Simultaneous Equation Models (SiEM) Inter-University Consortium for Political and Social Research (ICPSR) Summer 2010 Sandy Marquart-Pyatt Department of Sociology Michigan State University marqua41@msu.edu This course considers systems of equations, drawing from two complementary approaches: the structural equation modeling with latent variables (SEM) literature and the econometrics literature (SiEM). In contrast to single equation models, these models have at least two equations. These simultaneous models can be grouped into two major types: recursive models, which do not create any special problems, and nonrecursive models, which require special treatment. For each of these major types, we will discuss the specification, identification, estimation, and assessment of these systems of simultaneous equations. Nonrecursive models introduce the problem of identification, or how to establish that the parameters of the model are estimable. These models also require alternative estimation techniques. As time permits, advanced topics including limited dependent variables, measurement error, and handling longitudinal data will be covered. Students should have a good understanding of multiple regression and matrix algebra. Most of the readings are drawn from four econometric texts: Greene, William H. 2008. Econometric Analysis (6th ed.). Upper Saddle River, NJ: Prentice Hall. Gujarati, Damodar. 2009. Basic Econometrics (5th ed.). New York: McGraw-Hill. (4 th ed in parentheses) Johnston, J. and J. DiNardo. 1997 Econometric Methods 4th ed.. New York: McGraw- Hill. (Note: pages for Johnston, J. Econometric Methods 3 rd ed. (in parentheses)). Kmenta, Jan. 1997. Elements of Econometrics (2nd ed.). New York: Macmillan Additional readings are drawn from the following structural equation modeling (SEM) texts: Bollen, Kenneth. 1989. Structural Equations with Latent Variables. New York: Wiley. Kaplan, David. 2009. Structural Equation Modeling: Foundations and Extensions. Thousand Oaks, CA: SAGE. All of the readings are available in the summer program library in the Newberry House. There will be approximately 6 assignments. Due dates of assignments will be announced in class. We will also be discussing application papers as appropriate to recursive and nonrecursive models (listed on last page of syllabus). Lab sessions will be announced in class.
Topics and I. Introduction to Simultaneous Equation Models a. A brief introduction to simultaneous equation models II: Review of the Classical Linear Regression model a. Review of matrix algebra Bollen, Kenneth A. 1989. Structural Equations with Latent Variables. New York: Wiley. Appendix A. OR Gill, Jeff. 2006. Essential Mathematics for Political and Social Research. Cambridge University Press. Chapters 3 and 4. OR Fox, John. 2009. A Mathematical Primer for Social Statistics. SAGE Publications, Inc. QASS. Chapter 1, Section 1.1 pp. 2-18 and Section 1.4 pp. 30-40. OR Johnston and DiNardo: pp. 459-483 b. Classical linear regression model Gujarati: ch.4 Greene: ch.2 (ch. 6) Johnston & Dinardo: ch.3 (ed 3: ch 5) Note: for further review, read Gujarati ch.1-3 & 6, or Johnston &DiNardo chp.1-2, etc. first. III: Overview of simultaneous equation models Recursive vs. nonrecursive models; path diagrams/equations/matrices; reduced vs. structural form; direct, indirect and total effects. Gujarati: chp.18 Bollen: pp.32-34; 36-39 Kmenta: 13.1 or Greene: 13.1-13.2 (earlier editions of Greene 16.1, 16.2) IV: Recursive models a. Specification Kenny, David. 1979. Correlation and Causality. Wiley. p. 13-21 (chap 2) Gujarati: p. 764 Johnston & DiNardo: pp.305-309 (ed 3: 467-468) Kmenta: pp.719-720
IV: Recursive models (cont.) b. Identification Bollen: p. 88-98 Kenny: p. 34-41, 61-62 Greene: 13.3 c. Estimation Gujarati: p. 681-682 Johnston: p. 468-469 (ed. 4: 314-318) Kmenta: p. 720 d. Decomposition of effects Bollen: pp.36-39 Fox, John. 1980. Effect Analysis in Structural Equation Models. Sociological Methods and Research 9(1): 3-14 and 19-22. Sobel, Michael. 1988. "Direct and Indirect Effects in Structural Equation Models." pp.46-53 in J. Scott Long (ed.) Common Problems/Proper Solutions: Avoiding Error in Quantitative Research. Newbury Park, CA: Sage. Defining mediation** (**see extended list on z: drive). Baron, Reuben M., and David A. Kenny. 1986. The Moderator-Mediator Variable Distinction in Social Psychological Research: Conceptual, Strategic, and Statistical Considerations. Journal of Personality and Social Psychology 51(6): 1173-1182. *Classic* MacKinnon, David P. and Amanda Fairchild. 2009. Current Directions in Mediation Analysis. Current Directions in Psychological Science 18(1): 16-20. And references therein! Optional Reading: Sobel, Michael. 1982. Asymptotic Confidence Intervals for Indirect Effects in Structural Equation Models. Sociological Methodology 13:290-312. Sobel, Michael. 1986. Some new results on indirect effects and their standard errors in covariance structure models. Sociological Methodology 16: 159-186. Preacher, Kristopher and Andrew Hayes. 2008. Asymptotic and Resampling Strategies for Assessing and Comparing Indirect Effects in Multiple Mediator Models. Behavior Research Methods 40(3):879-891.
