Economic Growth From a Classical Perspective

8/14/2019 Economic Growth From a Classical Perspective

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Economic Growth from a ClassicalPerspective

by Duncan K. Foley and Adalmir Marquetti

Department of Economics, Barnard College, Columbia University, New York, NY 10027 USA ([email protected])and Department of Economics, Graduate Faculty, New School for Social Research, 65 Fifth Avenue, New York, NY

10003 USA

The efficiency schedule for an economy, a line having for its vertical intercept output per worker, orlabor productivity, and for its horizontal intercept output per unit of capital, or capital productivity,is a method of visualizing patterns of economic growth and technical change over time. Efficiency

schedules constructed from the long data series of Dumnil and Lvy for the U.S. economy reveal apattern of labor-saving, capital-using (Marx-biased) technical change, corresponding to the patternunderlying Marx's explanation of the falling rate of profit, punctuated by a period of pure factor-augmenting (Hicks-neutral) technical change. Data from the Penn World Tables supplemented byour capital stock estimates reveal a similar pattern of Marx-biased technical change over manyeconomies in many time periods. The Marx-biased pattern of technical change appears in over halfof the sample observations. There appears, however, to be no strong quantitative correlation in thedata between the magnitudes of labor-saving and capital-using technical progress.Keywords: economic growth, technical change, Marx-bias.


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Introduction

The purpose of this paper is to explore the existence of patterns of biased technical change in economic growth.

The basic tool of analysis we use is the efficiency schedule, a version of Piero Sraffa's (1961) wage-profit raterelation.The efficiency schedule for an economy in a given time period, developed in detail in the next section, is

determined by real labor productivity and the output-capital ratio, which we will, abusing language slightly, often

refer to as capital productivity. The comparisons of efficiency schedules for a given economy over time reveals

the pattern of technical change the economy has experienced. Using extensive data from the Penn World Tables

(Summers and Heston, 1991) and long-run data for the U.S. economy (Dumnil and Lvy, 1993), we look for

systematic tendencies toward bias in the pattern of technical change.

The data reveal a striking pervasive tendency for rises in labor productivity over time to be accompanied by

declines in capital productivity. There are, however, significant and interesting exceptions to this pattern, in

particular, periods in which both labor and capital productivity either rise or decline together. These periods of

uniform technical progress and regress appear to be associated with historical watersheds in economic

development which separate epochs of technical change biased toward labor productivity and against capital

productivity.Economists have recognized this basic tendency for labor productivity to rise and capital productivity to fall

for a long time, and have explained it from a variety of perspectives. The two broad approaches are the Classical

interpretation, which sees these movements as the reflection of a bias in the adoption of technical changes induced

by systematic incentives in the capitalist economy, and the Neoclassical interpretation, which sees these

movements as occurring along the isoquant of a historically stable production function. We lean toward the

Classical interpretation, and will comment below on this issue. But our main purpose here is to document the

underlying tendency itself, rather than to offer explanations for it.

The data we use are aggregated national output measures based on the market valuation of outputs, aggregated

labor inputs, and aggregated capital measures based on the market valuation of different capital goods. The simple

analytical framework we employ assumes a single measure of output, labor and capital to parallel the structure of

the data. There are important issues of aggregation to be addressed in the use of each of these measures. They

implicitly neglect changes in labor skills and the composition of labor inputs by skill, for example. They alsocannot distinguish between changes in capital measure due to changes in price and composition of the stock of

capital goods from changes due to uniform changes in the quantity of capital goods of each type, an issue raised

sharply in the Cambridge Capital Debates. We will not address these issues explicitly in this paper, except to point

out here that the existence of a pervasive pattern in the aggregate data poses a problem of explanation for any

theoretical approach, and to note that our analytical apparatus, based as it is on Sraffa's conceptions, can in

principle be extended to accomodate disaggregated capital data.

