solow_residualbis

7/23/2019 Solow_Residualbis

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The Solow Residual

A growth accounting exercise is intended to break down the growth of output into the

growth of the factors of production--capital and labor-- and the growth of the efficiency

in the utilization of these factors. The measure of this efficiency is usually referred to as

Total Factor Productivity TFP henceforth!. For policy purposes it may matter whether

output growth stems from factor accumulation or from increases in TFP.

"obert #. $olow %&'(! set up the grounds for growth accounting. )e considered a

neoclassical production function

!*t t t t

L K F AY = %!

where t Y is aggregate output* t

K is the stock of physical capital* t L is the labor force

and t A represents TFP* which appears in a )icks neutral way. After some simple

transformations this e+uation can be written in terms of the growth rates of these

variables. For simplicity* consider a ,obb-ouglas production function

α α −

=%

!*t t t t

L K L K F with %. << α . Then* taking natural logarithms and differentiating

both sides of %! with respect to time t the growth rate of aggregate output can be

expressed as

!/!%!/// L L K K A AY Y α α −++= 0!

For a variable L K AY E ***=

the term E

stands for the derivative of E with respect

to time t * and so E E / stands for the growth rate.! 1ote that the growth rates of

physical capital and labor are weighted by α and !% α − . As is well known* these

weights correspond to the respective shares of rental payments for capital and labor in

total income. 2ith available data on α and the growth rates for output* physical capital

and labor* TFP growth can be computed from 0! as the residual. Accordingly* TFP

growth is the so called Solow residual.



$olow carried out this exercise for the 3$ economy for the period %&&-4& where

output per man hour approximately doubled. According to his estimates about one-

eighth of the increment in labor productivity could be attributed to increased capital per

man hour* and the remaining seven-eighths to the residual. The residual seemed too big5

To be sure* TFP is conformed by a broad range of influences6a variety of

technological* economic and cultural factors. Think of technological innovations*

underemployed labor shifting from agriculture to more productive sectors* economic

policies aimed at liberalization and competition* and changes in shopping habits --from

tiny shops to department stores. 3sually* these changes will increase TFP.

1otwithstanding* TFP may go down for some other reasons such as trade unions

restrictions* environmental regulations and safety measures that limit the use of

production factors. 7y way of example* suppose that for some weight-lifting exercises

your gym re+uires a spotter8 then* two people are needed for a single task and so this

rule would decrease TFP.! 9ther factors that may influence TFP are frictions in financial

markets* physical and human capital externalities* public expenditures or any other

element that affect the aggregate productivity of the economy.

#easurement is also crucial for comprehending the $olow residual. First* observe that

aggregate output is roughly the value of market goods and services produced in a

society* but for most purposes this measure is too narrow as it leaves out many basic

activities that enhance welfare. For instance* from the preceding example we can see

that a safety measure will usually decrease output in the benefit of protecting human



lives* and it should be clear that the beneficial effects of this rule will not affect output

directly. Also* output and other aggregate variables may be measured with error8 indeed*

many internet activities are not satisfactorily treated in the 1ational Accounts. $econd*

there is the problem of +uality ad:ustment. ;arious goods and services e.g.* cars*

cellular phones! did not exist in the past or are now of much better +uality* but these

+uality improvements are not well recorded in the statistics. Third* there are lags in the

processes of innovation* learning and implementation of technologies. $ome current

investments will have most of their payoffs in a far future* and cannot be evaluated

according to today<s productivity. For a period ranging from %&(= to %&>& the 3$ and

some other 2estern economies experienced a slowdown in TFP growth. Presumably*

this productivity slowdown happened because these advanced economies were getting

transformed to the era of information and communication technologies* and in the

meantime productivity --as shown in the statistics -- was +uite low.

?n spite of these measurement problems* various works have analyzed the determinants

of the $olow residual @e.g.* dward F. enison %&B0! and ale 2. Corgenson and Dvi

Eriliches %&B(! with emphasis on embodied and disembodied technological progress.

Advances in technology may be embodied in the latest vintages of capital. Thus* new

capital is better than old capital* not :ust because old capital has suffered wear and tear*

but also because of the +uality improvement that comes with new capital. Therefore* a

part of technological progress is embodied in t K and failure to allow for this rise in

+uality may overstate the growth assigned to TFP. $imilar considerations apply to

laborG 1ew generations entering the labor force are better educated and by all counts are

more productive. $izeable estimates have been reported for the contribution of

embodied technological progress in physical capital to growth* but it seems puzzling



that many cross-country studies @e.g.* Hant Pritchett 0%! have found that the

estimates for human capital to growth are insignificant or do not have the desired sign.

?n contrast* disembodied technological progress* included in TFP* will be associated

with new modes of organization and operation of inputs as well as other improvements

not incorporated into the +uality of factors of production. ?n practice* it has proved +uite

difficult to offer reliable estimates for the importance of embodied and disembodied

technological progress.

2ith the availability of broad sets of data in recent years* it has been possible to make

cross-country comparisons of $olow residuals. These exercises offer new possibilities to

test theories of economic growth. For a broad collection of countries that includes the

fast growing countries of ast Asia* some studies contend that the growth process can

be explained by factor accumulation. This suggests that the observed high growth rates

for output may not be long lasting* since there may be decreasing returns in the

accumulation of these factors and further investments may become less productive.

These works have been criticized on the grounds of poor measurement of human

capital* high physical capital shares and biased estimates from endogeneity in the

variables @see Peter C. Ilenow and AndrJs "odrKguez-,lare %&&(! and 2illiam asterly

and "oss Hevine 0%!. Therefore* the prevailing view is that to a great extent cross-

country differences in output should be attributed to the $olow residual.

?n summary* the $olow residual is that part of output growth that cannot be attributed to

the accumulation of capital and labor. There is a variety of factors that may contribute to

output growth and hence the residual may be +uite sizable. Luantifying the main

determinants of the $olow residual may be instrumental in comparisons of growth

experiences across countries and to test theories of economic growth.

References



enison* dward. F. %&B0. MThe $ources of conomic Erowth in the 3nited $tates and

the Alternatives 7efore 3s.N $upplementary Paper 1o. %=* 1ew Oork* ,ommittee for

conomic evelopment.

asterly* 2illiam and "oss Hevine 0%. ?tQs 1ot Factor Accumulation The World

Bank Economic Review %'0!G %((-0%&.

Ilenow Peter C. and AndrJs "odrKguez-,lare %&&(. MThe 1eoclassical "evival in

Erowth conomicsG )as ?t Eone Too FarRN NBER Macroeconomics Annual 1! * %0G

%=-%=.

Corgenson* ale 2. and Dvi Eriliches. %&B(. MThe xplanation of Productivity ,hange.N

The Review o" Economic #tudies =4 0!G 04&-0>.

Pritchett* Hant 0%. 2here )as All the ducation EoneR The World Bank Economic

Review %'=!G =B(-=&%.

$olow* "obert #.. %&'(. MTechnical ,hange and the Aggregate Production Function.N

"eview of Economics and #tatisticsl =&G =%0-=0.

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