Questions and Answers of Econometric Analysis 8th Edition

Residential Demand for Electricity. Belotti, Hughes and Piano Mortari (2017) estimated residential demand for electricity covering the 48 states in the continental United States plus the district of
For the Grunfeld example, replicate Tables 13.6, 13.7 and 13.8, i.e., (i) obtain the Breusch and Pagan test based on the fixed effects residuals using Stata's command xttest2. (ii) obtain Pesaran's
Test for cross-section dependence for the Gasoline example (as in problem 13.4). Do the same for the Public Capital example. What do you conclude?Data From Problem 13.4:For the Grunfeld example,
This is based on problem 95.5.4 in Econometric Theory by Baltagi (1995). Davidson and MacKinnon (1993) derive an artificial regression for testing hypotheses in a binary response model. For the fixed
This is based on problem 97.2.1 in Econometric Theory by Baltagi and Krämer (1997). Consider the following simple linear trend: model\[y_{i t}=\alpha+\beta t+u_{i t} \quad i=1,2, \ldots, N, \text {
(a) Show that the variancecovariance matrix of the disturbances in (9.1) is given by (9.2).(b) Show that the two nonzero block matrices in (9.2) can be written as in (9.3).(c) Show that \(\sigma_{u}
Wallace and Hussain type estimators for the variance components of a one-way unbalanced panel data model.(a) Verify the \(E\left(\widehat{q}_{1}\right)\) and \(E\left(\widehat{q}_{2}\right)\)
Using the Monte Carlo setup for the unbalanced one-way error component model considered by Baltagi and Chang (1994), compare the various estimatorsof the variance components and the regression
Using the Harrison and Rubinfeld (1978) data published in Belsley, Kuh and Welsch (1980) and provided on the Springer website as Hedonic.xls, reproduce Table 9.1. Perform the Hausman test based on
Consider the following unbalanced one-way analysis of variance model\[y_{i t}=\mu_{i}+u_{i t} \quad i=1, \ldots, N \quad t=1,2, \ldots, T_{i}\]where for simplicity's sake no explanatory variables are
For \(X=\left(X_{1}, X_{2}\right)\), the generalized inverse of \(\left(X^{\prime} X\right)\) is given by\(\left(X^{\prime} X\right)^{-}=\left[\begin{array}{cc}\left(X_{1}^{\prime} X_{1}\right)^{-} &
Consider the three-way error component model described in problem 3.15. The panel data can be unbalanced and the matrices of dummy variables are \(\Delta=\left[\Delta_{1}, \Delta_{2},
(a) For \(\Delta_{1}\) and \(\Delta_{2}\) defined in (9.28), verify that \(\Delta_{N} \equiv \Delta_{1}^{\prime} \Delta_{1}=\operatorname{diag}\left[T_{i}\right]\) and \(\Delta_{T} \equiv
Using the Monte Carlo setup for the unbalanced two-way error component model considered by Wansbeek and Kapteyn (1989), compare the MSE performance of the variance components and the regression
Assuming normality on the disturbances, verify (9.37), (9.40) and (9.41).\[\begin{equation*}\partial \Omega / \partial \sigma_{\mu}^{2}=\Delta_{1} \Delta_{1}^{\prime} ; \partial \Omega / \partial
Verify that the King and Wu (1997) test for the unbalanced two-way error component model is given by (9.49).\[\begin{equation*}K W=\frac{\sqrt{M_{11}-n}}{\sqrt{M_{11}+M_{22}-2 n}} L
Verify that the SLM version of the KW and HO tests are given by (9.47) with \(D\) defined in (9.50) and (9.51).\[\begin{equation*}S L M=\frac{L M_{1}-E\left(L
Using the Munnell (1990) data set considered in the empirical example, estimate the Cobb-Douglas production function investigating the productivity of public capital in each state's private output
Consider Mundlak's (1978) augmented regression in (7.35) except now allow for unbalanced panel data. Show that OLS on this augmented regression yields the unbalanced Within estimator for \(\beta\)
This is based on Baltagi and Liu (2020). (a) Derive the BLUP for an unbalanced one-way error component \(S\) periods ahead. Show that this predictor corrects the GLS prediction by a fraction of the
Measurement error and panel data. This problem is based upon Griliches and Hausman (1986). Using the simple regression given in (10.1)-(10.3):(a) Show that for the first-difference (FD) estimator of
For the rotating panel considered, assume that \(T=3\) and that the number of households being replaced each period is equal to \(N / 2\).(a) Derive the variance-covariance of the disturbances
Residential natural gas and electricity. Download the Maddala et al. (1997) data set on residential natural gas and electricity consumption for 49 states over 21 years (1970-90) from the Journal of
