11. 09. 2026 Statistika: Statistics and Economy Journal - No. 3/2026

Petr Musil, Jana Fischerová, Jaroslav Kahoun

Statistika, 106(3): 259–275
https://doi.org/10.54694/stat.2025.61

Abstract

Statistical descriptions of regions or even cities are usually more popular with users than those at the national level. Users can more easily identify themselves with regional indicators such as the average wage. However, the production of regional indicators is more demanding in terms of data sources. National statistical institutes mostly do not officially publish all components of regional GDP, but rather select a few, such as gross value added or gross fixed capital formation, due to a lack of data. This paper aims at regional GDP in Czechia in particular to estimate missing components of regional GDP as well as analyse the results. It uncovers difficulties connected with the estimates. In addition, the effect of different regional price levels is assessed, regional indicators are adjusted accordingly. The findings indicate substantial differences in the regional GDP structure as well as notable variations of regional price levels. The analysis is conducted for the year 2020.

Keywords
Regional expenditures, GDP, national accounts, regional accounts, experimental estimates, NUTS 3 regions

Jacek Białek

Statistika, 106(3): 276–293
https://doi.org/10.54694/stat.2025.58

Abstract

The GEKS index is a well-known multilateral index used by many statisticians to measure inflation based on scanner data. As a rule, it is assumed that the underlying index within the GEKS formula satisfies the time reversal test. Most often, this underlying index is assumed to be superlative, and therefore, the GEKS index based on the Fisher, Tornqvist (GEKS-T or CCDI) or Walsh (GEKS-W) formulas are most often considered. However, the ’classic’ GEKS index does not meet the stringent identity test. Unfortunately, most of the known multilateral indices do not meet the time reversal test, which many researchers consider a weakness. This paper reviews both well-known and lesser-known modifications and generalizations of the GEKS index. We discuss three new and general classes of indices based on the GEKS method, as well as some special cases of these classes, which include the GEKS, GEKS-T, and GEKS-W indices and, additionally, the GEKS-L and GEKS-GL indices. One class uses elasticity of substitution, so it is close to the economic approach, while another class - like the multilateral Geary-Khamis index- uses quality-adjusted prices and quantities. Not all the GEKS modifications discussed require the underlying index to meet the time reversal test. It should be noted that in cases where this assumption has been dropped, an identity test has been gained. We present the basic axiomatic properties of the proposed indices and compare them empirically based on real and available scanner datasets. The simulation study verifies the impact of price and quantity volatilities on the differences between the price indices discussed.

Keywords
inflation measurement, Consumer Price Index (CPI), scanner data, multilateral indices, identity test, GEKS method

Zouheir Mighri

Statistika, 106(3): 294–313
https://doi.org/10.54694/stat.2025.57

Abstract

This study investigates the direction and magnitude of linear and nonlinear Granger causality-in-quantiles between inflation and inflation uncertainty, as well as from global geopolitical risks to inflation in Saudi Arabia over the period January 2008–December 2025. While no causality is detected in the mean, the results reveal significant quantile-dependent relationships. Linear Granger causality-in-quantiles indicates significant bidirectional causality between inflation and inflation uncertainty, with a predominantly positive and significant causal effect running from inflation to its uncertainty across most quantiles, thereby supporting the Friedman (1977) hypothesis. In contrast, nonlinear Granger causality-in-quantiles uncovers state-dependent effects, with inflation uncertainty exerting a significant negative influence on inflation at lower and middle quantiles, thereby supporting the Friedman-Ball hypothesis. Meanwhile, both linear and nonlinear Granger causalityin-quantiles reveal significant causal effects from global geopolitical risk measures to inflation across most quantiles; however, the sign analysis indicates that these effects are unstable and largely insignificant, providing no consistent or robust sign pattern linking external risk factors to inflation dynamics in Saudi Arabia. Robustness checks using the world uncertainty index confirm that global uncertainty has a limited and non-systematic influence on inflation dynamics. Overall, the findings emphasize strong state-dependent and asymmetric effects, with domestic uncertainty playing a central role, while external risk factors contribute marginally to inflation dynamics in Saudi Arabia.

