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The causal relationship between money and income (output) has been an important topic and has been extensively studied. However, those empirical studies are almost entirely on Granger-causality in the conditional mean. Compared to conditional mean, conditional quantiles give a broader picture of an economy in various scenarios. In this paper, we explore whether forecasting conditional quantiles of output growth can be improved using money growth information. We compare the check loss values of quantile forecasts of output growth with and without using past information on money growth, and assess the statistical significance of the loss-differentials. Using U.S. monthly series of real personal income or industrial production for income and output, and M1 or M2 for money, we find that out-of-sample quantile forecasting for output growth is significantly improved by accounting for past money growth information, particularly in tails of the output growth conditional distribution. On the other hand, money–income Granger-causality in the conditional mean is quite weak and unstable. These empirical findings in this paper have not been observed in the money–income literature. The new results of this paper have an important implication on monetary policy, because they imply that the effectiveness of monetary policy has been under-estimated by merely testing Granger-causality in conditional mean. Money does Granger-cause income more strongly than it has been known and therefore information on money growth can (and should) be more utilized in implementing monetary policy.

We provide straightforward new nonparametric methods for testing conditional independence using local polynomial quantile regression, allowing weakly dependent data. Inspired by Hausman's (1978) specification testing ideas, our methods essentially compare two collections of estimators that converge to the same limits under correct specification (conditional independence) and that diverge under the alternative. To establish the properties of our estimators, we generalize the existing nonparametric quantile literature not only by allowing for dependent heterogeneous data but also by establishing a weak consistency rate for the local Bahadur representation that is uniform in both the conditioning variables and the quantile index. We also show that, despite our nonparametric approach, our tests can detect local alternatives to conditional independence that decay to zero at the parametric rate. Our approach gives the first nonparametric tests for time-series conditional independence that can detect local alternatives at the parametric rate. Monte Carlo simulations suggest that our tests perform well in finite samples. We apply our test to test for a key identifying assumption in the literature on nonparametric, nonseparable models by studying the returns to schooling.

To date, the literature on quantile regression and least absolute deviation regression has assumed either explicitly or implicitly that the conditional quantile regression model is correctly specified. When the model is misspecified, confidence intervals and hypothesis tests based on the conventional covariance matrix are invalid. Although misspecification is a generic phenomenon and correct specification is rare in reality, there has to date been no theory proposed for inference when a conditional quantile model may be misspecified. In this paper, we allow for possible misspecification of a linear conditional quantile regression model. We obtain consistency of the quantile estimator for certain “pseudo-true” parameter values and asymptotic normality of the quantile estimator when the model is misspecified. In this case, the asymptotic covariance matrix has a novel form, not seen in earlier work, and we provide a consistent estimator of the asymptotic covariance matrix. We also propose a quick and simple test for conditional quantile misspecification based on the quantile residuals.

There is a growing literature in nonparametric econometrics in the recent two decades. Given the space limitation, it is impossible to survey all the important recent developments in nonparametric econometrics. Therefore, we choose to limit our focus on the following areas. In Section 2, we review the recent developments of nonparametric estimation and testing of regression functions with mixed discrete and continuous covariates. We discuss nonparametric estimation and testing of econometric models for nonstationary data in Section 3. Section 4 is devoted to surveying the literature of nonparametric instrumental variable (IV) models. We review nonparametric estimation of quantile regression models in Section 5. In Sections 2–5, we also point out some open research problems, which might be useful for graduate students to review the important research papers in this field and to search for their own research interests, particularly dissertation topics for doctoral students. Finally, in Section 6 we highlight some important research areas that are not covered in this paper due to space limitation. We plan to write a separate survey paper to discuss some of the omitted topics.

The purpose of this paper is to investigate the gender wage disparity in paid employment and self-employment. To achieve this objective, the Cameroon Household Consumption Survey of 2007 is used. The main question considered in this paper is why women paid employment and self-employment wages are relatively low. In a whole, what are the underlying factors that generate and explain wage gap between men and women householders in employment?

First, the paper uses the Oaxaca-Blinder Decomposition to explain wage gap. Thereafter, the Quantile Regression Decomposition using Machado and Mata approach is applied in order to see the gap at different levels of the wage distribution.

The main finding indicates that in both methods, the wage gap is due to an unexplained component in self-employment and explained component in paid employment, particularly with strong effects at the extreme of wage distribution.

The topic of this paper helps to explain and analyse the functioning of the Cameroonian labour market.

The findings can be applied to narrow the gender wage gap by eliminating discrimination and approving the principle of equal opportunity, support policies that reduce obstacles preventing women from starting and developing their businesses to encourage more women to become entrepreneurs and achieve harmonisation between work and family life.

Using available data survey, this paper is the first to identify and decompose the causes of paid employment and self-employment gender wage gap in Cameroon.

A number of studies have investigated the relationship between energy performance certificates (EPCs) and house prices. A majority of studies have tended to model energy performance pricing effects within a traditional hedonic conditional mean estimate model. There has been limited analysis that has accounted for the relationship between EPCs and the effects across the pricing distribution. Moreover, there has been limited research examining the “standard cost improvements EPC score”, or “potential score”. Therefore, this paper aims to quantify and measure the dynamic effects of EPCs on house prices across the price spectrum and account for standardised cost-effective retrofit improvements.

