رشد بهره وری و نرخ پس انداز آمریکا

Over the last half century, the saving rate in the United States exhibited significant variations. In this paper, I examine whether a general equilibrium model that allows for shifts in the growth rate of total factor productivity can account for these variations. The model generates significant medium-run variations in the U.S. saving rate, and establishes a link between episodes of productivity growth slowdowns or accelerations and the saving rate—two concepts that have often been treated in isolation. While a productivity-growth based explanation is able to account for broader trends in the rising consumption–income ratio from about 1980 to 2000, there are other episodes during which the model is less successful.

Over the last quarter century, the growth rate of consumption in the U.S. has far outstripped the growth rate of its GDP, leading to what is coined as a “saving slump” (Lusardi, 2009). Fig. 1 shows personal consumption expenditures as a percentage of GDP since 1952. Both the actual and Hodrick–Prescott filtered series exhibit an upward trend, especially after the 1970s—although there has been a slight decrease in this ratio since 2005. A more familiar restatement of this trend is the declining personal saving rate in the United States. 1 The literature has so far considered several factors including large capital gains, an aging population and financial innovations (see below for a more detailed discussion). One of the possible and hitherto overlooked explanations of this decline in the saving rate is the consequences of changes in productivity growth (such as productivity slowdown during the 1970s and 1980s, and productivity resurgence in the second half of the 1990s). Yet, basic economic theory suggests that such changes in productivity growth affect both the rate of return to capital and households' permanent income, and as such will likely to have significant income and substitution effects on consumption–saving decisions. This paper explores the significance of these effects for understanding the variations in the U.S. saving rate.Although it is unlikely that a single factor is responsible for the observed variations in the consumption–income ratio, there are at least two reasons to examine the strength of the productivity channel alone. First, it is largely complementary to the existing explanations, and thus may improve our overall understanding of the saving rate in the United States. Second, in a dynamic general equilibrium setting, current and anticipated growth of productivity on the one hand, and consumption–saving decisions on the other hand are related through a range of factors. These factors include interactions among anticipated growth rate of productivity in the medium and long run, the elasticity of intertemporal substitution and the real rate of return to capital both in the short and long run. In particular, consider these relations in a Ramsey model (e.g., Barro and Sala-i Martin, 1995, Chp. 2). In the steady-state solution of this model, when the elasticity of intertemporal substitution is relatively high, a permanent increase in the growth rate of productivity leads to a higher steady-state saving rate. This across steady-state comparison has two components. First, a higher productivity growth leads to a higher rate of return to capital per effective worker at the new steady state. This corresponds to lower capital per effective worker, and thus to lower demand for saving. The strength of this response depends on the elasticity of intertemporal substitution. At the same time, there is a positive income effect, as higher productivity growth will allow for more saving and investment without sacrificing consumption. Of course, outside the steady state, there are similar income and substitution effects, and the response of the saving rate to a change in the growth rate of productivity depends on the initial conditions, as well as on the magnitude of the elasticity of intertemporal substitution relative to the new steady-state saving rate ( Barro and Sala-i Martin, 1995, pp. 89–90). Moreover, when the long-run productivity growth varies over time, these factors have complex interactions. So, this paper investigates the combined effects of intertemporal substitution and income channels using a quantitative model, and examines the stand-alone contribution of a productivity-growth based explanation in accounting for the U.S. consumption–income ratio. 2 To this end, I consider a dynamic general equilibrium model, use actual productivity growth data and examine whether the model-based consumption–income ratios are consistent with the observed data. I find that the model matches the important medium-term variations in the U.S. consumption–income ratio, especially from 1980 to 2000, and establishes a link between episodes of productivity slowdowns or accelerations and the saving rate—two concepts that have often been treated in isolation.3 However, while a productivity-growth based explanation is able to account for broader trends in the rising consumption–income ratio from about 1980 to 2000, there are other episodes during which the model has much less success—for instance, the failure of the model to account for the high consumption–income ratio during the early 2000s. In the model, changes in productivity growth are responsible both for income effects and intertemporal substitution effects, which have ramifications for the consumption–income ratio, and in this general equilibrium setting, it is not possible to isolate the independent contributions of these channels. However, I find that the rate of return to capital over the last 50 years has not been constant, and that the model closely tracks these changes. As such, these findings suggest that the intertemporal substitution channel—a core classical theme in macroeconomics—has been a potentially important contributor to the variations in the observed consumption–income ratio in the United States since 1952. The quantitative approach followed here also distinguishes between actual and real-time forecasts of productivity growth, both of which enrich the empirical analysis in distinctive ways. In the Ramsey model, along a balanced-growth path, the time paths of consumption and income are typically determined by a unique long-run growth rate of the productivity factor, and both consumption and income grow at constant rates. Moreover, since the consumption–income ratio is bounded between zero and one, they must also grow at identical rates. Hence, in a deterministic neoclassical growth model, the steady-state consumption–income ratio is constant, and the model quickly converges to its long-run equilibrium. 4 This paper, on the other hand, accounts for the rising consumption–income ratio by appealing to shifts in the actual growth rate of total factor productivity. I also consider the distinction between perceived and actual long-run productivity growth. I compare the consumption–income ratios based on real-time forecasts of productivity growth with those based on currently available revised data, and find significant differences. 5 More recently, with the run-up and subsequent collapse in house prices, the “low” saving rate in the United States has become a focal point of economic policy debates. Within this context, housing poses conceptual challenges, and raises measurement issues. From a measurement standpoint, conventional national income accounting treats housing (imputed rent) as a final personal consumption expenditure. In this paper I exclude housing value added from consumption expenditures. Instead, in an extension of the baseline model, I model housing as an input into the production of nonmarket goods, and explore quantitatively the indirect influence of housing on the consumption–income ratio. Overall, relative to the baseline model without housing, the extended model matches the actual data better, but the extended model still fails to account for the persistently high consumption–income ratio in the 2000s. The rest of the paper is organized as follows. Section 2 discusses the existing explanations for the rising consumption–income ratio in the United States since the early 1980s. Section 3 presents a baseline neoclassical growth model. Section 4 presents the simulation results, and discusses the quantitative significance of the productivity-growth based explanation of the U.S. saving rate. Section 5 contains concluding remarks. A technical (online) appendix and a data appendix complement the paper.

