decade averages for 1960, 1970, and 1980. D. the risk premium of 75 stocks on the market premium for the years 1998-2006."

B

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

B

" The AR(p) model: A. is defined as Yt = β0 + βpYt-p + ut. B. represents Yt as a linear function of p of its lagged values. C. can be represented as follows: Yt = β0 + β1Xt + βpYt-p + ut. D. can be written as Yt = β0 + β1Yt-1 + ut-p."

B

" The Akaike Information Criterion (AIC) is given by the following formula: A. AIC(p) = ln [SSR(p)/T] + (p+1)ln(T)/T B. AIC(p) = ln [SSR(p)/T] + (p+1)2/T C. AIC(p) = ln [SSR(p)/T} + (P+2)/T D. AIC(p) = ln [SSR(p)/T] × (p+1)2/T"

B

" The best way to interpret polynomial regressions is to: A. take a derivative of Y with respect to the relevant X. B. plot the estimated regression function and to calculate the estimated effect on Y associated with a change in X for one or more values of X. C. look at the t-statistics for the relevant coefficients. D. analyze the standard error of estimated effect."

B

" The conditions for a valid instrument do not include the following: A. each instrument must be uncorrelated with the error term. B. each one of the instrumental variables must be normally distributed. C. at least one of the instruments must enter the population regression of X on the Zs and the Ws. D. perfect multicollinearity between the predicted endogenous variables and the exogenous variables must be ruled out."

B

" The following are properties of the logarithm function with the exception of: A. ln(1/ x) = -ln(x) +ln(x) B. ln(a + x) = ln(a) + ln(x) + ln (x) C. ln(ax) = ln(a) + ln(x) +ln (x) D. ln(xa) a ln(x)."

B

" The following problems could be analyzed using probit and logit estimation with the exception of whether or not: A. a college student decides to study abroad for one semester. B. being a female has an effect on earnings. C. a college student will attend a certain college after being accepted. D. applicants will default on a loan."

B

" The interpretation of the slope coefficient in the model ln(Yi) = β0 + β1Xi + ui is as follows: A. a 1% change in X is associated with a β1 % change in Y. B. a change in X by one unit is associated with a 100 β1 % change in Y. C. a 1% change in X is associated with a change in Y of 0.01 β1. D. a change in X by one unit is associated with a β1 change in Y."

B

" The logit model can be estimated and yields consistent estimates if you are using: A. OLS estimation. B. maximum likelihood 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."

B

" The reduced form equation for X: A. regresses the endogenous variable X on the smallest possible subset of regressors. B. relates the endogenous variable X to all the available exogenous variables, both those included in the regression of interest and the instruments. C. uses the predicted values of X from the first stage as a regressor in the original equation. D. uses smaller standard errors, such as homoskedasticity-only standard errors, for inference."

B

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

B

" 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. the included explanatory variables, other than the state fixed effects, are unimportant. B. state fixed effects account for a large amount of the variation in the data. C. the coefficients on the other included explanatory variables will not change. D. time fixed effects are unimportant."

B

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

B

" (Requires Advanced material) Nonlinear least squares estimators in general are not: A. consistent. B. normally distributed in large samples. C. efficient. D. used in econometrics."

C

" (Requires Calculus) In the equation = 607.3 + 3.85 Income - 0.0423Income2, the following income level results in the maximum test score: A. 607.3. B. 91.02. C. 45.50. D. cannot be determined without a plot of the data."

C

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

C

" Assume that you had estimated the following quadratic regression model = 607.3 + 3.85 Income - 0.0423 Income2. If income increased from 10 to 11 ($10,000 to $11,000), then the predicted effect on test scores would be: A. 3.85. B. 3.85-0.0423. C. 2.96. D. Cannot be calculated because the function is non-linear."

C

" Estimation of the IV regression model: A. requires exact identification. B. allows only one endogenous regressor, which is typically correlated with the error term. C. requires exact identification or overidentification. D. is only possible if the number of instruments is the same as the number of regressors."

C

" If the future differs fundamentally from the past, then: A. the time series is stationary. B. regression models estimated using past data can be used to forecast future values. C. historical relationships might not be reliable guides to the future. D. the joint distribution of (, ,... , does not depend on s, regardless of the value of T."

C

" If you included both time and entity fixed effects in the regression model which includes a constant, then: A. one of the explanatory variables needs to be excluded to avoid perfect multicollinearity. B. you can use the ""before and after"" specification even for T > 2. C. you must exclude one of the entity binary variables and one of the time binary variables for the OLS estimator to exist. D. the OLS estimator no longer exists."

