Unconditional Distribution Research Articles

Housing and Income Inequality in Europe: Distributional Effects of Non‐Cash Income From Imputed Rents

This article uses survey data to estimate non‐cash income from imputed rents, using a consistent methodology for all countries to assemble comparable statistics that allow for a valid inter‐country comparison. We can confirm a significant impact of non‐cash income and find an inequality‐decreasing effect for the unconditional income distribution which highly correlates with the proportion of owner‐occupiers in the respective countries. However, aggregated inequality measures are not suited to analyze the increase in the conditional income inequality between owner‐occupiers and renters, who do not obtain income from imputed rents by definition. Therefore, we apply a reweighting decomposition that controls for the heterogeneous housing characteristics among European countries and allows us to decompose the distributional changes into a part that is explained by the proportion of tenure types and household size and a remaining part that reflects the relative dispersion of imputed rents along the income distribution.

Non‐base compensation and the gender pay gap

AbstractThis paper investigates whether non‐base compensation contributes to the gender pay gap (GPG). Using administrative data from Germany, we find in wage decompositions that lower bonus payments to women explain about 10 per cent of the gap at the mean and at different quantiles of the unconditional wage distribution whereas the lower prevalence of shift premia and overtime pay among women is unimportant. Among managers, the contribution of bonuses to the mean gap more than doubles and is steadily rising as one moves up the wage distribution. Our findings suggest that gender differences in bonuses are an important contributor to the GPG, particularly in top jobs.

Design and implementation of distribution-free Phase-II charting schemes based on unconditional run-length percentiles

Traditionally, the mean of the run-length distribution (ARL) of an in-control (IC) process is used to design and implement statistical process charting schemes. When standards are unknown (Case U), the unconditional ARL is considered during Phase-II monitoring—surprisingly, by suppressing the term “unconditional.” The literature has recently highlighted the difference between the unconditional and the conditional ARL in studying the properties of Phase-II charting schemes under the Case U. The effects of bias in the Phase-I sample may lead to remarkably high rates of early false alarms. We explore the idea of restricting the probability of unconditional early false alarms by using lower percentile points of the unconditional run-length distribution to design nonparametric charting schemes. This new approach is named “the lower percentile-based (LPL) design.” We consider the design and implementation of six distribution-free schemes: five precedence-type schemes and the rank-sum scheme. We carry out simulations to compare the six schemes with a prefixed value of some lower percentile point of the IC run-length distribution. The best scheme is the one with the lowest value for a specific higher percentile point of the out-of-control run-length distribution. We illustrate the new design and implementation strategies with real data, and offer a summary and concluding remarks.

Scientific discussion on the essence of state financial regulation of socio-economic inequality in modern conditions

The article is devoted to the analysis of contemporary problems and peculiarities of regulating socio-economic inequality during the crisis and describes the financial crises’ impact mechanism on the state financial regulation evolution of economic inequality.In times of economic crises developed countries make unconditional distributions of money transfers to households to stimulate demand. New liquidity is distributed across the world economy, launching inflationary processes against the backdrop of significant problems with the supply of raw materials and materials due to the consequences of the COVID-19 pandemic. Public interest to the problem of growing socio-economic inequality is increasing along with the rise in the number of dollar millionaires and the financial assets prices. In many ways, this phenomenon is associated with the financial regulation specifics of the economy during times of crises.As a result of the study, the specifics and paradoxes of modern state financial regulation of economic inequality during times of crises have been substantiated, recommendations for state financial regulation of socio-economic inequality during the crisis have been formulated. Regulators should pay particular attention to the top 10 % of the population, for whom there are now many opportunities for tax optimisation and avoidance, with the result that even theoretically effective progressive tax systems do not work properly in practice. Developed countries should promote international tax cooperation to solve this problem, and developing countries should focus on improving their progressive tax systems.

