Structural estimation

<h2 id="structured-and-reduced-form-models">Structured and reduced form models</h2>
<p class="note">See also: <a href="/facts/Reduced_form/tAoNWduK">Reduced form</a></p>
<p>When the Cowles Commission introduced the term "reduced form" it was used to define a set of equations where the "left-hand" <a href="/facts/Dependent_variables/dINfzIF2">dependent variables</a> never appeared on the right-hand of the equations, as opposed to the <a href="/facts/Simultaneous_equations/KzP6TJ4u">simultaneous equations</a>, where the dependent variable of an equation can appear as an input in other formulas.<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a>  
</p><p>The original distinction between structure and reduced-form was between the underlying system and the direct relationship between observables implied by the system. 
</p><p>Different combinations of structural parameters can imply the same reduced-form parameters, so structural estimation must go beyond the direct relationship between variables.<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a><a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a>
</p><p>Many economists now use the term "reduced form" to mean statistical estimation without reference to a specific economic model. For example, a <a href="/facts/Regression_analysis/n6z5Tf7K">regression</a> is often called a reduced-form equation even when no standard economic model would generate it as the reduced form relationship between variables.
</p><p>These conflicting distinctions between structural and reduced form estimation arose from the increasing complexity of economic theory since the formalization of simultaneous equations estimation. A structural model often involves sequential decision-making under uncertainty or strategic environments where beliefs about other agents' actions matter. Parameters of such models are estimated not with regression analysis but non-linear techniques such as <a href="/facts/Generalized_method_of_moments/mNc3410V">generalized method of moments</a>, <a href="/facts/Maximum_likelihood/0Yq2dpQD">maximum likelihood</a>, and <a href="/facts/Indirect_inference/PEmXJ1UV">indirect inference</a>. The reduced-form of such models may result in a regression relationship but often only for special or trivial cases of the structural parameters.
</p>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Methodology_of_econometrics/nrdbuqkL">Methodology of econometrics</a></li></ul>
<h2 id="notes">Notes</h2>

