Period Utility Function Research Articles

Macroeconomic stability under balanced‐budget rules and no‐income‐effect preferences

AbstractIt has been shown that under an additively separable preference formulation between consumption and hours worked, indeterminacy and sunspots may arise in a standard one‐sector or two‐sector real business cycle model when the labor tax rate is endogenously determined by a balanced‐budget rule with a pre‐specified constant level of government expenditures. Our analysis finds that this indeterminacy result will completely disappear within either setting if the period utility function is postulated to exhibit no income effect on the householdʼs demand for leisure. In particular, the modelʼs low‐tax steady state displays saddle‐path stability and equilibrium uniqueness; whereas the high‐tax steady state is either a source or a saddle point.

Maximal Distance Discounted and Weighted Revisit Period: A Utility Approach to Persistent Unmanned Surveillance

Autonomous unmanned vehicles are well suited for long-endurance, persistent intelligence, surveillance and reconnaissance (PISR) missions. In order to conduct missions, vehicles must implement a method of task selection. We propose the Maximal Distance Discounted & Weighted Revisit Period ([Formula: see text]) utility function as a solution. We derive [Formula: see text] as a zeroth-order approximation to an infinite horizon solution of PISR when formulated as a dynamic programming (DP) problem. We then use the DP solution to develop a heuristic utility function for autonomous task selections, with the goal of minimizing the prioritized revisit time to each task. Our function adapts to different task maps and task priorities, is scalable in the number of tasks, and is robust to the ad-hoc addition or removal of tasks. We demonstrate how the [Formula: see text] parameters influence vehicle behavior. We also prove that the policy results in steady-state task selections that are periodic and that such periodicity occurs regardless of initial conditions. We then demonstrate periodicity via numerical simulations on a set of test scenarios. We present a two-step heuristic methodology for selecting utility function parameters that deliver empirically good performance, which we demonstrate through a simulation-based comparison to a single-vehicle Traveling Salesman Problem (TSP) solution. The comparisons are based on four sample task maps designed to resemble operational scenarios.

Dynamic Quantile Preferences

This paper axiomatizes static and dynamic quantile preferences. Static quantile preferences specify that a prospect should be preferred if it has a higher $$\tau $$ -quantile, for some $$\tau \in (0,1)$$ , while its dynamic counterpart extends this to take into account a sequence of decisions and information disclosure. An important motivation for the axiomatization that leads to this preference is the separation of tastes and beliefs. We first axiomatize quantile preferences for the static case with finite state space and then extend the axioms to the dynamic context. The dynamic preferences induce an additively separable quantile model with standard discounting, that is, the recursive equation is characterized by the sum of the current period utility function and the discounted value of the certainty equivalent, which is a quantile function. These preferences are time consistent and have a simple quantile recursive representation, which gives the model the analytical tractability needed in several fields in financial and economic applications. Finally, we study the notion of risk attitude in both the static and recursive quantile models. In quantile models, the risk attitude is completely captured by the quantile $$\tau $$ , a single-dimensional parameter. This is simpler than in expected utility models, where in general the risk attitude is determined by a function.

A class of tractable incomplete-market models for studying asset returns and risk exposure

We present a class of tractable incomplete-market models, where agents face both aggregate risk and limited participation in financial markets. Tractability relies on the assumptions of small asset volumes and of a period utility function that is linear beyond a threshold, in line with Fishburn’s (1977) contribution in decision theory. We prove the existence of an equilibrium and derive theoretical results regarding asset prices and consumption choices. This small-trade model is able to reproduce a low safe return and a high equity premium, together with a realistic representation of household exposure to both idiosyncratic and aggregate risks.

Land-price dynamics and macroeconomic fluctuations with nonseparable preferences

In this paper, we introduce a complementary relationship between consumption and labor hours by revising the household’s period utility function in Liu et al. (2013). The revision concomitantly allows for a finite Frisch elasticity of labor supply and a stronger consumption smoothing motive. We find that, in general, the estimation of Liu et al. (2013) is quite robust. In addition, the propagation mechanism of the credit constraint triggered by a housing demand shock still persists. However, the amplification effect of the credit constraint triggered by the housing demand shock on key macroeconomic variables is greatly muted. We also find that, except for land price fluctuations, the housing demand shock cannot act as the primary force to drive the fluctuations in other macroeconomic variables.

The Impact of Biases in Survival Beliefs on Savings Behavior

We construct and solve a dynamically inconsistent Choquet expected utility life-cycle model for naive and sophisticated agents, respectively. Pollak (1968) shows that the realized saving behavior of naive and sophisticated agents be- comes identical for a logarithmic period-utility function. As a generalization of Pollak's analysis, we compare the saving behavior of both types of agents for the family of isoelastic utility functions. We show that a sophisticated agent saves more in every period than her naive counterpart if and only if her period- utility function is more concave than the logarithmic function. This relationship holds for arbitrary survival beliefs and time-discount factors. Quantitatively, the difference in saving behavior across the two types can be large.