How heterogeneous is the impact of energy efficiency on dwelling prices? Evidence from the application of the unconditional quantile hedonic model to the Portuguese residential market

This paper studies the impact of energy efficiency on the unconditional distribution of residential property prices in Portugal. Using a dataset of more than 256,000 residential property sales from 2009 to 2013, a period that covers an economic depression, unconditional quantile regression analysis reveals that the responsiveness to energy efficiency improvements is different not only as we move from low- to high-priced residential units but also between apartments and houses. While apartments show a downward trend in the magnitude of energy efficiency coefficient estimates, the opposite occurs for houses. This last property type exhibits clear price discounts at the lowest quantiles of the price distribution, something that is not observable through conditional mean and quantile regression analysis. Our results suggest the existence of a different level of responsiveness to energy efficiency improvements in the Lisbon region when compared to the rest of the country and that the impact of the Energy Performance Certificate label increases throughout time across all price quantiles. As a by-product of this paper, an unconditional quantile price index shows how the impact of the crisis was not the same across different market segments, with more severe price decreases for low- than high-priced properties.

Quantile Mixed Hidden Markov Models for Multivariate Longitudinal Data: An Application to Children's Strengths and Difficulties Questionnaire Scores

AbstractThe identification of factors associated with mental and behavioural disorders in early childhood is critical both for psychopathology research and the support of primary health care practices. Motivated by the Millennium Cohort Study, in this paper we study the effect of a comprehensive set of covariates on children's emotional and behavioural trajectories in England. To this end, we develop a quantile mixed hidden Markov model for joint estimation of multiple quantiles in a linear regression setting for multivariate longitudinal data. The novelty of the proposed approach is based on the multivariate asymmetric Laplace distribution which allows to jointly estimate the quantiles of the univariate conditional distributions of a multivariate response, accounting for possible correlation between the outcomes. Sources of unobserved heterogeneity and serial dependency due to repeated measures are modelled through the introduction of individual-specific, time-constant random coefficients and time-varying parameters evolving over time with a Markovian structure respectively. The inferential approach is carried out through the construction of a suitable expectation–maximization algorithm without parametric assumptions on the random effects distribution.

Interpolation of Quantile Regression to Estimate Driver’s Risk of Traffic Accident Based on Excess Speed

Quantile regression provides a way to estimate a driver’s risk of a traffic accident by means of predicting the percentile of observed distance driven above the legal speed limits over a one year time interval, conditional on some given characteristics such as total distance driven, age, gender, percent of urban zone driving and night time driving. This study proposes an approximation of quantile regression coefficients by interpolating only a few quantile levels, which can be chosen carefully from the unconditional empirical distribution function of the response. Choosing the levels before interpolation improves accuracy. This approximation method is convenient for real-time implementation of risky driving identification and provides a fast approximate calculation of a risk score. We illustrate our results with data on 9614 drivers observed over one year.

Interval Privacy: A Framework for Privacy-Preserving Data Collection

The emerging public awareness and government regulations of data privacy motivate new paradigms of collecting and analyzing data that are transparent and acceptable to data owners. We present a new concept of privacy and corresponding data formats, mechanisms, and theories for privatizing data during data collection. The privacy, named Interval Privacy, enforces the raw data conditional distribution on the privatized data to be the same as its unconditional distribution over a nontrivial support set. Correspondingly, the proposed privacy mechanism will record each data value as a random interval (or, more generally, a range) containing it. The proposed interval privacy mechanisms can be easily deployed through survey-based data collection interfaces, e.g., by asking a respondent whether its data value is within a randomly generated range. Another unique feature of interval mechanisms is that they obfuscate the truth but do not perturb it. Using narrowed range to convey information is complementary to the popular paradigm of perturbing data. Also, the interval mechanisms can generate progressively refined information at the discretion of individuals, naturally leading to privacy-adaptive data collection. We develop different aspects of theory such as composition, robustness, distribution estimation, and regression learning from interval-valued data. Interval privacy provides a new perspective of human-centric data privacy where individuals have a perceptible, transparent, and simple way of sharing sensitive data.

The Unconditional Probability Distribution of Future Emission and Temperatures

The Unconditional Probability Distribution of Future Emission and Temperatures

The distributional impact of the Sierra Leone conflict on household welfare

Abstract This study examines the impact of the Sierra Leone civil war on household expenditure inequality. The paper exploits three rounds of household survey data for Sierra Leone in an attempt to estimate the impact of the conflict on the distribution of household welfare over both short-run and long-run periods. The empirical approach uses RIF measures based on the Gini index and also provides estimates of treatment effects at selected quantiles of the unconditional household expenditure distribution. The key findings reveal that localities subject to a protracted period of occupation by rebel forces experienced a sharp reduction in household expenditure inequality in the immediate aftermath of the conflict with most of the contraction evident at the top end of the distribution.

