Estimating bias of technical progress with a small dataset

Abstract

Economic historians frequently face the challenge of estimation and inference when only a small sample of the relevant data is available. We illustrate solutions to the challenges through a case study analysis of the Uselding and Juba (1973) data. They have only seven observations available to estimate of the bias of technical progress in United States manufacturing in the nineteenth century. They are able to offer estimates of the bias only by assuming that production technology is not Cobb-Douglas, technical progress is non-neutral and that elasticity of substitution between labour and capital is less than 0.9. These assumptions could not be tested owing to the paucity of the required historical data. This case study illustrates the use of both additional theoretical information and appropriate statistical techniques to alleviate problems of estimation and inference with small samples.