《计量经济学 Econometrics》课程教学资源（PPT讲稿）Linear Models for Panel Data

Econometrics 17. Linear Models for panel data

Econometrics 17. Linear Models for Panel Data

Panel Data sets 口 Longitudinal data National longitudinal survey of youth (nls) British household panel survey ( Bhps Panel Study of Income Dynamics( PsiD a Cross section time series Grunfeld's investment data Penn world tables a Financial data by firm year t-rt=β(rmt-rt)+ti=1,,many;t=1,…many EXchange rate data, essentially infinite T, large n Effects:β=β+

Panel Data Sets  Longitudinal data ◼ National longitudinal survey of youth (NLS) ◼ British household panel survey (BHPS) ◼ Panel Study of Income Dynamics (PSID)  Cross section time series ◼ Grunfeld’s investment data ◼ Penn world tables  Financial data by firm, year ◼ rit – rft = i (rmt - rft) + εit, i = 1,…,many; t=1,…many ◼ Exchange rate data, essentially infinite T, large N ◼ Effects: i=  + vi

Terms of art a Cross sectional vs, time series variation (history consumption function studies Heterogeneity a group effects(individual effects) Fixed effects and or random effects Substantive differences? Is it possible to tell them apart in observed data?

Terms of Art  Cross sectional vs. time series variation - (history: consumption function studies)  Heterogeneity  Group effects (individual effects)  Fixed effects and/or random effects ◼ Substantive differences? ◼ Is it possible to tell them apart in observed data?

Panel data u Rotating panels: Spanish household survey Spanish income study http://www.cemfi.es/valbarran/0008r.pdf) Efficiency analysis: Efficiency measurement in rotating panel data,Heshmati, A, Applied conomics30,1998,pp.919930 o Hierarchical(nested )data sets: Student outcome, by year, district, school, teacher

Panel Data  Rotating panels: Spanish household survey ◼ Spanish income study (http://www.cemfi.es/~albarran/0008r.pdf) ◼ Efficiency analysis: “Efficiency measurement in rotating panel data,” Heshmati, A, Applied Economics, 30, 1998, pp. 919-930  Hierarchical (nested) data sets: Student outcome, by year, district, school, teacher

Nested panel data a Antweiler. w nested random effects Journal of econometrics 101, 2001, 295-313 Sulfide concentration year, country, station B+B,(logGDP/kmst+B3log(k/Lct+B4Communist+ +阝sog(O∥ Pr ice)2+βt+st+vs+Ws

Nested Panel Data  Antweiler, W., Nested Random Effects…” Journal of Econometrics, 101, 2001, 295-313 2 1 2 c,s,t 3 c,t 4 8 9 , , , Sulfide concentration(year,country,station=t,c,s) = β +β (logGDP/km ) +β log(K/L) ... + log( Pr ) c t c s t c s s Communist Oil ice t v w +  +  +  +  + +

Balanced and unbalanced panels 口 Distinction o a notation to help with mechanics a The role of the assumption Mathematical and notational convenience 口 Balanced,NT Unbalanced: 2L T Is the fixed Ti assumption ever necessary? sUr models

Balanced and Unbalanced Panels  Distinction  A notation to help with mechanics zi,t, i = 1,…,N; t = 1,…,Ti  The role of the assumption ◼ Mathematical and notational convenience:  Balanced, NT  Unbalanced: ◼ Is the fixed Ti assumption ever necessary? SUR models. N i i=1  T

Benefits of panel data a Time and individual variation in behavior unobservable in cross sections or aggregate t ime series a observable and unobservable individual heterogeneity a Rich hierarchical structures a Dynamics in economic behavior

Benefits of Panel Data  Time and individual variation in behavior unobservable in cross sections or aggregate time series  Observable and unobservable individual heterogeneity  Rich hierarchical structures  Dynamics in economic behavior

Fixed and Random Effects a Unobserved individual effects in regression ELyit Xt, CI Notation: yit=X B+C+ 12 T rows K columns a Linear specification Fixed Effects E[C X]=g(i); effects are correlated with included variables. Common CovlXitC]#0 Random Effects E[C X]=F; effects are uncorrelated with included variables. If X, contains a constant term, H=O WLOG Common CovXt C]=O, but ELc X]= His needed for the full model

Fixed and Random Effects  Unobserved individual effects in regression: E[yit | xit, ci ] ◼ Notation: ◼  Linear specification: ◼ Fixed Effects: E[ci | Xi ] = g(Xi ); effects are correlated with included variables. Common: Cov[xit,ci ] ≠0 ◼ Random Effects: E[ci | Xi ] = μ; effects are uncorrelated with included variables. If Xi contains a constant term, μ=0 WLOG. Common: Cov[xit,ci ] =0, but E[ci | Xi ] = μ is needed for the full model it it i it y = + c + x  i i1 i2 i i iT T rows, K columns         =          x x X x

Convenient notation 口 Fixed Effects Yt=01+x1β+ct Individual specific constant terms 口 Random effects Yt=X1β+ct+u Compound c"disturbance;error components

Convenient Notation  Fixed Effects  Random Effects it i it it y = + +   x Individual specific constant terms. it it it i y = + + u x  Compound (“composed”) disturbance; “error components

Assumptions for Asymptotics o Convergence of moments involving cross section X o Increasing T or Ti assumed fixed Fixed T asymptotics"(see text, p. 196) Time series characteristics are not relevant( may be nonstationary) If T is also growing need to treat as multivariate time series o Ranks of matrices. X must have full column rank. x may not if Ti< k) a Strict exogeneity and dynamics. If Xit contains yi t-1 then xit cannot be strictly exogenous. Xit will be correlated with the unobservables in period t-1.(To be revisited later.) o Empirical characteristics of microeconomic data

Assumptions for Asymptotics  Convergence of moments involving cross section Xi .  N increasing, T or Ti assumed fixed. ◼ “Fixed T asymptotics” (see text, p. 196) ◼ Time series characteristics are not relevant (may be nonstationary) ◼ If T is also growing, need to treat as multivariate time series.  Ranks of matrices. X must have full column rank. (Xi may not, if Ti < K.)  Strict exogeneity and dynamics. If xit contains yi,t-1 then xit cannot be strictly exogenous. Xit will be correlated with the unobservables in period t-1. (To be revisited later.)  Empirical characteristics of microeconomic data