https://en.wikipedia.org/w/index.php?action=history&feed=atom&title=Endogeneity_with_an_exponential_regression_function Endogeneity with an exponential regression function - Revision history 2025-06-10T06:54:00Z Revision history for this page on the wiki MediaWiki 1.45.0-wmf.4 https://en.wikipedia.org/w/index.php?title=Endogeneity_with_an_exponential_regression_function&diff=993551067&oldid=prev Wikiacc: retarget following merge 2020-12-11T05:15:26Z <p>retarget following merge</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Previous revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 05:15, 11 December 2020</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>#REDIRECT [[<del style="font-weight: bold; text-decoration: none;">Instrumental</del> <del style="font-weight: bold; text-decoration: none;">variables</del> <del style="font-weight: bold; text-decoration: none;">estimation</del>#Endogeneity <del style="font-weight: bold; text-decoration: none;">with</del> <del style="font-weight: bold; text-decoration: none;">an exponential</del> regression<del style="font-weight: bold; text-decoration: none;"> function</del>]]</div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>#REDIRECT [[<ins style="font-weight: bold; text-decoration: none;">Control</ins> <ins style="font-weight: bold; text-decoration: none;">function</ins> <ins style="font-weight: bold; text-decoration: none;">(econometrics)</ins>#Endogeneity <ins style="font-weight: bold; text-decoration: none;">in</ins> <ins style="font-weight: bold; text-decoration: none;">Poisson</ins> regression]]</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{R from merge}}</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{R from merge}}</div></td> </tr> </table> Wikiacc https://en.wikipedia.org/w/index.php?title=Endogeneity_with_an_exponential_regression_function&diff=966287155&oldid=prev Klbrain: Merged content to Instrumental variables estimation#Endogeneity with an exponential regression function, redirecting (easy-merge) 2020-07-06T07:05:17Z <p>Merged content to <a href="/wiki/Instrumental_variables_estimation#Endogeneity_with_an_exponential_regression_function" title="Instrumental variables estimation">Instrumental variables estimation#Endogeneity with an exponential regression function</a>, redirecting (<a href="/wiki/User:SD0001/easy-merge" title="User:SD0001/easy-merge">easy-merge</a>)</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Previous revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 07:05, 6 July 2020</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">{{merge</del> <del style="font-weight: bold; text-decoration: none;">to|Instrumental variables estimation|discuss=Talk:</del>Instrumental variables estimation#Endogeneity with an exponential regression function<del style="font-weight: bold; text-decoration: none;">|date=May 2019}}</del></div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">#REDIRECT</ins> <ins style="font-weight: bold; text-decoration: none;">[[</ins>Instrumental variables estimation#Endogeneity with an exponential regression function<ins style="font-weight: bold; text-decoration: none;">]]</ins></div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{notability|date=January 2018}}</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In statistics as applied to [[econometrics]], exponential regression models constitute a very large and popular class of [[Regression analysis|regression]] models. Standard [[econometric]] concerns such as [[Endogeneity (econometrics)|endogeneity]] or [[Omitted-variable bias|omitted variables]] can be accounted for in a more general framework. Wooldridge and Terza provide a methodology to both deal with and test for endogeneity within the exponential regression framework, which the following discussion follows closely.&lt;ref&gt;Wooldridge 1997; Terza 1998&lt;/ref&gt; While the example focuses on a [[Poisson regression]] model, it is possible to generalize the test to other exponential regression models, although this may come at the cost of additional assumptions (e.g. for binary response or censored data models). </div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{R from merge}}</div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Assume the following exponential regression model, where &lt;math&gt;a_i&lt;/math&gt; is an unobserved term in the latent variable. We allow for correlation between &lt;math&gt;a_i&lt;/math&gt; and &lt;math&gt;x_i&lt;/math&gt; (implying &lt;math&gt;x_i&lt;/math&gt; is possibly endogenous), but allow for no such correlation between &lt;math&gt;a_i&lt;/math&gt; and &lt;math&gt;z_i&lt;/math&gt;. </div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{R to section}}</div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>: &lt;math&gt;\operatorname E[y_i \nu x_i, z_i, a_i] = \exp(x_i b_0 + z_i c_0+a_i) &lt;/math&gt; (1) </div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The variables &lt;math&gt;z_i&lt;/math&gt; serve as [[instrumental variable]]s for the potentially endogenous &lt;math&gt;x_i&lt;/math&gt;. One can assume a linear relationship between these two variables or alternatively project the endogenous variable &lt;math&gt;x_i&lt;/math&gt; onto the instruments to get the following reduced form equation:</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>: &lt;math&gt;x_i=z_i\Pi+v_i&lt;/math&gt; (2) </div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The usual rank condition is needed to ensure identification. The endogeneity is then modeled in the following way, where &lt;math&gt;\rho&lt;/math&gt; determines the severity of endogeneity and &lt;math&gt;v_i&lt;/math&gt; is assumed to be independent of &lt;math&gt;e_i&lt;/math&gt;. </div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>: &lt;math&gt;a_i=v_i \rho+e_i&lt;/math&gt; (3)</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Imposing these assumptions, assuming the models are correctly