Obsolescence and Productivity by Fernando del Rio* Antonio R. Sampayo** DOCUMENTO DE TRABAJO 2005-25

November 2005

* Universidade de Santiago de Compostela. aedelrio@usc.es.

** Corresponding author. Universidade de Santiago de Compostela. Departamento de Fundamentos da Análise Económica. Facultade de CC. Económicas e Empresariais. Avda. Burgo das Nacións s/n, 15782, Santiago de Compostela (Spain). aesamp@usc.es.

Los Documentos de trabajo se distribuyen gratuitamente a las Universidades e Instituciones de Investigación que lo solicitan. No obstante están disponibles en texto completo a través de Internet: http://www.fedea.es/.

Fernando del Rio†and Antonio R. Sampayo‡

November 4, 2005

Abstract

In this paper we argue that the increase in the obsolescence costs caused by the adoption of new information technologies, can play an important role in accounting for the productivity slowdown undergone by the US economy after 1974. We develop a standard growth model with physical and intangible capital in which technical progress is embodied in equipment. In this framework, we assume that the obsolescence of intangible capital increases when the embodied technical progress accelerates. The model is calibrated for the period 1957—1973 and the response of the economy to an increase in the rate of embodied technical progress –as observed after 1974– is simulated. We show that the increase in the obsolescence cost caused by the acceleration of embodied technical progress can account for a large part of the productivity slowdown post—1974.

Keywords: Embodied technical progress, obsolescence, intangible capital, productivity slowdown.

Journal of Economic Literature: O40.

^∗We would like to thank Antonia Diaz, Omar Licandro, Francisco J. Lores, Mikel Pérez-Nievas, Luis Puch and Ramón Ruiz-Tamarit for stimulating and useful comments. The authors also acknowledge the financial support from the Spanish Ministry of Education research project SEJ2004-0459/ECON.

^†Universidade de Santiago de Compostela. aedelrio@usc.es.

^‡Corresponding author. Universidade de Santiago de Compostela. Departamento de Fundamentos da Análise Económica. Facultade de CC. Económicas e Empresariais. Avda. Burgo das Nacións s/n, 15782, Santiago de Compostela (Spain). aesamp@usc.es.

1 Introduction

The US economy after 1974 has been characterized by a low growth rate of productivity when compared with the period after the World War II – the so—called productivity slowdown–, and by an acceleration of the decline of the relative price of equipment. Firstly, according to NIPA, the annual average growth rate of US GDP per worker has been 2.28% and 1.37% during the periods 1957—1973 and 1974—2003 respectively. Secondly, the same data show that the annual decline rate of the relative price of equipment has been 1.45% and 2.76% respectively during the same two periods. Figures 1 and 2 illustrate these two facts. As the decline rate of the relative price of equipment can be used as a proxy for the rate of equipment—specific technical progress –see Greenwood, Hercowitz and Krusell (1997), for instance–, it can be concluded that the latter has increased after 1974.

This paper provides an explanation of the productivity slowdown which relates these two facts. We argue that an increase in the rate of the equipment— specific technical progress can account for the productivity slowdown because a higher rate of equipment—specific technical progress increases the obsolescence costs of tangible and intangible capital. This increase lowers the accumulation of capital in the short—run giving rise to a period of low productivity growth.

We assume that the depreciation of intangible capital is completely due to economic obsolescence caused by equipment—specific technical progress, so that the introduction of better equipment makes intangible capital obsolete. In particular, we assume that the depreciation rate of intangible capital is an increasing function of the rate of equipment—specific technical progress, implying that an increase in this rate provokes an increase in obsolescence costs not only in equipment but also in intangible capital. A simple example illustrating the idea behind this assumption can be the introduction of new and better computers in the production process, that makes obsolete the qualifications acquired to operate older computer vintages. More generally, we argue that this idea can be applied to reproduce the dynamics of productivity after the Information Technology Revolution, by assuming that technical progress embodied in equipment makes obsolete the accumulated intangible capital.

Some papers link the IT revolution with the accumulation of intangible capital. Hall (2000) argues that “e—capital” which is human capital created by combining labor and computers, is an important factor behind the recent rise in equity prices. Brynjolfsson and Yang (1999) argue that the importance of computer equipment in accounting for the value of securities is due to a strong correlation between the stock of computers in a corporation and the unmeasured –and much larger– stock of intangible capital. Brynjolfsson and Hitt (2005) say:

We have studied intangibles related to information technology (IT) especially closely, and found evidence that they may exceed the value of computer hardware itself by an order of magnitude, or more. In particular, one of the biggest categories of IT investment is process enabling IT,...According to McAfee (2001), these systems account for the majority of IT spending in large corporations. These projects inevitably require extensive redesign (emphasized is ours) of business processes and employee training, in conjunction with expenditures on new hardware and software.

