998 research outputs found
Estimation and Inference with Near Unit Roots
No full textNew methods are developed for identifying, estimating and performing inference with nonstationary time series that have autoregressive roots near unity. The approach subsumes unit root (UR), local unit root (LUR), mildly integrated (MI) and mildly explosive (ME) specifications in the new model formulation. It is shown how a new parameterization involving a localizing rate sequence that characterizes departures from unity can be consistently estimated in all cases. Simple pivotal limit distributions that enable valid inference about the form and degree of nonstationarity apply for MI and ME specifications and new limit theory holds in UR and LUR cases. Normalizing and variance stabilizing properties of the new parameterization are explored. Simulations are reported that reveal some of the advantages of this alternative formulation of nonstationary time series. A housing market application of the methods is conducted that distinguishes the differing forms of house price behavior in Australian state capital cities over the past decade
Modeling speculative bubbles with diverse investor expectations
No full textWe construct a model of asset market exuberance, collapse and recovery using subjective investor-based rational expectations about the impact of fundamentals on the market price. Investors are assumed to have heterogeneous market sentiments, allowing them to be exuberant, cautious, or fundamentalist via boundary conditions that describe their respective views of the market impact of the same economic fundamentals. Equilibrium solution paths of the model take varying forms, depending on the parameter settings that reflect the importance of each type of market participant. This rational expectations model of asset pricing is shown to be consistent with a simple explosive continuous time autoregression when exuberant sentiment dominates the market. The model explains asset price bubbles, including expansion and subsequent collapse, together with long-term recovery. Extensions of the model allow for contagion effects in which market sentiments are transmitted from a primary market to a secondary market, reproducing speculative behavior and corrections in the secondary market. Some of the implications of the model for empirical work are explored
IV and GMM inference in endogenous stochastic unit root models
No full textLieberman and Phillips (2017; LP) introduced a multivariate stochastic unit root (STUR) model, which allows for random, time varying local departures from a unit root (UR) model, where nonlinear least squares (NLLS) may be used for estimation and inference on the STUR coefficient. In a structural version of this model where the driver variables of the STUR coefficient are endogenous, the NLLS estimate of the STUR parameter is inconsistent, as are the corresponding estimates of the associated covariance parameters. This paper develops a nonlinear instrumental variable (NLIV) as well as GMM estimators of the STUR parameter which conveniently addresses endogeneity. We derive the asymptotic distributions of the NLIV and GMM estimators and establish consistency under similar orthogonality and relevance conditions to those used in the linear model. An overidentification test and its asymptotic distribution are also developed. The results enable inference about structural STUR models and a mechanism for testing the local STUR model against a simple UR null, which complements usual UR tests. Simulations reveal that the asymptotic distributions of the NLIV and GMM estimators of the STUR parameter as well as the test for overidentifying restrictions perform well in small samples and that the distribution of the NLIV estimator is heavily leptokurtic with a limit theory which has Cauchy-like tails. Comparisons of STUR coefficient and standard UR coefficient tests show that the one-sided UR test performs poorly against the one-sided STUR coefficient test both as the sample size and departures from the null rise. The results are applied to study the relationships between stock returns and bond spread changes
Nonparametric Cointegrating Regression with Endogeneity and Long Memory
No full textThis paper explores nonparametric estimation, inference, and specification testing in a nonlinear cointegrating regression model where the structural equation errors are serially dependent and where the regressor is endogenous and may be driven by long memory innovations. Generalizing earlier results of Wang and Phillips (2009a,b, Econometric Theory 25, 710–738, Econometrica 77, 1901–1948), the conventional nonparametric local level kernel estimator is shown to be consistent and asymptotically (mixed) normal in these cases, thereby opening up inference by conventional nonparametric methods to a wide class of potentially nonlinear cointegrated relations. New results on the consistency of parametric estimates in nonlinear cointegrating regressions are provided, extending earlier research on parametric nonlinear regression and providing primitive conditions for parametric model testing. A model specification test is studied and confirmed to provide a valid mechanism for testing parametric specifications that is robust to endogeneity. But under long memory innovations the test is not pivotal, its convergence rate is parameter dependent, and its limit theory involves the local time of fractional Brownian motion. Simulation results show good performance for the nonparametric kernel estimates in cases of strong endogeneity and long memory, whereas the specification test is shown to be sensitive to the presence of long memory innovations, as predicted by asymptotic theory
Asset pricing with financial bubble risk
