The behavior of the power function of autocorrelation tests such as the Durbin–Watson test in time series regressions or the Cliff-Ord test in spatial regression models has been intensively studied in the literature. When the correlation becomes strong, Krämer (1985, Journal of Econometrics 28, 363–370.) (for the Durbin–Watson test) and Krämer (2005, Journal of Statistical Planning and Inference, 128, 489–496) (for the Cliff-Ord test) have shown that power can be very low, in fact can converge to zero, under certain circumstances. Motivated by these results, Martellosio (2010, Econometric Theory, 26, 152–186) set out to build a general theory that would explain these findings. Unfortunately, Martellosio (2010) does not achieve this goal, as a substantial portion of his results and proofs suffer from nontrivial flaws. The present paper now builds a theory as envisioned in Martellosio (2010) in an even more general framework, covering general invariant tests of a hypothesis on the disturbance covariance matrix in a linear regression model. The general results are then specialized to testing for spatial correlation and to autocorrelation testing in time series regression models. We also characterize the situation where the null and the alternative hypothesis are indistinguishable by invariant tests.

The main contribution of this paper is to propose a bootstrap method for inference on integrated volatility based on the pre-averaging approach, where the pre-averaging is done over all possible overlapping blocks of consecutive observations. The overlapping nature of the pre-averaged returns implies that the leading martingale part in the pre-averaged returns are kn-dependent with kn growing slowly with the sample size n. This motivates the application of a blockwise bootstrap method. We show that the “blocks of blocks” bootstrap method is not valid when volatility is time-varying. The failure of the blocks of blocks bootstrap is due to the heterogeneity of the squared pre-averaged returns when volatility is stochastic. To preserve both the dependence and the heterogeneity of squared pre-averaged returns, we propose a novel procedure that combines the wild bootstrap with the blocks of blocks bootstrap. We provide a proof of the first order asymptotic validity of this method for percentile and percentile-t intervals. Our Monte Carlo simulations show that the wild blocks of blocks bootstrap improves the finite sample properties of the existing first order asymptotic theory. We use empirical work to illustrate its use in practice.

This paper discusses nonparametric estimation of the distribution of random coefficients in a structural model that is nonlinear in the random coefficients. We establish that the problem of recovering the probability density function (pdf) of random parameters falls into the class of convexly-constrained inverse problems. The framework offers an estimation method that separates computational solution of the structural model from estimation. We first discuss nonparametric identification. Then, we propose two alternative estimation procedures to estimate the density and derive their asymptotic properties. Our general framework allows us to deal with unobservable nuisance variables, e.g., measurement error, but also covers the case when there are no such nuisance variables. Finally, Monte Carlo experiments for several structural models are provided which illustrate the performance of our estimation procedure.

Granger noncausality in distribution is fundamentally a probabilistic conditional independence notion that can be applied not only to time series data but also to cross-section and panel data. In this paper, we provide a natural definition of structural causality in cross-section and panel data and forge a direct link between Granger (G–) causality and structural causality under a key conditional exogeneity assumption. To put it simply, when structural effects are well defined and identifiable, G–non-causality follows from structural noncausality, and with suitable conditions (e.g., separability or monotonicity), structural causality also implies G–causality. This justifies using tests of G–non-causality to test for structural noncausality under the key conditional exogeneity assumption for both cross-section and panel data. We pay special attention to heterogeneous populations, allowing both structural heterogeneity and distributional heterogeneity. Most of our results are obtained for the general case, without assuming linearity, monotonicity in observables or unobservables, or separability between observed and unobserved variables in the structural relations.

An influential paper by Kleibergen (2005, Econometrica 73, 1103–1123) introduces Lagrange multiplier (LM) and conditional likelihood ratio-like (CLR) tests for nonlinear moment condition models. These procedures aim to have good size performance even when the parameters are unidentified or poorly identified. However, the asymptotic size and similarity (in a uniform sense) of these procedures have not been determined in the literature. This paper does so.