Probabilistic Forecasting of Regional Net-Load With Conditional Extremes and Gridded NWP

The increasing penetration of embedded renewables makes forecasting net-load, consumption less embedded generation, a significant and growing challenge. Here a framework for producing probabilistic forecasts of net-load is proposed with particular attention given to the tails of predictive distributions, which are required for managing risk associated with low-probability events. Only small volumes of data are available in the tails, by definition, so estimation of predictive models and forecast evaluation requires special attention. We propose a solution based on a best-in-class load forecasting methodology adapted for net-load, and model the tails of predictive distributions with the Generalised Pareto Distribution, allowing its parameters to vary smoothly as functions of covariates. The resulting forecasts are shown to be calibrated and sharper than those produced with unconditional tail distributions. In a use-case inspired evaluation exercise based on reserve setting, the conditional tails are shown to reduce the overall volume of reserve required to manage a given risk. Furthermore, they identify periods of high risk not captured by other methods. The proposed method therefore enables user to both reduce costs and avoid excess risk.

Childbearing and the distribution of the reservation price of fertility: The case of the Korean baby bonus program

We study the fertility effects of a Korean pro-natalist policy. We show that using the same assumptions and the same binary-choice models used in this literature, and we can estimate the entire unconditional distribution of the reservation price of fertility, which is the minimal compensation an agent must receive to induce her to have a (or an additional) child. Our estimates show that the program’s benefit level and budget would have to be orders of magnitude (about 15 times) larger for the program to bring South Korea back to desired levels of fertility. We also found that over 74% of the program’s expenditures are associated with infra-marginal births – these are births that would have occurred even in the absence of the financial incentive. We show that this is likely not a unique characteristic of the Korean pro-natalist policy but instead a problem of most programs of this nature.

On the exact distributions of the maximum of the asymmetric telegraph process

In this paper we present the distribution of the maximum of the asymmetric telegraph process in an arbitrary time interval [0,t] under the conditions that the initial velocity V(0) is either c1 or −c2 and the number of changes of direction is odd or even. For the case V(0)=−c2 the singular component of the distribution of the maximum displays an unexpected cyclic behavior and depends only on c1 and c2, but not on the current time t. We obtain also the unconditional distribution of the maximum for either V(0)=c1 or V(0)=−c2 and its expression has the form of series of Bessel functions. We also show that all the conditional distributions emerging in this analysis are governed by generalized Euler–Poisson–Darboux equations. We recover all the distributions of the maximum of the symmetric telegraph process as particular cases of the present paper.We underline that it rarely happens to obtain explicitly the distribution of the maximum of a process. For this reason the results on the range of oscillations of a natural process like the telegraph model make it useful for many applications.

Impacts of a Gender Ratio Change on China’s Wage Income Distributions

ABSTRACT This study examines the possible effects of a gender ratio change on China’s wage income distributions with the unconditional quantile estimation. Using data from the China Health and Nutrition Survey for 1989–2011, the unconditional wage income distributions before and after a change in gender ratio are studied graphically. The estimated wage income density functions are confirmed to be skewed to the right and leptokurtic. An increase in gender ratio increases wage income and mitigate wage income inequality. We conclude that, other things being equal, the decreasing trend in gender ratio will enhance the wage income inequality.

Conditional Monte Carlo revisited

AbstractConditional Monte Carlo refers to sampling from the conditional distribution of a random vector given the value for a function . Classical conditional Monte Carlo methods were designed for estimating conditional expectations of functions by sampling from unconditional distributions obtained by certain weighting schemes. The basic ingredients were the use of importance sampling and change of variables. In the present paper we reformulate the problem by introducing an artificial parametric model in which is a pivotal quantity, and next representing the conditional distribution of given within this new model. The approach is illustrated by several examples, including a short simulation study and an application to goodness‐of‐fit testing of real data. The connection to a related approach based on sufficient statistics is briefly discussed.

Probabilistic forecasting of maximum human lifespan by 2100 using Bayesian population projections.

