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Simultaneous equations model
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<p>Simultaneous equations models are a type of <a href="/facts/Statistical_model/jKkT5ftm">statistical model</a> in which the <a href="/facts/Dependent_and_independent_variables/dINfzIF2">dependent variables</a> are functions of other dependent variables, rather than just independent variables. This means some of the explanatory variables are <a href="/facts/Endogeneity_(econometrics)/NvtsxNYE">jointly determined</a> with the dependent variable, which in <a href="/facts/Economics/HYctA2Dn">economics</a> usually is the consequence of some underlying <a href="/facts/Economic_equilibrium/lFTmEyUS">equilibrium mechanism</a>. Take the typical <a href="/facts/Supply_and_demand/KprL1fvc">supply and demand</a> model: whilst typically one would determine the quantity supplied and demanded to be a function of the price set by the market, it is also possible for the reverse to be true, where producers observe the quantity that consumers demand <i>and then</i> set the price. </p><p>Simultaneity poses challenges for the <a href="/facts/Point_estimation/AYsuptFp">estimation</a> of the statistical parameters of interest, because the <a href="/facts/Gauss%25E2%2580%2593Markov_theorem/j85SGhrw">Gauss–Markov assumption</a> of <a href="/facts/Gauss%25E2%2580%2593Markov_theorem/j85SGhrw">strict exogeneity</a> of the regressors is violated. And while it would be natural to estimate all simultaneous equations at once, this often leads to a <a href="/facts/Computational_complexity/Qenh22Ja">computationally costly</a> non-linear optimization problem even for the simplest <a href="/facts/System_of_linear_equations/fk9CFdgp">system of linear equations</a>. This situation prompted the development, spearheaded by the <a href="/facts/Cowles_Commission/uprvmdSa">Cowles Commission</a> in the 1940s and 1950s, of various techniques that estimate each equation in the model seriatim, most notably <a href="/facts/Limited_information_maximum_likelihood/QtJbu6bV">limited information maximum likelihood</a> and <a href="/facts/Two-stage_least_squares/cEQ1xwT6">two-stage least squares</a>. </p>