This paper shows that the LM test has correct asymptotic size and is asymptotically similar for a suitably chosen parameter space of null distributions. It shows that the CLR tests also have these properties when the dimension p of the unknown parameter θ equals 1. When p ≥ 2, however, the asymptotic size properties are found to depend on how the conditioning statistic, upon which the CLR tests depend, is weighted. Two weighting methods have been suggested in the literature. The paper shows that the CLR tests are guaranteed to have correct asymptotic size when p ≥ 2 when the weighting is based on an estimator of the variance of the sample moments, i.e., moment-variance weighting, combined with the Robin and Smith (2000, Econometric Theory 16, 151–175) rank statistic. The paper also determines a formula for the asymptotic size of the CLR test when the weighting is based on an estimator of the variance of the sample Jacobian. However, the results of the paper do not guarantee correct asymptotic size when p ≥ 2 with the Jacobian-variance weighting, combined with the Robin and Smith (2000, Econometric Theory 16, 151–175) rank statistic, because two key sample quantities are not necessarily asymptotically independent under some identification scenarios.

Analogous results for confidence sets are provided. Even for the special case of a linear instrumental variable regression model with two or more right-hand side endogenous variables, the results of the paper are new to the literature.

In recent years, stationary time series models based on copula functions became increasingly popular in econometrics to model nonlinear temporal and cross-sectional dependencies. Within these models, we consider the problem of testing the goodness-of-fit of the parametric form of the underlying copula. Our approach is based on a dependent multiplier bootstrap and it can be applied to any stationary, strongly mixing time series. The method extends recent i.i.d. results by Kojadinovic et al. (2011) and shares the same computational benefits compared to methods based on a parametric bootstrap. The finite-sample performance of our approach is investigated by Monte Carlo experiments for the case of copula-based Markovian time series models.

In this paper we develop a nonparametric estimation technique for semiparametric transformation models of the form: H (Y) = φ(Z) + X′β + U where H,φ are unknown functions, β is an unknown finite-dimensional parameter vector and the variables (Y,Z) are endogenous. Identification of the model and asymptotic properties of the estimator are analyzed under the mean independence assumption between the error term and the instruments. We show that the estimators are consistent, and a $\sqrt N$-convergence rate and asymptotic normality for $\hat \beta$ can be attained. The simulations demonstrate that our nonparametric estimates fit the data well.

We study the consequences of substituting an error-laden proxy W for an instrument Z on the interpretation of Wald, local instrumental variable (LIV), and instrumental variable (IV) estimands in an ordered discrete choice structural system with heterogeneity. A proxy W need only satisfy an exclusion restriction and that the treatment and outcome are mean independent from W given Z. Unlike Z, W need not satisfy monotonicity and may, under particular specifications, fail exogeneity. For example, W could code Z with error, with missing observations, or coarsely. We show that Wald, LIV, and IV estimands using W identify weighted averages of local or marginal treatment effects (LATEs or MTEs). We study a necessary and sufficient condition for nonnegative weights. Further, we study a condition under which the Wald or LIV estimand using W identifies the same LATE or MTE that would have been recovered had Z been observed. For example, this holds for binary Z and therefore the Wald estimand using W identifies the same “average causal response,” or LATE for binary treatment, that would have been recovered using Z. Also, under this condition, LIV using W can be used to identify MTE and average treatment effects for e.g., the population, treated, and untreated.

