The measurement of growth under embodied technical change

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EUI WORKING PAPERS

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European University Institute 3 0001 0034 9701 5 © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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EUROPEAN UNIVERSITY INSTITUTE, FLORENCE

ECONOMICS DEPARTMENT

fP

330

EUI Working Paper ECO No. 2001/14

The Measurement of Growth under Embodied Technical Change

Om a r l i c a n d r o, Ja v i e r Ru i z-Ca s t i l l o an d

J O R G E D U R Â N

BADIA FIESOLANA, SAN DOMENICO (FI)

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No part o f this paper may be reproduced in any form without permission o f the authors.

European University Institute Badia Fiesolana I - 50016 San Domenico (FI)

Italy © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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The Measurement of Growth under

Embodied Technical Change*

O m ar Licandro Javier R uiz-C astillo Jorge Duran

E U I a n d F E D E A U. C a r lo s III d e M a d r id C E P R E M A P

A b s t r a c t

N e w U .S . e v id e n c e fr o m N I P A c o n tr a d ic ts s o m e o f t h e w e ll-k n o w n K a ld o r sty liz e d fa cts, a n d c a ll fo r a r e fo r m u la tio n o f t h e m o d e r n t h e o r y o f e c o n o m ic g r o w th . A m o n g th e s e n e w fa c t s , t w o m u st b e stressed : A p e rm a n e n t d e c lin e in th e r e la tiv e p r ic e o f d u r a b le g o o d s , a n d a p e rm a n e n t in crea se in th e rea l e q u ip m e n t t o real G D P r a tio . T o b e c o n s is te n t w it h th e se n e w fa cts , g r o w th m o d els m u st in c lu d e a t lea st t w o s e c to r s a n d a d d ress t h e p r o b le m o f d e fin in g a g g re g a te o u t p u t . In th is p a p e r , th e e c o n o m ic t h e o r y o f in d e x n u m b ers is u sed t o d e fin e t h e g r o w th ra te o f r e a l o u t p u t in a g r o w th m o d e l w ith e m b o d ie d te ch n ic a l c h a n g e. T h e m a in fin d in gs are: (i) N I P A ’s m e t h o d o lo g y m easu res g r o w th in a c c o r d a n c e w it h t h e e c o n o m ic t h e o r y o n in d e x n u m b ers, a n d (ii) w h e n t h e g r o w th r a te is m ea su red as in N I P A , t h e c o n t r ib u t io n o f e m b o d ie d t e c h n ic a l c h a n g e t o p e r c a p ita l G D P g r o w th in t h e U .S . is 6 9 % , w h ic h re in fo r c e t h e c la im t h a t e m b o d ie d te ch n ic a l c h a n g e is im p o r ta n t for g r o w th . J E L C l a s s i f i c a t i o n : 0 3 0 , 0 4 1 , 0 4 7 K e y w o r d s : E m b o d ie d te ch n ic a l ch a n g e, G r o w t h fa cts, G r o w th a c c o u n tin g , I n d e x n u m b e r t h e o r y

‘ T h e authors have benefited from com m ents o f R a ou f Boucekkine, Fernando del R io, B erthold Herrendorf, Juan Francisco Jim eno, Michael Reiter and an anonym ous referee. W e also thank R obert G ordon for his helpful advice on N IP A ’s m ethodol ogy. Finally, Licandro and R uiz-Castillo acknowledge the financial support o f the Spanish M inistry o f Sciences and Technology (SEC2000-0260 and SE2000-0173, re spectively). Correspondence author: Om ar Licandro, European University Institute, Badia Fiesolana, V ia dei R occettin i 9, 50016 S. D om enico di Fiesole (F I), IT A L Y , e-mail: om ar.licandro@ iue.es.

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1 Introduction

The well-known Kaldor stylized facts have guided from the sixties the research agenda on economic growth, giving empirical support to the neoclassical growth theory. Most o f the developments o f this theory are based on the one-sector Solow-Ramsey model, which predicts that the economy converges to a balanced growth path (B G P ) where, among other things, relative prices are constant, all components o f aggregate demand grow at the same rate, and the capital-output ratio stays unchanged.

