Essays on non-linear aggregation in macroeconomics

In this PhD thesis I investigate the implications of heterogeneity and aggregation in
macroeconomic models. The importance of aggregation lies ~n the fact that when
heterogeneity is allowed, we cannot expect macro models to have the same characteristics
as the underlying micro models. In particular, a direct consequence of aggregation is that
the dynamic properties of the micro model do not hold in general for the macr,? model.
Despite this problem, modern macroeconomics tends to model aggregate data alone,
through the construction of models where the individual consumer or firm is related to
aggregate data under the guise of a 'representative agent'. In this thesis, I present a
heterogeneous real business cycle model where I allow for cross sectional heterogeneity in
the dynamics of the firm productivities. I show that heterogeneity allows the model to
generate very persistent dynamics that can mimic impressively those of actual data. This is
because, the dynamics of the model are now the result of the interactions between
heterogeneous firms. Another problem that often arises with heterogeneity is that through
aggregation, the dynamics that describe the co-movements between two variables can be
more persistent and complex than the dynamics observed for the individual behaviour.
Standard co-integration techniques are not able to deal with such persistent co-movements
since they cannot distinguish between persistent deviations from the equilibrium and
spurious relations. Therefore, many intuitive economic relations are often empirically
rejected. To this purpose, I introduce in the thesis a methodology which can test robustly for
co-integration between two variables, which deviate persistently from their long-run
equilibrium. I test for a co-integration in the Uncovered Interest Parity and the Purchasing
Power Parity with my approach and, unlike the standard approaches, it does not reject the
hypothesis that they hold in the long run.