On the throughput-WIP trade-off in queueing systems, diminishing returns and the threshold property: A linear programming approach

We present a new unifying framework for investigating throughput-WIP(Work-in-Process) optimal control problems in queueing systems,based on reformulating them as linear programming (LP) problems withspecial structure: We show that if a throughput-WIP performance pairin a stochastic system satisfies the Threshold Property we introducein this paper, then we can reformulate the problem of optimizing alinear objective of throughput-WIP performance as a (semi-infinite)LP problem over a polygon with special structure (a thresholdpolygon). The strong structural properties of such polygones explainthe optimality of threshold policies for optimizing linearperformance objectives: their vertices correspond to the performancepairs of threshold policies. We analyze in this framework theversatile input-output queueing intensity control model introduced byChen and Yao (1990), obtaining a variety of new results, including (a)an exact reformulation of the control problem as an LP problem over athreshold polygon; (b) an analytical characterization of the Min WIPfunction (giving the minimum WIP level required to attain a targetthroughput level); (c) an LP Value Decomposition Theorem that relatesthe objective value under an arbitrary policy with that of a giventhreshold policy (thus revealing the LP interpretation of Chen andYao's optimality conditions); (d) diminishing returns and invarianceproperties of throughput-WIP performance, which underlie thresholdoptimality; (e) a unified treatment of the time-discounted andtime-average cases.

Restless bandits, partial conservation laws and indexability

We show that if performance measures in a stochastic scheduling problem satisfy a set of so-called partial conservation laws (PCL), which extend previously studied generalized conservation laws (GCL), then the problem is solved optimally by a priority-index policy for an appropriate range of linear performance objectives, where the optimal indices are computed by a one-pass adaptive-greedy algorithm, based on Klimov's. We further apply this framework to investigate the indexability property of restless bandits introduced by Whittle, obtaining the following results: (1) we identify a class of restless bandits (PCL-indexable) which are indexable; membership in this class is tested through a single run of the adaptive-greedy algorithm, which also computes the Whittle indices when the test is positive; this provides a tractable sufficient condition for indexability; (2) we further indentify the class of GCL-indexable bandits, which includes classical bandits, having the property that they are indexable under any linear reward objective. The analysis is based on the so-called achievable region method, as the results follow fromnew linear programming formulations for the problems investigated.

An experimental test of loss aversion and scale compatibility

This paper studies two important reasons why people violate procedure invariance, loss aversion and scale compatibility. The paper extends previous research on loss aversion and scale compatibility by studying loss aversion and scale compatibility simultaneously, by looking at a new decision domain, medical decision analysis, and by examining the effect of loss aversion and scale compatibility on "well-contemplated preferences." We find significant evidence both of loss aversion and scale compatibility. However, the sizes of the biases due to loss aversion and scale compatibility vary over trade-offs and most participants do not behave consistently according to loss aversion or scale compatibility. In particular, the effect of loss aversion in medical trade-offs decreases with duration. These findings are encouraging for utility measurement and prescriptive decision analysis. There appear to exist decision contexts in which the effects of loss aversion and scale compatibility can be minimized and utilities can be measured that do not suffer from these distorting factors.

A consistency test of the time trade-off

This paper tests the internal consistency of time trade-off utilities.We find significant violations of consistency in the direction predictedby loss aversion. The violations disappear for higher gauge durations.We show that loss aversion can also explain that for short gaugedurations time trade-off utilities exceed standard gamble utilities. Ourresults suggest that time trade-off measurements that use relativelyshort gauge durations, like the widely used EuroQol algorithm(Dolan 1997), are affected by loss aversion and lead to utilities thatare too high.

A test of the predictive validity of non-linear QALY models using time trade-off utilities

This paper presents a test of the predictive validity of various classes ofQALY models (i.e., linear, power and exponential models). We first estimatedTTO utilities for 43 EQ-5D chronic health states and next these states wereembedded in health profiles. The chronic TTO utilities were then used topredict the responses to TTO questions with health profiles. We find that thepower QALY model clearly outperforms linear and exponential QALY models.Optimal power coefficient is 0.65. Our results suggest that TTO-based QALYcalculations may be biased. This bias can be avoided using a power QALY model.

A scaled difference chi-square test statistic for moment structure analysis

A family of scaling corrections aimed to improve the chi-square approximation of goodness-of-fit test statistics in small samples, large models, and nonnormal data was proposed in Satorra and Bentler (1994). For structural equations models, Satorra-Bentler's (SB) scaling corrections are available in standard computer software. Often, however, the interest is not on the overall fit of a model, but on a test of the restrictions that a null model say ${\cal M}_0$ implies on a less restricted one ${\cal M}_1$. If $T_0$ and $T_1$ denote the goodness-of-fit test statistics associated to ${\cal M}_0$ and ${\cal M}_1$, respectively, then typically the difference $T_d = T_0 - T_1$ is used as a chi-square test statistic with degrees of freedom equal to the difference on the number of independent parameters estimated under the models ${\cal M}_0$ and ${\cal M}_1$. As in the case of the goodness-of-fit test, it is of interest to scale the statistic $T_d$ in order to improve its chi-square approximation in realistic, i.e., nonasymptotic and nonnormal, applications. In a recent paper, Satorra (1999) shows that the difference between two Satorra-Bentler scaled test statistics for overall model fit does not yield the correct SB scaled difference test statistic. Satorra developed an expression that permits scaling the difference test statistic, but his formula has some practical limitations, since it requires heavy computations that are notavailable in standard computer software. The purpose of the present paper is to provide an easy way to compute the scaled difference chi-square statistic from the scaled goodness-of-fit test statistics of models ${\cal M}_0$ and ${\cal M}_1$. A Monte Carlo study is provided to illustrate the performance of the competing statistics.

