Should Exact Index Numbers Have Standard Errors? Theory and Application to Asian Growth

In this paper we derive the standard error of a price index when both prices and tastes or technology are treated as stochastic. Changing tastes or technology are a reason for the weights in the price index to be treated as stochastic, which can interact with the stochastic prices themselves. We derive results for the constant elasticity of substitution expenditure function (with Sato-Vartia price index), and also the translog function (with Törnqvist price index), which proves to be more general and easier to implement. In our application to Asian growth, we construct standard errors on the total factor productivity (TFP) estimates of Hsieh (2002) for Singapore. We find that TFP growth is insignificantly different from zero in any year, but cumulative TFP over fifteen years is indeed positive.