WORKING PAPER SERIES
What Happens When the Technology Growth Trend Changes? Transition Dynamics and Growth Accounting
Michael R. Pakko
Working Paper 2000-014A http://www.stls.frb.org/research/wp/2000-014.html
May 2000
FEDERAL RESERVE BANK OF ST. LOUIS Research Division 411 Locust Street St. Louis, MO 63102
The views expressed are those of the individual authors and do not necessarily reflect official positions of the Federal Reserve Bank of St. Louis, the Federal Reserve System, or the Board of Governors.
What Happens When the Technology Growth Trend Changes?: Transition Dynamics and Growth Accounting Michael R. Pakko* Federal Reserve Bank of St. Louis 411 Locust Street St. Louis, MO 63102 (314) 444-8564
[email protected] May 2000 Keywords: Capital deepening, productivity, stochastic growth JEL Classification: E13, E22
Abstract Rising rates of economic growth during the 1990s have inspired speculation about a shift in the underlying growth rates of technology and productivity. This paper considers the adjustment dynamics of such a change in a basic neoclassical framework that incorporates stochastic growth. Simulations of the model suggest that the dynamics of capital stock adjustment in response to changing growth paths can have important implications for measuring productivity trends and interpreting the results of growth accounting exercises, particularly when technological change is capital-embodied.
*The views expressed in this paper are those of the author and do not necessarily reflect official positions of the Federal Reserve Bank of St. Louis, the Federal Reserve System or the Board of Governors.
What Happens When the Technology Growth Trend Changes?: Transition Dynamics and Growth Accounting The remarkably robust and durable economic expansion of the 1990s has inspired interest in the notion that a fundamental change has taken place in the U.S. economy. Broadly stated, the “new paradigm” or “new economy” theories that have emerged in recent years suggest that rapid economic growth can continue unabated into the future. Put more concretely, there is a perception that the trend rates of productivity and potential output growth have increased. Although most economists remain skeptical about many aspects of new-economy theories, the conjecture of a shift in the potential growth trend has been seriously entertained. Indeed, the issue is often cast in terms of whether recent trends suggest a return to growth conditions prior to the great productivity slowdown of the 1970s and 1980s. Typically, evidence of a shift in the productivity trend is sought within the classic growth accounting framework associated with Solow (1957): the average contributions of labor, capital, and multifactor productivity growth are decomposed and compared over sample periods, with the objective of uncovering changes in growth trends. Because the role of new information technologies is commonly seen as central to the emergence of the “new economy,” recent growth accounting analyses have been particularly concerned with finding a role for computer-related productivity gains. For example, Gordon (1999) examines a sectoral decomposition, finding that most productivity gains in multifactor productivity are in the computer-producing sector. Oliner and Sichel (1994, 2000) consider the importance of computers in the capital component of their growth accounts, -1-
finding an important role for the use of computers embedded in the growth of capital services. Jorgenson and Stiroh (1999) explicitly incorporate computer related growth in demand for investment and consumer durables. Whelan (1999) adjusts the growth contribution of capital deepening by modeling the rapid obsolescence of computer hardware, and Kiley (1999) incorporates investment adjustment costs associated with new technologies into a growth accounting framework. Studies of this type generally compare growth averages across time periods, sometimes with an implicit assumption that sub-sample means represent distinct steadystate growth paths. None of these analyses explicitly consider the complications of shortrun transition dynamics between one growth regime and another. In this paper, I demonstrate the potential importance of these transition dynamics when evaluating a change in the underlying growth rate of technological progress. The nature of the issue being investigated–an apparent acceleration of productivity growth in the latter half of the 1990s–necessitates analysis with limited data. With the hypothesized increase in the growth trend being manifested only since 1995 or 1996, comparisons of growth rates over periods of as short as four or five years are common. Figure 1 shows that in the data, there is a considerable amount of variation in 5-year average rates of productivity growth over the past 30 years.1
Using a simple growth
accounting decomposition of labor productivity into capital-deepening and multifactor productivity terms, Figure 1 also suggests that changes in the rate of capital deepening are
1
The data used for Figure 1 are: the nonfarm business sector component of GDP, labor input from the BLS's productivity accounts, and the BEA's net stock of nonresidential equipment and software. Growth accounting calculations are based on a capital share of 0.3.
