# 1 Introduction

Standard models in many ...elds of economics posit the existence of a representative household in either a static or a dynamic setting, and then seek to relate the welfare of that household to observable aggregate data. A separate large literature examines the productivity residual de...ned by Solow (1957), and interprets it as a measure of technical change or policy e¤ectiveness. Yet a third literature, often termed "development accounting," studies productivity di¤erences across countries, and interprets them as measures of technology gaps or institutional quality. To our knowledge, no one has suggested that these three literatures are intimately related. We show that they are. We start from the standard framework of a representative household that maximizes intertemporal welfare over an in...nite horizon, and use it to derive methods for comparing economic well-being over time and across countries. Our results show that under a wide range of assumptions, welfare can be measured using just two variables, productivity and capital accumulation. We take our framework to the data, and measure welfare change within countries and welfare di¤erences across countries.

In the simplest case of a closed economy with no distortionary taxes we show that to a ...rst-order approximation the welfare change of a representative household can be fully characterized by three objects: the expected present discounted value of total factor productivity (TFP) growth as de...ned by Solow, the change in expectations of the same quantity, and the growth in the stock of capital per person. The result sounds similar to one that is often proven in the context of a competitive optimal growth model, which might lead one to ask what assumptions on technology and product market competition are required to obtain this result. The answer is, None. The result holds for all types of technology and market behavior, as long as consumers take prices as given and are not constrained in the amount they can buy or sell at those prices. Thus, for example, the same result holds whether the TFP growth is generated by exogenous technological change, as in the Ramsey-Cass-Koopmans model; by changes in the size of the economy combined with increasing returns to scale, as in the "semi-endogenous growth" models of Arrow (1962) and Jones (1995); or by externalities or public policy in fully-endogenous growth models, such as Romer (1986) or Barro (1990). As we discuss below, aggregate TFP can also change without any change in production technology in multi-sector models with heterogeneous distortions (for example, markups that di¤er across sectors): our results show that an increase in aggregate TFP due to reallocation would be as much of a welfare gain for the representative consumer as a change in exogenous technology with the same magnitude and persistence.

Our ...ndings suggest a very di¤erent interpretation of TFP from the usual one. Usually one argues that TFP growth is interesting because it provides information on the change or di¤usion of technology, or measures improvement in institutional quality, the returns to scale in the production function, or the markup of price over marginal cost. We show that whether all or none of these things is true, TFP is interesting for a very di¤erent reason. Using only the ...rst-order conditions for optimization of the representative household, we can show that TFP is key to measuring welfare changes within a country and welfare di¤erences across countries. We interpret TFP purely from 2