Two-Step Estimation of Incomplete Information Social Interaction Models With Sample Selection

ABSTRACT

This article considers linear social interaction models under incomplete information that allow for missing outcome data due to sample selection. For model estimation, assuming that each individual forms his/her belief about the other members’ outcomes based on rational expectations, we propose a two-step series nonlinear least squares estimator. Both the consistency and asymptotic normality of the estimator are established. As an empirical illustration, we apply the proposed model and method to National Longitudinal Study of Adolescent Health (Add Health) data to examine the impacts of friendship interactions on adolescents’ academic achievements. We provide empirical evidence that the interaction effects are important determinants of grade point average and that controlling for sample selection bias has certain impacts on the estimation results. Supplementary materials for this article are available online.     

A simplified algorithm for the all pairs shortest path problem with O(n 2logn) expected time

The best known expected time for the all pairs shortest path problem on a directed graph with non-negative edge costs is O(n ²logn) by Moffat and Takaoka. Let the solution set be the set of vertices to which the given algorithm has so far established shortest paths. The Moffat-Takaoka algorithm maintains complexities before and after the critical point in balance, which is the moment when the size of the solution set is n?n/logn. In this paper, we remove the concept of critical point, whereby we make the algorithm simpler and seamless, resulting in a simpler analysis.     

Fluctuations of grasshopper populations on aMiscanthus sinensis grassland

Summary Population densities of the three grasshopper species onMiscanthus sinensis grassland in the Kawatabi IBP Area, Japan,Parapleurus alliaceus, Mongolotettix japonicus andChorthippus latipennis, were estimated principally by the release-and-recapture method for five years from 1968 to 1972. The total number of individuals of all three grasshopper species was about 42 per 100m² in August. The number of individuals ofP. alliaceus adult, the dominant species on this grassland, showed a tendency to decline during the five years, though the amplitude was not so large. The number of eggs laid was, however, nearly constant and the mortality from the second nymphal instar to adult was relatively low and constant during the survey period. The weather conditions during the periods of egg and the first instar, such as snowfall and temperature decreasing, are suggested to be one of the factors causing variation in numbers. Contributions from JIBP-CT No. 145. A part of this study was supported by the special project, “Studies on the dynamic status of biosphere”, sponsored by the Ministry of Education.     

Semiparametric Spatial Autoregressive Models With Endogenous Regressors: With an Application to Crime Data

This study considers semiparametric spatial autoregressive models that allow for endogenous regressors, as well as the heterogenous effects of these regressors across spatial units. For the model estimation, we propose a semiparametric series generalized method of moments estimator. We establish that the proposed estimator is both consistent and asymptotically normal. As an empirical illustration, we apply the proposed model and method to Tokyo crime data to estimate how the existence of a neighborhood police substation (NPS) affects the household burglary rate. The results indicate that the presence of an NPS helps reduce household burglaries, and that the effects of some variables are heterogenous with respect to residential distribution patterns. Furthermore, we show that using a model that does not adjust for the endogeneity of NPS does not allow us to observe the significant relationship between NPS and the household burglary rate. Supplementary materials for this article are available online.     

Homogeneity of variances in normal linear regression with a change point

Two methods for testing the equality of variances in straight lines regression with a change point are considered. One is likelihood ratio test and the other is Bayesian confidence interval, based on the highest posterior density for the ratio of variances, using non-informative priors. Methods are applied to the renal transplant data analyzed by Smith and Cook(1980) and Stephens(1994).     

Institutional Completeness and Interpersonal Ties among Japanese American Immigrants*

The integration of immigrants is a multidirectional process. A web of social contacts with the larger society, within the ethnic fold, or away from either to remain as isolates can be established. It is argued that the direction of integration is determined by the ability of the immigrant community to contain within its ethnic boundaries the social ties of its members. This is accomplished by the development of institutional completeness.     

Quantile regression estimation of partially linear additive models

In this paper, we consider the estimation of partially linear additive quantile regression models where the conditional quantile function comprises a linear parametric component and a nonparametric additive component. We propose a two-step estimation approach: in the first step, we approximate the conditional quantile function using a series estimation method. In the second step, the nonparametric additive component is recovered using either a local polynomial estimator or a weighted Nadaraya–Watson estimator. Both consistency and asymptotic normality of the proposed estimators are established. Particularly, we show that the first-stage estimator for the finite-dimensional parameters attains the semiparametric efficiency bound under homoskedasticity, and that the second-stage estimators for the nonparametric additive component have an oracle efficiency property. Monte Carlo experiments are conducted to assess the finite sample performance of the proposed estimators. An application to a real data set is also illustrated.     

日中民间经济交流与东亚经济合作

日中民间经济交流不仅仅是在过去,即使是在今后仍然需要加强。此外,在全球经济一体化,特别是东亚区域经济合作的浪潮中,日中民间经济交流和合作的范围已经不仅仅局限于中国和日本两国之间,应将视野从日中扩大到东亚整个地区去考察。尤其是在中国经济繁荣和加入世贸组织后,中国和日本都应重新审视世贸组织协定以及经济合作协定对今后经济贸易的影响,并考虑出对策。而为此,“官”和“民”都应该发挥其各自的作用和职能。