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econometric analysis 8th edition

Questions and Answers of Econometric Analysis 8th Edition

Mincer wage equation. Using the Cornwell and Rupert (1988) panel data set described in the empirical example in Sect. 7.4 and given on the Springer website as wage.xls, replicate Table 7.6 and the
A Hausman test based on the difference between fixed effects two-stage least squares and error components two-stage least squares. This is based on Problem 04.1.1 in Econometric Theory by Baltagi
Fixed Effects v.s. Omission of time-invariant variables. This is based on Oaxaca and Geisler (2003). Consider the case where the fixed effects \(\mu_{i}=\) \(Z_{i}^{\prime} \pi\) are just omitted
Economic growth and foreign aid. This is the empirical example in Sect. 7.3 based on Bruckner (2013) who investigates the simultaneity problem between per capita GDP growth and foreign aid. The data
Two-way fixed effects regression(a) Prove that the Within estimator \(\widetilde{\beta}=\left(X^{\prime} Q Xight)^{-1} X^{\prime} Q y\) with \(Q\) defined in (3.3) can be obtained from OLS on the
OLS and GLS are equivalent for the two-way Within transformed model.(a) Using generalized inverse, show that OLS or GLS on (2.6) with \(Q\) defined in (3.3) yields \(\widetilde{\beta}\), the Within
Fuller and Battese (1973) transformation for the two-way random effects model.(a) Verify (3.10) and (3.13) and check that \(\Omega^{-1} \Omega=I\) using (3.14).(b) Verify that \(\Omega^{-1 / 2}
System estimation of the two-way model: OLS versus GLS.(a) Perform OLS on the system of equations given in (3.22) and show that the resulting estimate is \(\widehat{\beta}_{O L S}=\left(X\left(I_{N
Unbiased estimates of the variance components: The two-way model. Show that the Swamy and Arora (1972) estimators of \(\lambda_{1}, \lambda_{2}\) and \(\lambda_{3}\) given by (3.19), (3.20), and
Maximum likelihood estimation of the two-way random effects model.}(a) Using the concentrated likelihood function in (3.32), solve \(\partial L_{C} / \partial \beta=0\), given \(\phi_{2}^{2}\) and
Prediction in the two-way random effects model.}(a) For the two-way error component model in (3.1), verify (3.39) and (3.42).(b) Also, show that if there is a constant in the regression \(\iota_{N
Using Grunfeld's data given on the Springer website as Grunfeld.fil, reproduce Table 3.1. Table 3.1 Grunfeld's data: Two-way error component results B B 0.116 (0.006)a 0.231 (0.025)a OLS Within
Using the gasoline data of Baltagi and Griffin (1983), given as Gasoline.dat on the Springer website, reproduce Table 3.6. Table 3.6 Gasoline demand data. Two-way error component results 3 B 0.889
Using the public capital data of Munnell (1990) given as Produc.prn on the Springer website, reproduce Table 3.7. Table 3.7 Public capital data. Two-way error component results B B3 0.309 0.594 OLS
Using the Monte Carlo setup for the two-way error component model given in (3.27) and (3.28) (see Baltagi 1981), compare the various estimators of the variance components and regression coefficients
Variance component estimation under misspecification. This is based on problem 91.3 .3 in Econometric Theory by Baltagi and Li (1991). This problem investigates the consequences of under- or
Bounds for \(s^{2}\) in a two-way random effects model. For the random two-way error component model described by (2.1) and (3.1), consider the OLS estimator of \(\operatorname{var}\left(u_{i
Nested effects. This is based on problem 93.4.2 in Econometric Theory by Baltagi (1993). In many economic applications, the data may contain nested groupings. For example, data on firms may be
Three-way error component model. Ghosh (1976) considered the following error component model:\[u_{i t q}=\mu_{i}+\lambda_{t}+\eta_{q}+u_{i t q}\]where \(i=1, \ldots, N ; T=1, \ldots, T\); and \(q=1,
A mixed-error component model. This is based on problem 95.1.4 in Econometric Theory by Baltagi and Krämer (1995). Consider the panel data regression equation with a two-way mixed error component
Openness, country size, and government size. Ram (2009) questions the body of influential research that suggests that there is a negative association between country size (as measured by logarithm of
Verify the relationship between \(M\) and \(M^{*}\), i.e., \(M M^{*}=M^{*}\), given below (4.7). Hint: use the fact that \(Z=Z^{*} I^{*}\) with \(I^{*}=\left(\iota_{N} \otimes I_{K^{\prime}}ight)\).
Verify that \(\dot{M}\) and \(\dot{M}^{*}\) defined below (4.10) are both symmetric, idempotent, and satisfy \(\dot{M} \dot{M}^{*}=\dot{M}^{*}\). = *8* + (4.10)
For Grunfeld's data given as Grunfeld.fil on the Springer website, verify the testing for the poolability results given in example 1, Sect.4.1.3.
