  Citation: Sobieraj, J.; Metelski, D. Private Renting vs. Mortgage Home Buying: Case of British Housing Market—A Bayesian Network and Directed Acyclic Graphs Approach. Buildings 2022, 12, 189. https:// doi.org/10.3390/buildings12020189 Academic Editors: Mats Wilhelmsson and Agnieszka Zalejska Jonsson Received: 31 December 2021 Accepted: 2 February 2022 Published: 7 February 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). buildings Article Private Renting vs. Mortgage Home Buying: Case of British Housing Market—A Bayesian Network and Directed Acyclic Graphs Approach Janusz Sobieraj 1 and Dominik Metelski 2, * 1 Department of Building Engineering, Warsaw University of Technology, 00-637 Warsaw, Poland; jsob@il.pw.edu.pl 2 Department of International and Spanish Economics, University of Granada, 18071 Granada, Spain * Correspondence: dominik@correo.ugr.es Abstract: The worsening of housing problems in many countries has become a topic of global interest. Researchers point to a variety of factors that influence individual housing tenure decisions. Our study is based on longitudinal English Housing Survey (EHS) data (2008–2009 to 2019–2020, with survey years matching financial years, i.e., running April–March) and identifies flows between different forms of housing tenure in the U.K. and analyses conditional dependencies of a range of EHS variables using a directed acyclic graph (DAG). More specifically, we take into account variables such as first-time buyers (FTB), mortgage payments, rent payments, share of mortgage/rent in household income, and receipt of housing benefit (HB), with some variables also reflecting a regional breakdown (captured separately for London and England excluding London) to illustrate the complex nature of regional differences in explaining changes in housing tenure. We address some of the problems and challenges of the housing market in the U.K. today, and, in particular, examine what influences private renters and those buying with a mortgage. A key conclusion from this study is that housing benefit does not necessarily ease the way for private renters into their own housing. The study is quantitative in nature and uses the English Housing Survey and Bayesian network (BN) analysis. Unlike traditional methods, such as multiple regression or panel regression, where the researcher somehow suggests the type of a relationship between certain variables, BN’s learning algorithm analyses different iterations between variables and finds the most appropriate relationships between them. Keywords: housing tenure in U.K.; private renters; buying with mortgage; Bayesian network (BN) analysis; directional acyclic graph (DAG) 1. Introduction In the U.K. market, there has been a multi-year process of relevant shifts in the structure of housing tenure [1–3]. For a number of years, the private rented sector (PRS) has been growing, whereas the owner-occupier market has been shrinking [1]. This has been highlighted by various researchers, including Clair [4], Mulheirn [1], Rugg and Rhodes [2], and Balchin and Rhoden [3]. Interestingly, despite an adequate supply of housing, the availability of housing on the U.K. market for certain groups of people is consistently declining [1]. This mainly affects young adults [5]. A similar problem has been described in other studies cover- ing other countries [6,7]. These problems obviously have their causes, namely for the British market: the erosion of the social housing stock, the stagnation of young people’s incomes, and the policy of reducing housing benefits, which mainly affects young adults and single individuals. Unfortunately, such problems cannot be solved by building more dwellings and thereby increasing the supply of housing in the market sector. Some solutions already Buildings 2022, 12, 189. https://doi.org/10.3390/buildings12020189 https://www.mdpi.com/journal/buildings