The efficiency schedule

We begin by constructing the efficiency schedule as a framework for analyzing technical change in the course

of economic growth. In any period we can measure the gross real output per year of an economy, X, which will be

represented by the Penn World Table estimate of real GDP, its aggregate labor input, N, represented by the Penn

World Table estimate of employed labor, and the capital stock net of depreciation, K, represented by our estimate

of the real value of net capital, constructed by the methods described in the Appendix. It is convenient to work

with ratios that are independent of the absolute scale of the economy, x = X/N, the ratio of real output to labor

input, is a measure of labor productivity, and r = X/K, the ratio of real output to capital, which is a measure of

capital productivity. Labor productivity has the units of real output per worker-year, and capital productivity has

the units % per year, like an interest rate or growth rate. The ratio x/r = k is the capital-labor ratio for the economy.

2 Economic Growth Foley-Marquetti


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The efficiency schedule for an economy in (x,r) space is a straight line with vertical intercept equal to x and

horizontal intercept equal to r. The capital-labor ratio is the negative of the slope of this line.

r% per year

x

output per worker

slope = -k

Figure 1:The efficiency schedule represents labor productivity, x, capital productivity, r, and the capital labor ratio, k, as a straight

line connecting (0,x) to (r,0) with slope = -k.

The efficiency schedule is also the basis for a convenient representation of the national income accounts.

Taking the basic national product identity X = C + I, where C is consumption, I is gross investment, and

government purchases of goods and services, and net exports have been consolidated into consumption and gross

investment respectively, we can represent the product account on the efficiency schedule as a vertical line of

height x at the gross growth rate g + d = I/K, divided by the efficiency schedule into social consumption (including

the consumption of non-workers), c = C/N, and gross investment per worker, i = I/N. Here d represents

depreciation charges as a fraction of the stock of capital.

Similarly, we can represent the income side of the national accounts, X = W + Z, where W is the wage bill and

Z = X - W is aggregate non-wage income and depreciation, as a vertical line at the gross profit rate, r + d = Z/K

divided by the efficiency schedule into the wage per worker, w = W/N, and cash flow per worker, z = Z/N.

Foley-Marquetti Economic Growth 3


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% per year

output per worker

x

i

c

g+d

z

w

rr+d

Figure 2:The efficiency schedule can also represent the output and income sides of the national accounts in per-worker terms.

Technical Change and the Efficiency Schedule

The movement of the efficiency schedule over time gives a vivid representation of the pattern of technical

change in a growing economy.

Technical change that raises labor productivity while keeping capital productivity constant (purely labor-

saving, or labor-augmenting, or Harrod-neutral technical change) corresponds to a clockwise rotation of the

efficiency schedule around its horizontal axis intercept. We measure the degree of labor-saving technical change

by the percentage increase in labor productivity between two periods, which we denote by g = Hx+1/x) - 1. A

negative value for g indicates declining labor productivity.

Technical change that raises capital productivity while keeping labor productivity constant (purely capital-saving, or capital augmenting technical change) corresponds to a counter-clockwise rotation of the efficiency

schedule around its vertical axis intercept. In what turns out to be the common case of declines in capital

productivity this type of technical change is called capital-using. We measure the degree of capital-saving

technical change by the percentage increase in capital productivity between two periods, which we denote by c =

Hr+1/r) - 1. In many historical cases it turns out that c < 0, corresponding to capital-using technical change. Ifc =

0, we have the case of Harrod-neutral technical change, and if c = g the efficiency schedule shifts out parallel to

itself, which is the case of Hicks-neutral technical change.

Any arbitrary pattern of technical change can be decomposed into a combination of labor-saving and capital-

saving changes, corresponding to the pair (c,g), representing the degrees of capital-saving and labor-saving

change experienced, and the corresponding movements of the horizontal and vertical intercepts of the efficiency

schedule. The pattern of technical change can also be observed by looking directly at the pair ( c,g).



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% per year

output per worker

x

w

r

x+1

w+1

r+1r+dr+1+d

Figure 3:A falling rate of profit with Marx-biased technical progress and a constant wage share in income.

Long-run patterns of growth in the U.S.

