Research

Work in progress

  • Kostyrka, A. V. Step size selection in numerical differences using a regression kink. University of Luxembourg, Department of Economics and Management Discussion Paper 2025-09. orbilu.uni.lu/handle/10993/64958.
    Abstract. We propose a new step-size selection procedure for numerical differences based on fitting a piecewise linear shape to the observed estimate of truncation error and determining the position of its kink. The novelty of this method is in its use of the full information about the estimated total error behaviour at both sides around the optimum and in the incorporation of robust statistical tools for estimating the best V-shaped fit. The added safety checks ensure that the kink is detected if it exists, or a reasonable step size is returned in the case there is no kink. In numerical simulations, the proposed method algorithm outperforms two existing algorithms in terms of median error when tested on 5 well-behaved and 3 pathological functions.

  • Cosma, A., Kostyrka, A. V., & Tripathi, G. (2025). Missing endogenous variables in conditional moment restriction models. University of Luxembourg, Department of Economics and Management Discussion Paper 2024-01. orbilu.uni.lu/handle/10993/60100.
    Abstract. We estimate finite dimensional parameters in conditional moment restriction (CMR) models when at least one of the endogenous variables (outcomes and/or explanatory variables) in the model is missing for some individuals in the sample. We demonstrate that efficiency gains in estimation occur if and only if there is at least one endogenous variable – included in or excluded from the CMR model – that is nonmissing (observed for all individuals in the sample), which we show characterizes informative imputation. We propose a semiparametrically efficient estimator which is also ‘doubly robust’. To illustrate the insights our estimator can provide in empirical applications with large sample sizes, we artificially induce missingness in the female labor supply model of Angrist and Evans (1998). Despite medium levels of missingness in female labor income (the outcome) and a sample size exceeding 200,000 observations, the inverse propensity score weighted generalized method of moments (GMM) estimator finds only a statistically insignificant negative effect of having a third child (the endogenous regressor) on labor income. In contrast, our efficient estimator yields point estimates of this effect that are not only comparable to the GMM estimates but are also statistically significant.

  • ‘The good, the bad, and the asymmetric: Evidence from a new conditional density model’. Kostyrka, A. V. & Malakhov, D. I. (2021). hdl.handle.net/10993/47435
    Abstract. We propose a novel univariate conditional density model family where asset returns are decomposed into a sum of copula-connected unobserved positive and negative shocks, both continuous and discrete, thus yielding up to 4 distinct shocks. We compare our models to many commonly used GARCH variants by backtesting them on a sample of S&P500 daily data (via VaR and volatility forecast quality testing). A subset of our models performs better both in sample and out of sample compared with standard models. We show that the independence assumption for signed shocks does not hold, and that covariance is an important component of total variance, and it is time-dependent with a leverage-like effect. Conditional skewness behaviour reveals naïve investors’ expectations.

Peer-reviewed

In English

  • Cosma, A., Kostyrka, A. V. & Tripathi, G. (2019). ‘Inference in conditional moment restriction models when there is selection due to stratification’. Advances in Econometrics, vol. 39 (titled ‘The econometrics of complex survey data: Theory and applications’), pp. 137–171, 2019. DOI: 10.1108/S0731-905320190000039010
    Abstract. We show how to use a smoothed-empirical-likelihood approach to conduct efficient semi-parametric inference in models characterised as conditional moment equalities when data are collected by variable probability sampling. Results from a simulation experiment suggest that the smoothed-empirical-likelihood-based estimator can estimate the model parameters very well in small to moderately sized stratified samples.

In other languages

  • Kostyrka, A. V. & Malakhov, D. I. (2021). ‘Was there ever a shift: Empirical analysis of structural-shift tests for return volatility’. Prikladnaya Ekonometrika (Applied Econometrics), vol. 61, pp. 110–139. DOI: 10.22394/1993-7601-2021-61-110-139
    Abstract. In this article, two popular tests for structural breaks are considered for return volatilities: the ICSS algorithm employing the AIT test, and the least-squares (LS) estimator. We show that the AIT test is sensitive to many features of the time series, and the use of asymptotic critical values is not always justified. The LS method was found to detect breaks more accurately, especially if there are many, in comparative simulations. Real data analysis revealed that LS estimation yields results in better accordance with general economic intuition, although its results are somewhat sensitive to the sample length. In general, we recommend the LS estimator for practical purposes.

Other publications

Vignettes

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