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Topics in nonparametric comparative statics and stability

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Abstract

This paper presents the analysis of the Jacobian matrix of a small, macroeconomic model to determine the robustness of the model's comparative statics. The values of the model's coefficients are assessed with respect to seven alternative estimation strategies such as ordinary least squares or two-stage least squares. For each alternative version, the invertibility and stability of the Jacobian matrix is studied. The model is robust to the degree that these characteristics are shared by any matrix with the same sign pattern or other similar nonparametric conditions on its entries. One way to address the relative success of the different estimation strategies is through the robustness of the comparative statics of the resulting model.

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References

  • Bassett, Lowell; Maybee, John; Quirk, James. "Qualitative Economics and the Scope of the Correspondence Principle,"Econometrica, 36, 1968, pp. 544–63.

    Google Scholar 

  • Berndt, Ernst R.The Practice of Econometrics, Classic and Comtemporary, New York, NY: Addison Wesley, 1991.

    Google Scholar 

  • Gillen, W. J.; Guccione, A. "The Introduction Of Constraints In Lancaster's Qualitative Comparative Statics Algorithm,"Quarterly Journal of Economics, 105, 1990, pp. 1053–61.

    Google Scholar 

  • Gorman, Terrance. "More Scope for Qualitative Economics,"Review of Economic Studies, 31, 1964, pp. 65–8.

    Google Scholar 

  • Hale, D.; Lady, G. "Qualitative Comparative Statics and Audits of Model Performance,"Linear Algebra and Its Applications, 217, 1995, pp. 141–54.

    Article  Google Scholar 

  • Hale, D.; Lady, G.; Maybee, J.; Quirk, J.Nonparametric Comparative Statics and Stability, Princeton, NJ: Princeton University Press, 1999.

    Google Scholar 

  • Hicks, J. R.Value and Capital, 2nd ed., London, United Kingdom: Oxford University Press, 1946.

    Google Scholar 

  • Klee, Victor; Ladner, R.; Manber, R. "Signsolvability Revisited,"Linear Algebra and Its Applications, 59, 1984, pp. 181–97.

    Article  Google Scholar 

  • Klein, L.Economic Fluctuations in the U.S., 1921–1941, Cowles Commission for Research in Economics Monograph No. 11, New York, NY: John Wiley and Sons, 1950.

    Google Scholar 

  • Lady, George. "On Organizing Analysis," in Harvey Greenberg; John Maybee, eds.,Computer-Assisted Analysis and Model Simplification, New York, NY: Academic Press, 1981, pp. 1–17.

    Google Scholar 

  • __. "The Structure of Qualitatively Determinate Relationship,"Econometrica, 51, 1983, pp. 197–218.

    Google Scholar 

  • __. SGNSOLVE.EXE and PREPARE.EXE Analysis Packages, conveyed to the Energy Information Administration, U.S. Department of Energy, Contract PN 0890-055-07-L01 under agreement with ANSTEC, 1993.

  • __. "Robust Economic Models,"Journal of Economic Dynamics and Control, 19, 1995, pp. 481–501.

    Article  Google Scholar 

  • __. "Detecting Stable Matrices,"Annuals of Mathematics and Artificial Intelligence, 17, 1996, pp. 29–36.

    Google Scholar 

  • Lady, George; Lundy, Thomas; Maybee, John. "Nearly Sign-Nonsingular Matrices,"Linear Algebra and Its Applications, 220, 1995, pp. 229–48.

    Article  Google Scholar 

  • Lady, George; Maybee, John. "Qualitatively Invertible Matrices,"Mathematical Social Sciences, 6, 1983, pp. 397–407.

    Article  Google Scholar 

  • Lancaster, Kelvin. "The Scope of Qualitative Economics,"Review of Economic Studies, 29, 1962, pp. 99–132.

    Google Scholar 

  • __. "The Solution of Qualitative Comparative Statics Problems,"Quarterly Journal of Economics, 53, 1966, pp. 278–95.