specified, and normalizing &lt;math&gt;\operatorname E[\exp(e_i)]=1,&lt;/math&gt;, we can rewrite the conditional mean as follows:</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>: &lt;math&gt; \operatorname E[y_i v x_i, z_i , a_i] = \exp (x_i b_0 + z_i c_0 +e_i\rho)&lt;/math&gt; (4) </div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>If &lt;math&gt;e_i&lt;/math&gt; were known at this point, it would be possible to estimate the relevant parameters by [[quasi-maximum likelihood estimation]]. Following the two step procedure strategies, Wooldridge and Terza propose estimating equation [2] by standard [[Ordinary least squares|OLS methods]]. The fitted residuals from this regression can then be plugged into the estimating equation [4] and QMLE methods will lead to consistent estimators of the parameters of interest. Significance tests on &lt;math&gt;\hat\rho&lt;/math&gt; can then be used to test for endogeneity within the model. </div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The methodology proposed here is often used for exponential regression functions. However, the specific assumptions that need to be made can differ across models. Binary response models impose distributional assumptions on ''y''&lt;sub&gt;''i''&lt;/sub&gt; and ''x''&lt;sub&gt;''i''&lt;/sub&gt;, whereas this model imposed independence between &lt;math&gt;v_i&lt;/math&gt; and &lt;math&gt;e_i&lt;/math&gt;.</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>== See also ==</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* [[Binary response model with continuous endogenous explanatory variables]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* [[Endogeneity in multinomial response model]]</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>== References ==</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{Reflist}}</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>== Bibliography ==</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Wooldridge, J. (1997): Quasi-Likelihood Methods for Count Data, Handbook of Applied Econometrics, Volume 2, ed. M. H. Pesaran and P. Schmidt, Oxford, Blackwell, pp. 352–406</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Terza, J. V. (1998): "Estimating Count Models with Endogenous Switching: Sample Selection and Endogenous Treatment Effects." ''Journal of Econometrics'' (84), pp. 129–154</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Wooldridge, J. (2002): "Econometric Analysis of Cross Section and Panel Data", ''MIT Press'', Cambridge, Massachusetts.</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Poisson distribution]]</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Poisson distribution]]</div></td> </tr> </table> Klbrain https://en.wikipedia.org/w/index.php?title=Endogeneity_with_an_exponential_regression_function&diff=898277481&oldid=prev AnomieBOT: Dating maintenance tags: {{Merge to}} 2019-05-22T15:20:09Z <p>Dating maintenance tags: {{Merge to}}</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Previous revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:20, 22 May 2019</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{merge to|Instrumental variables estimation|discuss=Talk:Instrumental variables estimation#Endogeneity with an exponential regression function}}</div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{merge to|Instrumental variables estimation|discuss=Talk:Instrumental variables estimation#Endogeneity with an exponential regression function<ins style="font-weight: bold; text-decoration: none;">|date=May 2019</ins>}}</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{notability|date=January 2018}}</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{notability|date=January 2018}}</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In statistics as applied to [[econometrics]], exponential regression models constitute a very large and popular class of [[Regression analysis|regression]] models. Standard [[econometric]] concerns such as [[Endogeneity (econometrics)|endogeneity]] or [[Omitted-variable bias|omitted variables]] can be accounted for in a more general framework. Wooldridge and Terza provide a methodology to both deal with and test for endogeneity within the exponential regression framework, which the following discussion follows closely.&lt;ref&gt;Wooldridge 1997; Terza 1998&lt;/ref&gt; While the example focuses on a [[Poisson regression]] model, it is possible to generalize the test to other exponential regression models, although this may come at the cost of additional assumptions (e.g. for binary response or censored data models). </div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In statistics as applied to [[econometrics]], exponential regression models constitute a very large and popular class of [[Regression analysis|regression]] models. Standard [[econometric]] concerns such as [[Endogeneity (econometrics)|endogeneity]] or [[Omitted-variable bias|omitted variables]] can be accounted for in a more general framework. Wooldridge and Terza provide a methodology to both deal with and test for endogeneity within the exponential regression framework, which the following discussion follows closely.