Recent work on econometric detection mechanisms has shown the effectiveness of recursive procedures in identifying and dating financial bubbles in real time. These procedures are useful as warning ...alerts in surveillance strategies conducted by central banks and fiscal regulators with real-time data. Use of these methods over long historical periods presents a more serious econometric challenge due to the complexity of the nonlinear structure and break mechanisms that are inherent in multiple-bubble phenomena within the same sample period. To meet this challenge, this article develops a new recursive flexible window method that is better suited for practical implementation with long historical time series. The method is a generalized version of the sup augmented Dickey–Fuller (ADF) test of Phillips et al. ("Explosive behavior in the 1990s NASDAQ: When did exuberance escalate asset values?" International Economic Review 52 (2011), 201–26; PWY) and delivers a consistent real-time date-stamping strategy for the origination and termination of multiple bubbles. Simulations show that the test significantly improves discriminatory power and leads to distinct power gains when multiple bubbles occur. An empirical application of the methodology is conducted on S&P 500 stock market data over a long historical period from January 1871 to December 2010. The new approach successfully identifies the well-known historical episodes of exuberance and collapses over this period, whereas the strategy of PWY and a related cumulative sum (CUSUM) dating procedure locate far fewer episodes in the same sample range.
This article provides the limit theory of real-time dating algorithms for bubble detection that were suggested in Phillips, Wu, and Yu (PWY; International Economic Review 52 2011, 201–26) and in a ...companion paper by the present authors (Phillips, Shi, and Yu, 2015; PSY; International Economic Review 56 2015a, 1099–1134. Bubbles are modeled using mildly explosive bubble episodes that are embedded within longer periods where the data evolve as a stochastic trend, thereby capturing normal market behavior as well as exuberance and collapse. Both the PWY and PSY estimates rely on recursive right-tailed unit root tests (each with a different recursive algorithm) that may be used in real time to locate the origination and collapse dates of bubbles. Under certain explicit conditions, the moving window detector of PSY is shown to be a consistent dating algorithm even in the presence of multiple bubbles. The other algorithms are consistent detectors for bubbles early in the sample and, under stronger conditions, for subsequent bubbles in some cases. These asymptotic results and accompanying simulations guide the practical implementation of the procedures. They indicate that the PSY moving window detector is more reliable than the PWY strategy, sequential application of the PWY procedure, and the CUSUM procedure.
We propose a procedure of iterating the HP filter to produce a smarter smoothing device, called the boosted HP (bHP) filter, based on L2‐boosting in machine learning. Limit theory shows that the bHP ...filter asymptotically recovers trend mechanisms that involve integrated processes, deterministic drifts, and structural breaks, covering the most common trends that appear in current modeling methodology. A stopping criterion automates the algorithm, giving a data‐determined method for data‐rich environments. The methodology is illustrated in simulations and with three real data examples that highlight the differences between simple HP filtering, the bHP filter, and an alternative autoregressive approach.
Economic transition and growth Phillips, Peter C. B.; Sul, Donggyu
Journal of applied econometrics (Chichester, England),
November/December 2009, Letnik:
24, Številka:
7
Journal Article
Recenzirano
Some extensions of neoclassical growth models are discussed that allow for cross-section heterogeneity among economies and evolution in rates of technological progress over time. The models offer a ...spectrum of transitional behavior among economies that includes convergence to a common steady-state path as well as various forms of transitional divergence and convergence. Mechanisms for modeling such transitions, measuring them econometrically, assessing group behavior and selecting subgroups are developed in the paper. Some econometric issues with the commonly used augmented Solow regressions are pointed out, including problems of endogeneity and omitted variable bias which arise under conditions of transitional heterogeneity. Alternative regression methods for analyzing economic transition are given which lead to a new test of the convergence hypothesis and a new procedure for detecting club convergence clusters. Transition curves for individual economies and subgroups of economies are estimated in a series of empirical applications of the methods to regional US data, OECD data and Penn World Table data.
Expansion and collapse are two key features of a financial asset bubble. Bubble expansion may be modeled using a mildly explosive process. Bubble implosion may take several different forms depending ...on the nature of the collapse and therefore requires some flexibility in modeling. This paper first strengthens the theoretical foundation of the real time bubble monitoring strategy proposed in Phillips, Shi and Yu (2015a,b, PSY) by developing analytics and studying the performance characteristics of the testing algorithm under alternative forms of bubble implosion which capture various return paths to market normalcy. Second, we propose a new reverse sample use of the PSY procedure for detecting crises and estimating the date of market recovery. Consistency of the dating estimators is established and the limit theory addresses new complications arising from the alternative forms of bubble implosion and the endogeneity effects present in the reverse regression. A real-time version of the strategy is provided that is suited for practical implementation. Simulations explore the finite sample performance of the strategy for dating market recovery. The use of the PSY strategy for bubble monitoring and the new procedure for crisis detection are illustrated with an application to the Nasdaq stock market.
