Stochastic Dominance Tests Research Articles

A nonparametric test of [formula omitted]th-degree inverse stochastic dominance

This paper proposes a nonparametric test for mth-degree inverse stochastic dominance which is a powerful tool for ranking distribution functions according to social welfare. We construct the test based on empirical process theory. The test is shown to be asymptotically size controlled and consistent. The good finite sample properties of the test are illustrated via Monte Carlo simulations. We apply our test to the inequality growth in the United Kingdom from 1995 to 2010, and obtain a more complete ranking of the income distributions.

Tests for the first‐order stochastic dominance

AbstractWe study the first‐order stochastic dominance (SD) test in the context of two independent random samples. We introduce several test statistics that effectively capture violations of the dominance relationship, particularly in the tail regions. Additionally, we develop a resampling procedure to compute the ‐values or critical values for these tests. The proposed tests have asymptotic type I error rates for frontal configurations equal to the nominal level . Furthermore, their powers approach 1 for any fixed alternatives. Through simulation experiments, we demonstrate that our SD tests outperform the recentring test proposed by Donald and Hsu (2016) as well as the integral‐type test presented by Linton et al. (2010) in various scenarios discussed in existing literature. We also employ the proposed tests to analyze changes in the distribution of household income in the United Kingdom over time. The proposed tests offer some insights into potential dominance relationships within this context.

Too-systemic-to-fail: Empirical comparison of systemic risk measures in the Eurozone financial system

This paper quantifies the Too-Systemic-To-Fail (TSTF) paradigm in the Eurozone since the introduction of the Euro through three primary dimensions: Too-Big-To-Fail (TBTF), Too-Interconnected-To-Fail (TITF), and Too-Many-To-Fail (TMTF). We apply prominent systemic risk measures based on public data, including the Granger-causality network (GCN), Delta Conditional Value-at-Risk (ΔCoVaR), Marginal Expected Shortfall (MES), and Systemic Risk Index (SRISK). Financial interconnectedness and systemic risk exposure within the 17-member states of the Eurozone are measured on two levels: (i) identifying which financial sectors (banking, diversified financials, insurance, and real estate) are most exposed to systemic risk in the Eurozone at the union level; and (ii) identifying which member state is most exposed to systemic risk within each financial sector at the country level. We extend the original ΔCoVaR, MES and SRISK models by incorporating the bootstrap Kolmogorov-Smirnov stochastic dominance test to rank institutions based on their exposure to systemic risk formally.

Exploring skill distribution tails through stochastic dominance

SummaryLocation choices of differently skilled workers are analyzed in previous work on labor mobility, which proposes a model that suggests thicker tails in the skill distributions of large cities. This paper replicates the empirical findings of this work by using quantile regression and density plots as employed in the existing study, while also suggesting an alternative testing method for thick tails in the form of an initial stochastic dominance test. The test reveals clear evidence of a thicker lower tail, but the results are less clear for the upper tail, which raises some questions on how to best handle extreme upper tails of skill distributions.

Utility of inequality sensitive measures of the gender wage gap: Evidence from South Africa

We examine the trend in the gender wage gap in South Africa taking into consideration the high level of general inequality in the country. To do this, we utilize the information-theoretic approach of the Generalised Entropy (GE) measures of divergence supplemented by stochastic dominance analysis and tests. Under this approach, male and female wage distributions are summarized by suitable evaluation functions and then the difference between the evaluations is computed. Unlike conventional measures of the gender wage gap based on the mean and quantiles, this approach does not assume rank invariance and makes explicit the evaluation functions used. We find that the rate of convergence of the gender wage gap depends on the measure used to aggregate the gap across the entire distribution. Comparison of the aggregate measures of the gender wage gap (mean, median and the entropy measure) reveals that the convergence of the gender wage gap is faster under the entropy measure. This is because unlike the mean, the entropy measure captures the dispersion of wages across individuals. Stochastic dominance test results reveal that male wages dominate female wages mostly in the second-order sense i.e., only for evaluation functions that are increasing in wages and concave. Finally, decomposition results show that across measures, the persistent gender wage gap is attributable to wage structure effects as opposed to composition effects. Therefore, to effectively address the persistent gender wage gap in the middle of the income distribution, policies should be geared towards the returns to characteristics at the median. The implication of these findings is that measures of the gender wage gap that ignore the overall inequality are likely to skew the estimate of the gender wage gap.