Grard Dumnil and Dominique Lvy (1993) have compiled aggregate statistics for the U.S. economy from

1869 to 1992, which they have kindly made available to us. In particular these statistics include careful estimates

of the real value of gross output, employed labor, and the real value of the capital stock which allow us to plot

efficiency schedules for the U.S. economy for these years, and to visualize the long-run tendencies of technical

change in the U.S. economy.

Figures 4 and 5 show rather typical 15-yr shifts in the U.S. efficiency schedule, estimated from the Dumnil-

Lvy data.

0.2 0.4 0.6 0.8 1% per year

5

10

15

20

25

30

output per

worker U.S. 1970-1985

1970

1985

Figure 4:U.S. efficiency schedule shift from 1970 to 1985 (Dumnil-Lvy data).



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0.2 0.4 0.6 0.8 1% per year

1

2

3

4

5

output per

worker U.S. 1870-1885

1870

1885

Figure 5:U.S. efficiency schedule shift from 1870 to 1885 (Dumnil-Lvy data).

Despite the century that separates the two periods, the qualitative pattern of change is remarkably consistent,

and reflects the labor-saving and capital-using Marx bias. A comparison of the two Figures as a whole, however,

reveals that both labor productivity and capital productivity rose substantially between the two periods. Labor

productivity increased almost 10-fold, while capital productivity rose on the order of 25%.

The rise in capital productivity over the century we have just examined is shows that the Marx-bias pattern is

not uniform in the U.S. data. Indeed, if we look at the period 1929-1949, as in Figure 6, we see a strikingly

different pattern of technical change that appears to have augmented the productivity of both factors almost

equally (that is, to be essentially Hicks-neutral.)

0.2 0.4 0.6 0.8 1% per year

2.5

5

7.5

10

12.5

15

17.520

output per

worker U.S. 1929-1949

1929

1949

Figure 6:U.S. efficiency schedule shift from 1929 to 1945 (Dumenil-Lvy data).

As Dumnil and Lvy argue, using somewhat different methods of analysis, the period around 1919-1949 in

the U.S. economy was a sharply anomalous period in terms of the patterns of technical change accompanying

capital accumulation. The Marx bias that characterizes both the previous and succeeding periods in the U.S. gives

way to a period of uniform factor-augmenting technical change that increases both labor and capital productivity.

This finding supports the view that the 1919-1949 period was a watershed in U.S. economic history, a period

during which there were deep and lasting structural changes in the organization and technique of production.



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Figure 7 shows the efficiency schedules at 5 year intervals for the period 1949-1989, and confirms the view

that the Marx-biased pattern returned.

0.2 0.4 0.6 0.8 1% per year

5

10

15

20

25

30

output per

worker

U.S. 1949-1989

5 year intervals

Figure 7:

U.S. efficiency schedules at 5 year intervals from 1949-1989 (Dumnil-Lvy data).

The efficiency schedule in Brazil, 1959-1990

We can also use the Penn World Tables data together with our own reconstruction of national capital stocks to

estimate efficiency schedules for a wide range of countries over the period 1959-1992 which the PWT covers. In

some cases we have created our own estimates of missing capital stock data for particular countries and years in

the PWT, using the method described in the Appendix.

Before we turn to an analysis of the whole of this data set, we will examine the experience of one country,

Brazil.

Figure 8 shows the evolution of the efficiency schedule for Brazil from 1959 to 1979. This period exhibits the

pattern of Marx-biased (labor-saving, capital-using) technical change we have seen arising already in the U.S. data.

0.2 0.4 0.6 0.8 1 1.2% per year

2000

4000

6000

8000

10000

12000

14000

output per

worker Brazil 1959-79

1959

1979

Figure 8:Brazilian efficiency schedules 1959-1979 at 5-yr intervals (Penn World Table data: our reconstruction of national capital

stock).



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This classic pattern was interrupted, however in the 1980s, as Figure 9 shows. In the 1980s the Marx-bias in

technical change in Brazil gives way to fluctuations of a Hicks-neutral type, in which capital and labor

productivity move together. Furthermore, as Figure 10 indicates, the strong upward movement of labor

productivity in the period 1959-1979 changes in the 1980s to a pattern of fluctuation around a constant level.

