Intertemporal Allocation Research Articles

Theory of Stochastic Optimal Economic Growth

Stochastic optimal growth involves the study of the optimal intertemporal allocation of capital and consumption in an economy where production is subject to random disturbances. The theory traces its roots to the seminal work on deterministic optimal growth by Ramsey [106], Cass [21] and Koopmans [55]. Its influence has been enhanced by research that shows how the convex stochastic growth model can be decentralized to represent the behavior of consumers and firms in a dynamic competitive equilibrium of a productive economy ([102], [115], [15]). This makes the stochastic optimal growth model useful both as a normative exercise and in the development of positive theories of how the economy works. As a consequence, the theory has emerged as one of the central paradigms of dynamic economics. It is based on a simple, yet powerful model that encompasses fundamental questions that are basic to any theory of dynamic economic behavior: What are the characteristics and determinants of optimal policies? What are the economic incentives that govern the optimal intertemporal allocation of resources? What is the transient and long run behavior of variables in the model? Under different assumptions the model admits a rich set of answers to these questions. Historically, the main focal point of the theory has been issues of aggregate economic growth. At the same time its primary variable, capital, has a flexible interpretation that allows the model and its extensions to represent a wide variety of economic problems ranging from the study of business cycles ([59], [63]) and asset pricing ([14], [15]) to the allocation of renewable natural resources ([77], [82], [83]). Equally important, the model provides a strong theoretical foundation for applied analysis of these problems. The model can be solved numerically and has proved a testing ground for many numerical techniques used today in the analysis of dynamic economic problems. This chapter provides an overview of key results the theory of discounted stochastic optimal growth in discrete time.1 The paper begins with an analysis of

CAPITAL GAINS: BLUE MACHINES AND RED MACHINES

Capital gains play an essential role in the intertemporal allocation of resources, but they can also fuel self-fulfilling bubbles. The simple case of 2 "identical" capitals is analyzed in an overlapping generations model. The only trajectory in which expectations are realized at every date is the one in which blue machines and red machines have the same price. If ever their prices differ, then there is a "bubble" which must burst in finite time.

Growth in economies with non convexities: sunspots and lottery equilibria

We investigate the relation between lotteries and sunspot allocations in a dynamic economy where the utility functions are not concave. In an intertemporal competitive economy, the household consumption set is identified with the set of lotteries, while in the intertemporal sunspot economy it is the set of measurable allocations in the given probability space of sunspots. Sunspot intertemporal equilibria whenever they exist are efficient, independently of the sunspot space specification. If feasibility is, at each point in time, a restriction over the average value of the lotteries, competitive equilibrium prices are linear in basic commodities and intertemporal sunspot and competitive equilibria are equivalent. Two models have this feature: Large economies and economies with semi-linear technologies. We provide examples showing that in general, intertemporal competitive equilibrium prices are non-linear in basic commodities and, hence, intertemporal sunspot equilibria do not exist. The competitive static equilibrium allocations are stationary, intertemporal equilibrium allocations, but the static sunspot equilibria need not to be stationary, intertemporal sunspot equilibria. We construct examples of non-convex economies with indeterminate and Pareto ranked static sunspot equilibrium allocations associated to distinct specifications of the sunspot probability space.

EXPANSIONARY FISCAL CONTRACTION: GOVERNMENT SPENDING FINANCED BY LUMP-SUM TAXES

Barry and Devereux (2003) have identified two conditions for permanent fiscal contractions to be expansionary. The first condition is that households do not face an effective infinite horizon. The second is that the wealth effect of reduced tax liabilities on labor supply must be small if labor supply is endogenous. However, Barry and Devereux have not allowed for the possibility that government spending may affect the intertemporal allocation of private consumption. By allowing for the possibility, this paper identifies a third condition for permanent fiscal contractions to be expansionary, namely that public and private consumption must not be too highly substitutable.

Optimal human investment allocation

In the present treatment, we study the optimal intertemporal allocation of human investment by verifying the equivalence between the command optimum and the decentralised competitive equilibrium.

Government Transfers and the Samaritan's Dilemma in the Family

This paper examines the effectiveness of government transfersin overcoming the Samaritan's dilemma in a family in which thechild saves an insufficient amount in order to induce largerbequests from the parent. The results are as follows. First,exogenous government transfers do not affect intergenerationalconsumption allocation if bequests are operative. Second,assuming that government transfers are chosen strategically,the government precommits to such a level of transfers fromthe parent to the child that bequests become inoperative, andthus rids the child of the incentive for undersaving. Thisengenders an efficient intertemporal allocation ofconsumption.

