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Session 2: The two-­‐way error component model ! 
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First: a look back! general panel data linear model Individuals (country, group)
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so far, one-­‐way error component models !  pooled model !  fixed effects models ! 
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between within random effects models !  various es;ma;on methods ! 
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swar walhus amemiya nerlove Session 2: The two-­‐way error component model ! 
What is the main purpose of panel data analysis (in microeconomics)? !  increased precision in es;ma;on !  more data (pooling) !  modeling unobserved heterogeneity !  in individuals !  over ;me ! 
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spliEng error into idiosyncra;c part and unobserved heterogeneity idiosyncra;c error is usually assumed to be well-­‐behaved ! 
homogeneous ! 
exogeneous (uncorrelated with anything else) individual heterogeneity ! 
heterogenous ! 
endogeneous (correlated with regressors) Two-­‐way error component regression model ! 
general panel data linear model Individuals (country, group)
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we combine the unobserved individual effects model and the unobserved 1me effects model Individuals (country, group)
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Two-­‐way error component regression models Unobserved effects model (separate error terms for each individual and for each ;me period) "  models individual heterogeneity that is constant over ;me and ;me period heterogeneity that is constant for all individuals ! 
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Can be es;mated in two ways: as fixed effects or as random effects " 
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Es;ma;on as fixed effects (within or least squares dummy variable) Es;ma;on as random effects Two-­‐way error component regression models Estimation as fixed effects (within or least squares dummy variable)
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Two-­‐way error component regression models Estimation as fixed effects (within or least squares dummy variable)
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Within estimator can not estimate the effect of time-invariant and
individual invariant variables (because Q transformation sweeps them
out)
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Two-­‐way fixed effects models for Grunfeld data Two-­‐way fixed effects models for Grunfeld data Fixed effects for unobserved individual heterogeneity
Two-­‐way fixed effects models for Grunfeld data Fixed effects for unobserved time period heterogeneity
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Two-­‐way error component regression models " 
Es;ma;on as random effects " 
We can define a corresponding transforma;on matrix " 
with homoscedas;c, but correlated disturbances Two-­‐way error component regression models " 
Es;ma;on as random effects " 
this yields the following correla;ons Two-­‐way error component regression models " 
Es;ma;on as random effects " 
can be tackled as a general least squares problem (GLS) resul;ng in " 
various feasible GLS es;mators are equivalent to OLS on par;ally demeaned data " 
with 4
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Two-­‐way random effects models for Grunfeld data Two-­‐way random effects models for Grunfeld data Partially demeaning parameters
1: Swamy and Aurora
2: Wallace and Hussain
3: Amemiya
Various computa?onal approaches " 
Linear model approach "  Ordinary Least Squares "  Weighted Least Squares "  Generalized Least Squares (feasible GLS) " 
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Least squares es;ma;on typically involves three steps: "  data-­‐transforma;on or first stage es;ma;on "  parameter es;ma;on using OLS "  variance-­‐covariance es;ma;on of the es;mates (VCE) to correct for panel structure parameter es;mates are some;mes refined using itera;vely reweighted least squares / Maximum likelihood es;ma;on 5
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Various computa?onal approaches " 
es;ma;on of models with variable coefficients Various computa?onal approaches " 
es;ma;on of models with variable coefficients Various computa?onal approaches " 
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es;ma;on of models with variable coefficients general methods of moments es;ma;on "  mostly for dynamic panel models general feasible generalized least squares es;ma;on "  used for variance covariance es;ma;on for es;mates "  robust es;ma;on for cluster structure "  requires n much larger than T 6
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One/Two-­‐way error component regression models " 
Some tests "  Test of Poolability "  standard F-­‐test comparing the model with variable coefficients with the pooled model One/Two-­‐way error component regression models " 
Some tests "  Tests for individual and ;me effects "  Lagrange mul;plier tests "  four different types implemented in plm package One/Two-­‐way error component regression models " 
Some tests "  Tests for individual and ;me effects "  F tests "  comparing within and pooling models 7
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One/Two-­‐way error component regression models " 
Some tests "  Hausman tests "  mainly used to compare fixed and random effects models "  applicable to compare any two panel models One/Two-­‐way error component regression models " 
Some tests "  Tests of serial correla;on " 
a rich list in plm package One/Two-­‐way error component regression models " 
Some tests "  Tests of serial correla;on " 
a rich list in plm package 8
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One/Two-­‐way error component regression models " 
Some tests "  Tests of cross-­‐sec;onal dependence One/Two-­‐way error component regression models " 
Some tests "  Unit root tests One/Two-­‐way error component regression models " 
Some tests "  Robust covariance matrix es;ma;on "  tests in the package lmtest 9
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Panel data: CigareDe consump?on in US ! 
a panel of 46 observa;ons from 1963 to 1992 " 
total number of observa1ons : 1380 " 
number of different variables: 9 of which two are iden1fiers ! 
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state: state abbrevia;on year; the year price: price per pack of cigare^es pop: popula;on pop16: popula;on above the age of 16 cpi: consumer price index (1983=100) ndi: per capita disposable income sales: cigare^e sales in packs per capita ! 
pimin: minimum price in adjoining states per pack of cigare^es Source: Online complements to Baltagi (2001). h^p://www.wiley.com/legacy/wileychi/baltagi References: Baltagi, B. H. (2001) Econometric Analysis of Panel Data, 2nd ed., John Wiley and Sons. Baltagi, B.H. and D. Levin (1992) “Cigare^e taxa;on: raising revenues and reducing consump;on”, Structural Changes and Economic Dynamics, 3, 321–335. Baltagi, B.H., J.M. Griffin and W. Xiong (2000) “To pool or not to pool: homogeneous versus heterogeneous es;mators applied to cigare^e demand”, Review of Economics and Sta;s;cs, 82, 117–126. Summary " 
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Two-­‐way error component models "  unobservable individual and ;me effects model fixed effects models "  within random effects models different es;ma;on procedures various tests
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