Testing for Proportional Hazards with Unrestricted Univariate Unobserved Heterogeneity

We develop tests of the proportional hazards assumption, with respect to a continuous covariate, in the presence of unobserved heterogeneity with unknown distribution at the individual observation level. The proposed tests are specially powerful against ordered alternatives useful for modeling non-proportional hazards situations. By contrast to the case when the heterogeneity distribution is known up to …nite dimensional parameters, the null hypothesis for the current problem is similar to a test for absence of covariate dependence. However, the two testing problems di¤er in the nature of relevant alternative hypotheses. We develop tests for both the problems against ordered alternatives. Small sample performance and an application to real data highlight the usefulness of the framework and methodology.

Entrepreneurial Orientation, Intangible Assets and Firm Growth: the impact of ‘Spirit and Material’ on the growth of Chinese private firms

This paper has three contributions. First, it shows how field work within small firms in PR Chinese has provided new evidence which enables us to measure and calibrate Entrepreneurial Orientation (EO), as ‘spirit’, and Intangible Assets (IA), as ‘material’, for use in models of small firm growth. Second, it uses inter-item correlation analysis and both exploratory and confirmatory factor analysis to provide new measures of EO and IA, in index and in vector form, for use in econometric models of firm growth. Third, it estimates two new econometric models of small firm employment growth in PR China, under the null hypothesis of Gibrat’s Law, using our two new index-based and vector-based measures of EO and IA. Estimation is by OLS with adjustment for heteroscedasticity, and for sample selectivity. Broadly, it finds that EO attributes have had little significant impact on small firm growth, and indeed innovativeness and pro-activity paradoxically may even dampen growth. However, IA attributes have had a positive and significant impact on growth, with networking, and technological knowledge being of prime importance, and intellectual property and human capital being of lesser but still significant importance. In the light of these results, Gibrat’s Law is generalized, and Jovanovic’s learning theory is extended, to emphasise the importance of IA to growth. These findings cast new empirical light on the oft-quoted national slogan in PR China of “spirit and material”. So far as small firms are concerned, this paper suggests that their contribution to PR China’s remarkable economic growth is not so much attributable to the ‘spirit’ of enterprise (as suggested by propaganda) as, more prosaically, to the pursuit of the ‘material’.

Nominal Interest Rates and Stationarity

This paper investigates the (break) stationarity null hypothesis using data for 25 interest rates with different maturities and risk characteristics in Canada and the US. In contrast to a large part of the literature, this paper reports strong empirical evidence in favour of the null hypothesis of stationarity for the interest rate series.

A Nonlinear Panel Unit Root Test under Cross Section Dependence

We propose a nonlinear heterogeneous panel unit root test for testing the null hypothesis of unit-roots processes against the alternative that allows a proportion of units to be generated by globally stationary ESTAR processes and a remaining non-zero proportion to be generated by unit root processes. The proposed test is simple to implement and accommodates cross sectional dependence. We show that the distribution of the test statistic is free of nuisance parameters as (N, T) −! 1. Monte Carlo simulation shows that our test holds correct size and under the hypothesis that data are generated by globally stationary ESTAR processes has a better power than the recent test proposed in Pesaran [2007]. Various applications are provided.

A Consistent Nonparametric Bootstrap Test of Exogeneity

This paper proposes a novel way of testing exogeneity of an explanatory variable without any parametric assumptions in the presence of a "conditional" instrumental variable. A testable implication is derived that if an explanatory variable is endogenous, the conditional distribution of the outcome given the endogenous variable is not independent of its instrumental variable(s). The test rejects the null hypothesis with probability one if the explanatory variable is endogenous and it detects alternatives converging to the null at a rate n..1=2:We propose a consistent nonparametric bootstrap test to implement this testable implication. We show that the proposed bootstrap test can be asymptotically justi.ed in the sense that it produces asymptotically correct size under the null of exogeneity, and it has unit power asymptotically. Our nonparametric test can be applied to the cases in which the outcome is generated by an additively non-separable structural relation or in which the outcome is discrete, which has not been studied in the literature.

Atomic Cournotian Traders May Be Walrasian.

In a bilateral oligopoly, with large traders, represented as atoms, and small traders, represented by an atomless part, when is there a non-empty intersection between the sets of Walras and Cournot-Nash allocations? Using a two commodity version of the Shapley window model, we show that a necessary and sufficient condition for a Cournot- Nash allocation to be a Walras allocation is that all atoms demand a null amount of one of the two commodities. We provide two examples which show that this characterization holds non-vacuously. When our condition fails to hold, we also confirm, through some examples, the result obtained by Okuno, Postlewaite, and Roberts (1980): small traders always have a negligible influence on prices, while the large traders keep their strategic power even when their behavior turns out to be Walrasian in the cooperative framework considered by Gabszewicz and Mertens (1971) and Shitovitz (1973).

A test of long memory hypothesis based on self-similarity

This paper develops a new test of true versus spurious long memory, based on log-periodogram estimation of the long memory parameter using skip-sampled data. A correction factor is derived to overcome the bias in this estimator due to aliasing. The procedure is designed to be used in the context of a conventional test of significance of the long memory parameter, and composite test procedure described that has the properties of known asymptotic size and consistency. The test is implemented using the bootstrap, with the distribution under the null hypothesis being approximated using a dependent-sample bootstrap technique to approximate short-run dependence following fractional differencing. The properties of the test are investigated in a set of Monte Carlo experiments. The procedure is illustrated by applications to exchange rate volatility and dividend growth series.