Patents and \(R \& D\) expenditures. Download the Hausman, Hall and Griliches (1984) panel data on patents and R\&D expenditures using 346 U.S. firms observed over the period 1975-1979.(a)
Doctor's visits. Winkelmann (2004) fits a Poisson model to explain the number of doctor's visits using panel data drawn from the GSOEP from 1995-1999. The explanatory variables include, age,
Hospital visits. Geil et al. (1997) fit a negative binomial random effects model to explain the number of hospital visits using panel data on 5180 individuals drawn from 8 waves of the GSOEP from
Matched panels: smoking and birthweight. Abrevaya (2006) estimates the effect of smoking on birth outcomes from panel data (i.e., data on mothers with multiple births). Panel data allows the
European Patents. Cincera (1997) performed count panel data regressions of patent activity using 181 international manufacturing firms investing substantial amounts in R\&D over the period 1983 to
We considered the fixed effects logit model with \(T=2\).(a) In this problem, we look at \(T=3\) and we ask the reader to compute the conditional probabilities that would get rid of the individual
Consider the Chamberlain (1985) fixed effects conditional logit model with a lagged dependent variable given in (11.16). Show that for \(T=3, \operatorname{Pr}\left[A / y_{i l}+y_{i 2}=1,
Consider the Honore and Kyriazidou (2000b) fixed effects logit model given in (11.19).(a) Show that for \(T=3, \operatorname{Pr}\left[A / x_{i}^{\prime}, \mu_{i}, A \cup B\right]\) and
This is based on Abrevaya (1997). Consider the fixed effects logit model given in (11.4) with \(T=2\). In (11.10) and (11.11) we showed the conditional maximum likelihood of \(\beta\), call it
Using the Vella and Verbeek (1998) study, download their data set which is posted on the Journal of Applied Econometrics web site and(a) Replicate their descriptive statistics given in Table I.
Using the Wooldridge (2005) study, download the data set posted on the Journal of Applied Econometrics web site and (a) Replicate the results given in Table I in that article using (xtprobit, re) in
Ruhm (1996) considered the effect of beer taxes and a variety of alcohol-control policies on motor vehicle fatality rates. The data is for 48 states (excluding Alaska, Hawaii, and the District of
This is based on the Appendix of Honoré and Tamer (2006). Suppose that \(\left(y_{i 1}, y_{i 2}, y_{i 3}\right)\) is a random vector such that \(P\left(y_{i 1}=1 /
Willis (2006) re-examines the study of Cecchetti (1986) on price adjustment behavior in the magazine industry. Cecchetti assumes that a firm's pricing rules are fixed for non-overlapping three-year
Grossman (2001) investigated the effect of multiple liabilities of bank share holders on bank failure rates in U.S. states before the Great Depression. Grossman found that double liability did reduce
This is the empirical example used in Fernandez-Val (2009) and used as example 1 in this chapter. This data is available in Stata as lfp_psid.(a) Replicate the conditional logit fe results in Table
To Trade or Not to Trade. This is based on the empirical application to bilateral trade flows between countries using data from Helpman, Melitz and Rubinstein (2008). The data set includes trade
Download the International \(R \& D\) spillovers panel data set used by Kao, Chiang and Chen (1999) along with the GAUSS subroutines from https://sites.google.com/site/chihwakao/programs.Using this
Using the Banerjee, Marcellino and Osbat (2005) quarterly data set on real exchange rate for 18 OECD countries over the period 1975:1-2002:4.(a) Replicate the panel unit root test in Table 12.1 with
Using the EViews G7 countries work file (Poolg7) containing the GDP of Canada, France, Germany, Italy, Japan, UK, and US.(a) Perform the panel unit root tests using individual effects in the
This problem is based on the Hansen and King (1996) data set and the replication by McCoskey and Selden (1998). Hansen and King (1996) studied the stationarity properties of real per capita health
Using the Penn World Table exchange rates in Stata (webuse pennxrate):(a) Perform the LLC panel unit root tests for \(\ln\) (exchange rates) for OECD countries with trend and without trend. This can
Luintel (2000) studies the behavior of real exchange rates (relative to the US dollar) using monthly data obtained from the black markets for foreign exchange of eight Asian developing countries. The
Culver and Papell (1997) test for unit roots using the inflation rates of 13 OECD countries. With individual country tests, they find evidence of stationarity in only four of the thirteen countries.
