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Appendix A Matrix Algebra ◼ Exercises 1. For the matrices A = 1 3 3 2 4 1    and B =  AB = , 23 25 14 30    BA = , 10 22 […]

© 2012 Pearson Education, Inc. Publishing as Prentice Hall Appendix B Probability and Distribution Theory ◼ Exercises 1. How many different 5-card poker hands can be dealt from a deck of 52 cards? There are 48(13) possible hands containing 4 […]

Appendix C Estimation and Inference ◼ Exercises 1. The following sample is drawn from a normal distribution with mean  and standard deviation : x = 1.3, 2.1, 0.4, 1.3, 0.5, 0.2, 1.8, 2.5, 1.9, 3.2. Compute the mean, median, […]

Appendix D Large-Sample Distribution Theory There are no exercises for Appendix D. © 2012 Pearson Education, Inc. Publishing as Prentice Hall

Appendix E Computation and Optimization ◼ Exercises 1. Show how to maximize the function 2 ( ) /2 1 () 2 c fe − − =  d f ()/d = 2 ( ) /2 1 2 c e− − […]

Chapter 1 Econometrics There are no exercises or applications in Chapter 1. © 2012 Pearson Education, Inc. Publishing as Prentice Hall Chapter 2 The Linear Regression Model There are no exercises or applications in Chapter 2. © 2012 Pearson Education, […]

86 Greene • Econometric Analysis, Seventh Edition Applications 1. By adding the share equations vertically, we find the restrictions 1 + 2 + 3 = 1 11 + 12 + 13 = 0 12 + 22 + 23 = 0 […]

Chapter 10 Systems of Equations ◼ Exercises 1. The model can be written as 11 22 .       =+             yi yi Therefore, the […]

ˆ y = − 0.747476 + 1.058959x, ee = 120.6687 (0.95595) (0.058656) Chapter 11 Models for Panel Data ◼ Exercises 1. The pooled least squares estimator is ˆ y = −1.4684i1 − 2.8362i2 + 0.12166i3 + 1.102192x ee = 79.183 […]

failures of the assumptions of the parametric model. Consider, for example, the binary probit model of Chapter 21, which makes a strong assumption of normality and homoscedasticity. If the assumptions are correct, the probit estimator is the most efficient use […]

Chapter 13 Minimum Distance Estimation and the Generalized Method of Moments ◼ Exercises 1. The elements of J are −−       = − = =    2 3 4 2 2 2 32 […]

Therefore, the expected value is E[z] = 1 0 [ / ] [ /( 1)][ / ] /( 1). n n n E z z dz n n n n +  =  +  =  +  […]

Chapter 15 Simulation-Based Estimation and Inference and Random Parameter Models ◼ Exercises 1. Exponential: The pdf is f(x) = exp(−x). The CDF is   =  − =  − − − − − = − −   […]

L(y|) = 1 1 1 exp( ) 1 ( | ) exp( ) . ( 1) ( 1) i ii y n n n y i i i i ii f y n yy      = […]

Chapter 17 Discrete Choice © 2012 Pearson Education, Inc. Publishing as Prentice Hall convenient approach is to estimate F() and F(). These functions can then be inverted to estimate the original parameters. The invariance of maximum likelihood estimators to transformation […]

(−), (μ1 − ), (μ2 − ), and (μ3 − ) as the unknown parameters, , , , and , respectively. If we can find estimators of these, we can solve for the underlying parameters. We may write the log […]

© 2012 Pearson Education, Inc. Publishing as Prentice Hall lnL = (−n1/2)[ln(2) + ln2] − (1/(22))1(yi − )2 + 0ln(−/). In terms of  and , this is lnL = (−n1/2)[ln(2) − ln2] − (1/2)1(yi − )2 + 0ln(−) = […]

Chapter 20 Serial Correlation ◼ Exercises 1. For the first-order autoregressive model, the autocorrelation is . Consider the first difference, 1, t t t v− =  −  which has Var[vt] = 2Var[t] − 2Cov[(t, 1t−  )] = […]

Chapter 21 Nonstationary Data ◼ Exercise 1. The autocorrelations are simple to obtain just by multiplying out 2 1 ,, t t t v v v − and so on. The autocovariances are 22 1 2 2 2 2 1 […]

Chapter 4 The Least Squares Estimator ◼ Exercises 1. Consider the optimization problem of minimizing the variance of the weighted estimator. If the estimate is to be unbiased, it must be of the form c1 1 ˆ + c2 2 […]

Chapter 5 Hypothesis Tests and Model Selection ◼ Exercises 1. The estimated covariance matrix for the least squares estimator is −     1 29 0 0 0.689655 0 0 yMy = 520/(52/60) = 600. The means are […]

© 2012 Pearson Education, Inc. Publishing as Prentice Hall The regression coefficients are () . cc =                 −       […]

Chapter 7 Nonlinear, Semiparametric, and Nonparametric Regression Models ◼ Exercises 1. We cannot simply take logs of both sides of the equation as the disturbance is additive rather than multiplicative. So, we must treat the model as a nonlinear regression. […]

Chapter 8 Endogeneity and Instrumental Variable Estimation ◼ Exercises 1. There is no need for a separate proof different from the usual for OLS. Formally, however, it follows from the results at (8-4) that −      […]

Chapter 9 The Generalized Regression Model and Heteroscedasticity ◼ Exercises 1. Write the two estimators as ˆ  =  + (X−1X)−1X−1 and b =  + (XX)−1X. Then, ( ˆ  − b) = [(X−1X)−1X−1 − (XX)− 1X]  […]