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# st: RE: RE: how many d.f. in the vcv for the within estimator?

 From "Impavido, Gregorio" To "statalist@hsphsun2.harvard.edu" Subject st: RE: RE: how many d.f. in the vcv for the within estimator? Date Wed, 12 Dec 2012 08:49:13 -0500

```Mark, thank you.  I do not have your text at hand but so does Baltagi "Econometric Analysis of Panel Data" fourth edition page 16. I am not disputing the point.  I was trying to understand the rationale. I would have thought that the Q transform is not simply a computational expedient but a way to improve efficiency re LSDV.

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Schaffer, Mark E
Sent: Tuesday, December 11, 2012 7:55 PM
To: statalist@hsphsun2.harvard.edu
Subject: st: RE: how many d.f. in the vcv for the within estimator?

Gregorio,

The classical VCV does indeed need to incorporate the dof adjustment associated with the N individual effects.  See e.g. Hayashi's Econometrics p. 334 (the textbook I have at hand - you can find it in other texts as well).

HTH,
Mark

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
> statalist@hsphsun2.harvard.edu] On Behalf Of Impavido, Gregorio
> Sent: 12 December 2012 00:41
> To: statalist@hsphsun2.harvard.edu
> Subject: st: how many d.f. in the vcv for the within estimator?
>
> Dear all,
>
> I am trying to replicate the result of -xtreg, fe- in mata. Given that
the
> individual effects are not estimated after the within transform,
shouldn't the
> degrees of freedom used for the estimate of the variance of the
residuals be
> (N*T-k-1) instead of N*(T-1)-k (where N=number of panels,
> T=periods,k=number of regressors)?  I have added the intercept = the
meant
> of the dep variable as in STATA manual.
>
> I paste the code used below which reproduces the results after if
force df_r=
> N*(T-1)-k.  Any suggestion would be welcome.
>
> With kind regards
> Gregorio
> ==================
> * this do file reproduces the results of -xtreg, fe- using mata
> * it works only with balanced panels
> * For corrections and suggestions, Gregorio Impavido
(gimpavido@imf.org)
> **********************************************************
> *********************
> ************************************ START
> ************************************
> **********************************************************
> *********************
> use "http://www.stata-press.com/data/r9/grunfeld.dta ", clear rename
> invest I rename mvalue F rename kstock C sort company time
> gen touse=(I!=. & F!=. & C!=.)      // ignore eventual missing obs
>
> * example of panel within estimator
> mata:
> mata clear                          // clear the workspace
>
> T = 20                              // Number of observations per
groups
> N = 10                              // Number of groups
>
> Z = st_data(.,("F","C"),"touse")    // (NTxk) matrix of regressors
> Y = st_data(.,("I"),"touse")        // (NTx1) vector of dep var
> i = J(rows(Z),1,1)                  // (NTx1) vector of ones, declare
a
> X = Z,i
> it = J(T,1,1)                       // (Tx1) vector of ones, declare a
> in = J(N,1,1)                       // (Tx1) vector of ones, declare a
> B = pinv(T)*I(N)#(it*it')           // (NTxNT) between-individual
operator
> Bbar = pinv(N)*(in*in')#I(T)        // (NTxNT) between-individual
operator
> Q = I(N*T)-B                        // (NTxNT) Q within transform
> * Qbar = I(N*T)-Bbar                  // (NTxNT) Qbar within period
operator
> Ybar = B*Bbar*Y                     // (NTx1) vector of mean dep var
> Zbar = B*Bbar*Z                     // (NTxk) matrix of mean regressor
var
> Ytilda = Q*Y + Ybar                 // added overall mean
> Ztilda = Q*Z + Zbar                 // added overall mean
> Xtilda = Ztilda,i                   // (NTxk+1) add column of 1s
(intercept)
> b_fe = pinv(Xtilda'Xtilda)*Xtilda'*Ytilda	// (k+1x1) vector of
beta hat
> k = cols(Z)                         // (1x1) No of regressors
> u = (Ytilda-Xtilda*b_fe)            // (NTx1) uhat, fitted residuals
> df_r = (N*(T-1)-k)                  // (1x1) residual d.f. (shouldn't
be NT-k-1??)
> rss = (u'*u)                        // (1x1) unrestricted residual sum
of squares
> mse = rss/df_r                      // (1x1) mean squared error
> vcv = mse*pinv(Xtilda'Xtilda)       // (NTxk+1) VCOV matrix
> se = sqrt(diagonal(vcv))            // (k+1x1) vector of s.e. of the
beta hat
> t = b_fe:/se                        // (k+1x1) vector of t statistics
> pt = 2*ttail(df_r,abs(t))           // (k+1x1) vector of pvalues
> crit = invttail(df_r,0.025)         // (k+1x1) bhat~T(df_r)(b,V(b))
> cil = b_fe-crit*se                  // (k+1x1) vector of low CI
> cih = b_fe+crit*se                  // (k+1x1) vector of high CI
>
> b_fe, se, t, pt, cil, cih
>
> end
> xtset company time
> xtreg I F C, fe                     // to cross check
> **********************************************************
> *********************
> ************************************* END
> *************************************
> **********************************************************
> *********************
>
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