However, new evidence from National Income Product Accounts (NIPA) for the U.S. published by the Bureau o f Economic Analysis (BEA) contradicts some o f the predictions o f the neoclassical growth model. Over the last decades, the U.S. economy shows the following pattern:

i. A permanent decline in the price of equipment investment relative to the price o f non durable consumption.

ii. A permanent increase in the ratio of real equipment investment to real GDP, and, consequently, a long-run growth rate o f equipment investment larger than the long-run growth rate o f non durable consumption.

These two facts call for a reformulation o f modern growth theory in order to generate predictions consistent with the new evidence. As stated in Whelan (2001), such a reformulation requires a multisector dy namic general equilibrium model. A first step in this direction is the two-sector version o f the optimal growth model proposed in Greenwood, Hercowitz and Krusell (1997), hereafter GHK. The first sector produces one non durable good, which is used both for consumption and as an input for the production o f durable goods. This sector benefits from dis embodied technological change. The second sector produces one durable g ood which is only used for investment, and it benefits from an additional source o f technological progress, the so-called embodied technical change. This is the simplest way o f accommodating the permanent decline in the

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relative price o f equipment, and having predictions consistent with fact

2

.

This paper raises the fundamental question o f how to aggregate consumption and investment in a common measure o f real output in the framework o f such a two-sector optimal growth model. The economic theory o f index numbers, which is at least as old as consumer theory, has addressed the problem o f aggregating different final goods in an index o f real output.1 In this literature, a quantity index for an individual agent is obtained by evaluating two bundles o f goods at different moments in time in terms o f the agent’s preferences for these goods. In order to differentiate it from other types o f quantity indexes, such an index is called a ‘ true quantity index.’ Fisher and Shell (1971) have extended this notion to the case in which preferences are time dependent. In order to apply index number theory in a two-sector optimal growth model, this paper argues that intertemporal preferences for a representative agent can be represented by an indirect utility function o f current consumption and investment. Since such preferences are time dependent, following Fisher and Shell (1971) a true index o f real output growth can be defined.

In evaluating the quantitative properties o f their model, GHK argue that for ‘growth accounting’ output can be identified with the produc tion in the non durable sector. But this measure o f real output growth differs from the one published by the BEA according to NIPA conven tions. Such a discrepancy has theoretical and quantitative implications. In particular, it affects the estimation o f the contribution o f embodied technical change to the growth rate o f per-capita output.

In this paper, a true quantity index is applied to the measurement of real output growth in a simplified version o f the two-sector growth model proposed by GHK. Parameters are calibrated to the U.S. economy as close as possible to GH K’s calibration, and the proposed true index o f real output growth is computed. The main findings are the following two. First, NIPA’s methodology leads to a very good approximation to our true index o f real output growth. Second, once real output growth is appropriately measured, it is found that embodied technical change

'D iew ert (1981, 2001) are g o o d surveys on the econom ic theory o f index numbers.

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accounts for 69% o f per capita G D P growth in the U.S., a larger con tribution than the 58% found in GHK. This result reinforces the G H K ’s claim that embodied technical change is important for growth.

The paper is organized as follows. Section 2 describes the facts. A simplified version o f the G H K ’s model is presented and solved in Section 3. In Section 4, the aggregation problem is analyzed and, based in the economic theory o f index numbers, a true index o f real output growth is proposed. The quantitative implications o f using this index are discussed in Section 5, where the contribution o f embodied technical change to U.S. per capita growth is estimated. Finally, conclusions and extensions are discussed in Section 6.

2 New Evidence

Concerning the first o f the two facts referred to in the Introduction, Figure 1 shows the evolution o f the relative price o f durable consumption and equipment investment in NIPA relative to the price o f non durable consumption. The observed decline in the relative price o f equipment is a clear evidence o f a permanent improvement in the efficiency o f the durable goods sector relative to the non durable sector. This phenomenon has been called embodied technical change, since new investments are required in order to profit from the progress in technology. From an empirical perspective, this fact is closely related to the introduction of quality adjustments in the measurement o f prices and quantities in NIPA. In particular, the introduction of hedonic prices in NIPA’s methodology for computers is at the basis o f the observed decline in the relative price o f equipment. From 1969 to 1999, the relative price o f computers has declined at the cumulative rate o f 20% per year, which explains most of the 1.8% annual decline in the relative price o f equipment.

