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# Aggregation and the Microfoundations of Dynamic Macroeconomics

By: Mario Forni; Marco Lippi et al. | Book details

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Page 19
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2
How Many Common Shocks?

In the previous chapter we discussed a model with many common shocks and response functions which may differ across agents. Since the simpler model (1.1), with only one common shock, encompasses almost all time series models with heterogeneous agents proposed in recent literature, one may wonder whether such a generalization is really needed.

In the present chapter we conduct an empirical analysis based on US incomes and wages data, in order to get some indication about the number of common shocks. The result is that the single common shock hypothesis is strongly rejected. Moreover, even small numbers of common shocks, like two or three, appear inadequate.

Other evidence on the number of common shocks in macroeconomic data will be presented in Part III. Our purpose here is to show with a paradigmatic case that current models have poor empirical performance, so that a richer heterogeneity not only is theoretically interesting but also has a solid empirical motivation.

2.1. Perfect Correlation

2.1.1. For convenience let us rewrite equation (1.1) here:

(2.1)

In this section we evaluate the empirical performance of this model.

REMARK 2.1. When (2.1) is fulfilled, we can shift to the one-shock repre-sentation

where ut is a scalar unit variance white noise and a(L) is fundamental. However, this does not necessarily mean that there is only one structural common source of variation in the economy. Going back to model (1.2), we see that (2.1) can be obtained either by assuming h = 1, along with response functions identical across agents, up to multiplication by a constant, or by imposing and setting
ζt = a1(L)u1t + a2(L)u2t + + ah (L)uht.

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