Illiquidity,transaction cost,and optimal holding period for real estate: Theory and application

Choosing the optimal holding period is an important part of real estate investment decisions, because “when to sell” affects “whether to buy”. This paper presents a theoretical model for such decision making. Our model indicates that the optimal holding period is affected by both systematic and non-systematic factors—market conditions (illiquidity and transaction cost) and property performance (return and return volatility). Other things being equal, higher illiquidity and transaction costs lead to longer holding periods, while higher return volatility implies shorter holding periods. Our empirical application suggests that the optimal holding period based on our model is quite consistent with previous empirical findings. In addition, we find that when illiquidity risk is incorporated the true real estate risk is significantly higher than the conventional risk estimate. Therefore, the current practice of real estate valuation, which is naively borrowed from finance theory, substantially underestimates real estate risk.     

A model of population distribution,traffic congestion,and neighborhood crowding in a circular city

An idealized static equilibrium model of a circularly symmetric city is presented. The model allows one to compute the spatial distribution of residences, given certain simple and plausible assumptions about the “costs” of transport, housing and neighborhood crowding. The model is chosen so as to guarantee that in first approximation, the residential population distribution which would be considered optimal by a perfect planner is identical to the distribution reached in a push-shove, laissez-faire equilibrium. This aspect of the construction is shown to be related in a simple way to the familiar “external diseconomy” situation in which a free resource is allocated among alternative uses by equating average, rather than marginal products. The existence of an infinite class of models in which the associated planner's optimum and laissez-faire equilibria are equivalent follows naturally from the standard theory of the private and social costs of highway congestion. The model leads naturally to exponentially falling population distributions which exhibit an “urban-suburban” dichotomy, to a particular overall city size, and to an optimal allocation of land between transport and residential uses.     

Urban population distribution,family income,and social prejudice: I. The long,narrow city

We present an idealized model of a one-dimensional “city”, characterized by interactions between the costs of social prejudice, transportation, and housing.Using variational techniques, we show that under rather simple assumptions the model leads to a “suburban-urban” dichotomy, and also to a “segregated” neighborhood structure.In this abstract city, optimal “social policies” result in Pareto-efficient population distributions.     

Optimal consumption under uncertainty,liquidity constraints,and bounded rationality

I study how boundedly rational agents can learn a “good” solution to an infinite horizon optimal consumption problem under uncertainty and liquidity constraints. Using an empirically plausible theory of learning I propose a class of adaptive learning algorithms that agents might use to choose a consumption rule. I show that the algorithm always has a globally asymptotically stable consumption rule, which is optimal. Additionally, I present extensions of the model to finite horizon settings, where agents have finite lives and life-cycle income patterns. This provides a simple and parsimonious model of consumption for large agent based models.     

Taming the spread of an epidemic by lockdown policies

We study the problem of a policymaker who aims at taming the spread of an epidemic while minimizing its associated social costs. The main feature of our model lies in the fact that the disease’s transmission rate is a diffusive stochastic process whose trend can be adjusted via costly confinement policies. We provide a complete theoretical analysis, as well as numerical experiments illustrating the structure of the optimal lockdown policy. In all our experiments the latter is characterized by three distinct periods: the epidemic is first let to freely evolve, then vigorously tamed, and finally a less stringent containment should be adopted. Moreover, the optimal containment policy is such that the product “reproduction number $\times$ percentage of susceptible” is kept after a certain date strictly below the critical level of one, although the reproduction number is let to oscillate above one in the last more relaxed phase of lockdown. Finally, an increase in the fluctuations of the transmission rate is shown to give rise to an earlier beginning of the optimal lockdown policy, which is also diluted over a longer period of time.     

