LABOR PRODUCTIVITY AND CAPITAL INTENSITY: A NOTE DAVID B. HUMPHREY’

S A N FRANCISCO STATE COLLEGE

Professor Hirschman has put forth the hypothesis that capital intensive production, under certain conditions, will lead to increases in labor productivity not otherwise forthcoming [2]. As this would constitute a “benefit” that would reduce the social, if not private, costs of an investment program, this hypothesis is of obvious importance for selecting investment criteria. But how important? Using U.S. and Argentine data, Diaz Alejandro has attempted to determine the empirical validity of the Hirschman hypothesis [ 11 and hence implicitly to gauge its absolute importance as an investment criteri0n.l

The hypothesis takes as given a considerable supply shortage of managerial skills in developing nations-possibly !he binding constraint. It follows that forms of pro- duction that augment this supply-via methods that make decision.making easier or lessen the degree of management necessary per unit of output-will result in higher productivity. Examples would be: making more obvious the errors stemming from certain tasks (say, machine upkeep) that may not be performed well, or in choosing machine- paced operations (smelting, etc.-process-centered) over man-paced operations (metal- working, etc.-product-centered) which, as generally believed, would increase worker productivity. These Hirschman termed “built-in spurs” in that thc method of pro- duction itself, as opposed to competition with other firms, will tend to increase efficiency or productivity [ 2 , pp. 145-521.

According to Hirschman,

. . . labor productivity differentials between an underdeveloped and an industrial country should be much larger in certain industries le.g., product-centered1 than in certain others leg. , process-centered] even when essentially similar techniques are used in both countries [2, p. 1521.

These industries are assumed to be distinguished by their relative degree of capital intensity. Such an assumption entails equating process-centered industries with capital- intensive production methods, which may not always be true; however, Hirschmail feels this is generally the case (p. 146). Diaz Alejandro concludes that “the data presented tend to support in a general way the modified Hirschman hypothesis” (p. 212). In this sense, a low sectoral ratio of Argentine wages and salaries to total value added-implying high capital intensity-was shown to be related to a high ratio of Argentine to U.S. labor productivity. In short, the lower the labor intensity of Argentine manufacturing sectors, the lower the differential between Argentine to U.S. labor productivity. Other variables besides the labor productibity ratio were in- cluded in his regression analysis “to isolate the ‘pure’ effect of capital intensity” but they played a less significant role.* With some qualification^,^ Diaz Alejandro’s results can be taken to imply that the Hirschman hypothesis is significant enough to be considered along with other criteria for investment.

*While the errors are my own, I should like to thank Theodore Tsukahara, Jr., and referees

‘Hirschman proposed the form of the test ultimately used by Diaz Alejandro. “2. pp. 208-91. The two additional variables were: average absolute size of establishment in

Argentina (measured by average number of production workers per establishment) and average absolute size of establishment relative t3 U.S. e;tablishmmts.

’Namely: (a ) that comparative advantage in certain export goods, while labor intensive, may be grest enough to offset the consequent loss of labor productivity implied by the Hirschrnan hypothesis; and ( b ) , that Argentine protection structure and choice of techniques will bias the results. While Diaz Alejandro shows that (a ) definitely exists and is important, he leaves ( b ) to conlecture 11. pp. 211-121.

413

of this Journal for comments.

414 WESTERN ECONOMIC JOURNAL

The point of this note is to show that Diaz Alejandro's test, due to his organization of the available Argentine data, is unnecessarily biased (requiring a reassessment of the hypothesis' importance for investment criteria). Specifically, we attempt to show that :

(1) the proffered measure of relative labor productivity measures both the return to factors-productivity, if paid their marginal products-and relative labor intensity, thereby introducing an unnecessary bias that can be, in part, corrected with existing data;

(2) the actual fulfillment of an explicit assumption concerning "rough" wage rate equality between Argentine industries would \ rtiate the nature of the causative hypothesis being tested; and lastly,

(3) contrary to Diaz Alejandro's cont luhn , the modified Hirschman hypothesis has no reasonable statistical support when his independent variables are regressed against a corrected relative productivity measure and hence can be deleted as a strong considera- tion of investment criteria.

