1 / 17

MODELS FOR PANEL DATA

MODELS FOR PANEL DATA. PANEL DATA REGRESSION. Double subscript on variables (observations) i … households, individuals, firms, countries t … period (time-series dimension) … scalar … vector K × 1 … vector of i , t th observation on K explanatory var. ONE-WAY ERROR COMPONENT MODEL.

regis
Télécharger la présentation

MODELS FOR PANEL DATA

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. MODELS FOR PANEL DATA

  2. PANEL DATA REGRESSION • Double subscript on variables (observations) i… households, individuals, firms, countries t… period (time-series dimension) … scalar … vector K × 1 … vector of i,tth observation on K explanatory var.

  3. ONE-WAY ERROR COMPONENT MODEL • Utilized by most ofthe panel data applications … denotes unobservable individual specific effect time-invariant accounts for any individual-specific factor not included in the regression … theremainder disturbance term … varies both with individual and in time

  4. TWO-WAY ERROR COMPONENT MODEL • Potentialextension … denotesunobservabletimeeffect individual-invariant accounts for any time-specific effect that is not included in the regression

  5. PANEL DATA REGRESSION • vector form of the model … vector of ones of dimension NT stacked observations the slower index is index over INDIVIDUALS, the faster index is over TIME

  6. PANEL DATA REGRESSION • Vectorofdisturbances … matrix ofindividualdummies

  7. Notes aboutmatrices … square matrix of ones of dimension T • matrix P • theprojection matrix on • averages the observations across time for each individual • generates individual means

  8. Notes aboutmatrices • matrix Q • obtains deviations from individual means • Application of P and Q:

  9. PropertiesofPandQ • Symmetric, idempotent • P and Q are othogonal • They sum to the identity matrix

  10. THE FIXED EFFECTS MODEL (FE) • mi’s … assumed to be fixed parameters to be estimated • … assumed to be independent of the vit for all i and t • FE model is an appropriate specification if we are focusing on a specific set of N individuals (firms, countries,…) • Inference is restricted to the behavior of these sets of individuals

  11. THE FIXED EFFECTS MODEL (FE) • Model can be rewritten • OLS can be used to obtain estimates of unknown parameters • BUT! If N is large: • Too many individual dummies are included into the model • Matrix to be inverted by OLS is of dimension (N+K)

  12. THE FIXED EFFECTS MODEL (FE) • LSDV (least squares dummy variable) estimator • The model is premultiplied by Q Using the fact that: and • OLS performed on the resulting transformed model • matrix Q wipes out the individual specific effects • LSDV involves the inversion of a K × K matrix

  13. THE FIXED EFFECTS MODEL (FE) • LSDV (least squares dummy variable) estimator • unbiased estimate of • residual sum of squares from LSDV regression divided by (NT-N-K) • Not by (NT-K)!

  14. THE FIXED EFFECTS MODEL (FE) • Dummy variable trap (perfect multicolinearity) Without additional restriction just (a+mi)’s are estimable, not a and mi‘s separately • Possible restrictions: • Particular • Ad 3:

  15. THE FIXED EFFECTS MODEL (FE) • Limitations: • FE is not feasible for large panels (N is large) N-1 dummies included in the model large loss of degrees of freedom (extra N-1 parameters are to be estimated) Too many dummies may aggravate the problem of multicollinearity among regressors • (LSDV) estimator cannot estimate the effect of any time-invariant variable (race, religion, sex,…) Time-invariant variables are wiped out by the Q transformation

  16. THE FIXED EFFECTS MODEL (FE) • Properties of LSDV estimator: If is the true model: • LSDV is the BLUE as long as • as T  LSDV is consistent • If T is fixed and N  : • LSDV estimator of b is consistent • Estimators of the individual-specific effects (a+mi) are not consistent (the number of parameters increases as N increases) • OLS on (pooled OLS estimator) yields biased and inconsistent estimates (due to omission variable bias)

  17. THE FIXED EFFECTS MODEL (FE) • Testing for fixed effects: • test of the joint significance of the individual dummies • H0: • F-test: • Restricted model : model without individual dummies • Unrestricted model : model with individual dummies (FE model)

More Related