Bounding the CRRA Utility Functions

The constant-relative-risk-aversion (CRRA) utility function is now predominantly used in quantitative macroeconomic studies. This function, however, is not bounded and thus creates problems when applying the standard tools of dynamic programming. This paper devises a method for "bounding" the CRRA utility functions. The proposed method is based on a set of conditions that can establish boundedness among a broad class of utility functions. These results are then used to construct a bounded utility function that is identical to a CRRA utility function except when consumption is very small or very large. It is shown that the constructed utility function also satisfies the Inada condition and is consistent with balanced growth.Utility Function; Elasticity of Marginal Utility; Boundedness

Bounding the CRRA Utility Functions

The constant-relative-risk-aversion (CRRA) utility function is now predominantly used in quantitative macroeconomic studies. This function, however, is not bounded and thus creates problems when applying the standard tools of dynamic programming. This paper devises a method for "bounding" the CRRA utility functions. The proposed method is based on a set of conditions that can establish boundedness among a broad class of utility functions. These results are then used to construct a bounded utility function that is identical to a CRRA utility function except when consumption is very small or very large. It is shown that the constructed utility function also satisfies the Inada condition and is consistent with balanced growth.Utility Function; Elasticity of Marginal Utility; Boundedness

Finite State Markov-Chain Approximations to Highly Persistent Processes

This paper re-examines the Rouwenhorst method of approximating first-order autoregressive processes. This method is appealing because it can match the conditional and unconditional mean, the conditional and unconditional variance and the first-order autocorrelation of any AR(1) process. This paper provides the first formal proof of this and other results. When comparing to five other methods, the Rouwenhorst method has the best performance in approximating the business cycle moments generated by the stochastic growth model. In addition, when the Rouwenhorst method is used, moments computed directly off the stationary distribution are as accurate as those obtained using Monte Carlo simulations.Numerical Methods; Finite State Approximations; Optimal Growth Model

Finite State Markov-Chain Approximations to Highly Persistent Processes

This paper re-examines the Rouwenhorst method of approximating first-order autoregressive processes. This method is appealing because it can match the conditional and unconditional mean, the conditional and unconditional variance and the first-order autocorrelation of any AR(1) process. This paper provides the first formal proof of this and other results. When comparing to five other methods, the Rouwenhorst method has the best performance in approximating the business cycle moments generated by the stochastic growth model. It is shown that, equipped with the Rouwenhorst method, an alternative approach to generating these moments has a higher degree of accuracy than the simulation method.Numerical Methods; Finite State Approximations; Optimal Growth Model

Finite State Markov-Chain Approximations to Highly Persistent Processes

This paper re-examines the Rouwenhorst method of approximating first-order autoregressive processes. This method is appealing because it can match the conditional and unconditional mean, the conditional and unconditional variance and the first-order autocorrelation of any AR(1) process. This paper provides the first formal proof of this and other results. When comparing to five other methods, the Rouwenhorst method has the best performance in approximating the business cycle moments generated by the stochastic growth model. It is shown that, equipped with the Rouwenhorst method, an alternative approach to generating these moments has a higher degree of accuracy than the simulation method.Numerical Methods, Finite State Approximations, Optimal Growth Model

Suburbanization and the Automobile

During the period 1910 to 1970, an increasing fraction of the urban population in the US chose to live on the outskirts of central cities. This was also a time when a major innovation in transportation technology, the automobile, was introduced and widely adopted. The objective of this paper is to assess quantitatively the relationship between the two. To achieve this, a simple model is constructed in which agents can choose where to live and whether or not to buy a car. When the model is calibrated, it can explain about 70 percent of the rise in car-ownership over the period 1910 to 1970 and all of the suburbanization trend. According to the model, rising income and falling car prices alone are not enough to generate the suburbanization trend. It is essential to have also: (i) a declining cost of commuting by car which allows car-owners to live further away from the city center, and (ii) a rising cost of using public transportation which encourages agents to make the swith to automobiles.automobiles, suburbanization, population density gradients

Time Preference and the Distributions of Wealth and Income

This paper presents a dynamic competitive equilibrium model with heterogeneous time pref- erences that can account for the observed patterns of wealth and income inequality in the United States. This model generalizes the standard neoclassical growth model by including (i) a demand for status by the consumers and (ii) human capital formation. The Örst feature prevents the wealth distribution from collapsing into a degenerate distribution. The second feature generates a strong positive correlation between earnings and wealth across agents. A calibrated version of this model succeeds in replicating the wealth and income distributions of the United States.Length: 38 pagesInequality, Heterogeneity, Time Preference, Human Capital