آموزش و تغییرات در رشد بهره وری بلند مدت

An extensive literature has analyzed the macroeconomic effects of shocks to the level of aggregate productivity; however, there has been little corresponding research on sustained shifts in the growth rate of productivity. In this paper, we examine the effects of shocks to productivity growth in a dynamic general equilibrium model where agents do not directly observe whether shocks are transitory or persistent. We show that an estimated Kalman filter model using real-time data describes economists’ long-run productivity growth forecasts in the United States extremely well and that filtering has profound implications for the macroeconomic effects of shifts in productivity growth.

An extensive literature has studied the macroeconomic effects of shocks to the level of productivity in dynamic general equilibrium models; see, for example, Galí and Rabanal (2004) and references therein. However, there has been far less research on the effects of a sustained shift in the growth rate of productivity. This lack of attention is somewhat surprising given the notable shifts in productivity growth that have occurred in the United States, Japan, and other industrialized economies in recent decades, and the widespread view that these developments had profound effects on economic performance. 1 Simple filtering exercises of the annual growth rate of U.S. nonfarm business output per hour (such as that shown in Fig. 1), as well as formal statistical tests, support the occurrence of low frequency variation in the rate of labor productivity growth in the United States. Roberts (2001), Fernald (2005), and Benati (2006) are all able to reject the null hypothesis of constant trend labor productivity growth in post-war U.S. data and find evidence of economically significant low frequency variation in productivity growth. In addition, Kahn and Rich (2003) estimate a two-state Markov switching model for trend productivity growth and find evidence of shifts in the early 1970s and the late 1990s.Theoretical research has highlighted what may seem a paradoxical result: a sustained decrease in the rate of productivity growth yields positive responses of the saving rate, hours, investment, and output. Viard (1993) and Carroll and Weil (1994) showed that a decline in the productivity growth rate should elicit an immediate rise in the saving rate. Campbell (1994) showed that in a real business cycle model a persistent decline in the productivity growth rate yielded the “perverse” response of a rise in employment and output. These predictions occur as a result of a negative permanent income effect implied by lower growth, which induces a decline in the consumption of goods and leisure. More recently, Pakko (2002) showed that qualitatively the same results hold true if the productivity growth shock is limited to the capital goods sector. These studies all point to negative comovement between long-run productivity growth and standard cyclical measures of economic activity, namely, hours, investment, and output, during the transition period. The empirical evidence appears to be inconsistent with some aspects of these predictions. As predicted by theory, the U.S. investment rate—as measured by total fixed investment divided by GDP—was indeed higher during the low productivity growth period of the mid 1970s through the mid 1990s than the preceding high productivity growth period. But, contrary to the predictions of theory, the investment rate rose even higher during the high productivity period starting in the latter part of the 1990s. Measures of employment also appear to be at odds with the predictions of theory. The unemployment rate has been on average low during periods of rapid productivity growth and high during periods of low productivity growth, a pattern seemingly the opposite of what one would expect based on standard macroeconomic theory. A key assumption in this theoretical research is that agents immediately recognize the shift in long-run growth. As seen in Fig. 1, however, transitory swings in productivity growth dwarf lower-frequency movements in the rate of growth, making precise real-time measurement of the trend growth rate very difficult. In the first part of this paper, we model the process by which agents update in real time their estimates of long-run productivity growth and compare the model's predictions to a data set of economists’ real-time forecasts of long-run productivity growth. We find that an estimated Kalman filter model using real-time data tracks closely the year-to-year movements in economists’ long-run productivity growth forecasts during both the 1970s and the 1990s. We show that the use of real-time data is crucial for understanding the historical evolution of long-run expectations during both of these episodes. We then examine the effects of incorporating real-time learning of long-run productivity growth on the responses to shifts in the long-run growth rate in a dynamic general equilibrium model. We assume that agents in the model economy possess only aggregate information regarding the future trajectory of productivity growth (and thereby real wages and interest rates) and therefore use the estimated Kalman filter for updating their estimates of long-run productivity growth. Specifically, agents face the same signal extraction problem as macroeconomic forecasters. We then analyze transitory and permanent shocks to productivity growth. We find that gradual recognition of a shift in long-run productivity growth dramatically affects the macroeconomic response to such a shift. In our model, an immediately recognized increase in long-run productivity growth generates a positive wealth effect that leads to a significant decline in employment and investment and a rise in consumption and real interest rates. The rise in the real interest rate and cost of capital resulting from faster long-run growth lowers the equilibrium ratio of capital to output below its current level, depressing investment. In contrast, with gradual recognition of the shift in the long-run growth rate, agents initially believe that the shock is primarily transitory in nature and therefore has minimal implications for permanent income and real interest rates. As a result, these depressing influences on hours and investment are restrained at first and surface only gradually. Consequently, the economy initially responds to the shift in long-run growth as it would have had productivity growth been only temporarily higher. In the model studied in this paper, hours and investment boom for several years in response to a rise in long-run growth.2 We also find that real-time learning has important implications for the macroeconomic responses to shocks to the level of productivity. With learning, an unanticipated increase in the level of productivity is perceived to in part reflect an increase in the trend growth rate, which elicits permanent income effects that depress hours, investment, and output, relative to the complete information benchmark. This implies that incorporating learning in models could help reconcile empirical and theoretical responses to technology shocks. The paper is organized as follows. Section 2 examines the evidence on real-time estimates of long-run productivity growth during the 1970s and 1990s. Section 3 describes and estimates a Kalman filter model for estimating long-run productivity growth and compares the resulting real-time predictions to estimates reported in surveys. Section 4 describes the model and its equilibrium conditions. Section 5 analyzes the steady-state and dynamic implications of shifts in the growth rates of aggregate and sector-specific TFP and considers the robustness of these results. Section 6 concludes.

This paper shows that an estimated Kalman filter model provides a very good description of the evolution of economists’ real-time estimates of long-run productivity growth during both the 1970s and 1990s and that incorporating the gradual recognition of shifts in the trend growth rate that results from the Kalman filter has important implications for macroeconomic responses to productivity shocks. These findings have implications for a broader set of issues than those studied here. In a companion paper, Edge et al. (2003) explore the effects and monetary policy implications of shifts in long-run growth in a model with nominal rigidities.