&lt;ref&gt;Wooldridge 1997; Terza 1998&lt;/ref&gt; While the example focuses on a [[Poisson regression]] model, it is possible to generalize the test to other exponential regression models, although this may come at the cost of additional assumptions (e.g. for binary response or censored data models). </div></td> </tr> </table> AnomieBOT https://en.wikipedia.org/w/index.php?title=Endogeneity_with_an_exponential_regression_function&diff=898274853&oldid=prev Wikiacc: Propose merge to instrumental variables estimation 2019-05-22T14:58:08Z <p>Propose merge to <a href="/wiki/Instrumental_variables_estimation" title="Instrumental variables estimation">instrumental variables estimation</a></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Previous revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 14:58, 22 May 2019</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{merge to|Instrumental variables estimation|discuss=Talk:Instrumental variables estimation#Endogeneity with an exponential regression function}}</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{notability|date=January 2018}}</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{notability|date=January 2018}}</div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><br /></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In statistics as applied to [[econometrics]], exponential regression models constitute a very large and popular class of [[Regression analysis|regression]] models. Standard [[econometric]] concerns such as [[Endogeneity (econometrics)|endogeneity]] or [[Omitted-variable bias|omitted variables]] can be accounted for in a more general framework. Wooldridge and Terza provide a methodology to both deal with and test for endogeneity within the exponential regression framework, which the following discussion follows closely.&lt;ref&gt;Wooldridge 1997; Terza 1998&lt;/ref&gt; While the example focuses on a [[Poisson regression]] model, it is possible to generalize the test to other exponential regression models, although this may come at the cost of additional assumptions (e.g. for binary response or censored data models). </div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In statistics as applied to [[econometrics]], exponential regression models constitute a very large and popular class of [[Regression analysis|regression]] models. Standard [[econometric]] concerns such as [[Endogeneity (econometrics)|endogeneity]] or [[Omitted-variable bias|omitted variables]] can be accounted for in a more general framework. Wooldridge and Terza provide a methodology to both deal with and test for endogeneity within the exponential regression framework, which the following discussion follows closely.&lt;ref&gt;Wooldridge 1997; Terza 1998&lt;/ref&gt; While the example focuses on a [[Poisson regression]] model, it is possible to generalize the test to other exponential regression models, although this may come at the cost of additional assumptions (e.g. for binary response or censored data models). </div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td colspan="2" class="diff-lineno">Line 9:</td> <td colspan="2" class="diff-lineno">Line 9:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The variables &lt;math&gt;z_i&lt;/math&gt; serve as [[instrumental variable]]s for the potentially endogenous &lt;math&gt;x_i&lt;/math&gt;. One can assume a linear relationship between these two variables or alternatively project the endogenous variable &lt;math&gt;x_i&lt;/math&gt; onto the instruments to get the following reduced form equation:</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The variables &lt;math&gt;z_i&lt;/math&gt; serve as [[instrumental variable]]s for the potentially endogenous &lt;math&gt;x_i&lt;/math&gt;. One can assume a linear relationship between these two variables or alternatively project the endogenous variable &lt;math&gt;x_i&lt;/math&gt; onto the instruments to get the following reduced form equation:</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>: &lt;math&gt;x_i=z_i\<del style="font-weight: bold; text-decoration: none;">prod</del>+v_i&lt;/math&gt; (2) </div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>: &lt;math&gt;x_i=z_i\<ins style="font-weight: bold; text-decoration: none;">Pi</ins>+v_i&lt;/math&gt; (2) </div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The usual rank condition is needed to ensure identification. The endogeneity is then modeled in the following way, where &lt;math&gt;\rho&lt;/math&gt; determines the severity of endogeneity and &lt;math&gt;v_i&lt;/math&gt; is assumed to be independent of &lt;math&gt;e_i&lt;/math&gt;. </div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The usual rank condition is needed to ensure identification. The endogeneity is then modeled in the following way, where &lt;math&gt;\rho&lt;/math&gt; determines the severity of endogeneity and &lt;math&gt;v_i&lt;/math&gt; is assumed to be independent of &lt;math&gt;e_i&lt;/math&gt;. </div></td> </tr> </table> Wikiacc https://en.wikipedia.org/w/index.php?title=Endogeneity_with_an_exponential_regression_function&diff=828133604&oldid=prev LilHelpa: typo; mnr copy edit 2018-02-28T19:23:17Z <p>typo; mnr copy edit</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Previous revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 19:23, 28 February 2018</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{notability|date=January 2018}}</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{notability|date=January 2018}}</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In statistics as applied to [[econometrics]], exponential regression models constitute a very large and popular class of [[Regression analysis|regression]] models. Standard [[econometric]] concerns such as [[Endogeneity (econometrics)|endogeneity]] or [[Omitted-variable bias|omitted variables]] can be accounted for in a more general framework. Wooldridge and Terza provide a <del style="font-weight: bold; text-decoration: none;">methodologies</del> to both deal with and test for endogeneity within the exponential regression framework, which the following discussion follows closely.&lt;ref&gt;Wooldridge 1997; Terza 1998&lt;/ref&gt; While the example focuses on a [[Poisson regression]] model, it is possible to generalize the test to other exponential regression models, although this may come at the cost of additional assumptions (e.g. for binary response or censored data models). </div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In statistics as applied to [[econometrics]], exponential regression models constitute a very large and popular class of [[Regression analysis|regression]] models. Standard [[econometric]] concerns such as [[Endogeneity (econometrics)|endogeneity]] or [[Omitted-variable bias|omitted variables]] can be accounted for in a more general framework. Wooldridge and Terza provide a <ins style="font-weight: bold; text-decoration: none;">methodology</ins> to both deal with and test for endogeneity within the exponential regression framework, which the following discussion follows closely.