Working Papers

The WNE Working Papers series has been published by the Faculty of Economic Sciences at the University of Warsaw since 2008.

The WNE Working Papers series provides a fast, open channel for disseminating research conducted at the Faculty of Economic Sciences, University of Warsaw. The papers hosted here are working versions (pre-prints) and may evolve as authors refine their analyses, incorporate feedback, or progress through formal peer-review. What you read is the current version released by the authors, timestamped and assigned DOI/ISSN identifiers to ensure precise citation and version tracking. Copyright remains with the authors, who may, at any time, upload a revised file or add a note directing readers to a later, peer-reviewed publication.

The Working Papers series accepts articles by research employees of the Faculty and publications from conferences organised at the Faculty of Economic Sciences at the University of Warsaw. Articles should be original research papers which have not been previously published, on the subject of economics.

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Number of Results 7

WP(8/2026)502. Keynes vs. Kolmogorov: Two Axiomatics of Probability

Authors: Ryłow Jakub
The paper examines the logical theory of probability formulated by John Maynard Keynes in A Treatise on Probability (1921) as an axiomatic project competing with the measure-theoretic approach codified by Andrei Kolmogorov in Grundbegriffe der Wahrsc…

WP502. Keynes vs. Kolmogorov: Two Axiomatics of Probability

The paper examines the logical theory of probability formulated by John Maynard Keynes in A Treatise on Probability (1921) as an axiomatic project competing with the measure-theoretic approach codified by Andrei Kolmogorov in Grundbegriffe der Wahrscheinlichkeitsrechnung (1933). Beyond a synthetic comparison of both systems and their contemporary successors, the paper makes two original contributions. First, we identify and formally prove the Boolean presupposition of Ramsey's Dutch book argument: the argument establishes only a conditional result — if the event domain is a Boolean algebra, then coherence requires classical probability — whose antecedent is precisely what Keynes's partial order postulate denies. Ramsey therefore did not refute Keynesian logicism unconditionally; he refuted it within a domain whose universality Keynes contested. This formalises, using the Wroński–Godziszewski (2016) theorem, a gap in the standard history of the debate that has gone unnamed in the literature. Second, we propose the imprecision index of a credal set as the first candidate formal analogue of Keynes's weight of evidence within the established framework of imprecise probabilities.


DOI: https://doi.org/10.33138/2957-0506.2026.8.502
Ryłow Jakub
logical probability measure theory weight of evidence imprecise probabilities Bayesianism

WP(30/2022)406. Quantile regression analysis to predict GDP distribution using data from the US and UK

Authors: Tran Thi Huyen, Ślepaczuk Robert
This paper aims to find the best models to forecast one-quarter-ahead and one-year-ahead US and UK real GDP growth distributions by employing quantile regression with skewed-t distribution on different sets of relevant near-term predictors. The resea…

WP406. Quantile regression analysis to predict GDP distribution using data from the US and UK

This paper aims to find the best models to forecast one-quarter-ahead and one-year-ahead US and UK real GDP growth distributions by employing quantile regression with skewed-t distribution on different sets of relevant near-term predictors. The research data period starts in 1947Q1/1955Q1 for US/UK data and ends in 2021Q3/2020Q4 for one-quarter-ahead/one-year-ahead prediction. The out-of-sample period ranges from 1996Q3 to 2021Q3 for one-quarter-ahead prediction and to 2020Q4 for one-year-ahead forecasting. The author applies a two-step testing procedure, in which models with the lowest average error in out-of-sample period are selected to the next step where the cumulative distribution functions of probability integral transforms are computed for the out-of-sample period, to select the best models. The improvement in the final forecasts of the tested models results, among others, from the use of new macroeconomic data with a higher frequency and focusing on the specific properties of the tested models separately for the US and UK. The chosen best models indicate that there exist better models than the model proposed by Adrian et al. (2016) to predict US growth distributions and that near-term predictors can produce good UK growth forecasts. Additionally, some simplified models associated with significantly lower portion of model risk are detected to produce meaningful forecasts for both US and UK case. For the US data, there exist several models that can produce timely predicted results.


Tran Thi Huyen, Ślepaczuk Robert
GDP growth density forecast quantile regression US GDP UK GDP cumulative distribution function probability integral transform out-of-sample forecasting

WP(22/2021)370. Predicting football outcomes from Spanish league using machine learning models

Authors: Lewandowski Michał, Chlebus Marcin
High-quality football predictive models can be very useful and profitable. Therefore, in this research, we undertook to construct machine learning models to predict football outcomes in games from Spanish LaLiga and then we compared them with histori…

WP370. Predicting football outcomes from Spanish league using machine learning models