The general equilibrium analysis I presented in this paper relies on a highly compact (and stylized) modeling approach. It emphasizes a quantitative strategy that maps model-based variables to their empirical counterparts as closely as possible. In fact, throughout much of the analysis, I focused on relatively narrow concepts of market consumption and income, and particularly on those to which the model can speak. The baseline model matches the broader (medium-run) variations in the consumption–income ratio and rate of return to capital in the United States, especially during the remarkable decline in the U.S. saving rate from 1980 to 2000, but it is not completely satisfactory. The extended model with housing leads to a better match between the actual and model-based series. However, this model also fails to account for the persistent and relatively higher consumption–income ratio at the end of the period of analysis (from 2000 to 2006). Although an open economy extension of this model with a current account is beyond the scope of this paper, it is worth mentioning several pertinent issues.28 First, despite significant fluctuations in the U.S. current account deficits since the early 1980s, the U.S. personal saving rate declined unabated. This suggests that predominantly domestic factors might have been responsible for the “saving slump” in the United States. Second, Curcuru et al. (2008, pp. 1523–1525) argue that available measures of the U.S. current account deficits are plagued by relatively underappreciated measurement errors. For instance, they argue that U.S. current account deficits may be significantly overstated—as much as 0.8% of GDP. So, an analysis of the U.S. saving rate in an open economy context faces a different set of conceptual and measurement issues. This paper has argued that the economy-wide productivity growth in the United States exhibited substantial variations since the 1950s, and used these variations to account for the variations in the U.S. saving rate. The results suggest that real-time forecasts of long-term productivity growth provide a better understanding of the actual data. In this context, building models with learning as a way to study aggregate saving rates strikes me as a promising avenue for future research.