Essays on Life-Cycle Savings and Consumption
Hay Jin Kim L.
Tesis, Doctorado en Economía, IE-PUC, 2020
Abstract: This dissertation is divided into four chapters. The first chapter includes a brief literature survey on life-cycle precautionary saving. It presents a stochastic life-cycle model of consumption and savings and summarizes the empirical evidence on the degree of precautionary saving. The second chapter studies the savings behavior of households over the life-cycle by revisiting Gourinchas and Parker (2002). They conclude that “consumer behavior changes strikingly over the life cycle”1 based on the age-profile of target level of liquid wealth. The main finding is that target wealth behavior differs substantially from actual savings behavior by households based on the consumption life-cycle model. While the target value of wealth is a good indicator of the overall direction to which the distribution of normalized cash-on-hand moves, it fails to describe the magnitude of household overall savings. Furthermore, the age-profile of the target value of liquid wealth depends crucially on the retirement age’s consumption rules, retirement income risks, and on the systematic-age variation of the consumption functions. Each of these factors are implied by the model’s assumptions instead of observed consumer behavior. Moreover, by definition, the target value of cash-on-hand is sensitive to small changes (within confidence intervals for such parameter values) in the model’s parameters, such as the interest rate, when the marginal propensity to consume is less than one. The third chapter examines the implications of the individual life-cycle behavior predicted by Gourinchas and Parker (2002) for average liquid wealth, average consumption and average marginal propensity in light of Carroll (2000). Here, I show that the appropriateness of a representative-agent depends on the age distribution of the population and on the assumed values of the preference and retirement rule parameters of the life-cycle model. Under the base-line parameter values, individuals optimally choose to accumulate a substantial amount of liquid wealth: they quickly adjust their consumption and saving decisions so as to avoid the regions where borrowing constraints are binding. In fact, households’ probability to hold low amounts of liquid wealth is almost zero by age 45. As a result, all individuals have the same marginal propensity to consume in their mid-forties and up. Thus, the aggregate dynamics of a representative-consumer model possessing liquid wealth equal to the mean of the distribution would resemble the aggregate predictions of the life-cycle model for middle-aged individuals. However, I also find that the predicted distribution of cash-on-hand does not match the wealth holdings in microeconomic data despite the various combinations of parameter values that are considered. This discrepancy sheds light in the suitability of the life-cycle model to reproduce the observed saving behavior across U.S. households.
The fourth chapter evaluates the use of the endogenous grid-points solution method when estimating a stochastic life-cycle model. The main finding is that the numerical solution method to solve theconsumer problem affects its structural estimation. The Monte Carlo results suggest that one must be cautious when adopting the endogeneous grid-points solution method when numerically minimizing the Simulated Method of Moments estimators’ objective function. The mode of the SMM estimates for the coefficient of risk aversion is approximately zero when its true value is small.