&lt;ref&gt;Wooldridge 1997; Terza 1998&lt;/ref&gt; While the example focuses on a [[Poisson regression]] model, it is possible to generalize the test to other exponential regression models, although this may come at the cost of additional assumptions (e.g. for binary response or censored data models). </div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Assume the following exponential regression model, where &lt;math&gt;a_i&lt;/math&gt; is an unobserved term in the latent variable. We allow for correlation between &lt;math&gt;a_i&lt;/math&gt; and &lt;math&gt;x_i&lt;/math&gt; (implying &lt;math&gt;x_i&lt;/math&gt; is possibly endogenous), but allow for no such correlation between &lt;math&gt;a_i&lt;/math&gt; and &lt;math&gt;z_i&lt;/math&gt;. </div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Assume the following exponential regression model, where &lt;math&gt;a_i&lt;/math&gt; is an unobserved term in the latent variable. We allow for correlation between &lt;math&gt;a_i&lt;/math&gt; and &lt;math&gt;x_i&lt;/math&gt; (implying &lt;math&gt;x_i&lt;/math&gt; is possibly endogenous), but allow for no such correlation between &lt;math&gt;a_i&lt;/math&gt; and &lt;math&gt;z_i&lt;/math&gt;. </div></td> </tr> <tr> <td colspan="2" class="diff-lineno">Line 30:</td> <td colspan="2" class="diff-lineno">Line 30:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Reflist}}</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Reflist}}</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>== <del style="font-weight: bold; text-decoration: none;">Bibliograhpy</del> ==</div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>== <ins style="font-weight: bold; text-decoration: none;">Bibliography</ins> ==</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Wooldridge, J. (1997): Quasi-Likelihood Methods for Count Data, Handbook of Applied Econometrics, Volume 2, ed. M. H. Pesaran and P. Schmidt, Oxford, Blackwell, pp. 352–406</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Wooldridge, J. (1997): Quasi-Likelihood Methods for Count Data, Handbook of Applied Econometrics, Volume 2, ed. M. H. Pesaran and P. Schmidt, Oxford, Blackwell, pp. 352–406</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Terza, J. V. (1998): "Estimating Count Models with Endogenous Switching: Sample Selection and Endogenous Treatment Effects." ''Journal of Econometrics'' (84), pp. 129–154</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Terza, J. V. (1998): "Estimating Count Models with Endogenous Switching: Sample Selection and Endogenous Treatment Effects." ''Journal of Econometrics'' (84), pp. 129–154</div></td> </tr> </table> LilHelpa https://en.wikipedia.org/w/index.php?title=Endogeneity_with_an_exponential_regression_function&diff=820428925&oldid=prev Insertcleverphrasehere: Added tags to the page using Page Curation (notability) 2018-01-14T18:23:23Z <p>Added tags to the page using <a href="/wiki/Wikipedia:Page_Curation" title="Wikipedia:Page Curation">Page Curation</a> (notability)</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Previous revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:23, 14 January 2018</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{notability|date=January 2018}}</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In statistics as applied to [[econometrics]], exponential regression models constitute a very large and popular class of [[Regression analysis|regression]] models. Standard [[econometric]] concerns such as [[Endogeneity (econometrics)|endogeneity]] or [[Omitted-variable bias|omitted variables]] can be accounted for in a more general framework. Wooldridge and Terza provide a methodologies to both deal with and test for endogeneity within the exponential regression framework, which the following discussion follows closely.&lt;ref&gt;Wooldridge 1997; Terza 1998&lt;/ref&gt; While the example focuses on a [[Poisson regression]] model, it is possible to generalize the test to other exponential regression models, although this may come at the cost of additional assumptions (e.g. for binary response or censored data models). </div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In statistics as applied to [[econometrics]], exponential regression models constitute a very large and popular class of [[Regression analysis|regression]] models. Standard [[econometric]] concerns such as [[Endogeneity (econometrics)|endogeneity]] or [[Omitted-variable bias|omitted variables]] can be accounted for in a more general framework. Wooldridge and Terza provide a methodologies to both deal with and test for endogeneity within the exponential regression framework, which the following discussion follows closely.&lt;ref&gt;Wooldridge 1997; Terza 1998&lt;/ref&gt; While the example focuses on a [[Poisson regression]] model, it is possible to generalize the test to other exponential regression models, although this may come at the cost of additional assumptions (e.g. for binary response or censored data models). </div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> </table> Insertcleverphrasehere https://en.wikipedia.org/w/index.php?title=Endogeneity_with_an_exponential_regression_function&diff=818825345&oldid=prev 86.158.194.215: deleted a duplicate "between" 2018-01-05T20:31:13Z <p>deleted a duplicate &quot;between&quot;</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Previous revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 20:31, 5 January 2018</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In statistics as applied to [[econometrics]], exponential regression models constitute a very large and popular class of [[Regression analysis|regression]] models. Standard [[econometric]] concerns such as [[Endogeneity (econometrics)|endogeneity]] or [[Omitted-variable bias|omitted variables]] can be accounted for in a more general framework. Wooldridge and Terza provide a methodologies to both deal with and test for endogeneity within the exponential regression framework, which the following discussion follows closely.