C

" In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by: A. △Y = f(X1 + X1, X2,... Xk). B. △Y = f(X1 + △X1, X2 + △X2,..., Xk+ △Xk)- f(X1, X2,...Xk). C. △Y = f(X1 + △X1, X2,..., Xk)- f(X1, X2,...Xk). D. △Y = f(X1 + X1, X2,..., Xk)- f(X1, X2,...Xk)."

C

" In the case of exact identification: A. you can use the J-statistic in a test of overidentifying restrictions. B. you cannot use TSLS for estimation purposes. C. you must rely on your personal knowledge of the empirical problem at hand to assess whether the instruments are exogenous. D. OLS and TSLS yield the same estimate."

C

" In the regression model Yi = β0 + β1Xi + β2Di + β3(Xi × Di) + ui, where X is a continuous variable and D is a binary variable, β3: A. indicates the slope of the regression when D=1. B. has a standard error that is not normally distributed even in large samples since D is not a normally distributed variable. C. indicates the difference in the slopes of the two regressions. D. has no meaning since (Xi × Di) = 0 when Di = 0."

C

" Instrument relevance: A. means that the instrument is one of the determinants of the dependent variable. B. is the same as instrument exogeneity. C. means that some of the variance in the regressor is related to variation in the instrument. D. is not possible since X and u are correlated and Z and u are not correlated."

C

" The AIC is a statistic: A. that is used as an alternative to the BIC when the sample size is small (T < 50). B. often used to test for heteroskedasticity. C. used to help a researcher chose the number of lags in a time series with multiple predictors. D. all of the above."

C

" The IV estimator can be used to potentially eliminate bias resulting from: A. multicollinearity. B. serial correlation. C. errors in variables. D. heteroskedasticity."

C

" The binary dependent variable model is an example of a: A. regression model, which has as a regressor, among others, a binary variable. B. model that cannot be estimated by OLS. C. limited dependent variable model. D. model where the left-hand variable is measured in base 2."

C

" The logit model derives its name from: A. the logarithmic model. B. the probit model. C. the logistic function. D. the tobit model."

C

" The main advantage of using panel data over cross sectional data is that it: A. gives you more observations. B. allows you to analyze behavior across time but not across entities. C. allows you to control for some types of omitted variables without actually observing them.. "

C

" The notation for panel data is (Xit, Yit), i = 1, ..., n and t = 1, ..., T because: A. we take into account that the entities included in the panel change over time and are replaced by others. B. the X's represent the observed effects and the Y the omitted fixed effects. C. there are n entities and T time periods. D. n has to be larger than T for the OLS estimator to exist."

C

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

C

" (Requires Chapter 8) When using panel data and in the presence of endogenous regressors: A. the TSLS does not exist. B. you do not have to worry about the validity of instruments, since there are so many fixed effects. C. the OLS estimator is consistent. D. application of the TSLS estimator is straightforward if you use two time periods and difference the data."

D

" A nonlinear function: A. makes little sense, because variables in the real world are related linearly. B. can be adequately described by a straight line between the dependent variable and one of the explanatory variables. C. is a concept that only applies to the case of a single or two explanatory variables since you cannot draw a line in four dimensions. D. is a function with a slope that is not constant."

D

" An example of the interaction term between two independent, continuous variables is: A. Yi = β0 + β1Xi + β2Di + β3(Xi × Di) + ui. B. Yi = β0 + β1X1i + β2X2i + ui. C. Yi = β0 + β1D1i + β2D2i + β3 (D1i × D2i) + ui. D. Yi = β0 + β1X1i + β2X2i + β3(X1i × X2i) + ui."

D

" 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. 21 B. 6 C. 28 D. 26"

D

" 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 nationally by the federal government rather than by the states, then: A. it would not make sense to use state fixed effect. B. you can test state fixed effects using homoskedastic-only standard errors. C. the OLS estimator will be biased. D. you should not use time fixed effects since beer taxes are the same at a point in time across states."

D

" F-statistics computed using maximum likelihood estimators: A. cannot be used to test joint hypothesis. B. are not meaningful since the entire regression R2 concept is hard to apply in this situation. C. do not follow the standard F distribution. D. can be used to test joint hypothesis."