Clearly the 1980s in Brazil, like the 1929-1949 period in the U.S., represent a period of structural change in the

economy. In the U.S. the 1929-49 period marked a substantial advance in both labor and capital productivity,

setting the stage for a period of renewed Marx-biased technical change. In Brazil the 1980s marked a period of

stagnation in both capital and labor productivity.

0.2 0.4 0.6 0.8 1 1.2% per year

2000

4000

6000

8000

10000

12000

14000

output per

worker Brazil 1980,83,88,91

Figure 9:

Brazilian efficiency schedules 1980-1990 (Penn World Table data: our reconstruction of national capital stock).

1962 1967 1972 1977 1982 1987year

7000

8000

9000

10000

11000

output per

worker Brazil

Figure 10:

The evolution of labor productivity in Brazil, 1959-1990 (Penn World Table data: our reconstruction of national capital

stock).



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World patterns of economic growth

The remarkable comprehensiveness of the Penn World Table data allows us to look for world patterns of

technical change as well. If a labor-saving, capital-using Marx bias is typical of capitalist economic development,

we would expect to see a strong downward-sloping relation between x and r over the whole world economy.

Figure 11 plots (r,x) observations for all 126 countries and years for which data is available for any part of the

period 1959-1990. The data is fitted using a robust non-parametric method (Cleveland, 1993) called robust loess.

The loess technique calculates a weighted least-squares fit to the data at each point on a grid, with weights that

decline sharply with the distance of the data point from the grid point. The loess fit is made robust by calculating

robustness weights that decline sharply with the size of the residual for each data point from the loess fit, and then

iterating the loess fit with these robustness weights.

2 4 6 8 10 12r

10000

20000

30000

40000

50000

x Full Sample

Figure 11:Full sample of (r,x) points, 1959-1990 (Penn World Table data: our reconstructions of national capital stock).

The existence of powerful pattern of negative correlation between capital productivity and labor productivity

in the course of economic development is unmistakable in this data. There are some striking exceptions

(represented by the sprinkling of data points to the northeast of the main cluster). It is equally clear that there are

substantial variations in the exact paths that national economies follow in the course of economic development, as

shown by the wide scattering of the points around the sharp turning point of the fitted curve. But the dramatic

clustering of the points around the pattern of negative tradeoff and the sharp identification of the monotonic

relation between r and x by the robust loess fit, leave little doubt that there is a powerful tendency for national

economies to follow a path of declining capital productivity and rising labor productivity in the course of

economic development.

The explanation for this striking pattern lies beyond the scope of this paper, which is concerned with an

exploration of the gross features capitalist economic development. We will briefly mention two hypotheses which

have been put forward in the economics literature. The enormous literature on the neoclassical growth model(running from Solow, 1970 through Mankiw, Romer and Weil, 1992) attempts to interpret this pattern as arising at

least partially from the existence of a stable production-function relationship between capital and labor inputs.

There are serious quantitative anomalies in this line of explanation, which remains immensely influential. The

much smaller literature putting forward a Classical/Marxian alternative to the neoclassical production function

(Dumnil and Lvy, 1995 is a leading example) suggests that these patterns are the results of biases in induced

technical change, rather than movements along a stable production function isoquant.



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Patterns of technical change

The evidence we have presented up to this point supports the hypothesis that capitalist economic development

typically but not universally follows a pattern of combined labor-saving and capital-using technical change. In this

section we look at data directly on rates of change in labor productivity and capital productivity, c and g.

Figure 12 plots c and g measured over 5 year periods (that is, for each country and year we calculate the rate

of change in r and x between that year and 5 years later) for the 126 countries in our sample. There is, as we

would expect, a strong tendency for the points to cluster in the northeast quadrant, corresponding to negative c

and positive g, though there is a scattering of points in all the quadrants. The loess curve fitted to the data,

however, reveals no negative quantitative correlation between c and g. In the northeast quadrant the curve is

basically flat, indicating no systematic correlation between the magnitude of changes in c and the corresponding

period's changes in g. This seems inconsistent with the hypothesis of a stable production function isoquant along

which national economies are moving, since such an isoquant would introduce some negative correlation between

c and g.

