In practice, bootstrap tests must use a finite number of bootstrap samples. This means that the outcome of the test will depend on the sequence of random numbers used to generate the bootstrap samples, and it necessarily results in some loss of power. We examine the extent of this power loss and propose a simple pretest procedure for choosing the number of bootstrap samples so as to minimize experimental randomness. Simulation experiments suggest that this procedure will work very well in practice

We present experimental evidence that promises and threats mitigate the hold–up problem. While investors rely as much on their own threats as on their trading partner’s promises, the latter are more credible. Building on recent work in psychology and behavioral economics, we then present a simple model within which agents are concerned about both fairness and consistency. The model can account for several of our experimental findings. Its most striking implication is that fairmindedness strengthens the credibility of promises to behave fairly, but weakens the credibility of threats to punish unfair behavior. JEL classification: L14, C78.

We show that the power of a bootstrap test will generally be very close to the level-adjusted power of the asymptotic test on which it is based, provided the latter is calculated properly. Our result, when combined with previous results on approximating the rejection frequency of bootstrap tests, provides a way to simulate the power of both asymptotic and bootstrap tests easily and inexpensively. Some Monte Carlo results for omitted variable tests in logit models illustrate the theoretical results of the paper, demonstrate that the level-adjusted power of asymptotic tests can vary greatly depending on the method used for level adjustment, and show how useful our approximate method can be.

this paper is to study the performance in finite samples of tests for parameter restrictions on cointegrating vectors. The Monte Carlo method is employed for these purposes. Testing hypotheses suggested by economic theory is a central concern of econometrics and testing hypotheses about restrictions on parameters in cointegrating vectors is no exception. The goal is to apply tests that have close to correct size and high power. Wald tests have been proposed for testing linear restrictions on cointegrating vectors for different, though asymptotically equivalent, estimation methods. This Monte Carlo analysis studies the effects of varying the estimation technique on calculating the Wald test. The Wald test statistics are distributed as Ø

This paper considers computer intensive methods for inference on cointegrating vectors in maximum likelihood analysis. It investigates the robustness of LR, Wald tests and an F-type test for linear restrictions on cointegrating space to misspecification of the number of cointegrating relations. In addition, since all the distributional results within the maximum likelihood cointegration model rely on asymptotic considerations, it is important to consider the sensitivity of inference procedures to the sample size. In this paper we use bootstrap hypothesis testing as a way to improve inference for linear restriction on the cointegrating space. We …nd that the resampling procedure is a very useful device for tests that lack the in variance property such as the Waldtest, where the size distortion of the bootstrap test is small even for a sample size T =50. Moreover, it turns out that when the number of cointegrating vectors are correctly specified the bootstrap succeeds where the asymptotic approximation is not satisfactory, that is, for a sample size T < 200. The only valid alternative to the resampling procedure is the F-type test proposed by Podivinsky (1992). However, when the number of cointegrating vectors is over-fitted relying on the asymptotic approximation is misleading, since the tests considered exhibit sizes very far from the nominal size. In this situation the bootstrap test is much more robust to misspecifications. The analysis of the power reveals that the procedures have power. However, it is difficult to evaluate the power properties without investigating the asymptotic power, so further work is needed.

this paper we are concerned with the problem of verifying if the postulated model ts the data. Tests of this kind are known as goodness{of{t or specications tests and play a central role in time series analysis. In the classical \linear" time series analysis, such tests, known also as diagnostic checks, fall roughly into four categories: 1) examination of the residual plot, 2) Portmanteau type tests basedonweighted sums of covariances of residuals, 3) Lagrange{multiplier tests, 4) tests based on the empirical distribution function of the estimated residuals or on the spectral empirical distribution function (integrated periodogram). Goodness{of{t tests for non{linear time series models have only recently become an object of a more systematic researcheven though basic tools like residual plots have, of course, been used in a more or less automatic way for a long time. It is worth noting, however, that even in such simple procedures some care is called for; it is not clear, for example, whether the signicance lines obtained under the assumption that the residuals have a normal distribution give useful information for ARCH type models, especially if the observations have heavy tails. This issue was examined by Davis and Mikosch (1999) but in the context of sample autocorrelations of the observations themselves rather than the residuals. An interesting result obtained byDavis and Mikosch (1999) states that if the probability tails of the observations assumed to follow an ARCH model are suciently heavy (variance is innite), then the sample autocorrelations at any xed lag tend to a random variable, not to the population autocorrelations (which are not dened in this case). Returning now to the goodness{of{t tests, Li and Mak (1994) and Horvath and Kokoszka (2000) stu...

To test the existence of spatial dependence in an econometric model, a convenient test is the Lagrange Multiplier (LM) test. However, evidence shows that, in finite samples, the LM test referring to asymptotic critical values may suffer from the problems of size distortion and low power, which become worse with a denser spatial weight matrix. In this paper, residual-based bootstrap methods are introduced for asymptotically refined approximations to the finite sample critical values of the LM statistics. Conditions for their validity are clearly laid out and formal justifications are given in general, and in details under several popular spatial LM tests using Edgeworth expansions. Monte Carlo results show that when the conditions are not fully met, bootstrap may lead to unstable critical values that change significantly with the alternative, whereas when all conditions are met, bootstrap critical values are very stable, approximate much better the finite sample critical values than those based on asymptotics, and lead to significantly improved size and power. The methods are further demonstrated using more general spatial LM tests, in connection with local misspecification and unknown heteroskedasticity.

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This paper investigates the near unit root behavior of interest rate differentials across countries using a symmetric-Band-TAR model that allows for a heteroscedastic error process. We find that the time series properties of monthly short-term interest differentials over the period 1974-2005