Implicitly Brynjolfson and Hitt (2005) recognize that the introduction of the information technology raised the obsolescence of intangible capital. We capture this fact by making the depreciation rate of intangible capital to depend on the equipment—specific technical progress.

We use a standard growth model with tangible and intangible capital, in order to simulate the efects on productivity growth of an acceleration in the equipment—specific technical progress, implied by the observed increase in the decline rate of the NIPA relative price of equipment. We show that this shock can account for a productivity slowdown of the observed length. However, the intensity of the simulated productivity slowdown is lower than the observed one. Therefore, our simulation suggests that obsolescence of capital can play an important role in the productivity slowdown, but it is not the whole story.

The importance of intangible capital into the production process is now beyond question. Parente and Prescott (2000) calculate that investment in intangible capital in the US economy is between 30 and 50 per cent of GDP.¹ Corrado, Hulten and Sichel (2005) estimate that by the end of the

¹Several types of investment unmeasured by NIPA are accounted for as intangible capital by Parente and Prescott (2000): maintenance and repair activities, R&D expenditures, development of new manufacturing processes and products, launching of new products, investment in organizational capital, software, learning—by—doing, learning—on— the—job and schooling investment.

90s, business fixed investment in intangibles was at least as large as business investment in traditional, tangible capital. However, Prescott (2005) argues that the numbers of Corrado, Hulten and Sichel (2005) are conservative. As pointed out by Hall (2001), if firms purchase capital up to the point where there is no further marginal benefit and firm’s securities equal the value of capital, then the market value of securities measures the quantity of capital. Under this hypothesis the value of the Tobin’s q can be used to asses the importance of the intangible capital. Hall (2001) reports that the Tobin’s q in the non—financial corporate sector of the US economy was as high as 1.7 in the 60s and the 90s and it felt to less than one in the period 1974— 1982. This evidence suggests that the amount of intangible capital in the US non—financial corporate sector is equal to the amount of tangible capital. Klock and Megna (2000) investigate whether measures of intangible capital contribute significantly to variations in Tobin’s q in the wireless telecommunication industry and find that licenses and advertising explain over 60% of the change in q, whose average value exceeds 10. Under the assumption that the after—tax returns on tangible and intangible capital are equal, McGrattan and Prescott (2000) find that corporate intangible capital was 65% of GNP in 1990s and 60% in 1955—1962. They also calibrate corporate investment in intangible capital to be 20% of GNP. Atkenson and Kehoe (2002), using a standard growth model, show that manufacturing output that is unaccounted for by payments to labor and physical capital in U S during the period 1969— 1999, was roughly 9% in average. If this unaccounted—for output corresponds to payments to diferent forms of intangible capital, the value of intangible capital is about 120% of the value of the physical capital stock.²

There are several works in the macroeconomic literature linking an acceleration of the technical progress embodied in capital with the productivity slowdown. Firstly, del Rio (2002) and Boucekkine, del Rio and Licandro (2003) have shown that an increase in the obsolescence costs of physical capital caused by an acceleration of the technical progress embodied in capital, can generate a productivity slowdown. However, in del Rio (2002) the length of the slowdown is very small compared to data, and in Boucekkine, del Rio and Licandro (2003) a shift in the relative eficiency of learning—by—doing from the consumption to investment sector is required to generate the productivity slowdown.³ Secondly, Hornstein and Krusell (1996) and Greenwood and Yorukoglu (1997) have developed a theory of the productivity slowdown post—1974 based in the existence of learning costs of adopting new technologies embodied in equipment, although they do not calibrate their model as we do here.⁴ Atkenson and Kehoe (2003) present a model that accounts for the productivity slowdown after the Second Industrial Revolution where agents are reluctant to abandon the built up knowledge in plants embodying older technologies, delaying the adoption of new technologies also embodied in plants. However, as they point out, their theory quantitatively fails to explain the length of the productivity slowdown after 1974. They also suggest that a level of organization other than plants would be more accurate to capture the embodiment of information technology. The model we present here, with embodied technical progress in aggregate equipment causing the obsolescence of intangible capital, captures this idea by assuming an aggregate representative firm.

²They also find that the share of output unaccounted for is much higher in the manufacturing sector than in the non—financial corporate sector as a whole. They estimate that only 2.7% of output is not accounted for in the non—financial corporate sector, and the value of intangible capital implied is only 28% of the value of the physical capital stock.

The rest of the paper is organized as follows. Section 2 describes the economy. In Section 3 the model is calibrated. Section 4 simulates the dynamics of productivity after an acceleration in the equipment—specific technical progress. Finally, Section 5 concludes.