We consider the problem of quantifying the human lifespan using a statistical approach that probabilistically forecasts the maximum reported age at death (MRAD) through 2100. We seek to quantify the probability that any person attains various extreme ages, such as those above 120, by the year 2100. We use the exponential survival model for supercentenarians (people over age 110) of Rootzén and Zholud (2017) but extend the forecasting window, quantify population uncertainty using Bayesian population projections, and incorporate the most recent data from the International Database on Longevity (IDL) to obtain unconditional estimates of the distribution of MRAD this century in a fully Bayesian analysis. We find that the exponential survival model for supercentenarians is consistent with the most recent IDL data and that projections of the population aged 110-114 through 2080 are sensible. We integrate over the posterior distributions of the exponential model parameter and uncertainty in the supercentenarian population projections to estimate an unconditional distribution of MRAD by 2100. Based on the Bayesian analysis, there is a greater than 99% probability that the current MRAD of 122 will be broken by 2100. We estimate the probabilities that a person lives to at least age 126,128, or 130 this century, as 89%, 44%, and 13%, respectively. We have updated the supercentenarian survival model of Rootzén and Zholud using the most recent IDL data, incorporated Bayesian population projections, and extended the forecasting window to create the first fully Bayesian and unconditional probabilistic projection of MRAD by 2100.

Asymmetric dependence of intraday frequency components in the Brazilian stock market.

The multivariate dependence plays an important role in financial instrument management. Due to the inherent characteristics in the financial market, such as heavy tails in the returns unconditional distribution and asymmetry between gain and loss, we obtained the asymmetric dependence structure in different short-term variation scales based on the wavelet technique MODWT. The study sought to capture the relations between financial returns represented by its frequency components. Intraday returns series was used in the 15-min sampling interval from stocks and applied the D-Vine pair-copula to decompose in trade frequencies of 15 min, 1 h, 1 day, and 1 week with margin adjustments of ARIMA-APARCH class and BB7 copula function, responsible for measuring the dependence on tails. The results indicated the prevalence of a high dependence during market upturns, rising over the analyzed frequencies. Being an important tool in financial management and allowing short-term strategies of diversification.

GATT/WTO membership–poverty nexus: An unconditional quantile regression approach

AbstractThis paper uses unconditional quantile regression methods to evaluate the incidence of GATT/WTO membership on poverty in countries with different poverty rates. My results suggest that GATT/WTO membership increases significantly poverty across the entire unconditional distribution of poverty. Countries with the highest poverty rates incur larger poverty increases after joining GATT/WTO than countries with lower poverty rates. However, the results point out heterogeneity among countries depending on the reforms carried upon GATT/WTO membership. The results indicate that countries that conducted extensive policy reforms and were not subject to Article XXVI 5(c) are associated with poverty reduction. Also, by splitting the sample into groups of countries that have and do not have a comparative advantage in agriculture, I find that countries with lower poverty rates that are net exporters of agricultural products experience poverty reduction, whereas poverty increases in net importing countries across poverty quantiles. These results are robust across different unconditional quantile regression methods and to the selection bias.

Simultaneous inference for Kendall’s tau

We introduce multiple contrast tests and simultaneous confidence intervals for rank correlation measures in general multivariate factorial designs. To this end, we derive the unconditional asymptotic joint sampling distribution of multiple correlation coefficients under the null and arbitrary alternatives. We neither require distributions to be discrete nor continuous and adjust for ties using a normalized version of the bivariate distribution function and scale point estimators appropriately to obtain Kendall’s τA and τB, Somers’ D, and Goodman and Kruskal’s γ. Simulation studies for a range of scenarios indicate that the proposed methods control the family wise error rate in the strong sense even when sample sizes are rather small. A case study on the iris flower data set demonstrates how to perform inference in practice.

On the distribution of the maximum of the telegraph process

In this paper we present the distribution of the maximum of the telegraph process in the cases where the initial velocity is positive or negative with an even and an odd number of velocity reversals. For the telegraph process with positive initial velocity a reflection principle is proved to be valid while in the case of an initial leftward displacement the conditional distributions are perturbed by a positive probability of never visiting the half positive axis. Various relationships are established among the mentioned four classes of conditional distributions of the maximum. The unconditional distributions of the maximum of the telegraph process are obtained for positive and negative initial steps as well as their limiting behaviour. Furthermore the cumulative distributions and the general moments of the conditional maximum are presented.