Original scientific paper
https://doi.org/10.62366/crebss.2025.1.005
Causal analysis in econometrics using reproducing kernel Hilbert space
Želimir Kurtanjek
orcid.org/0000-0001-5453-6255
; Faculty of Food Technology and Biotechnology, University of Zagreb, Croatia
*
* Corresponding author.
Abstract
A procedure for determining nonlinear causal relationships between two variables is proposed by mapping them into a reproducing kernel Hilbert space (RKHS). The analysis of bivariate dependencies is a component of developing causal models in artificial intelligence for the purpose of managing complex systems. Understanding causality provides key information that underpins diagnostics, consequence forecasting, and business decision-making. The determination of causal relationships between variables is performed by estimating the empirical probability density using kernel density estimation (KDE) within the RKHS framework. The direction of the causal link is assessed using the Nadaraya-Watson approximation and by comparing Pearson correlations of the variables X and Y with those of the models in RKHS space, XH(Y) and YH(X). The proposed method was tested on several examples: a neuron model, simulations of complex bivariate models with heteroskedastic disturbances, well-known datasets from the University of Tubingen, marketing "Datarium" data on social media impact, and dependencies between stock indices S&P500 and VIX. Additionally, an analysis of the causal structure related to the gender pay gap was conducted using data of IT company from a U.S. Ambiguity in the direction of the causal relationship is indicated by the overlap of confidence intervals for Pearson correlations. For linear systems, due to the symmetry of conditional distributions in both directions, the proposed method cannot unambiguously determine the direction of causality.
Keywords
causality; RKHS; Hilbert space; kernels; Bayesian causal network
Hrčak ID:
332292
URI
Publication date:
17.6.2025.
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