Trevor Breusch

A Simple Test for Heteroscedasticity and Random Coefficient Variation

A simple test for heteroscedastic disturbances in a linear regression model is developed using the framework of the Lagrangian multiplier test. For a wide range of heteroscedastic and random coefficient specifications, the criterion is given as a readily computed function of the OLS residuals. Some finite sample evidence is presented to supplement the general asymptotic properties of Lagrangian multiplier tests.

Dynamic Specification, the Long Run and the Estimation of Transformed Regression Models

This paper discusses the best way to formulate and estimate a dynamic econometric model when interest focuses mainly upon its long-run properties. Using results derived for the more general context of transformed regression models, it is shown how point estimates and the standard errors of long-run multipliers and long-run structural coefficients can be obtained using standard estimation methods. It is argued that such formulations are preferable to other specifications such as the error correction model. If the explanatory variables that enter the long-run solution are trend-stationary then it is found that no harm is done to the asymptotic properties of the long-run coefficients by omitting short-run dynamics entirely, though this is not recommended in practice. The results of this paper are related to the concept of co-integration and to the work of Engle and Granger. Finally, a new methodology for the construction of dynamic models is proposed.

EFFICIENT ESTIMATION USING PANEL DATA

IN AN IMPORTANT RECENT PAPER, Hausman and Taylor (1981)-hereafter HT-considered the instrumental-variable estimation of a regression model using panel data, when the individual effects may be correlated with a subset of the explanatory variables. They provided a simple consistent estimator and an efficient estimator. More recently, Amemiya and MaCurdy (1986)-hereafter AM-have suggested an alternative estimator which is more efficient than the HT estimator, under certain conditions and given stronger assumptions than HT made. However, the relationship between the HT and AM papers is less clear than it might be, in part because of notational differences between the two papers. In this paper we clarify the relationship between the HT and AM estimators, and we show that the difference between these estimators lies in the treatment of the time-varying explanatory variables which are uncorrelated with the effects: HT use each such variable as two instruments (means and deviations from means), while AM use such variables as T + 1 instruments (as deviations from means and also separately for each of the T available time periods). This enables us to make clear the conditions under which the AM estimator is more efficient than the HT estimator. We also present each estimator in a form which allows it to be calculated using standard instrumental-variables (two-stage least squares) software. Following the AM path one step further, we then define a third (BMS) estimator which, under yet stronger assumptions, is more efficient than the AM estimator. Both HT and AM use as instruments the deviations from means of the time-varying variables which are correlated with the effects. A more efficient estimator may be obtained by using separately the (T - 1) linearly independent values of these deviations from individual means. Consistency requires that these be legitimate instruments, and whether this is so depends on why these time-varying variables are correlated with the effects. For example, if such correlation arises solely because of a time-invariant component which is removed in taking deviations from individual means, these instruments are legitimate.

Redundancy of moment conditions

It is well known that adding moment conditions cannot decrease asymptotic efficiency. However, sometimes additional moment conditions are redundant, in the sense that they do not increase the asymptotic efficiency of estimation for some or all of the parameters of interest. This paper gives a general treatment of redundancy of moment conditions. It provides necessary and sufficient conditions for redundancy, in several equivalent forms. The paper also provides interesting results for the case that there are three (or more) sets of moment conditions.

Useful invariance results for generalized regression models

Abstract Certain exact finite-sample invariance results are established for the usual estimators and test statistics in the generalized regression model with non-scalar covariance matrix. By inferring properties of an estimator from the criterion function which defines it, results can be obtained even when there is no explicit solution for the estimator as a function of the data (as, e.g., with maximum likelihood). Applications are illustrated by an examination of some recently published Monte Carlo simulation studies.

Maximum likelihood estimation of random effects models

Abstract Iterated GLS has a remarkable property when applied to the random effects model in its usual parameterization. The values for the parameter that measures relative variance, obtained through successive iterations, form a monotonic sequence. This property provides convenient checks for multiple maxima of the likelihood function and for existence of a local maximum that satisfies the non-negativity condition.

Alternative forms of the wald test: how long is a piece of string?

It is possible to obtain any positive value for the Wald test statistic, by rewriting the null hypothesis being tested In an algebraically equivalent form.

Language, Mixed Communes and Infrastructure: Sources of Inequality and Ethnic Minorities in Vietnam

This paper re-examines the sources of inequality in Vietnam, a transitional economy with large reductions in poverty from recent and dramatic economic growth, but vastly unequal gains across ethnic groups. Using an instrumental variable approach to provide consistent estimators of explanatory variables at household and commune levels for ethnic differences in real household expenditure per person, we draw four key conclusions. First, removing language barriers would signifcantly reduce inequality among ethnic groups, narrowing the ethnic gap, and especially so through enhancing the gains earned by minorities from education. Second, variations in returns to education exist in favour of the majority in mixed communes, suggesting that either the special needs of minority children have not been adequately addressed in the classroom, or preferential treatment and the possibility of some form of discrimination exists in the labour market. Third, in contrast to recent literature, there is little di erence between ethnic groups in terms of the benefits drawn from enhanced infrastructure, such as power and clean water, at the commune level. An exception is the returns to roads, which differentially benefits the minority group. Finally, contrary to established views, we find that as much as 50 to 70 percent of the ethnic gap is attributed to differences in endowments, and not to differences in the returns to endowments.

Negotiating the Life Course, 2003, Wave 3

11.6Mb SPSS Portable; 37Mb Stata v8; 37Mb Stata v7; 17.1Mb Nesstar Publisher; 17.1Mb NSDStat; 31.6Mb DIF; 11.8Mb dBase; 11.8Mb Fixed width text; 10.7Mb Delimited; 11.9Mb SAS; 11.2Mb CSV File.