Results 1  10
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95
Nonlinear IV unit root tests in panels with crosssectional dependency
 Journal of Econometrics
, 2002
"... We propose a unit root test for panels with crosssectional dependency. We allow general dependency structure among the innovations that generate data for each of the crosssectional units. Each unit may have di®erent sample size, and therefore unbalanced panels are also permitted in our framework. ..."
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Cited by 65 (6 self)
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We propose a unit root test for panels with crosssectional dependency. We allow general dependency structure among the innovations that generate data for each of the crosssectional units. Each unit may have di®erent sample size, and therefore unbalanced panels are also permitted in our framework. Yet, the test is asymptotically normal, and does not require any tabulation of the critical values. Our test is based on nonlinear IV estimation of the usual ADF type regression for each crosssectional unit, using as instruments nonlinear transformations of the lagged levels. The actual test statistic is simply de¯ned as a standardized sum of individual IV tratios. We show in the paper that such a standardized sum of individual IV tratios has limit normal distribution as long as the panels have large individual time series observations and are asymptotically balanced in a very weak sense. We may have the number of crosssectional units arbitrarily small or large. In particular, the usual sequential asymptotics, upon which most of the available asymptotic theories for panel unit root models heavily rely, are not required. Finite sample performance of our test is examined via a set of simulations, and compared to those of other commonly used panel unit root tests. Our test generally performs better than the existing tests in terms of both ¯nite sample sizes and powers. We apply our nonlinear IV method to test for the purchasing power parity hypothesis in panels.
Rank1/2: A Simple Way to Improve the OLS Estimation of Tail Exponents,” mimeo
, 2006
"... A popular way to estimate a Pareto exponent is to run an OLS regression: log (Rank) = c − b log (Size), and take b as an estimate of the Pareto exponent. Unfortunately, this procedure is strongly biased in small samples. We provide a simple practical remedy for this bias, and argue that, if one want ..."
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Cited by 60 (8 self)
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A popular way to estimate a Pareto exponent is to run an OLS regression: log (Rank) = c − b log (Size), and take b as an estimate of the Pareto exponent. Unfortunately, this procedure is strongly biased in small samples. We provide a simple practical remedy for this bias, and argue that, if one wants to use an OLS regression, one should use the Rank −1/2, and run log (Rank − 1/2) = c − b log (Size). The shift of 1/2 is optimal, and cancels the bias to a leading order. The standard error on the Pareto exponent is not the OLS standard error, but is asymptotically (2/n) 1/2 b. To obtain this result, we provide asymptotic expansions for the OLS estimate in such loglog ranksize regression with arbitrary shifts in the ranks.
Nonparametric estimation in a nonlinear cointegration type model. Working paper, 2005. URL http://www.mi.uib.no/∼karlsen/working paper/NonlinCoint05.pdf
"... We derive an asymptotic theory of nonparametric estimation for a time series regression model Zt = f(Xt)+Wt, where {Xt} and {Zt} are observed nonstationary processes and {Wt} is an unobserved stationary process. In econometrics, this can be interpreted as a nonlinear cointegration type relationship, ..."
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Cited by 37 (4 self)
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We derive an asymptotic theory of nonparametric estimation for a time series regression model Zt = f(Xt)+Wt, where {Xt} and {Zt} are observed nonstationary processes and {Wt} is an unobserved stationary process. In econometrics, this can be interpreted as a nonlinear cointegration type relationship, but we believe that our results are of wider interest. The class of nonstationary processes allowed for {Xt} is a subclass of the class of null recurrent Markov chains. This subclass contains random walk, unit root processes and nonlinear processes. We derive the asymptotics of a nonparametric estimate of f(x) under the assumption that {Wt} is a Markov chain satisfying some mixing conditions. The finitesample properties of ̂f(x) are studied by means of simulation experiments.