For the gasoline data given as Gasoline.dat on the Springer website, verify the testing for the poolability results given in example 2, Sect.4.1.3.
Breusch and Pagan (1980) Lagrange multiplier test. Under normality of the disturbances, show that for the likelihood function given in (4.15),(a) The information matrix is block-diagonal between
Locally mean most powerful one-sided test. Using the results of Baltagi, Chang and \(\mathrm{Li}\) (1992), verify that the King and \(\mathrm{Wu}\) (1997) \(\mathrm{LM}\) test for \(H_{0}^{c} ;
Standardized LM tests. For \(H_{0}^{c} ; \sigma_{\mu}^{2}=\sigma_{\lambda}^{2}=0\),(a) Verify that the standardized Lagrange multiplier (SLM) test statistics derived by Honda (1991) is as described
Using the Monte Carlo setup for the two-way error component model described in Baltagi (1981),(a) Compare the performance of the Chow \(F\)-test and the Roy-Zellner test for various values of the
For the Grunfeld data, replicate Table 4.1. Table 4.1 Test results for the grunfeld example Ho Ho 798.162 (3.841) 6.454 (3.841) 28.252 (1.645) -2.540 (1.645) -2.540 (1.645) -2.433 (1.645) Null
For the gasoline data, derive a similar table to test the hypotheses given in Table 4.1. Table 4.1 Test results for the grunfeld example Ho Ho 798.162 (3.841) 6.454 (3.841) 28.252 (1.645) -2.540
For the public capital data, derive a similar table to test the hypotheses given in Table 4.1. Table 4.1 Test results for the grunfeld example Ho Ho 798.162 (3.841) 6.454 (3.841) 28.252 (1.645)
Hausman (1978) test based on an artificial regression. Show that Hausman's test can be alternatively obtained from any one of the following artificial regressions:\[\begin{aligned}& y^{*}=X^{*}
Three contrasts yield the same Hausman test.(a) Verify that \(m_{2}\) is numerically exactly identical to \(m_{1}\) and \(m_{3}\), where \(m_{i}=\widehat{q}_{i}^{\prime} V_{i}^{-1} \widehat{q}_{i}\)
Testing for correlated effects in panels. This is based on problem 95.2.5 in Econometric Theory by Baltagi (1995a). This problem asks the reader to show that Hausman's test, studied in Sect. 4.3, can
For the Grunfeld data, replicate the Hausman test results given in example 1 of Sect.4.3.
For the gasoline data, replicate the Hausman test results given in example 2 of Sect.4.3.
Perform Hausman's test for the public capital data.
The relative efficiency of the Between estimator with respect to the Within estimator. This is based on problem 99.4.3 in Econometric Theory by Baltagi (1999). Consider the simple panel data
Investment and Tobin's \(q\). Schaller (1990) uses data based on financial statements of 188 large publicly traded US firms, over the period 1951-1985, to estimate an investment equation based on
LSDV is identical to the Within estimator. Prove that β given in (2.7) can be obtained from OLS on (2.5) using results on partitioned inverse. This can be easily obtained using the
OLS and GLS are equivalent for the Within transformed model.(a) Using generalized inverse, show that OLS or GLS on (2.6) yields \(\widetilde{\beta}\), the Within estimator given in (2.7).(b) Show
Robust FE variance-covariance estimates. Verify that by stacking the panel as an equation for each individual in (2.13) and performing the Within transformation as in (2.14), one gets the Within
Fuller and Battese (1973) transformation for the one-way random effects model.(a) Verify (2.17) and check that \(\Omega^{-1} \Omega=I\) using (2.18).(b) Verify that \(\Omega^{-1 / 2} \Omega^{-1 /
Unbiased estimates of the variance components: The one-way model. Using (2.21) and (2.22), show that \(E\left(\widehat{\sigma}_{1}^{2}ight)=\sigma_{1}^{2}\) and
Swamy and Arora (1972) estimates of the variance components: The one-way model.(a) Show that \(\widehat{\hat{\sigma}}_{v}^{2}\) given in (2.24) is unbiased for \(\sigma_{v}^{2}\).(b) Show that
System estimation for the one-way model: OLS versus GLS.(a) Perform OLS on the system of equations given in (2.28) and show that the resulting estimator is pooled OLS \(\widehat{\delta}_{O L
GLS is more efficient than Within. Using the \(\operatorname{var}\left(\widehat{\beta}_{G L S}ight)\) expression below (2.30) and \(\operatorname{var}\left(\widetilde{\beta}_{W i \text { thin
Maximum likelihood estimation of the random effects model.(a) Using the concentrated likelihood function in (2.34), solve \(\partial L_{C} / \partial \phi^{2}=0\) and verify (2.35).(b) Solve