Forecast accuracy is typically measured in terms of a given loss function. However, as a consequence of the use of misspecified models in multiple model comparisons, relative forecast rankings are loss function dependent. In order to address this issue, a novel criterion for forecast evaluation that utilizes the entire distribution of forecast errors is introduced. In particular, we introduce the concepts of general-loss (GL) forecast superiority and convex-loss (CL) forecast superiority; and we develop tests for GL (CL) superiority that are based on an out-of-sample generalization of the tests introduced by Linton, Maasoumi, and Whang (2005, Review of Economic Studies 72, 735–765). Our test statistics are characterized by nonstandard limiting distributions, under the null, necessitating the use of resampling procedures to obtain critical values. Additionally, the tests are consistent and have nontrivial local power, under a sequence of local alternatives. The above theory is developed for the stationary case, as well as for the case of heterogeneity that is induced by distributional change over time. Monte Carlo simulations suggest that the tests perform reasonably well in finite samples, and an application in which we examine exchange rate data indicates that our tests can help identify superior forecasting models, regardless of loss function.

Consider testing the null hypothesis that a single structural equation has specified coefficients. The alternative hypothesis is that the relevant part of the reduced form matrix has proper rank, that is, that the equation is identified. The usual linear model with normal disturbances is invariant with respect to linear transformations of the endogenous and of the exogenous variables. When the disturbance covariance matrix is known, it can be set to the identity, and the invariance of the endogenous variables is with respect to orthogonal transformations. The likelihood ratio test is invariant with respect to these transformations and is the best invariant test. Furthermore it is admissible in the class of all tests. Any other test has lower power and/or higher significance level. In particular, this likelihood ratio test dominates a test based on the Two-Stage Least Squares estimator.

In this paper, we derive uniform convergence rates of nonparametric estimators for continuous time diffusion processes. In particular, we consider kernel-based estimators of the Nadaraya–Watson type, introducing a new technical device called a damping function. This device allows us to derive sharp uniform rates over an infinite interval with minimal requirements on the processes: The existence of the moment of any order is not required and the boundedness of relevant functions can be significantly relaxed. Restrictions on kernel functions are also minimal: We allow for kernels with discontinuity, unbounded support, and slowly decaying tails. Our proofs proceed by using the covering-number technique from empirical process theory and exploiting the mixing and martingale properties of the processes. We also present new results on the path-continuity property of Brownian motions and diffusion processes over an infinite time horizon. These path-continuity results, which should also be of some independent interest, are used to control discretization biases of the nonparametric estimators. The obtained convergence results are useful for non/semiparametric estimation and testing problems of diffusion processes.

In this paper, we consider the nonparametric estimation of a broad class of quantile regression models, in which the partially linear, additive, and varying coefficient models are nested. We propose for the model a two-stage kernel-weighted least squares estimator by generalizing the idea of local partitioned mean regression (Christopeit and Hoderlein, 2006, Econometrica 74, 787–817) to a quantile regression framework. The proposed estimator is shown to have desirable asymptotic properties under standard regularity conditions. The new estimator has three advantages relative to existing methods. First, it is structurally simple and widely applicable to the general model as well as its submodels. Second, both the functional coefficients and their derivatives up to any given order can be estimated. Third, the procedure readily extends to censored data, including fixed or random censoring. A Monte Carlo experiment indicates that the proposed estimator performs well in finite samples. An empirical application is also provided.

The moment conditions or estimating equations for instrumental variables quantile regression involve the discontinuous indicator function. We instead use smoothed estimating equations (SEE), with bandwidth h. We show that the mean squared error (MSE) of the vector of the SEE is minimized for some h > 0, leading to smaller asymptotic MSE of the estimating equations and associated parameter estimators. The same MSE-optimal h also minimizes the higher-order type I error of a SEE-based χ2 test and increases size-adjusted power in large samples. Computation of the SEE estimator also becomes simpler and more reliable, especially with (more) endogenous regressors. Monte Carlo simulations demonstrate all of these superior properties in finite samples, and we apply our estimator to JTPA data. Smoothing the estimating equations is not just a technical operation for establishing Edgeworth expansions and bootstrap refinements; it also brings the real benefits of having more precise estimators and more powerful tests.