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prevalent at the frequency of five-year averages, and that there is an apparent tendency for capital's contribution to co-vary positively with the labor productivity growth rate itself. Specifically, the rate of capital deepening declined as productivity growth slowed during the 1970s and 1980s, and increased with the productivity pickup in the 1990s.2 These observations provide prima facie evidence to suggest that transition dynamics between longrun growth paths involving the adjustment of the capital stock might play a role in productivity growth patterns observed in recent decades. In simulations of a simple neoclassical growth model that is subject to growth shocks, the analysis of this paper shows that transition dynamics between long-run growth paths have short-run implications that can significantly affect growth accounting decompositions over short sample periods like those shown in Figure 1. These dynamics also suggest that shifts in the underlying growth rate of technological progress may not be clearly manifested in measured productivity data for several years after the actual event.
The Model In order to incorporate the notion that emerging growth trends are associated with new technologies, the model examined in this paper is based on a neoclassical growth framework that incorporates a role for investment-specific, or capital-embodied technological change. Simulations of the model's responses to a shift in the underlying growth trend are the focus of the analysis.3
2
The slowdown and subsequent increase in capital growth are the subject of recent analyses by Ho, Jorgenson and Stiroh (1999) [the slowdown] and Tevlin and Whelan (1999) [the increase]. 3
Examples of similar approaches to modeling stochastic growth in a computable general
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Consumers (represented by a social planner) maximize logarithmic utility over consumption and leisure, ∞
max å β t [ln(Ct ) + ν ln(1 − N t )], t=0
subject to an overall resource constraint with Cobb-Douglas production: Yt = (1 − τ ) Z t Kt a N t 1− a + T = Ct + I t
(1)
In equation 1, Ct , Kt , Nt, and It represent consumption, capital, labor, and gross investment, respectively. Zt represents an index of total-factor, or neutral, productivity. Income is subject to a tax rate, τ, with government revenues rebated lump sum via T=τY (taken as given in the representative agent's optimization).4 The capital accumulation equation incorporates a role for investment-specific technological change, as modeled by Greenwood, Hercowitz and Krusell (1997,2000): K t +1 = (1 − δ ) K t + Qt I t
(2)
Improvements in the productive efficiency of new investment goods are represented by growth in the capital-quality index, Q. When Q is fixed and normalized to one, the model is a standard balanced-growth model. Growth in Q is associated with technological progress that becomes embodied in a higher-quality capital stock.5
equilibrium framework include King, Plosser and Rebelo (1988b); and King and Rebelo (1993). 4
Taxes are included in order to incorporate their importance for marginal decision-making (particularly their effects on capital formation), abstracting from wealth effects. 5
Hercowitz (1998) discusses recent models of investment-specific technological change in the context of the "embodiment" controversy of Solow (1960) and Jorgenson (1966) .
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Aggregate economic growth depends on the growth of both technology indices, Zt and Qt. I assume that each of these technology variables can be decomposed into trend and cyclical components as Zt+1 = XZ,t+1 zt+1 and Qt+1 = XQ,t+1qt+1, where Xi,t+1= γi,t Xi,t with the γi, i=z,q, representing trend growth rates, and with zt and qt representing stationary cyclical components that reflect transitory shocks to technology. The latter pair of technology variables are associated with the stationary shocks commonly assumed in the real business cycle (RBC) literature. Our focus here is on the idea that the underlying long-run growth trends are not literally permanent, but are subject to some stochastic variation.
Methodology In the model examined in this paper, growth trends depend on both embodied and neutral technological change. With a stationary supply of labor (so that the model represents per-capita quantities), standard steady-state restrictions require that output, consumption and investment will grow at a common rate γy. The accumulation equation implies that capital will grow at a higher rate than output, as determined by the growth rate of capital-embodied, investment specific technological progress: γk = γyγq .
