Aggregation in Large Dynamic Panels

This paper considers the problem of aggregation in the case of large linear dynamic panels, where each micro unit is potentially related to all other micro units, and where micro innovations are allowed to be cross sectionally dependent. Following Pesaran (2003), an optimal aggregate function is derived, and the limiting behavior of the aggregation error is investigated as N (the number of cross section units) increases. Certain distributional features of micro parameters are also identified from the aggregate function. The paper then establishes Granger's (1980) conjecture regarding the long memory properties of aggregate variables from 'a very large scale dynamic, econometric model', and considers the time profiles of the effects of macro and micro shocks on the aggregate and disaggregate variables. Some of these findings are illustrated in Monte Carlo experiments, where we also study the estimation of the aggregate effects of micro and macro shocks. The paper concludes with an empirical application to consumer price inflation in Germany, France and Italy, and re-examines the extent to which ‘observed’ inflation persistence at the aggregate level is due to aggregation and/or common unobserved factors. Our findings suggest that dynamic heterogeneity as well as persistent common factors are needed for explaining the observed persistence of the aggregate inflation.aggregation, large dynamic panels, long memory, weak and strong cross section dependence, VAR models, impulse responses, factor models, inflation persistence

Econometric analysis of high dimensional VARs featuring a dominant unit

This paper extends the analysis of infinite dimensional vector autoregressive models (IVAR) proposed in Chudik and Pesaran (2010) to the case where one of the variables or the cross section units in the IVAR model is dominant or pervasive. This extension is not straightforward and involves several technical difficulties. The dominant unit influences the rest of the variables in the IVAR model both directly and indirectly, and its effects do not vanish even as the dimension of the model (N) tends to infinity. The dominant unit acts as a dynamic factor in the regressions of the non-dominant units and yields an infinite order distributed lag relationship between the two types of units. Despite this it is shown that the effects of the dominant unit as well as those of the neighborhood units can be consistently estimated by running augmented least squares regressions that include distributed lag functions of the dominant unit. The asymptotic distribution of the estimators is derived and their small sample properties investigated by means of Monte Carlo experiments. JEL Classification: C10, C33, C51Dominant Units, Factor models, IVAR Models, Large Panels, Weak and Strong Cross Section Dependence

Size, openness, and macroeconomic interdependence

The curse of dimensionality, a problem associated with analyzing the interaction of a relatively large number of endogenous macroeconomic variables, is a prevailing issue in the open economy macro literature. The most common practise to mitigate this problem is to apply the so-called Small Open Economy Framework (SOEF). In this paper, we aim to review under which conditions the SOEF is a justifiable approximation and how severe the consequences of violation of key conditions might be. Thereby, we use a multicountry general equilibrium model as a laboratory. First, we derive the conditions that ensure the existence of the equilibrium and study the properties of the equilibrium using large N asymptotics. Second, we show that the SOEF is a valid approximation only for economies (i) that have a diversified foreign trade structure and if (ii) there is no globally dominant economy in the system. Third, we illustrate that macroeconomic interdependence is primarily related to the degree of trade diversification, and not to the extent of trade openness. Furthermore, we provide some evidence on the pattern of global macroeconomic interdependence by calculating probability impulse response functions in our calibrated multicountry model using data for 153 economies. JEL Classification: F41DSGE Models, Factor models, Open Economy Macroeconomics, Weak and Strong Cross Section Dependence

Infinite-dimensional VARs and factor models

This paper introduces a novel approach for dealing with the 'curse of dimensionality' in the case of large linear dynamic systems. Restrictions on the coefficients of an unrestricted VAR are proposed that are binding only in a limit as the number of endogenous variables tends to infinity. It is shown that under such restrictions, an infinite-dimensional VAR (or IVAR) can be arbitrarily well characterized by a large number of finite-dimensional models in the spirit of the global VAR model proposed in Pesaran et al. (JBES, 2004). The paper also considers IVAR models with dominant individual units and shows that this will lead to a dynamic factor model with the dominant unit acting as the factor. The problems of estimation and inference in a stationary IVAR with unknown number of unobserved common factors are also investigated. A cross section augmented least squares estimator is proposed and its asymptotic distribution is derived. Satisfactory small sample properties are documented by Monte Carlo experiments. JEL Classification: C10, C33, C51Large N and T Panels, Factor models, Global VAR, VAR, Weak and Strong Cross Section Dependence

Liquidity, risk and the global transmission of the 2007-08 financial crisis and the 2010-2011 sovereign debt crisis

The paper analyses the transmission of liquidity shocks and risk shocks to global financial markets. Using a Global VAR methodology, the findings reveal fundamental di¤erences in the transmission strength and pattern between the 2007-08 financial crisis and the 2010-11 sovereign debt crisis. Unlike in the former crisis, emerging market economies have become much more resilient to adverse shocks in 2010-11. Moreover, a flight-to-safety phenomenon across asset classes has become particularly strong during the 2010-11 sovereign debt crisis, with risk shocks driving down bond yields in key advanced economies. The paper relates this evolving transmission pattern to portfolio choice decisions by investors and finds that countries' sovereign rating, quality of institutions and their financial exposure are determinants of cross-country differences in the transmission. JEL Classification: E44, F3, C5.Global financial crisis, sovereign debt crisis, liquidity, risk, capital flows, transmission, high dimensional VARs, advanced economies, emerging market economies.

