Econometrics Final
Which of the following is a drawback of including proxy variables in a regression model?
It exacerbates multicollinearity.
Functional Form Misspecification
Omitting a key variable can cause correlation between the error and some explanatory variables which leads to bias and inconsistancy
Increasing the number of overidentifying restrictions can cause severe biases in two stage least squares estimators.
True
The two stage least squares estimator is less efficient than the ordinary least squares estimator when the explanatory variables are exogenous.
True
Which of the following problems can arise in policy analysis and program evaluation using a multiple linear regression model?
The model can produce predicted probabilities that are less than zero and greater than one.
What will you conclude about a regression model if the Breusch-Pagan test results in a small p-value?
The model contains heteroskedasticty.
General T Stat
t = (estimated - hypothesized value )/ Standard error
A test for heteroskedasticty can be significant if _____.
the functional form of the regression model is misspecified
The order condition for identification of an equation requires that there should be _____.
at least as many excluded exogenous explanatory variables as there are included endogenous explanatory variables
Measurement Error
difference between the observed and actual value e0 = y- y_star
Consider the following simple regression model y = β0 + β1x1 + u. Suppose Corr(x,u) > 0, Corr(z,x) > 0, and Corr(z,u) < 0. Then, the IV estimator has a(n) _____.
downward bias
The following simple model is used to determine the annual savings of an individual on the basis of his annual income and education. Savings = β0 + 0 Edu + β1Inc + u The variable 'Edu' takes a value of 1 if the person is educated and the variable 'Inc' measures the income of the individual. Refer to the above model. If 0 > 0, _____.
educated people have higher savings than those who are not educated
The procedure of comparing different instrumental variables estimates of the same parameter is an example of testing _____.
overidentifying restrictions (tested using 2SLS estimators)
Proxy Variable
related to the unobserved variable that we would like to control for in analysis. Assumption that error is uncorrelated with proxy Correlation with another independent variable
The square root of the quantity Var(Bj(hat))= sum(r^2*u^2)/SSR^2 is called the _____ for Bj(hat) .
heteroskedasticity-robust standard error
Dummy Variables
Allow for two different intercepts Compared to a base group , always has to omit one group
SLR Assumptions
1. Linear in Parameter (dep. y is related to ind. x and error) 2. Random Sampling (follows pop. model) 3. Sample Variation in the explanatory variable (no constant numbers) 4. Zero Conditional Mean (sum of residuals=0) 5. Homoskedacity (error has same variance from mean)
MLR Assumption
1. Linear in Parameters 2. Random Sampling 3. No Perfect Colinearity 4. Zero Conditional Mean 5. Homoskedasity 6. Normality
The income of an individual in Budopia depends on his ethnicity and several other factors which can be measured quantitatively. If there are 5 ethnic groups in Budopia, how many dummy variables should be included in the regression equation for income determination in Budopia?
4
Heteroskedactic Robust Errors
Attributed to White Always advisable to do with large sample sizes
Multiple Probability Model (LMP)
Binary dependent variable. With a response probability is linear in the parameters Bj in the LPM, Bj measures the probability of success when xj changes
Consider the following simple regression model: y = 0 + 1x1 + u. Suppose z is an instrument for x. Which of the following conditions denotes instrument exogeneity?
Cov(z,u) = 0
Which of the following types of sampling always causes bias or inconsistency in the ordinary least squares estimators?
Endogenous sampling
Chow Statistic
F test that is only valid under homoskedacity F = [ SSR1 - (SSR1 + SSR2 )] * [n-2(k+1)] SSR1 + SSR2 k
RESET Test
General Test for Functional Form Misspecifications, adds polynomials into the OLS fitted values to equasions to detect general kinds of fitted values to include in an expanded regression. Can be made robust to heteroskedacity Does not give direction if model is rejected
Which of the following is true of measurement error?
If measurement error in an independent variable is uncorrelated with the variable, the ordinary least squares estimators are unbiased.
Which of the following is true of Chow test?
It is only valid under homoskedasticty.