D

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

D

" In the Fixed Effects regression model, you should exclude one of the binary variables for the entities when an intercept is present in the equation: A. because one of the entities is always excluded. B. because there are already too many coefficients to estimate. C. to allow for some changes between entities to take place. D. to avoid perfect multicollinearity."

D

" In the case of regression with interactions, the coefficient of a binary variable should be interpreted as follows: A. there are really problems in interpreting these, since the ln(0) is not defined. B. for the case of interacted regressors, the binary variable coefficient represents the various intercepts for the case when the binary variable equals one. C. first set all explanatory variables to one, with the exception of the binary variables. Then allow for each of the binary variables to take on the value of one sequentially. The resulting predicted value indicates the effect of the binary variable. D. first compute the expected values of Y for each possible case described by the set of binary variables. Next compare these expected values. Each coefficient can then be expressed either as an expected value or as the difference between two or more expected values."

D

" In the case of the simple regression model Yi = β0 + β1Xi + ui, i = 1,..., n, when X and u are correlated, then: A. the OLS estimator is biased in small samples only. B. OLS and TSLS produce the same estimate. C. X is exogenous. D. the OLS estimator is inconsistent."

D

" In the regression model Yi = β0 + β1Xi + β2Di + β3(Xi × Di) + ui, where X is a continuous variable and D is a binary variable, to test that the two regressions are identical, you must use the: A. t-statistic separately for β2 = 0, β2 = 0. B. F-statistic for the joint hypothesis that β0 = 0, β1 = 0. C. t-statistic separately for β3 = 0. D. F-statistic for the joint hypothesis that β2 = 0, β3= 0."

D

" It is advisable to use clustered standard errors in panel regressions because: A. without clustered standard errors, the OLS estimator is biased. B. hypothesis testing can proceed in a standard way even if there are few entities (n is small). C. they are easier to calculate than homoskedasticity-only standard errors. D. the fixed effects estimator is asymptotically normally distributed when n is large."

D

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

D

" The ""before and after"" specification, binary variable specification, and ""entity-demeaned"" specification produce identical OLS estimates: A. as long as there are observations for more than two time periods. B. if you use the heteroskedasticity-robust option in your regression program. C. for the case of more than 100 observations. D. as long as T = 2 and the intercept is excluded from the ""before and after"" specification."

D

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

D

" The distinction between endogenous and exogenous variables is: A. that exogenous variables are determined inside the model and endogenous variables are determined outside the model. B. dependent on the sample size: for n > 100, endogenous variables become exogenous. C. depends on the distribution of the variables: when they are normally distributed, they are exogenous, otherwise they are endogenous. D. whether or not the variables are correlated with the error term."

D

" The following tools from multiple regression analysis carry over in a meaningful manner to the linear probability model, with the exception of the: A. F-statistic. B. significance test using the t-statistic. C. 95% confidence interval using ± 1.96 times the standard error. D. regression R2."

D

" The jth autocorrelation coefficient is defined as: A. Cov(Y_t, Y_t-1)/ √ (Var(Yt) * var(Y_t-1)) B. Cov(Y_t, Y_(t-1-1))/ √ (Var(Yt) * var(Y_t-1)) C. Cov(Y_t, u_t)/ √ (Var(Yt) * var(u_t)) D. Cov(Y_t, Y_t-j)/ √ (Var(Yt) * var(Y_(t-j))"

D

" The linear probability model is: 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. an example of probit estimation. C. another word for logit estimation. D. the application of the linear multiple regression model to a binary dependent variable."

D

" The major flaw of the linear probability model is that: A. the actuals can only be 0 and 1, but the predicted are almost always different from that. B. the regression R2 cannot be used as a measure of fit. C. people do not always make clear-cut decisions. D. the predicted values can lie above 1 and below 0."

D

" The rule-of-thumb for checking for weak instruments is as follows: for the case of a single endogenous regressor: A. a first stage F must be statistically significant to indicate a strong instrument. B. a first stage F > 1.96 indicates that the instruments are weak. C. the t-statistic on each of the instruments must exceed at least 1.64. D. a first stage F < 10 indicates that the instruments are weak."

D

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

D

" Time series analysis can answer questions regarding: A. dynamic causal effects. B. treatment and control groups at a point in time. C. economic forecasting. D. both (A) and (C)."

D

" cov (uit, uis /Xit, Xis ) = 0 for t ≠ s means that: A. there is no perfect multicollinearity in the errors. B. division of errors by regressors in different time periods is always zero. C. there is no correlation over time in the residuals. D. conditional on the regressors, the errors are uncorrelated over time."

D