Construction of Semi-Parametric Simultaneous Equation Models with An Application
DOI:
https://doi.org/10.37375/esj.v9i2.4396Abstract
This research aims to construct a semi-parametric simultaneous equation model with internal variables, then reduce, characterize, and estimate the model using kernel estimators and the least squares method in two stages. This provides a statistical framework for addressing the problem of internal homogeneity and nonlinear relationships in semi-parametric simultaneous equation models. Consumption, GDP, money supply, and government spending data for the Iraqi economy were used to implement the model. The results showed the model's superiority in detecting sharp structural changes and tracking sudden shocks. The estimated parameters demonstrated a strong nonlinear behavioral response to consumption and a significant positive impact of fiscal and monetary policy tools. The randomness of errors and the statistical validity of the estimated inference model were confirmed through residual analysis.
References
[1] Kim, H. S. (2000). Semiparametric estimation of nonlinear simultaneous equations models (Doctoral dissertation, The Ohio State University). OhioLINK Electronic Theses and Dissertations Center. DOI: 10.1214/25-AOAS2021
[2] Rodríguez-Póo, J.M., Sperlich, S. and Fernández, A.I. (2005), Semiparametric three-step estimation methods for simultaneous equation systems. J. Appl. Econ., 20: 699-721. https://doi.org/10.1002/jae.796
[3] Imbens, G. W., & Newey, W. K. (2002). Identification and estimation of triangular simultaneous equations models without additivity (Technical Working Paper No. 285). National Bureau of Economic Research. DOI 10.3386/t0285
[4] Kelejian, H. H., & Prucha, I. R. (2004). Estimation of simultaneous systems of spatially interrelated cross sectional equations. Journal of econometrics, 118(1-2), 27-50. https://doi.org/10.1016/S0304-4076(03)00133-7
[5] Su, L., & Ullah, A. (2008). Local polynomial estimation of nonparametric simultaneous equations models. Journal of Econometrics, 144(1), 193-218. https://doi.org/10.1016/j.jeconom.2008.01.002
[6] Gao, J., & Phillips, P. C. B. (2010). Semiparametric estimation in time series of simultaneous equations (Cowles Foundation Discussion Paper No. 1769). Yale University. file:///C:/Users/bfhgf/Downloads/ssrn-1676269%20(3).pdf
[7] Ando, T., & Zellner, A. (2010). Hierarchical Bayesian analysis of the seemingly unrelated regression and simultaneous equations models using a combination of direct Monte Carlo and importance sampling techniques. Bayesian Analysis, 5(1), 65-96. DOI:10.1214/10-BA503
[8] Ackerberg, D., Chen, X., Hahn, J., & Liao, Z. (2014). Asymptotic efficiency of semiparametric two-step GMM. Review of Economic Studies, 81(3), 919-943 https://doi.org/10.1093/restud/rdu011.
[9] Hsiao, C., & Zhou, Q. (2015). Statistical inference for panel dynamic simultaneous equations models. Journal of Econometrics, 189(2), 383-396. https://doi.org/10.1016/j.jeconom.2015.03.031
[10] Chen, X., & Qiu, Y. J. J. (2016). Methods for nonparametric and semiparametric regressions with endogeneity: A gentle guide. Annual Review of Economics, 8(1), 259-290.
http://www.annualreviews.org/doi/10.1146/annurev-economics-080213-041155
[11] Yang, K. (2016). Essays on multivariate and simultaneous equations spatial autoregressive models (Doctoral dissertation, The Ohio State University). OhioLINK Electronic Theses and Dissertations Center.https://etd.ohiolink.edu/acprod/odb_etd/ws/send_file/send?accession=osu1461277549&disposition=inline
[12] Berry, S. T., & Haile, P. A. (2016). Identification of nonparametric simultaneous equations models with a residual index structure (Cowles Foundation Discussion Paper No. 2008R). Yale University. https://doi.org/10.3982/ECTA13575Digital Object Identifier (DOI)
[13] Wang, D. (2017). Bias assessment and reduction for limited information estimation in general dynamic simultaneous equations models (Doctoral dissertation, Cardiff University). Cardiff University Repository. https://orca.cardiff.ac.uk/id/eprint/98538
[14] Yang, L. (2017). Semi-parametric generalized estimating equations with kernel smoother: A longitudinal study in financial data analysis (Doctoral dissertation, Florida State University). DigiNole: FSU Digital Library. https://www.proquest.com/openview/bc2b5f32901f1016cceae109eb5a5db1/1?pq-origsite=gscholar&cbl=18750
[15] Pérez-Sánchez, B., González, M., Perea, C., & López-Espín, J. J. (2021). A new computational method for estimating simultaneous equations models using entropy as a parameter criteria. Mathematics, 9(7), 700. https://doi.org/10.3390/math9070700
[16] Ding, X., & Zhou, Z. (2025). Simultaneous sieve estimation and inference for time-varying nonlinear time series regression (arXiv preprint arXiv:2506.23069v1). arXiv. https://doi.org/10.48550/arXiv.2506.23069
[17] Central Bank of Iraq (CBI), Annual Economic Reports (1990–2022).
[18] Ministry of Planning, Central Statistical Organization , Iraq





























