Economics Insights @ CBS

No one has derived closed-form solutions for consumption with stochastic labor income and constant relative risk aversion utility. A numerical technique is used here to give an accurate approximation to the solution. The resulting consumption function is often dramatically different than the certainty equivalence solution typically used, in which consumption is proportional to the sum of financial wealth and the present value of expected future income.

This paper is motivated by two facts: failure of log-linear empirical exchange rate models of the 1970's and the observed variability of risk premiums in the forward market. Rational maximizing models predict that changes in conditional variances of monetary policies, government spendings, and income growths affect risk premiums and induce conditional volatility of exchange rates.

Several recent studies have suggested that empirical rejections of the permanent income/life cycle model might be due to the existence of liquidity constraints. This paper tests the permanent income hypothesis against the alternative hypothesis that consumers optimize subject to a well-specified sequence of borrowing constraints. Implications for consumption in the presence of borrowing constraints are derived and then tested using time-series/cross-section data on families from the Panel Study of Income Dynamics.

Trading on private information creates inefficiencies because there is less than optimal risk sharing. This occurs because the response of market makers to the existence of traders with private information is to reduce the liquidity of the market. The institution of the monopolist specialist may ease this inefficiency somewhat by increasing the liquidity of the market. While competing market makers will expect a zero profit on every trade, the monopolist will average his profits across trades. This implies a more liquid market when there is extensive trading on private information.