Applied Econometrics

How do discrete and continuous random variables differ?

A discrete random variable takes a countable set of distinct values, while a continuous random variable can take any value within a range.

Which of these is not an unbiased estimator of the population mean?

The geometric mean of the observations.

What statistical meaning does a p-value convey in hypothesis testing?

The probability of obtaining test results at least as extreme as those observed, if the null hypothesis were true.

What does the R-squared statistic reveal about a regression model?

The proportion of variation in the dependent variable that is predictable from the regressors.

Which assumption must hold for OLS estimators to be interpreted as measuring causal effects?

The expectation of the error term conditional on X must be zero: E[u|X] = 0.

Which is a consequence of heteroskedasticity in regression analysis?

Unreliable calculated standard errors from standard formulae.

In the multiple regression model Yi = β0 + β1X1i + β2X2i + ui, what specific interpretation applies to β1?

The marginal effect of X1 on Y when X2 remains unchanged.

What causes omitted variable bias in econometric analysis?

Excluding a relevant explanatory variable that correlates with included variables.

Which of the following is the most important statistical problem caused by imperfect multicollinearity?

The coefficient standard errors are large, reducing statistical precision.

What should researchers conclude if a confidence interval for a difference between two population means contains zero?

The observed difference is not large enough to reject the null hypothesis of equal means.

What statistical property ensures that an estimator converges to the true parameter value as sample size approaches infinity?

Consistency.

In the wage equation Salaryi = β0 +β1Femalei +ui, if β1 = −8000, what does this imply?

On average, females earn $8000 less than males, all else equal.

Which regression diagnostic statistic is expressed in the same units as the dependent variable?

The standard error of the regression (root MSE).

What is the primary difference between testing individual hypotheses and joint hypotheses in regression analysis?

Joint tests account for correlations between estimators, while individual tests examine coefficients in isolation.

What does the null hypothesis H0 : β1 = β2 = β3 = 0 test in a regression model with three education variables?

Whether education as a whole has any significant effect on the dependent variable.

Which test measures the improvement in model fit when comparing nested models?

F-test.

What might occur during hypothesis testing if two highly correlated variables are included in a regression model?

The variables might be jointly significant (significant F-test) but individually insignificant (insignificant t-tests).

What does a low p-value for the F-statistic indicate in a joint hypothesis test of H0 : β1 = β2 = β3 = 0?

There is strong evidence against the hypothesis that all three coefficients are simultaneously zero.

In a regression of salary on years of education, what would be the most likely direction of bias if ability is omitted?

Upward bias because ability is positively correlated with both education and salary.

What is the reason economists report multiple specifications of the same model in research papers?

To test whether key results are robust to changes in model formulation.

In a regression model with a quadratic term, how does the effect of X on Y differ from a linear model?

The effect varies with the value of X and equals β1 + 2β2X.

What is a key advantage of using natural logarithms in regression models?

They compress wide-ranging data and reduce the influence of extreme values.

In a log-linear model ln(Y) = β0 + β1X + u, if β1 = 0.03, what is the effect of a 1-unit increase in X on Y?

Y increases by approximately 3%.

In a regression model with an interaction term, what does β3 measure?

How the effect of X1 on Y changes with different values of X2.

In a wage equation, if β1 = 2.5, β2 = −5, and β3 = −0.5, what is the gender wage gap for someone with 10 years of experience?

−15.

What is a limitation of the Linear Probability Model for binary outcomes?

It can predict probabilities outside the [0,1] range.

In binary response models like logit and probit, what is a 'latent variable'?

An unobserved continuous variable that determines the binary outcome when it exceeds a threshold.

What is the key difference between logit and probit models?

They assume different distributions for the error term in the latent variable model.

In maximum likelihood estimation for binary response models, what are we trying to maximize?

The probability of observing our exact sample pattern of ones and zeros given the model parameters.

What can make a coefficient estimate statistically significant but economically trivial?

A very large sample size combined with a small effect size.

What does the interaction term in a regression model indicate?

It indicates how the relationship between one independent variable and the dependent variable changes at different levels of another independent variable.

Why might a researcher choose to use a log-linear model?