优衣库电子商务仓库选址研究

以优衣库一年订单的地域分布情况以及各项物流成本做为依据,使用总运输成本最优和总运输耗时最优方法,探讨如何通过增加仓库来降低配送成本、缩短配送时间。并提出保留上海仓库为总仓,增设北京、广州分仓的方案。     

On optimal investiment strategies

Suppose an investor has a fixed decision horizon and an appropriate utility function for measuring his or her utility of wealth. If there are only two investment vehicles, a risky and a risk-free asset, then the optimal investment strategy is such that, at any time, the amount invested in the risky asset must be the product of his or her “current risk tolerance” and the risk premium on the risky asset, divided by the square of the diffusion coefficient of the risky asset. In the case of more than one risky asset, the optimal investment strategy is similar, with the ratios of the amounts invested in the different risky assets being constant over time.     

On the retention of finished goods inventory when reorder-occurrence is uncertain

Finished goods inventory may accumulate for a variety of reasons in the production of lowdemand or slow-moving items. In this article a simple model is developed and some results are presented to aid in making inventory retention decisions when there exists uncertainty about whether reorders for a slow-moving item will be received in the future. In formulating the model, it is assumed that some excess inventory remains after filling a customer order and that a single reorder for the item is possible. The problem is to determine how long to retain the inventory before disposing of it.The relevant expected costs of retaining some quantity of inventory for a period of time consist of two types: (1) the inventory carrying cost less the salvage value from disposal; and (2) the future production cost incurred due to premature disposal. Using conventional optimization, a relationship for finding the optimal retention period is derived and conditions are identified that ensure that the optimal retention period can be obtained directly from the relationship.To determine the optimal retention period, probability distributions are required for the interarrival time until the reorder occurs and for the reorder quantity. While it seems logical to assume that each item would have its own distributions, this argument leads to a specification problem since the data needed to establish distributions for individual items will generally not be available for slow-moving items. One approach used to overcome this problem in practice is to combine data for a selected group of items and use the combined data to obtain distributions useful for any or all of the items in the group. An example illustrating this approach is provided.     

我国现代化仓储管理的发展方向

仓储管理在物流业和整个经济活动中都具有重要的地位和作用。对仓储进行管理,主要是为了使仓库空间的利用与库存货品的处置成本实现平衡。它是降低仓储物流成本的重要途径之一。通过高效率的仓储活动,可使商品仓储在最有效的时间段发挥作用,创造商品仓储的＂时间价值＂和＂空间价值＂。文中通过分析我国仓储管理的现状和存在的问题,重点阐述了现代化仓储管理的发展方向。     

The Problem of Epistemic Cost: Why Do Economists Not Change Their Minds (About the “Coase Theorem”)?

Errors in the history of economic analysis often remain uncorrected for long periods due to positive epistemic costs (PEC) involved in allocating time to going back over what older generations wrote. In order to demonstrate this in a case study, economists' practice of the “Coase Theorem” is reconsidered from a PEC point of view.     

Existence and transversality conditions for a general ‘unbounded-horizon’ model of the mining firm

This paper derives conditions under which optimal programs exist for a general model of the competitive or monopolistic mining firm. The model significantly extends and synthesizes previous formulations by including both resource extraction and discoveries of new reserves, with stock-dependent resource exploitation costs and incomplete resource exhaustion, endogenous technical innovation, and state-dependent resource demand. In addition, the analysis addresses complications arising from having optimal programs defined over an ‘unbounded horizon’, with the possibility of either a finite or infinite terminal time and a non-zero terminal (‘salvage’) valuation if the terminal time is finite. The necessity of the infinite-horizon transversality conditions also is established. The paper illustrates a strongly intuitive approach to existence questions for infinite-horizon or unbounded-horizon control problems, with weaker concavity and interiority assumptions than are often encountered in the literature.     