Figure 2 shows the evolution of both the real (continuous line) and the nominal (dotted line) equipment to GD P ratios. Both lines coincide in 1959, which has been taken as the base year. The important obser vation, fact 2 in the Introduction, is that the real ratio diverges from

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I---Equipments...DmaPI»s|

F ig u r e 1: Equipm ent investment and durable consum ption prices relative to non durable consum ption prices. Source: BEA.

the nominal one. In 1999, the nominal ratio is around 10%, but the real ratio is around 22%, more than twice as large.2 Under embodied techni cal change, even if the equipment investment share on nominal GD P is stable, the ratio of real equipment to real G D P is increasing over time. When equipment investment benefits from embodied technical change, real equipment grows faster than GD P implying that the real equip ment to GD P ratio increases. According to new NIPA measurements, the output-capital ratio is non stationary but permanently decreasing, which contradicts one o f the Kaldor stylized facts.

Specifically, as Table 1 shows, equipment investment is growing faster than GDP, and GD P is growing faster than non durable

consump-2 A s W helan (2000) points ou t, this ratio must b e carefully interpreted, because chained quantity indexes actually em ployed in N IPA are n on additive. In particular, the real investment ratio is n o longer a share, and it can becom e larger than unity if the relative price o f equipm ent continues to decline.

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Nominal ratio--- Real ratio |

Figure 2 : T h e ratio o f equipm ent and software t o G D P , in nom inal and real terms. Source: B EA.

tion.

Table 1: Annual growth rates (in % ) for 1969/1999

Non durable consumption 2.55

G D P 3.08

Equipment investment 6.68

3 Growth under Embodied Technical Change

The new evidence on the U.S. growth patterns during the last decades o f the 20th century calls for a reformulation of the modern theory o f growth.

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A first and important attempt in this direction is in GHK. These authors propose a two sector version o f the optimal growth model with embodied technical change. A simplified version o f this model can be represented by the following planner’s problem:

oo 1 - a maXX ! l /?*> «=0 1 a (1) z t k f = Ct + t-t (2) i t = 9t Lt (3) k t + i = (1 ~ S ) kt~ \r i t (4) <h+1 = ( 1 + 7q ) q t zt+1 = (1 + 7*) z t ,

given ko > 0, go = 1, and z o = 1. The endogenous variables ct, t(, it and kt are in per capita terms. Equation (2) is the feasibility constraint in the

non durable sector: technology is Cobb-Douglas, and non durable pro duction is allocated to consumption, ct, and as an input in the production

o f equipment, tt. The variable zt is total factor productivity in the non

durable sector, and 72 is the rate o f disembodied technical change. From (3), technology in the investment goods sector is linear, with productiv ity qt. Technological progress also affects the investment goods sector,

with q , being the rate o f embodied technical change. Equation (4) is the law o f motion for capital. Investment it and capital kt are measured in

units o f the durable good, and consumption c( is measured in units of the non durable good. Concerning parameters, a is the capital share, 8

is the depreciation rate o f capital, /? is the time preference parameter, and o is the inverse of the intertemporal elasticity o f substitution.

In addition, GHK (i) distinguish two types o f investment goods, structures and equipment, (ii) assume that preferences are also defined on leisure, and (iii) introduce taxes. The version presented in this paper selects the minimum assumptions required to reproduce the evidence presented in Section 2. 6 © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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f t r )

+

Given the exogenous process o f technological progress, the equilibrium o f this economy is thus characterized by equations (2) to (5) and the initial condition ko > 0. This model is consistent with fact 1 in the Introduction,

since the relative price o f equipment, declines permanently at the rate

7g. It is very important to notice that, if is calibrated as the decline rate o f equipment prices in NIPA relative to non durable consumption, then it and kt should be measured in the same units as real investment

and the capital stock in NIPA.