New evidence on crude oil market efficiency

AbstractThis paper examines the Efficient Market Hypothesis (EMH) in crude oil amid the “financialization of commodity markets” and the “fracking revolution”. It applies the generalized spectral derivative test (Hong and Lee 2005) on both West Texas Intermediate and Brent spot and futures markets, alongside a stochastic dominance test (Linton et al., 2005) to investigate arbitrage opportunities across markets and benchmarks. The findings indicate that financialization has made each market more efficient but also created more arbitrage opportunities in spot‐futures markets at both benchmarks. The fracking revolution has fragmented oil markets but had little impact on EMH in individual markets or across markets.

Trading time seasonality in electricity futures

Trading time seasonality reflects the seasonal behavior of futures prices with the same time of maturity. Hence, it differs from classical seasonality, which reflects seasonal behavior induced by the spot price observed for varying maturities. This type of seasonality is linked to the pricing kernel which in turn accounts for seasonal changes in preferences of agents and tied to risk aversion and thus the demand for hedging. In the present study we empirically examine trading time seasonality in yearly Nordic and German electricity futures contracts. Visual inspection of both average monthly futures prices and the futures backward curves provides strong indications of futures prices systematically varying over the trading year. On average both Nordic and German futures prices are lowest in first quarter and highest in third quarter trading months. This is confirmed by statistical tests of stochastic dominance. Exploiting this insight in a simple trading strategy induces positive and significant alphas in the sense of the capital asset pricing model. We relate the findings to potential seasonal risk preferences and hedging pressure in the electricity futures market.

Testing for the presence of treatment effect under selection on observables

The evaluation of the possible effects of a treatment on an outcome plays a central role in both theoretical and applied statistical and econometrical literature. This paper focuses on nonparametric tests for possible difference in the distribution of potential outcomes due to receiving or not receiving a treatment. The approach is based on weighting observed data on the basis on the estimated propensity score. Kolmogorov–Smirnov type and Wilcoxon–Mann–Whitney type tests are constructed, and their limiting distributions are studied. Rejection regions are obtained by inverting confidence intervals. This involves the study of appropriate estimators of the limiting variance of test statistics. Approximations of quantiles via subsampling are also considered. The merits of the different tests are studied by Monte Carlo simulation. An application to the construction of tests for stochastic dominance is provided.

Testing for time stochastic dominance

We propose nonparametric tests for the null hypothesis of time stochastic dominance. Time stochastic dominance makes a partial order of different prospects over time based on the net present value criteria for general utility and time discount function classes. For example, time stochastic dominance can be used for ranking investment strategies or environmental policies based on the expected net present value of the future benefits. We consider an Lp-type test statistic and derive its large sample distribution under standard panel data sampling scheme with fixed time dimension. We suggest a path-wise (or cluster) bootstrap procedure that allows individual time series dependence over the time horizon. We describe two approaches, the contact-set approach and the numerical delta method, that may lead to enhanced power compared to the conventional least-favorable-case based approach. We prove the asymptotic validity of our testing procedures. We investigate the finite sample performance of the tests in simulation studies. As an illustration, we apply the proposed tests to evaluate the Million Baht Village Fund Program in Thailand and carbon emission trading scheme in China.