Which of the following is true of Regression Specification Error Test (RESET)?
It tests if the functional form of a regression model is misspecified.
Exogenous Smapling
Non random sampling selection based on the independent variables
Endogenous Sampling
Non random sampling sampling based on the dependent variable will always be biased
Micronumerosity
Problem of small sample size
Goodness of Fit
R^2 = SSE / SST = 1-SSR/SST
Which of the following tests helps in the detection of heteroskedasticity?
The Breusch-Pagan test
Which of the following is true of heteroskedasticity?
The Ordinary Least Square estimators are not the best linear unbiased estimators if heteroskedasticity is present.
Which of the following Gauss-Markov assumptions is violated by the linear probability model?
The assumption of constant variance of the error term.
Which of the following assumptions is known as exclusion restrictions?
The assumption that an exogenous explanatory variable is excluded from a regression model and is uncorrelated with the error term.
Which of the following assumptions is required for two-stage least squares estimation method?
The error term has zero mean.
Which of the following is true of the OLS t statistics?
The heteroskedasticity-robust t statistics are justified only if the sample size is large.
Which of the following is true of two stage least squares estimators?
The two stage least squares estimators are biased if the regression model exhibits multicollinearity.
In a regression model, which of the following will be described using a binary variable?
Whether it rained on a particular day or it did not
Lagged Dependent Variable
accounts for historical factors that cause current differences from a previous past time period
Heteroskedacity
fails whenever the variance of the unobserved factos changes across different segments of the population, where the segments are determined by different values of the explanatory variable OLS unbiased and consistent under heteroskedacity However, invalidates variance formuals for OLS estimators (can't use normal F or T test
Consider the following simple regression model: y = 0 + 1 x 1 + u. In order to obtain consistent estimators of 0 and 1, when x and u are correlated, a new variable z is introduced into the model which satisfies the following two conditions: Cov(z,x) 0 and Cov (z,u) = 0. The variable z is called a(n) _____ variable.
instrumental
Consider the following equation for household consumption expenditure: Consmptn= 0 + 1 Inc + 2Consmptn-1+ u where 'Consmptn' measures the monthly consumption expenditure of a household, 'Inc' measures household income and 'Consmptn-1' is the consumption expenditure in the previous month. Consmptn-1 is a _____ variable.
lagged dependent
The quarterly increase in an employee's salary depends on the rating of his work by his employer and several other factors as shown in the model below: Increase in salary= 0 +0Rating + other factors. The variable 'Rating' is a(n) _____.
ordinal variable
Stratified Sampling
population divided into non overlapping exhaustive groups
The method of data collection in which the population is divided into nonoverlapping, exhaustive groups is called _____.
stratified sampling
The following simple model is used to determine the annual savings of an individual on the basis of his annual income and education. Savings = β0 + 0 Edu + β1Inc + u The variable 'Edu' takes a value of 1 if the person is educated and the variable 'Inc' measures the income of the individual. Refer to the model above. The benchmark group in this model is _____.
the group of uneducated people
The classical errors-in-variables (CEV) assumption is that _____.
the measurement error is uncorrelated with the unobserved explanatory variable
The test for overidentifying restrictions is valid if _____.
the regression model exhibits homoskedasticity
Consider the following simple regression model y = β0 + β1x1 + u. Suppose Corr(x,u) > 0, Corr(z,x) > 0, and Corr(z,u) < 0. Then, the OLS estimator has a(n) _____.
upward bias
F Stat
used to test to see if variables are jointly significant or insignificant F = ((SSRr - SSRur) / Q) ( SSRur / (n-k-1)) where Q is number of restrictions SSRr sum of squared residuals from restricted model Always non negative
Consider the following regression equation: y= 0+ 1x1 + ... + kxk + u In which of the following cases, is 'y' a discrete variable?
y indicates the number of children in a family
Consider the following regression equation: y= 0+ 1x1+ ...+ kxk + u In which of the following cases, the dependent variable is binary?
y indicates whether an adult is a college dropout