Periodical Preventive-Maintenance Contract for a Leased Facility with Weibull Life-Time

This paper develops a mathematical model to derive the optimal periodical preventive maintenance (PM) policy for a leased facility with Weibull life-time. Within a lease period, any failures of the facility are rectified by minimal repairs and a penalty may occur to the lessor when the time required to perform a minimal repair exceeds a reasonable time limit. To reduce failures of the facility, additional PM actions are carried out periodically during the lease period. When the life-time distribution of a product is Weibull, the optimal number of PM actions and the corresponding maintenance degrees are derived such that the expected total maintenance cost is minimized. The structural properties of the optimal policy are investigated and an efficient algorithm is provided to search for the optimal policy. Finally, numerical examples are provided to illustrate the features of the proposed model.     

The optimality of (s,S) inventory policies in the infinite period model*

Summary The infinite period stationary inventory model is considered. There is a constant lead time, a nonnegative set-up cost, a linear purchase cost, a holding and shortage cost function, a fixed discount factor β, 0 < β < 1, and total backlogging of unfilled demand. Both the total discounted cost (β < 1) and the average cost (β= 1) criteria are considered. Under the assumption that the negatives of the one period holding and shortage costs are unimodal, a unified proof of the existence of an optimal (s.S) policy is given. As a by-product of the proof upper and lower bounds on the optimal values of s and S are found. New results simplify the algorithm of Veinott and Wagner for finding an optimal (s, S) policy for the case β< 1. Further it is shown that the conditions imposed on the one period holding and shortage costs can be weakened slightly.     

The generation gap and optimal economic growth

Among the problems confronting those who aspire to the development of a realistic and practicable optimal growth theory is that the human population is not homogeneous with respect to age. Those who are relatively young are apt to prefer a different pattern of capital accumulation from that preferred by those who are relatively old. This paper proposes a tentative solution to this particular problem. Essentially the proposal is that society should remain with what is an optimal private plan of an individual who is at the median age of the population at the beginning of the planning period, for one planning period, after which it revises the plan to switch to the optimal private plan of another individual (one planning period younger than the first) who is at the median age at the commencement of the new planning period. Thus the optimal social plan consists of a succession of one planning period implementations of the first periods of the optimal private plans of individuals who are at the median age at that time period. An example of the application of the method is given. An important sidelight of the paper is a critique of standard constant-rate exponential discounting in social planning of optimal capital accumulation, and the proposal that it be replaced by “mortality discounting.”     

Risk premium or irrational expectations? An investigation into the causes of forward discount bias across 27 developed and developing economies forward rates

This study investigates the causes of forward discount bias in 27 forward rates for the period 2007–2016. First, it analyzes the forward discount bias across two horizons: 3-month and 12-month; across two sub-periods: financial crisis and non-crisis; and across two country groups: developed and developing. The regression results show that forward discount bias is present and significant, but has become smaller compared to many earlier studies. In general, 12-month forward discount is less biased compared to the 3-month. The study confirms that during the non-crisis period, developing country forward discount is less biased compared to the developed country across both the horizons. The crisis period has impacted the magnitude of the bias. For the developed country, the bias is higher during the crisis period compared to the non-crisis period at the 3-month horizon but lower at the 12-month horizon. Developing country forward discount is less biased during the crisis period compared to the non-crisis period at the 3-month horizon, but slightly more biased at the 12-month horizon. Second, the study decomposes the bias into two components: irrational expectations and risk premium. The results show that both irrationality and time varying risk premium are present in the bias. However, the irrationality component plays a minor role in the 3-month forward discount bias, but plays a major role in the 12-month forward discount bias. Irrationality is high during the crisis period for both the country groups. The risk premium component of the bias is highly significant across both the periods, country groups and horizons, and thus, plays a major role in the overall bias. Further, the non-parametric tests of comparison of statistical significance of the beta coefficient values between country groups, periods and horizons indicate that many differences are statistically significant supporting our conclusions.     