A dynamic model for intertemporal allocation of old-growth forests in the Pacific Northwest

Across the globe, continued policy debates regarding the management of old-growth forests center around the difficult task of balancing economic and ecological considerations. Though the forests of the Pacific Northwest United States are among the most studied old-growth ecosystems, ecological and economic analyses have yielded public land management directives that remain controversial. Specifically, the recently adopted Northwest Forest Plan lacks explicit goals for maintaining intergenerational equity for the use of forest resources and the diversity of old-growth ecosystems. Unlike previous studies which rely on monetary quantification of costs and benefits, this study develops and applies a conceptual framework for evaluating socially optimal Pacific Northwest old-growth forest utilization strategies. Conditions for the optimal management of old-growth forests are derived using dynamic programming. The objective function synthesizes relevant biological and economic attributes of the old-growth allocation problem. Results in the form of extraction paths are compared given social pressure for consumptive and non-consumptive benefits, as well as different planning horizons, rates of social time preference, and environmental variance. Lengthening the planning horizon results in a vast divergence of optimal policies in the absence of discounting. Extraction rates appear to approach zero as the planning horizon approaches infinity. While higher rates of social time preference increase the rate of extraction, forest stocks remaining at the terminal time period equal levels remaining with a lower discount rate. Increasing environmental variance results in a higher level of stock remaining at the terminal time period. This analysis, while specific to the old-growth controversy of the Pacific Northwest, does provide general guidelines for addressing similar problems of multiple uses of natural areas, particularly where such uses are mutually incompatible, or where one use may be irreversibly destructive to another.

When She Lives Longer: An Experimental Study of Saving Decisions by Couples

We investigate the intertemporal allocation behavior of spouses with di erent deterministic life expectations in an experiment. In each period of their life both partners propose a consumption level one of which is then randomly implemented. To allow for learning one experiences many “lives”. In spite of the complex dynamics optimal behavior is rather simple and straightforward in the sense of conditional consumption smoothing. Participants achieve a rather high degree of e ciency that does not change over time. A substantial number of participants does not care whether their partner receives any payo . This extremely selfish behavior is punished by their respective partners.

Stabilizing properties of monetary feedback rules: A representative-agent approach

Evidence from theoretical models fails to support the obvious preference that many stabilization-policy advocates have for monetary policies that feature negative feedback over those that feature positive feedback. In this paper, I employ a representative-agent model to investigate the stabilizing properties of positive- and negative-feedback monetary policy rules. I consider two alternative policy objectives—price-level stabilization and inflation-rate stabilization—along with two alternative versions of the agent's intertemporal allocation problem. None of the results supports the notion that negative-feedback policies are more likely than positive-feedback policies to be successful in stabilizing the price level or the inflation rate.

Spatially and Intertemporally Efficient Waste Management: The Costs of Interstate Trade Restrictions

We examine the intertemporal allocation of the solid waste of cities within the United States to spatially distributed landfills and incinerators, taking into account that capacity at existing and potential landfills is scarce. Amendments have been proposed to restrict waste flows between states by means of quotas and surcharges. We assess the aggregate surplus loss (and its regional distribution) resulting from proposed policies. In addition, we find that limitations on the size of shipments to any one state can have the perverse effect of substantially increasing interstate waste shipments as states export smaller volumes to more destinations.

The Effect of Credit on Spending Decisions: The Role of the Credit Limit and Credibility