For the simple autoregressive model with no regressors given in (8.3)(a) Write the first-differenced form of this equation for \(t=5\) and \(t=6\) and list the set of valid instruments for these two
Consider the Monte Carlo setup given in Arellano and Bond (1991) (p. 283) for a simple autoregressive equation with one regressor with \(N=100\) and \(T=7\).(a) Compute the bias and mean squared
For \(T=5\), list the moment restrictions available for the simple autoregressive model given in (8.3). What overidentifying restrictions are being tested by Sargan's statistic given below
Consider three \((T-1) \times T\) matrices defined in (8.15) as follows: \(C_{1}=\) the first \((T-1)\) rows of \(\left(I_{T}-\bar{J}_{T}\right), C_{2}=\) the first-difference operator, \(C_{3}=\)
(a) Verify that GLS on (8.19) yields (8.20).(b) For the error component model with \(\widetilde{\Omega}=\widetilde{\sigma}_{u}^{2} I_{T}+\widetilde{\sigma}_{\mu}^{2} J_{T}\) and
For \(T=4\) and the simple autoregressive model considered in (8.3)(a) What are the moment restrictions given by (8.25)? Compare with Problem 8.3.(b) What are the additional moment restrictions given
Consider the Baltagi and Levin (1986) cigarette demand example for 46 states. This data, updated from 1963-92, is available on the Springer web site as cigar.txt.(a) Estimate equation (8.43) using
Consider the Arellano and Bond (1991) dynamic employment equation for 140 UK companies over the period 1979-1984. Stata has this data set as abdatal. Replicate Table 4 of Arellano and Bond (1991)
Consider the Acemoglu et al. (2005) dynamic democracy equation. Replicate all the estimation results in Table 1 of Acemoglu et al. (2005). Check the sensitivity of these results to running system
We replicated Neumayer (2003)'s two-way fixed effects estimates using a panel of homicide data from up to 117 countries over the period 1980-97. Neumayer (2003) also ran dynamic panel data estimation
For the investment equation based on Tobin's q described in Problem 4.20, perform the dynamic regressions given in Table IV of Schaller (1990), only do that using the Arellano and Bond (1991)
Acemoglu et al. (2019) provide evidence that democracy has a significant and robust positive effect on log GDP per capita. They estimate a dynamic panel data model of log GDP per capita for 175
Using Kripfganz (2016) xtdpdqml command in Stata, replicate his illustration using the Arellano and Bond (1991) dynamic employment empirical application in Problem 8.8. Unlike the original study,
Using the gravity model for foreign direct investment (FDI) of Egger and Pfaffermayr (2004) considered in Problem 7.17 where they applied a static Hausman and Taylor (1981) model, you are asked to
We considered a Hausman and Taylor (1981) estimator for a static earnings equation using the study of Cornwell and Rupert (1988); see Table 7.5. This used data on 595 individuals drawn from the PSID
Heteroskedastic individual effects. (a) For the one-way error component model with heteroskedastic \(\mu_{i}\), i.e., \(\mu_{i} \sim\left(0, w_{i}^{2}ight)\), verify that \(\Omega=E\left(u
(a) Using (5.3) and (5.4), verify that \(\Omega \Omega^{-1}=I\) and that \(\Omega^{-1 / 2} \Omega^{-1 / 2}=\Omega^{-1}\). (b) Show that \(y^{*}=\sigma_{u} \Omega^{-1 / 2} y\) has a typical element
An LM test for heteroskedasticity in a one-way error component model. Holly and Gardiol (2000) derived a score test for homoskedasticity in a one-way error component model where the alternative model