Interacting mechanisms of time inconsistency

We interact two prominent behavioral mechanisms of time inconsistency that have been used to study inadequate saving: hyperbolic discounting and short-term planning. Hyperbolic discounting is a conventional way to model impulsive decision making, and short planning horizons have been used to represent myopia. One might expect that interacting both mechanisms within the same model would compound the inadequacy of saving. However, our key finding takes the form of a paradox: hyperbolic discounting does not affect consumption and saving allocations if the planning horizon is short and fixed, although it will affect allocations if the planning horizon is equal to the remaining life span. We demonstrate analytically that this finding is robust to the shape of the disposable income path, to the coarseness of the time grid, and to alternative forms of the period utility function.

A leisurely reading of the life-cycle consumption data

A puzzle in consumption theory is the observation of a hump in age–consumption profiles. This paper studies a general equilibrium life-cycle economy with capital in which households include both consumption and leisure in their period utility function. A calibrated version of the model shows that a significant hump in life-cycle consumption is a feature of the equilibrium. Thus inclusion of leisure in household preferences may provide part of the explanation of observed life-cycle consumption humps.

A Leisurely Reading of the Life Cycle Consumption Data

A puzzle in consumption theory is the observation of a hump in age-consumption profiles. This paper studies a general equilibrium life-cycle economy with capital in which households include both consumption and leisure in their period utility function. A calibrated version of the model shows that a significant hump in life-cycle consumption is a feature of the equilibrium. Thus inclusion of leisure in household preferences may provide part of the explanation of observed lifecycle consumption humps.

A Leisurely Reading of the Life Cycle Consumption Data

A puzzle in consumption theory is the observation of a hump in age-consumption profiles. We study a general equilibrium life-cycle economy with capital in which households include both consumption and leisure in their period utility function. We calibrate the model and find that a significant hump in life-cycle consumption is a feature of the equilibrium. Thus inclusion of leisure in household preferences may provide part of the explanation of observed life-cycle consumption humps.

Existence of Equilibrium for Segmented Markets Models with Interest Rate Monetary Policies

Several studies have recently adopted the segmented markets model as a framework for monetary analysis. The characteristic assumption is that some households never participate in financial markets. This paper proves the existence of an equilibrium for segmented markets models where monetary policy is defined in terms of the short-term nominal interest rate. The model allows us to consider the important cases where monetary policy affects output, and responds to any sources of uncertainty, including output itself. The assumptions required for existence constrain the maximum value and the variability of the nominal interest rate. The period utility function is logarithmic. The proof is constructive, and shows how the model can be solved numerically. A similar proof can be used in the case that monetary policy is defined in terms of the bond supply.

Government size and macroeconomic stability: A comment

We show that in a standard, technology shock-driven one-sector real business cycle model, the stabilization effects of government fiscal policy depend crucially on how labor hours enter the household's period utility function and the associated labor-market behavior. In particular, as Galí [European Economic Review 38 (1994), 117–132] has shown, when the household utility is logarithmic in both consumption and leisure, income taxes are destabilizing and government purchases are stabilizing. However, the results are reversed when preferences are instead convex in hours worked. That is, income taxes are now stabilizing and public spending is destabilizing. Furthermore, under both preference specifications, the magnitude of cyclical fluctuations in output remains unchanged when the income tax rate and the share of government purchases in GDP are equal (including laissez-faire).

Consumption, Durable Goods, and Transaction Costs

We study consumption of durable and nondurable goods when the durable good is subject to transaction costs. In the model, agents derive utility from a service flow of a durable good and a consumption flow of a nondurable good. The key feature of the model is the existence of a fixed transaction cost in the durable good market. The fixed cost induces an inaction region in the purchase of the durable good. More importantly, the inability to adjust the durable stock induces variation in consumption of the nondurable good over the inaction region. The variation is a function of the degree of complementarity between durable and nondurable goods in the period utility function, the rate of intertemporal substitution, and a precautionary motive induced by incomplete markets. We test the model using the PSID. Housing serves as the durable good. The data indicate an increase in consumption before moving to a smaller house and a decrease in consumption before moving to a larger house. This result is consistent with the model when there exists complementarity between the durable and nondurable good or when there is a strong precautionary effect.

