Econometrics — Open Access Journal

Value-at-Risk (VaR) has become the most important benchmark for measuring risk in portfolios of different types of financial instruments. However, as reported by many authors, estimating VaR is subject to a high level of uncertainty. One of the sources of uncertainty stems from the dependence of the VaR estimation on the choice of the computation method. As we show in our experiment, the lower the number of samples, the higher this dependence. In this paper, we propose a new nonparametric approach called maxitive kernel estimation of the VaR. This estimation is based on a coherent extension of the kernel-based estimation of the cumulative distribution function to convex sets of kernel. We thus obtain a convex set of VaR estimates gathering all the conventional estimates based on a kernel belonging to the above considered convex set. We illustrate this method in an empirical application to daily stock returns. We compare the approach we propose to other parametric and nonparametric approaches. In our experiment, we show that the interval-valued estimate of the VaR we obtain is likely to lead to more careful decision, i.e., decisions that cannot be biased by an arbitrary choice of the computation method. In fact, the imprecision of the obtained interval-valued estimate is likely to be representative of the uncertainty in VaR estimate. Full article

In this paper, we borrow some of the key concepts of nonequilibrium statistical systems, to develop a framework for analyzing a self-organizing-optimizing system of independent interacting agents, with nonlinear dynamics at the macro level that is based on stochastic individual behavior at the micro level. We demonstrate the use of entropy-divergence methods and micro income data to evaluate and understand the hidden aspects of stochastic dynamics that drives macroeconomic behavior systems and discuss how to empirically represent and evaluate their nonequilibrium nature. Empirical applications of the information theoretic family of power divergence measures-entropic functions, interpreted in a probability context with Markov dynamics, are presented. Full article

In this paper, we investigate several variable selection procedures to give an overview of the existing literature for practitioners. “Let the data speak for themselves” has become the motto of many applied researchers since the number of data has significantly grown. Automatic model selection has been promoted to search for data-driven theories for quite a long time now. However, while great extensions have been made on the theoretical side, basic procedures are still used in most empirical work, e.g., stepwise regression. Here, we provide a review of main methods and state-of-the art extensions as well as a topology of them over a wide range of model structures (linear, grouped, additive, partially linear and non-parametric) and available software resources for implemented methods so that practitioners can easily access them. We provide explanations for which methods to use for different model purposes and their key differences. We also review two methods for improving variable selection in the general sense. Full article

A standard test for weak instruments compares the first-stage F-statistic to a table of critical values obtained by Stock and Yogo (2005) using simulations. We derive a closed-form solution for the expectation from which these critical values are derived, as well as present some second-order asymptotic approximations that may be of value in the presence of multiple endogenous regressors. Inspection of this new result provides insights not available from simulation, and will allow software implementations to be generalised and improved. Finally, we explore the calculation of p-values for the first-stage F-statistic weak instruments test. Full article

This paper provides a new statistical model for repeated voluntary contribution mechanism games. In a repeated public goods experiment, contributions in the first round are cross-sectionally independent simply because subjects are randomly selected. Meanwhile, contributions to a public account over rounds are serially and cross-sectionally correlated. Furthermore, the cross-sectional average of the contributions across subjects usually decreases over rounds. By considering this non-stationary initial condition—the initial contribution has a different distribution from the rest of the contributions—we model statistically the time varying patterns of the average contribution in repeated public goods experiments and then propose a simple but efficient method to test for treatment effects. The suggested method has good finite sample performance and works well in practice. Full article

This paper draws upon influence function regression methods to determine where foreign workers stand in the distribution of private sector wages in Luxembourg, and assess whether and how much their wages contribute to wage inequality. This is quantified by measuring the effect that a marginal increase in the proportion of foreign workers—foreign residents or cross-border workers—would have on selected quantiles and measures of inequality. Analysis of the 2006 Structure of Earnings Survey reveals that foreign workers have generally lower wages than natives and therefore tend to haul the overall wage distribution downwards. Yet, their influence on wage inequality reveals small and negative. All impacts are further muted when accounting for human capital and, especially, job characteristics. Not observing any large positive inequality contribution on the Luxembourg labour market is a striking result given the sheer size of the foreign workforce and its polarization at both ends of the skill distribution. Full article

