On 22 september 2023 we had the pleasure to present two papers at XII National Scientific Conference named after Professor Zbigniew Czerwiński "Mathematics and computer science at the service of economics" (MIUE 2023). The conference was organised by Economic University of Poznan.

Hubert Drążkowski presented his working paper at the Statistics session:

Contextual multi armed bandit model is a popular framework for describing sequential decision making under uncertainty. We introduce a novel variant of the problem that aims at describing disruption of the system by the entrance of an external sponsor. Sponsored content is ubiquitous in the modern world, it is present most profoundly in the recommender systems, but more broadly in any scheme involving lobbying. The consequences of introduction of the sponsor are few fold, however in the paper we focus on the differences in assignment mechanisms between standard learner and sponsor. We might not have access to the description of the process that governs the willingness to sponsor. This might be due to the fact that model specifications can be confidential between companies, the decision might be human determined or arise as a consequence of a complicated system not fully modeled, such as auctions between advertisers. In particular the sponsoring mechanism can be confounded. 

We use a tool from causal inference topic of combining randomized controlled trials with observational studies and adjust the Inverse Gap Weighting algorithm to account for confounded sponsor targeting mechanism. We show in a simulation that this adjustment improves learning.

This research proposes a novel tool to analyze interaction of a recommender system with sponsor. Moreover, it shows that ignoring the sponsoring act might lead to worse outcomes, interpreted for example as less user engagement. Most importantly the research shows an adjustment to tackle the problem combining causal inference with sequential decision making.

Sylwia Radomska presented her working paper at the Mathematical economics session:

The problem of financing the educational system is paramount and permanent policy relevance for all economies because every single economy has some mechanism to fund investment in human capital. Investment in human capital can be funded either through private sources (e.g., credit or wealth accumulated by previous generations) or through public sources (subsidies yielding free education to all financed through general taxation). The choice between these two mechanisms is at the core of defining the optimal financing of the educational system. The pros and cons of these two mechanisms have been studied in both empirical and theoretical contexts, positing important trade-offs for each policy and country. In this article, I propose a novel approach to this long-standing debate: I provide normative inference (ex-ante evaluation) of the two standard instruments (education subsidies (ES) and income – contingent loans (ICL)) in a novel model environment with altruistic dynasties, unobservable heterogeneity and income uncertainty (uninsurable idiosyncratic income shocks) in the set up with optimal taxation approach pioneered by Mirrlees (1971, 1976, 1986). I derive the human capital wedge for the dynamic Mirrlees model with altruistic dynasties and present the relation between the marginal tax on human capital accumulation and the wedge for human capital. The theoretical results are consistent with the literature, suggesting that human capital expenditures should be fully tax-deductible (see, i.e., Bovenberg and Jacobs, 2005; Stantcheva, 2015; Koeniger and Prat, 2018). The article quantifies the impact of the introduction of ICL and ES on social welfare and inequality. I study the properties of instruments in an economy with altruistic parents, heterogeneous unobservable innate abilities and income shocks. Further, I quantify the effect of these model features on welfare and social inequality in a world with education subsidies and income-contingent loans relative to laissez-faire, thus reconciling at least part of the conflicting results in the existing literature. I compare the steady-state results of introducing the income-contingent loans and income-independent and income-dependent education subsidies relative to the current US economy.