&lt;ref&gt;Wooldridge 1997; Terza 1998&lt;/ref&gt; While the example focuses on a [[Poisson regression]] model, it is possible to generalize the test to other exponential regression models, although this may come at the cost of additional assumptions (e.g. for binary response or censored data models). </div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In statistics as applied to [[econometrics]], exponential regression models constitute a very large and popular class of [[Regression analysis|regression]] models. Standard [[econometric]] concerns such as [[Endogeneity (econometrics)|endogeneity]] or [[Omitted-variable bias|omitted variables]] can be accounted for in a more general framework. Wooldridge and Terza provide a methodologies to both deal with and test for endogeneity within the exponential regression framework, which the following discussion follows closely.&lt;ref&gt;Wooldridge 1997; Terza 1998&lt;/ref&gt; While the example focuses on a [[Poisson regression]] model, it is possible to generalize the test to other exponential regression models, although this may come at the cost of additional assumptions (e.g. for binary response or censored data models). </div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Assume the following exponential regression model, where &lt;math&gt;a_i&lt;/math&gt; is an unobserved term in the latent variable. We allow for correlation between<del style="font-weight: bold; text-decoration: none;"> between </del> &lt;math&gt;a_i&lt;/math&gt; and &lt;math&gt;x_i&lt;/math&gt; (implying &lt;math&gt;x_i&lt;/math&gt; is possibly endogenous), but allow for no such correlation between &lt;math&gt;a_i&lt;/math&gt; and &lt;math&gt;z_i&lt;/math&gt;. </div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Assume the following exponential regression model, where &lt;math&gt;a_i&lt;/math&gt; is an unobserved term in the latent variable. We allow for correlation between &lt;math&gt;a_i&lt;/math&gt; and &lt;math&gt;x_i&lt;/math&gt; (implying &lt;math&gt;x_i&lt;/math&gt; is possibly endogenous), but allow for no such correlation between &lt;math&gt;a_i&lt;/math&gt; and &lt;math&gt;z_i&lt;/math&gt;. </div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: &lt;math&gt;\operatorname E[y_i \nu x_i, z_i, a_i] = \exp(x_i b_0 + z_i c_0+a_i) &lt;/math&gt; (1) </div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: &lt;math&gt;\operatorname E[y_i \nu x_i, z_i, a_i] = \exp(x_i b_0 + z_i c_0+a_i) &lt;/math&gt; (1) </div></td> </tr> </table> 86.158.194.215 https://en.wikipedia.org/w/index.php?title=Endogeneity_with_an_exponential_regression_function&diff=817178417&oldid=prev Michael Hardy at 18:20, 26 December 2017 2017-12-26T18:20:18Z <p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Previous revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:20, 26 December 2017</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Exponential</del> regression models constitute a very large and popular class of [[Regression analysis|regression]] models. Standard [[econometric]] concerns such as [[Endogeneity (econometrics)|endogeneity]] or [[Omitted-variable bias|omitted variables]] can be accounted for in a more general framework. Wooldridge and Terza provide a methodologies to both deal with and test for endogeneity within the exponential regression framework, which the following discussion follows closely.&lt;ref&gt;Wooldridge 1997; Terza 1998&lt;/ref&gt; While the example focuses on a [[Poisson regression]] model, it is possible to generalize the test to other exponential regression models, although this may come at the cost of additional assumptions (e.g. for binary response or censored data models). </div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">In statistics as applied to [[econometrics]], exponential</ins> regression models constitute a very large and popular class of [[Regression analysis|regression]] models. Standard [[econometric]] concerns such as [[Endogeneity (econometrics)|endogeneity]] or [[Omitted-variable bias|omitted variables]] can be accounted for in a more general framework. Wooldridge and Terza provide a methodologies to both deal with and test for endogeneity within the exponential regression framework, which the following discussion follows closely.&lt;ref&gt;Wooldridge 1997; Terza 1998&lt;/ref&gt; While the example focuses on a [[Poisson regression]] model, it is possible to generalize the test to other exponential regression models, although this may come at the cost of additional assumptions (e.g. for binary response or censored data models). </div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Assume the following exponential regression model, where &lt;math&gt;<del style="font-weight: bold; text-decoration: none;">a_{i}</del>&lt;/math&gt; is an unobserved term in the latent variable. We allow for correlation between between &lt;math&gt;<del style="font-weight: bold; text-decoration: none;">a_{i}</del>&lt;/math&gt; and &lt;math&gt;<del style="font-weight: bold; text-decoration: none;">x_{i}</del>&lt;/math&gt; (implying &lt;math&gt;<del style="font-weight: bold; text-decoration: none;">x_{i}</del>&lt;/math&gt; is possibly endogenous), but allow for no such correlation between &lt;math&gt;<del style="font-weight: bold; text-decoration: none;">a_{i} </del>&lt;/math&gt; and &lt;math&gt;<del style="font-weight: bold; text-decoration: none;">z_{i}</del>&lt;/math&gt;. </div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Assume