Along the BGP, non durable consumption grows at the rate

1

+

9c

=

(1

+

(1

+

,

and the growth rate o f investment is

1 + 9k = (1 + 7z)Tr“ (1 + 7«)Tr“ > 1 + ga

in agreement with fact 2 in the Introduction, GH K’s model predicts that

the long-run growth rate o f equipment investment is larger than the long- run growth rate o f non durable consumption.

In this framework, consumption and investment are different goods. Prices can be used to aggregate them in nominal terms. In what follows, the non durable good is taken as the numeraire. Thus, the price o f the non durable good is constant over time and equal to unity, while the price o f the durable g ood is equal to W Using these prices, consumption and investment can be aggregated in a common measure o f nominal output:

1 .

Ct H---- it — Cj + i f Qt

W hen the non durable good is taken as the numeraire, ct and it measures

nominal consumption and investment, respectively, and total production in the non durable sector is equal to nominal output. However, real consumption, ct, and real investment, it, are measured in different units,

and the problem o f measuring real output remains open. The aim o f the next section is to propose a measure o f real output growth consistent with preferences in (1).

The Euler equation associated to this problem is:

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4 The Measurement of Real Output Growth

GHK claim that for ‘growth accounting’ real output should be identified with the production in the non durable sector. In order to calibrate their model, measurements o f both sources o f technological progress, embod ied and disembodied, are required. They use the series o f durable prices estimated by Gordon (1990) as an appropriate measure o f qt. In order

to measure disembodied technical change, they proceed in the following way. First, they take nominal consumption and investment from NIPA, and they deflate them using the NIPA‘ s price index o f non durable con sumption in order to obtain measurements o f ct and tt. Second, given

their measurements o f qt and /,£, they use equations (3) and (4) to com

pute series for it and kt. Finally, disembodied technical change is derived

from equation (2), using the constructed series o f ct + it and kt. In this

sense, output in the non durable goods sector, ct + tt, is a useful concept

for growth accounting because it allows for a consistent estimation o f dis embodied technical change. However, as it is shown in the next section, it does not provide an appropriate measurement o f real output.

4.1 Index Number Theory

The economic theory o f index numbers was developed to provide theo retical foundations for the construction o f price and quantity indexes. It assumes that individuals have well defined preferences on a commodity space, and that they optimally allocate a given amount o f income to the consumption o f these goods at given prices. The problem is purely static, in the sense that current income cannot be transferred to the future.3

Suppose for simplicity that an agent has access to two different goods, which he consumes in quantities x t = (x } , x f) in period t. Pref

erences are represented by the continuous utility function U ( x },x f), in

creasing in both arguments and concave. Given nominal prices pt =

3Pollak (1975) is an exception. He extends the standard theory o f the cost o f living index to a m ultiperiod setting. M ore recently, Reiter (1999) proposes true quantity indexes for real wealth and real savings in a similar framework.

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(p\,pl) and nominal income Yt, the solution of the agent’s problem in each period t is u (pt, Yt) = max U (x t) l^t} st. PtXt = Yt.

The optimal utility level u{.) depends on nominal income and prices. The

dual associated to this problem is

k {pt,w ) = min ptx t

{it}

st.

U (x t) = w,

where K,(pt,w ) is the so-called cost function, and represents the minimum

cost required to achieve a given level o f utility w at prices pt. Under the

assumptions made on consumer preferences, Yt = n {pt,u (p t,Yt)) for all t.

Suppose that prices, nominal income and consumption allocations

— Pi, Y{ and ay, respectively— are observed for two adjacent periods,

i = t — l,t . In order to compare the quantity vectors x t- i and x t in

terms o f the utility levels they provide in each situation, wt = u (p,, Yj)

for i = t — l , t , a reference price vector must be selected. For example,

take current prices as reference prices and compute the minimum cost of obtaining past utility, wt_ i, at those prices, Y^_x = K(pt,w t_ i). Thus,

the variable Y*_x measures the minimum income required at reference

prices to achieve the utility level that the agent obtained at past prices and income. The true quantity index Q (xt, x t-\]Pt) defined by

Q(xt, xt-i;pt)

= K ( P t , W t) K(pt,wt-. i) Yt \Y* Xt- 1

provides a measure o f real income change at reference prices pt.