Is the observed persistence spurious? A test for fractional integration versus short memory and structural breaks

Although it is commonly accepted that most macroeconomic variables are nonstationary, it is often difficult to identify the source of the non-stationarity. In particular, it is well-known that integrated and short memory models containing trending components that may display sudden changes in their parameters share some statistical properties that make their identification a hard task. The goal of this paper is to extend the classical testing framework for I(1) versus I(0)+ breaks by considering a a more general class of models under the null hypothesis: non-stationary fractionally integrated (FI) processes. A similar identification problem holds in this broader setting which is shown to be a relevant issue from both a statistical and an economic perspective. The proposed test is developed in the time domain and is very simple to compute. The asymptotic properties of the new technique are derived and it is shown by simulation that it is very well-behaved in finite samples. To illustrate the usefulness of the proposed technique, an application using inflation data is also provided.

On the accuracy of Latin American trade statistics: A nonparametric test for 1925

This paper proposes a nonparametric test in order to establish the level of accuracy of theforeign trade statistics of 17 Latin American countries when contrasted with the trade statistics of the main partners in 1925. The Wilcoxon Matched-Pairs Ranks test is used to determine whether the differences between the data registered by exporters and importers are meaningful, and if so, whether the differences are systematic in any direction. The paper tests for the reliability of the data registered for two homogeneous products, petroleum and coal, both in volume and value. The conclusion of the several exercises performed is that we cannot accept the existence of statistically significant differences between the data provided by the exporters and the registered by the importing countries in most cases. The qualitative historiography of Latin American describes its foreign trade statistics as mostly unusable. Our quantitative results contest this view.

Market institutions and judicial rulemaking

Assuming that the degree of discretion granted to judges was the main distinguishing feature between common and civil law until the 19th century, we argue that constraining judicial discretion was instrumental in protecting freedom of contract and developing the market order in civil law. We test this hypothesis by analyzing the history of Western law. In England, a unique institutional balance between the Crown and the Parliament guaranteed private property and prompted the gradual evolution towards a legal framework that facilitated market relationships, a process that was supported by the English judiciary. On the Continent, however, legal constraints on the market were suppressed in a top-down fashion by the founders of the liberal state, often against the will of the incumbent judiciary. Constraining judicial discretion there was essential for enforcing freedom of contract and establishing the legal order of the market economy. In line with this evidence, our selection hypothesis casts doubts on the normative interpretation of empirical results that proclaim the superiority of one legal system over another, disregarding the local conditions and institutional interdependencies on which each legal system was grounded.

What is what?: A simple time-domain test of long-memory vs. structural breaks

This paper proposes a new time-domain test of a process being I(d), 0 < d = 1, under the null, against the alternative of being I(0) with deterministic components subject to structural breaks at known or unknown dates, with the goal of disentangling the existing identification issue between long-memory and structural breaks. Denoting by AB(t) the different types of structural breaks in the deterministic components of a time series considered by Perron (1989), the test statistic proposed here is based on the t-ratio (or the infimum of a sequence of t-ratios) of the estimated coefficient on yt-1 in an OLS regression of ?dyt on a simple transformation of the above-mentioned deterministic components and yt-1, possibly augmented by a suitable number of lags of ?dyt to account for serial correlation in the error terms. The case where d = 1 coincides with the Perron (1989) or the Zivot and Andrews (1992) approaches if the break date is known or unknown, respectively. The statistic is labelled as the SB-FDF (Structural Break-Fractional Dickey- Fuller) test, since it is based on the same principles as the well-known Dickey-Fuller unit root test. Both its asymptotic behavior and finite sample properties are analyzed, and two empirical applications are provided.

Comparing and validating hypothesis test procedures: Graphical and numerical tools

When the behaviour of a specific hypothesis test statistic is studied by aMonte Carlo experiment, the usual way to describe its quality is by givingthe empirical level of the test. As an alternative to this procedure, we usethe empirical distribution of the obtained \emph{p-}values and exploit itsinformation both graphically and numerically.

Level shifts in a panel data based unit root test : an application to the rate of unemployment

Several unit root tests in panel data have recently been proposed. The test developed by Harris and Tzavalis (1999 JoE) performs particularly well when the time dimension is moderate in relation to the cross-section dimension. However, in common with the traditional tests designed for the unidimensional case, it was found to perform poorly when there is a structural break in the time series under the alternative. Here we derive the asymptotic distribution of the test allowing for a shift in the mean, and assess the small sample performance. We apply this new test to show how the hypothesis of (perfect) hysteresis in Spanish unemployment is rejected in favour of the alternative of the natural unemployment rate, when the possibility of a change in the latter is considered.

Level shifts in a panel data based unit root test : an application to the rate of unemployment

Several unit root tests in panel data have recently been proposed. The test developed by Harris and Tzavalis (1999 JoE) performs particularly well when the time dimension is moderate in relation to the cross-section dimension. However, in common with the traditional tests designed for the unidimensional case, it was found to perform poorly when there is a structural break in the time series under the alternative. Here we derive the asymptotic distribution of the test allowing for a shift in the mean, and assess the small sample performance. We apply this new test to show how the hypothesis of (perfect) hysteresis in Spanish unemployment is rejected in favour of the alternative of the natural unemployment rate, when the possibility of a change in the latter is considered.