2 The Economy

2.1 The Household

The economy is inhabited by a infinitely lived household who maximizes the value of his lifetime utility as given by

\[\sum_ {t = 0} ^ {\infty} L _ {0} \left(1 + \eta\right) ^ {t} \beta^ {t} \left[ \ln c _ {t} + \phi \ln d _ {t} \right], 0 < \beta < 1, \phi > 0,\tag{1}\]

where indexes time, is per capita consumption, is the per capita stock of durable consumption goods, and is the number of household’s members at time t, and is the population growth rate. The parameter is the subjective time discount factor and is the durable goods expenditure share parameter.

³Boucekkine, del Rio and Licandro (2005) analyze the role of obsolescence costs and modernization of capital, in a framework of R&D—based endogenous growth when technica progress is embodied in capital.

⁴See also Greenwood and Jovanovic (1998).

The per capita stock of durables of the household evolves according to

\[(1 + \eta) d _ {t + 1} = (1 + \gamma_ {d}) ^ {t} x _ {d, t} + (1 - \delta_ {d}) d _ {t}\tag{2}\]

where is per capita expenditure at time t in durable consumption goods, is the physical depreciation rate of durable consumption goods, and is the rate of technological progress embodied in consumer durable goods. The stock of consumer durable goods can be also measured at market value in terms of consumption, , which evolves according to

\[(1 + \eta) k _ {d, t + 1} = x _ {d, t} + \frac {1 - \delta_ {d}}{1 + \gamma_ {d}} k _ {d, t}\tag{3}\]

where is the economic depreciation of durables owned by the household. The economic depreciation rate takes into account both physical depreciation and obsolescence.

At date 0, the representative household is endowed with an stock of durables, , and he has a claim to the dividends of the representative firm. date t each member of the representative household receives a wage and dividends from the representative firm, . Taking into account the definition of , the problem of the representative household is to maximize (1) subject to (2) and the following budget constraint

\[\sum_ {t = 1} ^ {\infty} (1 + \eta) ^ {t} p _ {t} (c _ {t} + x _ {d, t}) \leq \sum_ {t = 1} ^ {\infty} (1 + \eta) ^ {t} p _ {t} [ w _ {t} + v _ {t} ].\]

Here, is the sequence of Arrow—Debreu prices of the composite commodity. The household, like the firm, takes prices as given.

2.2 The Firm

Output per capita of the representative firm depends on the productive services per worker of equipment, structures, , and intangible capital, Output per worker is given by the following technology:

\[y _ {t} = A \left(1 + \gamma_ {y}\right) ^ {t - 1} k _ {z, t} ^ {\theta_ {z}} k _ {s, t} ^ {\theta_ {s}} e _ {t} ^ {\theta_ {e}},\tag{4}\]

where and are higher than 0, and is the rate of neutral technological progress.

The productive services per worker of equipment, structures and intangible capital evolve according to

\[(1 + \eta) e _ {t + 1} = (1 + \gamma_ {e}) ^ {t} x _ {e, t} + (1 - \delta_ {e}) e _ {t},\tag{5}\]

\[\left(1 + \eta\right) k _ {s, t + 1} = x _ {s, t} + \left(1 - \delta_ {s}\right) k _ {s, t},\tag{6}\]

\[(1 + \eta) k _ {z, t + 1} = x _ {z, t} + \frac {1}{(1 + \gamma_ {e}) ^ {\sigma}} k _ {z, t}.\tag{7}\]

where and respectively are the physical depreciation rates of equipment and structures, and are investments per worker in equipment, structures and intangible capital at time t, and is the rate of equipment— specific technological progress. We assume that the economic depreciation rate of intangible capital is completely due to obsolescence and it positively depends on the rate of equipment—specific technical progress.⁵

As pointed out by Greenwood, Hercowitz and Krusell (1997), can be interpreted in two diferent ways. Firstly, can be thought as representing the production cost of a new unit of equipment or consumer durable good in terms of consumption of non durables. This cost declines over time. Secondly, one can assume that each period a new vintage of equipment or consumer durable good is produced and the productivity of a new unit of equipment or consumer durable good is given by , which is increasing over time. The cost of producing a new unit of equipment or consumer durable good is fixed over time, however, at one unit of consumption. This is often labeled as embodied technical change. In both cases the quality—adjusted relative price of each type of durable good is

The per capita stock of equipment can be also measured at market value in terms of consumption of non durables, , which evolves according to

\[(1 + \eta) k _ {e, t + 1} = x _ {e, t} + \frac {1 - \delta_ {e}}{1 + \gamma_ {e}} k _ {e, t}\tag{8}\]

⁵As in Parente and Prescott (2000) we assume that the physical depreciation rate of intangible capital is zero.

