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Economics Appendix A The Relationship Between Yield And Fertilizer Graphed
260 (ii) 3 + .2(5) = 4 classes. (iii) 10(.2) = 2 classes. A.3 If price = 15 and income = 200, quantity = 120 – 9.8(15) + .03(200) = –21, which is nonsense. This shows that linear demand functions […]
Economics Appendix B The actual score depends on numerous factors
263 APPENDIX B SOLUTIONS TO PROBLEMS B.1 Before the student takes the SAT exam, we do not know – nor can we predict with certainty B.2 (i) P(X 6) = P[(X – 5)/2 (6 – 5)/2] = P(Z […]
Economics Appendix C Even if this is hard liquor
265 APPENDIX C SOLUTIONS TO PROBLEMS C.1 (i) This is just a special case of what we covered in the text, with n = 4: E( Y ) = µ and Var( Y ) = 2/4. (ii) Var(Wa) = […]
Economics Appendix D But Can Write This Quadratic Form XAP
269 APPENDIX D SOLUTIONS TO PROBLEMS diagonal matrix with jth diagonal element ajbj. Similarly, BA is an n n diagonal matrix with jth diagonal element bjaj, which, of course, is the same as ajbj. D.2 This result is easy […]
Economics Appendix E Because the Gauss-Markov assumptions hold
271 APPENDIX E SOLUTIONS TO PROBLEMS E.1 This follows directly from partitioned matrix multiplication in Appendix D. Write 1 x 1 y As shown in Section E.4, this expression is the basis for the asymptotic analysis of OLS […]
Economics Chapter 1 But Would Not Claiming That One
1 CHAPTER 1 TEACHING NOTES You have substantial latitude about what to emphasize in Chapter 1. I find it useful to talk about the economics of crime example (Example 1.1) and the wage example (Example 1.2) so that students see, […]
Economics Chapter 1 Therefore Data The Gross Domestic Product Country
Answer: b Difficulty: Easy Bloom’s: Knowledge A-Head: What is Econometrics? BUSPROG: Feedback: © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Answer: a […]
Economics Chapter 1 Under The Headings Listed Below Provide
i Chapter 15 Instrumental Variables Estimation and Two Stage 187 Least Squares Chapter 16 Simultaneous Equations Models 205 Chapter 17 Limited Dependent Variable Models and Sample 219 Selection Corrections CONTENTS PREFACE iii SUGGESTED COURSE OUTLINES iv Chapter 1 The Nature […]
Economics Chapter 10 Because This Estimate Large Magnitude Use Equation
117 Although the text is careful in stating the assumptions, in class, after discussing strict exogeneity, I leave the conditioning on X implicit, especially when I discuss the no serial correlation assumption. As the absence of serial correlation is a […]
Economics Chapter 10 A static model is postulated when a change in
Answer: a Difficulty: Easy Bloom’s: Knowledge A-Head: The Nature of Time Series Data BUSPROG: Feedback: A stochastic process refers to a sequence of random variables indexed by time. © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied […]
Economics Chapter 11 the joint probability distribution remains unchanged
Answer: c Difficulty: Moderate Bloom’s: Knowledge A-Head: Stationary and Weakly Dependent Time Series BUSPROG: Feedback: A stochastic process {xt: t = 1,2,….} with a finite second moment [E(xt2) < ∞] is covariance stationary if E(xt) is constant, Var(xt) is constant, […]
Economics Chapter 11 When Goutphrt2 Added The Regression From Part
series regressions are the hallmark of many student projects that use time series data. Therefore, students need to be alerted to the dangers of using highly persistent processes in time series regression equations. (Spurious regression problem and the notion of […]
Economics Chapter 12 In a model based on a weakly dependent time series
Answer: d Difficulty: Moderate Bloom’s: Knowledge A-Head: Properties of OLS with Serially Correlated Errors BUSPROG: Feedback: When a series is stationary, weakly dependent, and has serial correlation both the adjusted R2 and R2 are consistent estimators of the population parameter […]
Economics Chapter 12 With Only Observations Not Clear Should Prefer
143 Section 12.3, on GLS and FGLS estimation, is fairly standard, although I try to show how comparing OLS estimates and FGLS estimates is not so straightforward. Unfortunately, at the beginning level (and even beyond), it is difficult to choose […]
Economics Chapter 13 Teaching Notes While This Falls
156 Having more than two periods of panel data causes slight complications in that the errors in the differenced equation may be serially correlated. (However, the traditional assumption that the errors in the original equation are serially uncorrelated is not […]
Economics Chapter 13 The Explanatory Variable Does Not Change Over
Answer: a Difficulty: Easy Bloom’s: Knowledge A-Head: Pooling Independent Cross Sections across Time BUSPROG: Feedback: Pooling independent cross sections across time is useful in providing precise estimators if the relationship between the dependent variable and at least some of the […]