Dynamic incentive contracts with termination threats

We consider a dynamic moral hazard model where the principal offers a series of short-run contracts. We study the optimal mix of two alternative instruments for incentive provision: a performance based wage (a “carrot”) and a termination threat (a “stick”). At any given point in time, these instruments are substitutes in the provision of incentives. We are particularly interested in the dynamic interaction of these two instruments. Both carrot and stick are used more intensively as the agent approaches the end of his finite life. The sharing of the surplus of the relationship plays a key role: a termination threat is included in the optimal contract if and only if the agent’s expected future gain from the relationship is sufficiently high, compared to the principal’s expected future gain. Also, a termination threat is more likely to be optimal if output depends more on “luck” than on effort, if the discount factor is high, or if the agent’s productivity is low. The model, provided that the optimal contract includes a termination threat, essentially provides an alternative explanation for upward-sloping wage profiles even in the absence of full-commitment.     

基于供应链的大规模定制的多阶段生产模型研究

采用生产延迟和物流延迟策略将大规模定制生产过程分为三个地点四个阶段,即在企业的制造车间：根据预测大规模生产通用件、根据订单的批量生产半成品;在中央仓库：集中存储按需运输分配;在各分销地点：根据顾客个性化需求生产最终产品。随后对大规模定制下的成本和交货期作了简单分析,给出了优化模型。     

Comparison of exact and approximate methods of solving the uncapacitated plant location problem

This study was prompted by a recently published article in this journal on facility location by D. R. Sule. We show that the claim made by Sule of a novel and extremely simple algorithm yielding optimum solutions is not true. Otherwise, the algorithm would represent a breakthrough in decision-making for which a number of notoriously hard problems could be efficiently recast as location problems and easily solved.In addition, several variants of common location problems addressed by Sule are reviewed. In the last twenty years, many methods of accurately solving these problems have been proposed. In spite of their increased sophistication and efficiency, none of them claims to be a panacea. Therefore, researchers have concurrently developed a battery of fast but approximate solution techniques. Sule's method was essentially proposed by Kuehn and Hamburger in 1963, and has been adapted many times since.We exhibit several examples (including the one employed by Sule) in which Sule's algorithms lead to nonoptimal solutions. We present computational results on problems of size even greater than those utilized by Sule, and show that a method devised by Erlenkotter is both faster and yields better results.In a cost-benefit analysis of exact and approximate methods, we conclude that planning consists of generating an array of corporate scenarios, submitting them to the “optimizing black box,” and evaluating their respective merits. Therefore, much is to be gained by eliminating the vagaries of the black box—that is, by using an exact method—even if the data collection and the model representation introduce sizable inaccuracies. Ironically, large problems (those that typically require most attention) cannot be solved exactly in acceptable computational times. Pending the imminent design of a new generation of exact algorithms, the best heuristics are those that guarantee a certain degree of accuracy of their solutions.     

Barriers and breakthroughs: an “expanding frontiers” model of the technology-industry life cycle

It is argued that technological progress is marked by a series of discrete “barriers” and “breakthroughs,” which create new fields of technological opportunity. These are not random events, although their exact timing is undoubtedly very difficult to predict. They occur when and where they do because of discontinuities in the laws of nature. The technological life cycle can be defined as the period from a major breakthrough which opens up a new territory for exploitation to the next major barrier. It is characterized by a rapid increase in marginal productivity of R&D to a peak, followed by a more-or-less continuous decline thereafter, as the territory is gradually exhausted. This model is qualitatively consistent with the well-known “S-shaped curve” phenomenon, describing measures of technological performance over time. The model is also qualitatively consistent with Schumpeter's explanation of the so-called Kondratieff or “long” wave.     

Nowcasting in real time using popularity priors

We construct a “Google Recession Index” (GRI) using Google Trends data on internet search popularity, which tracks the public’s attention to recession-related keywords in real time. We then compare nowcasts made with and without this index using both a standard dynamic factor model and a Bayesian approach with alternative prior setups. Our results indicate that using the Bayesian model with GRI-based “popularity priors,” we could identify the 2008Q3 turning point in real time, without sacrificing the accuracy of the nowcasts over the rest of the sample periods.