where is the economic depreciation rate of equipment. The production function can be rewritten

\[y _ {t} = A (1 + g) ^ {(1 - \theta_ {z} - \theta_ {e} - \theta_ {s}) (t - 1)} k _ {e, t} ^ {\theta_ {e}} k _ {s, t} ^ {\theta_ {s}} k _ {z, t} ^ {\theta_ {z}},\tag{9}\]

where

\[1 + g = \left[ (1 + \gamma_ {y}) (1 + \gamma_ {e}) ^ {\theta_ {e}} \right] ^ {\frac {1}{1 - \theta_ {z} - \theta_ {s} - \theta_ {e}}}\tag{10}\]

The firm per capita dividend at date t is

\[v _ {t} = y _ {t} - w _ {t} - x _ {e, t} - x _ {s, t} - x _ {z, t},\tag{11}\]

and the problem facing the firm is the maximization of the present value of its dividends,

\[V \left(k _ {z, 0}, k _ {e, 0}, k _ {s, 0}\right) \equiv \max \sum_ {t = 0} ^ {\infty} p _ {t} \left(1 + \eta\right) ^ {t} v _ {t}\tag{12}\]

subject to technological constraints (6), (7), (8) and (9), and taking the sequence of prices, as given.

2.3 Equilibrium

Given for , the following set of equations, along with equations (6), (7), (8), (9), (11) and the transversality conditions, are necessary and suficient conditions for a competitive equilibrium:

\[i _ {t} \equiv \frac {p _ {t}}{p _ {t + 1}} - 1\tag{13}\]

\[r _ {e, t + 1} \equiv 1 + i _ {t} - \frac {1 - \delta_ {e}}{1 + \gamma_ {e}}\tag{14}\]

\[r _ {s, t + 1} \equiv i _ {t} + \delta_ {s}\tag{15}\]

\[r _ {z, t + 1} \equiv 1 + i _ {t} - \frac {1}{(1 + \gamma_ {e}) ^ {\sigma}}\tag{16}\]

⁶With these changes of variables the technological constraints can be rewritten as the standard neoclassical model with only neutral technological change. Solow (1960) in his pioneer work on embodied technical progress, developed this alternative specification of the model.

\[r _ {d, t + 1} \equiv 1 + i _ {t + 1} - \frac {1 - \delta_ {d}}{1 + \gamma_ {d}}\tag{17}\]

\[r _ {e, t + 1} k _ {e, t + 1} = \theta_ {e} y _ {t + 1}\tag{18}\]

\[r _ {s, t + 1} k _ {s, t + 1} = \theta_ {s} y _ {t + 1}\tag{19}\]

\[r _ {z, t} k _ {z, t + 1} = \theta_ {z} y _ {t + 1}\tag{20}\]

\[w _ {t} = \left(1 - \theta_ {e} - \theta_ {s} - \theta_ {z}\right) y _ {t}\tag{21}\]

\[\frac {c _ {t + 1}}{c _ {t}} = \beta (1 + i _ {t})\tag{22}\]

\[r _ {d, t + 1} k _ {d, t + 1} = \phi c _ {t + 1}\tag{23}\]

\[c _ {t} + x _ {e, t} + x _ {s, t} + x _ {d, t} = y _ {t} - x _ {z, t}\tag{24}\]

Equation (13) is the definition of the interest rate. Equations (14), (15), (16) and (17) respectively are the implicit rental prices of and The implicit rental prices depends on the interest rate and on the economic depreciation rates. Equations (18), (19) and (20) follow from the firm’s maximization of the present value of dividends, and they state that marginal productivity of each kind of capital equals its user cost. Equation (21) follows from constant returns to scale. Equations (22) and (23) follow from the household’s maximization problem. Finally, equation (24) is the goods market clearing condition.

3 Model Calibration

Along the balanced growth path, output per capita , expenditure categories per capita , stocks of durable consumption goods, equipment, structures and intangible capital measured in terms of consumption , and income categories all grow at the same rate, which is given by (10).

The following eleven necessary steady—state conditions are used in the calibration:

\[1 + i - \frac {1 - \delta_ {e}}{1 + \gamma_ {e}} = \theta_ {e} \frac {\widehat {y}}{\widehat {k} _ {e}}\tag{25}\]

\[i + \delta_ {s} = \theta_ {s} \frac {\widehat {y}}{\widehat {k} _ {s}}\tag{26}\]

\[1 + i - \frac {1}{(1 + \gamma_ {e}) ^ {\sigma}} = \theta_ {z} \frac {\widehat {y}}{\widehat {k} _ {z}}\tag{27}\]

\[1 + i - \frac {1 - \delta_ {d}}{1 + \gamma_ {d}} = \phi \frac {\widehat {c}}{\widehat {k} _ {d}}\tag{28}\]

\[1 + g = \beta (1 + i)\tag{29}\]