The objective of the present research is to study consumer decisions to utilize a line of credit. The life-cycle hypothesis from economics argues that consumers should intertemporally reallocate their incomes over their life stream to maximize lifetime utility. One form of intertemporal allocation is to use past income (in the form of savings) in the future. A second form is the use of future income in the present. This can only be done if consumers have access to a temporary pool of money that they can draw from and replenish in the future—a function performed by consumer credit. However, our research reinforces prior findings that consumers are unable to correctly value their future incomes, and that they lack the cognitive capability to solve the intertemporal optimization problem required by the life-cycle hypothesis. Instead, we argue that consumers use information such as the credit limit as a signal of their future earnings potential. Specifically, if consumers have access to large amounts of credit, they are likely to infer that their lifetime income will be high and hence their willingness to use credit (and their spending) will also be high. Conversely, consumers who are granted lower amounts of credit are likely to infer that their lifetime income will be low and hence their spending will be lower. However, based on research in the area of consumer skepticism and inference making, we also argue for a moderating role of the credibility associated with the credit limit. Specifically, we argue that the above effect of credit availability would be particularly strong for consumers who believe that the credit limit credibly signals their future earnings potential (i.e., a naïve consumer who has limited experience with consumer credit). However, as consumers gain experience with credit, they start discounting credit availability as a predictor of their future and start questioning the validity of the process used to set the credit limit. Hence, with experience the effect of credit limit on the willingness to use credit should be attenuated. We test these predictions in five separate studies. In the first experimental study, we manipulate credit limit and credibility and pose subjects with a hypothetical purchase opportunity. Consistent with our prediction, credit limit impacted the propensity to spend, but only when the credibility was high. In the second experimental study, we replicate these findings even when subjects were given information about their expected future salaries, and also show that the credit limit influences their expectation of future earnings potential. In the third study, we show that the mere availability (and increase) of current liquidity cannot explain our findings. In the fourth study, we conduct a survey of consumers in which we measure a number of demographic characteristics and also ask them for their propensity to spend in a given purchase situation. In the fifth study we use the Survey of Consumer Finances (SCF) dataset, a triennial survey of U.S. families that is designed to provide detailed information on the use of financial services, spending behaviors, and selected demographic characteristics. Results from both studies 4 and 5 provide further support for our proposed framework—credit limits influence spending to a greater extent for consumers with lower credibility: younger consumers and less-educated consumers. Across all studies we achieved triangulation by using a variety of approaches (surveys and experiments), subjects types (young students and older consumers), nature of predictor variables (manipulated and measured), dependent measures (purchase likelihood, credit card balance, new charges), and methods of analysis (ANOVA and regression), and consistently found that increasing credit limits on a credit card increases spending, especially when the credibility of the limit is high. This paper joins a growing body of literature in marketing and behavioral decision theory that goes beyond the traditional domains of inquiry (e.g., product choice, effects of marketing mix variables) and focuses on consumer decisions relating to the appropriate use of income to finance consumption. Our framework differs from prior research on the effect of payment mechanisms on spending in two significant ways. First, we are interested in the effects of the availability of credit on spending, and not necessarily in the effect of the transaction format that is associated with each payment mechanism. Second, while prior research has studied the point-of-purchase and historic (i.e., prepurchase) effects of credit, the present research is concerned with the availability of credit in the future. Specifically, our framework is invariant to the current and prior usage of credit by the consumer.

National Debt, Borrowing Constraints, and Human Capital Accumulation in an Endogenous Growth Model

This paper presents an overlapping-generations endogenous growth model of human capital accumulation with borrowing constrained young individuals. On a small open economy's equilibrium growth path, production, human capital, and physical capital all grow at a uniform rate that depends, apart from a vector of parameters, only on the amount of time that decentrally optimizing, borrowing constrained private households allocate to education and training. An increase in public debt that is used to redistribute tax burdens from every individual's youth to his middle age raises the equilibrium growth rate of the economy and improves the intertemporal allocation of resources.

Traditional Irrigated Agriculture in Oman

Traditional methods were developed to allow farmers to live in harmony with a harsh environment. The farming techniques employed required only limited inputs of capital and caused minimal disturbance to the environment. The patterns of production were truly sustainable and skills were passed from generation to generation. Traditional surface irrigation systems of aflaj provide more than 60 percent of the freshwater supply in the Sultanate of Oman and irrigate around 55 percent of the cropped area. Over the years, these systems have set traditions for inter-temporal water resources allocation and a process of user's rights established on ownership and/or rent basis. A management system has been generated to organize, maintain, and distribute aflaj water resources. This paper examined the sight of aflaj system in terms of physical structure, administration, and ownership. Specific actions are recommended to improve the use and distribution of aflaj water resources. These include restructuring the aflaj management, improving the operation of water trade system, improving the sustainable use of aflaj water, and specific actions to promote aflaj water sustainability.

