Impact of the Degree of Relative Risk Aversion, the Interest Rate and the Exchange Rate Depreciation on Economic Welfare in a Small Open Economy

Soriano-Morales, Yazmín Viridiana and Vallejo-Jiménez, Benjamín and Venegas-Martínez, Francisco (2017): Impact of the Degree of Relative Risk Aversion, the Interest Rate and the Exchange Rate Depreciation on Economic Welfare in a Small Open Economy.

Abstract

This paper is aimed at assessing the impact of the degree of relative risk aversion on economic welfare for different levels of the interest rate and the exchange rate depreciation in a small open economy. To do this, a representative consumer-producer makes decisions on consumption, money balances, and leisure. In order to find a closed-form solution of the household’s economic welfare, it is assumed that individual’s preferences belong to the family of Constant Relative Risk Aversion (CRRA) utility functions. Several comparative statics graphical experiments about the effects of the degree of relative risk aversion on economic welfare for different levels of nominal variables are carried out. Finally, we find that, under the stated assumptions, household’s economic welfare seen as a function of the degree of relative risk aversion is responsive to different values of nominal variables.

• Item Type: MPRA Paper
• Language: English
• Keywords: Consumer-producer economics, economic welfare, degree of relative risk aversion, small open economy, interest rate, foreign exchange.
• Subjects: E - Macroeconomics and Monetary Economics > E4 - Money and Interest Rates > E43 - Interest Rates: Determination, Term Structure, and Effects; F - International Economics > F3 - International Finance > F31 - Foreign Exchange

References

Barro, R. and X. Sala-i-Martin. (1995). Economic Growth. Mc. McGraw-Hill, New York.

Battermann, H., U. Broll and J. Wahl. (1997). Constant Relative Risk Aversion and Form Equivalence Classes. Working Paper Series II, N. 345.

Betts, C. and M. B. Devereux (2000). Exchange Rate Dynamics in a Model of Pricing-to-Market. Journal of International Economics, Vol. 50, No. 1, pp. 215–244.

Boulier, J., S. Huang, and G. Taillard, (2001). Optimal Management under Stochastic Interest Rates: the Case of a Protected Defined Contribution Pension Fund. Insurance: Mathematics and Economics. Vol. 28, No. 2, pp. 173-189.

Cairns, A., D. Blake, and K. Dowd, (2006). Stochastic Life styling: Optimal dynamic asset allocation for defined-contribution pension plans, Journal of Economic Dynamic and Control. Vol. 30, No. 5, pp. 843-877.

Deelstra, G., M. Grasselli, and P. Koehl, (2003). Optimal Investment Strategies in the Presence of a Minimum Guarantee. Insurance: Mathematics and Economics. Vol. 33, No. 1, pp. 189-207.

Devereux, M. B. and Engel C. (2003). Monetary Policy in the Open Economy Revisited: Price Setting and Exchange-Rate Flexibility. Review of Economic Studies, Vol. 70, No. 4, pp. 765-783.

Dohmen, T., A. Falk, D. Huffman and U. Sunde (2010). Are Risk Aversion and Patience Related to Cognitive Ability? American Economic Review, Vol. 100, pp. 1238-1260.

Gao, J. (2008). Stochastic Optimal Control of DC Pension Funds. Insurance: Mathematics and Economics. Vol. 42, No. 3, pp. 1159-1164.

González-Aréchiga, B., J. Díaz-Tinoco y F. Venegas-Martínez (2001). Riesgo cambiario, brecha de madurez y cobertura con futuros: análisis local y de valor en riesgo. Economía Mexicana, Nueva Época, Vol. 10, No. 2, pp. 259-290.

Kim, J. (2003). Welfare Evaluation of Monetary Policy Rules in a Model with Nominal Rigidities. Federal Reserve Bank of Minneapolis. Working Paper. Retrievable from: https://www.mpls.frb.org/~/media/files/pubs/bankingpolicy/papers/wp3-03.pdf

Krause, A. (2012). Optimal Saving Taxation when Individuals have Different CRRA Utility Functions. Annals of Economics and Statistics. No. 113-114, pp. 207.

Moreno-Bromberg, S., T. Pirvu, and A. Réveillac. (2012). CRRA Utility Maximization under Risk Constraints. arXiv preprint arXiv:1106.1702.

Pugsley, B., and H. Rubinton (2016). Inequality in the Welfare Costs of Disinflation. Princeton University. Working Paper. Retrievable from: https://www.newyorkfed.org/medialibrary/media/research/economists/pugsley/mpinequality_april2016.pdf?la=en

Shi, J. (2015). The Short Run Welfare Implications of Openness to FDI and Monetary Policy. Peking University, Working Paper. Retrievable from: https://www.nottingham.ac.uk/gep/documents/conferences/2015-16/china/shi.pdf

Soriano-Morales, Y. V., F. Venegas-Martínez, y B. Vallejo-Jiménez (2015). Determination of the Equilibrium Expansion Rate of Money when Money Supply is driven by a Time-homogeneous Markov Modulated Jump Diffusion Process. Economics Bulletin, Vol. 35, No. 4, pp. 2074-2084.

Venegas-Martínez, F. y A. Islas Camargo (2005). Volatilidad en los mercados de América Latina. Efectos de Largo plazo. Comercio Exterior, Vol. 55. No. 11, pp. 936-947.

Venegas-Martínez, F. (2000). On Consumption, Investment, and Risk. Economía Mexicana, Nueva Época, Vol. 9, No. 2, pp. 227-244.

Venegas-Martínez, F. (2005). Política fiscal, estabilización de precios y mercados incompletos. Estudios Económicos, Vol. 20, No. 1, pp. 3-18.

Venegas-Martínez, F. (2006). Fiscal Policy in a Stochastic Temporary Stabilization Model: Undiversifiable Devaluation Risk. Journal of World Economic Review, Vol. 1, No. 1, pp. 87-106.

Venegas-Martínez, F. (2009). Temporary Stabilization in Developing Countries and Real Options on Consumption. International Journal of Economic Research, Vol. 6, No. 2, pp. 237-257.

Venegas-Martínez, F. y B. González-Aréchiga (2000). Mercados financieros incompletos y su impacto en los programas de estabilización de precios: el caso mexicano. Momento Económico, No. 111, pp. 20-27.

Vigna, E. (2009). Mean-variance Inefficiency of CRRA and CARA Utility Function for Portfolio Selection in Defined Contribution Pension Schemes. Working Paper No. 108.

Xie, D. (2000). Power Risk Aversion Utility Functions. Annals of Economics and Finance. Vol. 1, No. 2, pp. 265-282.