Existing EPC studies produce one coefficient for the entirety of the pricing distribution, culminating in a single marginal implicit price effect. The approach within this study applies a quantile regression approach to empirically estimate how quantiles of house prices respond differently to unitary changes in the proximal effects of EPCs and structural property characteristics across the conditional distribution of house prices. Using a data set of 1,476 achieved transaction prices, the quantile regression models apply both assessed EPC score and bands and further examine the potential EPC rating for improved energy performance based on an average energy cost improvement.

The findings show that EPCs are valued differently across the quantiles and that conditional quantiles are asymmetrical. Only property prices in the upper quantiles of the price distribution show significant capitalisation effects with energy performance, and only properties with higher EPC scores display positive significant effects at the higher end of the price distribution. There are also brown discount effects evident for lower-rated properties within F- and G-rated EPC properties at the higher end of the pricing distribution. Moreover, the potential energy efficiency rating (score) also shows increased effects with sales prices and appears to minimise any brown discount effects. The findings imply that energy performance is a complex feature that is not easily “averaged” for valuation effect purposes.

While numerous studies have investigated the pricing effects of EPCs, they have tended to provide a single estimate to determine the relationship with price. This paper extends the traditional analytical insights beyond the conditional mean estimate by examining the quantiles of the relationship between EPCs and house prices to enhance the understanding of this esoteric and complex issue. In addition, this research applies the assessed energy efficiency potential to establish whether effective cost improvements enhance the relationship with sales price and capitalisation effects.

Understanding the key locational and neighbourhood determinants and their accessibility is a topic of great interest to policymakers, planners and property valuers. In Northern Ireland, the high level of market segregation means that it is problematic to understand the nature of the relationship between house prices and the accessibility to services and prominent neighbourhood landmarks and amenities. Therefore, this paper aims to quantify and measure the (dis)amenity effects on house pricing levels within particular geographic housing sub-markets.

Most hedonic models are estimated using regression techniques which produce one coefficient for the entirety of the pricing distribution, culminating in a single marginal implicit price. This paper uses a quantile regression (QR) approach that provides a “more complete” depiction of the marginal impacts for different quantiles of the price distribution using sales data obtained from 3,780 house sales transactions within the Belfast Housing market over 2014.

The findings emerging from this research demonstrate that housing and market characteristics are valued differently across the quantile values and that conditional quantiles are asymmetrical. Pertinently, the findings demonstrate that ordinary least squares (OLS) coefficient estimates have a tendency to over or under specify the marginal mean conditional pricing effects because of their inability to adequately capture and comprehend the complex spatial relationships which exist across the pricing distribution.

Numerous studies have used OLS regression to measure the impact of key housing market externalities on house prices, providing a single estimate. This paper uses a QR approach to examine the impact of local amenities on house prices across the house price distribution.

In this article we design an econometric test for monotone comparative statics (MCS) often found in models with multiple equilibria. Our test exploits the observable implications of the MCS prediction: that the extreme (high and low) conditiona l quantiles of the dependent variable increase monotonically with the explanatory variable. The main contribution of the article is to derive a likelihood-ratio test, which to the best of our knowledge is the first econometric test of MCS proposed in the literature. The test is an asymptotic “chi-bar squared” test for order restrictions on intermediate conditional quantiles. The key features of our approach are: (1) we do not need to estimate the underlying nonparametric model relating the dependent and explanatory variables to the latent disturbances; (2) we make few assumptions on the cardinality, location, or probabilities over equilibria. In particular, one can implement our test without assuming an equilibrium selection rule.

Most epidemic transmission forecasting methods can only provide deterministic outputs. This study aims to show that probabilistic forecasting, in contrast, is suitable for stochastic demand modeling and emergency medical resource planning under uncertainty.

Two probabilistic forecasting methods, i.e. quantile regression convolutional neural network and kernel density estimation, are combined to provide the conditional quantiles and conditional densities of infected populations. The value of probabilistic forecasting in improving decision performances and controlling decision risks is investigated by an empirical study on the emergency medical resource planning for the COVID-19 pandemic.

The managerial implications obtained from the empirical results include (1) the optimization models using the conditional quantile or the point forecasting result obtain better results than those using the conditional density; (2) for sufficient resources, decision-makers' risk preferences can be incorporated to make tradeoffs between the possible surpluses and shortages of resources in the emergency medical resource planning at different quantile levels; and (3) for scarce resources, the differences in emergency medical resource planning at different quantile levels greatly decrease or disappear because of the existing of forecasting errors and supply quantity constraints.

Very few studies concern probabilistic epidemic transmission forecasting methods, and this is the first attempt to incorporate deep learning methods into a two-phase framework for data-driven emergency medical resource planning under uncertainty. Moreover, the findings from the empirical results are valuable to select a suitable forecasting method and design an efficient emergency medical resource plan.

This study aims to introduce a tree-structured linear and quantile regression framework to the analysis and modeling of equity returns, within the context of asset pricing.

The approach is based on the idea of a binary tree, where every terminal node parameterizes a local regression model for a specific partition of the data. A Bayesian stochastic method is developed including model selection and estimation of the tree structure parameters. The framework is applied on numerous U.S. asset pricing models, using alternative mimicking factor portfolios, frequency of data, market indices, and equity portfolios.

The findings reveal strong evidence that asset returns exhibit asymmetric effects and non- linear patterns to different common factors, but, more importantly, that there are multiple thresholds that create several partitions in the common factor space.

To the best of the authors' knowledge, this paper is the first to explore and apply a tree-structured and quantile regression framework in an asset pricing context.