(3)
The production technology determines the relationship between output and the underlying technological growth rates as:
γ y = γ z 1/(1−α )γ q α /(1−α )
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(4)
A stationary representation of the model can be derived by dividing each of the time-t variables by growth factors, Xit, where Xit+1 = γx Xit. [each of the γx are related to underlying growth trends from (3) and (4)]. As a result of this transformation, long-run growth rates emerge as parameters of the stationary problem. For example, using lower case variables to represent transformed variables [e.g. kt = Kt/Xkt], the capital accumulation becomes:6 (2′)
γ k kt +1 = (1 − δ )kt + qt it By treating the underlying growth rates, γq and γz, as being subject to exogenous shocks, it is possible to simulate approximate dynamics of a model in which growth is
stochastic. Growth rates of key model variables can be recovered from simulations as the sum of the underlying growth trend, the deviations from the trend represented by the growth shocks themselves, and the first-differences of the simulated dynamics of the stationary system. The dynamics of the stationary system itself are found as the solution to a log-linear approximation, using the technique of King, Plosser and Rebelo (1988a).7 The first-order condition determining the optimal capital stock can be expressed as:
{
}
γ k (λt / q t ) = βE (λt +1 / q t +1 )[q t +1 zt +1 F ( k t +1 , N t +1 ) + (1 − δ )]
(5)
6
For general time-separable CRRA utility, the stationary transformation also involves a modification of the discount factor, β. See King et al. (1988a). 7
The inclusion of stochastic growth rates in a log-linear approximation introduces a potentially important source of approximation error. A full-blown second-moment evaluation dynamics would require more careful attention to this issue. For the purpose of simulating basic impulse-response functions and transition paths, however, the importance of approximation error can be evaluated against exact nonlinear steady-state solutions. For the magnitude of growth changes examined in this paper, these errors are negligible.
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where λ is the shadow value of utility (in consumption units). In its steady-state form, equation (5) determines the optimal capital-labor ratio as a function of the trend growth rate of capital, γk . In particular, just as in a simple Solow growth model, an increase in the growth rate of labor efficiency-units raises the optimal marginal product of capital — requiring a lower capital/labor ratio. When the growth-trend component is stochastic, the target capital stock becomes variable, depending on the current perceived growth trend. It is the transition dynamics from one optimal capital-labor ratio to another that gives the model in this paper its unique dynamic implications.8
Calibration The model is calibrated at an annual frequency, generally using standard values that are consistent both with typical RBC analyses and growth accounting exercises. Values for the key model parameters are listed in Table 1. Capital's share of output, α, is set to 0.30, the preference parameter v is selected so that the fraction of time spent working of 0.24, and the discount factor, β, is based on a real return to capital of 6%. The capital depreciation rate, δ, is set to 6%, [the average value of depreciation to the net stock of nonresidential fixed private capital in the BEA's Fixed
8
King and Rebelo (1993) employ a very similar approach. Rather than considering the growth rates as stochastic directly, however, they evaluate perturbations of the capital stock from its desired long-run value, and generate transition dynamics back to the steady state.
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Reproducible Tangible Wealth estimates for1960-98]. The marginal tax rate, τ, is assumed to be 0.40.9 The baseline growth rate of (per capita) output is set to 1.5%, the approximate growth rate of labor productivity over the 1973-94 period. Over the same sample period, the data used in Figure 1 reveal that capital stock growth exceeded output growth by an average of 0.85%. Accordingly, the growth rate of investment-specific technical progress is calibrated to that figure.
Simulations To demonstrate the dynamic adjustment path that follows a change in the growth rate of technological progress, I consider an increase that raises the trend rate of output and labor-productivity growth from 1.5% to 2.0%. To capture the role of the underlying growth parameters as the determinants of long-run trends, it is assumed that changes in the growth trend are statistically permanent, i.e. the γit , i=z,q, follow random-walks,
γ it = γ it −1 + eit
(6)
Simulations involve the response of the model to the underlying shocks, eit. Shifts in the underlying growth trends occur as unexpected events to agents, although the distribution of the shocks is known ex ante. Figure 2, showing the behavior of the capital stock following a 0.5% increase in the growth rate of neutral technological change, highlights one key feature of the dynamics of this experiment. The higher productivity-growth profile calls for a lower capital/labor ratio 9
Greenwood, et al (1997,2000) include labor and capital income tax rates separately, calibrating their values at 0.40 and 0.42, respectively.