Keywords
Inflation, inflation uncertainty, geopolitical risk, Granger causality-in-quantiles

Andrii Hrabariev, Vasyl Derbentsev, Mykhailo Baraniuk

Statistika, 106(3): 314–331
https://doi.org/10.54694/stat.2025.40

Abstract

This study investigates structural shifts in European Union countries banking system typologies during the COVID-19 period from 2019 to 2021. Using the k-means clustering method (compared with hierarchical agglomerative clustering and Gaussian mixture models) on 10 financial and macroeconomic indicators (e.g., non-performing loans, z-score, GDP growth) at the country level for 25 European Union countries, we identified four distinct clusters with stable typological definitions but evolving country compositions. Comparison of cluster profiles reveals the pandemic period as a structural catalyst, reinforcing the resilience of Nordic Resilience Systems) and Core Stability Systems clusters. Significant compositional shifts occurred: Dynamic Growth Systems absorbed advanced economies, balancing growth and stability, while High Intermediation Systems transformed into a vulnerable typology, marked by high fiscal risk and low stability buffers. These findings highlight structural shifts associated with the pandemic period and differentiated policy responses, and inform regulatory strategies for enhancing EU banking resilience.

Keywords
EU banking systems, COVID-19, cluster analysis, financial resilience, banking and macroeconomic indicators, structural shifts, temporal analysis

Yee Sheng Mak, Siok Kun Sek, Mohsen Ayyash

Statistika, 106(3): 332–352
https://doi.org/10.54694/stat.2025.56

Abstract

This paper examines the cost of living (COL) in six selected Asian countries: Indonesia, Japan, Korea, Malaysia, Singapore, and Thailand. Motivated by rising inflationary pressures and limitations of traditional economic indicators – such as reporting delays and limited granularity – this study explores whether real-time data from Google Trends searches can improve the tracking and prediction of COL patterns in several country-specific settings. The analysis covers the period from 2010 to 2024 and employs Mixed Data Sampling (MIDAS) regression. The results demonstrate that MIDAS models provide superior flexibility and responsiveness by accommodating high-frequency Google Trends data alongside lower-frequency macroeconomic variables. Notably, MIDAS models yield improved predictive accuracy and timeliness in capturing COL dynamics. The findings also highlight the significance of search terms like debt, inflation, and unemployment as behavioural proxies for public economic concerns. This study underscores the potential of integrating search engine data into COL analysis to improve the timeliness and sensitivity of economic monitoring.

Keywords
Cost of living, Google Trends, macroeconomic indicators, Mixed Data Sampling (MIDAS) regression, real time data

Jesus A. Trevino-Cantu

Statistika, 106(3): 353–371
https://doi.org/10.54694/stat.2025.59

Abstract

This study employs a performance-interval approach to assess health performance across Mexico's 32 states, addressing limitations of traditional single-value indices. Using OECD-selected indicators covering resources, health status, and risks, the methodology calculates a midpoint (MP) for average performance and an amplitude (A) for the balance of internal indicators. Extending this approach, the research develops a typology classifying states based on MP and A values to guide policy. Results reveal significant regional inequalities and institutional fragmentation; for instance, Mexico City exhibits high resource density yet high mortality rates due to its fragmented institutions. The analysis identifies four state groups, ranging from robust systems to those facing severe risks and uncertainty. By capturing internal disparities often obscured by single-value indices, the extended approach incorporates health system fragmentation into a composite index and a typology, as identified analytically in the current literature. The findings suggest that effective policy requires addressing resource scarcity and institutional coordination to reduce health disparities and improve outcomes across regions.

Keywords
Composite index; Performance interval; Health indicators; Health fragmentation; Mexico

Stanislava Hronová