In many economic problems, including the growth model in this paper, the relevant preference map is time dependent. Fisher and Shell (1971) have extended the definition o f price and quantity indexes to a

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situation where preferences change over time. Let the utility function be Ut {xt), which implies that the optimal utility level ut (pt, Yt) and the

cost function Kt (pt, w) are both time dependent. The problem is to com

pare the optimal output vectors x t-\ and x t, chosen at different price

vectors and money incomes, pt and Yi for i = t — 1, t, respectively. Notice

that the corresponding optimal utility levels are evaluated in terms of each situation’s preferences: wt_ i = ut- i (pt-\,Y t-\) and wt = ut (pt,Yt).

Fisher and Shell suggest to compare the two situations in terms o f cur rent preferences.4 Define wt-\ = ut (pt- i ,Y t- i ) , the utility that could

be achieved with yesterday budget constraint according to today’s pref erences. Let Y £ f = Kt (pt, wt- i ) be the minimum income necessary to

obtain the utility level wt- i at current prices. In Fisher and Shell own

words, Y *_f measures “ How much income is required ‘today’ to make me

indifferent between facing yesterday’s budget constraint and facing ... to day’s prices and the income in question.” Recall that Yt = Kt (j>t, wt) is

the minimum income necessary to attain the optimal utility level wt at

current prices. Taken current prices as reference prices, the Fisher-Shell true quantity index F S t (xt, x t-\, Ut,p t) is defined by

T S t (x t,Xt-i\Ut,pt) Kt (pt,wt)

Kt (pt,w t-1) (6) and provides a measure o f real income change. The Fisher-Shell true quantity index compares, in terms o f today preferences Ut, the minimum

cost of acquiring the consumption bundles x t and x t- i , at reference prices pt. For example, if T S t > 1, then at current prices and current prefer

ences the minimum income required to achieve today’s optimal utility level wt is larger than that required to achieve the utility level Wt-u

indicating that there has been an increase in real income.5

4Com parisons could also b e done in terms o f past preferences. However, Fisher and Shell find it ‘natural’ to use current preferences, since evaluations are m ade today, n ot yesterday.

5Naturally, such an increase in real incom e will b e different if the evaluation o f the m inimum cost t o achieve these utility levels is done at a different price vector, say

Pt-1, or if the evaluation is m ade at ‘ past’ preferences.

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4.2 Value Function and Indirect Utility

In G H K ’s growth model, a representative agent owns an initial stock o f capital and an endowment o f labor. At each time t, he produces

consumption and investment goods in order to consume today and ac cumulate capital for future production. His preferences in (1), however, are defined on the space of intertemporal consumption flows. In order to apply index number theory, intertemporal preferences can be repre sented by an indirect utility function defined on current consumption and investment. Consider the Bellman representation o f the problem:

cl~a v{qt, zt,kt) = max — — + f3 v (qt+u zt+l, kt+1) {ctM} 1 — O St.

Ztk? = ct + —

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Qt kt+i = (1 — S) kt + it, (8) where v{qt zt kt) is the value function. The right hand side of the Bellman

equation can be interpreted as the maximization o f an indirect utility function on current consumption and investment:

Ut (c£, it) = ---b/3v(qt ( 1 + 7q) , z t (1 + 72) , (1 - <5) kt + it) ■ (9) i — a

The indirect utility function is time dependent, since it depends on cur rent states qt, Zt, and kt. Along the BGP the value function takes the

following form

v(qt,zt, kt) = vs (qtizt, kt) = A (ztkt ~ (S + 9k)

1 — (T ( 10)

where

A = ( l / J ( l + P e )1_0r) 1

-Using such indirect utility function, index number theory can now be applied to compute the rate o f real output growth.

11 © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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4.3 The T S Index of Real Output Growth

Let the economy be in its B G P at least from time t — 1, and let the non

durable good be the numeraire. Prices at time t are given by the vector pt = and Yt = ztk f is nominal income in per capita terms. Denote

by xt = (ct, it) an allocation at time t. The indirect utility function Ut (x t)

in equation (9) is time dependent. In order to compute a true quantity index according to Fisher and Shell, comparisons must be done in terms o f today’s preferences. Taking prices pt as reference prices, a Fisher-Shell

true quantity index to measure real output growth in the GHK economy,

T S t (xt,x t- i , Ut,pt), can be defined as in equation (6).