The Response of Expenditures to Anticipated Income Changes: Panel Data Estimates

Standard models of intertemporal allocation predict that the time path of expenditures should be independent of the time path of income. Recently two papers, Parker (1999) and Souleles (1999) have suggested that U.S. households have a high marginal propensity to spend within year anticipated income changes. We use an expenditure survey panel from Spain to re-examine this issue. We exploit two important features of the Spanish data. First, we have quarterly panel data that follows households for more than four quarters. Second, we use the fact that workers are exogenously sorted into one of two payment schemes: some receive the same amount each month of the year and others receive an extra payment in June and December. The extra payment is large and predictable. We examine the detailed pattern of expenditures over the year to see whether they differ between the two groups. We fail to find even weak differences. We complement this with a conventional Euler equation analysis of excess sensitivity. Our predicting equation for (quarterly) earnings growth is much better than usual and is likely to give a powerful test of the hypothesis that predictable changes in income do not lead to changes in expenditure patterns. The results of this analysis confirm the graphical analysis: we find no evidence of excess sensitivity. We conclude that households in normal times do smooth consumption over the year. We suggest a reconciliation of our results with those of Parker and Souleles.

Dynamics of irrigation water use in Sudan Gezira scheme

Sudan's irrigated agriculture faces water shortages with the current method of water use. How can Sudan allocate its water quota stipulated in the 1959 Nile Waters Agreement? This paper examines water policy with a dynamic optimal control model to determine steady-state optimal inter-crop and inter-temporal allocation. Control of land, water, and price to ensure that cotton is grown has a negative impact on overall farm income, and water conservation. Incomes drop significantly if free market prices are adopted without the freedom to allocate land. Water shortages could develop if other schemes claim more water, irrigated area increases, and/or high water requiring crops are planted.

Optimal intergenerational redistribution in a two-country model with endogenous fertility

We analyze a model with two countries that are linked by anintegrated capital market. Fertility, and thus population growth, isendogenously determined by households. Our analysis proceeds inthree steps: First, we characterize an optimal intertemporal andinterregional allocation in a model with endogenous fertility andtwo countries. Second, we look for an institution supporting theoptimal allocation. It turns out that in general, a decentralizedequilibrium is inefficient. National public-pension systems withbenefits that are related to the number of children implements theoptimal allocation. This provides a justification for governmentinterventions beyond its role as a ``night-watchman.'' Third, weanalyze whether national governments have the right incentives toimplement the optimal system. It turns out that every nationalgovernment has an incentive to deviate from the optimal structureand to shift part of the burden to the other country. Policyimplications for the institutional arrangements within the EuropeanUnion are discussed.

Social time preference

The observed practice of discounting the future should not be rationalised on the grounds of myopia or selfishness. A positive rate of pure time preference is necessary to ensure that heterogeneous generations are treated in an egalitarian fashion. A zero social discount rate would yield intertemporal allocations which are biased against the current generations. Endogenous productivity growth requires that the social discount rate be set above the subjective rate of pure time preference. Positive social time preference, far from discriminating against future generations, is essential for a fairer intertemporal allocation of resources.

Capital income taxation, wealth distribution and borrowing constraints

The theorem of zero taxation of capital income is reexamined and is shown to hinge critically on the assumptions of a long horizon and perfect markets for the inter-temporal allocation of resources. The theorem does not hold when borrowing constraints prevent individuals from insuring against idiosyncratic shocks and have a precautionary motive for savings. Structural assumptions are made such that with no taxation, aggregate savings are socially ‘excessive’ in the long-run, i.e. the rate of return is smaller than the discount rate. Sufficient conditions for a Pareto efficient taxation or subsidization of capital in the long-run depend on the correlation between individuals’ consumption and savings. A subsidy may be efficient when individuals’ incomes follow a predictable pattern of life-cycles with no negative bequest.

Liquidity Creation through Banks and Markets: A Theoretical Perspective on Securitization

Securitization is a process that transforms some traditional non-traded banking assets into marketable securities. To evaluate this process, this paper surveys theories of the intertemporal allocation of funds through demand deposits and anonymous markets, first separately and then in an integrated model. It reviews some work on the role of market frictions and asset characteristics, and concludes that the interplay between these two is crucial in explaining the observed co-existence of demand deposits and anonymous markets. This suggests that securitization is an opportunity, rather than a threat, to banks. (J.E.L.: D50, G21)

An experimental analysis of intertemporal allocation behavior

If the future is uncertain, optimal intertemporal decisions rely on anticipating one's own optimal future behavior as is typical in dynamic programming. Our aim is to detect experimentally stylized facts about intertemporal decision making in a rich stochastic environment. Compared to previous experimental studies our experimental design is more complex since the time horizon is uncertain and termination probabilities have to be updated. In particular the decision task is non-stationary as in real life which seriously complicates the task of diagnosing behavioral regularities. In this study we give some illustrative results and provide some general perspectives. Our main result is that subjects'reaction to information about termination probablilities are qualitatively correct.