V: SUR (seemingly unrelated regressions) models Greene: 10.2, 15.6.3 Kmenta: 12.3 Example: Sampson, Robert J. 1987. Urban Black Violence: The Effect of Male Joblessness and Family Disruption. American Journal of Sociology 93(2): 348-382. VI: Nonrecursive simultaneous equation models a. Specification. Reading: Gujarati: 18.3-18.4 b. Identification Gujarati: chp.19.1-19.3 Greene: 13.3.1-13.3.2 Rigdon, Edward E. 1995. "A Necessary and Sufficient Identification Rule for Structural Models Estimated in Practice." Multivariate Behavioral Research 30:359-383. c. Estimation: ILS, 2SLS, 3SLS, ML Reading: Gujarati: 20.1 c1. Indirect least squares Gujarati: 20.3 Johnston & DiNardo: pp. 314 (ed 3: 469-472) c2. Two Stage Least Squares, aka 2SLS Gujarati: 20.4, 20.5 Greene: 13.4, 13.5.2, and 13.5.3 Kmenta: pp.681-687 Examples: Bollen, Kenneth A., and Robert W. Jackman. 1985. Political Democracy and the Size Distribution of Income. American Sociological Review 50: 438-457. Brehm, John and Wendy Rahn. 1997. "Individual-level evidence for the causes and consequences of social capital." American Journal of Political Science 41:999-1023.
VI: Nonrecursive simultaneous equation models (cont.) c3. 3SLS Johnston: pp.486-490 Kmenta: pp.695-701 Greene 13.6, 13.6.1 c4. MLE Greene: 13.6.2 d. Comparison of Estimation Methods Reading: Greene: 13.7 Kmenta: pp.711-714 e. Decomposition of Effects Bollen: pp.376-389 Fox, J. 1980. "Effect Analysis in Structural Equation Models." Sociological Methods and Research 9:3-28. Bollen, Kenneth A. 1987. "Total, Direct, and Indirect Effects in Structural Equation Models." pp. 37-69 in C.C. Clogg, ed., Sociological Methodology 1987. Washington D.C.: American Sociological Association. VII. Assessment of models a. Equation by equation a1. Endogeneity tests: Gujarati: 19.4-19.5 Greene: 13.8 Hausman, J. A. 1978. "Specification Tests in Econometrics." Econometrica 6:1251-1271 a2. Assessment of Instruments Bound, John, David A. Jaeger, and Regina M. Baker. 1995. Problems with Instrumental Variables Estimation When the Correlation Between the Instruments and the Endogenous Explanatory Variable is Weak. Journal of the American Statistical Association 90(430): 443-450. Hausman, J. A. 1983. Specification and Estimation of Simultaneous Equation Models. Pp. 392-448 in Handbook of Econometrics, vol. 1, edited by Z. Griliches and M.D. Intriligator. New York: North-Holland.