To actually compute T S t, the utility function Ut (ct, it) can be eval

uated near the BGP. For that purpose, in equation (9) v (.) can be substi

tuted for its expression in (10). Given this parametric function Ut (.), the

cost function nt (.) and the utility levels wt and wt-\ can be computed.

It can be easily proved that Yf_ f < Yt- i , which implies that T S t >

1 + g c- Notice that production measured in units of the non durable good

is growing at the rate gc. However, because capital is cheaper today than

it was yesterday, if yesterday’s firms had access to today’s prices, they could have obtained the realized t — 1 level o f utility with less production than they actually undertook (because they wouldn’t have had to allocate so much resources to purchasing capital). For this reason, the Fisher- Shell index gives a larger measure o f output growth than the growth rate o f consumption. This result has important consequences for the measurement o f growth, because measuring real output in units o f the non durable g ood does not take into account the increase in efficiency due to the embodied nature o f technical progress.

5 Calibration

5.1 Measuring Real Output Growth

In order to measure real growth, the model is calibrated as close as possible to G H K ’ calibration. The following parameter values are taken

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directly from GHK: a = 0.17, /3 = 0.95, 7, = 0.0321, 7* = 0.0039,

6 = 0.124 and a = .999.6 Along the BGP, the growth rate of consumption is gc = 0.0112 and the growth rate o f investment is Qk = 0.0437. The

growth rate o f consumption is here slightly smaller than in GHK, because structures are excluded. Nominal output shares are 51 = 0.87 and ^ =

r yt vt

0.13, where yt is nominal production (i.e., production in the non durable

sector).

Using NIPA’s methodology, the chained Fisher index gives an an nual growth rate in real terms o f 1.532% along the B G P.7 The Fisher- Shell quantity index o f output growth is 1.524% per year, very close to the NIPA measurement. In addition, both the J-S and the NIPA growth

rates have been computed for different values o f a in the interval [.01,10]. The T S growth rate ranges in the [1.366,1.558] interval, in percentage

points, but it is in all cases very close to the corresponding NIPA mea surement. It must be concluded that NIPA’s methodology provides an appropriate measurement o f real output growth in this framework.

5.2 The Contribution of Embodied Technical Change

The main result in GHK is the estimation of the contribution o f embodied technical change to per capita real output growth. By assuming that real G D P must be measured in units o f the non durable good, they actually measure the contribution of embodied technical change to the growth of per capita output only in the non durable goods sector. However, as it has been argued in this paper, NIPA gives a more accurate measurement of the growth rate o f per capita real output, which calls for a new estimation o f the contribution o f embodied technical change.

First, in our simplified version o f the G H K ’s model, the contri bution o f embodied technical change to the growth rate o f per capita real output in the non durable goods sector is estimated as 58%. This

6In G H K , consum ption preferences are represented b y a logarithm ic function. 7T h e chained Laspeyres quantity index o f output growth is C = (1 + gc)(1 + ~fgs), the chained Paasche quantity index is V = (1 + gc) (1 + 7, (1 — s ) ) - 1 , while the chained Fisher quantity index is a geom etric mean o f b oth : T — (C V ) 2 .

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is a very good approximation to the contribution o f embodied techni cal change reported in GHK. Second, when NIPA’s m ethodology is used to measure real output growth, the contribution o f embodied technical change to the growth rate o f per capita output is raised to 69%. The reason is that in NIPA’s methodology the growth rate o f real output is a weighted average o f the growth rate o f consumption and the growth rate o f investment. The weights are approximately equal to the correspond ing shares on nominal output. Therefore, the growth rate o f real output is approximately equal to the growth rate o f real consumption plus s "/q. This is a pure contribution of embodied technical change, which is

not taken into account when real output is measured in units o f the non durable good.