the following exponential regression model, where &lt;math&gt;<ins style="font-weight: bold; text-decoration: none;">a_i</ins>&lt;/math&gt; is an unobserved term in the latent variable. We allow for correlation between between &lt;math&gt;<ins style="font-weight: bold; text-decoration: none;">a_i</ins>&lt;/math&gt; and &lt;math&gt;<ins style="font-weight: bold; text-decoration: none;">x_i</ins>&lt;/math&gt; (implying &lt;math&gt;<ins style="font-weight: bold; text-decoration: none;">x_i</ins>&lt;/math&gt; is possibly endogenous), but allow for no such correlation between &lt;math&gt;<ins style="font-weight: bold; text-decoration: none;">a_i</ins>&lt;/math&gt; and &lt;math&gt;<ins style="font-weight: bold; text-decoration: none;">z_i</ins>&lt;/math&gt;. </div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;math&gt;E[<del style="font-weight: bold; text-decoration: none;">y_{i} </del> \nu <del style="font-weight: bold; text-decoration: none;">x_{i</del>,<del style="font-weight: bold; text-decoration: none;">}</del> <del style="font-weight: bold; text-decoration: none;">z_{i}</del>, <del style="font-weight: bold; text-decoration: none;">a _{i}</del>] =exp(<del style="font-weight: bold; text-decoration: none;">x_{i}b_{0}</del>+<del style="font-weight: bold; text-decoration: none;">z_{i}c_{0}</del>+<del style="font-weight: bold; text-decoration: none;">a_{i}</del>) &lt;/math&gt; (1) </div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">: </ins>&lt;math&gt;<ins style="font-weight: bold; text-decoration: none;">\operatorname </ins>E[<ins style="font-weight: bold; text-decoration: none;">y_i</ins> \nu <ins style="font-weight: bold; text-decoration: none;">x_i</ins>, <ins style="font-weight: bold; text-decoration: none;">z_i</ins>, <ins style="font-weight: bold; text-decoration: none;">a_i</ins>] =<ins style="font-weight: bold; text-decoration: none;"> \</ins>exp(<ins style="font-weight: bold; text-decoration: none;">x_i b_0 </ins>+<ins style="font-weight: bold; text-decoration: none;"> z_i c_0</ins>+<ins style="font-weight: bold; text-decoration: none;">a_i</ins>) &lt;/math&gt; (1) </div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The variables &lt;math&gt;<del style="font-weight: bold; text-decoration: none;">z_{i}</del>&lt;/math&gt;<del style="font-weight: bold; text-decoration: none;"> </del> serve as instrumental <del style="font-weight: bold; text-decoration: none;">variables</del> for the potentially endogenous &lt;math&gt;<del style="font-weight: bold; text-decoration: none;">x_{i}</del>&lt;/math&gt;. One can assume a linear relationship between these two variables or alternatively project the endogenous variable &lt;math&gt;<del style="font-weight: bold; text-decoration: none;">x_{i}</del>&lt;/math&gt; onto the instruments to get the following reduced form equation:<del style="font-weight: bold; text-decoration: none;"> </del></div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The variables &lt;math&gt;<ins style="font-weight: bold; text-decoration: none;">z_i</ins>&lt;/math&gt; serve as <ins style="font-weight: bold; text-decoration: none;">[[</ins>instrumental <ins style="font-weight: bold; text-decoration: none;">variable]]s</ins> for the potentially endogenous &lt;math&gt;<ins style="font-weight: bold; text-decoration: none;">x_i</ins>&lt;/math&gt;. One can assume a linear relationship between these two variables or alternatively project the endogenous variable &lt;math&gt;<ins style="font-weight: bold; text-decoration: none;">x_i</ins>&lt;/math&gt; onto the instruments to get the following reduced form equation:</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;math&gt;<del style="font-weight: bold; text-decoration: none;">x_{i}</del>=<del style="font-weight: bold; text-decoration: none;">z_{i}</del>\prod+<del style="font-weight: bold; text-decoration: none;">v_{i}</del>&lt;/math&gt;<del style="font-weight: bold; text-decoration: none;"> </del> (2) </div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">: </ins>&lt;math&gt;<ins style="font-weight: bold; text-decoration: none;">x_i</ins>=<ins style="font-weight: bold; text-decoration: none;">z_i</ins>\prod+<ins style="font-weight: bold; text-decoration: none;">v_i</ins>&lt;/math&gt; (2) </div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The usual rank condition is needed to ensure identification. The endogeneity is then modeled in the following way, where &lt;math&gt;\rho&lt;/math&gt; determines the severity of endogeneity and &lt;math&gt;<del style="font-weight: bold; text-decoration: none;">v_{i}</del>&lt;/math&gt; is assumed to be independent of &lt;math&gt;<del style="font-weight: bold; text-decoration: none;">e_{i}</del>&lt;/math&gt;. </div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The usual rank condition is needed to ensure identification. The endogeneity is then modeled in the following way, where &lt;math&gt;\rho&lt;/math&gt; determines the severity of endogeneity and &lt;math&gt;<ins style="font-weight: bold; text-decoration: none;">v_i</ins>&lt;/math&gt; is assumed to be independent of &lt;math&gt;<ins style="font-weight: bold; text-decoration: none;">e_i</ins>&lt;/math&gt;. </div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;math&gt;<del style="font-weight: bold; text-decoration: none;">a_{i}</del>=<del style="font-weight: bold; text-decoration: none;">v_{i}</del>\rho+<del style="font-weight: bold; text-decoration: none;">e_{i}</del>&lt;/math&gt;<del style="font-weight: bold; text-decoration: none;"> </del> (3)</div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">: </ins>&lt;math&gt;<ins style="font-weight: bold; text-decoration: none;">a_i</ins>=<ins style="font-weight: bold; text-decoration: none;">v_i </ins>\rho+<ins style="font-weight: bold; text-decoration: none;">e_i</ins>&lt;/math&gt; (3)</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Imposing these assumptions, assuming the