Simultaneous Equation Modeling Essay ⋆ Political Science Essay Examples ⋆ EssayEmpire

Simultaneous equation models (SEMs) are useful for testing hypotheses involving complex causal ordering, which are common to research questions in political science and public policy. SEM examples include instrumental variables, two-stage least squares, and seemingly unrelated regression models.

A classic example of complex causal ordering is the impact of policing on crime rates. A larger police force may indeed lead to a reduction in crime. However, a reverse causal order is equally plausible; for example, an increase in the crime rate may lead to the hiring of more police. Another example is the estimation of campaign contributions (X; predictor) on votes received (Y; outcome). In this case, both campaign contributions and votes may be influenced by how voters feel about the challenger, essentially both X and Y are effected by yet another variable. When a predictor is a function of other variables in the system, it is not truly independent or exogenous. We refer to these dependent variables as endogenous and they are problematic because they are likely to be correlated with the error term. Ordinary least squares (OLS) regression will produce a biased estimator unless we untangle the system of equations. However, simultaneous equation models remove the bias that would result from an OLS approach.

A common SEM technique employs an instrumental variable with two-stage least squares (2SLS). This involves isolating the variation in the endogenous variable that is problematic (correlated with the error) from the part of the variation that is not problematic (uncorrelated with the error). In the first stage of the process, X is decomposed to obtain the component that can be predicted by an instrument and the problematic component. Then the predicted value of X from the stage 1 regression is used to estimate the effect on Y.

Consider the example of the impact of policing on crime rates given above. Some researchers have pointed out police forces tend to increase in election years; since election years are predetermined (exogenous) they may be the source of a good instrument. Applying a 2SLS, in stage 1 we would isolate the police force new hires that can be predicted by the election cycle, which we assume are uncorrelated with the error. In stage 2 we would use the predicted values of Y (police) from the first stage regression to estimate the effect on crime. To specify:

Stage 1: policei = a0 + a1 electioni + mi

Stage 2: crimei = g0 + g1 police-hati + ni

As is probably evident by now, the challenge with 2SLS is finding a good instrument, a variable that is correlated with the endogenous regressor but not correlated with the error term. The good news is that most basic econometric textbooks discuss statistical tests for instrument validity and the logic behind them. Popular statistical software packages are also indispensable tools for analyses.

Bibliography:

Abadie, Alberto. “Poverty, Political Freedom, and the Roots of Terrorism.” American Economic Review 96, no. 2 (2006): 50–56.
Angrist, Joshua D., Kathryn Graddy, and Guido W. Imbens. “The Interpretation of Instrumental Variables Estimators in Simultaneous Equations Models with an Application to the Demand for Fish.” Review of Economic Studies 67, no. 3 (2000): 499–527.
Angrist, Joshua D., and Alan B. Krueger. “Instrumental Variables and the Search for Identification: From Supply and Demand to Natural Experiments.” Journal of Economic Perspectives (2001): 69–85.
Gerber, Alan. “Estimating the Effect of Campaign Spending on Senate Election Outcomes Using Instrumental Variables.” American Political Science Review 92, no. 2 (1998): 401–411.
Heckman, James J. “The Scientific Model of Causality.” Sociological Methodology 35, no. 1 (2005): 1–97.
Jackson, John E. “A Seemingly Unrelated Regression Model for Analyzing Multiparty Elections.” Political Analysis 10, no. 1 (2002): 49–65.
Levitt, Steven D. “Using Electoral Cycles in Police Hiring to Estimate the Effect of Police on Crime.” American Economic Review 87, no. 3 (1997): 270–290.
Simon, Herbert A. “Causal Ordering and Identifiability.” In Studies in Econometric Method, edited by William Clarence Hood and Tjalling C. Koopmans, 49–74. New York: Wiley, 1953.
Staiger, Douglas, and James H. Stock. “Instrumental Variables Regression with Weak Instruments.” Econometrica: Journal of the Econometric Society 65 (May 1997): 557–586.
Wooldridge, Jeffrey M. Introductory Econometrics: A Modern Approach, 4th ed. South-Western, 2008.

This example Simultaneous Equation Modeling Essay is published for educational and informational purposes only. If you need a custom essay or research paper on this topic please use our writing services. EssayEmpire.com offers reliable custom essay writing services that can help you to receive high grades and impress your professors with the quality of each essay or research paper you hand in.