Economics Chapter 14 I Different Occupations Are Unionized Different
Choosing between the fixed effects transformation and first differencing is harder, although useful evidence can be obtained by testing for serial correlation in the first-difference estimation. If the AR(1) coefficient is significant and negative (say, less than −.3, to pick […]
Economics Chapter 14 The Cre Approach Assumes That The Unobserved
Answer: b Difficulty: Easy Bloom’s: Knowledge A-Head: Fixed Effects Estimation BUSPROG: Feedback: A pooled OLS estimator that is based on the time-demeaned variables is called the fixed effects estimator. © 2014 Cengage Learning. All Rights Reserved. May not be scanned, […]
Economics Chapter 15 The sampling variance for the instrumental variables
Answer: b Difficulty: Easy Bloom’s: Knowledge A-Head: Motivation: Omitted Variables in a Simple Regression Model BUSPROG: Feedback: Variable z is called an instrumental variable since Cov(z,x)≠0 and Cov(z,u)=0. Answer: c Difficulty: Easy Bloom’s: Knowledge A-Head: Motivation: Omitted Variables in a […]
Economics Chapter 15 When Add Electric Tv And Bicycle The
187 A leading example is estimating the return to education when unobserved ability is in the error term. We are not thinking that education and wages are jointly determined; for the vast majority of people, education is completed before we […]
Economics Chapter 16 I have seen many bad applications of SEMs
more) variables are jointly determined does not mean that it is appropriate to specify and estimate an SEM. I have seen many bad applications of SEMs where no equation in the system can stand on its own with an interesting […]
Economics Chapter 16 Which of the following tests can be used to test
Answer: b Difficulty: Easy Bloom’s: Knowledge A-Head: The Nature of Simultaneous Equations Models BUSPROG: Feedback: Pi and Qi are the endogenous variables in the given simultaneous equation model. © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied […]
Economics Chapter 17 A spurious regression refers to a situation
Answer: b Difficulty: Easy Bloom’s: Knowledge A-Head: Specifying Logit and Probit Models BUSPROG: Answer: d Difficulty: Easy Bloom’s: Knowledge A-Head: Specifying Logit and Probit Models BUSPROG: Feedback: The logit model is an example of a binary response model. Answer: a […]
Economics Chapter 17 Several new time series data sets include OKUN
231 C17.6 The results of an OLS regression using only the uncensored durations are given in the following table: Dependent Variable: log(durat) Independent Variable Coefficient (Standard Error) workprg .092 (.083) (.08221) married .239 (.099) educ −.019 (.019) age .00053 (.00042) […]
Economics Chapter 17 The Model Can Estimated Ols Maximum Likelihood
CHAPTER 17 TEACHING NOTES I emphasize to the students that, first and foremost, the reason we use the probit and logit models is to obtain more reasonable functional forms for the response probability. Once we move to a nonlinear model […]
Economics Chapter 18 A good research question should be backed by
© 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Answer: c Difficulty: Easy Bloom’s: Knowledge A-Head: Infinite Distributed Lag Models BUSPROG: Feedback: The […]
Economics Chapter 18 The apparent attenuation bias of OLS for the coefficient
243 The forecasting section is heavily oriented towards regression methods and, in particular, autoregressive models. These can be estimated using any econometrics package, and forecasts and mean absolute errors or root mean squared errors are easy to obtain. The interest […]
Economics Chapter 19 Teaching Notes Students Should Read This
259 forces them to interpret their findings. While leaving the topic to each student’s discretion is more interesting, I find that many students flounder with an open-ended assignment until it is too late. For a second-semester course, or a senior […]
Economics Chapter 19 In a stepwise regression, the dependent variable is regressed
Answer: a Difficulty: Easy Bloom’s: Knowledge A-Head: Literature Review BUSPROG: Feedback: A good research paper should contain a review of relevant literature. © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a […]
Economics Chapter 2 Again Can Apply Part II With And
6 difference between an estimator that is unbiased conditional on the outcome of the covariates and one that is unconditionally unbiased. If the distribution of the 𝑥𝑖 is such that they can all equal the same value with positive probability […]
Economics Chapter 2 The error u has the same variance given any value
