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##### Eco504 midterm exam (spring 2014)

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Question;Terms and ConceptsExplain the zero condition mean assumption E(u|x) = 0Define an unbiased estimatorExplain the zero mean and zero covariance assumption E(u) = 0 and Cov(u, x) = 0Define an exogenous explanatory variableDefine an endogenous explanatory variableList the three main causes of endogeneityOmitted variablesMeasurement ErrorSimultaneityDescribe omitted variable bias ? our example was abilityDefine an instrumental variableKnow that an instrumental variable must satisfy:Cov (z, u) = 0 ? z should have no partial effect on y after x and omitted variablesare controlled for. z should be uncorrelated with omitted variables. (instrumentexogeneity).Cov (z, x)? 0 - z should be related to x. (instrument relevance)Write the reduced form for an endogenous variableShow how to write the IV estimator in terms of the population moments Cov(z, x) andCov (z, y). What assumption is needed?Write the formula for the IV estimator using sample analogs of the Cov (z, y) andCov (z, x)Define a consistent estimator ? write in terms of probability limits (plims).Sketch a short proof that the instrumental variables estimator is consistent. I am thinkingabout Problem #1 on your first homework here. You may rely on the law of largenumbers and you may rely on the result that the sample variance and sample covarianceare consistent estimators of the population variance and the population covariance.Be able to write the variance of the IV estimator in the simple case of one explanatoryvariable. Be able to compare the variance of the IV estimator to the variance of the OLSestimator. Illustrate the cost of estimating a model by IV.Review Lab # 2.Describe what happens if (z, u) are moderately correlated and the instruments are weak.Describe and explain 2 consequences of weak instrumentsDescribe how you would test the relationship between z and x in both the simpleregression model with one explanatory variable and the multiple regression model.What do we do if we have one endogenous explanatory variable and more than oneinstrument? Describe the two parts of Two-Stage Least Squares (2SLS).Describe the Hausman test. What is the null hypothesis? Be able to explain the steps youwould take to carry out the Hausman test.Review Lab # 3Be able to prove that the OLS estimator for the coefficient for the variable X is biasedtowards zero (attenuation bias) when X is measured with error and we have the classicalerrors-in-variables assumption.Be able to discuss simultaneous equations bias using a simple supply and demand model.Be able to illustrate the problem using a supply and demand graph.In the context of a simultaneous equations model, be able to illustrate simultaneousequations bias. I am not looking for a formal proof. Suppose we have two equations.Focus on the first equation and write the endogenous right-hand side variable as areduced form. Then discuss why the right-hand side endogenous variable is correlatedwith the error term in the first structural equation. The trick is to look at the reducedform error term and note that it is a function of the error term in the first structuralequation.Discuss the order condition for identification. How would you show that the ordercondition is satisfied?Discuss the rank condition for identification. How would you show that the rankcondition is satisfied in the simple two-equation model?Review Lab #4.What is a binary dependent variable?What is a latent variable model for a binary dependent variable?List three reasons why we should not estimate the binary dependent variable model as alinear probability model.What is the underlying cumulative distribution function for the logit model?What is the underlying cumulative distribution function for the probit model?Write the expression for the marginal effect of a continuous variable on the probabilitythat Y = 1 for a binary dependent variable model. Simply use the g() function. I justwant the general expression.Write the expression for the marginal effect of a dummy variable on the probability thatY = 1 for the binary dependent variable model. Simply use the G (). I just want thegeneral expression.Be able to write the expressions for the average marginal effects for both continuous andbinary explanatory variables.Be able to interpret the marginal effects.Review Lab # 5 (Parts I and II).Be able to write down the log likelihood function (using the G() function) for the simplebinary dependent variable model.Be able to use log likelihoods (Likelihood Ratio Test) to test general exclusionrestrictions.Be able to calculate the Pseudo R-SquareReview Lab # 6Describe when we would use a multinomial logit model.Be able to write the odds ratio for two alternatives, say Pi3/Pi1Write the expression for the change in the log odds with respect to a change in theexplanatory variable.Be able to interpret marginal effects from the multinomial logit model.What is an ordered probit model?Be able to construct the relevant probabilities for an ordered probit model.Be able to interpret the marginal effects from an ordered probit.Review Lab 7, Parts I and II and III.

Paper#57491 | Written in 18-Jul-2015

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