No full textThis paper characterizes systematic risk stemming from the possible occurrence of price bubbles and measures the impact of this additional risk factor on asset prices. Historical stock market behavior and recent empirical experience have led economists and policy makers to acknowledge that price bubbles in financial markets do occur and need to be accounted for in risk analysis. New econometric tools for analyzing mildly explosive behavior (Phillips and Magdalinos, 2007; Phillips et al., 2011) have made it possible to detect the presence of bubbles in data and to date stamp their origination and collapse, providing empirical confirmation of such episodes in recent data. The potential for price bubbles and market collapse provides another source of stock market risk and adds to the risk premium. We provide an analytic and empirical investigation of this additional risk factor. The standard present value model is extended to allow for possible price bubbles and the effects of integrating bubble behavior into a consumption-based asset pricing model are analyzed. The theory involves attention to the investor time horizon and a study of the validity of conventional log linear approximations in the presence of nonstationary and mildly explosive data. Finite decision horizons accommodate myopic investors and are a component of speculative behavior that focuses on short run market gains rather than long run effects of fundamentals. An econometric approach to estimate bubble risk effects is developed and the methods are applied to composite stock market index data, giving new model-based equity premium and market volatility estimates that more closely match the data than traditional consumption based asset pricing models
Two New Zealand pioneer econometricians
No full textTwo distinguished New Zealanders pioneered some of the foundations of modern econometrics. Alec Aitken, one of the most famous and well-documented mental arithmeticians of all time, contributed the matrix formulation and projection geometry of linear regression, generalized least squares (GLS) estimation, algorithms for Hodrick Prescott (HP) style data smoothing (six decades before their use in economics), and statistical estimation theory leading to the Cramr Rao bound. Rex Bergstrom constructed and estimated by limited information maximum likelihood (LIML) the largest empirical structural model in the early 1950s, opened up the field of exact distribution theory, developed cyclical growth models in economic theory, and spent nearly 40 years of his life developing the theory of continuous time econometric modeling and its empirical application. We provide an overview of their lives, discuss some of their accomplishments, and develop some new econometric theory that connects with their foundational work
Bootstrapping I(1) data
No full textA functional law for an I(1) sample data version of the continuous-path block bootstrap of Paparoditis and Politis (2001) is given. The results provide an alternative demonstration that continuous-path block bootstrap unit root tests are consistent under the null
Folklore theorems, implicit maps, and indirect inference
No full textThe delta method and continuous mapping theorem are among the most extensively used tools in asymptotic derivations in econometrics. Extensions of these methods are provided for sequences of functions that are commonly encountered in applications and where the usual methods sometimes fail. Important examples of failure arise in the use of simulation-based estimation methods such as indirect inference. The paper explores the application of these methods to the indirect inference estimator (IIE) in first order autoregressive estimation. The IIE uses a binding function that is sample size dependent. Its limit theory relies on a sequence-based delta method in the stationary case and a sequence-based implicit continuous mapping theorem in unit root and local to unity cases. The new limit theory shows that the IIE achieves much more than (partial) bias correction. It changes the limit theory of the maximum likelihood estimator (MLE) when the autoregressive coefficient is in the locality of unity, reducing the bias and the variance of the MLE without affecting the limit theory of the MLE in the stationary case. Thus, in spite of the fact that the IIE is a continuously differentiable function of the MLE, the limit distribution of the IIE is not simply a scale multiple of the MLE, but depends implicitly on the full binding function mapping. The unit root case therefore represents an important example of the failure of the delta method and shows the need for an implicit mapping extension of the continuous mapping theorem
Dynamic panel Anderson-Hsaio estimation with roots near unity
No full textLimit theory is developed for the dynamic panel IV estimator in the presence of an autoregressive root near unity. In the unit root case, Anderson-Hsiao lagged variable instruments satisfy orthogonality conditions but are well known to be irrelevant. For a fixed time series sample size (T ) IV is inconsistent and approaches a shifted Cauchy-distributed random variate as the cross-section sample size n→ ∞ But when T→ ∞, either for fixed n or as n→ ∞, IV is √T consistent and its limit distribution is a ratio of random variables that converges to twice a standard Cauchy as n→ ∞. In this case, the usual instruments are uncorrelated with the regressor but irrelevance does not prevent consistent estimation. The same Cauchy limit theory holds sequentially and jointly as (n,T )→ ∞with no restriction on the divergence rates of n and T. When the common autoregressive root p = 1+c/√T the panel comprises a collection of mildly integrated time series. In this case, the IV estimator is √n consistent for fixed T and √nT consistent with limit distribution N (0,4) when n,T→ ∞sequentially or jointly. These results are robust for common roots of the form P = 1 +c/T γ for all γ ϵ (0,1) and joint convergence holds. Limit normality holds but the variance changes when γ = 1. When γ >1 joint convergence fails and sequential limits differ with different rates of convergence. These findings reveal the fragility of conventional Gaussian IV asymptotics to persistence in dynamic panel regressions.</p
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