Michał Bernardelli

Hidden Markov Models as a Tool for the Assessment of Dependence of Phenomena of Economic Nature

The assessment of dependence between time series is a common dilemma, which is often solved by the use of the Pearson’s correlation coefficient. Unfortunately, sometimes, the results may be highly misleading. In this paper, an alternative measure is presented. It is based on hidden Markov models and Viterbi paths. The proposed method is in no way universal but seems to provide quite an accurate image of the similarities between time series, by disclosing the periods of convergence and divergence. The usefulness of this new measure is verified by specially crafted examples and real‑life macroeconomic data. There are some definite advantages to this method: the weak assumptions of applicability, ease of interpretation of the results, possibility of easy generalization, and high effectiveness in assessing the dependence of different time series of an economic nature. It should not be treated as a substitute for the Pearson’s correlation, but rather as a complementary method of dependence measure.

Optimal Allocation of the Sample in the Poisson Item Count Technique

Indirect methods of questioning are of utmost importance when dealing with sensitive questions. This paper refers to the new indirect method introduced by Tian et al. (2014) and examines the optimal allocation of the sample to control and treatment groups. If determining the optimal allocation is based on the variance formula for the method of moments (difference in means) estimator of the sensitive proportion, the solution is quite straightforward and was given in Tian et al. (2014). However, maximum likelihood (ML) estimation is known from much better properties, therefore determining the optimal allocation based on ML estimators has more practical importance. This problem is nontrivial because in the Poisson item count technique the study sensitive variable is a latent one and is not directly observable. Thus ML estimation is carried out by using the expectation‑maximisation (EM) algorithm and therefore an explicit analytical formula for the variance of the ML estimator of the sensitive proportion is not obtained. To determine the optimal allocation of the sample based on ML estimation, comprehensive Monte Carlo simulations and the EM algorithm have been employed.

The Application of Hidden Markov Models to the Analysis of Real Convergence

This paper employs hidden Markov models and the Viterbi path to analyze the process of real convergence. Such an approach combines the analysis of cyclical and income-level convergence. Twelve macroeconomic variables in the sample of 28 EU countries observed in the 1995-2016 period are within the scope of the study. The results indicate, among others, the existence of real convergence of Poland toward the remaining EU countries in terms of the levels of GDP per capita at PPP and GDP growth rates, with a short-run period of divergence during the global crisis.