Prediction in the one-way random effects model.(a) For the predictor \(y_{i, T+S}\) given in (2.37), compute \(E\left(u_{i, T+S} u_{i t}ight)\) for \(t=\) \(1,2, \ldots, T\) and verify that
Bounds for \(s^{2}\) in a one-way random effects model. For the random one-way error component model given in (2.1) and (2.2), consider the OLS estimator of \(\operatorname{var}\left(u_{i
Heteroskedastic fixed effects models. This is based on problem 96.5.1 in Econometric Theory by Baltagi (1996). Consider the fixed effects model\[y_{i t}=\alpha_{i}+u_{i t} \quad i=1,2, \ldots, N ;
Bounds for \(s^{2}\) in a one-way random effects model. For the random one-way error component model given in (2.1) and (2.2), consider the OLS estimator of \(\operatorname{var}\left(u_{i
LSDV is identical to the Within estimator. Prove that β given in (2.7) can be obtained from OLS on (2.5) using results on partitioned inverse. This can be easily obtained using the
OLS and GLS are equivalent for the Within transformed model.(a) Using generalized inverse, show that OLS or GLS on (2.6) yields \(\widetilde{\beta}\), the Within estimator given in (2.7).(b) Show
Robust FE variance-covariance estimates. Verify that by stacking the panel as an equation for each individual in (2.13) and performing the Within transformation as in (2.14), one gets the Within
Fuller and Battese (1973) transformation for the one-way random effects model.(a) Verify (2.17) and check that \(\Omega^{-1} \Omega=I\) using (2.18).(b) Verify that \(\Omega^{-1 / 2} \Omega^{-1 /
Unbiased estimates of the variance components: The one-way model. Using (2.21) and (2.22), show that \(E\left(\widehat{\sigma}_{1}^{2}ight)=\sigma_{1}^{2}\) and
Swamy and Arora (1972) estimates of the variance components: The one-way model.(a) Show that \(\widehat{\hat{\sigma}}_{v}^{2}\) given in (2.24) is unbiased for \(\sigma_{v}^{2}\).(b) Show that
System estimation for the one-way model: OLS versus GLS.(a) Perform OLS on the system of equations given in (2.28) and show that the resulting estimator is pooled OLS \(\widehat{\delta}_{O L
GLS is more efficient than Within. Using the \(\operatorname{var}\left(\widehat{\beta}_{G L S}ight)\) expression below (2.30) and \(\operatorname{var}\left(\widetilde{\beta}_{W i \text { thin
Maximum likelihood estimation of the random effects model.(a) Using the concentrated likelihood function in (2.34), solve \(\partial L_{C} / \partial \phi^{2}=0\) and verify (2.35).(b) Solve
Prediction in the one-way random effects model.(a) For the predictor \(y_{i, T+S}\) given in (2.37), compute \(E\left(u_{i, T+S} u_{i t}ight)\) for \(t=\) \(1,2, \ldots, T\) and verify that
Using Grunfeld's data given as Grunfeld.fil on the Springer website, reproduce Table 2.1. Table 2.1 Grunfeld's data. One-way error component results B 0.231 (0.025)* OLS Between Within WALHUS AMEMIYA
Using the gasoline data of Baltagi and Griffin (1983), given as Gasoline.dat on the Springer website, reproduce Table 2.5. Table 2.5 Gasoline demand data. One-way error component results B B P 0.890
Using the Monte Carlo setup for the one-way error component model, given in Maddala and Mount (1973), compare the various estimators of the variance components and regression coefficients studied in
Bounds for \(s^{2}\) in a one-way random effects model. For the random one-way error component model given in (2.1) and (2.2), consider the OLS estimator of \(\operatorname{var}\left(u_{i
Using the public capital data of Munnell (1990) given as Produc.prn on the Springer website, reproduce Table 2.6. Table 2.6 Public capital productivity data. One-way error component results B B B4
Using the Monte Carlo design of Baillie and Baltagi (1999), compare the four predictors described in Sect. 2.5.
Heteroskedastic fixed effects models. This is based on problem 96.5.1 in Econometric Theory by Baltagi (1996). Consider the fixed effects model\[y_{i t}=\alpha_{i}+u_{i t} \quad i=1,2, \ldots, N ;
Dummy variable for one observation. Suppose the data set consists of n observations, (yn, Xn) and an additional observation, (ys, x's). The full data set contains a dummy variable, d, that equals
The National Institute of Standards and Technology (NIST) has created a Web site that contains a variety of estimation problems, with data sets, designed to test the accuracy of computer programs.
Consider a model for the mix of male and female children in families. Let Ki denote the family size (number of children), Ki = 1, c. Let Fi denote the number of female children, Fi = 0, ... , Ki.

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