Hybrid exponential-hyperbolic discounting and growth without commitment

Tsoukis

Abstract

We analyse the time-consistent intertemporal behaviour of an individual who discounts the future hyperbolically (HD) in the absence of commitment. In continuous-time, we extend Barro's (Quarterly Journal of Economics, Vol. 114 (1999), pp. 1125–1152) analysis of a ‘sophisticated’ present-bias in a deterministic setup and characterize consumption in an analytically tractable way. Furthermore, we embed this analysis into a ‘flexible AK’ model. Greater present bias increases the consumption-capital ratio, decreases the steady-state growth rate, while it increases the interest rate-growth rate wedge. Dynamically, as the interest rate fluctuates over the business cycle, a greater present bias causes the consumption-output ratio to be more procyclical and volatile, thus helping to resolve the ‘consumption-output puzzle’. In the transitional dynamics, greater present bias causes a lower steady state capital stock. All of these effects are only present or at least more pronounced under HD than present value-equivalent exponential discounting.

Citation

Tsoukis. (2017). Hybrid exponential-hyperbolic discounting and growth without commitment. https://doi.org/10.1111/manc.12197

• Acceptance Date: Jun 23, 2017
• Publication Date: Aug 6, 2017
• Journal: The Manchester School
• Print ISSN: 1467-9957
• Pages: e45-e74
• DOI: https://doi.org/10.1111/manc.12197
• Keywords: Hyperbolic discounting, growth, business cycles,; time inconsistency
• Publisher URL: https://doi.org/10.1111/manc.12197