Exam 2 Study Guide

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Exam 2 Study Guide

study guide

Study Guide
Cornell University
Econ 3120 - Applied Econometrics

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Exam # 2 Study Guide In three or fewer sentences, describe each of the following concepts. Do not use or simply translate any formulas. (a) Gauss-Markov Theorem Answer. The Gauss-Markov Theorem states that under assumptions MLR.1-MLR.5, the OLS estimators are the best (minimum variance) linear unbiased estimators. (b) Collinearity Answer. In the linear regression context, collinearity occurs when one independent variable can be expressed as a linear combination of the other independent variables. When this occurs, the OLS estimates for the collinear variables cannot be computed. (c) Slope parameter Answer. The slope parameter tells us how the dependent variable changes when there is a change in the independent variable. It may be interpreted differently based on the functional forms of both the dependent and independent variables. (d) Explained sum of squares (SSE) Answer. The explained sum of squares (SSE) is the sample variation in the predicted values that result from a regression. It captures the variation in the dependent variable that can be explained by the independent variable. 2. Suppose you estimate the following model of weight on height for a random sample of 20-year-old men: Weight = α0 +α1 ·Height +u, where Weight is measured in pounds and Height is measured in inches. (a) Give an interpretation of the estimated slope coefficient. 1 Answer. The slope coefficient, α1, is the change in Weight (in pounds) for a one-inch change in Height. (b) Suppose instead that you estimate: log(Weight) = β0 +β1 · Height +ε. Now what is the interpretation of the estimated slope coefficient? Answer. The slope coefficient, β1, is the percentage change in Weight for a one-inch change in Height. (c) Finally, suppose you estimate: log(Weight) = γ0 +γ1 · log(Height) +ψ. What is the interpretation of the estimated slope coefficient in this case? Answer. The slope coefficient, γ1, is the percentage change in Weight for a one- percent change in Height. 3. Consider the wage regression model: log(wage) = β0 + β1educ + β2exper + β3exper2 + u, where exper represents the worker’s experience in the labor market (usually calculated as age-18) (d) Explain what the coefficient β1 represents. Show how to derive this by taking the derivative of both sides of the equation with respect to education, holding experience fixed. Solution: taking the derivative of both sides of the equation with respect to educ, we have β1 = dlog(wage) deduc = dwage wage deduc = ∆wage wage ∆educ , By rearranging the above equation, we have ∆wage wage ×100% = β1 ×100% ×∆educ. Thus, based on these math derivation, we claim that additional one year of education will predict β1 ×100% increase in salary. (e) Perform the following hypothesis tests. For each tests, state the null hypothesis, the alternative, the test statistic, the distribution of the test statistic under the null, the rejection rule, and the outcome of your test. The Appendix contains Stata output of OLS regressions that may be useful. Note that we have supressed some of the statistics in the output. i. Test ...

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