This paper explores the determinants of demand for voluntary comprehensive car insurance (CASCO) in Poland. The study aims to identify the impact of acquisition costs and household disposable income on insurance uptake. Utilizing a multilayer perceptron neural network model, the research analyzes the relationship between motor insurance expenditures and two key variables: the disposable income of households and the acquisition costs ratio between voluntary CASCO and Mandatory Third-Party Liability insurance. The findings, validated by robust diagnostic tests, a linear ordinary least squares model as a benchmark and a leave-one-out cross-validation procedure, reveal that both factors are statistically significant predictors of demand. The results indicate that the expansion of the CASCO market in Poland is driven not only by rising consumer affluence but also by the commission ratio, which motivates intermediaries to prioritize voluntary products. This suggests a supply push mechanism where distribution costs shape market dynamics.
The aim of this article is to indicate the relevance of the challenges faced by statisticians in the analysis of socio-economic processes, which requires breaking many of the well-trodden paths of analysis. Until now a preference for linear, parametric methods was observed, supposedly allowing the discovery of cause-and-effect relationships. According to Kant’s philosophy, ‘a thing in itself’ is not knowable and from this perspective, the main task of statistics is to approximate reality. In statistical studies, only stochastic approximation is made and determining the stochastic structure of processes is as important as studying their regression. The presented review of the literature leads to the conclusion that stochasticity and nonlinearity are the primary features of socio-economic processes and that nowadays their analysis is most effective when based on non-parametric methods. Thus, the paper presents a basic catalogue of methods used for studying non-linearity, the stochastic character and approximation of economic processes using non-parametric methods. An additional aim of this paper is to emphasize the importance of fundamental statistical monographs to the development of statistical research methodology. The contribution of Polish publications to the advancement of contemporary knowledge is also discussed.
The aim of the study presented in this paper is to analyse the distributions of trade durations for WIG20 stocks using data from May 2025, with a particular focus on modelling doubly truncated data. Left-truncated distributions for trade durations have already been described in the literature, which is justified, as the values of an excessive proportion of observations were equal to zero. In this study, it is assumed that the data are also righttruncated due to time limitations between the trading sessions. Three doubly truncated continuous distributions were analysed in the study, namely the lognormal, the Pareto and the Weibull distribution. To satisfy the assumptions of stationarity and independence, the data were divided into smaller subsamples. Goodness-of-fit tests were then performed to determine which theoretical distribution best describes the empirical data. The results indicate that the quality of the fit depends on the lower truncation level – the higher the truncation threshold, the better the lognormal distribution fits the empirical trade durations.
The aim of the study is to provide an explanation for the factors that most influence the differences in wage levels between Polish powiats (equivalent to counties). This study investigates regional wage disparities in Poland by applying machine learning models enhanced by Explanatory Model Analysis techniques. Using powiat-level data from the Local Data Bank (Pol. Bank Danych Lokalnych – BDL) for 2010 and 2023, a neural network framework was developed to predict wage levels based on economic, demographic, infrastructural and environmental variables. To interpret the model, we employed the Variable Importance over Permutation (VIP) and SHapley Additive exPlanations (SHAP) approaches, which provide insights into both the global feature importance and the local contributions of individual variables. The results indicate that the share of the productive population, unemployment rates and social vulnerability remain key determinants of wage differences, although their relative influence shifts significantly over time. The SHAP analysis demonstrates how regional contexts such as the Jelenia Góra and Wrocław powiats exhibit distinct factor dynamics, with demographic and infrastructural variables playing varying roles across the studied years. The findings highlight the potential of combining machine learning with explainability methods to uncover complex, nonlinear determinants of wages, offering a more transparent analytical basis for understanding evolving regional disparities.
The aim of the study was to construct a two-asset optimal investment portfolio using machine learning and macroeconomic data at monthly and quarterly intervals. The auxiliary objective was to identify which macroeconomic variables significantly impact the estimation of the S&P 500 stock index and the USD/GBP currency pair. The framework included two steps: firstly, time series forecasts were conducted using tree ensemble methods, namely the random forest and XGBoost, and secondly, the forecasts were used as expected values to construct the portfolios. We analyze the extent to which the structure of a portfolio based on the estimated data differs from the one built using historical data. The results of the research showed that it was possible to use the macroeconomic data to efficiently forecast the considered time series and construct an optimal investment portfolio.
Saving is a crucial step towards investing. Several factors influence the decision to save, including religion, economic conditions, cultural attitudes and the interest rate on savings accounts. This study investigates low savings rates in West Africa and tries to find out whether higher interest rate would stimulate regional saving. The lack of empirical understanding of how interest rate affects saving behaviour challenges economic development. Using the lifecycle hypothesis, the study analysed savings as a function of a deposit interest rate, per capita income and the inflation rate through panel autoregressive distributed lag analysis. The findings show that deposit interest rate does not significantly impact savings in the region, in contrast to per capita income and inflation. The conclusion of the study is that the relationship between interest rates and savings is complex and influenced by multiple factors other than the deposit interest rate. The study suggests implementing policies that promote long-term investment strategies beyond relying on interest rates, which helps balance immediate investments with savings and encourages firms to set aside funds for future use.
This article has two goals. The first (main) goal is to introduce a new flexible distribution defined on an infinite domain (-∞, ∞). This distribution has been named the skew plasticising component normal distribution. The second (additional) goal is to present a chronological overview of distributions belonging to the large family of normal plasticising distributions. Some properties of the proposed distribution such as the PDF, CDF, quantiles, generator, moments, skewness, kurtosis and moments of order statistics are presented. The unknown parameters of the new distribution are estimated by means of the maximum likelihood method. The Shannon entropy, the Hessian Matrix and the Fisher Information Matrix are also presented. The study provides illustrative examples of the applicability and flexibility of the introduced distribution. The most important R codes are provided in Appendix 2.