\[\widehat {c} + \widehat {x} _ {e} + \widehat {x} _ {s} + \widehat {x} _ {d} = \widehat {y} - \widehat {x} _ {z}\tag{30}\]

\[(1 + g) (1 + \eta) - \frac {1 - \delta_ {e}}{1 + \gamma_ {e}} = \frac {\widehat {x} _ {e}}{\widehat {k} _ {e}}\tag{31}\]

\[(1 + g) (1 + \eta) - (1 - \delta_ {s}) = \frac {\widehat {x} _ {s}}{\widehat {k} _ {s}}\tag{32}\]

\[(1 + g) (1 + \eta) - \frac {1}{(1 + \gamma_ {e}) ^ {\sigma}} = \frac {\widehat {x} _ {z}}{\widehat {k} _ {z}}\tag{33}\]

\[(1 + g) (1 + \eta) - \frac {1 - \delta_ {d}}{1 + \gamma_ {d}} = \frac {\widehat {x} _ {d}}{\widehat {k} _ {d}}\tag{34}\]

\[\widehat {y} = A \widehat {k} _ {z} ^ {\theta_ {z}} \widehat {k} _ {e} ^ {\theta_ {e}} \widehat {k} _ {s} ^ {\theta_ {s}}\tag{35}\]

where denotes the corresponding variable divided by . The first three conditions are just the profit—maximizing conditions equalizing marginal products to rental prices. The fourth and fifth equations are the first order conditions of the household’s optimization problem. The sixth equation is the economy’s resource constraint. The following four equations establish that accumulation of consumer durable goods, investment in equipment, structures and intangible capital are such that their per capita stocks grow at rate . The last equation is the production function.

We calibrate the model for the period 1957—1973. The parameters whose values can be fixed upon a priori information are:

(i) The average annual decline rates of the NIPA relative prices of equipment and durable consumption goods respectively were 1.45% and 1.78% during the period 1957—1973. As the quality—adjusted relative price of equipment and consumer durable goods are we set and

(ii) The physical depreciation rates of durable consumption goods, equipment and structures are fixed to and These physical depreciation rates have been obtained using data on capital and depreciation from the Bureau of Economic Analysis (BEA). We take the chain—type quantity index for both the net stock and the depreciation of private nonresidential structures. Both indexes are multiplied, respectively, by the historical—cost net stock and the depreciation of private nonresidential structures in year 1996. The depreciation rate is the result of dividing the chain—dollar series of depreciation by the chain—dollar series of net stock of private nonresidential structures. The value of the depreciation rate for structures used in calibration is an average over the period 1957—1973. The physical depreciation rate of equipment and the consumer durable goods’ stock are calculated in a similar way.

(iii) The economic depreciation rate of intangible capital is given by Parente and Prescott (2000) estimate that 2.5% is a lower bound for the depreciation rate of intangible capital. Taking into account the computed value for we calibrate . Parente and Prescott (2000) also find that an economic depreciation rate of intangible capital of about 3.5% is adequate to reproduce the Japanese growth experience after the World War II. Therefore, the model is also calibrated for , which yields a depreciation rate of intangible capital of 3.5% for . We also calibrate the model for , in which case the economic depreciation rate is 0, in order to check the sensibility of results with respect to this parameter.

Normalizing NIPA consumption of non durables and services to 1, 2 the observations to which the model is calibrated are the following:

(i) The nominal ratios of the several expenditures categories to consumption of non durables and services during the period 1957—1973 were 0.115,

(ii) The interest rate is set to be , just like Greenwood, Hercowitz and Krusell (1997).

(iii) The average annual growth rate of consumption of non durables and services per worker in the period 1957—1973 was 2.17% and, therefore, we take

(iv) The average annual growth rate of workers during the same period was 1.7%, implying

(v) Parente and Prescott (2000) compute the size of investment in intangible capital in the United States to be between 30 and 50 percent of NIPA GDP. We calibrate the model for these two values as well as for an intermediate one, 40% of NIPA GDP, in order to test the model’s sensibility with respect to this magnitude. These numbers, if we take into account that during the period 1957—1973 the nominal ratio of consumption of non durables and services to NIPA GDP was about 0.71, imply a nominal ratio of investment in intangible capital to non durables and services consumption of about 42%, 56% and 70% for each value of intangible investment considered in increasing order.

Table 1 summarizes the information used for calibration. Using the values from Table 1 into the equations system (10) and (25)—(35), the remaining parameters and variables of the model are calibrated. Results are shown in Tables 2 and 3.

4 Simulations and results

The decline rate of the relative price of equipment increased after 1974 from an annual average of 1.45% to 2.76%. With the economy in the calibrated balanced growth path, we perform a quantitative exercise in which increases to 0.284 to capture this fact, and show the subsequent dynamics of the growth rate of real GDP per worker.