In what follows we detail the Diaz Alejandro test, correct his dependent variable, and re-test the Hirschman hypothesis.

Diaz Alejandro ran the following regression:

P k 67.77- ,935 L -+ .035 5- .018 E; R = .523 (.256) (.023) (.016) Standard error

(1)

99% <909 <80% Significance level (two-tailed t test)

where: P = average productivity of production workers in Argentina relative to U.S.

L = index of labor intensity = wages and salaries in Argentina as a percent-

S = average number of production workers per establishment in Argentina;

E = the ratio: S / (average number of production workers per U.S. establish-

production workers for each of 63 industries;

age of total value added ;

and

ment) = average relative size of establishment in Argentina.

From a verbal definition,* we write P for each industry as

(2) P = (V' /W.) / (V- k / W )

where: Y = domestic value added ;

W = number of production workers;

R = purchasing power parity exchange rate of pesos to one dollar; and ' denotes Argentine data as opposed to (no primes) U.S. figures. All U.S.

figures are in dollars while those for Argentina are in pesos.

As V in both nations is composed of wages paid to production workers, salaries paid to all other workers, and returns paid to all other factor inputs, (2) is equivalent to

(3) P i i + P2(0Wi /Wi ) + P3'(Fi/Wi) = [PI + PZ(OW/W) + P3(F/W)]/k

"2, p. 2081. W e delete t i m e y o d notation for simplicity of presentation. Argentine figures are averages of 1953 and 1957 ata while US. data refer only to 1958. U.S. data for 1954 are available but, on numerous occasions, are deemed by U.S. authorities to be inconsistent with the 1958 classification. Presumably, this is the reason why the 1954 figures are deleted. Diaz Alejandro's Appendix contains sources and data on P, t, S, and E.

HUMPHREY: CAPITAL INTENSITY

where: PI = average return to production workers ;

P2 and P.? = average return to all other workers (factor inputs) ;

OW = number of all other workers;

F = quantum measure of all other factors used; and thus

415

V = P I ( K ’ ) + P Z ( 0 W ) + P?fF)--the first two terms on the right hand side comprise total wages and salaries.

I f F is construed as a proxy for the factor “capital stock,” then. F/W represents the capitaliproduction worker ratio (for which no separate Argentine capital data exists) while O W / W is the ratio of, essentially, salaried workers to production workers (for which separate data does exist). The point here is that the relative labor productivity ratio of (3) includes not only relative returns (PI, P2, P3) but also ratios of relative labor intensity (a, OW, F) that act as weights for the factor returns. Thus, to call P a measure of relative labor productivity and. correlate it with measures of absolute (L , 3 ) and relative (F) capital-labor intensity #confuses the issue for, unless corrected, the empirical test does not fully correspond to the hypothesis to be tested. That is, lower Argentine labor intensity dictates a higher F’/W’ weight which would raise the numerator of (3) and result in the desired negative correlation with L even with unchanging Argentine factor ~ e t u r n s . ~ Further, the use of P to measure relative labor productivity implies that productivity increases are not passed on in the form of final price decreases. Domestic pricing policy is apparently such that the return of each factor reflects its productivity level.

The correction available is limited to deleting each nation’s P3(F,’W) from (3) in order to derive a more pure measure of factor return.u Dividing numerator and de- nominator by W + OW instead of W yields the weighted average of (wages and salaries)/(W + OW) to represent labor’s return. This division lies within the con- fines of the data used by Diaz Alejandro. The result is that the weighting ratios between industries with different capital intensities will not vary so much as the s u m of variation of the deleted ratios. Along this line, Diaz Alejandro himself has noted (p. 212) that if there exist larger average differences in actual capital-labor ratios between Argentina and the U.S. as the sectors covered become more labor intensive, then his regression between P and L could yield spurious results for the Hirschman hypothesis. That is, greater Argentine labor intensity (L) here automatically implies less capital per worker-a lower V’/W’‘-than would exist in the U.S. “his alone would give a greater relative roductivity differential (P). This bias, that we have

that this factor by itself may explain to a considerable degree the results obtained” and hence the validity of the Hirschman hypothesis as it applies to Argentina.

