Work in progress

  • Cosma, A., Kostyrka, A., & Tripathi, G. (2024). Missing endogenous variables in conditional moment restriction models. University of Luxembourg, Department of Economics and Management Discussion Paper 2024-01.
    Abstract. We consider the estimation of finite dimensional parameters identified via a system of conditional moment equalities when at least one of the endogenous variables (outcomes and/or explanatory variables) is missing at random for some individuals in the sample. We derive the semi-parametric efficiency bound for estimating the parameters and use it to demonstrate that efficiency gains occur only if there exists at least one endogenous variable that is non-missing, i.e. observed for all individuals in the sample. We show how to construct ‘doubly robust’ estimators and propose an estimator that achieves the efficiency bound. A simulation study reveals that our estimator works well in medium-sized samples for point estimation as well as for inference. To see what insights our estimator can deliver in empirical applications with very large sample sizes, we revisit the female labour supply model of Angrist and Evans (1998) and show that if there is even medium missingness in female labour income (the outcome variable), then having more than 200,000 observations is not enough for a researcher using inverse propensity score weighted GMM to find a statistically significant negative effect of having a 3rd child (the endogenous explanatory variable) on labour income. In contrast, our semiparametrically efficient estimator can deliver point estimates of this effect that are comparable to the GMM estimates as well as being statistically significant.

  • ‘The good, the bad, and the asymmetric: Evidence from a new conditional density model’. Kostyrka, A. V. & Malakhov, D. I. (2021).
    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.


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.