An alternative heteroskedastic error component model. (a) For the one-way error component model with heteroskedastic remainder disturbances, i.e., \(u_{i t} \sim\) (0, \(w_{i}^{2}\) ), verify that
(a) Using (5.6) and (5.7), verify that \(\Omega \Omega^{-1}=I\) and \(\Omega^{-1 / 2} \Omega^{-1 / 2}=\Omega^{-1}\).(b) Show that \(y^{*}=\Omega^{-1 / 2} y\) has a typical element \(y_{i
AR(1) process. (a) For the one-way error component model with remainder disturbances \(u_{i t}\) following a stationary \(\mathrm{AR}(1)\) process as in (5.8), verify that \(\Omega^{*}=E\left(u^{*}
(a) Using (5.12) and (5.13), verify that \(\Omega^{*} \Omega^{*-1}=I\) and \(\Omega^{*-1 / 2} \Omega^{*-1 / 2}=\) \(\Omega^{*-1}\).(b) Show that \(y^{* *}=\sigma_{\epsilon} \Omega^{*-1 / 2} y^{*}\)
Unbiased estimates of the variance components under the AR(1) model. Prove that \(\widehat{\sigma}_{\epsilon}^{2}\) and \(\widehat{\sigma}_{\alpha}^{2}\) given by (5.15) are unbiased for
AR(2) process. (a) For the one-way error component model with remainder disturbances \(u_{i t}\) following a stationary \(\operatorname{AR}(2)\) process as in (5.16), verify that
AR(4) process for quarterly data. For the one-way error component model with remainder disturbances \(u_{i t}\) following a specialized AR(4) process \(u_{i t}=\) \(ho u_{i, t-4}+\epsilon_{i t}\)
MA(1) process. For the one-way error component model with remainder disturbances \(v_{i t}\) following an MA(1) process given by (5.22), verify that \(y^{* *}=\) \(\sigma_{\epsilon} \Omega^{-1 / 2}
Prediction in the serially correlated error component model. For the BLU predictor of \(y_{i, T+1}\) given in (5.25), show that when \(v_{i t}\) follows(a) the AR(1) process, the GLS predictor is
A joint LM test for serial correlation and random individual effects. Using (4.17) and (4.19), verify (5.34) and (5.35) and derive the \(\mathrm{LM}_{1}\) statistic given in (5.36). NT NT 8L(0)/03 =
(a) Verify that \(\left(\partial V_{ho} / \partial hoight)_{ho=0}=G=\left(\partial V_{\lambda} / \partial \lambdaight)_{\lambda=0}\) where \(G\) is the bidiagonal matrix with bidiagonal elements all
Conditional LM test for serial correlation assuming random individual effects. For \(H_{4}^{b}: ho=0\) (given \(\sigma_{\mu}^{2}>0\) ),(a) Derive the score, the information matrix, and the LM
An LM test for first-order serial correlation in a fixed effects model. For \(H_{5}^{b} ; ho=\) 0 (given the \(\mu_{i}\) are fixed),(a) Verify that the likelihood is given by (5.40) and derive the
(a) Verify (5.52) for the MA(1) model. Hint: Use the fact that \(\lim E\left(u^{\prime} uight) /\) \((N T)=\lim \operatorname{tr}(\Omega) /(N T)\) for deriving plim \(Q_{0}\). Similarly, use the fact
Using the Monte Carlo setup in Baltagi and Li (1995), study the performance of the tests proposed in Table 5.4. Table 5.4 Testing for serial correlation and individual effects Null hypothesis Ho
For the gasoline data given on the Springer website, perform the tests described in Table 5.4. Table 5.4 Testing for serial correlation and individual effects Null hypothesis Ho Alternative
For the public capital data, given on the Springer website, perform the tests described in Table 5.4. Table 5.4 Testing for serial correlation and individual effects Null hypothesis Ho Alternative