In forecasting a variable (forecast target) using many predictors, a factor model with principal components (PC) is often used. When the predictors are the yield curve (a set of many yields), the Nelson–Siegel (NS) factor model is used in place of the PC factors. These PC or NS factors are combining information (CI) in the predictors (yields). However, these CI factors are not “supervised” for a specific forecast target in that they are constructed by using only the predictors but not using a particular forecast target. In order to “supervise” factors for a forecast target, we follow Chan et al. (1999) and Stock and Watson (2004) to compute PC or NS factors of many forecasts (not of the predictors), with each of the many forecasts being computed using one predictor at a time. These PC or NS factors of forecasts are combining forecasts (CF). The CF factors are supervised for a specific forecast target. We demonstrate the advantage of the supervised CF factor models over the unsupervised CI factor models via simple numerical examples and Monte Carlo simulation. In out-of-sample forecasting of monthly US output growth and inflation, it is found that the CF factor models outperform the CI factor models especially at longer forecast horizons. Full article

We propose and study the stochastic stationary root model. The model resembles the cointegrated VAR model but is novel in that: (i) the stationary relations follow a random coefficient autoregressive process, i.e., exhibhits heavy-tailed dynamics, and (ii) the system is observed with measurement error. Unlike the cointegrated VAR model, estimation and inference for the SSR model is complicated by a lack of closed-form expressions for the likelihood function and its derivatives. To overcome this, we introduce particle filter-based approximations of the log-likelihood function, sample score, and observed Information matrix. These enable us to approximate the ML estimator via stochastic approximation and to conduct inference via the approximated observed Information matrix. We conjecture the asymptotic properties of the ML estimator and conduct a simulation study to investigate the validity of the conjecture. Model diagnostics to assess model fit are considered. Finally, we present an empirical application to the 10-year government bond rates in Germany and Greece during the period from January 1999 to February 2018. Full article

This paper proposes an approach to measure the extent of nonlinearity of the exposure of a financial asset to a given risk factor. The proposed measure exploits the decomposition of a conditional expectation into its linear and nonlinear components. We illustrate the method with the measurement of the degree of nonlinearity of a European style option with respect to the underlying asset. Next, we use the method to identify the empirical patterns of the return-risk trade-off on the SP500. The results are strongly supportive of a nonlinear relationship between expected return and expected volatility. The data seem to be driven by two regimes: one regime with a positive return-risk trade-off and one with a negative trade-off. Full article

We use a cointegrated structural vector autoregressive model to investigate the relation between monetary policy in the euro area and the stock market. Since there may be an instantaneous causal relation, we consider long-run identifying restrictions for the structural shocks and also used (conditional) heteroscedasticity in the residuals for identification purposes. Heteroscedasticity is modelled by a Markov-switching mechanism. We find a plausible identification scheme for stock market and monetary policy shocks which is consistent with the second-order moment structure of the variables. The model indicates that contractionary monetary policy shocks lead to a long-lasting downturn of real stock prices. Full article

Econometric analysis requires filtering techniques that are adapted to cater to data sequences that are short and that have strong trends. Whereas the economists have tended to conduct their analyses in the time domain, the engineers have emphasised the frequency domain. This paper places its emphasis in the frequency domain; and it shows how the frequency-domain methods can be adapted to cater to short trended sequences. Working in the frequency domain allows an unrestricted choice to be made of the frequency response of a filter. It also requires that the data should be free of trends. Methods for extracting the trends prior to filtering and for restoring them thereafter are described. Full article