Consumption, Durable Goods, and Transaction Costs

We study consumption of durable and nondurable goods when the durable good is subject to transaction costs. In the model, agents derive utility from a service flow of a durable good and a consumption flow of a nondurable good. The key feature of the model is the existence of a fixed transaction cost in the durable good market. The fixed cost induces an inaction region in the purchase of the durable good. More importantly, the inability to adjust the durable stock induces variation in consumption of the nondurable good over the inaction region. The variation is a function of the degree of complementarity between durable and nondurable goods in the period utility function, the rate of intertemporal substitution, and a precautionary motive induced by incomplete markets. We test the model using the PSID. Housing serves as the durable good. The data indicate an increase in consumption before moving to a smaller house and a decrease in consumption before moving to a larger house. This result is consistent with the model when there exists complementarity between the durable and nondurable good or when there is a strong precautionary effect.

Adjustment Costs and Nominal Rigidities in a Small Open Economy / Anpassungskosten und nominelle Rigiditäten in einer kleinen offenen Volkswirtschaft

Summary What does account for the persistence of monetary shocks in dynamic general equilibrium models of the business cycle? A number of papers have dealt with that question and point at labor market frictions besides those introduced by overlapping wage contracts. In this paper I investigate an obvious source of persistence, namely small adjustment costs of labor at the firm level. These introduce indeed hump shaped impulse responses of hours worked in simulated time series. Compared with a benchmark model without nominal and real frictions my model outperforms the former in most respects. However, its account of the time series properties of monetary variables is not satisfactory. This holds true for closely related models that change the current period utility function, that introduce money into the utility function, or that posit a cash in advance constraint. I take this as suggestive to think about more sophisticated models of money demand.

CONSUMPTION SPENDING AND THE PAPER‐BILL SPREAD: THEORY AND EVIDENCE

This paper explains recent findings that the paper‐bill spread helps forecast consumption spending using an intertemporal optimizing model of consumption and portfolio allocation. The spread is simply the opportunity cost in terms of foregone future consumption of holding government debt rather than higher yielding private debt. Thus, if government debt appears along with consumption in the single period utility function, the spread appears in one of the Euler equations for consumption and asset accumulation. Empirical tests strongly support the model. Finally, including the spread in a rule of thumb model of consumption reduces the importance of non‐optimizing behavior. (JEL E21, E43, C22, C32)

Crazy Explanations of International Business Cycles

International real business cycle models have been unable to provide a good explanation for the consumption-output anomaly: in theoretical economies, consumption is more strongly correlated across countries than is output, whereas the opposite is the case in the data. This paper examines an increasing returns-to-scale model in which the economy is subject to 'belief' shocks that affect the consumption Euler equations rather than productivity. Under the assumption that there are no contingent claim markets on the realizations of 'sunspots,' the belief-driven model can account for the consumption-output anomaly even with a separable period utility function. Copyright 1998 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Evaluating risky consumption paths: The role of intertemporal substitutability

In dynamic stochastic welfare comparisons, a failure clearly to distinguish between risk aversion and intertemporal substitutability can result in misleading assessments of the impact of risk aversion on the welfare costs of consumption-risk changes. The problem arises in any setting in which uncertainty is propagated over time, notably, but not exclusively, in economies with stochastic consumption trends. Regardless of the preference setup adopted, an increase in risk aversion amplifies the per-period costs of risks. The weights consumers use to cumulate the per-period costs of risks with persistent effects should, however, depend on intertemporal substitutability as well as on risk aversion. Under time-separable expected-utility preferences, an increase in the period utility function's curvature therefore alters the welfare effect of risk for reasons that are in part unrelated to risk aversion. To illustrate these points I reconsider Lucas's estimate of the ‘cost of consumption instability’ for the postwar United States.

On The Robustness of Forward Market Efficiency in Consumption-Based Models of Exchange Rates

Euler equation models with consumption risk premia have shown promise of reconciling exchange rate data with the hypothesis of efficiency of the forward exchange rate. We examine the robustness of these models to variation in (1) the period utility function, (2) assumptions about the underlying forward trading mechanism, (3) the measure of consumption in the risk premium and (4) the weighting matrix applied to the model orthogonality conditions. In generalized method of moments estimations using a six-currency sample we find evidence that forward efficiency is robust to perturbations of the first two kinds, but not to the latter two. [F31, G14]

Infinite Horizon Investment—Consumption Policies

We consider an infinite horizon investment-consumption problem in which the objective is to mmimize the discounted sum of the one period utilities. The one period utility function is assumed to be concave but may be unbounded. Both the state and action spaces are uncountable. If the average growth rate of assets is less than the reciprocal of the discount rate and if a weak regularity condition is satisfied an optimal stationary policy is shown to exist. Also the optimal return function satisfies the functional equation of dynamic programming and inherits several properties of the one period utility function.