There are a large number of tests for instability or breaks in coefficients in regression models designed for different possible departures from the stable model. We make two contributions to this literature. First, we consider a large class of persistent breaking processes that lead to asymptotically equivalent efficient tests. Our class allows for many or relatively few breaks, clustered breaks, regularly occurring breaks, or smooth transitions to changes in the regression coefficients. Thus, asymptotically nothing is gained by knowing the exact breaking process of the class. Second, we provide a test statistic that is simple to compute, avoids any need for searching over high dimensions when there are many breaks, is valid for a wide range of data-generating processes and has good power and size properties even in heteroscedastic models.

The paper analyzes the impact of the initial condition on the problem of testing for unit roots. To this end, we derive a family of optimal tests that maximize a weighted average power criterion with respect to the initial condition. We then investigate the relationship of this optimal family to popular tests. We find that many unit root tests are closely related to specific members of the optimal family, but the corresponding members employ very different weightings for the initial condition. The popular Dickey-Fuller tests, for instance, put a large weight on extreme deviations of the initial observation from the deterministic component, whereas other popular tests put more weight on moderate deviations. Since the power of unit root tests varies dramatically with the initial condition, this paper explains the results of comparative power studies of unit root tests. The results allow a much deeper understanding of the merits of particular tests in specific circumstances, and a guide to choosing which statistics to use in practice.

Forecasts guide decisions in all areas of economics and finance and their value can only be understood in relation to, and in the context of, such decisions. We discuss the central role of the loss function in helping determine the forecaster's objectives. Decision theory provides a framework for both the construction and evaluation of forecasts. This framework allows an understanding of the challenges that arise from the explosion in the sheer volume of predictor variables under consideration and the forecaster's ability to entertain an endless array of forecasting models and time-varying specifications, none of which may coincide with the “true” model. We show this along with reviewing methods for comparing the forecasting performance of pairs of models or evaluating the ability of the best of many models to beat a benchmark specification.

This paper derives the asymptotic power envelope for tests of a unit autoregressive root for various trend specifications and stationary Gaussian autoregressive disturbances. A family of tests is proposed, members of which are asymptotically similar under a general 1(1) null (allowing nonnormality and general dependence) and which achieve the Gaussian power envelope. One of these tests, which is asymptotically point optimal at a power of 50%, is found (numerically) to be approximately uniformly most powerful (UMP) in the case of a constant deterministic term, and approximately uniformly most powerful invariant (UMPI) in the case of a linear trend, although strictly no UMP or UMPI test exists. We also examine a modification, suggested by the expression for the power envelope, of the Dickey-Fuller (1979) t-statistic; this test is also found to be approximately UMP (constant deterministic term case) and UMPI (time trend case). The power improvement of both new tests is large: in the demeaned case, the Pitman efficiency of the proposed tests relative to the standard Dickey-Fuller t-test is 1.9 at a power of 50%. A Monte Carlo experiment indicates that both proposed tests, particularly the modified Dickey-Fuller t-test, exhibit good power and small size distortions in finite samples with dependent errors.

In situations where a sequence of forecasts is observed, a common strategy is to examine “rationality” conditional on a given loss function. We examine this from a different perspective— supposing that we have a family of loss functions indexed by unknown shape parameters, then given the forecasts can we back out the loss function parameters consistent with the forecasts being rational even when we do not observe the underlying forecasting model? We establish identification of the parameters of a general class of loss functions that nest popular loss functions as special cases and provide estimation methods and asymptotic distributional results for these parameters. This allows us to construct new tests of forecast rationality that allow for asymmetric loss. The methods are applied in an empirical analysis of IMF and OECD forecasts of budget deficits for the G7 countries. We find that allowing for asymmetric loss can significantly change the outcome of empirical tests of forecast rationality.

We theoretically analyze the problem of testing for p ‐hacking based on distributions of p ‐values across multiple studies. We provide general results for when such distributions have testable restrictions (are non‐increasing) under the null of no p ‐hacking. We find novel additional testable restrictions for p ‐values based on t ‐tests. Specifically, the shape of the power functions results in both complete monotonicity as well as bounds on the distribution of p ‐values. These testable restrictions result in more powerful tests for the null hypothesis of no p ‐hacking. When there is also publication bias, our tests are joint tests for p ‐hacking and publication bias. A reanalysis of two prominent data sets shows the usefulness of our new tests.

A flourishing empirical literature investigates the prevalence of p-hacking based on the distribution of p-values across studies. Interpreting results in this literature requires a careful understanding of the power of methods for detecting p-hacking. We theoretically study the implications of likely forms of p-hacking on the distribution of p-values to understand the power of tests for detecting it. Power can be low and depends crucially on the p-hacking strategy and the distribution of true effects. Combined tests for upper bounds and monotonicity and tests for continuity of the p-curve tend to have the highest power for detecting p-hacking.