Tests of stochastic dominance with repeated measurements data

The paper explores a testing problem which involves four hypotheses, that is, based on observations of two random variables X and Y, we wish to discriminate between four possibilities: identical survival functions, stochastic dominance of X over Y, stochastic dominance of Y over X, or crossing survival functions. Four-decision testing procedures for repeated measurements data are proposed. The tests are based on a permutation approach and do not rely on distributional assumptions. One-sided versions of the Cramér–von Mises, Anderson–Darling, and Kolmogorov–Smirnov statistics are utilized. The consistency of the tests is proven. A simulation study shows good power properties and control of false-detection errors. The suggested tests are applied to data from a psychophysical experiment.

Improved inference for vaccine-induced immune responses via shape-constrained methods

We study the performance of shape-constrained methods for evaluating immune response profiles from early-phase vaccine trials. The motivating problem for this work involves quantifying and comparing the IgG binding immune responses to the first and second variable loops (V1V2 region) arising in HVTN 097 and HVTN 100 HIV vaccine trials. We consider unimodal and log-concave shape-constrained methods to compare the immune profiles of the two vaccines, which is reasonable because the data support that the underlying densities of the immune responses could have these shapes. To this end, we develop novel shape-constrained tests of stochastic dominance and shape-constrained plug-in estimators of the squared Hellinger distance between two densities. Our techniques are either tuning parameter free, or rely on only one tuning parameter, but their performance is either better (the tests of stochastic dominance) or comparable with the nonparametric methods (the estimators of the squared Hellinger distance). The minimal dependence on tuning parameters is especially desirable in clinical contexts where analyses must be prespecified and reproducible. Our methods are supported by theoretical results and simulation studies.

A stochastic dominance test under survey nonresponse with an application to comparing trust levels in Lebanese public institutions

Stochastic dominance comparisons of distributions based on ordinal data arise in many areas of economics. This paper develops a testing procedure for such comparisons under survey sampling from large finite populations with nonresponse using the worst-case bounds of the distributions. The advantage of using these bounds in distributional comparisons is that conclusions are robust to the nature of the nonresponse-generating mechanism. While these bounds on the distributions are often too wide in practice, we show that they can be informative for distributional comparisons in an empirical analysis. This paper examines the dynamics of trust in Lebanese public institutions using the 2013 wave of the World Values Survey as well as the 2016 and 2018 waves of the Arab Barometer, and finds convincing evidence of a decrease in confidence in most public institutions between 2013 and 2016.

Estimation and inference for the counterfactual distribution and quantile functions in continuous treatment models

Donald and Hsu (2014) studied the estimation and inference for the counterfactual distribution and quantile functions in a binary treatment model. We extend their work to the continuous treatment model. Specifically, we propose a weighted regression estimator for the counterfactual distribution but we estimate the weighting function from a covariate balancing equation by maximizing a globally concave criterion function. We estimate the quantile function by inverting the estimated counterfactual distribution. To test the distributional effect, we consider the (uniform) confidence bands, the sup and L2 distance, and the Mann–Whitney test. We also consider the stochastic dominance test for the distributional effect and the L2 test for constant quantiles. A simulation study reveals that our tests exhibit a satisfactory finite-sample performance, and an application shows their practical value.

An improved bootstrap test for restricted stochastic dominance

Bootstrap Testing for restricted stochastic dominance of a pre-specified order between two distributions is of interest in many areas of economics. This paper develops a new method for improving the performance of such tests that employ a moment selection procedure: tilting the empirical distribution in the moment selection procedure. We propose that the amount of tilting be chosen to maximize the empirical likelihood subject to the restrictions of the null hypothesis, which are a continuum of unconditional moment inequality conditions. We characterize sets of population distributions on which a modified test is (i) asymptotically equivalent to its non-modified version to first-order, and (ii) superior to its non-modified version according to local power when the sample size is large enough. We report simulation results that show the modified versions of leading tests are noticeably less conservative than their non-modified counterparts and have improved power. Finally, an empirical example is discussed to illustrate the proposed method.