This paper presents semiparametric identification results for the Rust (1994) class of discrete choice dynamic programming (DCDP) models. We develop sufficient conditions for identification of the deep structural parameters for the case where the per-period utility function ascribed to one choice in the model is parametric but the distribution of unobserved state variables is nonparametric. The proposed identification strategy does not rely on availability of the terminal period data and can therefore be applied to infinite horizon structural dynamic models. Identifying power comes from assuming that the agent’s per-period utilities admit continuous choice-specific state variables that are observed with sufficient variation and satisfy certain conditional independence assumptions on the joint time series of observables. These conditions allow us to formulate exclusion restrictions for identifying the primitive structural functions of the model.

The phenomenon of multiple transactions at each recording time is a common occurrence for high-frequency financial data because of the heavy trading of the market and limitation of the recording mechanism. This situation has existed for many years, but has become more common in recent years because of heavier trading. Surprisingly, there have been few studies on this important issue, in spite of some ad hoc approaches to treat multiple transactions. In this paper we investigate how to handle multiple transactions, particularly in the context of estimating the integrated volatility and integrated quarticity, which are of great interest in financial econometrics. Two approaches are proposed for this purpose, and their asymptotic properties are investigated. Their performances are confirmed by simulation studies. The estimators are also applied to some real world problems. The work represents only the first step in this direction, and some future research problems are discussed.

For a bivariate time series ((Xi ,Yi))i=1,...,n, we want to detect whether the correlation between Xi and Yi stays constant for all i = 1,...n. We propose a nonparametric change-point test statistic based on Kendall’s tau. The asymptotic distribution under the null hypothesis of no change follows from a new U-statistic invariance principle for dependent processes. Assuming a single change-point, we show that the location of the change-point is consistently estimated. Kendall’s tau possesses a high efficiency at the normal distribution, as compared to the normal maximum likelihood estimator, Pearson’s moment correlation. Contrary to Pearson’s correlation coefficient, it shows no loss in efficiency at heavy-tailed distributions, and is therefore particularly suited for financial data, where heavy tails are common. We assume the data ((Xi ,Yi))i=1,...,n to be stationary and P-near epoch dependent on an absolutely regular process. The P-near epoch dependence condition constitutes a generalization of the usually considered Lp-near epoch dependence allowing for arbitrarily heavy-tailed data. We investigate the test numerically, compare it to previous proposals, and illustrate its application with two real-life data examples.

This paper investigates bootstrap-based bias correction of semiparametric estimators of the long memory parameter, d, in fractionally integrated processes. The re-sampling method involves the application of the sieve bootstrap to data prefiltered by a preliminary semiparametric estimate of the long memory parameter. Theoretical justification for using the bootstrap technique to bias adjust log periodogram and semiparametric local Whittle estimators of the memory parameter is provided in the case where the true value of d lies in the range 0 ≤ d < 0.5. That the bootstrap method provides confidence intervals with the correct asymptotic coverage is also proven, with the intervals shown to adjust explicitly for bias, as estimated via the bootstrap. Simulation evidence comparing the performance of the bootstrap bias correction with analytical bias-correction techniques is presented. The bootstrap method is shown to produce notable bias reductions, in particular when applied to an estimator for which some degree of bias reduction has already been accomplished by analytical means.

We analyze linear panel regression models with interactive fixed effects and predetermined regressors, for example lagged-dependent variables. The first-order asymptotic theory of the least squares (LS) estimator of the regression coefficients is worked out in the limit where both the cross-sectional dimension and the number of time periods become large. We find two sources of asymptotic bias of the LS estimator: bias due to correlation or heteroscedasticity of the idiosyncratic error term, and bias due to predetermined (as opposed to strictly exogenous) regressors. We provide a bias-corrected LS estimator. We also present bias-corrected versions of the three classical test statistics (Wald, LR, and LM test) and show their asymptotic distribution is a χ2-distribution. Monte Carlo simulations show the bias correction of the LS estimator and of the test statistics also work well for finite sample sizes.