NIPA methodology uses chain—type quantity and price indexes to calculate real magnitudes and their prices. The formula used to calculate the annual change in real GDP per worker is a Fisher index. In our model such

a Fisher index, , is⁷

\[Q _ {t} ^ {F} = \sqrt {\frac {c _ {t} + x _ {e , t} (1 + \gamma_ {e}) + x _ {s , t} + x _ {d , t} (1 + \gamma_ {d})}{c _ {t - 1} + x _ {e , t - 1} \frac {1}{1 + \gamma_ {e}} + x _ {s , t - 1} + x _ {d , t - 1} \frac {1}{1 + \gamma_ {d}}} \frac {c _ {t} + x _ {e , t} + x _ {s , t} + x _ {d , t}}{c _ {t - 1} + x _ {e , t - 1} + x _ {s , t - 1} + x _ {d , t - 1}}}\]

As investment in intangible capital is not accounted for by NIPA, we do not take it into account to compute the Fisher index. In our simulations we show the behavior of , which is the theoretical counterpart of the percent change from year to t in real NIPA GDP per worker.

Figures 3—5 show the path of the productivity growth rate after the shock implied by our model as well as the growth rate of NIPA GDP per worker. The simulations are displayed for the diferent values of and we are considering. The assumption that the economic depreciation of intangible capital depends on the rate of embodied technical progress in equipment is necessary in order to generate a period of productivity slowdown, since productivity growth does not undergoes any slowdown when , no matter how high intangible investment is. Therefore, economic obsolescence in equipment alone is not enough to generate a productivity slowdown of the observed magnitude. Simulations for and yield very similar results for each one of the values we are considering for the investment rate in intangibles: after the shock, there is a period of low productivity growth and the economy’s recovery is slow. But the fall in productivity growth is larger for higher values of σ because the increase of the obsolescence cost of intangible capital is also larger. Finally, our simulations show that the scale and the length of the productivity slowdown increase when a higher investment rate in intangible capital is considered. However, even for the highest reasonable value of intangible investment –see Figure 5–, the fall in productivity growth is small compared to data, suggesting that the mechanism

\[Q _ {t} ^ {F} = \sqrt {\frac {c _ {t} + p _ {e , t} i _ {e , t} + p _ {s , t} i _ {s , t} + p _ {d , t} i _ {d , t}}{c _ {t - 1} + p _ {e , t} i _ {e , t - 1} + p _ {s , t} i _ {s , t - 1} + p _ {d , t} i _ {d , t - 1}}} \frac {c _ {t} + p _ {e , t - 1} i _ {e , t} + p _ {s , t - 1} i _ {s , t} + p _ {d , t - 1} i _ {d , t}}{c _ {t - 1} + p _ {e , t - 1} i _ {e , t - 1} + p _ {s , t - 1} i _ {s , t - 1} + p _ {d , t - 1} i _ {d , t - 1}}\]

⁷The Fisher index is defined as

Pj

1 1 (1+γ_d)^t

where p_j is the relative price of each type of goods. The theoretical counterpart of the NIPA relative prices of structures, equipment and consumer durable goods are 1, ¹(1+γ )^t 1 and (1+γe)t and real NIPA consumption of durables are and i_e,t = (1 + γ_e)^t x_e,t, i_s,t = x_s,t i_d,t = (1 + γ_d)^t x_d,t. After some algebra, the expression for results. Q^F_t

of obsolescence developed in this paper is not enough to explain the observed slowdown in productivity.

The reason of the simulated productivity slowdown is that a higher rate of embodied technical progress in equipment, increases the economic depreciation of both equipment and intangible capital and therefore their user cost, as can easily be deduced from equations (18) and (20). This reduces the incentives to invest so that the increase in productivity is lower. The length of the productivity slowdown is similar to that observed in data. The main reason of the low speed of recovery in our model is that the introduction of intangible capital in the Cobb—Douglas production function with constant returns to scale, gives a low calibrated value for the elasticity of output with respect to labor, . It is well—known that the speed of convergence of the neoclassical growth model is an increasing function of this elasticity.

5 Conclusion

Many empirical works have shown that the adoption of new technologies, in particular the new information technologies, is costly. Some authors have pointed out that the existence of learning costs and the slow difusion of the new information technologies can help to explain the observed low productivity growth of the US economy after 1974. However, less attention have been payed to another cost of adoption of new technologies, in particular to the obsolescence of accumulated investments in previous technologies. Moreover, as is presently recognized, an important fraction of these investments are investments in intangible capital. In this paper we have explored the consequences of considering costs of obsolescence in intangible capital for the post—1974 dynamics of productivity.