6 Conclusions and Extensions

New U.S. evidence from NIPA contradicts some o f the well-known Kaldor stylized facts, and calls for a reformulation of the modern theory o f eco nomic growth. Am ong the new facts, two must be stressed: A permanent decline in the relative price o f durable goods, and a permanent increase in the real equipment to real G D P ratio. In order to be consistent with these new facts, growth models must contain at least two sectors. Con sequently, the problem o f defining aggregate output must be addressed. The definition of real output growth proposed in this paper is in accor dance with the economic theory o f index numbers, and it follows closely Fisher and Shell’s (1971) proposal.

A simplified version o f GHK model is calibrated on U.S. data and the Fisher and Shell index o f real output growth is computed. The first finding is that NIPA’s m ethodology measures growth consistently with a Fisher-Shell true quantity index. Secondly, when the growth rate is measured as in NIPA the contribution of embodied technical change to per capita GD P growth in the U.S. is o f around 69%, larger than the 58% found by GHK. In this sense, this paper reinforce the GH K’s claim that embodied technical change is important for growth.

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The GHK model constitutes an important step fo i3 tion of the modern growth theory with the new evidence. (El.

new facts call for a more general framework, since new NIPA’s data i n - ^ dicate that embodied technical change also affects durable consumption. Therefore, in line with Whelan (2001), the following step is to extend the growth model with embodied technical change in order to include durable consumption and services. This would allow for a permanent substitution o f durable services for non durable consumption. In the far future we will still eat potatoes, bu t robots will cook them for us.

References

[1] Diewert, W . (1981), “The Economic Theory o f Index Numbers: A Survey.” In A. Deaton, ed, The Theory and Measurement o f Con sumer Behavior: Essays in Honor of Sir Richard Stone, Cambridge University Press.

[2] Diewert, W . (2001), “The Consumption Price Index and Index Num ber Theory: A Survey” , Department o f Economics, The University o f British Columbia, DP 01-02, h ttp ://w eb.arts.u bc.ca/econ .

[3] Fisher, F. and Shell (1971), “Taste and quality change in the pure theory o f the true-cost-of-living index.” In Z. Griliches, ed, Price in dexes and quality change, Harvard University Press.

[4] Gordon, R. J. (1990), The measurement o f durable goods prices, Chicago University Press.

[5] Greenwood, J., Z. Hercowitz and P. Krusell (1998), “ Lung-run impli cations o f investment-specific technological change,” American Eco nomic Review 87, 342-362.

[6] Poliak, R (1975), “The intertemporal cost o f living index,” Annals of Economic and Social Measurement 4, 179-195.

[7] Reiter, M. (1999), “Asset prices and the Measurement o f Wealth and Saving,” Universitat Pompeu Fabra, W P 396.

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[8] Whelan, K. (2000), “A guide to the use o f chain aggregated NIPA data,” Federal Reserve Board, DP 2000-35.

[9] Whelan, K. (2001), “A two sector approach to modelling U.S. NIPA data,” Federal Reserve Board, DP 2001-4.

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Working Papers of the Department of Economics Published since 2000

ECO 2000/1

M arcelo FERNANDES

Central Limit Theorem for Asymmetric Kernel Functionals

ECO 2000/2

Ray BARRELL/Alvaro M. PINA How Important are Automatic Stabilizers in Europe? A Stochastic Simulation Assessment

ECO 2000/3

Karen D U R Y / Alvaro M. PINA Fiscal Policy in EMU: Simulating the Operation o f the Stability Pact

ECO 2000/4

M arcelo FERNANDES/Joachim G R A M M IG

Non-parametric Specification Tests for Conditional Duration M odels

ECO 2000/5

Yadira G O N ZAL E Z DE L A R A Risk-sharing, Enforceability, Information and Capital Stmcture

ECO 2000/6 Karl H. SCH LAG

The Impact o f Selling Information on Competition

ECO 2000/7

Anindya BANERJEE/Bill RUSSELL The Relationship Between the Markup and Inflation in the G7 Plus One Economies

