A model is developed in this paper which allows the growth rate of public sector productivity to be estimated without an explicit measure of sectoral output. In this model, communities are regarded as generalized households, and the goods and services provided by the community's government are interpreted as internally produced household goods. The model is then fitted to quarterly data from the U. S. National Income and Product Accounts, and the rate of productivity change is found to average 0.50% per year for the period 1959-1979. THE sources-of-growth approach to productivity measurement distinguishes between the growth in real output due to the growth in factor inputs-capital, labor, materials-and the growth in output due to advances in technology, managerial practice, and other factors related to productive efficiency.' The former are collectively associated with the movement along an aggregate or sectoral production function, while the latter are associated with the shift in that function.2 In practice, the shift in the production function is measured by the residual real output not attributed to the growth of the share-weighted inputs, and termed total factor The sources-of-growth model is based on the underlying assumption that real output and real input can be measured with a reasonable degree of accuracy. While this presumption is correct for many types of economic activity, it is essentially incorrect for those sectors which produce services. As Kendrick (1982) has recently noted, approximately one-third of the real gross product originating in the service sector of U.S. private business economy is estimated using employment, manhours, or labor earnings. Such procedures systematically misstate the true growth of real output, and thus systematically bias the estimated growth in total factor productivity. The situation is even worse in the public sector: in the U.S. National Income and Product Accounts, the output of general government is defined to be equal to labor input, implying that the growth of total factor productivity exactly offsets the effect of nonlabor inputs. A model is developed in this paper which allows the growth rate of public sector productivity to be estimated without an explicit measure of sectoral output. In this model, communities are regarded as generalized households, and the goods and services provided by the community's government are interpreted as internally produced household goods. This interpretation allows us to appropriate the analytical apparatus of the household production model, and thereby permits us to estimate the key parameters of the model-including a government total factor productivity parameter-without first having to measure the output of the govern-

This paper revisits the hypothesis that technical change is embodied in capital. It extends old results to make them more relevant to the contemporary debates about the adjustment of investment goods for quality change and about the role of embodied technical change as a source of economic growth. It is shown that the failure to adjust capital for quality change has the effect of suppressing the quality effects into the conventional total-factor-productivity residual, and it is found that approximately 20 percent of the residual growth of quality-adjusted output could be attributed to embodied technical change.

The poor performance of U.S. productivity in recent years has renewed interest in the relationship between tax incentives, capital formation, and economic growth. Particular attention has been given to the impact of inflation on effective tax rates, and to the possibility that an inflation-induced increase in tax burdens contributed to the productivity slowdown through a reduction in the rate of capital formation. Attention has also focused on the role of relative tax burdens in explaining international differences in savings rates and economic growth, and on the extent to which differences in relative tax treatment of various types of capital results in an inefficient allocation of resources. These issues are the subject matter of the emerging doctrine of economics, which may be loosely defined as the application of microeconomic principles to macroeconomic problems. While supply-side economics is concerned with the response of all inputs to a change in tax policy, I shall restrict attention to the response of investment spending to changes in business tax incentives. I shall first consider how business tax incentives in the U.S. Internal Revenue Tax Code have changed over time, and then provide an overview of the recently developed cost of capital literature on marginal effective tax rates. I will then turn to the question of how these tax incentives have influenced investment behavior. A concluding section offers comments on the relative importance of supply-side effects on economic growth. I. Marginal Effective Corporate Tax Rates

Robert Solow's paper on technical change provides an economic rationale for the so-called total factor productivity residual-the growth rate of real product not explained by the share-weighted growth rates of the real factor inputs. Solow demonstrated that under the assumptions of a Hicks-neutral aggregate production function and competitive equilibrium, the residual is equivalent to the growth rate of the Hicksian efficiency parameter, which in turn is equivalent to the rate at which the aggregate production function is shifting over time. An important implication of this result is that, under the appropriate assumptions, the shift in the production function can be measured using price and quantity data alone, without the need of estimating or assuming the values of such parameters as the elasticity of substitution between capital and labor.' Although the residual is a valid measure of the shift in technology, it does not indicate the true importance of productivity change as a source of economic growth. An increase in total factor productivity will in general lead to an increase in output (as the inputs are used more efficiently) and thus to additional saving and capital formation. Part of the historically observed growth rate of capital stock is, therefore, the result of productivity change, and must be recognized as such when assessing the importance of productivity change as a source of growth. This paper suggests an accounting framework for measuring the importance of productivity change using price and quantities alone. It is based on an intertemporal specification of technology closely related to the framework proposed by Edmond Malinvaud (1953, 1961). An effective rate of productivity change (termed the dynamic residual) is defined to be the residual growth in total consumption not explained by the rate of change of total primary input. This residual is then related to the change in the Malinvaud intertemporal production possibility frontier due to changes in total factor efficiency. Since capital accumulation is endogenous in the intertemporal framework, the dynamic residual measures the impact of annual changes in factor efficiency inclusive of the induced accumulation of capital. It thus provides a measure of the importance of productivity change in economic growth. John R. Hicks and T. K. Rymes have also emphasized the need to measure technical change in a dynamic (capital endogenous) framework,2 but, have implicitly (and explicitly, in the case of Rymes) rejected the conventional residual as a measure of changing technical efficiency. The main result of this paper is, however, that the conventional and dynamic residuals are complements rather than substitutes. They measure different aspects of the same process within a common analytical framework. As will be seen in Table 1, the conventional (atemporal) accounting framework is embedded in a more general *The Urban Institute. I acknowledge the financial support of the National Science foundation in the preparation of this paper. I would also like to thank Larry Epstein, Melvyn Fuss, Dale Jorgenson, and Mieko Nishimizu. IThe recent empirical literature on U.S. productivity change includes Laurits Christensen and Dale Jorgenson (1969, 1970), Edward Denison (1962, 1967, 1974), Jorgenson and Zvi Griliches (1967), John Kendrick (1961, 1973), and Spencer Star. Estimates of the residual have varied greatly: for example, Jorgenson and Griliches (1967) obtain an average annual estimate of 0.10 percent for the period 1945--65, while Kendrick (1973) obtains 2.0 percent for the same period. For a discussion of some of the issues in productivity analysis, see the 1972 Survey of Current Business exchange between Denison and Jorgenson and Griliches. 2Richard Nelson also notes the interaction between productivity change and capital accumulation, but concentrates on the embodied technical change aspects of the problem. See also Denison (1974, pp. I 33-35).

It is hardly news that we are in the midst of rapid economic change. The advances in information and communication technology (ICT), in the life and other sciences and their profusion of innovative products from the newest electronic devices to the latest drugs and treatments are ample evidence. Equally pervasive are new business models in services (big box retail, online banking, on-demand media) and the explosion in social networking and new business practices ushered in by the Internet (telework, virtual meetings, job boards). Given the magnitude of the changes brought on by these innovations, it is useful to step back and ask: What does economic analysis have to say about the sources and mechanisms of these shifts and revolutions, and what economic metrics are available to measure their overall size and impact? The received theory of economic growth is the natural candidate for this job. It came of age in the 1950s and 1960s with the neoclassical models and emergence of aggregate growth accounting. The latter has become the work horse of empirical macroeconomic growth analysis and the basis for official productivity statistics put out by the Bureau of Labor Statistics (BLS) since 1983. A technological revolution appears, in this framework, as an increase in the fruits of innovation, as measured by the shift in an aggregate production function (termed multifactor