A novel class of dimension reduction methods is combined with a stochastic multi-factor panel regression-based state-space model in order to model the dynamics of yield curves whilst incorporating regression factors. This is achieved via Probabilistic Principal Component Analysis (PPCA) in which new statistically-robust variants are derived also treating missing data. We embed the rank reduced feature extractions into a stochastic representation for state-space models for yield curve dynamics and compare the results to classical multi-factor dynamic Nelson–Siegel state-space models. This leads to important new representations of yield curve models that can be practically important for addressing questions of financial stress testing and monetary policy interventions, which can incorporate efficiently financial big data. We illustrate our results on various financial and macroeconomic datasets from the Euro Zone and international market. Full article

${\ell }_1$ polynomial trend filtering, which is a filtering method described as an ${\ell }_1$-norm penalized least-squares problem, is promising because it enables the estimation of a piecewise polynomial trend in a univariate economic time series without prespecifying the number and location of knots. This paper shows some theoretical results on the filtering, one of which is that a small modification of the filtering provides not only identical trend estimates as the filtering but also extrapolations of the trend beyond both sample limits. Full article

Statistical methods are widely used for valuation (prediction of the value at sale or auction) of a unique object such as a work of art. The usual approach is estimation of a hedonic model for objects of a given class, such as paintings from a particular school or period, or in the context of real estate, houses in a neighborhood. Where the object itself has previously sold, an alternative is to base an estimate on the previous sale price. The combination of these approaches has been employed in real estate price index construction (e.g., Jiang et al. 2015); in the present context, we treat the use of these different sources of information as a forecast combination problem. We first optimize the hedonic model, considering the level of aggregation that is appropriate for pooling observations into a sample, and applying model-averaging methods to estimate predictive models at the individual-artist level. Next, we consider an additional stage in which we incorporate repeat-sale information, in a subset of cases for which this information is available. The methods are applied to a data set of auction prices for Canadian paintings. We compare the out-of-sample predictive accuracy of different methods and find that those that allow us to use single-artist samples produce superior results, that data-driven averaging across predictive models tends to produce clear gains, and that, where available, repeat-sale information appears to yield further improvements in predictive accuracy. Full article

In applied econometric literature, the causal inferences are often made based on temporally aggregated or systematically sampled data. A number of studies document that temporal aggregation has distorting effects on causal inference and systematic sampling of stationary variables preserves the direction of causality. Contrary to the stationary case, this paper shows for the bivariate VAR(1) system that systematic sampling induces spurious bi-directional Granger causality among the variables if the uni-directional causality runs from a non-stationary series to either a stationary or a non-stationary series. An empirical exercise illustrates the relative usefulness of the results further. Full article

It is sometimes observed and frequently assumed that top incomes in household surveys worldwide are poorly measured and that this problem biases the measurement of income inequality. This paper tests this assumption and compares the performance of reweighting and replacing methods designed to correct inequality measures for top-income biases generated by data issues such as unit or item non-response. Results for the European Union’s Statistics on Income and Living Conditions survey indicate that survey response probabilities are negatively associated with income and bias the measurement of inequality downward. Correcting for this bias with reweighting, the Gini coefficient for Europe is revised upwards by 3.7 percentage points. Similar results are reached with replacing of top incomes using values from the Pareto distribution when the cut point for the analysis is below the 95th percentile. For higher cut points, results with replacing are inconsistent suggesting that popular parametric distributions do not mimic real data well at the very top of the income distribution. Full article

In 2002, the Israeli government decided to build a wall inside the occupied West Bank. The wall had a marked effect on the access to land and water resources as well as to the Israeli labour market. It is difficult to include the effect of the wall in an econometric model explaining poverty dynamics as the wall was built in the richer region of the West Bank. So a diff-in-diff strategy is needed. Using a Bayesian approach, we treat our two-period repeated cross-section data set as an incomplete data problem, explaining the income-to-needs ratio as a function of time invariant exogenous variables. This allows us to provide inference results on poverty dynamics. We then build a conditional regression model including a wall variable and state dependence to see how the wall modified the initial results on poverty dynamics. We find that the wall has increased the probability of poverty persistence by 58 percentage points and the probability of poverty entry by 18 percentage points. Full article