This paper develops exact finite sample and asymptotic distributions for structural equation tests based on partially restricted reduced form estimates. Particular attention is given to models with large numbers of instruments, wherein the use of partially restricted reduced form estimates is shown to be especially advantageous in statistical testing even in cases of uniformly weak instruments and reduced forms. Comparisons are made with methods based on unrestricted reduced forms, and numerical computations showing finite sample performance of the tests are reported. Some new results are obtained on inequalities between noncentral chi-squared distributions with different degrees of freedom that assist in analytic power comparisons.
Lieberman and Phillips (2016; Journal of Econometrics; LP) introduced a multivariate stochastic unit root (STUR) model, which allows for random, time varying local departures from a unit root (UR) model, where nonlinear least squares (NLLS) may be used for estimation and inference on the STUR coefficient. In a structural version of this model where the driver variables of the STUR coefficient are endogenous, the NLLS estimate of the STUR parameter is inconsistent, as are the corresponding estimates of the associated covariance parameters. This paper develops a nonlinear instrumental variable (NLIV) as well as GMM estimators of the STUR parameter which conveniently addresses endogeneity. We derive the asymptotic distributions of the NLIV and GMM estimators and establish consistency under similar orthogonality and relevance conditions to those used in the linear model. An overidentification test and its asymptotic distribution are also developed. The results enable inference about structural STUR models and a mechanism for testing the local STUR model against a simple UR null, which complements usual UR tests. Simulations reveal that the asymptotic distributions of the the NLIV and GMM estimators of the STUR parameter as well as the test for overidentifying restrictions perform well in small samples and that the distribution of the NLIV estimator is heavily leptokurtic with a limit theory which has Cauchy-like tails. Comparisons of STUR coefficient and a standard UR coefficient test show that the one-sided UR test performs poorly against the one-sided STUR coefficient test both as the sample size and departures from the null rise.
We provide a methodology for testing a polynomial model hypothesis by extending the approach and results of Baek, Cho, and Phillips (2015; Journal of Econometrics; BCP) that tests for neglected nonlinearity using power transforms of regressors against arbitrary nonlinearity. We examine and generalize the BCP quasi-likelihood ratio test dealing with the multifold identification problem that arises under the null of the polynomial model. The approach leads to convenient asymptotic theory for inference, has omnibus power against general nonlinear alternatives, and allows estimation of an unknown polynomial degree in a model by way of sequential testing, a technique that is useful in the application of sieve approximations. Simulations show good performance in the sequential test procedure in identifying and estimating unknown polynomial order. The approach, which can be used empirically to test for misspecification, is applied to a Mincer (1958, 1974) equation using data from Card (1995). The results confirm that Mincer’s log earnings equation is easily shown to be misspecified by including nonlinear effects of experience and schooling on earnings, with some flexibility required in the respective polynomial degrees.
This paper re-examines changes in the causal link between money and income in the United States for over the past half century (1959 - 2014). Three methods for the data-driven discovery of change points in causal relationships are proposed, all of which can be implemented without prior detrending of the data. These methods are a forward recursive algorithm, a recursive rolling algorithm and the rolling window algorithm all of which utilize subsample tests of Granger causality within a lag-augmented vector autoregressive framework. The limit distributions for these subsample Wald tests are provided. The results from a suite of simulation experiments suggest that the rolling window algorithm provides the most reliable results, followed by the recursive rolling method. The forward expanding window procedure is shown to have worst performance. All three approaches find evidence of money-income causality during the Volcker period in the 1980s. The rolling and recursive rolling algorithms detect two additional causality episodes: the turbulent period of late 1960s and the starting period of the subprime mortgage crisis in 2007.
Causal relationships in econometrics are typically based on the concept of predictability and are established in terms of tests for Granger causality. These causal relationships are susceptible to change, especially during times of financial turbulence, making the real-time detection of instability an important practical issue. This paper develops a test for detecting changes in causal relationships based on a recursive rolling window, which is analogous to the procedure used in recent work on financial bubble detection. The limiting distribution of the test takes a simple form under the null hypothesis and is easy to implement in conditions of homoskedasticity, conditional heteroskedasticity and unconditional heteroskedasticity. Simulation experiments compare the efficacy of the proposed test with two other commonly used tests, the forward recursive and the rolling window tests. The results indicate that both the rolling and the recursive rolling approaches offer good finite sample performance in situations where there are one or two changes in the causal relationship over the sample period, although the performance of the rolling window algorithm seems to be the best. The testing strategies are illustrated in an empirical application that explores the causal impact of the slope of the yield curve on real economic activity in the United States over the period 1985–2013.
Climate change remains one of the major international environmental challenges facing nations. Yet nations have to date taken minimal policies to slow climate change. Moreover, there has been no major improvement in emissions trends as of the latest data. The current study uses the updated DICE model to present new projections and the impacts of alternative climate policies. It also presents a new set of estimates of the uncertainties about future climate change and compares the results will those of other integrated assessment models. The study confirms past estimates of likely rapid climate change over the next century if there are not major climate-change policies. It suggests that it will be extremely difficult to achieve the 2°C target of international agreements even if ambitious policies are introduced in the near term. The required carbon price needed to achieve current targets has risen over time as policies have been delayed.
In centralized school admissions systems, rationing at oversubscribed schools often uses lotteries in addition to preferences. This partly random assignment is used by empirical researchers to identify the effect of entering a school on outcomes like test scores. This paper formally studies if the two most popular empirical research designs successfully extract a random assignment. For a class of data-generating mechanisms containing those used in practice, I show: One research design extracts a random assignment under a mechanism if and almost only if the mechanism is strategy-proof for schools. In contrast, the other research design does not necessarily extract a random assignment under any mechanism.
Online retail gives consumers access to an astonishing variety of products. However, the additional value created by this variety depends on the extent to which local retailers already satisfy local demand. To quantify the gains and account for local demand, we use detailed data from an online retailer and propose methodology to address a common issue in such data-sparsity of local sales due to sampling and a significant number of local zeros. Our estimates indicate products face substantial demand heterogeneity across markets; as a result, we find gains from online variety that are 45% lower than previous studies.
Online retail gives consumers access to an astonishing variety of products. However, the additional value created by this variety depends on the extent to which local retailers already satisfy local demand. To quantify the gains and account for local demand, we use detailed data from an online retailer and propose methodology to address a common issue in such data-sparsity of local sales due to sampling and a significant number of local zeros. Our estimates indicate products face substantial demand heterogeneity across markets; as a result, we find gains from online variety that are 45% lower than previous studies.