Factor models, VARMA processes and parameter instability with applications in macroeconomics

As information technology improves, the availability of economic and finance time series grows in terms of both time and cross-section sizes. However, a large amount of information can lead to the curse of dimensionality problem when standard time series tools are used. Since most of these series are highly correlated, at least within some categories, their co-variability pattern and informational content can be approximated by a smaller number of (constructed) variables. A popular way to address this issue is the factor analysis. This framework has received a lot of attention since late 90's and is known today as the large dimensional approximate factor analysis.  Given the availability of data and computational improvements, a number of empirical and theoretical questions arises. What are the effects and transmission of structural shocks in a data-rich environment? Does the information from a large number of economic indicators help in properly identifying the monetary policy shocks with respect to a number of empirical puzzles found using traditional small-scale models? Motivated by the recent financial turmoil, can we identify the financial market shocks and measure their effect on real economy? Can we improve the existing method and incorporate another reduction dimension approach such as the VARMA modeling? Does it help in forecasting macroeconomic aggregates and impulse response analysis? Finally, can we apply the same factor analysis reasoning to the time varying parameters? Is there only a small number of common sources of time instability in the coefficients of empirical macroeconomic models?  This thesis concentrates on the structural factor analysis and VARMA modeling and answers these questions through five articles. The first two articles study the effects of monetary policy and credit shocks in a data-rich environment. The third article proposes a new framework that combines the factor analysis and VARMA modeling, while the fourth article applies this method to measure the effects of credit shocks in Canada. The contribution of the final chapter is to impose the factor structure on the time varying parameters in popular macroeconomic models, and show that there are few sources of this time instability.  The first article analyzes the monetary transmission mechanism in Canada using a factor-augmented vector autoregression (FAVAR) model. For small open economies like Canada, uncovering the transmission mechanism of monetary policy using VARs has proven to be an especially challenging task. Such studies on Canadian data have often documented the presence of anomalies such as a price, exchange rate, delayed overshooting and uncovered interest rate parity puzzles. We estimate a FAVAR model using large sets of monthly and quarterly macroeconomic time series. We find that the information summarized by the factors is important to properly identify the monetary transmission mechanism and contributes to mitigate the puzzles mentioned above, suggesting that more information does help. Finally, the FAVAR framework allows us to check impulse responses for all series in the informational data set, and thus provides the most comprehensive picture to date of the effect of Canadian monetary policy.  As the recent financial crisis and the ensuing global economic have illustrated, the financial sector plays an important role in generating and propagating shocks to the real economy. Financial variables thus contain information that can predict future economic conditions. In this paper we examine the dynamic effects and the propagation of credit shocks using a large data set of U.S. economic and financial indicators in a structural factor model. Identified credit shocks, interpreted as unexpected deteriorations of the credit market conditions, immediately increase credit spreads, decrease rates on Treasury securities and cause large and persistent downturns in the activity of many economic sectors. Such shocks are found to have important effects on real activity measures, aggregate prices, leading indicators and credit spreads. In contrast to other recent papers, our structural shock identification procedure does not require any timing restrictions between the financial and macroeconomic factors, and yields an interpretation of the estimated factors without relying on a constructed measure of credit market conditions from a large set of individual bond prices and financial series.  In third article, we study the relationship between VARMA and factor representations of a vector stochastic process, and propose a new class of factor-augmented VARMA (FAVARMA) models. We start by observing that in general multivariate series and associated factors do not both follow a finite order VAR process. Indeed, we show that when the factors are obtained as linear combinations of observable series, their dynamic process is generally a VARMA and not a finite-order VAR as usually assumed in the literature. Second, we show that even if the factors follow a finite-order VAR process, this implies a VARMA representation for the observable series. As result, we propose the FAVARMA framework that combines two parsimonious methods to represent the dynamic interactions between a large number of time series: factor analysis and VARMA modeling. We apply our approach in two pseudo-out-of-sample forecasting exercises using large U.S. and Canadian monthly panels taken from Boivin, Giannoni and Stevanovic (2010, 2009) respectively. The results show that VARMA factors help in predicting several key macroeconomic aggregates relative to standard factor forecasting models. Finally, we estimate the effect of monetary policy using the data and the identification scheme as in Bernanke, Boivin and Eliasz (2005). We find that impulse responses from a parsimonious 6-factor FAVARMA(2,1) model give an accurate and comprehensive picture of the effect and the transmission of monetary policy in U.S.. To get similar responses from a standard FAVAR model, Akaike information criterion estimates the lag order of 14. Hence, only 84 coefficients governing the factors dynamics need to be estimated in the FAVARMA framework, compared to FAVAR model with 510 VAR parameters.  In fourth article we are interested in identifying and measuring the effects of credit shocks in Canada in a data-rich environment. In order to incorporate information from a large number of economic and financial indicators, we use the structural factor-augmented VARMA model. In the theoretical framework of the financial accelerator, we approximate the external finance premium by credit spreads. On one hand, we find that an unanticipated increase in US external finance premium generates a significant and persistent economic slowdown in Canada; the Canadian external finance premium rises immediately while interest rates and credit measures decline. From the variance decomposition analysis, we observe that the credit shock has an important effect on several real activity measures, price indicators, leading indicators, and credit spreads. On the other hand, an unexpected increase in Canadian external finance premium shows no significant effect in Canada. Indeed, our results suggest that the effects of credit shocks in Canada are essentially caused by the unexpected changes in foreign credit market conditions. Finally, given the identification procedure, we find that our structural factors do have an economic interpretation.  The behavior of economic agents and environment may vary over time (monetary policy strategy shifts, stochastic volatility) implying parameters' instability in reduced-form models. Standard time varying parameter (TVP) models usually assume independent stochastic processes for all TVPs. In the final article, I show that the number of underlying sources of parameters' time variation is likely to be small, and provide empirical evidence on factor structure among TVPs of popular macroeconomic models. To test for the presence of, and estimate low dimension sources of time variation in parameters, I apply the factor time varying parameter (Factor-TVP) model, proposed by Stevanovic (2010), to a standard monetary TVP-VAR model. I find that one factor explains most of the variability in VAR coefficients, while the stochastic volatility parameters vary in the idiosyncratic way. The common factor is highly and positively correlated to the unemployment rate. To incorporate the recent financial crisis, the same exercise is conducted with data updated to 2010Q3. The VAR parameters present an important change after 2007, and the procedure suggests two factors. When applied to a large-dimensional structural factor model, I find that four dynamic factors govern the time instability in almost 700 coefficients.

Keyphrases: factor analysis, VARMA model, forecasting, impulse responses, structural analysis, time varying parameter model