Essays on tail risk in macroeconomics and finance: measurement and forecasting

This thesis is composed of three chapters that propose some novel approaches on tail risk for financial market and forecasting in finance and macroeconomics. The first part of this dissertation focuses on financial market correlations and introduces a simple measure of tail correlation, TailCoR, while the second contribution addresses the issue of identification of non- normal structural shocks in Vector Autoregression which is common on finance. The third part belongs to the vast literature on predictions of economic growth; the problem is tackled using a Bayesian Dynamic Factor model to predict Norwegian GDP.Chapter I: TailCoRThe first chapter introduces a simple measure of tail correlation, TailCoR, which disentangles linear and non linear correlation. The aim is to capture all features of financial market co- movement when extreme events (i.e. financial crises) occur. Indeed, tail correlations may arise because asset prices are either linearly correlated (i.e. the Pearson correlations are different from zero) or non-linearly correlated, meaning that asset prices are dependent at the tail of the distribution.Since it is based on quantiles, TailCoR has three main advantages: i) it is not based on asymptotic arguments, ii) it is very general as it applies with no specific distributional assumption, and iii) it is simple to use. We show that TailCoR also disentangles easily between linear and non-linear correlations. The measure has been successfully tested on simulated data. Several extensions, useful for practitioners, are presented like downside and upside tail correlations.In our empirical analysis, we apply this measure to eight major US banks for the period 2003-2012. For comparison purposes, we compute the upper and lower exceedance correlations and the parametric and non-parametric tail dependence coefficients. On the overall sample, results show that both the linear and non-linear contributions are relevant. The results suggest that co-movement increases during the financial crisis because of both the linear and non- linear correlations. Furthermore, the increase of TailCoR at the end of 2012 is mostly driven by the non-linearity, reflecting the risks of tail events and their spillovers associated with the European sovereign debt crisis. Chapter II: On the identification of non-normal shocks in structural VARThe second chapter deals with the structural interpretation of the VAR using the statistical properties of the innovation terms. In general, financial markets are characterized by non- normal shocks. Under non-Gaussianity, we introduce a methodology based on the reduction of tail dependency to identify the non-normal structural shocks.Borrowing from statistics, the methodology can be summarized in two main steps: i) decor- relate the estimated residuals and ii) the uncorrelated residuals are rotated in order to get a vector of independent shocks using a tail dependency matrix. We do not label the shocks a priori, but post-estimate on the basis of economic judgement.Furthermore, we show how our approach allows to identify all the shocks using a Monte Carlo study. In some cases, the method can turn out to be more significant when the amount of tail events are relevant. Therefore, the frequency of the series and the degree of non-normality are relevant to achieve accurate identification.Finally, we apply our method to two different VAR, all estimated on US data: i) a monthly trivariate model which studies the effects of oil market shocks, and finally ii) a VAR that focuses on the interaction between monetary policy and the stock market. In the first case, we validate the results obtained in the economic literature. In the second case, we cannot confirm the validity of an identification scheme based on combination of short and long run restrictions which is used in part of the empirical literature.Chapter III :Nowcasting NorwayThe third chapter consists in predictions of Norwegian Mainland GDP. Policy institutions have to decide to set their policies without knowledge of the current economic conditions. We estimate a Bayesian dynamic factor model (BDFM) on a panel of macroeconomic variables (all followed by market operators) from 1990 until 2011.First, the BDFM is an extension to the Bayesian framework of the dynamic factor model (DFM). The difference is that, compared with a DFM, there is more dynamics in the BDFM introduced in order to accommodate the dynamic heterogeneity of different variables. How- ever, in order to introduce more dynamics, the BDFM requires to estimate a large number of parameters, which can easily lead to volatile predictions due to estimation uncertainty. This is why the model is estimated with Bayesian methods, which, by shrinking the factor model toward a simple naive prior model, are able to limit estimation uncertainty.The second aspect is the use of a small dataset. A common feature of the literature on DFM is the use of large datasets. However, there is a literature that has shown how, for the purpose of forecasting, DFMs can be estimated on a small number of appropriately selected variables.Finally, through a pseudo real-time exercise, we show that the BDFM performs well both in terms of point forecast, and in terms of density forecasts. Results indicate that our model outperforms standard univariate benchmark models, that it performs as well as the Bloomberg Survey, and that it outperforms the predictions published by the Norges Bank in its monetary policy report.