To interpret coefficients as elasticities, which represent percentage changes.

What does the term 'indeterminate bias' refer to in econometric models?

It refers to bias that depends on other factors in the model.

What is the effect of a quadratic term in a regression model?

It allows for a non-linear relationship between the independent variable and the dependent variable.

What is the significance of β1 in a log-linear model?

It represents the percentage change in Y for a one-unit change in X.

What does a confidence interval that includes zero indicate about a coefficient?

It suggests that the coefficient may not be statistically significant.

What is the role of maximum likelihood estimation in econometrics?

To estimate the parameters of a model by maximizing the likelihood of the observed data.

What does it mean if a model predicts probabilities outside the [0,1] range?

It indicates a limitation of the model, specifically the Linear Probability Model.

In the context of econometrics, what is an interaction term?

A term in a regression model that represents the combined effect of two variables on the dependent variable.

What is the implication of having a large standard error in a coefficient estimate?

It suggests that the estimate is less precise and may not be statistically significant.

What is the primary focus of causal inference in econometrics?

Determining whether X causes Y, rather than just being associated with

What is the difference between a discrete and a continuous random variable?

A discrete random variable takes a finite number of values while a continuous random variable takes values on a continuum.

In hypothesis testing, what does the p-value represent?

The probability of observing data at least as extreme as the sample data assuming the null hypothesis is true

What is the interpretation of a 95% confidence interval for a parameter?

If we repeated sampling many times, approximately 95% of similarly constructed intervals would contain the true parameter

In the regression model Yi = β0+β1Xi+ui, what does the coefficient β1 represent?

The change in Y associated with a one-unit increase in X

What is the computational objective of Ordinary Least Squares (OLS) estimation?

To find the line that minimizes the sum of squared residuals

What does the R-squared value in a regression analysis represent?

The fraction of variance in the dependent variable explained by the independent variable(s)

Which of the following is a necessary assumption for the OLS estimator to have a causal interpretation?

The error term has mean zero given X: E[u|X] =0

What is heteroskedasticity in the context of regression analysis?

When the variance of the error term is not constant across all values of the independent variables

If heteroskedasticity is present in a regression model, which of the following statements is true?

The standard errors of the coefficients are incorrect, affecting hypothesis tests and confidence intervals

In a multiple regression model Yi = β0 + β1X1i + β2X2i + ui, what does the coefficient β1 represent?

The change in Y associated with a one-unit increase in X1, holding X2 constant

Consider a crop yield model: Y ieldi = β0 + β1Rainf alli + β2T emperaturei + UI. If β1 = 0.5 and β2 = −0.3, how would you interpret these coefficients?

Each additional inch of rainfall is associated with a 0.5 bushel/acre increase in yield, holding temperature constant; each additional degree Fahrenheit is associated with a 0.3 bushel/acre decrease in yield, holding rainfall constant

What is omitted variable bias in regression analysis?

The bias in coefficient estimates that occurs when a relevant variable is excluded from the model and is correlated with included variables

How do R-squared and adjusted R-squared differ in multiple regression?

R-squared never decreases when adding variables, while adjusted R-squared penalizes for additional regressors and can decrease

What happens under perfect multicollinearity in a regression model?

Unique coefficient estimates cannot be determined because one regressor is an exact linear function of others

When imperfect multicollinearity exists in a regression model, what is the primary consequence?

The standard errors of the coefficients increase, making estimates less precise

When interpreting a confidence interval for the difference between two means, if the interval includes zero, what can be concluded?

There is no statistically significant difference between the means

Which of the following is an example of an biased estimator of the population mean?

The root mean square (RMS)

What property describes an estimator gets closer to the true parameter value as the sample size increases?

Consistency

What is perfect multicollinearity in a regression model?

When one regressor is an exact linear function of other regressors

In a regression model Yi = β0 + β1Di with a Di being binary explanatory, what is the interpretation of β0?

The expected value of Y when D = 0

In a simple wage regression model W agei = β0 + β1M alei + ui, if β1 = 5000, what is the correct interpretation?

Males earn $5000 more than females, on average

Which measure of regression fit maintains the same units as the dependent variable?

Standard Error of Regression (SER)