models are correctly specified, and normalizing &lt;math&gt;E[exp(<del style="font-weight: bold; text-decoration: none;">e_{i}</del>)]=1,&lt;/math&gt;, we can rewrite the conditional mean as follows:</div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Imposing these assumptions, assuming the models are correctly specified, and normalizing &lt;math&gt;<ins style="font-weight: bold; text-decoration: none;">\operatorname </ins>E[<ins style="font-weight: bold; text-decoration: none;">\</ins>exp(<ins style="font-weight: bold; text-decoration: none;">e_i</ins>)]=1,&lt;/math&gt;, we can rewrite the conditional mean as follows:</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;math&gt;E[<del style="font-weight: bold; text-decoration: none;">y_{i}</del> v <del style="font-weight: bold; text-decoration: none;">x_{i}</del>, <del style="font-weight: bold; text-decoration: none;">z_{i}</del> , <del style="font-weight: bold; text-decoration: none;">a_{i}</del>] =exp (<del style="font-weight: bold; text-decoration: none;">x_{i}</del> <del style="font-weight: bold; text-decoration: none;">b_{0}</del> + <del style="font-weight: bold; text-decoration: none;">z_{i}</del> <del style="font-weight: bold; text-decoration: none;">c_{0}</del> +<del style="font-weight: bold; text-decoration: none;">e_{i}</del>\rho)&lt;/math&gt;<del style="font-weight: bold; text-decoration: none;"> </del> (4) </div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">: </ins>&lt;math&gt;<ins style="font-weight: bold; text-decoration: none;"> \operatorname </ins>E[<ins style="font-weight: bold; text-decoration: none;">y_i</ins> v <ins style="font-weight: bold; text-decoration: none;">x_i</ins>, <ins style="font-weight: bold; text-decoration: none;">z_i</ins> , <ins style="font-weight: bold; text-decoration: none;">a_i</ins>] =<ins style="font-weight: bold; text-decoration: none;"> \</ins>exp (<ins style="font-weight: bold; text-decoration: none;">x_i</ins> <ins style="font-weight: bold; text-decoration: none;">b_0</ins> + <ins style="font-weight: bold; text-decoration: none;">z_i</ins> <ins style="font-weight: bold; text-decoration: none;">c_0</ins> +<ins style="font-weight: bold; text-decoration: none;">e_i</ins>\rho)&lt;/math&gt; (4) </div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>If &lt;math&gt;<del style="font-weight: bold; text-decoration: none;">e_{i}</del>&lt;/math&gt; were known at this point, it would be possible to estimate the relevant parameters by [[quasi-maximum likelihood estimation]]. Following the two step procedure strategies, Wooldridge and Terza propose estimating equation [2] by standard [[Ordinary least squares|OLS methods]]. The fitted residuals from this regression can then be plugged into the estimating equation [4] and QMLE methods will lead to consistent estimators of the parameters of interest. Significance tests on &lt;math&gt;\hat\rho&lt;/math&gt;<del style="font-weight: bold; text-decoration: none;"> </del> can then be used to test for endogeneity within the model. </div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>If &lt;math&gt;<ins style="font-weight: bold; text-decoration: none;">e_i</ins>&lt;/math&gt; were known at this point, it would be possible to estimate the relevant parameters by [[quasi-maximum likelihood estimation]]. Following the two step procedure strategies, Wooldridge and Terza propose estimating equation [2] by standard [[Ordinary least squares|OLS methods]]. The fitted residuals from this regression can then be plugged into the estimating equation [4] and QMLE methods will lead to consistent estimators of the parameters of interest. Significance tests on &lt;math&gt;\hat\rho&lt;/math&gt; can then be used to test for endogeneity within the model. </div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The methodology proposed here is often used for exponential regression functions. However, the specific assumptions that need to be made can differ across models. Binary response models impose distributional assumptions on <del style="font-weight: bold; text-decoration: none;">yi</del> and <del style="font-weight: bold; text-decoration: none;">xi</del>, whereas this model imposed independence between &lt;math&gt;<del style="font-weight: bold; text-decoration: none;">v_{i}</del>&lt;/math&gt; and &lt;math&gt;<del style="font-weight: bold; text-decoration: none;">e_{i}</del>&lt;/math&gt;.</div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The methodology proposed here is often used for exponential regression functions. However, the specific assumptions that need to be made can differ across models. Binary response models impose distributional assumptions on <ins style="font-weight: bold; text-decoration: none;">''y''&lt;sub&gt;''i''&lt;/sub&gt;</ins> and <ins style="font-weight: bold; text-decoration: none;">''x''&lt;sub&gt;''i''&lt;/sub&gt;</ins>, whereas this model imposed independence between &lt;math&gt;<ins style="font-weight: bold; text-decoration: none;">v_i</ins>&lt;/math&gt; and &lt;math&gt;<ins style="font-weight: bold; text-decoration: none;">e_i</ins>&lt;/math&gt;.</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== See also ==</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== See also ==</div></td> </tr> <tr> <td colspan="2" class="diff-lineno">Line 29:</td> <td colspan="2" class="diff-lineno">Line 29:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Bibliograhpy ==</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Bibliograhpy ==</div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Wooldridge, J. (1997): Quasi-Likelihood Methods for Count Data, Handbook of Applied Econometrics, Volume 2, ed. M. H. Pesaran and P. Schmidt, Oxford, Blackwell, pp. <del style="font-weight: bold; text-decoration: none;">352-406</del></div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Wooldridge, J. (1997): Quasi-Likelihood Methods for Count Data, Handbook of Applied Econometrics, Volume 2, ed. M. H. Pesaran and P. Schmidt, Oxford, Blackwell, pp. <ins style="font-weight: bold; text-decoration: none;">352–406</ins></div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Terza, J. V. (1998): Estimating Count Models with Endogenous Switching: Sample Selection and Endogenous Treatment Effects. Journal of Econometrics (84), pp. <del style="font-weight: bold; text-decoration: none;">129-154</del></div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Terza, J. V. (1998): <ins style="font-weight: bold; text-decoration: none;">"</ins>Estimating Count Models with Endogenous Switching: Sample Selection and Endogenous Treatment Effects.