    Google Scholar 

  • Maybee, John. "Remarks on the Theory of Cycles in Matrices," mimeograph, Mathematics Department, Purdue University, 1966.

  • Maybee, John; Quirk, James. "Qualitative Problems in Matrix Theory,"SIAM Review, 11, 1969, pp. 30–51.

    Google Scholar 

  • Maybee, John; Wiener, G. M. "From Qualitative Matrices to Quantitative Restrictions,"Linear and Multilinear Algebra, 22, 1988, pp. 229–48.

    Google Scholar 

  • Maybee, Stuart. "A Method for Identifying Sign Solvable Systems," M.S. thesis, University of Colorado, 1986.

  • McKenzie, Lionel. "The Matrix with Dominant Diagonal and Economic Theory," in K. Arrow; S. Carlin; H. Scarf, eds.,Proceedings of a Symposium in Mathematical Methods in the Social Sciences, Stanford, CA: Stanford University Press, 1960.

    Google Scholar 

  • Metzlar, A. "Minimum Transversal of Cycles in Intercyclic Digraphs," Ph.D. dissertation, University of Waterloo, Canada, 1989.

    Google Scholar 

  • Milgrom, Paul. "Comparing Optima: Do Simplifying Assumptions Affect Conclusions?,"Journal of Political Economy, 102, 1994, pp. 607–15.

    Article  Google Scholar 

  • Milgrom, Paul; Roberts, John. "Rationalization, Learning and Equilibrium in Games with Strategic Complementarities,"Econometrica, 58, 1990, pp. 1255–78.

    Google Scholar 

  • __. "Comparing Equilibria,"American Economic Review, 84, 1994, pp. 441–59.

    Google Scholar 

  • Milgrom, Paul; Shannon, Chris. "Monotone Comparative Statics,"Econometrica, 62, 1994, pp. 157–80.

    Google Scholar 

  • Pindyck, R.; Rubinfeld, D.Econometric Models and Economic Forecasts, New York, NY: McGraw-Hill, 1981.

    Google Scholar 

  • Popper, K.The Logic of Scientific Discovery, 2nd ed., New York, NY: Harper and Row, 1959.

    Google Scholar 

  • Quirk, James. "Qualitative Stability of Matrices and Economic Theory: A Survey Article," in Harvey Greenberg; John Maybee, eds.,Computer-Assisted Analysis and Model Simplification, New York, NY: Academic Press, 1981, pp. 113–64.

    Google Scholar 

  • __. "Qualitative Economics,"The New Palgrave Dictionary of Economics, New York, NY: Macmillan, 1986.

    Google Scholar 

  • __. "Qualitative Analysis of Economic Models, Qualitative Matrices, and Related Matters: A Survey of the Literature," conveyed to the Energy Information Administration, U.S. Department of Energy, Contract PN 0890-055-07-L01 under agreement with ANSTEC, 1992.

  • __. "Qualitative Comparative Statics,"Journal of Mathematical Economics, 28, 1997, pp. 127–54.

    Article  Google Scholar 

  • Quirk, James; Ruppert, Richard. "Qualitative Economics and the Stability of Equilibrium,"Review of Economic Studies, 32, 1965, pp. 311–26.

    Google Scholar 

  • Ritschard, Gilbert. "Computable Qualitative Comparative Static Techniques,"Econometrica, 51, 1983, pp. 1145–68.

    Google Scholar 

  • Samuelson, Paul. "The Stability of Equilibrium: Comparative Statics and Dynamics,"Econometrica, 9, 1941, pp. 97–120.

    Google Scholar 

  • __.Foundations of Economic Analysis, Cambridge, MA: Harvard University Press, 1947.

    Google Scholar 

  • Stevens, S. "The Theory of Scales of Measurement,"Science, 103, 1946, pp. 677–80.

    Google Scholar 

Download references

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Lady, G.M. Topics in nonparametric comparative statics and stability. International Advances in Economic Research 6, 67–83 (2000). https://doi.org/10.1007/BF02295752

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