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in the long run, providing a depressing effect on investment and capital accumulation. On the other hand, the higher technology growth trend itself requires a higher growth rate for capital and investment in the long-run. Growth rates during the transition depend largely on which of these two effects dominate. Figure 3 illustrates how consumption is affected. A wealth effect raises consumption in the short run, while the downward level-shift in the capital stock is reflected gradually over time. In order to examine the growth dynamics of this type of exercise more clearly, Figure 4 shows the growth paths of key macroeconomic variables following an increase in the underlying rate of neutral technological change. For this simulation, a 0.5 percentage point increase in the growth trend is assumed to take place incrementally rising 0.1% in each of five years (ext=0.001 for t=0,1,2,3,4). This incremental approach is taken to clearly separate the dynamic effects of growth shifts into realization and post-realization periods, and to represent the notion that recognition of changes in a growth trend (if not the actual process itself) is likely to be gradual. In Figure 4, the wealth effect on consumption growth is apparent, and the same wealth effect is responsible for a decline in labor supply. Investment demand drops sharply in order to move the capital/labor ratio toward its new optimal value. The slowdowns in employment and investment imply that output growth also slows for a time, and suppressed capital-formation continues to provide a depressing effect on output growth as the underlying growth trend changes. In the post-shock adjustment dynamics, capital-stock growth accelerates to its new, higher steady state rate, with output, consumption, and
-9-
employment boosted by the associated investment boom. The real interest rate gradually adjusts to the new, higher long-run marginal product of capital. Figure 5 shows how these dynamics are modified when the underlying technologygrowth shift is of the capital-embodied variety. For this type of growth shock, capital stock adjustment plays an even more pivotal role. In order for a change in the growth rate of embodied technology to generate the same acceleration in productivity growth as a neutral technological growth shift, the growth rate of the capital stock must accelerate at an even greater rate (equation 3). Moreover, because the downward movement of the capital/labor ratio depends on the change in the growth rate of capital (equation 5), the requisite levelshift of the capital stock is larger as well. The magnified effects of an embodied technology growth shock on capital growth dynamics carry over to the behavior of other macroeconomic variables. Relative to the case of a neutral technological growth shift, the initial decline in investment demand is sharper. This puts downward pressure on the real interest rate, resulting in intertemporal substitution effects for consumption and the labor/leisure choice that reinforce the wealth effects. As the capital stock adjusts lower throughout the shock-realization period, consumption and output growth also slow sharply. An investment boom ensues as the growth rate of the capital stock accelerates in the post-shock transition period, while consumption and output growth recover and gradually adjust to their new long-run paths. The implications of these growth patterns for labor productivity are illustrated in Figure 6. In each case, measured labor productivity growth adjusts only gradually to the trend rate implied by underlying technology growth (shown by the dotted line in Figure 6).
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There is an initial surge in productivity reflecting the wealth effect on labor supply and the short-run fixity of capital. In the case of a capital-embodied growth shock, the falling capital/labor ratio during the shock-realization period depresses output growth, resulting in a decline in productivity growth, followed by very slow adjustment to the new long-run trend. In fact, measured productivity growth reaches only half of its eventual increase a full seven years after the underlying trend rate has been fully realized.
Implications for Growth Accounting The model simulations presented above suggest that transition dynamics between steady-state growth paths can have important implications for both trends and fluctuations in aggregate economic variables. Most relevant for the issue of assessing claims about the emergence of a “new economy” is the observation that an increase in the trend rate of technological progress, particularly one of the capital-embodied type, gives rise to a very gradual acceleration in measured labor productivity as capital accumulation slowly adjusts to its higher rate. Figure 7 illustrates the patterns of productivity growth and their decomposition into capital-deepening and multifactor productivity components for the model simulations. Just as for the data presented in Figure 1, these decompositions reveal an important role for changes in the rate of capital-deepening at frequencies captured in 5-year averages. For the case of a neutral-technological growth shift, the gradual adjustment of productivity growth to its new long-run value is accompanied by a rise in the contribution of capital deepening. For the capital-embodied growth shock, both the slowdown and subsequent acceleration of
- 11 -
measured productivity growth are associated with similar movements in the capitaldeepening component. The 5-year averages are also slow to reveal the true magnitude of the underlying growth shift until long after the change itself, particularly in the case of an embodiedgrowth shock. In that case, measured productivity growth falls to its lowest point in the 5 years after the underlying technological growth shift, and has risen less than half-way to its new long-run value in the subsequent 5-year average.
