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 T””rnqvist 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.

Price and Real Output Measures for the Education Function of Government: Exploratory Estimates for Primary & Secondary Education

In a previous paper, the authors took the first step in their research on measuring the education function of government by estimating real output measures (Fraumeni, et. al. 2004). In this paper, chain-type Fisher quantity indexes for those output measures are calculated to be more consistent with Bureau of Economic Analysis (BEA) methodology and the real output measures presented in the previous paper are refined. In addition, and more importantly, implicit price deflators are presented to give a more complete picture. Alternative price and real output measures are compared; it is clear that methodology choice matters. Price change is always greater than quantity change for the periods given; however, price changes are overstated to the extent quality changes are not captured in the quantity indexes. Quality-adjustments continue to be the most challenging aspect of decomposing nominal expenditures for government-provided education into price and quantity components.

Effects of Terms of Trade Gains and Tariff Changes on the Measurement of US Productivity Growth

The acceleration in US productivity growth since 1995 is often attributed to declining prices for information technology (IT ) goods, and therefore enhanced productivity growth in that sector. We investigate an alternative explanation for these IT price movements: gains in the US terms of trade and tariff reductions, especially for IT products, which led to greater gains than shown by official indexes. We do not, however, investigate the indexes used to deflate the domestic absorption components of GDP, and if upward biases are present in those indexes that could offset some of the effects of mismeasured export and import indexes. (JEL C43, E23, F13, F14, J24

Effects of Terms of Trade Gains and Tariff Changes on the Measurement of U.S. Productivity Growth

Since 1995, growth in productivity in the United States appears to have accelerated dramatically. In this paper, we argue that part of this apparent speed-up actually represents gains in the terms of trade and tariff reductions, especially for information-technology products. We demonstrate how unmeasured gains in the terms of trade and declines in tariffs can cause conventionally measured growth in real output and productivity to be overstated. Building on the GDP function approach of Diewert and Morrison, we develop methods for measuring these effects. From 1995 through 2006, the average growth rates of our alternative price indexes for U.S. imports are 1.5% per year lower than the growth rate of price indexes calculated using official methods. Thus properly measured terms-of-trade gain can account for close to 0.2 percentage points per year, or about 20%, of the 1995-2006 apparent increase in productivity growth for the U.S. economy. Bias in the price indexes used to deflate domestic output is a question beyond the scope of this paper, but if upward bias were also present in those indexes, this could offset some of the effects of mismeasurement of gains in terms of trade.

Sourcing Substitution and Related Price Index Biases

intermediate input. We define a class of bias problems that arise when purchasers shift their expenditures among sellers charging different prices for units the purchasers view as the same product but that are not regarded as being the same for the purposes of price measurement. For businesses purchasing from other businesses, these sorts of shifts can cause sourcing substitution bias in the Producer Price Index (PPI) and the Import Price Index (MPI), as well as potentially in the proposed new true Input Price Index (IPI). Similarly, when consumers shift their expenditures for the same products temporally to take advantage of promotional sales or among retailers charging different per unit prices, this can cause a promotions bias problem in the Consumer Price Index (CPI) or a CPI outlet substitution bias. We provide a common framework for these bias problems. Ideal target indexes are defined and discussed that could greatly reduce these biases. We also address the challenges national statistics agencies must surmount to produce price index measures more like the specified target ones. 1