A New Kind of Two-Stage Least Squares Based on Shapley Value Regression

Mishra, SK (2017): A New Kind of Two-Stage Least Squares Based on Shapley Value Regression.

Abstract

The Two-Stage Least squares method for obtaining the estimated structural coefficients of a simultaneous linear equations model is a celebrated method that uses OLS at the first stage for estimating the reduced form coefficients and obtaining the expected values in the arrays of current exogenous variables. At the second stage it uses OLS, equation by equation, in which the explanatory expected current endogenous variables are used as instruments representing their observed counterpart. It has been pointed out that since the explanatory expected current endogenous variables are linear functions of the predetermined variables in the model, inclusion of such expected current endogenous variables together with a subset of predetermined variables as regressors make the estimation procedure susceptible to the deleterious effects of collinearity, which may render some of the estimated structural coefficients with inflated variance as well as wrong sign. As a remedy to this problem, the use of Shapley value regression at the second stage has been proposed. For illustration a model has been constructed in which the measures of the different aspects of globalization are the endogenous variables while the measures of the different aspects of democracy are the predetermined variables. It has been found that the conventional (OLS-based) Two-Stage Least Squares (2-SLS) gives some of the estimated structural coefficients with an unexpected sign. In contrast, all structural coefficients estimated with the proposed 2-SLS (in which Shapley value regression has been used at the second stage) have an expected sign. These empirical findings suggest that the measures of globalization are conformal among themselves as well as they are positively affected by democratic regimes.

• Item Type: MPRA Paper
• Language: English
• Keywords: Simultaneous equations model; Two-Stage Least Squares; Instrumental Variables; Collinearity; Shapley Value Regression; Democracy Index; Index of Globalization
• Subjects: C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C30 - General; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C36 - Instrumental Variables (IV) Estimation; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C57 - Econometrics of Games and Auctions; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games; F - International Economics > F6 - Economic Impacts of Globalization > F63 - Economic Development

References

Anderson, T.W. (2005).Origins of the limited information maximum likelihood and two-stage least squares estimators. Journal of Econometrics, 127 (1): 1-16.

Basmann, R.L. (1957). A generalized classical method of linear estimation of coefficients in a structural equation. Econometrica, 25(1): 77–83.

Dreher, A. (2006). Does Globalization Affect Growth? Evidence from a new Index of Globalization. Applied Economics, 38(10): 1091-1110.

Dreher, A., Gaston, N. and Martens, P. (2008). Measuring Globalisation: Gauging its Consequences. New York: Springer.

Intriligator, M.D. (1978). Econometric Models, Techniques, and Applications. Amsterdam: North-Holland.

KOF [Konjunkturforschungsstelle or Economic Research Centre of ETH Zurich]. (2017). 2017 Index of globalization. http://globalization.kof.ethz.ch/media/filer_public/2017/04/19/rankings_2017.pdf

Lipovetsky, S. (2006). Entropy criterion in logistic regression and Shapley value of predictors. Journal of Modern Applied Statistical Methods, 5(1): 95-106.

Mishra, S.K. (2013). Global Optimization of Some Difficult Benchmark Functions by Host-Parasite Coevolutionary Algorithm", Economics Bulletin, 33(1): 1-18.

Mishra, S.K. (2016). Shapley Value Regression and the Resolution of Multicollinearity. Journal of Economics Bibliography, 3(3): 498-515.

Mishra, S.K. (2017a). Almost equi-marginal principle based composite index of globalization: China, India and Pakistan. Journal of Economic and Social Thought, 4(3): 335-351.

Mishra, S.K. (2017b). Are Democratic Regimes Antithetical to Globalization? Working Paper. SSRN: https://ssrn.com/abstract=3088921.

Reiersøl, O. (1945). Confluence Analysis by Means of Instrumental Sets of Variables. Arkiv for Mathematic, Astronomi, och Fysik. 32A. Uppsala: Almquist & Wiksells.

Smith, G. and Brainard, W. (1976). The value of a priori information in estimating a financial model. Journal of Finance, 31(5): 1299-1322.

Theil, H. (1953). Repeated least-squares applied to complete equation systems. Central Planbureau, Memorandum.

Theil, H. (1971). Principles of Econometrics. New York: Wiley.