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Register a new userBootstrapping Structural Change Tests
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Otilia Boldea
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This paper analyses the use of bootstrap methods to test for parameter change in linear models estimated via Two Stage Least Squares (2SLS). Two types of test are considered: one where the null hypothesis is of no change and the alternative hypothesis involves discrete change at k unknown break-points in the sample; and a second test where the null hypothesis is that there is discrete parameter change at l break-points in the sample against an alternative in which the parameters change at l + 1 break-points. In both cases, we consider inferences based on a sup-Wald-type statistic using either the wild recursive bootstrap or the wild fixed bootstrap. We establish the asymptotic validity of these bootstrap tests under a set of general conditions that allow the errors to exhibit conditional and/or unconditional heteroskedasticity, and report results from a simulation study that indicate the tests yield reliable inferences in the sample sizes often encountered in macroeconomics. The analysis covers the cases where the first-stage estimation of 2SLS involves a model whose parameters are either constant or themselves subject to discrete parameter change. If the errors exhibit unconditional heteroskedasticity and/or the reduced form is unstable then the bootstrap methods are particularly attractive because the limiting distributions of the test statistics are not pivotal.
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Classical two-sample permutation tests for equality of distributions have exact size in finite samples, but they fail to control size for testing equality of parameters that summarize each distribution. This paper proposes permutation tests for equality of parameters that are estimated at root-n or slower rates. Our general framework applies to both parametric and nonparametric models, with two samples or one sample split into two subsamples. Our tests have correct size asymptotically while preserving exact size in finite samples when distributions are equal. They have no loss in local-asymptotic power compared to tests that use asymptotic critical values. We propose confidence sets with correct coverage in large samples that also have exact coverage in finite samples if distributions are equal up to a transformation. We apply our theory to four commonly-used hypothesis tests of nonparametric functions evaluated at a point. Lastly, simulations show good finite sample properties of our tests.
Economic data are often generated by stochastic processes that take place in continuous time, though observations may occur only at discrete times. For example, electricity and gas consumption take place in continuous time. Data generated by a continuous time stochastic process are called functional data. This paper is concerned with comparing two or more stochastic processes that generate functional data. The data may be produced by a randomized experiment in which there are multiple treatments. The paper presents a method for testing the hypothesis that the same stochastic process generates all the functional data. The test described here applies to both functional data and multiple treatments. It is implemented as a combination of two permutation tests. This ensures that in finite samples, the true and nominal probabilities that each test rejects a correct null hypothesis are equal. The paper presents upper and lower bounds on the asymptotic power of the test under alternative hypotheses. The results of Monte Carlo experiments and an application to an experiment on billing and pricing of natural gas illustrate the usefulness of the test.
This paper investigates the (in)-consistency of various bootstrap methods for making inference on a change-point in time in the Cox model with right censored survival data. A criterion is established for the consistency of any bootstrap method. It is shown that the usual nonparametric bootstrap is inconsistent for the maximum partial likelihood estimation of the change-point. A new model-based bootstrap approach is proposed and its consistency established. Simulation studies are carried out to assess the performance of various bootstrap schemes.
In the high-dimensional sparse modeling literature, it has been crucially assumed that the sparsity structure of the model is homogeneous over the entire population. That is, the identities of important regressors are invariant across the population and across the individuals in the collected sample. In practice, however, the sparsity structure may not always be invariant in the population, due to heterogeneity across different sub-populations. We consider a general, possibly non-smooth M-estimation framework, allowing a possible structural change regarding the identities of important regressors in the population. Our penalized M-estimator not only selects covariates but also discriminates between a model with homogeneous sparsity and a model with a structural change in sparsity. As a result, it is not necessary to know or pretest whether the structural change is present, or where it occurs. We derive asymptotic bounds on the estimation loss of the penalized M-estimators, and achieve the oracle properties. We also show that when there is a structural change, the estimator of the threshold parameter is super-consistent. If the signal is relatively strong, the rates of convergence can be further improved and asymptotic distributional properties of the estimators including the threshold estimator can be established using an adaptive penalization. The proposed methods are then applied to quantile regression and logistic regression models and are illustrated via Monte Carlo experiments.
Time averaging has been the traditional approach to handle mixed sampling frequencies. However, it ignores information possibly embedded in high frequency. Mixed data sampling (MIDAS) regression models provide a concise way to utilize the additional information in high-frequency variables. In this paper, we propose a specification test to choose between time averaging and MIDAS models, based on a Durbin-Wu-Hausman test. In particular, a set of instrumental variables is proposed and theoretically validated when the frequency ratio is large. As a result, our method tends to be more powerful than existing methods, as reconfirmed through the simulations.
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