We have introduced durable consumption goods in preferences and distinguished three types of productive capital –equipment, structures and intangible capital–, in an otherwise standard neoclassical growth model. We have also assumed that exogenous technical progress is embodied in equipment capital, and that the depreciation rate of intangible capital is an increasing function of embodied technical progress in equipment. This last assumption tries to capture the idea that the adoption of new technologies makes obsolete the investment in previous technologies, and that this obsolescence is higher the more diferent is the new technology with respect to the older one.

In this framework an acceleration of the technical progress embodied in equipment generates a higher obsolescence of both equipment and intangible capital. The increase in the obsolescence cost of capital reduces investment in the short—run causing a period of low productivity growth. As the rate of technical progress embodied in equipment can be identified with the decreasing rate of the relative price of equipment, we have simulated the dynamic consequences for labor productivity of an increase in the former, in order to mimic the increase in the later observed in the US economy after 1974.

From our simulations we can infer that the increase in the obsolescence costs caused by the acceleration of the embodied technical progress, can help to explain a large part of the productivity slowdown post—1974 as well as its low recovery. However, the scale of the observed productivity slowdown is larger compared to our simulations. Therefore, the increase in the obsolescence costs of capital may be only a part of the whole story.

References

References

1. [1] Atkeson, A. and P. J. Kehoe (2002), “Measuring organization capital”, NBER Working Paper 8722.
2. [2] Atkeson, A. and P. J. Kehoe (2003), “The Transition to a New Economy After the Second Industrial Revolution”, Research Department Staf Report 296, Federal Reserve Bank of Minneapolis.
3. [3] Boucekkine, R. , F. del Rio and O. Licandro (2003), “Embodied Technological Change, Learning—by—doing and the Productivity Slowdown”, Scandinavian Journal of Economics, 105(1), 87—97.
4. [4] Boucekkine, R., F. del Rio and O. Licandro (2005), “Obsolescence and modernization in the growth process”, Journal of Development Economics, 77, 153—171. Forthcoming.
5. [5] Brynjolfsson, E. and S. Yang (1999), “The intangible costs and benefits of computer investments: evidence from financial markets”, Sloan School, MIT, April.
6. [6] Brynjolfsson, E.and L. Hitt (2005), “Intangibles but not unmeasurable: some thoughts on the measurement of intangible assets”, in C. Cor-
7. rado, J. Haltiwanger and D. Sichel, (eds.) Measuring Capital in the New Economy, The University of Chicago Press.
8. [7] del Rio, F. (2002) “Neutral and Investment—Specific Technical Progress and the Productivity Slowdown”, Louvain Economic Review, 68 (1—2), 37—54.
9. [8] Corrado, C., Ch. Hulten and D. Sichel (2005), “Measuring Capital and Technology: An Expanded Framework”, in C. Corrado, J. Haltiwanger and D. Sichel, (eds.) Measuring Capital in the New Economy, The University of Chicago Press.
10. [9] Greenwood, J., Z. Hercowitz and P. Krusell (1997), “Long—Run Implications of Investment—Specific Technological Change”, American Economic Review 87, 342—362.
11. [10] Greenwood, J and B.Jovanovic (1998), “Accounting for Growth", NBER Working Paper 6647.
12. [11] Greenwood, J. and M. Yorukoglu (1997): “1974”, Carnegie—Rochester Conference Series on Public Policy, 46, 49—95.
13. [12] Hall, R. E. (2000), “E—capital: the link between the stock market and the labor market in the 1990s”, manuscript, Hoover Institution, Stanford University.
14. [13] Hall, R. E. (2001), “The stock market and capital accumulation”, American Economic Review, 83, 2, 259—264.
15. [14] Hornstein, A. and P. Krusell (1996), “Can technology Improvements Cause the Productivity Slowdown?”, NBER Macroeconomics Annual, 209—275.
16. [15] Klock, M. and P. Megna (2000), “Measuring and valuing intangible capital in the wireless communications industry”, The Quarterly Review of Economics and Finance, 40, 519—532.
17. [16] McGrattan, E. R. and E. C. Prescott (2000) “Is the Stock Marker Overvaluated?”, Federal Reserve Bank of Minneapolis Quarterly Review, 24, 4, 20—40.
18. [17] Parente, S. L., and E. C. Prescott (1994), “Barriers to Technology Adoption and Development”, Journal of Political Economy, 102, 298—321.
19. [18] Parente, S. L., and E. C. Prescott (2000), Barriers to Riches, The MIT Press, Cambridge, Mass.
20. [19] Prescott, E. C. (2005), Comment to “ Measuring Capital and Technology: An Expanded Framework”, in C. Corrado, J. Haltiwanger and D. Sichel, (eds.) Measuring Capital in the New Economy, The University of Chicago Press.
21. [20] Solow, R. (1960), “Investment and Technological Progress” in K. Arrow, S.Karlin and P. Suppes (eds.), Mathematical Methods in the Social Sciences, 89—104. Stanford University Press: Stanford, CA.
22. [21] Tevlin, S. and K. Whelan (2002), “Explaining the investment boom of the 1990s”, Whasington DC: Board of Governors of the Federal Reserve.
23. [22] Whelan, K. (2002), “Computers, Obsolescence and Productivity”, The Review of Economics and Statistics, 84(3), 445—461.
24. [23] Whelan, K. (2003), “A Two—Sector Approach to Modeling U.S. NIPA DATA”, Journal of Money, Credit and Banking, 35(4), 627—656.