ECO 2000/8 Steffen HOERNIG

Existence and Comparative Statics in Heterogeneous Cournot Oligopolies

ECO 2000/9 Steffen HOERNIG

Asymmetry and Leapfrogging in a Step-by-Step R&D-race

ECO 2000/10

Andreas BEYER/Jurgen A . D O ORN IK/David F. HENDRY Constructing Historical Euro-Zone Data

ECO 2000/11 Norbert W UTHE

Exchange Rate Volatility's Dependence on Different Degrees o f Competition under Different Learning Rules - A Market Microstructure Approach

ECO 2000/12 Michael EHRM ANN Firm Size and Monetary Policy Transmission - Evidence from German Business Survey Data

ECO 2000/13 Gunther REHM E

Econom ic Growth and (Re-)Distributive Policies: A Comparative Dynamic Analysis

ECO 2000/14 Jarkko TURUNEN Leaving State Jobs in Russia

ECO 2000/15 Spren JOH ANSEN

A Small Sample Correction o f the Test for Cointegrating Rank in the Vector Autoregressive M odel

ECO 2000/16 Martin ZA G L E R

Economic Growth, Structural Change, and Search Unemployment

Aggregate Demand, Economic Growth, and Unemployment

Growth Externalities, Unions, and Long term W age Accords

ECO 2000/19

Joao A M A R O DE M A T O S / M arcelo FERNANDES

Market Microstructure M odels and the Markov Property © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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ECO 2000/20

Anindya BANERJEE/Massimiliano M ARCELLINO/Chiara O SBAT Som e Cautions on the Use o f Panel Methods for Integrated Series o f M acro- econom ic Data

ECO 2000/21

Anindya BANERJEE/Bill RUSSELL The Markup and the Business Cycle Reconsidered

ECO 2000/22

Anindya BANERJEE/Bill RUSSELL Industry Structure and the Dynamics o f Price Adjustment

ECO 2000/23

Jose Ignacio C O N D E-RU IZ/ Vincenzo G A L A SSO

Positive Arithmetic o f the Welfare State

ECO 2000/24

Jose Ignacio C O N D E -R U IZ/ Vincenzo G A L A SSO Early Retirement

ECO 2000/25 Klaus A D A M

Adaptive Learning and the Cyclical Behavior o f Output and Inflation

ECO 2001/1 Spren JOHANSEN

The Asymptotic Variance o f the Estimated Roots in a Cointegrated Vector

Autoregressive M odel

ECO 2001/2

Spren JOHANSEN/Katarina JUSELIUS Controlling Inflation in a Cointegrated Vector Autoregressive M odel with an Application to US Data

ECO 2001/3 Sascha O. BECKER/ Mathias HOFFM ANN

International Risk-Sharing in the Short Run and in the Long Run

ECO 2001/4

Thomas HINTERMAIER Lower Bounds on Externalities in Sunspot M odels

ECO 2001/5 Daniela VURI Fertility and Divorce

ECO 2001/6 R oel C .A . OOM EN

Using High Frequency Stock Market Index Data to Calculate, M odel & Forecast Realized Return Variance

ECO 2001/7

D.M . N A C H A N E /R . LAK SH M I Measuring Variability o f Monetary Policy Lags: A Frequency Domain Aproach

ECO 2001/8

M arco B U TI/W em er ROEGER/Jan IN'T VELD

Monetary and Fiscal Policy Interactions under a Stability Pact

ECO 2001/9

Sascha BECKER/Frank SIEBERN- T H O M A S

Returns to Education in Germany: A Variable Treatment Intensity Approach

ECO 2001/10

David FIELDING/Paul M IZEN The Relationship between Price Dispersion and Inflation: A Reassessment

ECO 2001/11 Dilip M. NACH AN E

Financial Liberalisation and Monetary Policy: The Indian Evidence

ECO 2001/12

Fragiskos A R C H O N T A K IS

Testing the Order o f Integration in a V A R M odel for 1(2) Variables

ECO 2001/13 Florin Ovidiu BILBIIE

Delegation and Coordination in Fiscal- Monetary Policy Games: Implementation o f the Best Feasible Equilibrium

ECO 2001/14

Omar LICANDRO/Javier RU IZ-CASTILLO /Jorge DU RAN The Measurement o f Growth under Embodied Technical Change

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