Optional reading** (see extended list on z: drive): Bartels, Larry M. 1991. "Instrumental and 'Quasi-Instrumental' Variables." American Journal of Political Science 35:777-800. Baum, Christopher, Mark Schaffer, and Steven Stillman. 2003. Instrumental Variables and GMM: Estimation and Testing. Stata Journal 3(1):1-31. Murray, Michael P. 2006. "Avoiding Invalid Instruments and Coping with Weak Instruments." Journal of Economic Perspectives, 20(4): 111 132. Kirby, James B. and Kenneth A. Bollen. 2009. Using Instrumental Variable Tests to Evaluate Model Specification in Latent Variable Structural Equation Models. Sociological Methodology 39(1):327-355. b. Global goodness of fit statistics for overidentified models Bollen: pp.263-289 Kaplan, David. 2009. Structural Equation Modeling: Foundations and Extensions. Thousand Oaks, CA: SAGE Publications. pp. 109-126. Hu, Li-tze and Peter M. Bentler. 1999. Cutoff Criteria for Fit Indexes in Covariance Structure Analysis: Conventional Criteria versus New Alternatives. Structural Equation Modeling 6(1):1-55. Additional Topics: (covered as time permits) Modeling change Finkel, Steven E. 1995. Causal Analysis with Panel Data. Sage. Optional Reading: Kessler, Ronald C. and David F. Greenberg. 1981. Linear panel analysis: Models of quantitative change. New York: Academic. [Classic textbook on longitudinal models] Consequences of measurement error Reading: Bollen: chp.5, Greene: 9.5
Simultaneous equations with limited dependent variables Winship, Christopher and Robert D. Mare. 1983. "Structural Equations and Path Analysis for Discrete Data." American Journal of Sociology 89:54-110. Muthen, Bengt. 1984. A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika 49:115-132. Bollen 1989: pp.433-446. Optional readings: Maddala 5.1, 5.8, chapter 7 and chapter 8. MacKinnon, David P. and James H. Dwyer. 1993. "Estimating mediated effects in prevention studies." Evaluation Review 17:144-158. [Discusses estimating mediation with a dichotomous mediator] Example: Bollen, Kenneth A., David K. Guilkey, and Thomas A. Mroz. 1995. "Binary Outcomes and Endogenous Explanatory Variables: Tests and Solutions with an Application to the Demand for Contraceptive Use in Tunisia." Demography 32:111-131. Standard Errors of indirect effects Sobel, Michael E. 1982. Asymptotic Confidence Intervals for Indirect Effects in Structural Equation Models. Sociological Methodology 13:290-312. Sobel, Michael E. 1986. Some New Results on Indirect Effects and Their Standard Errors in Covariance Structure Models. Sociological Methodology 16:159-186. Sobel, Michael E. 1988. Direct and Indirect Effects in Linear Structural Equation Models. Pp. 53-64 in Common Problems/Proper Solutions: Avoiding Error in Quantitative Research, edited by J. Scott Long. Sage. Preacher, Kristopher and Andrew Hayes. 2008. Asymptotic and Resampling Strategies for Assessing and Comparing Indirect Effects in Multiple Mediator Models. Behavior Research Methods 40(3):879-891. Power Issues in Simultaneous Equations Bielby, William T., and Ross L. Matsueda. 1991. Statistical Power in Nonrecursive Linear Models. Sociological Methodology 21:167-197. Matsueda, Ross and William Bielby. 1986. Statistical Power in Covariance Structure Models. Pp. 120-158 in N.B. Tuma, ed. Sociological Methodology 1986. Washington, D.C.: American Sociological Association.
Lagged Endogenous Variables with autocorrelation Kmenta: 13.5 Fair, Ray C. 1970. The Estimation of Simultaneous Equation Models with Lagged Endogenous Variables and First Order Serially Correlated Errors. Econometrica 38(3): 507-516. Using simultaneous equations to handle spatial effects Land, Kenneth C., and Glenn Deane. 1992. On the Large-Sample Estimation of Regression Models with Spatial- Or Network-Effects Terms: A Two-Stage Least Squares Approach. Sociological Methodology 22:221-248. Autocorrelation or heteroskedasticity in simultaneous equations Kmenta: 13.5 Harvey, A. C., and G. D. A. Phillips. 1980. Testing for Serial Correlation in Simultaneous Equation Models. Econometrica 48(3): 747-760. Application Papers: SUR: Presentation on Wednesday July 28. Sampson, Robert J. 1987. Urban Black Violence: The Effect of Male Joblessness and Family Disruption. American Journal of Sociology 93(2): 348-382. Nonrecursive: Presentation on Tuesday, Aug 3. Bollen, Kenneth A., and Robert W. Jackman. 1985. Political Democracy and the Size Distribution of Income. American Sociological Review 50: 438-457. Nonrecursive: Presentation on Thursday, Aug 5. Brehm, John and Wendy Rahn. 1997. "Individual-level evidence for the causes and consequences of social capital." American Journal of Political Science 41:999-1023. Issues to consider in your reading of the application paper 1. Describe what the paper is trying to do, highlighting the theoretical model and how it is implemented statistically. How well is this accomplished? 2. In what ways do complexities encountered by the authors intersect with issues we ve discussed in class?