Parameterized expectations approach; Some practical issues

We discuss some practical issues related to the use of the Parameterized Expectations Approach (PEA) for solving non-linear stochastic dynamic models with rational expectations. This approach has been applied in models of macroeconomics, financial economics, economic growth, contracttheory, etc. It turns out to be a convenient algorithm, especially when there is a large number of state variables and stochastic shocks in the conditional expectations. We discuss some practical issues having to do with the application of the algorithm, and we discuss a Fortran program for implementing the algorithm that is available through the internet.We discuss these issues in a battery of six examples.

Stochastic dominance and absolute risk aversion

In this paper we proose the infimum of the Arrow-Pratt index of absoluterisk aversion as a measure of global risk aversion of a utility function.We then show that, for any given arbitrary pair of distributions, thereexists a threshold level of global risk aversion such that all increasingconcave utility functions with at least as much global risk aversion wouldrank the two distributions in the same way. Furthermore, this thresholdlevel is sharp in the sense that, for any lower level of global riskaversion, we can find two utility functions in this class yielding oppositepreference relations for the two distributions.

The achievable region approach to the optimal control of stochastic systems

The achievable region approach seeks solutions to stochastic optimisation problems by: (i) characterising the space of all possible performances(the achievable region) of the system of interest, and (ii) optimisingthe overall system-wide performance objective over this space. This isradically different from conventional formulations based on dynamicprogramming. The approach is explained with reference to a simpletwo-class queueing system. Powerful new methodologies due to the authorsand co-workers are deployed to analyse a general multiclass queueingsystem with parallel servers and then to develop an approach to optimalload distribution across a network of interconnected stations. Finally,the approach is used for the first time to analyse a class of intensitycontrol problems.

Growing at the production frontier. European aggregate growth, 1870-1914

The view of a 1870-1913 expanding European economy providing increasing welfare to everybody has been challenged by many, then and now. We focus on the amazing growth that was experienced, its diffusion and its sources, in the context of the permanent competition among European nation states. During 1870-193 the globalized European economy reached a silver age . GDP growth was quite rapid (2.15% per annum) and diffused all over Europe. Even discounting the high rates of population growth (1.06%), per capita growth was left at a respectable 1.08%. Income per capita was rising in every country, and the rates of improvement were quite similar. This was a major achievement after two generations of highly localized growth, both geographically and socially. Growth was based on the increased use of labour and capital, but a good part of growth (73 per cent for the weighted average of the best documented European countries) came out of total factor productivity efficiency gains resulting from not well specified ultimate sources of growth. This proportion suggests that the European economy was growing at full capacity at its production frontier. It would have been very difficult to improve its performance. Within Europe, convergence was limited, and it only was in motion after 1900. What happened was more the end of the era of big divergence rather than an era of convergence.

Capital, wages and growth: Theory and evidence

Returns to scale to capital and the strength of capital externalities play a key role for the empirical predictions and policy implications of different growth theories. We show that both can be identified with individual wage data and implement our approach at the city-level using US Census data on individuals in 173 cities for 1970, 1980, and 1990. Estimation takes into account fixed effects, endogeneity of capital accumulation, and measurement error. We find no evidence for human or physical capital externalities and decreasing aggregate returns to capital. Returns to scale to physical and human capital are around 80 percent. We also find strong complementarities between human capital and labor and substantial total employment externalities.

A global view of economic growth

This paper integrates in a unified and tractable framework some of the key insights of the field of international trade and economic growth. It examines a sequence of theoretical models that share a common description of technology and preferences but differ on their assumptions about trade frictions. By comparing the predictions of these models against each other, it is possible to identify a variety of channels through which trade affects the evolution of world income and its geographical distribution. By comparing the predictions of these models against the data, it is also possible to construct coherent explanations of income differences and long-run trends in economic growth.

Social capital, government expenditures, and growth

Countries with greater social capital have higher economic growth. We show that socialcapital is also highly positively correlated across countries with government expenditureon education. We develop an infinite-horizon model of public spending and endogenousstochastic growth that explains both facts through frictions in political agency whenvoters have imperfect information. In our model, the government provides servicesthat yield immediate utility, and investment that raises future productivity. Voters aremore likely to observe public services, so politicians have electoral incentives to underprovidepublic investment. Social capital increases voters' awareness of all governmentactivity. As a consequence, both politicians' incentives and their selection improve.In the dynamic equilibrium, both the amount and the efficiency of public investmentincrease, permanently raising the growth rate.

High-growth cooperatives: Financial profile and key factors for competitiveness

Given the current economic environment, high-growth companies are particularly relevant for their contribution to employment generation and wealth.This paper discusses the results of a survey that was conducted in order to gain a deeper understanding of high-growth cooperatives through analyzing their financial profiles and then identifying key contributing factors to their growth. To do this, we compared this particular sample with other cooperatives and other high-growth mercantile companies.The results show the main drivers related to high-growth companies success. They are the competitive advantages based on the surveyed group, modern management techniques, quality and productivity, innovation and internationalization. Additionally, we have observed some financial strengths and weaknesses. In this sense, they are under capitalized companies with an unbalanced growth.

Beyond Smith's rule: An optimal dynamic index, rule for single machine stochastic scheduling with convex holding costs

Most research on single machine scheduling has assumedthe linearity of job holding costs, which is arguablynot appropriate in some applications. This motivates ourstudy of a model for scheduling $n$ classes of stochasticjobs on a single machine, with the objective of minimizingthe total expected holding cost (discounted or undiscounted). We allow general holding cost rates that are separable,nondecreasing and convex on the number of jobs in eachclass. We formulate the problem as a linear program overa certain greedoid polytope, and establish that it issolved optimally by a dynamic (priority) index rule,whichextends the classical Smith's rule (1956) for the linearcase. Unlike Smith's indices, defined for each class, ournew indices are defined for each extended class, consistingof a class and a number of jobs in that class, and yieldan optimal dynamic index rule: work at each time on a jobwhose current extended class has larger index. We furthershow that the indices possess a decomposition property,as they are computed separately for each class, andinterpret them in economic terms as marginal expected cost rate reductions per unit of expected processing time.We establish the results by deploying a methodology recentlyintroduced by us [J. Niño-Mora (1999). "Restless bandits,partial conservation laws, and indexability. "Forthcomingin Advances in Applied Probability Vol. 33 No. 1, 2001],based on the satisfaction by performance measures of partialconservation laws (PCL) (which extend the generalizedconservation laws of Bertsimas and Niño-Mora (1996)):PCL provide a polyhedral framework for establishing theoptimality of index policies with special structure inscheduling problems under admissible objectives, which weapply to the model of concern.

Calibration of stochastic volatility models via second order approximation: the Heston model case

Using a suitable Hull and White type formula we develop a methodology to obtain asecond order approximation to the implied volatility for very short maturities. Using thisapproximation we accurately calibrate the full set of parameters of the Heston model. Oneof the reasons that makes our calibration for short maturities so accurate is that we alsotake into account the term-structure for large maturities. We may say that calibration isnot "memoryless", in the sense that the option's behavior far away from maturity doesinfluence calibration when the option gets close to expiration. Our results provide a wayto perform a quick calibration of a closed-form approximation to vanilla options that canthen be used to price exotic derivatives. The methodology is simple, accurate, fast, andit requires a minimal computational cost.