Hybrid Exponential†Hyperbolic Discounting and Growth Without Commitment

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.