On nonparametric latent trait models

Some nonparametric latent trait models for dichotomous data are considered. We deal with n subjects, each answering to the same set of of k items, each item being scored dichotomously. We are interested in ordering item difficulties α₁,...α_k . In Sec. 2 it is shown that in the considered nonparametric models the ordering is identifiable. Then an order estimator is defined and its quality is described by the probabilities of correct, wrong and deferred decision. Asymptotic behaviour of these probabilities are considered for n→∞ and any k≥2. The hypothesis that the probability of wrong decision diminishes when the model is “more distant” from so called random response model, is proved for n≤3 and verified numerically for n≥3. In Sec. 4 we discuss critically some parameters of nonparametric models known in the literature as “coefficients of scalability”. In particular, for k=2 their connections with the evaluation of positive dependence are considered.     

Nonlinearities in Capital–Skill Complementarity

This paper uses a novel dataset to test the capital–skill complementarity hypothesis in a cross-section of countries. It is shown that for the full sample there exists evidence in favor of the hypothesis. When we arbitrarily split the full sample into OECD and non-OECD countries, we find no evidence in favor of the hypothesis for the OECD subsample, but strong evidence for the non-OECD subsample. When we use Hansens [Econometrica 68 (2000) P. 576] endogenous threshold methodology we find that initial literacy rates and initial per capita output are threshold variables that can cluster countries into three distinct regimes that obey different statistical models. In particular, the regime with moderate initial per capita income but low initial education exhibits substantially higher capital–skill complementarity than the regime with low income and low education and the regime with high education. This cross-country nonlinearity in capital–skill complementarity is consistent with the time-series nonlinearity found by Goldin and Katz [Quarterly Journal of Economics 113 (1998) 693] using U.S. manufacturing data, and promotes the view that the phenomenon maybe a transitory one.JEL classification: O40, O47     

Decomposition of technical efficiency under fixed proportion technologies: an application of data envelopment analysis

In this paper, we extend the four-component stochastic frontier model to allow for global spatial dependence via the endogenous spatial autoregressive variable. Our proposed model is more general than the model considered by (Glass et al., 2016) in the sense that we include a random effect as well as a permanent efficiency component. With the spatial autoregressive specification, our model is able to capture the asymmetric efficiency spillovers and also decompose the persistent/transient inefficiencies into direct and indirect efficiencies. Moreover, we also investigate the marginal effects of the exogenous variables on the persistent/transient efficiency. We suggest a maximum simulated likelihood method to estimate the frontier parameters of the model, and we predict the efficiencies using the simulated estimator. Monte Carlo simulations reveal that the suggested estimator performs well in finite samples. An empirical application is considered to illustrate the usefulness of our proposed model and method.