AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMPs) taking values in a general Borel space and with compact action space depending on the state variable. The control variable acts on the jump rate and transition measure of the PDMP, and the running and boundary costs are assumed to be positive but not necessarily bounded. Our first main result is to obtain an optimality equation for the long run average cost in terms of a discrete-time optimality equation related to the embedded Markov chain given by the postjump location of the PDMP. Our second main result guarantees the existence of a feedback measurable selector for the discrete-time optimality equation by establishing a connection between this equation and an integro-differential equation. Our final main result is to obtain some sufficient conditions for the existence of a solution for a discrete-time optimality inequality and an ordinary optimal feedback control for the long run average cost using the so-called vanishing discount approach. Two examples are presented illustrating the possible applications of the results developed in the paper.

The Policy Iteration Algorithm for Average Continuous Control of Piecewise Deterministic Markov Processes

The main goal of this paper is to apply the so-called policy iteration algorithm (PIA) for the long run average continuous control problem of piecewise deterministic Markov processes (PDMP`s) taking values in a general Borel space and with compact action space depending on the state variable. In order to do that we first derive some important properties for a pseudo-Poisson equation associated to the problem. In the sequence it is shown that the convergence of the PIA to a solution satisfying the optimality equation holds under some classical hypotheses and that this optimal solution yields to an optimal control strategy for the average control problem for the continuous-time PDMP in a feedback form.

THE VANISHING DISCOUNT APPROACH FOR THE AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This work is concerned with the existence of an optimal control strategy for the long-run average continuous control problem of piecewise-deterministic Markov processes (PDMPs). In Costa and Dufour (2008), sufficient conditions were derived to ensure the existence of an optimal control by using the vanishing discount approach. These conditions were mainly expressed in terms of the relative difference of the alpha-discount value functions. The main goal of this paper is to derive tractable conditions directly related to the primitive data of the PDMP to ensure the existence of an optimal control. The present work can be seen as a continuation of the results derived in Costa and Dufour (2008). Our main assumptions are written in terms of some integro-differential inequalities related to the so-called expected growth condition, and geometric convergence of the post-jump location kernel associated to the PDMP. An example based on the capacity expansion problem is presented, illustrating the possible applications of the results developed in the paper.

Generalized Coupled Algebraic Riccati Equations for Discrete-time Markov Jump with Multiplicative Noise Systems

In this paper we consider the existence of the maximal and mean square stabilizing solutions for a set of generalized coupled algebraic Riccati equations (GCARE for short) associated to the infinite-horizon stochastic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The weighting matrices of the state and control for the quadratic part are allowed to be indefinite. We present a sufficient condition, based only on some positive semi-definite and kernel restrictions on some matrices, under which there exists the maximal solution and a necessary and sufficient condition under which there exists the mean square stabilizing solution fir the GCARE. We also present a solution for the discounted and long run average cost problems when the performance criterion is assumed be composed by a linear combination of an indefinite quadratic part and a linear part in the state and control variables. The paper is concluded with a numerical example for pension fund with regime switching.

Nonparametric Measures of Capacity Utilization: A Dual Approach

This paper develops a nonparametric method of obtaining the minimum of the long run average cost curve of a firm to define its capacity output. This provides a benchmark for measuring of capacity utilization at the observed output level of the firm. In the case of long run constant returns to scale, the minimum of the short run average cost curve is determined to measure short run capacity utilization. An empirical application measures yearly rates of capacity utilization in U.S. manufacturing over the period 1968-1998. Nonparametric determination of the short run average cost curve under variable returns to scale using an iterative search procedure is described in an appendix to this paper.

Aggregate and welfare effects of long run inflation risk under inflation and price-level targeting

This paper presents a DSGE model in which long run inflation risk matters for social welfare. Aggregate and welfare effects of long run inflation risk are assessed under two monetary regimes: inflation targeting (IT) and price-level targeting (PT). These effects differ because IT implies base-level drift in the price level, while PT makes the price level stationary around a target price path. Under IT, the welfare cost of long run inflation risk is equal to 0.35 percent of aggregate consumption. Under PT, where long run inflation risk is largely eliminated, it is lowered to only 0.01 per cent. There are welfare gains from PT because it raises average consumption for the young and lowers consumption risk substantially for the old. These results are strongly robust to changes in the PT target horizon and fairly robust to imperfect credibility, fiscal policy, and model calibration. While the distributional effects of an unexpected transition to PT are sizeable, they are short-lived and not welfare-reducing.

Tracking cost savings from competitive tendering in the short and long run

A major initiative of the Thatcher and Major Conservative administrations was that public sector ancillary and professional services provided by incumbent direct service organisations [DSOs] be put out to tender. Analyses of this initiative, in the UK and elsewhere, found costs were often reduced in the short run. However, few if any studies went beyond the first round of tendering. We analyze data collected over successive rounds of tendering for cleaning and catering services of Scottish hospitals in order to assess the long term consequences of this initiative. The experience of the two services was very different. Cost savings for cleaning services tended to increase with each additional round of tendering and became increasingly stable. In accordance with previous results in the literature, DSOs produced smaller cost reductions than private contractors: probably an inevitable consequence of the tendering process at the time. Cost savings from DSOs tended to disappear during the first round of tendering, but they appear to have been more permanent in successive rounds. Cost savings for catering, on the other hand, tended to be much smaller, and these were not sustained.