Discussion and Conclusions The analysis of this paper suggests that changes in the technology growth trend give rise to capital stock transition dynamics, complicating the measurement of changes in technological growth trends. When evidence suggests an increase in productivityenhancing technology growth, there can be significant lags delaying the full effects of the change on labor productivity. Moreover, the analysis suggests that an increase in the growth rate of underlying technical progress can initially result in a slowdown of economic activity, particularly when the growth shift applies to investment-specific technology. The emergence of these effects is not unique to this particular model. Similar adjustment effects are present in dynamic models of endogenous growth. For example, Collard (1999), Perli and Sakellaris (1998), and Ozlu (1996) show that a role for human capital accumulation creates lags in the adjustment of the economy to technological breakthroughs. Models incorporating a role for endogenous R&D spending, [e.g. Freeman, Hong and Peled (1999), Phillips and Wrase (1999), Butler and Pakko (2000)], display
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similar lagged adjustment to technological advances, and are also capable of generating cyclical fluctuations in which innovation initially causes a slowdown in the goodsproducing sector (as resources are moved to R&D activities). Other papers are more explicit about modeling the process of technological adoption and diffusion [see, for example, Hornstein and Krusell (1996), Jovanovic and MacDonald (1994), Greenwood and Yorukoglu (1997), Andolfatto and MacDonald (1998), Hornstein (1999) and models of "general purpose technologies" such as those in Helpman (1998)]. These papers postulate that learning about the full potential of new technologies can generate long implementation lags, along with short-run growth slowdowns as resources are channeled into the adaptation process.10 Recent empirical work also lends support to the notion that technological advances can be associated with growth slowdowns. Gali (1999) identifies technology shocks using long-run restrictions in a structural VAR, specifically by assuming that technology shocks are the sole source of permanent changes in labor productivity. He finds that positive technology shocks are associated with short-run contractions in the utilization of productive inputs. Basu, Fernald and Kimball (1999) find the same pattern by examining the comovement of inputs with a measure of the Solow residual that is adjusted for nontechnological factors. In each of these papers, the authors suggest that such complex dynamics of growth and technological change cannot be reconciled with the implications of frictionless general equilibrium models.
10
Explicit models of technological diffusion draw their inspiration from case-study analyses of technological breakthroughs, like those described by David (1990).
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The novel feature of the analysis in this paper is that complex adjustment dynamics to technology shocks are generated in the context of a very basic neoclassical growth model, in which the trend rate of technology growth is subject to shocks. Analysis of optimal responses to these growth-shocks can be described in terms of wealth effects, intertemporal substitution, and optimal capital accumulation. Both the short-run fluctuations and the longer-run transition dynamics generated by the model are reflected in the contribution of capital deepening to productivity growth. An increase in the underlying growth rate of technological progress gives rise to gradual adjustment of labor productivity that is reflected in the rate of capital deepening. Particularly in the case where technology is embodied in the quality of productive capital, this channel can also generate short-run contractionary responses to a positive technological innovations, again manifested through adjustment of the capital/labor ratio. The analysis suggests that careful accounting for the growth and productive quality of the capital stock can be helpful in understanding and interpreting the underlying sources of labor productivity growth.