Asymptotic theory for local time density estimation and nonparametric cointegrating regression
, 2006
"... We provide a new asymptotic theory for local time density estimation for a general class of functionals of integrated time series. This result provides a convenient basis for developing an asymptotic theory for nonparametric cointegrating regression and autoregression. Our treatment directly involve ..."
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Cited by 32 (11 self)
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We provide a new asymptotic theory for local time density estimation for a general class of functionals of integrated time series. This result provides a convenient basis for developing an asymptotic theory for nonparametric cointegrating regression and autoregression. Our treatment directly involves the density function of the processes under consideration and avoids Fourier integral representations and Markov process theory which have been used in earlier research on this type of problem. The approach provides results of wide applicability to important practical cases and involves rather simple derivations that should make the limit theory more accessible and useable in econometric applications. Our main result is applied to offer an alternative development of the asymptotic theory for nonparametric estimation of a nonlinear cointegrating regression involving nonstationary time series. In place of the framework of null recurrent Markov chains as developed in recent work of Karlsen, Myklebust and Tjostheim (2007), the direct local time density argument used here more closely resembles conventional nonparametric arguments, making the conditions simpler and more easily verified.
Nonlinear Econometric Models with Cointegrated and Deterministically Trending Regressors
, 1999
"... This paper develops an asymptotic theory for a general class of nonlinear nonstationary regressions. The model considered accommodates a linear time trend and stationary regressors, as well as multiple I(1) regressors. We establish consistency and derive the limit distribution of the nonlinear least ..."
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Cited by 32 (13 self)
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This paper develops an asymptotic theory for a general class of nonlinear nonstationary regressions. The model considered accommodates a linear time trend and stationary regressors, as well as multiple I(1) regressors. We establish consistency and derive the limit distribution of the nonlinear least squares estimator. The estimator is consistent under fairly general conditions but the convergence rate and the limiting distribution are critically dependent upon the type of the regression function. For integrable regression functions, the parameter estimates converge at a reduced n 1=4 rate and have mixed normal limit distributions. On the other hand, if the regression functions are homogeneous at innity, the convergence rates are determined by the degree of the asymptotic homogeneity and the limit distributions are nonGaussian. It is shown that nonlinear least squares generally yields inecient estimators and invalid tests, just as in linear nonstationary regressions. The paper propos...
STRUCTURAL NONPARAMETRIC COINTEGRATING REGRESSION By
, 2008
"... Nonparametric estimation of a structural cointegrating regression model is studied. As in the standard linear cointegrating regression model, the regressor and the dependent variable are jointly dependent and contemporaneously correlated. In nonparametric estimation problems, joint dependence is kno ..."
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Cited by 31 (8 self)
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Nonparametric estimation of a structural cointegrating regression model is studied. As in the standard linear cointegrating regression model, the regressor and the dependent variable are jointly dependent and contemporaneously correlated. In nonparametric estimation problems, joint dependence is known to be a major complication that affects identification, induces bias in conventional kernel estimates, and frequently leads to illposed inverse problems. In functional cointegrating regressions where the regressor is an integrated time series, it is shown here that inverse and illposed inverse problems do not arise. Remarkably, nonparametric kernel estimation of a structural nonparametric cointegrating regression is consistent and the limit distribution theory is mixed normal, giving simple useable asymptotics in practical work. The results provide a convenient basis for inference in structural nonparametric regression with nonstationary time series. The methods may be applied to a wide range of empirical models where functional estimation of cointegrating relations is required.
A simple approach to the parametric estimation of potentially nonstationary diffusions
 Journal of Econometrics
, 2007
"... www.elsevier.com/locate/jeconom A simple approach to the parametric estimation of potentially nonstationary diffusions $ ..."
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Cited by 29 (5 self)
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www.elsevier.com/locate/jeconom A simple approach to the parametric estimation of potentially nonstationary diffusions $
2004: The Carbon Kuznets Curve: A cloudy picture emitted by lousy econometrics? Discussion Paper 0418
 University of Bern
"... In this paper we discuss three important econometric problems with the estimation of Environmental Kuznets Curves, which we exemplify with the particular example of the Carbon Kuznets Curve (CKC). The Carbon Kuznets hypothesis postulates an inverse U–shaped relationship between per capita GDP and pe ..."