Econometric Analysis of High Dimensional VARs Featuring a Dominant Unit

This paper extends the analysis of infinite dimensional vector autoregressive models (IVAR) proposed in Chudik and Pesaran (2010) to the case where one of the variables or the cross section units in the IVAR model is dominant or pervasive. This extension is not straightforward and involves several technical difficulties. The dominant unit influences the rest of the variables in the IVAR model both directly and indirectly, and its effects do not vanish even as the dimension of the model (N) tends to infinity. The dominant unit acts as a dynamic factor in the regressions of the non-dominant units and yields an infinite order distributed lag relationship between the two types of units. Despite this it is shown that the effects of the dominant unit as well as those of the neighborhood units can be consistently estimated by running augmented least squares regressions that include distributed lag functions of the dominant unit. The asymptotic distribution of the estimators is derived and their small sample properties investigated by means of Monte Carlo experiments.IVAR models, dominant units, large panels, weak and strong cross section dependence, factor models

Aggregation in large dynamic panels

This paper investigates the problem of aggregation in the case of large linear dynamic panels, where each micro unit is potentially related to all other micro units, and where micro innovations are allowed to be cross sectionally dependent. Following Pesaran (2003), an optimal aggregate function is derived and used (i) to establish conditions under which Granger's (1980) conjecture regarding the long memory properties of aggregate variables from "a very large scale dynamic, econometric model" holds, and (ii) to show which distributional features of micro parameters can be identified from the aggregate model. ; The paper also derives impulse response functions for the aggregate variables, distinguishing between the effects of macro and aggregated idiosyncratic shocks. Some of the findings of the paper are illustrated by Monte Carlo experiments. The paper also contains an empirical application to consumer price inflation in Germany, France and Italy, and re-examines the extent to which "observed" inflation persistence at the aggregate level is due to aggregation and/or common unobserved factors. Our findings suggest that dynamic heterogeneity as well as persistent common factors are needed for explaining the observed persistence of the aggregate inflation.Index numbers (Economics) ; Price levels

Aggregation in Large Dynamic Panels

This paper considers the problem of aggregation in the case of large linear dynamic panels, where each micro unit is potentially related to all other micro units, and where micro innovations are allowed to be cross sectionally dependent. Following Pesaran (2003), an optimal aggregate function is derived, and the limiting behavior of the aggregation error is investigated as N (the number of cross section units) increases. Certain distributional features of micro parameters are also identified from the aggregate function. The paper then establishes Granger’s (1980) conjecture regarding the long memory properties of aggregate variables from .a very large scale dynamic, econometric model., and considers the time profiles of the effects of macro and micro shocks on the aggregate and disaggregate variables. Some of these findings are illustrated in Monte Carlo experiments, where we also study the estimation of the aggregate effects of micro and macro shocks. The paper concludes with an empirical application to consumer price inflation in Germany, France and Italy, and re-examines the extent to which ‘observed’ inflation persistence at the aggregate level is due to aggregation and/or common unobserved factors. Our findings suggest that dynamic heterogeneity as well as persistent common factors are needed for explaining the observed persistence of the aggregate inflation.aggregation, large dynamic panels, long memory, weak and strong cross section dependence, VAR models, impulse responses, factor models, inflation persistence

Weak and strong cross section dependence and estimation of large panels

This paper introduces the concepts of time-specific weak and strong cross section dependence. A double- indexed process is said to be cross sectionally weakly dependent at a given point in time, t, if its weighted average along the cross section dimension (N) converges to its expectation in quadratic mean, as N is increased without bounds for all weights that satisfy certain ‘granularity’ conditions. Relationship with the notions of weak and strong common factors is investigated and an application to the estimation of panel data models with an infinite number of weak factors and a finite number of strong factors is also considered. The paper concludes with a set of Monte Carlo experiments where the small sample properties of estimators based on principal components and CCE estimators are investigated and compared under various assumptions on the nature of the unobserved common effects. JEL Classification: C10, C31, C33Panels, Strong and Weak Cross Section Dependence, Weak and Strong Factors