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References Andolfatto, David and Glenn M. MacDonald, "Technology Diffusion and Aggregate Dynamics," Review of Economic Dynamics 1 (1998), 338-370. Basu, Susanto, John Fernald, and Miles Kimble, "Are Technology Improvements Contractionary?" Manuscript, December 30, 1999. Butler, Alison, and Michael R. Pakko, "R&D Spending and Cyclical Fluctuations: Putting the 'Technology' in Technology Shocks," Federal Reserve Bank of St. Louis, Working Paper 98-011B, (February 2000). Collard, Fabrice "Spectral and Persistence Properties of Cyclical Growth," Journal of Economic Dynamics and Control 23 (1999) 463-488. David, Paul A., The Dynamo and the Computer: An Historical Perspective on the Modern Productivity Paradox, American Economic Review Papers and Proceedings (May 1990), 355-81. Freeman, Scott, Dong-Pyo Hong, and Dan Peled, "Endogenous Cycles and Growth with Indivisible Technological Developments," Review of Economic Dynamics 2 (1999), 403-432. Gali, Jordi, "Technology, Employment, and The Business Cycle: Do Technology Shocks Explain Aggregate Fluctuations?," The American Economic Review 89:1 (March 1999), 249-71. Gordon, Robert J., "Has the 'New Economy' Rendered the Productivity Slowdown Obsolete?, Manuscript," Northwestern University (June 14, 1999). Greenwood, Jeremy, Zvi Hercowitz, and Gregory W. Huffman, "Investment, Capacity Utilization and the Real Business Cycle," The American Economic Review 78:3 (June 1988), 402-17. Greenwood, Jeremy, Zvi Hercowitz, and Per Krusell, "Long-Run Implications of Investment-Specific Technological Change," The American Economic Review 87:3 (June 1997), 342-62. ____________, "The Role of Investment-Specific Technological Change in the Business Cycle," European Economic Review 44 (January 2000), 91-115. Greenwood, Jeremy and Mehmet Yorukoglu, "1974," Carnegie-Rochester Conference Series on Public Policy 46 (June 1997), 49-95.
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Helpman, Elhanan, ed. General Purpose Technologies and Economic Growth, MIT Press, 1998. Hercowitz, Zvi, "The 'Embodiment' Controversy: A Review Essay," Journal of Monetary Economics 41 (1998), 217-224. Ho, Mun S, Dale W. Jorgenson, and Kevin J. Stiroh, "U.S. High-Tech Investment and the Pervasive Slowdown in the Growth of Capital Services," Manuscript, September 14, 1999. Hornstein, Andreas, "Growth Accounting with Technological Revolutions," Federal Reserve Bank of Richmond, Economic Quarterly 85 (Summer 1999), 1-22. __________, and Per Krusell, "Can Technology Improvements Cause Productivity Slowdowns?" NBER Macroeconomics Annual 1996, 209-259 Jorgenson, Dale W., "The Embodiment Hypothesis," Journal of Political Economy 74:1 (February 1966), 1-17. ________, and Kevin J. Stiroh, "Productivity Growth: Current Recovery and Longer-Term Trends," The American Economic Review, Papers and Proceedings 89:2 (May 1999). Jovanovic, Boyan and Glenn M. MacDonald, "Competative Diffusion," Journal of Political Economy 109 (February 1994), 24-52. Kiley, Michael T., "Computers and Growth with Costs of Adjustment: Will the Future Look Like the Past?" Manuscript, Federal Reserve Board, July 1999. King, Robert G., John Plosser and Sergio Rebelo, "Production, Growth and Business Cycles: I. The Basic Neoclassical Model," Journal of Monetary Economics 21:2/3 (March/May 1988a), 195-232. ____________, "Production, Growth and Business Cycles: II. New Directions," Journal of Monetary Economics 21:2/3 (March/May 1988b), 309-342. King, Robert G., and Sergio Rebelo "Transitional Dynamics and Economic Growth in the Neoclassical Model," American Economic Review 83:4 (September 1993), 908-31. Oliner, Stephen D. and Daniel E. Sichel, "Computers and Output Growth Revisited: How Big is the Puzzle?" Brookings Papers on Economic Activity (1994), 273-317. _________, "The Reseurgence of Growth in the Late 1990s: Is Information Technology the Story?" Manuscript, Board of Governors of the Federal Reserve System, February 2000. - 16 -
Ozlu, Elvan "Aggregate Economic Fluctuations in Endogenous Growth Models," Journal of Macroeconomics 18 (Winter 1996), 27-47. Perli, Roberto and Plutarchos Sakellaris, "Human Capital Formation and Business Cycle Persistence," Journal of Monetary Economics 42 (1998), 67-92. Phillips, Kerk L., and Jeff Wrase, "Schumpeterian Growth and Endogenous Business Cycles," manuscript, 1999. Solow, Robert M, "Investment and Technical Progress," in Kenneth J. Arrow, Samuel Karlin, Patrick Suppes, eds., Mathematical Methods in the Social Sciences. Stanford University Press, Stanford CA, 1960. __________, "Technical Change and the Aggregate Production Function," Review of Economics and Statistics 39 (1957), 312-30. Tevlin, Stacey, and Karl Whelan, "Explaining the Equipment Investment Boom," Manuscript, Federal Reserve Board, August 16, 1999. Whelan, Karl, "Computers, Obsolescence, and Productivity," Manuscript, Federal Reserve Board (September 1999).
