On the indeterminacy of capital accumulation paths

In neoclassical optimal growth models the stability of the accumulation paths depends on the discount parameter. We prove that, for discount factors small enough, the policy function which describes an optimal path can be of any type. The result is achieved using the notion of α-concavity. We adopt a constructive approach. Given any twice differentiable map we show how to construct an optimal growth problem which produces that map as the optimal policy function. A consequence is that “chaos” can appear in these models. We also provide bounds on the values of the discount parameter for which “indeterminacy” is possible.     

Robust ergodic chaos in discounted dynamic optimization models

Summary We identify a family of discounted dynamic optimization problems in which the immediate return function depends on current consumption, capital input and a taste parameter. The usual monotonicity and concavity assumptions on the return functions and the aggregative production function are verified. It is shown that the optimal transition functions are represented by the quadratic family, well-studied in the literature on chaotic dynamical systems. Hence, Jakobson's theorem can be used to throw light on the issues of robustness of ergodic chaos and sensitive dependence on initial conditions.     

SECRET SEARCH

For high-profile positions, should applicant identities be made public within the organization (“open search”) or kept confidential (“secret search”)? We construct a model where an organization seeks to hire, but where candidates' abilities are private information unless it uses open search. Rejected applicants, under open search, suffer disutility. We find the following: Salaries are lower under secret search, the expected ability of applicants decreases as the posted (open search) salary increases, secret search is preferred by organizations where quality of candidate is relatively unimportant, and organizations will, for some parameter values, choose secret search even when open search is more efficient.     

Heterogeneous Households,the Distribution of Wealth,and the Laursen-Metzler Effect*

To study the effects of a terms-of-trade deterioration the paper constructs a dynamic model with heterogeneous households that maximize intertemporal utility. It shows that insofar as this shock leads to a redistribution of wealth-an outcome ignored by the literature because of the representative-agent assumption invariably adopted-it may give rise to an initial current-account deficit and nonmonotonic adjustment paths. the paper also buttresses the argument that heterogeneous-household models help explain the observed “excess smoothness” of consumption.     

Educational models for manpower development

In this paper a number of educational models are formulated and optimized. A single educational program multiperiod model is developed and optimized by means of dynamic programming. The type of results an educational administrator might obtain from this model and optimization are presented in an example which evaluates alternative future options. This single educational program model is extended to a multi-echelon model, allowing for the modifications to very realistic “compulsary-type” and “college-type” educational models. Linear programming generates the optimal decisions for the general multi-echelon multiperiod educational model.     

International capital mobility: An alternative test based on intertemporal current account models

This paper examines international capital mobility by estimating intertemporal current account models for nine major industrialized countries. To account for the large fluctuations of oil prices (the terms-of-trade) and their effects on the current account, an intertemporal current account model incorporating such effects is devised. The model estimation reveals significant terms-of-trade effects on the current account and, moreover, does not exhibit any “excess capital mobility” found in the previous literature. These results indicate that to achieve a more accurate measure of international capital mobility, a proper account of the terms-of-trade effect is essential.     

Macroeconomic implications of dynamically inconsistent preferences

Despite the widespread use of models of intertemporal choices in economics, previous studies have assumed that intertemporal preferences are dynamically consistent. This paper provides a fresh perspective on propagation mechanisms of a typical macroeconomic shock in a model with dynamically inconsistent preferences. To this end, I develop a prototypical neoclassical model that features dynamically inconsistent preferences to explore dynamic responses of key macro-aggregates, discounted cumulative effects and some characteristics of aggregate fluctuations in response to a technology shock. The main findings reveal that (a) consumption and investment in the proposed model show a larger increase than those in a standard neoclassical model; (b) unlike the standard model, the proposed model yields a short-run decline in labor, which is corroborated by previous studies; (c) all of these dynamic responses in the proposed model deliver smaller cumulative output effects; (d) the proposed model does a reasonably good job of matching key characteristics of aggregate fluctuations with the counterparts observed in the postwar U.S. data. The present-bias and sophistication effects are the linchpin of these main results. Various analyses on a set of different parameter values are also discussed.     

Inter-temporal choices with temporal reference dependence

I develop an intertemporal choice model for rational deviators whose preferences depend not only on their actual consumption but also on comparison to their beliefs about the optimal consumption. The standard decision maker is loss averse with respect to this belief-dependent reference point. When psychologically weighted loss aversion is low, a decision maker deviates from the standard intertemporal choice behavior and over-consumption, as well as the alternative possibility of under-consumption can be rationalized. When the decision maker has time-varying degrees of loss aversion, he re-optimizes the consumption plan through adjusted beliefs as subsequent selves realize that past decision for the present period is no longer optimal. In the dynamic model, I solve for consistent intertemporal optimization rules by which a dynamic deviator should meet rational intertemporal consistency at each point in time. Finally, I demonstrate that the dynamic reference dependent model can solve a puzzling feature in lifecycle consumption data.     

