This paper discusses the problem of testing misspecifications in semiparametric regression models for a large family of econometric models under rather general conditions. We focus on two main issues that typically arise in econometrics. First, many econometric models are estimated through maximum likelihood or pseudo-ML methods like, for example, limited dependent variable or gravity models. Second, often one might not want to fully specify the null hypothesis. Instead, one would rather impose some structure like separability or monotonicity. In order to address these points we introduce an adaptive omnibus test. Special emphasis is given to practical issues like adaptive bandwidth choice, general but simple requirements on the estimates, and finite sample performance, including the resampling approximations.

Semiparametric generalized additive models are a powerful tool in quantitative econometrics. With response Y, covariates X,T, the considered model is E(Y |X;T) = G{XTβ + α + m1(T1) + ··· + md(Td)}. Here, G is a known link, α and β are unknown parameters, and m1,…,md are unknown (smooth) functions of possibly higher dimensional covariates T1,…,Td. Estimates of m1,…,md, α, and β are presented, and asymptotic distributions are given for both the nonparametric and the parametric part. The main focus of the paper is application of bootstrap methods. It is shown how bootstrap can be used for bias correction, hypothesis testing (e.g., component-wise analysis), and the construction of uniform confidence bands. Further, bootstrap tests for model specification and parametrization are given, in particular for testing additivity and link function specification. The practical performance of the methods is illustrated in a simulation study.This research was supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 373 “Quantifikation und Simulation ökonomischer Prozesse,” Humboldt-Universität zu Berlin, DFG project MA 1026/6-2, the Spanish “Dirección General de Enseñanza Superior,” no. BEC2001-1270, and the grant “Nonparametric methods in finance and insurance” from the Danish Social Science Research Council. We thank Marlene Müller, Oliver Linton, and two anonymous referees for helpful discussion.

While the traditional R 2 value is useful to evaluate the quality of a fit, it does not work when it comes to evaluating the predictive power of estimated financial models in finite samples. In this paper we introduce a validated value useful for prediction. Based on data from the Danish stock market, using this measure we find that the dividend-price ratio has predictive power. The best horizon for prediction seems to be four years. On a one year horizon, we find that while inflation and interest rate do not add to the predictive power of the dividend-price ratio then last years excess stock return does.

In this paper we introduce a general method for estimating semiparametrically the different components in separable models. The family of separable models is quite popular in economic research because this structure offers clear interpretation, has straightforward economic consequences, and is often justified by theory. This family is also of statistical interest because it allows us to estimate high-dimensional complexity semiparametrically without running into the curse of dimensionality. We consider even the case when multiple indices appear in the objective function; thus we can estimate models that are typical in economic analysis, such as those that contain limited dependent variables. The idea of the new method is mainly based on a generalized profile likelihood approach. Although this requires some hypotheses on the conditional error distribution, it yields a quite general usable method with low computational costs but high accuracy even for small samples. We give estimation procedures and provide some asymptotic theory. Implementation is discussed; simulations and an application demonstrate its feasibility and good finite-sample behavior.This research was financially supported by Dirección General de Investigación del Ministerio de Ciencia y Tecnología under research grants BEC2001-1121 and BEC2001-1270; Dirección General de Enseñanza Superior del Ministerio de Educación y Ciencia under Subprograma de estancias de investigadores españoles en centros de investigación españoles y extranjeros, ref. PR2000-0096; and by the Danish Social Science Research fund. We also thank M. Delgado, O. Linton, two anonymous referees, and all participants of the working group STAPH on functional statistics in Toulouse, the activities of which are available on line at http://www.lsp.upstlse.fr/Fp/Ferraty/staph.html.