Economic Theory as Successive Approximations of Statistical Moments

Olkhov, Victor (2023): Economic Theory as Successive Approximations of Statistical Moments.

Abstract

This paper highlights the links between the descriptions of macroeconomic variables and statistical moments of market trade, price, and return. We consider economic transactions during the averaging time interval Δ as the exclusive matter that determines the change of any economic variables. We regard the stochasticity of market trade values and volumes during Δ as the only root of the random properties of price and return. We describe how the market-based n-th statistical moments of price and return during Δ depend on the n-th statistical moments of trade values and volumes or equally on sums during Δ of the n-th power of market trade values and volumes. We introduce the secondary averaging procedure that defines statistical moments of trade, price, and return during the averaging interval Δ2>>Δ. As well, the secondary averaging during Δ2>>Δ introduces statistical moments of macroeconomic variables, which were determined as sums of economic transactions during Δ. In the coming years, predictions of the market-based probabilities of price and return will be limited by Gaussian-type distributions determined by the first two statistical moments. We discuss the roots of the internal weakness of the conventional hedging tool, Value-at-Risk, that could not be solved and thus remain the source of additional risks and losses. One should consider economic theory as a set of successive approximations, each of which describes the next array of the n-th statistical moments of market transactions and macroeconomic variables, which are repeatedly averaged during the sequence of increasing time intervals.

• Item Type: MPRA Paper
• Language: English
• Keywords: economic theory; price and return; statistical moments; market-based probabilities
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C00 - General; E - Macroeconomics and Monetary Economics > E0 - General > E00 - General; E - Macroeconomics and Monetary Economics > E1 - General Aggregative Models > E17 - Forecasting and Simulation: Models and Applications; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E37 - Forecasting and Simulation: Models and Applications; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates; G - Financial Economics > G1 - General Financial Markets > G17 - Financial Forecasting and Simulation

References

Bachelier, L., (1900). Théorie de la speculation, Ann. Scientif. l’É.N.S. 3e série, 17, 21-86

Black, F. and M. Scholes, (1973). The Pricing of Options and Corporate Liabilities, J. Political Economy, 81 (3), 637-654

Berkowitz, S.A., Dennis, E., Logue, D.E., Noser, E.A. Jr. (1988). The Total Cost of Transactions on the NYSE, The Journal of Finance, 43, (1), 97-112

Blaug, M. (1985). Economic theory in retrospect, Cambridge Univ.Press, 4-th ed., 760

Campbell, J.Y., Grossman, S.J. and J.Wang, (1993). Trading Volume and Serial Correlation in Stock Return. Quatr. Jour. Economics, 108 (4), 905-939

Campbell, J.Y., (2018). Financial Decisions and Markets: A Course in Asset Pricing, Princeton Univ. Press, NJ, 477

Cantillon, R. (1730). An Essay on Economic Theory, 1-243, Translated Saucier C., Ed. Thornton, M., (2010). The Ludwig von Mises Institute, 254

Cochrane, J.H. and L.P. Hansen, (1992). Asset Pricing Explorations for Macroeconomics. Ed., Blanchard, O.J., Fischer, S. NBER Macroeconomics Annual 1992, v. 7, 115 – 182

Cochrane, J.H. (2001). Asset Pricing. Princeton Univ. Press, Princeton, US

DeFusco, A.A., Nathanson, C.G. and E. Zwick, (2017). Speculative Dynamics of Prices and Volume, Cambridge, MA, NBER WP 23449, 1-74

Duffie, D. and J. Pan, (1997). An Overview of Value-at-Risk, J. of Derivatives, 4, (3), 7-49

Duffie, D. and P. Dworczak, (2018). Robust Benchmark Design, NBER WP 20540, 1-56

Fama, E.F. (1965). The Behavior of Stock-Market Prices. J. Business, 38 (1), 34-105

Forbes, C., Evans, M., Hastings, N., and B. Peacock, (2011). Statistical Distributions. Wiley

Fox, D.R. et al. (2017). Concepts and Methods of the U.S. National Income and Product Accounts. BEA, US.Dep. Commerce, 1-447

Friedman, D.D. (1990). Price Theory: An Intermediate Text. South-Western Pub. Co., US

Gallant, A.R., Rossi, P.E. and G. Tauchen, (1992). Stock Prices and Volume, The Review of Financial Studies, 5(2), 199-242

Greenwald, B. and J. E. Stiglitz, (1987). Keynesian, New Keynesian and New Classical Economics, Oxford Economic Papers, 39 (1) 119-133

Hicks, J.R., (1937). Mr. Keynes and the "Classics"; A Suggested Interpretation, Econometrica, 5 (2), 147-159

Karpoff, J.M. (1987). The Relation Between Price Changes and Trading Volume: A Survey. The Journal of Financial and Quantitative Analysis, 22 (1), 109-126

Klyatskin, V.I. (2005). Stochastic Equations through the Eye of the Physicist, Elsevier B.V.

