Hello all!<div><br></div><div>I&#39;ve just joined the list and I&#39;m a brand new user of -gretl-. I&#39;ve only been using it for three days and I must praise the team for delivering a highly usable, flexible and interactive package that runs pretty much all of the econometric models that I want to fit (and a big, fat users&#39; guide, too!) - and for free. Can&#39;t say fairer than that.</div>
<div><br></div><div>I do have one query, however. Following Allison (2009), I&#39;m seeking to implement his alternative to the Hausman test after fitting a random effects panel model, which he argues has &quot;probably better statistical properties&quot; than Hausman. On pp. 23-27, he lays out the following steps:</div>
<div><br></div><div>(a) leave Y untransformed;</div><div>(b) calculate and include the unit-specific means (M) for each time-varying X variable (which I did quite easily by adding variables and using the -pmean()- command);</div>
<div>(c) calculate and include the mean deviations (D) from the same X variables&#39; unit-specific means (dvar=var-mvar));</div><div>(d) include all relevant time-invariant Z variables;</div><div>(e) run the random effects GLS panel model: Y = DX1 + MX1 +&nbsp;DX2 + MX2 +&nbsp;DXk + MXk + Z1 + Z2 + Zk + e)</div>
<div>(f) in place of the Hausman test of fixed vs. random, run the Wald test for the equality of all pairs of X coefficients, with the null representing equality.</div><div><br></div><div>I decided to test this out on the -abdata- dataset, regressing w on the transformed pairs of the variable set {n,k,ys} and the T-1 time dummies:&nbsp;</div>
<div><br></div><div><div>Model 2: Random-effects (GLS), using 1031 observations</div><div>Included 140 cross-sectional units</div><div>Time-series length: minimum 7, maximum 9</div><div>Dependent variable: w</div><div><br>
</div><div>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;coefficient &nbsp; std. error &nbsp; t-ratio &nbsp; p-value&nbsp;</div><div>&nbsp; --------------------------------------------------------</div><div>&nbsp; const &nbsp; &nbsp; &nbsp;&minus;2.58543 &nbsp; &nbsp; &nbsp;2.27350 &nbsp; &nbsp; &nbsp;&minus;1.137 &nbsp; &nbsp;0.2557 &nbsp;</div><div>&nbsp; m_n &nbsp; &nbsp; &nbsp; &nbsp;&minus;0.0900681 &nbsp; &nbsp;0.0361907 &nbsp; &nbsp;&minus;2.489 &nbsp; &nbsp;0.0130 &nbsp; **</div>
<div>&nbsp; d_n &nbsp; &nbsp; &nbsp; &nbsp;&minus;0.107425 &nbsp; &nbsp; 0.0200510 &nbsp; &nbsp;&minus;5.358 &nbsp; &nbsp;1.04e-07 ***</div><div>&nbsp; m_k &nbsp; &nbsp; &nbsp; &nbsp; 0.0852161 &nbsp; &nbsp;0.0320885 &nbsp; &nbsp; 2.656 &nbsp; &nbsp;0.0080 &nbsp; ***</div><div>&nbsp; d_k &nbsp; &nbsp; &nbsp; &nbsp; 0.0572876 &nbsp; &nbsp;0.0171438 &nbsp; &nbsp; 3.342 &nbsp; &nbsp;0.0009 &nbsp; ***</div><div>
&nbsp; m_ys &nbsp; &nbsp; &nbsp; &nbsp;1.27558 &nbsp; &nbsp; &nbsp;0.490848 &nbsp; &nbsp; &nbsp;2.599 &nbsp; &nbsp;0.0095 &nbsp; ***</div><div>&nbsp; d_ys &nbsp; &nbsp; &nbsp; &nbsp;0.214818 &nbsp; &nbsp; 0.0492901 &nbsp; &nbsp; 4.358 &nbsp; &nbsp;1.44e-05 ***</div><div>&nbsp; dt_2 &nbsp; &nbsp; &nbsp; &minus;0.0745933 &nbsp; &nbsp;0.0110719 &nbsp; &nbsp;&minus;6.737 &nbsp; &nbsp;2.70e-11 ***</div><div><br>
