An elementary proof of the Knaster-Kuratowski-Mazurkiewicz-Shapley Theorem

Summary This note provides an elementary short proof of the Knaster-Kuratowski-Mazurkiewicz-Shapley (K-K-M-S) Theorem based on Brouwer's fixed point theorem. The usefulness of the K-K-M-S Theorem lies in the fact that it can be applied to prove directly Scarf's (1967) Theorem, i.e. any balanced game has a non-empty core. We also show that the K-K-M-S Theorem and the Gale-Nikaido-Debreu Theorem can be proved by the same arguments.We wish to thank Roko Aliprantis for useful comments.     

Estimation of fixed effect models for time series of cross-sections with arbitrary intertemporal covariance

Models for time series of cross-sections with fixed effects and with intertemporal correlation are considered. The regression coefficients, and their standard errors, can be estimated by generalized least squares applied to a transformed model. The procedure is given a conditional likelihood interpretation.     

Performance criteria and multilateral aid allocation

This study raises questions about past models for aid allocation, in particular the ‘two-gap’ model. It proposes an alternative method for allocating aid among developing countries, on the basis of need (as represented by per capita income) and country performance (measured by variables for relative effort in savings, exports, control of inflation, tax policy, and efficiency of resource use). Statistical tests are applied to actual lending patterns of the World Bank to determine the extent to which in practice the Bank relates lending to these proposed measures of need and performance.     

Federally subsidized occupational training and the employment and earnings of male trainees

The impact of MDTA training on the earnings and employment probabilities of male trainees are studied on the basis of a longitudinal data set on trainees and non-trainees. Econometric techniques which eliminate many of the ambiguities in interpreting previous estimates are used. It is found that the program had little or no effect on employment or earnings of trainees in the late sixties (relative to continued normal employment). It is suggested that the program be interpreted as a pure income-maintenance program rather than a subsidized skill-acquisition program.     

Reinterpreting the convict labour market

The convicts transported to NSW between 1817 and 1840 were young, fit, highly literate and brought occupational skills which were broadly representative of the British and Irish working classes. In the colonial labour market where convicts were coerced, more labour was forthcoming and at a lower wage than in a free labour market. The assignment of convict labour in the colony was efficient; skilled urban and construction tradesmen were employed in the same jobs in NSW as they had held in Britain. Domestic servants and unskilled urban workers whose skills were not suited to the needs of the colony experienced job restructuring. The organization of convict workers into teams and gangs in Australia was similar to the way work was organized in free labour Britain, and a mbc of incentives and rewards characterized the extraction of work from convicts. The human capital of the transportees and the labour system within which they worked help to explain the rapid growth of the colonial economy before 1840.     

Identifying restrictions in limited information analysis of the schooling coefficient in a wage equation

Identifying restrictions underlying limited information estimates of the coefficients of a wage equation are considered from a Bayesian point of view. Within this framework ‘exclusion’ restrictions need not be imposed exactly, and it becomes possible to consider the marginal densities of interesting coefficients as functions of the tightness of these restrictions. In the application considered here the posterior mean for the schooling and test-score coefficients in a wage equation are examined as identifying restrictions are relaxed. The paper also serves as an example of the feasibility of Bayesian limited information analysis of a current economic issue.