Table 1: Information on parameters and variables used for calibration

Table 2: Calibrated parameters and variables which are independent of and

Table 3: Calibrated parameters and variables depending on and σ

Figure 1: Annual growth rate of GDP per worker and annual averages for 1958—1973 and 1974—2003.

Figure 2: Relative price of equipment 1957—1973.

Figure 3: Simulated versus observed annual growth rate of GDP per worker, for

Figure 4: Simulated versus observed annual growth rate of GDP per worker, for

Figure 5: Simulated versus observed annual growth rate of GDP per worker, for

DOCUMENTOS DE TRABAJO

References

1. 2005-25: “Obsolescence and Productivity”, Fernando del Rio y Antonio R. Sampayo.

References

1. 2005-24: “EU Structural Funds and Spain’s Objective 1 Regions: An Analysis Based on the Hermin Model”, Simón Sosvilla-Rivero.

References

1. 2005-23: “A sequential model for older workers’ labor transitions after a health shock”, Sergi Jiménez-Martín, José M. Labeaga y Cristina Vilaplana Prieto.

References

1. 2005-22: “Price Convergence in the European Car Market”, Salvador Gil-Pareja y Simón Sosvilla-Rivero.

References

1. 2005-21: “Implicit regimes for the Spanish Peseta/Deutschmark exchange rate”, Francisco Ledesma-Rodríguez, Manuel Navarro-Ibáñez, Jorge Pérez-Rodríguez y Simón Sosvilla-Rivero.

References

1. 2005-20: “A Projection of Spanish Pension System under Demographic Uncertainty”, Namkee Ahn, Javier Alonso-Meseguer y Juan Ramón García.

References

1. 2005-19: “The Dynamic of temporary jobs: Theory and Some Evidence for Spain (The Role of Skill)”, Elena Casquel y Antoni Cunyat.

References

1. 2005-18: “The Welfare Cost of Business Cycles in an Economy with Nonclearing Markets”, Luis A. Puch

References

1. 2005-17: “Life Satisfaction among Spanish Workers: Importance of Intangible Job Characteristics”, Namkee Ahn.

References

1. 2005-16: “Persistence and ability in the innovation decisions”, José M. Labeaga y Ester Martínez-Ros.

References

1. 2004-15: “Measuring Changes in Health Capital”, Néboa Zozaya, Juan Oliva y Rubén Osuna.

References

1. 2005-14: “Discrete choice models of labour Supply, behavioural microsimulation and the Spanish tax reforms”, José M. Labeaga, Xisco Oliver y Amedeo Spadaro.

References

1. 2005-13: “A Closer Look at the Comparative Statics in Competitive Markets”, J. R. Ruiz-Tamarit y Manuel Sánchez-Moreno.

References

1. 2005-12: “Wellbeing and dependency among European elderly: The role of social integration”, Corinne Mette.

References

1. 2005-11: “Demand for life annuities from married couples with a bequest motive”, Carlos Vidal-Meliá y Ana Lejárraga-García.

References

1. 2005-10: “Air Pollution and the Macroeconomy across European Countries”, Francisco Álvarez, Gustavo A. Marrero y Luis A. Puch.

References

1. 2005-09: “The excess burden associated to characteristics of the goods: application to housing demand”, Amelia Bilbao, Celia Bilbao y José M. Labeaga.

References

1. 2005-08: “La situación laboral de los inmigrantes en España: Un análisis descriptivo”, Ana Carolina Ortega Masagué

References

1. 2005-07: “Demographic Uncertainty and Health Care Expenditure in Spain”, Namkee Ahn, Juan Ramón García y José A. Herce.

References

1. 2005-06: “EL NO-MAGREB. Implicaciones económicas para (y más allá de) la región”, José A. Herce y Simón Sosvilla Rivero.

References

1. 2005-05: “The real picture: Industry specific exchange rates for the euro area”, Simón Sosvilla-Rivero y Sonia Pangusión.

TEXTOS EXPRESS

References

1. 2004-02: “¿Cuán diferentes son las economías europea y americana?”, José A. Herce.

References

1. 2004-01: “The Spanish economy through the recent slowdown. Current situation and issues for the immediate future”, José A. Herce y Juan F. Jimeno.