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Table 1: Calibrated Parameter Values Parameter
Description
Calibrated Value
α
Capital share of output
0.30
δ
Steady-state depreciation rate
0.06
v
Utility share parameter
1.56
β
Discount rate
0.96
τ
Marginal tax rate
0.40
γq
Growth rate of embodied technology
1.0085
γy
Growth rate of output
1.0150
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Figure 1: Contributions to Labor Productivity Growth in the Nonfarm Business Sector 2.5 2.26 Capital Deepening 2.0
Multifactor Productivity
1.80
1.56
1.49
1.45
Percent
1.5
2.05
1.12
1.32
0.91
0.22
0.58
0.77 1.0
1.10
0.5 0.82
0.89
70-74
75-79
0.99
0.93
90-94
95-99
0.72
0.0 80-84
85-89 Years
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Figure 2:
Response of the Capital Stock to a Growth Shift
1.6
2.0% path
Index
1.4
1.5% path
1.2
1.0
0.8 -5
0
5
10
15
20
Years
Figure 3:
Response of Consumption to a Growth Shift
1.5 1.4
2.0% path
Index
1.3 1.2 1.5% path
1.1 1 0.9 0.8 -5
0
5
10 Years
- 20 -
15
20
Figure 4:
Responses to An Increase in Neutral Technology Growth Consumption
Output 2.2
2.2
2.0
2.0
1.8
1.8
1.6
1.6
1.4
1.4
1.2
1.2 -5
0
5
10
15
20
25
-5
0
5
10
15
20
25
15
20
25
Real Interest Rate
Investment 6.6
3.5
6.5 3.0 6.4 2.5
6.3
2.0
6.2
1.5
6.1
1.0
6.0
0.5
5.9
0.0
5.8
-0.5
5.7 -5
0
5
10
15
20
25
-5
Capital 0.2
0.1 2.5
0.0
-0.1 2.0 -0.2
1.5
-0.3 0
5
5
10
Employment
3.0
5
0
10
15
20
25
- 21 -
Figure 5:
Responses to An Increase in Investment-Specific Technology Growth Consumption
Output 2.2
2.2
2.0
2.0
1.8
1.8
1.6
1.6
1.4
1.4
1.2
1.2
1.0
1.0
0.8
0.8 -5
0
5
10
15
20
25
-5
0
5
10
15
20
25
15
20
25
Real Interest Rate
Investment 6.6
6.0 5.0
6.4
4.0 6.2
3.0 2.0
6.0
1.0 0.0
5.8
-1.0 5.6
-2.0 -3.0
5.4
-4.0 5.2
-5.0 -5
0
5
10
15
20
-5
25
0
5
10
Employment
Capital 4.5
0.6
4.0
0.4
3.5
0.2
3.0
0.0
2.5
-0.2
2.0
-0.4
1.5
-0.6
1.0
-0.8
- 22 -
Figure 6:
Labor Productivity Growth
Growth Rate (Percent)
2.2 2.0 1.8 1.6 1.4 1.2 1.0 -5
0
5 Neutral
10 Embodied
- 23 -
15
20
Technology Trend
25
Figure7:
Contributions To Labor Productivity Growth in Model Simulations Response to a Shift in Neutral Technology Growth 2.5 Capital Deepening
2.0 1.5
Multifactor productivity
1.90
1.96
1.98
0.76
0.82
0.84
1.13
1.15
1.15
1.15
5 to 9
10 to14
15 to 19
20 to 24
1.76 1.50
0.71
1.58
0.63 0.70
1.0 0.5
0.80
0.88
-5 to -1
0 to 4
0.0
Response to a Shift in Embodied Technology Growth 2.5 Capital Deepening 2.0
Multifactor productivity
1.87
1.95
1.67 1.5
1.50
1.48 1.24
1.07
1.15
0.71
0.69
0.80
0.80
0.80
0.80
0.80
0.80
-5 to -1
0 to 4
5 to 9
10 to14
15 to 19
20 to 24
1.0 0.5
0.87
0.45
0.0
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