</div><div>&nbsp; [...]</div><div><br></div><div>&nbsp; dt_9 &nbsp; &nbsp; &nbsp; &nbsp;0.0319181 &nbsp; &nbsp;0.0176179 &nbsp; &nbsp; 1.812 &nbsp; &nbsp;0.0703 &nbsp; *</div><div><br></div><div>Mean dependent var &nbsp; 3.142988 &nbsp; S.D. dependent var &nbsp; 0.263008</div><div>Sum squared resid &nbsp; &nbsp;65.49712 &nbsp; S.E. of regression &nbsp; 0.253776</div>
<div>Log-likelihood &nbsp; &nbsp; &nbsp;&minus;42.06415 &nbsp; Akaike criterion &nbsp; &nbsp; 114.1283</div><div>Schwarz criterion &nbsp; &nbsp;188.2026 &nbsp; Hannan-Quinn &nbsp; &nbsp; &nbsp; &nbsp; 142.2399</div><div><br></div><div>&#39;Within&#39; variance = 0.0058566</div><div>&#39;Between&#39; variance = 0.0506465</div>
<div><br></div><div>Wald test for joint significance of time dummies</div><div>&nbsp; Asymptotic test statistic: Chi-square(8) = 224.855</div><div>&nbsp; with p-value = 3.62557e-44</div><div><br></div><div>Breusch-Pagan test -</div>
<div>&nbsp; Null hypothesis: Variance of the unit-specific error = 0</div><div>&nbsp; Asymptotic test statistic: Chi-square(1) = 2994.67</div><div>&nbsp; with p-value = 0</div><div><br></div><div>Hausman test -</div><div>&nbsp; Null hypothesis: GLS estimates are consistent</div>
<div>&nbsp; Asymptotic test statistic: Chi-square(11) = 21.8284</div><div>&nbsp; with p-value = 0.0257372</div></div><div><br></div><div>Everything goes to plan until I try to implement step (f). Clicking on the Tests tab and then selecting Lingg ear Restrictions, I typed:</div>
<div><br></div><div>b[m_n] = b[d_n]</div><div><br></div><div>but I receive a &quot;parse error in &#39;b[m_n] = b[d_n]&#39;&quot; error message. Deleting the spaces either side of the = made no difference.&nbsp;I only got results by running:&nbsp;</div>
<div><br></div><div><div>Restriction set</div><div>&nbsp;1: b[m_n] - b[d_n] = 0</div><div>&nbsp;2: b[m_k] - b[d_k] = 0</div><div>&nbsp;3: b[m_ys] - b[d_ys] = 0</div><div><br></div><div>Test statistic: F(3, 1016) = 3.27298, with p-value = 0.0205637</div>
</div><div><br></div><div>This test would appear to comprehensively reject the RE model in favour of retaining the FE model. Or does it? Is this an acceptable test in place of the Wald test for jointly equal parameters that I can&#39;t run in -gretl-?</div>
<div><br></div><div>Since the shape of the F and chi-square distributions are virtually identical and we have the obvious mathematical statement that (var1 = var2) = (var1 - var2 = 0), is it not acceptable to use the results of this test instead to come to the same conclusion? If not, how can I implement the Wald test in -gretl-? It must be possible!</div>
<div><br></div><div>Thanks once again.</div><div><div><br></div>-- <br>Clive Nicholas (<a href="http://clivenicholas.posterous.com" target="_blank">clivenicholas.posterous.com</a>)<br><br>[Please DO NOT mail me personally here, but at &lt;<a href="mailto:clivenicholas@hotmail.com" target="_blank">clivenicholas@hotmail.com</a>&gt;. Please respond to contributions I make in a list thread here. Thanks!]<br>
<br>Allison PD (2009) Fixed Effects Regression Models, QASS Series Paper 07-160, Thousand Oaks, CA: Sage</div>