American Journal of Agricultural Economics — Volume 89 (2007). The definitive version of this article will be available at www.blackwell-synergy.com . Rulon D. Pope is Professor, Department of Economics, Brigham Young University. Jeffrey T. La- France is Professor, Department of Agricultural and Resource Economics, University of Califor- nia, Berkeley and member of the Giannini Foundation of Agricultural Economics. Richard E. Just is Distinguished University Professor, Department of Agricultural and Resource Economics, Uni- versity of Maryland. IMPERFECT PRICE DEFLATION IN PRODUCTION SYSTEMS Rulon D. Pope, Jeffrey T. LaFrance, and Richard E. Just Numeraire prices that are measured with error create challenges for econometric estima- tion. A straightforward approach for a model with linear input demands, such as gener- ated from a quadratic normalized profit function, is proposed where the numeraire price is measured with error. Numeraire measurement error is likely because expected output price is measured imperfectly by actual output price. An approach using generalized method of moments is developed to estimate such errors-in-variables systems that avoids use of extra-sample data or additional structural specifications. Monte-Carlo examination of small sample properties shows promise. Measurement error is statistically significant using aggregate U.S. agricultural data. Keywords: errors-in-variables, expected prices, GMM estimation, input demands Running Head: Price Deflation in Production Systems The connection between economic theory and measurement is often tenuous and filled with compromises. There has long been a concern that substantially wrong conclusions can be reached if there is serious measurement error (e.g., Greene 2000). For example, standard errors-in-variables (EIV) models can lead to biased and inconsistent estimates and underidentification. Many of the proposals for dealing with EIV require extra sample data and/or very sophisticated methods based on simulation or characteristic functions (e.g., Hausman, et al. 1991; Cragg 1997; Amemiya 1990; Schennach 2004; Li and Vuong 1998; and Newey 2001). A wide variety of articles in agricultural economics have considered EIV. An incom- plete but representative list of articles includes: (i) EIV biases in production function es- timation (Griliches 1957), (i) an EIV AIDS demand system (Buse 1994) and reported in- come not being the income that belongs in demand equations or Engel curves (Newey 2001; Lewbel 1996), and (iii) EIV analyses of the conventional capital asset pricing model (Bjornson and Innes 1992; Johnson, Mittelhammer and Blayney 1994). Further- more, as noted by McCallum (1976), linear rational expectations models can also be viewed as EIV models, so a host of other models implicitly include EIV (e.g., Aradhyula and Holt 1989; Sheffrin 1983). 1 The particular problem addressed in this paper deals with price deflation. It is com- mon in agricultural economic studies to deflate by a numeraire, which may be a price in- dex or an expected price. For example, under zero-degree homogeneity in typical normal- ized profit function approaches such as popularized by Lau (1978), output price generally becomes a numeraire that normalizes or deflates all input prices. Lau (1978), and Lau and Yotopolous (1972) called this the “Unit-Output-Price” or UOP profit function. A com-