Applying efficiency measurement techniques to the measurement of productivity change

Deterministic frontier analysis (DFA), stochastic frontier analysis (SFA), and data envelopment analysis (DEA) are alternative analytical techniques designed to measure the efficiency of producers. All three techniques were originally developed within a cross-sectional context, in which the objective is to compare the efficiencies of producers. More recently all three techniques have been extended for use in a panel data context. In the latter context it is possible to measure productivity change, and to decompose measured productivity change into its sources, one of which is efficiency change. However when efficiency measurement techniques, particularly SFA, have been applied to panel data, it has infrequently been made clear what the objective of the analysis is: the measurement of efficiency, which may vary through time as well as across producers, or the measurement and decomposition of productivity change. In this paper I explore the use of each technique in a panel data context. I find DFA and DEA to have achieved a more satisfactory reorientation toward productivity measurement than SFA has.     

Robust consumption‐investment problem under CRRA and CARA utilities with time‐varying confidence sets

We consider a robust consumption‐investment problem under constant relative risk aversion and constant absolute risk aversion utilities. The time‐varying confidence sets are specified by Θ, a correspondence from [0, T] to the space of the Lévy triplets, and describe a priori drift, volatility, and jump information. For each possible measure, the log‐price processes of stocks are semimartingales, and the triplet of their differential characteristics is almost surely a measurable selector from the correspondence Θ. By proposing and investigating the global kernel, an optimal policy and a worst‐case measure are generated from a saddle point of the global kernel, and they constitute a saddle point of the objective function.     

Empirical analysis of profit maximization and cost minimization behaviour of Kansas farms

A farm-level deterministic and stochastic nonparametric tests of profit maximization and cost minimization behaviour for a sample of 112 Kansas farms was completed from 1996 to 2013. Allowing for monotonic non-regressive technological change and using a 10% significance level, 73 farms violated the profit-maximization hypothesis and 58 farms violated the cost minimization hypothesis. More profit maximization violations existed relative to cost minimization violations. However, comparing these results with results for 289 Kansas farms using data from 1973 to 1990, farms have significantly reduced profit maximizing violations. Cost minimizing behaviour has not changed substantially.     

Dynamic advertising and pricing with constant demand elasticities

In this paper we analyze a stochastic dynamic advertising and pricing model with isoelastic demand. The state space is discrete, time is continuous and the planing horizon is allowed to be finite or infinite. A dynamic version of the Dorfman–Steiner identity will be derived. Explicit expressions of the optimal advertising and pricing policies, of the value function and of the optimal advertising expenditures will be given. The general results will be used to analyze the case of impatient customers. Furthermore, particular time inhomogeneous models and homogeneous ones with and without discounting will be examined. We will study the social efficiency of a monopolist's optimal policies and the consequences of specific subsidies. From a buyer's perspective, our analysis reveals that waiting – when looking at (immediate) expected prices – is never profitable should two or more units be available. But we will also prove that the sequence of average sales prices is monotone decreasing. Moreover, the techniques applied to solve the discrete stochastic advertising and pricing problem will be used to solve a related deterministic control problem with continuous state space.     

Gibbsian and non-Gibbsian states at Eurandom

We review some of the work on non-Gibbsian states of the last 10 years, emphasizing the developments in which Eurandom played a role.     

Stress scenario generation for solvency and risk management

We derive worst-case scenarios in a life insurance model in the case where the interest rate and the various transition intensities are mutually dependent. Examples of this dependence are that (a) surrender intensities and interest rates are high at the same time, (b) mortality intensities of a policyholder as active and disabled, respectively, are low at the same time, and (c) mortality intensities of the policyholders in a portfolio are low at the same time. The set from which the worst-case scenario is taken reflects the dependence structure and allows us to relate the worst-case scenario-based reserve, qualitatively, to a Value-at-Risk-based calculation of solvency capital requirements. This brings out perspectives for our results in relation to qualifying the standard formula of Solvency II or using a scenario-based approach in internal models. Our results are powerful for various applications and the techniques are non-standard in control theory, exactly because our worst-case scenario is deterministic and not adapted to the stochastic development of the portfolio. The formalistic results are exemplified in a series of numerical studies.     

Approximation of Optimal Reinsurance and Dividend Payout Policies

We consider the stochastic process of the liquid assets of an insurance company assuming that the management can control this process in two ways: first, the risk exposure can be reduced by affecting reinsurance, but this decreases the premium income; and second, a dividend has to be paid out to the shareholders. The aim is to maximize the expected discounted dividend payout until the time of bankruptcy. The classical approach is to model the liquid assets or risk reserve process of the company as a piecewise deterministic Markov process. However, within this setting the control problem is very hard. Recently several papers have modeled this problem as a controlled diffusion, presuming that the policy obtained is in some sense good for the piecewise deterministic problem as well. We will clarify this statement in our paper. More precisely, we will first show that the value function of the controlled diffusion provides an asymptotic upper bound for the value functions of the piecewise deterministic problems under diffusion scaling. Finally it will be shown that the upper bound is achieved in the limit under the optimal feedback control of the diffusion problem. This property is called asymptotic optimality .     

An extension of the asymmetric causality tests for dealing with deterministic trend components

This article extends the asymmetric causality tests, as developed by Hatemi-J (2012), for dealing with deterministic trend parts. It is shown how integrated variables up to three degrees with deterministic trend parts can be transformed into positive and negative cumulative partial components. These cumulative components can be used for implementing the asymmetric causality tests based on a Wald test statistic that is shown to follow a chi-square distribution asymptotically. Each solution is expressed as a proposition and a mathematic proof is provided for each underlying proposition. This issue is important because most economic or financial variables seem to be characterized by both stochastic as well as deterministic trend parts. An empirical application is provided in order to show how the oil prices and the exchange rates as integrated variables with drift and trend can be transformed into cumulative partial sums of positive and negative components. The conducted causality tests reveal that allowing for asymmetry has important repercussions for the underlying causal inference between these two variables.     

The behaviour of seasonal unit root tests under neglected local drifts

This paper analyses the limit distributions of the seasonal unit root test procedures proposed by Dickey, Hasza and Fuller (1984) and Hylleberg, Engle, Granger and Yoo (1990), when local trends at different frequencies are present in data generation processes, but ignored in the test regressions used. The findings presented explicitly show that neglected deterministic trends have negative effects on the distributions of the test statistics. Analytical observations and Monte Carlo simulations reveal that seasonal unit root test statistics become severely undersized as the values of standardized local trends increase. Hence, failure to consider local trends may often bear the undesirable effect of biasing decisions towards non-rejection of unit roots.Received: February 2001, Accepted: September 2001, JEL Classification: C12, C22Paulo M. M. Rodrigues: I am thankful to two anonymous referees for their detailed and useful comments and suggestions.