High-quality football predictive models can be very useful and profitable. Therefore, in this research, we undertook to construct machine learning models to predict football outcomes in games from Spanish LaLiga and then we compared them with historical forecasts extracted from bookmakers, which knowledge is commonly considered to be deep and high-quality. The aim of the paper was to design models with the highest possible predictive performances, get results close to bookmakers or even building better estimators. The work included detailed feature engineering based on previous achievements of this domain and own proposals. A built and selected set of variables was used with four machine learning methods, namely Random Forest, AdaBoost, XGBoost and CatBoost. The algorithms were compared based on: Area Under the Curve (AUC) and Ranked Probability Score (RPS). RPS was used as a benchmark in the comparison of estimated probabilities from trained models and forecasts from bookmakers' odds. For a deeper understanding and explanation of the demonstrated methods, which are considered as black-box approaches, Permutation Feature Importance (PFI) was used to evaluate the impacts of individual variables. Features extracted from bookmakers odds’ occurred the most important in terms of PFI. Furthermore, XGBoost achieved the best results on the validation set (RPS equals 0.1989), which obtained similar predictive power to bookmakers' odds (their RPS between 0.1977 and 0.1984). Results of the trained estimators were promising and this article showed that competition with bookmakers is possible using demonstrated techniques.


Lewandowski Michał, Chlebus Marcin
predicting football outcomes machine learning betting adaboost random forest xgboost catboost ranked probability score auc permutation feature importance

WP(8/2017)237. Probability weighting under time pressure: applying the double-response method

Authors: Gawryluk Katarzyna, Krawczyk Michał
We conduct a laboratory experiment to investigate the impact of deliberation time on behavior under risk and uncertainty. Towards this end we let our participant make quick, intuitive evaluations of a number of lotteries and modify them, should they …

WP237. Probability weighting under time pressure: applying the double-response method

We conduct a laboratory experiment to investigate the impact of deliberation time on behavior under risk and uncertainty. Towards this end we let our participant make quick, intuitive evaluations of a number of lotteries and modify them, should they wish to do so, after deliberation. Both certainty equivalents are incentivized (a double-response method). The main finding is that additional deliberation time reduces pessimism, especially in the case of lotteries involving unknown probabilities.


DOI: https://doi.org/10.26405/WP/WNE/2017/237/008
Gawryluk Katarzyna, Krawczyk Michał
probability weighting prospect theory time pressure

WP(15/2014)132. Probability weighting in different domains: the role of stakes, fungibility, and affect

Authors: Krawczyk Michał
This paper reports the results of a laboratory experiment in which probability weighting functions for risky gains were elicited non-parametrically in over 500 incentivized subjects. I compare probability weights for monetary rewards to two less fung…

WP132. Probability weighting in different domains: the role of stakes, fungibility, and affect

This paper reports the results of a laboratory experiment in which probability weighting functions for risky gains were elicited non-parametrically in over 500 incentivized subjects. I compare probability weights for monetary rewards to two less fungible domains involving vouchers for different types of consumption, inducing stronger or weaker (positive) emotions. The level of stakes was also manipulated. I find that the probability to win monetary rewards is weighted almost linearly in the high stakes condition, the probability to win vouchers associated with positive affect is underweighted and the probability to win affect-poor vouchers is strongly underweighted. Substantial underweighting also prevails in all three domains in the low stakes condition.


Krawczyk Michał
prospect theory probability weighting functions fungibility affect

WP(8/2014)125. Wildfires in Poland: the impact of risk preferences and loss aversion on environmental choices

Authors: Bartczak Anna, Chilton Susan, Meyerhoff Jürgen
 This paper examines how risk preferences and loss aversion affect choices over a risky environmental good, wildfire prevention in Poland. We collect data in a stated preference survey that allows us to calculate both risk aversion and loss aver…

WP125. Wildfires in Poland: the impact of risk preferences and loss aversion on environmental choices

 This paper examines how risk preferences and loss aversion affect choices over a risky environmental good, wildfire prevention in Poland. We collect data in a stated preference survey that allows us to calculate both risk aversion and loss aversion parameters from individual respondents in both the financial and environmental domains. In doing so, we are able to confirm that this behaviour is consistent with prospect theory and holds for the majority of respondents. Additionally, we find little evidence of domain specificity of risk: responses to the financial risk questions were good predictors of responses to the environmental risk questions.


Bartczak Anna, Chilton Susan, Meyerhoff Jürgen
risk preferences over financial and environmental domains forest fires loss aversion probability weighting prospect theory

WP(3/2011)43. How do we value our income from which we save?

Authors: Liberda Zofia Barbara, Pęczkowski Marek, Gucwa-Leśny Ewa
In this paper we analyze the relationship between the perception of income as satisfying household needs and saving rate of this household. Using the multinomial logit regression function we measure the probability of a household to fall into one of …

WP43. How do we value our income from which we save?

In this paper we analyze the relationship between the perception of income as satisfying household needs and saving rate of this household. Using the multinomial logit regression function we measure the probability of a household to fall into one of the groups categorized by the subjective perception of income in relation to the current household disposable income. The variable specified for the valuation of income is income perception, defined as a class of observed disposable income located on the scale of the subjectively satisfying income. Factors determining the perception of income are: gender and education of the household head, family characteristics, source of income and place of residence. The analysis of relations between the income perception and the household saving rates shows that the perception of income affects both the household observed and predicted saving rates. The research is based on the Household Budget Surveys data for Poland in 2008. (Revised version: October 2012)


Liberda Zofia Barbara, Pęczkowski Marek, Gucwa-Leśny Ewa
household income needs valuation saving probability
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