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Title: Contagion and latent factors in large systems Authors:  Federico Carlini - USI, Lugano (Switzerland) [presenting]
Patrick Gagliardini - University of Lugano (Switzerland)
Abstract: A large-dimensional time series model is considered that disentangles dependence patterns due to either the effect of latent common stochastic factors or direct causality effects (i.e. contagion). Our model is $Y_t = C Y_{t-1} + B f_t + u_t$, $t=1,\ldots,T$ where $Y_t$ has dimension $N$, $f_t$ is a $K$-dimensional latent factor independent of $u_t$, a weakly dependent process over time, and $C$ is a contagion matrix. We study identification and estimation when $N$ and $T$ are large. The contagion matrix $C$ has $N^2$ parameters and we impose the structure $C= (1/N)(\alpha \beta^\prime +\varepsilon)$ for identifiability and interpretability purposes, where $\alpha$ and $\beta$ are $N \times r$ factors independent by $\varepsilon$, a $N\times N$ random matrix with i.i.d. elements across. We prove that $Y_t = \alpha g_t + B f_t + u_t = \Lambda h_t + u_t $, where $g_t$ is a $r-$dimensional unobservable factor that captures contagion, $h_t=(g_t^\prime,f_t^\prime)^\prime$ and $\Lambda=(\alpha:B)$. We estimate $\Lambda$ and $h_t$ with PCA. We identify $r$ and $K$ through tests on the canonical correlation of $h_t$ and $h_{t-1}$. Moreover, we estimate $g_t$, $f_t$, $\alpha$ and $\beta$. Finally, we find the asymptotic properties of the estimators and we illustrate the estimation method with an empirical application.