Re: [Gretl-devel] an Odd example with restrict -- NA as a standard error

Here is a followup that illustrates what Jack is saying about when is a small number really zero. Being too strict about the size of the value may lead to other unintended results. This example is based on the same dataset (br.gdt) but uses restrictions that are nearly true. ? square sqft bedrooms ? logs price ? series price = price/100 ? list xlist = const sqft sq_sqft sq_bedrooms bedrooms baths age ? matrix Rmat = zeros(3,4)~I(3) ? matrix r = { 700 ; 400; -10 } ? ols price xlist Model 1: OLS, using observations 1-1080 Dependent variable: price coefficient std. error t-ratio p-value --------------------------------------------------------------- const 168.782 216.484 0.7797 0.4358 sqft -0.758827 0.0741780 -10.23 1.68e-023 *** sq_sqft 0.000248214 1.03688e-05 23.94 8.12e-102 *** sq_bedrooms -117.075 19.4308 -6.025 2.32e-09 *** bedrooms 694.058 138.416 5.014 6.22e-07 *** baths 379.550 46.2502 8.206 6.48e-016 *** age -8.34062 1.14878 -7.260 7.40e-013 *** Mean dependent var 1548.632 S.D. dependent var 1229.128 Sum squared resid 4.01e+08 S.E. of regression 611.6813 R-squared 0.753717 Adjusted R-squared 0.752340 F(6, 1073) 547.2962 P-value(F) 0.000000 Log-likelihood -8458.451 Akaike criterion 16930.90 Schwarz criterion 16965.79 Hannan-Quinn 16944.11 ? restrict --full ? R=Rmat ? q=r ? end restrict Test statistic: F(3, 1073) = 0.955727, with p-value = 0.412961 Model 2: Restricted OLS, using observations 1-1080 Dependent variable: price coefficient std. error t-ratio p-value ------------------------------------------------------------------ const 201.080 88.6191 2.269 0.0235 ** sqft -0.783296 0.0645078 -12.14 6.88e-032 *** sq_sqft 0.000250439 9.22345e-06 27.15 4.42e-124 *** sq_bedrooms -118.625 5.21332 -22.75 6.95e-094 *** bedrooms 700.000 0.000000 NA NA baths 400.000 4.64027e-07 8.620e+08 0.0000 *** age -10.0000 0.000000 NA NA Notice that the std error on sq_sqft squared is very small (but not zero) and the one on baths (which is technically zero) is only 1 decimal smaller. If you didn't know that the se is supposed to be zero on a restricted coefficient (like many of my students) you'd report something that was obviously wrong. In the original example, the problem was not so much in the restrictions, but the conditioning of the data themselves, which remains very bad even in this case of "good" restrictions. It's not clear to me how sorting this out based on size is possible. Is there a complex eigenvalue associated with the R*inv(X'X)*R' that might identify which should be NA? Lee