necessarily indicate sustainable resource management. For example, Squires included conventional inputs only, while the resource stock, such<sup>as soil nutrient content, was considered</sup> as a technical constraint that influences trends in TFP.<sup>In contrast, Herdt and Lynam and Alston,</sup> Anderson, and Pardey have proposed a measure of<sup>Total Social Factor Productivity (TSFP) that</sup> incorporates changes in resource quality as well as externalities.<sup>3</sup> We prefer Squires's approach in the TFP estimation on<sup>both conceptual and empirical grounds.</sup> Conceptually estimates of TFP are based on the<sup>assumption of profit maximization, which is</sup> violated by attempts to account for market failure in<sup>TSFP measures.4In practice, it is difficult</sup> to value changes in resource quality and externalities,<sup>even where these changes can be</sup> physically quantified. Also, in the short to medium<sup>term covered by this paper, farmers may not</sup> be able to observe resource degradation and therefore<sup>it is exogenous to decision making rather</sup> than endogenous. The direct estimates of TFP using<sup>only conventional inputs and outputs is then</sup> the sum of i) technological progress, ii) changes in<sup>resource quality, and iii) improvement in</sup> technical and allocative efficiency due to investments<sup>in human capital and infrastructure. We</sup> then use a cost-function to decompose productivity<sup>growth into each of these effects. This</sup> provides a production system-specific estimate of the effects<sup>of changes in resource quality on</sup> productivity.

It should be noted that this measure overestimates TFP to<sup>the extent that resource degradation is</sup> internally induced-for example, depletion of soil nutrients to maintain current<sup>production</sup> levels. Also as a measure of sustainability, it ignores externalities<sup>such as effects on human and</sup> environmental health, which may be the major sustainability<sup>issues in some systems. However,</sup> in addition to practical difficulties, the theoretical case<sup>for including such externalities in</sup> agricultural productivity measures is questionable (Smith, 1998;<sup>Weaver, 1998).</sup> The chain-linked Tornqvist-Theil indexing procedure is commonly<sup>used to measure TFP because</sup> it is exact for a flexible linear homogeneous translog aggregate<sup>production function (Diewert,</sup> 1976, and Hulten, 1986). The index is estimated as follows.<sup>5</sup>

- 3 For empirical efforts to apply this approach see Ehui and<sup>Spencer (1993), Antle and McGuckin (1993), Oskam</sup> (1991), Archibald (1988) and Barnett, Payne and Steiner.<sup>(1995)</sup>

- 4 See Murgai (1999) and the recent exchange in American<sup>Journal of Agricultural Economics (Gollop and Swinand</sup> (1998); Weaver (1998) ; Smith (1998).

> 5 The measures of productivity growth will be biased if firms<sup>are in a temporary equilibrium rather than the long-run</sup> equilibrium, implicitly assumed by this estimation method<sup>(Berndt and Fuss (1986) and Hulten (1973)). This</sup> situation may arise, for example, with underutilized capital<sup>and labor capacity. We have no reason to expect this is</sup> the case in this study. Moreover, even if there is under<sup>utilization we have estimated values of the quasi-fixed</sup> inputs using the method specified in Bemdt and Fuss (1986).<sup>That is, we computed the</sup><sup>_value_of services from</sup> stocks of quasi-fixed inputs, rather than using the _quantity_<sup>of these stocks. For example, we took area planted</sup> (i.e., total capacity), not harvested area (utilized capacity)<sup>multiplied by the market rental rate of land. In the case</sup> of tractors and labor, we employed an annual utilization<sup>rate</sup>

3