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. The results help explain three important empirical consumption puzzles: excess sensitivity of consumption to transitory income, high growth of consumption in the presence of a low risk-free interest rate, and underspending of the elderly.

Several recent studies have suggested that empirical rejections of the permanent income/life cycle model may 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. The results generally support the hypothesis that an inability to borrow against future labor income affects the consumption of a significant portion of the population.

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. The results generally support the hypothesis that an inability to borrow against future labor income affects the consumption of a significant portion of the population.

Only one-fourth of U.S. families own stock. This paper examines whether the consumption of stockholders differs from the consumption of nonstockholders and, if so, whether these differences help explain the empirical failures of the consumption-based CAPM. Household panel data are used to construct time series on the consumption of each group. The results indicate that the consumption of stockholders is more volatile and more highly correlated with the excess return on the stock market. These differences help explain the size of the equity premium, although they do not fully resolve the equity premium puzzle.

A great deal of research on the empirical behavior of inventories examines some variant of the production smoothing model of finished goods inventories. The overall assessment of this model that exists in the literature is quite negative: there is little evidence that manufacturers hold inventories of finished goods in order to smooth production patterns. This paper examines whether this negative assessment of the model is due to one or both of two features: costs shocks and seasonal fluctuations. The reason for considering costs shocks is that if firms are buffeted more by cost shocks than demand shocks, production should optimally be more variable than sales. The reasons for considering seasonal fluctuations are that seasonal fluctuations account for a major portion of the variance in production and sales, that seasonal fluctuations are precisely the kinds of fluctuations that producers should most easily smooth, and that seasonally adjusted data is likely to produce spurious rejections of the production smoothing model even when it is correct. We integrate cost shocks and seasonal fluctuations into the analysis of the production smoothing model in three steps. First, we present a general production smoothing model of inventory investment that is consistent with both seasonal and non-seasonal fluctuations in production, sales, and inventories. The model allows for both observable and unobservable changes in marginal costs. Second, we estimate this model using both seasonally adjusted and seasonally unadjusted data plus seasonal dummies. The goal here is to determine whether the incorrect use of seasonally adjusted data has been responsible for the rejections of the production smoothing model reported in previous studies. The third part of our approach is to explicitly examine the seasonal movements in the data. We test whether the residual from an Euler equation is uncorrelated with the seasonal component of contemporaneous sales. Even if unobservable seasonal cost shocks make the seasonal variation in output greater than that in sales, the timing of the resulting seasonal movements in output should not necessarily match that of sales. The results of our empirical work provide a strong negative report on the production smoothing model, even when it includes cost shocks and seasonal fluctuations. At both seasonal and non-seasonal frequencies, there appears to be little evidence that firms hold inventories in order to smooth production. A striking piece of evidence is that in most industries the seasonal in production closely matches the seasonal in shipments, even after accounting for the movements in interest rates, input prices, and the weather.

How public pension plan assets should be invested is an important but unsettled question. Alicia H. Munnell and Mauricio Soto (2007) find that the share of state and local (S&L) plan assets held in equities has grown over time largely in parallel with private sector practices, from an average of about 40 percent in the late 1980s to about 70 percent in 2007. This exposure led to a loss of an estimated $1 trillion dollars following the decline of the stock market from October 2007 to October 2008 (Munnell et. al., 2008). Nevertheless, some observers endorse the standard practice of investing heavily in higher yielding but riskier equities, reasoning that the higher average returns will reduce future required tax receipts and also help to reduce under-funding over time. Others advocate a more conservative approach that reduces the volatility of funding levels and the likelihood of severe shortfalls during economic downturns when government resources are already constrained (e.g., Lawrence N. Bader and Jeremy Gold, 2007). The accounting rules for public pensions create a perverse incentive to invest in stocks: since projected liabilities are discounted at the expected return on assets 1

Under standard assumptions, individuals and the government are indifferent between traditional tax-deferred retirement accounts and “front-loaded” (Roth) accounts. Adding investment fees to this benchmark, individuals are still indifferent, but the government is not. We show that under weak conditions firms charge equal percent fees under both systems, yielding higher dollar fees under Traditional. We estimate that tax deferral increases demand for asset management services by $3.8 trillion, costing the government $23.4 billion in annual fees. In a general equilibrium differentiated-product model, tax deferral produces a larger asset management industry, higher taxes, and lower social welfare.

Micro data studies of household saving often find a significant group in the population with virtually no wealth, raising concerns about heterogeneity in motives for saving. In particular, this heterogeneity has been interpreted as evidence against the life cycle model of saving. This paper argues that a life cycle model can replicate observed patterns in household wealth accumulation after accounting explicitly for precautionary saving and asset-based, means-tested social insurance. We demonstrate theoretically that social insurance programs with means tests based on assets discourage saving by households with low expected lifetime income. In addition, we evaluate the model using a dynamic programming model with four state variables. Assuming common preference parameters across lifetime income groups, we are able to replicate the empirical pattern that low-income households are more likely than high-income households to hold virtually no wealth. Low wealth accumulation can be explained as a utility-maximizing response to asset-based, means-tested welfare programs.