Should investors include bitcoin in their portfolio? New evidence from a bootstrap-based stochastic dominance approach

ABSTRACT This paper investigates the potential portfolio diversification benefits by introducing the Bitcoin to the traditional diversified financial portfolio. Using a bootstrap-based stochastic dominance (SD) test and daily prices of the commodity and stock market indices, we find that the introduction of Bitcoin improves the performance of the traditional financial portfolio and the optimal portfolio choice changes according to the market regime. Principally, results show that the optimal portfolio diversification combining Bitcoin, US stock market and commodities indices can be a good hedge, offering risk-averse, more performing portfolio investments during any financial crisis.

Testing for Stochastic Dominance up to a Common Relative Poverty Line

Although a wide array of stochastic dominance tests exist for poverty measurement and identification, they assume the income distributions have independent poverty lines or a common absolute (fixed) poverty line. We propose a stochastic dominance test for comparing income distributions up to a common relative poverty line (i.e., some fraction of the pooled median). A Monte Carlo study demonstrates its superior performance over existing methods in terms of power. The test is then applied to some Canadian household survey data for illustration.

Stochastic dominance tests

We develop stochastic dominance tests of a given prospect compared with multiple choice alternatives. We account for all types of preferences. The tests are formulated in terms of linear as well as MIP models, and developed based on bayesian analysis, which relies on novel Markov Chain Monte Carlo procedures. Empirical results indicate that the market portfolio is Prospect stochastic dominance optimal. This implies that there are S-shaped utility functions that rationalize the market portfolio.

Assessing Deprivation with an Ordinal Variable: Theory and Application to Sanitation Deprivation in Bangladesh

AbstractThe challenges associated with poverty measurement using a cardinal variable have received much attention over the past four decades, but there is a dearth of literature on how to meaningfully assess poverty with an ordinal variable. This article proposes a class of simple, intuitive, and policy-relevant poverty measures for ordinal variables. The measures are sensitive to the depth of deprivations, unlike the headcount ratio. Moreover, under appropriate restrictions, the measures ensure that priority is given to the poorest among the poor when targeting, monitoring, and evaluating poverty alleviation programs. To assess the robustness of poverty comparisons to alternative choices of parameters, the article develops various stochastic dominance tests (some of which are novel contributions to the stochastic dominance literature). The empirical illustration documenting changes in sanitation deprivation in Bangladesh showcases the measures’ ability to identify instances in which overall sanitation deprivation improved while leaving the poorest behind.

Four-decision tests for stochastic dominance, with an application to environmental psychophysics

If the survival function of a random variable X lies to the right of the survival function of a random variable Y, then X is said to stochastically dominate Y. Inferring stochastic dominance is particularly complicated because comparing survival functions raises four possible hypotheses: identical survival functions, dominance of X over Y, dominance of Y over X, or crossing survival functions. In this paper, we suggest four-decision tests for stochastic dominance suitable for paired samples. The tests are permutation-based and do not rely on distributional assumptions. One-sided Cramér–von Mises and Kolmogorov–Smirnov statistics are employed but the general idea may be utilized with other test statistics. The power to detect dominance and the different types of wrong decisions are investigated in an extensive simulation study. The proposed tests are applied to data from an experiment concerning the individual’s willingness to pay for a given environmental improvement.

Inference on distribution functions under measurement error

This paper is concerned with inference on the cumulative distribution function (cdf) FX∗ in the classical measurement error model X=X∗+ϵ. We consider the case where the density of the measurement error ϵ is unknown and estimated by repeated measurements, and show validity of a bootstrap approximation for the distribution of the deviation in the sup-norm between the deconvolution cdf estimator and FX∗. We allow the density of ϵ to be ordinary or super smooth. We also provide several theoretical results on the bootstrap and asymptotic Gumbel approximations of the sup-norm deviation for the case where the density of ϵ is known. Our approximation results are applicable to various contexts, such as confidence bands for FX∗ and its quantiles, and for performing various cdf-based tests such as goodness-of-fit tests for parametric models of X∗, two sample homogeneity tests, and tests for stochastic dominance. Simulation and real data examples illustrate satisfactory performance of the proposed methods.