Depreciation and intergenerational altruism in the private provision of public goods

The static model of the private provision of public goods is refuted by empirical and experimental evidence which shows that contributions are above the levels predicted by the theory. The model is reconsidered here in an intertemporal framework that allows the formation of a stock of public good over time and admits intergenerational altruism into preferences. Both of these factors affect the level of private provision. An intertemporal version of the Samuelson rule is derived and it is shown that, for some parameter values, the provision level determined by this is matched by private provision. For other parameter values, it is shown how a system of taxation can achieve the optimum.     

INTERTEMPORAL COMPLEMENTARITY AND OPTIMALITY: A STUDY OF A TWO‐DIMENSIONAL DYNAMICAL SYSTEM*

We study the underlying structure of the two‐dimensional dynamical system generated by a class of dynamic optimization models that allow for intertemporal complementarity between adjacent periods, but preserve the time‐additively separable framework of Ramsey models. Specifically, we identify conditions under which the results of the traditional Ramsey‐type theory are preserved even when the intertemporal independence assumption is relaxed. Local analysis of this theme has been presented by Samuelson (Western Economic Journal 9 (1971), 21–26). We establish global convergence results and relate them to the local analysis, by using the mathematical theory of two‐dimensional dynamical systems. We also relate the local stability property of the stationary optimal stock to the differentiability of the optimal policy function near the stationary optimal stock, by using the Stable Manifold Theorem.     

Hamiltonian Approaches to The Analysis of External Debt

This paper investigates the borrowing aspect of LDC's debt problems from a short run and a borrower's perspective, taking “Hamiltonian” approaches. In analyzing a dynamic external debt problem, other studies have adopted a single-objective of maximizing intertemporal utility. This paper explores the optimum rate of external borrowing with different objectives and assumptions that may be more realistic for the economic planners of the developing countries. Altogether four cases are analyzed. The important finding is that even though all four cases exhibit the so called “bang-bang” phenomena, all four cases produce a different optimum rate of external borrowing with different policy implications. [400]     

MODELING MOVEMENTS IN INDIVIDUAL CONSUMPTION: A TIME‐SERIES ANALYSIS OF GROUPED DATA

We characterize the time‐series properties of group‐level consumption, income, and interest rates using microdata. We relate the coefficients of moving average representations to structural parameters of theoretical models of consumption behavior. Using long time series of cross sections to construct synthetic panel data for the United Kingdom, we find that for high‐educated individuals the Euler equation restrictions are not rejected, the elasticity of intertemporal substitution is higher than one, and there is evidence of “excess smoothness” of consumption. Low‐educated individuals, conversely, exhibit excess sensitivity of consumption to past income, and the elasticity of intertemporal substitution is not statistically different from zero.     

Finite Sample Limited Information Inference Methods for Structural Equations and Models With Generated Regressors

We propose exact tests and confidence sets for various structural models typically estimated by IV methods, such as models with unobserved regressors, which remain valid despite the presence of identification problems or weak instruments. Two approaches are considered: (1) an instrument substitution method, which generalizes the Anderson–Rubin procedure, and (2) a sample‐split method, that allows the use of “generated regressors.” Projection techniques are also proposed for inference on general parameter transformations. The asymptotic theory of the tests under weaker assumptions is discussed. Simulation results are presented. The suggested techniques are applied to a model of Tobin's q and to a model of academic performance.     

The effects of alternative fiscal policies on the intertemporal government budget constraint

This article presents the effects of alternative fiscal policies on the intertemporal government budget constraint when the time horizon of the policy maker varies. I show that the wealth effect associated with cuts in the skill-adjusted labor income tax rate improves the intertemporal budget balance, whereas the intertemporal substitution effect associated with the physical capital income tax rate deteriorates the intertemporal budget. Under plausible parameter values, the tax rate on skill-adjusted labor income cannot by itself balance the intertemporal budget at all horizons.     

