Three essays in continuous-time macro-finance

This doctoral dissertation consists of three chapters on continuous-time general equilibrium models in macro-finance. Each chapter relates to its peers as they all belong to the literature that studies how financial frictions over heterogeneous classes of agents may channel time-varying financial leverage, risk premiums and, in turn, affect aggregate economic dynamics. Chapter 1 reviews some topics of continuous-time methods as they relate to the core mechanisms prominent in the new-born macro-finance literature. The contents span across three sub-sections that, by progressively adding frictions and heterogeneity among economic actors, develop the modelling environment that act as a baseline for further developments in Chapters 2 and 3. The focus is on the role of market incompleteness and heterogeneity at determining long-run equilibrium dynamics. Chapter 2 studies the inter-dependence among intermediaries' risk-pooling activity, economic macro-dynamics, and households' welfare. To do so, it develops a suitable DSGE model of a productive economy, populated by heterogeneous households and homogeneous financial intermediaries. Moreover, the model features financial frictions in the form of market segmentation and intermediation costs. We find that intermediaries risk pooling associates to financial leverage that is, exogenous systematic shocks change the relative size of the financial sector, and makes its leverage state-dependent. In equilibrium, counter-cyclical leverage also channels counter-cyclical Sharpe ratios and pro-cyclical risk-free interest rates. Last, we investigate the relationship between financial sector capitalization (size) and households' welfare. According to our results, a too small financial sector associates to sub-optimal idiosyncratic risk pooling. Nonetheless, it fosters the growth rate of households' consumption. On the other hand, when the financial sector is too large, it destroys resources after the payment of intermediation costs. Therefore, households benefit the most when the financial sector is neither too small nor too big. Finally, Chapter 3 studies how banks resolution regimes may affect households' welfare in the short and in the long-run. It does so within the framework of a DSGE model of a productive economy populated by homogeneous households and banks.The model introduces financial frictions by assuming that: a) Banks benefit of a cost advantage at monitoring capital producing firms: b) The issuance of banks' equity is costly. In equilibrium, we find that it is micro-optimal for each bank to be recapitalized by its own shareholders up to a certain threshold where the marginal value of banks' equity equals the cost of its recapitalization. Nonetheless, as banks are homogeneous and uniformly exposed to aggregate shocks, their default is always systematic. It follows that, as the whole banking sector is jeopardized, a bailout resolution that tops up the micro-optimal recapitalization may improve long-run welfare, even when households are homogeneous themselves. This happens because, in a perfectly competitive environment, agents fail at internalizing the positive effect of a greater banks' aggregate capitalization over equilibrium prices.