Using the Grunfeld investment equation in (2.40),(a) Replicate Table 5.5 using the AR(1) estimation with common \(ho\) and heteroskedastic variances.(b) Replicate Table 5.6 using the
Seemingly unrelated regressions with one-way error component disturbances. Using the one-way error component structure on the disturbances of the \(j\) th equation given in (6.2) and (6.3), verify
Using (6.6) and (6.7), verify that \(\Omega \Omega^{-1}=I\) and \(\Omega^{-1 / 2} \Omega^{-1 / 2}=\Omega^{-1}\). = ( + ) & (IN & JT) + , & (IN & ET) V = & P + 8 - (6.6)
Special cases of the SUR model with error component disturbances. Consider a set of two equations with one-way error components disturbances.(a) Show that if the variance-covariance matrix between
Seemingly unrelated regressions with two-way error component disturbances. Using the two-way error component structure on the disturbances of the \(j\) th equation given in (6.9) and (6.10), verify
Using the form of \(\Omega\) given in (6.12) and the Wansbeek and Kapteyn (1982) trick verify (6.13). = E(uu) = Ep (IN JT) + Ex (JN IT) + v (IN IT) (6.12)
Using (6.13) and (6.14), verify that \(\Omega \Omega^{-1}=I\) and \(\Omega^{-1 / 2} \Omega^{-1 / 2}=\Omega^{-1}\). (6.13) I=! 100]= 4 25
Unbiased estimates of the variance components of the one-way SUR model. (a) Using (6.6), verify that \(\widehat{\Sigma}_{u}=U^{\prime} Q U / N(T-1)\) and \(\widehat{\Sigma}_{1}=U^{\prime} P U / N\)
Within 2SLS and Between 2SLS. Verify that GLS on (7.7) yields (7.6) and GLS on (7.9) yields (7.8), the Within 2SLS and Between 2SLS estimators of \(\delta_{1}\), respectively. 1,W2SLS = ( P) P (7.6)
Error component two-stage least squares. Verify that GLS on (7.10) yields the EC2SLS estimator of \(\delta_{1}\) given in (7.11) (see Baltagi (1981b)). X'y X'y Xx) = (x) 8 + X' X'u (7.10)
Equivalence of several EC2SLS estimators. (a) Show that \(A=[\tilde{X}, \bar{X}] ; B=\) \(\left[X^{*}, \tilde{X}ight]\) and \(C=\left[X^{*}, \bar{X}ight]\) yield the same projection, i.e.,
Within 3SLS and Between 3SLS. Verify that 3SLS on (7.21) with \(\left(I_{M} \otimes \tilde{X}ight)\) as the set of instruments yields (7.22). Similarly, verify that 3SLS on (7.23) with \(\left(I_{M}
Error component three-stage least squares. Verify that GLS on the stacked system (7.21) and (7.23) each premultiplied by \(\left(I_{M} \otimes \widetilde{X}^{\prime}ight)\) and \(\left(I_{M} \otimes
Equivalence of several EC3SLS estimators. (a) Prove that \(A=\left(I_{M} \otimes \tilde{X}, I_{M} \otimesight.\) \(\bar{X})\) yields the same projection as \(B=(H \otimes \widetilde{X}, G \otimes
Special cases of the simultaneous equations model with one-way error component disturbances. (a) Consider a system of two structural equations with one-way error component disturbances. Show that if
Mundlak's fixed effects result. (a) Using partitioned inverse, show that GLS on (7.35) yields \(\widehat{\beta}_{G L S}=\widetilde{\beta}_{\text {Within }}\) and \(\widehat{\pi}_{G L
EC2SLS and EC3SLS for the two-way error component Model. Consider the two-way error component model given in (6.9) and the covariance matrix \(\Omega_{j l}\) between the \(j\) th and \(l\) th
Using the Monte Carlo setup for a two-equation simultaneous model with error component disturbances, given in Baltagi (1984), compare EC2SLS and EC3SLS with the usual 2SLS and 3SLS estimators that

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