-30 -20 -10 10c5

-15

-10

-5

5

10

15

g5Full Sample

Figure 12:Full sample (c,g) points, measured over 5 year intervals, 1959-1990 (Penn World Table data: our estimates of national

capital stock).

The mean and standard deviation of the c and g data are presented in Table 1. The means confirm the general

hypothesis of Marx-biased technical change, but the wide scattering of the points makes the standard deviations

large relative to the means.

c g

mean - 1.80931 1.40838

sd 3.37411 3.02809

Table 1:Mean and standard deviation for full sample of (c,g), measured over 5 year intervals, 1959-1991 (Penn World Table data:

our estimates of national capital stock).

A chi-square test of the distribution of the sign patterns of c and g based on Table 2 rejects the hypothesis of

an equal likelihood of among the different patterns of technical change with a P (probability significance level)

indistinguishable from 0.



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c < 0 c > 0

g > 0 0.52907 0.21238

g < 0 0.192202 0.0663475

Table 2:Frequency of sign patterns for full sample (c,g), measured over 5 year intervals, 1959-1990 (Penn World Table data: our

estimates of national capital stock).

Conclusions

The Classical political economists, Smith and Ricardo, identified a tendency for the rate of profit to fall with

capital accumulation. Marx associated this tendency with a more fundamental bias in the patterns of technical

change in capitalist societies, toward labor-saving and capital-using technologies, a pattern we have dubbed

"Marx-biased" technical change.

Long data series compiled for the United States economy by Dumnil and Lvy show the Marx-bias pattern

dominating the 1869-1919 and 1949-1989 periods in the U.S. economy, but with a watershed period of Hicks-

neutral technical progress in the intervening years. The Penn World Tables supplemented by our estimates of

national capital stock also reveal a Marx-biased pattern of technical change for the Brazilian economy in the

1959-1980 period, followed by a stagnation of technical progress in Brazil in the 1980s.

An exploration of the evidence for Marx-bias in the patterns of technical change in the Penn World Table data

supplemented by our estimates of national capital stocks on national economic growth from 1959-1990 confirms

the predominance of the Marx-biased pattern, but reveals a substantial minority of cases with other patterns of

technical change. While the gross tradeoff of declines in capital productivity with increases in labor productivity is

consistent with the neoclassical production function, the details of the statistics raise substantial quantitative

problems for the production function view.

These preliminary findings suggest a number of avenues for further research. It would be useful to categorize

the "anomalous", non Marx-biased instances to understand which countries and years these represent, and to try to

identify those political, social, and economic factors that might explain their anomalous status. It would also be

useful to study the empirical dependency of the degree of labor-saving and capital-using technical change on other

factors, such as the size of national economies and their degree of absolute development as measured by their

labor productivity. Such studies could lead to a deeper understanding of the inward character of capitalist

economic growth.

Acknowledgments

This paper was prepared for the International Colloquium convened at the University of Braslia, April 2-4,

1997. We would like to thank Thomas R. Michl for extensive conversations on the efficiency schedule, and for

access to unpublished papers on this subject.



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References

Blades, Derek 1993. Comparing capital stocks. In Explaining economic growth: essays in honor of Angus

Maddison, eds. Adam Szirmai, bar Van Ark, and Dirk Pilat. Amsterdam: North-Holland.

Cleveland, William S. 1993. Visualizing Data. AT&T Bell Laboratories.

Dumnil, Grard, and Dominique Lvy. 1993. The Economics of the Profit Rate. Edward Elgar.

Dumnil, Grard, and Dominique Lvy. 1995. A Stochastic Model of Technical Change: An Application to

the U.S. Economy (1869-1989). Metroeconomica 46 (October), 213-45.

Foley, Duncan. 1986. Understanding Capital: Marx's Economic Theory. Harvard University Press.

Mankiw, N. Gregory, David Romer and David N. Weil. A Contribution to the Empirics of Economic Growth.

Quarterly Journal of Economics 152 (May), 407-37.

