Computation of non-linear continuous optimal growth models: experiments with optimal control algorithms and computer programs

In this paper we discuss the use of optimal control methods for computing non-linear continuous optimal growth models. We have discussed various recently developed algorithms for computing optimal control, involving step-function approximations, Runge–Kutta solutions of differential equations, and we suggest that the discretization approach is preferable to methods which solve first-order optimality conditions. We have surveyed some powerful computer programs by : , and for computing such models numerically. These programs have no substantial optimal growth modelling applications yet, although they have numerous engineering and scientific applications. A computer program named by is developed in this study. Results are reported for computing the Kendrick–Taylor optimal growth model using and programs based on the discretization approach. References are made to the computational experiments with and . The results are used to compare and evaluate mathematical and economic properties, and computing criteria. While several computer packages are available for optimal control problems, they are not always suitable for particular classes of control problems, including some economic growth models. The -based and , however, offer good opportunities for computing continuous optimal growth models. It is argued in this paper, that optimal growth modellers may find that these recently developed algorithms and computer programs are relatively preferable for a large variety of optimal growth modelling studies.     

Country of Origin Labeling (C.O.O.L.): How cool is it?

This paper develops a partial-equilibrium model of a small open-economy trading an unsafe product. The model is used to analyze the welfare effects of trade with and without a country-of-origin labeling (COOL) program. The welfare gains from trade in the absence of COOL are ambiguous, may justify the imposition of a trade ban. Even if a full ban does not improve welfare and some restriction of trade is always welfare-enhancing. Under a tariff regime, more COOL trade is better than less trade. Independently of domestic market power, free trade coupled with a COOL program maximizes national welfare.     

The continuous treatment effect of an antipoverty program on children's educational attainment: Colombia's Familias en Accion

Educational attainment is an important element in the formation of human capital. Although many developing countries have made strong efforts to expand the coverage of education services, children in poor households still struggle to attend school on a regular basis. Human development conditional cash transfers (known as CCT s) have emerged in response to this situation in developing countries. While the effects of the CCT s are well known and widely documented, their effects in relation to educational attainment and school participation are still unclear. This paper looks empirically into the continuous treatment effects of participation length in Familias en Accion , a CCT program in Colombia. The paper focuses on the continuous treatment effects on school registration and educational attainment of participants in the program. Although initial results show a fuzzy relationship between the program outcomes and the participation length, the empirical results confirm the fact that a longer exposure to the antipoverty program led to higher school registration rates, accumulation of years of education, and lower child labor participation levels.     

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1 Institute of Engineering Safety and Disaster Prevention, Hohai University, Nanjing, China 2 College of Civil and Transportation Engineering, Hohai University, Nanjing, China     

Estimating the long-term effects of utility energy conservation programs: A Pacific Northwest example

The Bonneville Power Administration operated a Residential Weatherization Pilot Program from 1980 through 1982. The program provided free home energy audits to 7200 electrically heated homes in the Pacific Northwest and gave zero-interest loans to weatherize 4100 of these homes. The total cost of the program was almost $11 million.The pilot program and its regionwide successor are intended to provide benefits to the Pacific Northwest region for roughly 30 years in terms of reduced residential energy consumption. Therefore, it is important to determine the durability of the electricity savings due to the program. Estimates of long-term savings affect power supply planning in the region and influence the economics of the program itself (i.e., the level of funding that BPA can justify for the program).This article presents empirical results concerning the total and net energy-saving affects of the BPA pilot program 1, 2, and 3 years after participation. The total annual electricity saving experienced by households that received an energy audit and a weatherization loan averaged 5300 kWh 1 year after participation, increasing to 6000 and 6500 kWh 2 and 3 years after participation, respectively. The net annual electricity saving that can be directly attributed to the program for these audit plus loan households averaged 4500 kWh (15% of preprogram use) 1 year after participation and declined slightly to about 4300 kWh 2 years and 4200 kWh 3 years after participation.The article uses these empirical findings with a simple simulation model to estimate the effects of the program into the future. Assuming that electricity prices remain constant after 1984, total energy savings increase to a level of 7000 kWh, while net energy savings decrease to 3600 kWh for the audit plus loan households. Alternative electricity price scenarios are discussed.     