© 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Answer: c Difficulty: Easy Bloom’s: Comprehension A-Head: Definition of the Simple Regression Model BUSPROG: […]
Economics Chapter 3 Consider the following regression equation
Answer: d Difficulty: Easy Bloom’s: Knowledge A-Head: Mechanics and Interpretation of Ordinary Least Squares BUSPROG: Analytic Answer: c Difficulty: Easy Bloom’s: Knowledge A-Head: Motivation for Multiple Regression BUSPROG: Feedback: In the equation, y = β0+ β1×1+ β2×2+ u, β2 is […]
Economics Chapter 3 The comparison of simple and multiple regression
19 I find extensive treatments of multicollinearity, where one “tests” or somehow “solves” the multicollinearity problem, to be misleading, at best. Even the organization of some texts gives the impression that imperfect collinearity is somehow a violation of the Gauss-Markov […]
Economics Chapter 4 A normal variable is standardized by
© 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Answer: c Difficulty: Moderate Answer: d Difficulty: Moderate Bloom’s: Knowledge A-Head: Sampling Distributions of […]
Economics Chapter 4 These Effects Certainly Cannot Ignored While The
34 CHAPTER 4 TEACHING NOTES At the start of this chapter is good time to remind students that a specific error distribution played no role in the results of Chapter 3. That is because only the first two moments were […]
Economics Chapter 5 But it is conceptually more difficult than the earlier
consistency and asymptotic normality of OLS. (Conveniently, the same assumptions that work for finite sample analysis work for asymptotic analysis.) More advanced students can follow the proof of consistency of the slope coefficient in the bivariate regression case. Section E.4 […]
Economics Chapter 5 then when the sample size tends to infinity
Answer: c Difficulty: Easy Answer: b Difficulty: Moderate Bloom’s: Knowledge A-Head: Consistency BUSPROG: Feedback: The standard error of a regression is not an unbiased estimator for the standard deviation of the error in a multiple regression model. Answer: b Difficulty: […]
Economics Chapter 6 A change in the unit of measurement of the dependent
Answer: a Difficulty: Moderate Bloom’s: Comprehension A-Head: Effects of Data Scaling on OLS Statistics BUSPROG: Feedback: Changing the unit of measurement of any independent variable, where log of the independent variable appears in the regression only affects the intercept. This […]
Economics Chapter 6 This Would Make The Calculation Easier Iv
54 I often have students and colleagues ask if there is a simple way to predict y when log(y) has been used as the dependent variable, and to obtain a goodness-of-fit measure for the log(y) model that can be compared […]
Economics Chapter 7 The income of an individual in Budopia depends on his ethnicity
Answer: a Difficulty: Medium Bloom’s: Comprehension A-Head: Describing Qualitative Information BUSPROG: Feedback: A binary variable is used to describe qualitative information in regression model. Therefore, such a variable will be used to describe whether it rained on a particular day […]
Economics Chapter 7 This is a fairly standard chapter on using qualitative
In allowing for different slopes, it is important, as in Chapter 6, to appropriately interpret the parameters and to decide whether they are of direct interest. For example, in the wage equation where the return to education is allowed to […]
Economics Chapter 8 Ols Fitted Values From Part I The
measures. The key is that these are estimates of the population R-squared, 1 – [Var(u)/Var(y)], where the variances are the unconditional variances in the population. The usual R-squared, and the adjusted version, consistently estimate the population R-squared whether or not […]
Economics Chapter 8 The White Test Assumes That The Square
Answer: a Difficulty: Easy Answer: c Difficulty: Easy Bloom’s: Knowledge A-Head: Consequences of Heteroskedasticity for OLS BUSPROG: Feedback: The Ordinary Least Square estimators are no longer the best linear unbiased estimators if heteroskedasticity is present in a regression model. Answer: […]
Economics Chapter 9 They Are Jointly Very Significant With F2925
103 9.3 and 9.4. The first shows that controlling for IQ can substantially change the estimated return to education, and the omitted ability “bias” is in the expected direction. (Controlling for IQ lowers the return to education.) Interestingly, education and […]
Economics Chapter 9 Which of the following is true of Regression Specification
Answer: c Difficulty: Easy Bloom’s: Knowledge A-Head: Functional Form Misspecification BUSPROG: Feedback: A regression model suffers from functional form misspecification if an interaction term is omitted. © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, […]