Final Report Summary - CSDPD_CP (Econometric Modelling of Short Panels with Applications in Financial Econometrics)
In recent years, there has been an increase in the availability of large panels of data (also known as large-N large-T panels), i.e. datasets which contain observations on a large number of individuals, firms, households etc. observed over a long period of time. The availability of such datasets is central to attaining a deeper understanding of complex interdependencies between economic and financial variables. Such an understanding, in turn, is fundamental to designing sound economic and financial policies, as the 2008 financial crisis has reminded us once again. Importantly, however, while large macro and financial panels are rich in valuable information, extracting this information requires econometric methods that are capable of dealing with computational and mathematical problems associated with large-dimensional data. Developing such methods is the general objective of this 4-year research project, which is supported by the Marie Curie Actions of the FP7 program. In particular:
(A) A general objective is to model and understand the structure of dependence between financial returns. One classical approach is to model time-varying covariances. This approach provides (i) a snapshot of the pattern of correlations at any given point in time, (ii) the dynamic evolution of this pattern over time, and (iii) the ability to predict this pattern. One can also go beyond correlations and consider more complex manifestations of dependence, in order to answer questions such as “what is the probability that 1/4 of all the firms trading in the stock market will suffer more than a 25% drop in their stock price?” Such questions can be investigated by copula methods and are clearly important to measuring the stability of financial markets. Unfortunately, both time-varying correlation models and copula methods become complicated and computationally too demanding when applied to more than a few dozen assets.
(B) Modelling large panels is also susceptible to more fundamental technical difficulties, beyond computational issues. A typical example is the well-known incidental parameter problem. This causes the econometric analysis to yield biased and, therefore, misleading results. In general, this becomes more acute when one conducts econometric analysis on a large number of individuals (or firms, assets etc.) in the absence of a comparably large number of time-series observations per individual. This problem is observed in a diverse set of literatures, ranging from labour economics to financial economics. A common solution is to utilize bias-correction methods. However, available methods cannot be freely applied to financial and macroeconomic panels, as these methods widely assume independence across individuals.
Work done so far, as well as the achievements, can be summarized as follows.
(1) Prof Pakel’s joint work with Professors Robert Engle (NYU Stern), Neil Shephard (Harvard University) and Kevin Sheppard (University of Oxford) has led to the development of a computationally fast method for modelling time-varying covariance matrices. Large scale estimation of such models via standard methods suffers from a bias problem which worsens as the number of assets under consideration increases. In this paper, they show by both theoretical and empirical results that their approach is free of this bias. Importantly, with this paper they also introduce large-N large-T asymptotics into the volatility modelling literature. The finished paper is titled “Fitting Vast Dimensional Time-Varying Covariance Models,” and is available online.
(2) Prof Pakel has also been working on the properties of the incidental parameter bias in nonlinear and dynamic panel data models. Although there is an active and sizeable literature on this topic, the possibility of cross-sectionally dependent datasets is generally assumed away. His main finding is that cross-section dependence leads to extra forms of bias in estimation (in addition to the incidental parameter bias), but this happens only under very strong types of dependence. He also proposes two options for correcting this bias based on the integrated likelihood and split panel jackknife methods. Moreover, he provides central limit theorems for various dependence scenarios, based on low-level conditions. The paper also provides a method for constructing valid confidence intervals. Since the analysis is conducted within a general framework, his results are potentially generally applicable. As an application, he proposes a novel method for modelling financial volatility when the available data are not rich enough for standard methods to work. The title of the finished paper is “Bias Reduction in Nonlinear and Dynamic Panels in the Presence of Cross-Section Dependence,” and is available online.
(3) Prof Pakel is also working on a joint project with Dr Dong Hwan Oh (Federal Reserve Board) and Prof Andrew Patton (Duke University). This project proposes a factor copula estimation method capable of modelling dependence between arbitrarily large numbers of financial variables. For this purpose, they develop a simulated method of moments (SMM) estimator for a non-differentiable estimation function. An important contribution of this paper is that it provides the theory for SMM-based estimation with non-smooth functions under large-N large-T asymptotics, and dependence across both time and cross-section. Their theoretical results are vindicated by simulation results for various relevant settings.
Prof Pakel’s research agenda has the potential to deliver important contributions that will significantly advance our theoretical and practical capabilities in dealing with large datasets. In particular, the methods he is developing will be instrumental in obtaining a fundamental grasp of the connections in financial markets. As recent economic and financial events also confirm, this is of key importance to policy making. It must be underlined that Prof Pakel’s work is not necessarily applicable to financial data only. For example, his research on the incidental parameter bias is based on a general panel data model framework. As such, his results are potentially relevant to other fields that use similar modelling frameworks, such as labour economics and development economics. In light of these points, the project promises to make a significant social impact by developing tools that will be useful to both practitioners and policy makers.
