## F-Statistic for 2SLS

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mckilem
Posts: 3
Joined: Sun Jul 03, 2011 11:34 pm

### F-Statistic for 2SLS

It is reported that: The summary statistics reported at the bottom of the table are computed using the formulae outlined in "Summary Statistics".
I’m trying to calculate F-statistic as
F = R2*(T-k) / (1-R2)*(k-1)
For instance:

R-squared = 0.91555469

T = 43 (observations)
k = 3 (2 explanatory variables and intercept)
Instrument specification: 2 instruments, Constant added to instrument list

According to this formula F = 216.8397
Eviews returns F = 229.4930

How should I change expression to get Eviews value?
I can not find something about it in literature.

startz
Non-normality and collinearity are NOT problems!
Posts: 2883
Joined: Wed Sep 17, 2008 2:25 pm

### Re: F-Statistic for 2SLS

Computation of Linear Hypothesis Tests for Two-Stage Least Squares,” Economics Letters, l983, ll (l-2), pp. l29-l3l.

mckilem
Posts: 3
Joined: Sun Jul 03, 2011 11:34 pm

### Re: F-Statistic for 2SLS

in article is written :
"The square of the standard error of the regression is given by s^2 = E’E/(n - k). Notice that the reported variance-covariance matrix of the
coefficients is s*V. Therefore, the difference of the restricted and unrestricted second-stage SSR, divided by the true SSR, times (n - k)/q, is
numerically identical to the F-statistic usually calculated."

I understood that f-stat = (R^2/(1-R^2))/((n-k)/q), but I have different result.
ex. F-stat = 822.8661 from LS
F-stat = 810.2886 from 2SLS

irulishka
Posts: 45
Joined: Fri Jun 03, 2011 9:38 am

### Re: F-Statistic for 2SLS

Hello.
I have a model y=c(1)+c(2)*x1+c(3)*x2+e
EViews gives me an estimate of 2SLS
Dependent Variable: Y
Method: Least Squares
Date: 07/25/11 Time: 17:59
Sample: 1 10
Included observations: 10

Variable Coefficient Std. Error t-Statistic Prob.

C 5.258429 14.21942 0.369806 0.7225
X1 0.324894 3.323727 0.097750 0.9249
X2 0.400823 0.274146 1.462076 0.1871

R-squared 0.236166 Mean dependent var 18.00000
Adjusted R-squared 0.017927 S.D. dependent var 17.49921
S.E. of regression 17.34164 Akaike info criterion 8.787423
Sum squared resid 2105.127 Schwarz criterion 8.878199
Log likelihood -40.93712 Hannan-Quinn criter. 8.687843
F-statistic 1.082146 Durbin-Watson stat 1.511508
Prob(F-statistic) 0.389491

To calculate F-statistics, I use the formula: F=((Hb-r)'(H(X'X)^-1H')^-1(Hb-r))/(s^2*q), where H - matrix of restrictions, b -vector of estimation coef.

Same formula I use to calculate statistics in the Vald-test, but here I got another result, different from F-statistics. Could you please help me to find the mistake?

startz
Non-normality and collinearity are NOT problems!
Posts: 2883
Joined: Wed Sep 17, 2008 2:25 pm

### Re: F-Statistic for 2SLS

That's the OLS formula. It doesn't apply to 2SLS.