A NOTE ON “A ONE‐SECTOR NEOCLASSICAL GROWTH MODEL WITH ENDOGENOUS RETIREMENT”: EXISTENCE OF MULTIPLE STEADY STATES*

This note extends Matsuyama's 0–1 endogenous retirement choice model to the framework with continuous endogenous retirement choice to study the consumption‐saving decision and capital accumulation in an overlapping generation model. The conditions for the existence of multiple steady states have been derived. In contrast to the 0 or 1 labour choice, the partial retirement may be a stable steady state under the continuous endogenous retirement choice in the second period. And this implies that partial retirement may be a stable optimal choice. Also, we find that the retirement choice depends on the initial capital stock when there are multiple steady states.     

A quantitative model for the evaluation of technological alternatives

This paper presents a quantitative model that may be of use to the national development planners, investment funding authorities, and entrepreneurs, who are confronted with the problems of choosing the appropriate technology among many available alternatives. The model provides a systematic and analyst-independent methodology for the multicriterion technology selection process, which requires consideration of socioeconomic as well as technological factors. The procedure is mathematically straightforward and has the capability of integrating both objective and subjective aspects of the evaluation process, resulting in a unified technology measure as a guide for decision making. A case study is presented to illustrate the applicability and workability of the development model.     

领导力发展项目的设计与实施

本文依据对美国一流组织经验的分析,总结得出领导力发展项目设计与实施基本原则、一般程序。基本原则包括:全面关照领导力在个人层次、关系层次和集体情境层次上的协调发展,使项目成为一个动态的、持续的过程,使项目具有针对性。而成功的项目设计与实施一般都包括组织诊断、项目参加者选择、领导力发展需求测评、项目设计、项目实施、后续支持和总体评价几个阶段;各阶段的具体经验也在文中进行了分析。     

The discrete time version of the Romer model

Summary. This paper presents a discrete time version of the Romer 1986 model of endogenous growth. The purpose of this work is to propose detailed and simple proofs of existence of optimal solutions and of a competitive equilibrium. The framework implemented here reduces the complexity of the proofs given by Romer (1983) in his Ph.D dissertation in a continuous time framework. Received: March 7, 2000; revised version: April 25, 2001     

Time-varying pricing may increase total electricity consumption: Evidence from Costa Rica

We study the implementation of a time-varying pricing (TVP) program by a major electricity utility in Costa Rica. Because of particular features of the data, we use recently developed understanding of the two-way fixed effects differences-in-differences estimator along with event-study specifications to interpret our results. Similar to previous research, we find that the program reduces consumption during peak-hours. However, in contrast with previous research, we find that the program increases total consumption. With a stylized economic model, we show how these seemingly conflicted results may not be at odds. The key element of the model is that previous research used data from rich countries, in which the use of heating and cooling devices drives electricity consumption, but we use data from a tropical middle-income country, where very few households have heating or cooling devices. Since there is not much room for technological changes (which might reduce consumption at all times), behavioral changes to reduce consumption during peak hours are not enough to offset the increased consumption during off-peak hours (when electricity is cheaper). Our results serve as a cautionary piece of evidence for policy makers interested in reducing consumption during peak hours—the goal can potentially be achieved with TVP, but the cost is increased total consumption     

ASSET‐BASED UNEMPLOYMENT INSURANCE*

This article studies a model of consumption, savings, and job search in which a borrowing constraint limits self‐insurance. The government administers the unemployment insurance program that may condition on an individual’s asset position, but not on her efforts of finding a job. To compensate for the impediments to self‐insurance, benefit payments should optimally be set higher at lower wealth levels and peak for borrowing‐constrained individuals with zero liquid funds. A quantitative exercise reveals that the U.S. unemployment insurance program is surprisingly close to optimal for the asset poor, but far too generous for wealthier individuals.     

AN ANALYSIS OF DURATION ON THE DISABILITY SUPPORT PENSION PROGRAM*

The paper examines the factors that determine the duration on the Disability Support Pension (DSP) program using administrative data. We estimate two models based on two competing assumptions: the first model takes the standard assumption in duration models that all recipients will eventually leave the program. The second one takes into account the possibility that there may be some recipients who will never recover from their disabilities and hence not leave the program. Both models indicate that female recipients, recipients who enter DSP at a very young or very old age, recipients with a partner on income support, and recipients who transfer from unemployment benefits have the potential of a longer DSP duration.     