The project website can be accessed at http://staff.bilkent.edu.tr/cavit/cig/ .
Contact:
Cavit Pakel
Assistant Professor
Department of Economics
Bilkent University
06800, Ankara, Turkey
Tel: +90 312 290 1406
e-mail: cavit.pakel@bilkent.edu.tr
(A) A general objective is to model and understand the structure of dependence between financial returns. One classical approach is to model time-varying covariances. This approach provides (i) a snapshot of the pattern of correlations at any given point in time, (ii) the dynamic evolution of this pattern over time, and (iii) the ability to predict this pattern. One can also go beyond correlations and consider more complex manifestations of dependence, in order to answer questions such as “what is the probability that 1/4 of all the firms trading in the stock market will suffer more than a 25% drop in their stock price?” Such questions can be investigated by copula methods and are clearly important to measuring the stability of financial markets. Unfortunately, both time-varying correlation models and copula methods become complicated and computationally too demanding when applied to more than a few dozen assets.
(B) Modelling large panels is also susceptible to more fundamental technical difficulties, beyond computational issues. A typical example is the well-known incidental parameter problem. This causes the econometric analysis to yield biased and, therefore, misleading results. In general, this becomes more acute when one conducts econometric analysis on a large number of individuals (or firms, assets etc.) in the absence of a comparably large number of time-series observations per individual. This problem is observed in a diverse set of literatures, ranging from labour economics to financial economics. A common solution is to utilize bias-correction methods. However, available methods cannot be freely applied to financial and macroeconomic panels, as these methods widely assume independence across individuals.
Work done so far, as well as the achievements, can be summarized as follows.
(1) Prof Pakel’s joint work with Professors Robert Engle (NYU Stern), Neil Shephard (Harvard University) and Kevin Sheppard (University of Oxford) has led to the development of a computationally fast method for modelling time-varying covariance matrices. Large scale estimation of such models via standard methods suffers from a bias problem which worsens as the number of assets under consideration increases. In this paper, they show by both theoretical and empirical results that their approach is free of this bias. Importantly, with this paper they also introduce large-N large-T asymptotics into the volatility modelling literature. The finished paper is titled “Fitting Vast Dimensional Time-Varying Covariance Models,” and is available online.
(2) Prof Pakel has also been working on the properties of the incidental parameter bias in nonlinear and dynamic panel data models. Although there is an active and sizeable literature on this topic, the possibility of cross-sectionally dependent datasets is generally assumed away. His main finding is that cross-section dependence leads to extra forms of bias in estimation (in addition to the incidental parameter bias), but this happens only under very strong types of dependence. He also proposes two options for correcting this bias based on the integrated likelihood and split panel jackknife methods. Moreover, he provides central limit theorems for various dependence scenarios, based on low-level conditions. The paper also provides a method for constructing valid confidence intervals. Since the analysis is conducted within a general framework, his results are potentially generally applicable. As an application, he proposes a novel method for modelling financial volatility when the available data are not rich enough for standard methods to work. The title of the finished paper is “Bias Reduction in Nonlinear and Dynamic Panels in the Presence of Cross-Section Dependence,” and is available online.
(3) Prof Pakel is also working on a joint project with Dr Dong Hwan Oh (Federal Reserve Board) and Prof Andrew Patton (Duke University). This project proposes a factor copula estimation method capable of modelling dependence between arbitrarily large numbers of financial variables. For this purpose, they develop a simulated method of moments (SMM) estimator for a non-differentiable estimation function. An important contribution of this paper is that it provides the theory for SMM-based estimation with non-smooth functions under large-N large-T asymptotics, and dependence across both time and cross-section. Their theoretical results are vindicated by simulation results for various relevant settings.
Prof Pakel’s research agenda has the potential to deliver important contributions that will significantly advance our theoretical and practical capabilities in dealing with large datasets. In particular, the methods he is developing will be instrumental in obtaining a fundamental grasp of the connections in financial markets. As recent economic and financial events also confirm, this is of key importance to policy making. It must be underlined that Prof Pakel’s work is not necessarily applicable to financial data only. For example, his research on the incidental parameter bias is based on a general panel data model framework. As such, his results are potentially relevant to other fields that use similar modelling frameworks, such as labour economics and development economics. In light of these points, the project promises to make a significant social impact by developing tools that will be useful to both practitioners and policy makers.
The project website can be accessed at http://staff.bilkent.edu.tr/cavit/cig/ .
Contact:
Cavit Pakel
Assistant Professor
Department of Economics
Bilkent University
06800, Ankara, Turkey
Tel: +90 312 290 1406
e-mail: cavit.pakel@bilkent.edu.tr