This paper provides a novel mechanism for identifying and estimating latent group structures in panel data using penalized techniques. We consider both linear and nonlinear models where the ...regression coefficients are heterogeneous across groups but homogeneous within a group and the group membership is unknown. Two approaches are considered—penalized profile likelihood (PPL) estimation for the general nonlinear models without endogenous regressors, and penalized GMM (PGMM) estimation for linear models with endogeneity. In both cases, we develop a new variant of Lasso called classifier-Lasso (C-Lasso) that serves to shrink individual coefficients to the unknown group-specific coefficients. C-Lasso achieves simultaneous classification and consistent estimation in a single step and the classification exhibits the desirable property of uniform consistency. For PPL estimation, C-Lasso also achieves the oracle property so that group-specific parameter estimators are asymptotically equivalent to infeasible estimators that use individual group identity information. For PGMM estimation, the oracle property of C-Lasso is preserved in some special cases. Simulations demonstrate good finite-sample performance of the approach in both classification and estimation. Empirical applications to both linear and nonlinear models are presented.
A new panel data model is proposed to represent the behavior of economies in transition, allowing for a wide range of possible time paths and individual heterogeneity. The model has both common and ...individual specific components, and is formulated as a nonlinear time varying factor model. When applied to a micro panel, the decomposition provides flexibility in idiosyncratic behavior over time and across section, while retaining some commonality across the panel by means of an unknown common growth component. This commonality means that when the heterogeneous time varying idiosyncratic components converge over time to a constant, a form of panel convergence holds, analogous to the concept of conditional sigma convergence. The paper provides a framework of asymptotic representations for the factor components that enables the development of econometric procedures of estimation and testing. In particular, a simple regression based convergence test is developed, whose asymptotic properties are analyzed under both null and local alternatives, and a new method of clustering panels into club convergence groups is constructed. These econometric methods are applied to analyze convergence in cost of living indices among 19 U.S. metropolitan cities.
A recursive test procedure is suggested that provides a mechanism for testing explosive behavior, date stamping the origination and collapse of economic exuberance, and providing valid confidence ...intervals for explosive growth rates. The method involves the recursive implementation of a right-side unit root test and a sup test, both of which are easy to use in practical applications, and some new limit theory for mildly explosive processes. The test procedure is shown to have discriminatory power in detecting periodically collapsing bubbles, thereby overcoming a weakness in earlier applications of unit root tests for economic bubbles. An empirical application to the Nasdaq stock price index in the 1990s provides confirmation of explosiveness and date stamps the origination of financial exuberance to mid-1995, prior to the famous remark in December 1996 by Alan Greenspan about irrational exuberance in the financial market, thereby giving the remark empirical content.
A new recursive regression methodology is introduced to analyze the bubble characteristics of various financial time series during the subprime crisis. The methods modify a technique proposed in ...Phillips, Wu, and Yu (2011) and provide a technology for identifying bubble behavior with consistent dating of their origination and collapse. The tests serve as an early warning diagnostic of bubble activity and a new procedure is introduced for testing bubble migration across markets. Three relevant financial series are investigated, including a financial asset price (a house price index), a commodity price (the crude oil price), and one bond price (the spread between Baa and Aaa). Statistically significant bubble characteristics are found in all of these series. The empirical estimates of the origination and collapse dates suggest a migration mechanism among the financial variables. A bubble emerged in the real estate market in February 2002. After the subprime crisis erupted in 2007, the phenomenon migrated selectively into the commodity market and the bond market, creating bubbles which subsequently burst at the end of 2008, just as the effects on the real economy and economic growth became manifest. Our empirical estimates of the origination and collapse dates and tests of migration across markets match well with the general dateline of the crisis put forward in the recent study by Caballero, Farhi, and Gourinchas (2008a).
This paper studies high-dimensional vector autoregressions (VARs) augmented with common factors that allow for strong cross-sectional dependence. Models of this type provide a convenient mechanism ...for accommodating the interconnectedness and temporal co-variability that are often present in large dimensional systems. We propose an ℓ1-nuclear-norm regularized estimator and derive the non-asymptotic upper bounds for the estimation errors as well as large sample asymptotics for the estimates. A singular value thresholding procedure is used to determine the correct number of factors with probability approaching one. Both the LASSO estimator and the conservative LASSO estimator are employed to improve estimation precision. The conservative LASSO estimates of the non-zero coefficients are shown to be asymptotically equivalent to the oracle least squares estimates. Simulations demonstrate that our estimators perform reasonably well in finite samples given the complex high-dimensional nature of the model. In an empirical illustration we apply the methodology to explore dynamic connectedness in the volatilities of financial asset prices and the transmission of ‘investor fear’. The findings reveal that a large proportion of connectedness is due to the common factors. Conditional on the presence of these common factors, the results still document remarkable connectedness due to the interactions between the individual variables, thereby supporting a common factor augmented VAR specification.
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