<ins style="font-weight: bold; text-decoration: none;">"</ins> <ins style="font-weight: bold; text-decoration: none;">''</ins>Journal of Econometrics<ins style="font-weight: bold; text-decoration: none;">''</ins> (84), pp. <ins style="font-weight: bold; text-decoration: none;">129–154</ins></div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Wooldridge, J. (2002): Econometric Analysis of Cross Section and Panel Data, MIT Press, Cambridge, <del style="font-weight: bold; text-decoration: none;">Mass</del>.</div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Wooldridge, J. (2002): <ins style="font-weight: bold; text-decoration: none;">"</ins>Econometric Analysis of Cross Section and Panel Data<ins style="font-weight: bold; text-decoration: none;">"</ins>, <ins style="font-weight: bold; text-decoration: none;">''</ins>MIT Press<ins style="font-weight: bold; text-decoration: none;">''</ins>, Cambridge, <ins style="font-weight: bold; text-decoration: none;">Massachusetts</ins>.</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Poisson distribution]]</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Poisson distribution]]</div></td> </tr> </table> Michael Hardy https://en.wikipedia.org/w/index.php?title=Endogeneity_with_an_exponential_regression_function&diff=817132277&oldid=prev Uanfala: typo 2017-12-26T10:25:27Z <p>typo</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Previous revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:25, 26 December 2017</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 17:</td> <td colspan="2" class="diff-lineno">Line 17:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;math&gt;E[y_{i} v x_{i}, z_{i} , a_{i}] =exp (x_{i} b_{0} + z_{i} c_{0} +e_{i}\rho)&lt;/math&gt; (4) </div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;math&gt;E[y_{i} v x_{i}, z_{i} , a_{i}] =exp (x_{i} b_{0} + z_{i} c_{0} +e_{i}\rho)&lt;/math&gt; (4) </div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>If &lt;math&gt;e_{i}&lt;/math&gt; were known at this point, it would be possible to estimate the relevant parameters by [[quasi-maximum likelihood <del style="font-weight: bold; text-decoration: none;">estimatation</del>]]. Following the two step procedure strategies, Wooldridge and Terza propose estimating equation [2] by standard [[Ordinary least squares|OLS methods]]. The fitted residuals from this regression can then be plugged into the estimating equation [4] and QMLE methods will lead to consistent estimators of the parameters of interest. Significance tests on &lt;math&gt;\hat\rho&lt;/math&gt; can then be used to test for endogeneity within the model. </div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>If &lt;math&gt;e_{i}&lt;/math&gt; were known at this point, it would be possible to estimate the relevant parameters by [[quasi-maximum likelihood <ins style="font-weight: bold; text-decoration: none;">estimation</ins>]]. Following the two step procedure strategies, Wooldridge and Terza propose estimating equation [2] by standard [[Ordinary least squares|OLS methods]]. The fitted residuals from this regression can then be plugged into the estimating equation [4] and QMLE methods will lead to consistent estimators of the parameters of interest. Significance tests on &lt;math&gt;\hat\rho&lt;/math&gt; can then be used to test for endogeneity within the model. </div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The methodology proposed here is often used for exponential regression functions. However, the specific assumptions that need to be made can differ across models. Binary response models impose distributional assumptions on yi and xi, whereas this model imposed independence between &lt;math&gt;v_{i}&lt;/math&gt; and &lt;math&gt;e_{i}&lt;/math&gt;.</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The methodology proposed here is often used for exponential regression functions. However, the specific assumptions that need to be made can differ across models. Binary response models impose distributional assumptions on yi and xi, whereas this model imposed independence between &lt;math&gt;v_{i}&lt;/math&gt; and &lt;math&gt;e_{i}&lt;/math&gt;.</div></td> </tr> </table> Uanfala https://en.wikipedia.org/w/index.php?title=Endogeneity_with_an_exponential_regression_function&diff=817072525&oldid=prev Uanfala: Uanfala moved page Draft:Endogeneity With An Exponential Regression Function to Endogeneity with an exponential regression function 2017-12-25T23:06:04Z <p>Uanfala moved page <a href="/wiki/Draft:Endogeneity_With_An_Exponential_Regression_Function" class="mw-redirect" title="Draft:Endogeneity With An Exponential Regression Function">Draft:Endogeneity With An Exponential Regression Function</a> to <a href="/wiki/Endogeneity_with_an_exponential_regression_function" class="mw-redirect" title="Endogeneity with an exponential regression function">Endogeneity with an exponential regression function</a></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <tr class="diff-title" lang="en"> <td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">← Previous revision</td> <td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:06, 25 December 2017</td> </tr><tr><td colspan="2" class="diff-notice" lang="en"><div class="mw-diff-empty">(No difference)</div> </td></tr></table> Uanfala