This paper contributes to the economic voting literature by evaluating the effect of a policy-determined income shock on individual-level support for the government. It examines the results of a natural experiment relating to the 2016 Polish job market reform that raised the minimal hourly wage to PLN 12 per hour for all workers, regardless of their contract type, thus asym- metrically affecting low-earning individuals engaged in precarious work. The study employs a detailed microeconomic dataset from the European Social Survey to perform a difference-indifferences analysis. It concludes that the reform had a significant, positive impact on the levels of support received by the government, notably higher than any macroeconomic variable.
The selection, weighting and transformation of variables are essential phases of the modelling process. Two approaches can be applied to improve a model’s accuracy: the selection of variables and the transformation of variables. In symbolic data analysis, two different approaches can be adopted: principal component analysis (PCA) and spectral clustering. In all the cases, we initially start with a set of symbolic variables and, after transformation, we obtain either classical variables (single numeric values) or symbolic variables that can be used in various models. The paper presents and compares PCA and spectral clustering for symbolic data when dealing with the problem of variable transformation. Artificial data with a known cluster structure were used to compare both single and ensemble clustering approaches. The results suggest that spectral clustering achieves better results for single and ensemble models.
The aim of this study is to trace the effects of fiscal policy shocks. We calculate the level of fiscal multipliers and short-term output fiscal elasticities for the United States. We do so by estimating a Bayesian three-variate fiscal vector autoregression model that accounts for uncertain identification assumptions. The government spending multiplier is equal to 1.65 on impact and 0.53 after one year, while the tax multiplier is equal to -2.00 on impact and -0.10 after one year. The posterior output elasticity of taxes is equal to 2.20. Increasing the prior assumptions for output elasticity of taxes leads to a lower tax multiplier. The study shows that both increasing spending and decreasing taxes can stimulate the economy. However, the effects of tax decreases may be larger for the economy.
Sustainable development remains one of the major challenges for contemporary Poland, where dynamic economic growth often collides with social inequalities and environmental degradation. In relation to these challenges, this paper aims to assess the level of sustainable development in voivodships (highest-level administrative division of Poland, equivalent to a province) based on an extended analytical framework that adds an institutionalpolitical dimension to the three core aspects of sustainable development – social, economic and environmental. The study relies on data from 2022 on individual voivodships, from which 20 variables describing the aforementioned aspects of sustainable development are selected. In the extended approach, these aspects are often referred to as ‘orders’. For each voivodship, Hellwig’s measure is calculated using multidimensional comparative analysis and linear ordering. Based on these calculations, rankings of Polish voivodships are created and visualised by means of cartograms created in R. Additionally, an analysis of the similarity of objects relative to each other is conducted using Euclidean distance matrices. The research shows, among other aspects, which orders of sustainable development constitute the strengths and which represent weaknesses of a given voivodship. The study refers to literature discussing the concept of sustainable development and methods of quantifying it, as well as literature describing the applied research methodology.
This study examines the strength of the consensus on the expected prices across the European Union (EU) countries with respect to various factors: seniority in the EU (‘old’ vs. ‘new’ EU Member States, i.e. those that joined the community in 2004), the size of the economy (small vs. large) and currency cohesion (eurozone vs. local-currency countries). The results show that the lowest consensus on expected prices and relatively little variation in such a consensus occur in the ‘old’ EU countries. Opinions on the direction of the expected price changes vary substantially, but this variation remains stable in time. For almost every EU country, the consensus on the expected prices is higher in the ‘regular times’ subsample than in the ‘pandemic and war’ subsample, and for many countries, the differences in the strength of the consensus are larger for the ‘pandemic and war’ subsample. As far as the correlation with the observed price changes is concerned, the highest correlation coefficients are noted for small economies. Analysing correlation coefficients across subsamples shows that during difficult times of the pandemic and war, seniority in the EU helps the respondents to predict the direction of the expected price changes more in line with the actual price developments.
The article concerns the share of expenditure on food and energy in the total spending of Polish households in 2021. The main objective of the study is to find out which socio-economic characteristics of Polish households determine how big the share of expenditure on food and energy in households’ total spending is, as well as to examine how energy poverty affects this expenditure. Tobit models estimated using the maximum likelihood method were used in the empirical study. The estimation results indicate that the household size and type, disposable income, extent of energy poverty, and being a retiree, a pensioner or a farmer is correlated with how big the share of expenditure on food and energy in a household’s total expenditure is.
The ability to perform an efficient digital transformation is one of the key capabilities which assures company competitiveness in turbulent times. The ongoing discussion on how to measure digital maturity was the inspiration behind the main aim of the research described in the article, i.e. to construct a digital maturity model called the Index of Digital Transformation (IDT). It is built on four pillars: Strategy, Financing, Technology and Organisation. The final assessment of the model is based on a survey of 205 executives, representing companies listed on the Warsaw Stock Exchange, who were asked to provide information on their companies’ performance before, during and after the COVID-19 pandemic. Statistical methods were used to calculate and validate the IDT. A significant increase in digital maturity over this period was reported in all four pillars. Moreover, the research showed that both the type of the industry and the size of the company matter. B2C industries seem to have been under greater digitalisation pressure in the pandemic period. Larger companies (which belong to WIG20, WIG40 and WIG80) were more digitally mature than the rest, and those belonging to WIG40 demonstrated the highest increase in digital maturity in the analysed period. The IDT allows a better understanding of the dynamics of digital transformation in turbulent times and provides a framework for the measurement of digital maturity.
