Technological Advance and the Growth in Health Care Spending

The second half of the twentieth century recorded a rapid growth in health care spending and a significant increase in life expectancy. This paper hypothesizes that the combination of techno-logical progress in medical treatment and rising incomes is the driving force behind these two trends. Using a stochastic, multi-period overlapping-generations model as the analytical vehicle, this paper argues that the rapid growth in medical spending is not driven by factors associated with market structures or insurance opportunities, but instead by factors underlying the production and accumulation of health. According to this model, improvements in medical treatment and rising incomes can explain all of the increase in medical spending and more than 60% of the increase in life expectancy at age 25 during the second half of the twentieth century.Technological progress, life expectancy, medical spending, health

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

Concave consumption function and precautionary wealth accumulation

This paper examines the theoretical foundations of precautionary wealth accumulation in a multi-period model where consumers face uninsurable earnings risk and borrowing constraints. We begin by characterizing the consumption function of individual consumers. We show that consumption function is concave when the utility function has strictly positive third derivative and the inverse of absolute prudence is a concave function. These conditions encompass all HARA utility functions with strictly positive third derivative as special cases. We then show that when consumption function is concave, a mean-preserving spread in earnings risk would encourage wealth accumulation at both the individual and aggregate levels.Consumption function, borrowing constraints, precautionary saving

Concave Consumption Function under Borrowing Constraints

This paper analyzes the optimal consumption behavior of a consumer who faces uninsurable labor income risk and borrowing constraints. In particular, it provides conditions under which the decision rule for consumption is a concave function of existing assets. The current study presents two main findings. First, it is shown that the consumption function is concave if the period utility function is drawn from the HARA class and has either strictly positive or zero third derivative. Second, it is shown that the same result can be obtained for certain period utility functions that are not in the HARA class.Consumption function, borrowing constraints, precautionary saving

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

Path integration in relativistic quantum mechanics

The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for a particle described by the simple relativistic action proportional to its proper time. This propagator is nonvanishing outside the light cone, implying that spacelike trajectories must be included in the path integral. The propagator matches the WKB approximation to the corresponding configuration-space path integral far from the light cone; outside the light cone that approximation consists of the contribution from a single spacelike geodesic. This propagator also has the unusual property that its short-time limit does not coincide with the WKB approximation, making the construction of a concrete skeletonized version of the path integral more complicated than in nonrelativistic theory.Comment: 14 page

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

A Quantitative Analysis of Suburbanization and the Diffusion of the Automobile

Suburbanization in the U.S. between 1910 and 1970 was concurrent with the rapid diffusion of the automobile. A circular city model is developed in order to access quantitatively the contribution of automobiles and rising incomes to suburbanization. The model incorporates a number of driving forces of suburbanization and car adoption, including falling automobile prices, rising real incomes, changing costs of traveling by car and with public transportation, and urban population growth. According to the model, 60 percent of postwar (1940-1970) suburbanization can be explained by these factors. Rising real incomes and falling automobile prices are shown to be the key drivers of suburbanization.automobile; suburbanization; population density gradients; technological progress

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