Intertemporal nonseparability,liquidity constraints,and seasonality of aggregate consumer expenditures: An empirical investigation

The paper proposes a simple framework for intertemporal nonseparability in consumer preferences. It relies on the distinction between consumption and expenditures. As only the latter are observable, a technology is postulated which gives current consumption as a weighted sum of current and past expenditures. The Euler equations of the modified maximization problem place restrictions on the autoregressive process of consumption and the real interest rate. Superimposing this model with an explicit seasonal model, results in a bivariate ARMA representation. Having investigated the issue of identification, the model is tested empirically by time series data on Austria. The main results of this investigation are. First, nonseparability is indeed an important element in characterizing aggregate expenditure behaviour. Current behaviour of households is therefore not exclusively forward looking but is committed by past expenditures. Second, this nonseparability is not due to habit formation but to a strong “durable component”. Third, Hall's orthogonality test presents no evidence for the presence of liquidity constrained households. Fourth, the misleading role of seasonal adjustment is documented. This raises serious doubts on the “excess sensitivity” and “smoothness” results which have been obtained with seasonally adjusted data.     

Robust tests for time-invariant individual heterogeneity versus dynamic state dependence

We derive tests for persistent effects in a general linear dynamic panel data context. Two sources of persistent behavior are considered: time-invariant unobserved factors (captured by an individual random effect) and dynamic persistence or “state dependence” (captured by autoregressive behavior). We will use a maximum likelihood framework to derive a family of tests that help researchers learn whether persistence is due to individual heterogeneity, dynamic effect, or both. The proposed tests have power only in the direction they are designed to perform, that is, they are locally robust to the presence of alternative sources of persistence, and consequently, are able to identify which source of persistence is active. A Monte Carlo experiment is implemented to explore the finite sample performance of the proposed procedures. The tests are applied to a panel data series of real GDP growth for the period 1960–2005.     

Prices or Quantities Can Dominate Banking and Borrowing*

The possibility of intertemporal banking and borrowing of tradable permits is often viewed as tilting the various policy debates about optimal pollution control instruments towards favoring such time-flexible quantities. This paper shows that this view can be misleading, at least for the simplest dynamic extension of the original “prices versus quantities” information structure. The model of this paper allows firms to know and act upon the realization of uncertain future costs two full periods ahead of the regulators. For any given circumstance, the paper shows that either a fixed price or a fixed quantity is superior in expected welfare to time-flexible banking and borrowing. Furthermore, the standard original formula for the comparative advantage of prices over quantities contains sufficient information to completely characterize the regulatory role of intertemporal banking and borrowing. The logic and implications of these results are analyzed and discussed.     

Endogenous skill heterogeneity and inflation

This paper examines the implications of ex ante skill heterogeneity for long run inflation. We develop a dynamic general equilibrium model in which there are two types of labor (skilled and unskilled), two types of capital (human and physical), and money is introduced via a cash in advance constraint on consumption purchases. Skill heterogeneity is characterized in terms of (i) a parameter governing the ease with which the two types of labor can be substituted for each other in production; and (ii) the “productivity” of human capital in the production of skill. The model includes the accumulation of human capital which in turn creates skill heterogeneity among workers through an efficiency wage mechanism. Numerical experiments indicate that there is a range of parameter estimates in which the Friedman Rule may not be optimal. Furthermore, our quantitative experiments also indicate that there is a range of parameter values in which a greater degree of skill heterogeneity may be associated with a greater preference for inflation. Empirically, we also find that the inflation and heterogeneity correlation is positive.     

Fiscal adjustment and labor market dynamics in an open economy

This paper studies the labor market effects of fiscal adjustment in a two-sector, three-good intertemporal framework. Key features of the model are an informal sector, minimum wages, unionized labor in the formal economy, imperfect labor mobility, and public production of intermediate inputs. “Luxury” and wait unemployment prevail in equilibrium. It is shown that if unions care sufficiently about employment, and if the degree of openness is high, an increase in the price of government services may reduce unemployment in the steady state. A similar result would hold in an efficiency-wage setting if the “disciplinary effect” of unemployment is sufficiently strong.     

Optimal stationary consumption with stochastic production and resources

Uncertainty about technology and resources is represented in terms of uncertainty about an (exogenous) environment whose successive states form a stationary stochastic process, with probabilities that are unaffected by economic decisions. The successive states of the economy depend both on the environment and on the decisions taken with regard to production and consumption. It is shown that, under conditions that are natural extensions of “neoclassical” conditions in the case of certainty, (1) Capital saturation is possible, i.e., an optimal stationary stochastic program exists, and (2) An optimal program can be sustained by a price system that takes the form of a stationary stochastic process of price vectors. In other words, an optimal stationary program can be sustained by a stochastic “equilibrium,” in which at each date the optimal production decisions maximize expected intertemporal profit, and the optimal aggregate consumption vector has minimum cost among all aggregate consumption vectors yielding no less (social) utility.