<ul><li>Angrist, Joshua D; Pischke, Jörn-Steffen (2010). <a href="http://cep.lse.ac.uk/pubs/download/dp0976.pdf">"The Credibility Revolution in Empirical Economics: How Better Research Design is Taking the Con out of Econometrics"</a> (PDF). <i>Journal of Economic Perspectives</i>. 24 (2). American Economic Association: 3–30. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1257%2Fjep.24.2.3">10.1257/jep.24.2.3</a>. <a href="/facts/ISSN_(identifier)/DPAflDvU">ISSN</a> <a href="https://search.worldcat.org/issn/0895-3309">0895-3309</a>.</li>
<li>Keane, Michael P. (2010). "Structural vs. atheoretic approaches to econometrics". <i>Journal of Econometrics</i>. 156 (1). Elsevier BV: 3–20. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1016%2Fj.jeconom.2009.09.003">10.1016/j.jeconom.2009.09.003</a>. <a href="/facts/ISSN_(identifier)/DPAflDvU">ISSN</a> <a href="https://search.worldcat.org/issn/0304-4076">0304-4076</a>.</li></ul>
<ul><li>Reiss, Peter C.; Wolak, Frank A. (2007). <a href="https://web.stanford.edu/group/fwolak/cgi-bin/sites/default/files/files/Structural%20Econometric%20Modeling_Rationales%20and%20Examples%20From%20Industrial%20Organization_Reiss%2C%20Wolak.pdf">"Chapter 64 Structural Econometric Modeling: Rationales and Examples from Industrial Organization"</a> (PDF). <i>Handbook of Econometrics</i>. Elsevier. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1016%2Fs1573-4412%2807%2906064-3">10.1016/s1573-4412(07)06064-3</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-444-50631-3. <a href="/facts/ISSN_(identifier)/DPAflDvU">ISSN</a> <a href="https://search.worldcat.org/issn/1573-4412">1573-4412</a>.</li>
<li>Rust, John (2014). "The Limits of Inference with Theory: A Review of Wolpin (2013)". <i>Journal of Economic Literature</i>. 52 (3). American Economic Association: 820–850. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1257%2Fjel.52.3.820">10.1257/jel.52.3.820</a>. <a href="/facts/ISSN_(identifier)/DPAflDvU">ISSN</a> <a href="https://search.worldcat.org/issn/0022-0515">0022-0515</a>.</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Reiss & Wolak 2007, p. 4282. - Reiss, Peter C.; Wolak, Frank A. (2007). "Chapter 64 Structural Econometric Modeling: Rationales and Examples from Industrial Organization" (PDF). Handbook of Econometrics. Elsevier. doi:10.1016/s1573-4412(07)06064-3. ISBN 978-0-444-50631-3. ISSN 1573-4412. <a href="https://web.stanford.edu/group/fwolak/cgi-bin/sites/default/files/files/Structural%20Econometric%20Modeling_Rationales%20and%20Examples%20From%20Industrial%20Organization_Reiss%2C%20Wolak.pdf" target="_blank">https://web.stanford.edu/group/fwolak/cgi-bin/sites/default/files/files/Structural%20Econometric%20Modeling_Rationales%20and%20Examples%20From%20Industrial%20Organization_Reiss%2C%20Wolak.pdf</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Reiss & Wolak 2007, p. 4411. - Reiss, Peter C.; Wolak, Frank A. (2007). "Chapter 64 Structural Econometric Modeling: Rationales and Examples from Industrial Organization" (PDF). Handbook of Econometrics. Elsevier. doi:10.1016/s1573-4412(07)06064-3. ISBN 978-0-444-50631-3. ISSN 1573-4412. <a href="https://web.stanford.edu/group/fwolak/cgi-bin/sites/default/files/files/Structural%20Econometric%20Modeling_Rationales%20and%20Examples%20From%20Industrial%20Organization_Reiss%2C%20Wolak.pdf" target="_blank">https://web.stanford.edu/group/fwolak/cgi-bin/sites/default/files/files/Structural%20Econometric%20Modeling_Rationales%20and%20Examples%20From%20Industrial%20Organization_Reiss%2C%20Wolak.pdf</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Reiss & Wolak 2007. - Reiss, Peter C.; Wolak, Frank A. (2007). "Chapter 64 Structural Econometric Modeling: Rationales and Examples from Industrial Organization" (PDF). Handbook of Econometrics. Elsevier. doi:10.1016/s1573-4412(07)06064-3. ISBN 978-0-444-50631-3. ISSN 1573-4412. <a href="https://web.stanford.edu/group/fwolak/cgi-bin/sites/default/files/files/Structural%20Econometric%20Modeling_Rationales%20and%20Examples%20From%20Industrial%20Organization_Reiss%2C%20Wolak.pdf" target="_blank">https://web.stanford.edu/group/fwolak/cgi-bin/sites/default/files/files/Structural%20Econometric%20Modeling_Rationales%20and%20Examples%20From%20Industrial%20Organization_Reiss%2C%20Wolak.pdf</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>Reiss & Wolak 2007, p. 4293. - Reiss, Peter C.; Wolak, Frank A. (2007). "Chapter 64 Structural Econometric Modeling: Rationales and Examples from Industrial Organization" (PDF). Handbook of Econometrics. Elsevier. doi:10.1016/s1573-4412(07)06064-3. ISBN 978-0-444-50631-3. ISSN 1573-4412. <a href="https://web.stanford.edu/group/fwolak/cgi-bin/sites/default/files/files/Structural%20Econometric%20Modeling_Rationales%20and%20Examples%20From%20Industrial%20Organization_Reiss%2C%20Wolak.pdf" target="_blank">https://web.stanford.edu/group/fwolak/cgi-bin/sites/default/files/files/Structural%20Econometric%20Modeling_Rationales%20and%20Examples%20From%20Industrial%20Organization_Reiss%2C%20Wolak.pdf</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>Reiss & Wolak 2007. - Reiss, Peter C.; Wolak, Frank A. (2007). "Chapter 64 Structural Econometric Modeling: Rationales and Examples from Industrial Organization" (PDF). Handbook of Econometrics. Elsevier. doi:10.1016/s1573-4412(07)06064-3. ISBN 978-0-444-50631-3. ISSN 1573-4412. <a href="https://web.stanford.edu/group/fwolak/cgi-bin/sites/default/files/files/Structural%20Econometric%20Modeling_Rationales%20and%20Examples%20From%20Industrial%20Organization_Reiss%2C%20Wolak.pdf" target="_blank">https://web.stanford.edu/group/fwolak/cgi-bin/sites/default/files/files/Structural%20Econometric%20Modeling_Rationales%20and%20Examples%20From%20Industrial%20Organization_Reiss%2C%20Wolak.pdf</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
<li id="fn:6"><p>Keane 2010. - Keane, Michael P. (2010). "Structural vs. atheoretic approaches to econometrics". Journal of Econometrics. 156 (1). Elsevier BV: 3–20. doi:10.1016/j.jeconom.2009.09.003. ISSN 0304-4076. <a href="https://doi.org/10.1016%2Fj.jeconom.2009.09.003" target="_blank">https://doi.org/10.1016%2Fj.jeconom.2009.09.003</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li>
</ol>

Structural estimation open-in-new

Structural estimation