Krueger, D. (2002). Macroeconomic Theory, Stanford Univ., 294

Kurz, H.D. and N. Salvadori, (2003). Classical economics and modern theory: studies in long-period analysis, Routledge, 325

Leontief, W., (1955). Some Basic Problems of Empirical Input-Output Analysis, 9-52, in Ed. Goldsmit,R.W., Input-Output Analysis: An Appraisal, Princeton Univ.Press, 369

Leontief, W., (1973). Structure of the World Economy, Nobel Memorial Lecture, 1-16

Llorente, G., Michaely R., Saar, G. and J. Wang. (2001). Dynamic Volume-Return Relation of Individual Stocks. NBER, WP 8312, Cambridge, MA., 1-55

Longerstaey, J. and M. Spencer, (1996). RiskMetrics, Technical Document, 4-th Ed., Morgan Guaranty Trust Company NY, 296 p

Merton, R.C. (1973). An Intertemporal Capital Asset Pricing Model, Econometrica, 41(5), 867-887

Muth, J.F. (1961). Rational Expectations and the Theory of Price Movements, Econometrica, 29, (3) 315-335

Neumann, J.V., (1945). A Model of General Economic Equilibrium, Rev. Econ. Studies, 13(1), 1-9

Olkhov, V. (2021a). Three Remarks On Asset Pricing, SSRN WP 3852261, 1-24

Olkhov, V., (2021b). Price, Volatility and the Second-Order Economic Theory, ACRN Jour. Finance and Risk Perspectives, 10, 139-165

Olkhov, V., (2021c). Theoretical Economics and the Second-Order Economic Theory. What is it?, MPRA WP 110893, 1-14

Olkhov, V. (2021d). To VaR, or Not to VaR, That is the Question, SSRN WPS3770615, 1-14

Olkhov, V. (2022a). The Market-Based Asset Price Probability, MPRA WP115382, 1-21

Olkhov, V. (2022b). Why Economic Theories and Policies Fail? Unnoticed Variables and Overlooked Economics, SSRN WP 4189851, 1-26

Olkhov, V., (2023a). The Market-Based Probability of Stock Returns, SSRN WP 4350975

Olkhov, V., (2023b). The Market-Based Statistics of 'Actual' Returns of investors, MPRA WP 116896, 1-16

Olkhov, V., (2023c). Economic Complexity Limits Accuracy of Price Probability Predictions by Gaussian Distributions, SSRN WP 4550635, 1-33

Romer, D. (1996). Advanced macroeconomics, McGraw-Hill, 550

Sargent, T.J. (1979). Macroeconomic Theory, Academic Press, 404

Sharpe, W.F. (1964). Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. The Journal of Finance, 19 (3), 425-442

Schumpeter, J.A. (1939). Business Cycles, McGraw-Hill, NY, 461

Shiryaev, A.N. (1999). Essentials Of Stochastic Finance: Facts, Models, Theory. World Sc. Pub., Singapore. 1-852

Shreve, S. E. (2004). Stochastic calculus for finance, Springer finance series, NY, USA

Solow, R.M., (1956). A Contribution to the Theory of Economic Growth, Quart. J. Economics, 70 (1), 65-94

Tauchen, G.E. and M. Pitts, (1983). The Price Variability-Volume Relationship On Speculative Markets, Econometrica, 51, (2), 485-505

Tobias, A. and M. K. Brunnermeier, (2016). CoVaR, Amer. Econ. Rev., 106(7), 1705–1741

Vines, D. and S. Wills (Ed.) (2018). Rebuilding Macroeconomic Theory, Oxford Rev. Econ. Policy, 34 (1–2), 353

Walck, C. (2011). Hand-book on statistical distributions. Univ.Stockholm, SUF–PFY/96–01

Wickens, M. (2008). Macroeconomic Theory, A Dynamic General Equilibrium Approach, Princeton Univ. Press, 489