Okishio, Nobuo. 1961.Technical Change and the Rate of Profit. Kobe University Economic Review 7, 86-99.

Solow, Robert. 1970. Growth Theory. Oxford University Press.

Sraffa, Piero. 1961. Production of Commodities by Means of Commodities. Cambridge University Press.

Srinivasan, T. 1995. Long-run growth theories and empirics: anything new? In Growth theories in light of the

East Asian experience, ed. Takatoshi Ito and Anne Krueger. Chicago: University of Chicago Press.

Summers, Robert and Heston, Allen. 1991. The Penn World Table (Mark 5): An expanded set of international

comparisons, 1950-1988. Quarterly Journal of Economics 106:327-68.



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Appendix on Data Sources and Methodology

Appendix on Data Source and Methodology

This appendix presents the data source and a brief description of the methodology used to calculate the series

employed in the article. The data source utilized is the Penn World Table (Mark 5.6) ( PWT v. 5.6). The PWT v.

5.6 displays for 152 countries a basic set of national accounts, relative prices, and demographic data which allows

the comparisons between countries and over time. For some countries the capital stock data is also reported for the

period 1965-1992. For the list of variables and the exposition of the PWT methodology, see Summers and Heston

(1991). The PWT v. 5.6 covers the 1950-1992 period for some countries and for others it starts after 1950 and/or

finishes before 1992. In the present article all countries with the first observation after 1960 were eliminated. The

result is a sample of 126 countries with the following distribution per continent: Africa, 48; America, 27; Asia, 22;

Europe, 25; Oceania, 4.

The real Gross Domestic Product utilized is the Chain Index expressed in 1985 purchasing power parity (PPP).

It was obtained by multiplying the total population and the real GDP per capita. The labor productivity is

presented in the PWT v. 5.6 measured as the real GDP per worker. However, this variable has its last observations

in 1990. Thus, this is the last year covered in the present paper.

The productivity of capital is calculated using our estimated capital stock data for 126 countries and our

"benchmark data", the PWT v. 5.6 estimates. Our stock of capital is obtained by the Perpetual Inventory Method

(PIM) using the investment series computed from the variable real investment share of GDP presented in the PWT

v. 5.6. An asset life of ten years and, consequently, a depreciation rate of ten percent was employed. Depreciation

is assumed to follow a straight-line basis. Furthermore, all the assets were considered to have the same life span.

Initially, the investment data was properly accumulated to generate the first observation, then the capital stock was

computed. It is the cumulated, depreciated sum of the past aggregate investment, while our benchmark is the

"cumulated, depreciated sum of past gross domestic investment in producer durables, nonresidential construction,

and other constructions" (Summers and Heston, 1991, p. 347) augmented by the stock of capital of the residential

construction.

Certain problems are inherent in this attempt to extend the PWT data. First, there is the problem of data quality

on investment of the PWT table. Srinivasan (1995) calls the attention for this problem. Second, as the investment

data is not presented by categories of gross fixed capital formation and they are reported for a short time, not only

are all categories of gross capital formation assumed to have the same asset life, but also the asset life is very short.

The PIM procedure understates the size of capital stock and its relative bias may change considerably for countries

with very different composition in the gross fixed capital formation when the 'true' asset life is considered. In

terms of the growth rate of the capital stock the effect of a short service life is to reduce it in an economy with

rapid investment expansion, and vice versa. But, as Blades (1993, p. 404) remarks the "use of erroneous service

lives does not introduce any systematic bias into capital stock growth rates". The estimation of the stock reduces

the period of time coverage in the present work in relation to the PWT v. 5.6. The first observation for the

countries analyzed extend from 1959 to 1969.

Despite the limits of the information and the limits of our procedure, the output-capital ratio and its growth

rate computed from our estimates are similar to those calculated with our benchmark PWT data when the PWT

capital stock data is available. The average correlation coefficient between our estimation of capital stock and the

PWT estimation is 0.97. First, for each country that the PWT v.5.6 reports a estimation of capital stock the

correlation coefficient was computed, then their average was calculated. This indicates a very high linear

association between the estimates.



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