The determinacy of equilibrium in economies of overlapping generations

We study the problem of uniqueness of equilibrium paths in the overlapping generations model. We show that, despite local calculation based on counting equations and unknowns, the equilibrium path may be unique. We do this by constucting an example of an economy of overlapping generations with just one equilibrium up to time shift, beside the steady states. Time is either discrete or continuous; in either case, it extend into the infinite future and, possibly, the infinite past. There is one, non-storable commodity at each date. The economy is stationary; intertemporal preferences are logarithmic; the endowments and discount factors of individuals need not depend continuously on time. With continuous time, equilibrium paths of prices are smooth; this, even for endowments and discount factors of individuals that do not depend continuously on time. With discrete time, as the number of periods in the life-span of individuals increases, equilibrium paths converge to the continuous time solutions. If time extends infinitely into the infinite past as well as into the infinite future, in continuous time, all non-stationary equilibrium paths of prices are time-shifts of a single path; in addition, there are two stationary solutions; in discrete time, there is a one dimensional family of non-stationary solutions, up to time-shift; however, the indeterminacy vanishes as the number of periods in the life span of individuals tends to infinity. If, alternatively, time has a finite starting point, in discrete time the degree of indeterminacy increases with the life-span of individuals, and, in continuous time, it is infinite; however, these are families of exponentially decreasing oscillations which, although they may exhibit pseudo-chaotic behaviour for a while, as time tends to infinity they all get damped, and asymptotic behaviour is that of the economy that originates in the infinite past. Stefano Lovo made interesting comments.     

退耕还林:私人承包与政府规制

本文在一种委托—代理框架下研究了退耕还林工程在实施过程中所面临的激励不相容问题。文章首先探讨了退耕还林私人承包的社会理性。然后 ,文章给出了一个双重任务委托—代理模型 ,解释市场冲击如何会使农户的自利性经营行为偏离社会生态目标。接着 ,文章以陕西省退耕还林现状为研究背景对退耕还林工程实施中的激励不相容问题做出了进一步的经验分析。最后 ,文章从政府规制的角度提出了若干公共政策建议 ,以期提高退耕还林工程的实施效率。     

Latent Consideration Sets and Continuous Demand Systems

This paper develops a theoretically consistent continuous demand system model that incorporates latent, probabilistic consideration sets. In contrast to existing discrete choice consideration models, the proposed model is econometrically tractable with consumption data for many goods. The model’s empirical properties are illustrated with an 89-site recreation data set from the 1994 National Survey of Recreation and the Environment (NSRE). Parameter and welfare estimates suggest that the latent consideration set models fit the data better and may imply a bias-variance tradeoff relative to traditional models.      

On perfect equilibria in stochastic models of growth with intergenerational altruism

Summary. The well-known model of altruistic growth/strategic bequest is studied. A stochastic transition function is considered and fairly general sufficient conditions for the existence of Markov-stationary subgame-perfect equilibrium are given. Also some special cases in which the equilibrium policy is continuous and nondecreasing are discussed.Received: 20 September 2003, Revised: 11 December 2004, JEL Classification Numbers: C73, D91, O40.Research was partially supported by KBN grant 5 PO3A 01420.     

Residential Mobility and the Housing Market in a Two-sector Neoclassical Growth Model

The impact of residential mobility and competitive housing markets on long run growth is examined using a two-sector general equilibrium overlapping-generations model in continuous time. There is an infinity of agents with finite lives who adjust their housing consumption by moving, which is costly. We explore the model's steady-state properties, first with a free housing market, then under rent control when the market clears through restrictions on the frequency of moves. Rent controls do not just reduce welfare; they may increase the steady-state capital-labor ratio.     

The economics of TV tune-in

TV tune-in, namely the preview of forthcoming programs, is an important type of TV advertising. We examine TV tune-in as a continuous variable. First, tune-in can increase profits when TV stations are sufficiently differentiated and the market is partially covered. Second, tune-in crowds out program quality. Third, tune-in lowers advertisement supply. Further, tune-in can increase profits in a partially covered market if firms are sufficiently differentiated. Otherwise, it leads to low profits. We also identify the effects of tune-in on consumer surplus and social welfare and suggest that tune-in should be prohibited whenever it lowers program quality and social welfare.     

On model ambiguity and money neutrality

We solve for the equilibrium of a stochastic neo-classical continuous time model without and with money under model ambiguity. We show that: (i) the correction for ambiguity stemming from the money supply is nil at equilibrium; (ii) money is neutral with respect to the stock market equilibrium (the equity risk premium); (iii) money is not neutral with respect to consumption and capital accumulation, and its effect may be quantitatively substantial; (iv) the preference for model robustness affects all the real economic variables as well as the expected inflation rate and the nominal interest rate.