The long-run performance of IPOs: the case of the Stock Exchange of Mauritius

This study examines the long-run performance of initial public offerings on the Stock Exchange of Mauritius (SEM). The results show that the 3-year equally weighted cumulative adjusted returns average −16.5%. The magnitude of this underperformance is consistent with most reported studies in different developed and emerging markets. Based on multivariate regression models, firms with small issues and higher ex ante financial strength seem on average to experience greater long-run underperformance, supporting the divergence of opinion and overreaction hypotheses. On the other hand, Mauritian firms do not on average time their offerings to lower cost of capital and as such, there seems to be limited support for the windows of opportunity hypothesis.

Bertrand and the long run

We propose a new model of simultaneous price competition, based on firms offering personalized prices to consumers. In a market for a homogeneous good and decreasing returns, the unique equilibrium leads to a uniform price equal to the marginal cost of each firm, at their share of the market clearing quantity. Using this result for the short-run competition, we then investigate the long-run investment decisions of the firms. While there is underinvestment, the overall outcome is more competitive than the Cournot model competition. Moreover, as the number of firms grows we approach the competitive long-run outcome.

Value and depreciation of mineral resources over the very long run: An empirical contrast of different methods

The paper contrasts empirically the results of alternative methods for estimating thevalue and the depreciation of mineral resources. The historical data of Mexico andVenezuela, covering the period 1920s-1980s, is used to contrast the results of severalmethods. These are the present value, the net price method, the user cost method andthe imputed income method. The paper establishes that the net price and the user costare not competing methods as such, but alternative adjustments to different scenariosof closed and open economies. The results prove that the biases of the methods, ascommonly described in the theoretical literature, only hold under the most restrictedscenario of constant rents over time. It is argued that the difference between what isexpected to happen and what actually did happen is for the most part due to a missingvariable, namely technological change. This is an important caveat to therecommendations made based on these models.

The Impact of Recycling on the Long-Run Stock of Trees

Interest in recycling of forest products has grown in recent years, one of the goals being to conserve the stock of trees or possibly increase it to compensate for positive externalities generated by the forest and neglected by the market. This paper explores the issue as to whether recycling is an appropriate measure to attain such a goal. We do this by considering the problem of the private owner of an area of land, who, acting as a price taker, decides how to allocate his land over time between forestry and some other use, and at what age to harvest the forest area chosen. Once the forest is cut, he makes a new land allocation decision and replants. He does so indefinitely, in a Faustmann-like framework. The wood from the harvest is transformed into a final product which is partly recycled into a substitute for the virgin wood, so that past output affects the current price. We show that in such a context, increasing the rate of recycling will result in less area being devoted to forestry. It will also have the effect of increasing the harvest age of the forest, as long as the planting cost is positive. The net effect on the flow of virgin wood being harvested to supply the market will as a result be ambiguous. The main point however is that recycling will result in a smaller, not a larger, stock of trees in the long run. It would therefore be best to resort to other means if the goal is to increase the stock of trees.

The long run economic impact of AIDS

This paper studies the long-run impact of HIV/AIDS on per capita income and education. We introduce a channel from HIV/AIDS to long-run income that has been overlooked by the literature, the reduction of the incentives to study due to shorter expected longevity. We work with a continuous time overlapping generations mo deI in which life cycle features of savings and education decision play key roles. The simulations predict that the most affected countries in Sub-Saharan Africa will be in the future, on average, a quarter poorer than they would be without AIDS, due only to the direct (human capital reduction) and indirect (decline in savings and investment) effects of life-expectancy reductions. Schooling will decline on average by half. These findings are well above previous results in the literature and indicate that, as pessimistic as they may be, at least in economic terms the worst could be yet to come.

The long-run economic impact of AIDS

This paper studies the long-run impact of HIV / AIDS on per capita income and education. We introduce a channel from HIV / AIDS to long-run income that has been overlooked by the literature, the reduction of the incentives to study due to shorter expected longevity. We work with a continuous time overlapping generations mo deI in which life cycle features of savings and education decision play key roles. The simulations predict that the most affected countries in Sub-Saharan Africa will be in the future, on average, a quarter poorer than they would be without AIDS, due only to the direct (human capital reduction) and indirect (decline in savings and investment) effects of life-expectancy reductions. Schooling will decline on average by half. These findings are well above previous results in the literature and indicate that, as pessimistic as they may be, at least in economic terms the worst could be yet to come.

Long-run performance of initial public offerings: The evidence for Switzerland

We estimate the underpricing and long-run performance of Swiss initial public offerings (IPOs) from 1983 to 2000. The average market adjusted initial return is 34.97%. To examine the long-run performance of Swiss IPOs, we compute buy-and-hold abnormal returns, skewness-adjusted wealth ratios, and cumulative abnormal returns using 120 months of secondary market returns. In contrast to previous findings for the U.S. and Germany, we do not find strong evidence for a distinct IPO effect. We attribute long-run underperformance to the fact that IPO firms tend to be small firms. It virtually vanishes when we use a small capitalization index as a benchmark. In spite of distinct economic implications and statistical properties, our basic results are similar for all performance measures applied.

This Time is Different: Causes and Consequences of British Banking Instability over the Long Run

This paper addresses three questions: (1) How severe were the episodes of banking instability
experienced by the UK over the past two centuries? (2) What have been the macroeconomic
indicators of UK banking instability? and (3) What have been the consequences of UK banking
instability for the cost of credit? Using a unique dataset of bank share prices from 1830 to 2010
to assess the stability of the UK banking system, we find that banking instability has grown more
severe since the 1970s. We also find that interest rates, inflation, lending growth, and equity
prices are consistent macroeconomic indicators of UK banking instability over the long run.
Furthermore, utilising a unique dataset of corporate-bond yields for the period 1860 to 2010, we
find that there is a significant long-run relationship between banking instability and the creditrisk
premium faced by businesses.