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Cited by 21 (3 self)
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In this paper we discuss three important econometric problems with the estimation of Environmental Kuznets Curves, which we exemplify with the particular example of the Carbon Kuznets Curve (CKC). The Carbon Kuznets hypothesis postulates an inverse U–shaped relationship between per capita GDP and per capita CO2 emissions. All three problems occur in the presence of unit root nonstationary regressors in panels. Two of them are rather fundamental: First, the use of nonlinear transformations of integrated regressors in the Kuznets curve, which usually contains GDP and its square is problematic. This stems from the fact that nonlinear transformations of integrated processes are in general not integrated, which implies that (panel) unit root and cointegration techniques, widely used by now in the Kuznets curve literature, cannot be applied meaningfully in this context. Second, all methods applied up to now rest upon the assumption of crosssectional independence. With a first application of factor model based methods that allow for crosssectional dependence, we find evidence for nonstationary common factors in both the GDP and CO2 emissions series. Estimating the CKC on stationary
Laws and limits of econometrics
 ECONOMIC JOURNAL
, 2003
"... We start by discussing some general weaknesses and limitations of the econometric approach. A template from sociology is used to formulate six laws that characterize mainstream activities of econometrics and the scientific limits of those activities. Next, we discuss some proximity theorems that qua ..."
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Cited by 16 (4 self)
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We start by discussing some general weaknesses and limitations of the econometric approach. A template from sociology is used to formulate six laws that characterize mainstream activities of econometrics and the scientific limits of those activities. Next, we discuss some proximity theorems that quantify by means of explicit bounds how close we can get to the generating mechanism of the data and the optimal forecasts of next period observations using a finite number of observations. The magnitude of the bound depends on the characteristics of the model and the trajectory of the observed data. The results show that trends are more elusive to model than stationary processes in the sense that the proximity bounds are larger. By contrast, the bounds are of smaller order for models that are unidentified or nearly unidentified, so that lack or near lack of identification may not be as fatal to the use of a model in practice as some recent results on inference suggest. Finally, we look at one possible future of econometrics that involves the use of advanced econometric methods interactively by way of a web browser. With these methods users may access a suite of econometric methods and data sets online. They may also upload data to remote servers and by simple web browser selections initiate the implementation of advanced econometric software algorithms, returning the results online and by file and graphics downloads.
Extracting a common stochastic trend: Theory with some applications
 Journal of Econometrics
, 2009
"... This paper investigates the statistical properties of the Kalman filter for state space models including integrated time series. In particular, we derive the full asymptotics of maximum likelihood estimation for some prototypical class of such models, i.e., the models with a single latent common sto ..."
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Cited by 16 (6 self)
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This paper investigates the statistical properties of the Kalman filter for state space models including integrated time series. In particular, we derive the full asymptotics of maximum likelihood estimation for some prototypical class of such models, i.e., the models with a single latent common stochastic trend. Indeed, we establish the consistency and asymptotic mixed normality of the maximum likelihood estimator and show that the conventional method of inference is valid for this class of models. The models considered explicitly in the paper comprise a special, yet useful, class of models that we may use to extract the common stochastic trend from multiple integrated time series. As we show in the paper, the models can be very useful to obtain indices that represent fluctuations of various markets or common latent factors that affect a set of economic and financial variables simultaneously. Moreover, our derivation of the asymptotics of this class makes it clear that the asymptotic Gaussianity and the validity of the conventional inference for the maximum likelihood procedure extends to a larger class of more general state space models involving integrated time series. Finally, we demonstrate the utility of the state space model by extracting a common stochastic trend in three empirical analyses: interest rates, return volatility and trading volume, and Dow Jones stock prices.