Essays on macroeconomics with financial frictions

The recent financial crisis that originated in the U.S. sub-prime mortgage sector elicited a redefinition of the macroeconomic research agenda. The crisis marked the end of the \u201cGreat Moderation\u201d, a period about 20 years long characterized by low volatility in inflation and output. In this environment, economists grew complacent on their theories and models. The crisis however shattered the profession's certainties and paved the way to a new strand of research. In particular, it became clear that in order to make sense of the strong decline in output that compounded with the turmoil in the financial sector, economists were to take into account financial frictions seriously in their models. Specifically, Dynamic Stochastic General Equilibrium (DSGE) models, which are the work-horse models in the analysis of the business cycle, have often been silent on financial aspects before the crisis, and therefore came under attack from many pundits as not being able to cope with the complexity of the real economy. This thesis is an attempt to contribute to the literature on DSGE models with financial frictions. In doing so, my research strategy consists of building on well renowned models in the literature and to add on them with the dual aim of providing new hindsight and to enhance the understanding of those models by exploring their theoretical underpinnings. The thesis is composed of three chapters. The first one profits from the contribution of my supervisor Prof. Patrizio Tirelli, while the second and third chapters are not co-authored. The three chapters can be read as separated works, with their own rationale and motivations. However, they are part of a research program and therefore they share a common ground. In particular, the elements that make the chapters part of a unitary body are related on the one hand to the necessity of considering some salient facts of the financial crisis and on the other hand follow directly from the modelling strategy adopted. The financial crisis made clear that the housing sector has a distinctive role in the economy, which singles it out from other sectors. Housing is not only a durable good, but also the most important asset in households\u2019 balance sheets and understanding how its presence affects the propagation of shocks is crucial. In all the models developed in this thesis, housing is always modelled explicitly, having the additional role of working as collateral for borrowers. Heterogeneity, and therefore the departure from the representative agent model and from the idea that credit circulation is frictionless is taken into account in all the chapters. The economies considered are indeed characterized by the presence of savers and borrowers that interact in the credit market and given intrinsic characteristics of the model economy this gives the rise to dynamics which are influenced by the balance sheet of agents and feed back to the rest of the economy. The reminder of the thesis is structured as follows: in the first chapter I introduce a distinction between sub-prime borrowers and ordinary borrowers, investigating the response of the economy to different shocks. In particular, I focus on the transmission channels of an unexpected increase in housing investment risk in the sub-prime sector and of a monetary policy shock. The model features risky mortgages and a non-trivial banking sector, characterized by monopolistic competition and therefore sticky loan rates, which in the context of the model can be seen as a proxy for longer term mortgage contracts. The dynamics of the model are influenced by financial frictions, which are given by endogenous variations in the balance sheet of both constrained agents and banks. As a consequence, the results of our baseline model are given by the interaction and coexistence of different channels. Borrowers face collateral constraints and run up nominal debt. As a result, changes in the asset values, i.e. house prices, and in the inflation rate \u2013 Fisher effect \u2013 have a direct impact on households\u2019 borrowing conditions. Binding collateral constraints are instead affected by changes in the real interest rate. Indeed, an increase in the cost of the mortgage impairs borrowers\u2019 ability to get loans. This, combined with the fact that debt is nominal, contributes to a magnification of shocks. Banks\u2019 balance sheets are instead important for they influence directly credit conditions and therefore affect the shadow value of borrowing and the loan rate. In the second chapter I investigate the response of private consumption and output to public consumption shocks and to changes in taxes. It is well known that in frictionless economies it may be difficult to rationalize the empirically observed positive or non-significant response of private consumption to such shocks. The model focuses on the introduction of a collateral constraint tied to the expected value of the housing stock for a group of households. The presence of this kind of financial friction has important consequences for the transmission of fiscal policy, given that constrained and unconstrained households reaction to the shock is at odds. The model designed in this work also allows to compare the effect of a relatively large menu of taxes on the main macro-aggregates and to study changes in one of the institutional characteristic of the credit market, namely the loan-to-value ratio. The third chapter focuses on a technical aspect of DSGE models with durable goods. In these models, a co-movement problem between consumption of durable and non-durable goods arises after a monetary policy shock in presence of flexible durable prices, i.e. a monetary contraction causes an expansion in the durable sector. I revisit the debate in the literature on this problem and I try to calrify what are the necessary elements that those models need to take into account to avoid a negative correlation between durable and non-durable goods