But this is not the only bias; it would be too much to expect that Argentina and the U.S. have congruent factor input structures in each sector for all classifications of

‘For example, if all Argentine factor returns were constant at 2 esos each and if OW’/W’= . I while F’/U”‘ = .4, then the numerator of ( 3 ) would be: 2 / 1 ) $ 2( .1 ) + 2 / 4 1 = 3 pesos as us”/K”, regardless of labor intensity, equals a weight of 1. Decreasing Argentine labor intensity ( i c . a lower L ) makes F‘/W’ > .4,,and (3)’s numerator > 3 pesos even with constant factor returns. The possibiIit7 that an F‘/if‘ increase is offset by a corresponding OW’/IF’’ decrease does not appear likely as ( a ) the latter is small relative to the former, and (b) with increasing capital intensity, a rise in OW‘/iV‘ is the more probable result.

‘As the factors are apparently assumed to be paid according to their productivity level (if not, the weights would necessarily have been different), labor’s return is hypothesized to rise with increased use of capital. Thus the modified Hirschman hypothcsis is consistent with our empirically measuring P as in footnote 8. As data on P j or F are not available, they c.m not be separated and w e thus must drop them both.

undertaken to correct, is signi R cant for Diaz Alejandro concludes that “one suspects

416 WESTERN ECONOMIC JOURNAL

labor.’ Thus even a corrected P 8 would reflect differences due to labor input structures as well as to individual return differentials unless the return in all classifications were equal in each nation (but not necessarily between them).

As a matter of fact, Diaz Alejandro did assume “rough” wage equality in order to use L as a measure of absolute labor intensity for Argentina.@ W e will first show that this assumption is not met (in our opinion) for Argentina and that even if met, the resulting correlation between P and L would vitiate the hypothesis being tested.

If the wage equality assumption holds, regardless of the specific Argentine industry labor input structure, total peso wages and salaries divided by total number of workers should yield the same average wage for each industry classification. Column 2 of the Appendix contains this calculation. In our opinion it reveals that average wages are not equal even in the “rough” sense stipulated by D i n Alejandro. While “rough” wage equality would resumedly have satisfied Diaz Alejandro, perfect equality (PI’ = P2’ = c, f!r each industry) would have meant that the regression P = Q + /3L could be written as

(4) p = a + Bc[I/(numerator of P) + OW’/V’],

since L is defined as

L = (peso wages and salaries)/V‘ = r(W’ + OW‘) /V.

Hence the regression results are bound to be favorable here as c is constant between industries and Owl/V’ is small relative to W‘/V‘-the inverted numerator of P [see

uation (2) . The assumption of wage equality,*O then, spoils the interesting aspects 3 the hppotb esis being tested, making it more a hypothesis that absolute Argentine labor intensity (L) explains Argentine relative to U.S. labor intensity.’I

We re-tested the modified Hirschman hypothesis using our corrected P (footnote 8 ) and derived the following results:

(6) Corrected P = 29.45 - .030 L + .009 S - .005 E ; R = .186 (.106) (dog) ( . O M ) Standard error

22% 70% 62% Significance level -.04 .15 -.13 Partial correlation

While Diaz Alejandro had 63 industries--he used only 1958 U.S. data, we could only calculate 49 as our corrected P utilized 1958 and 1954 U.S. along with 1953 and 1957 Argentine data (see footnote 4 ) . Our correlation coefficient is substantially lower than Diaz Alejandro’s (R = .523) as are the confidence levels of our regression

‘Taking the ratio W‘/(W‘ + OW’) / W / ( W + OW) for 6 3 industries: using 19S3 Argentine data (the 1957 census only covers establishments with 11 or more production workers) ; and taking 1958 U.S. data (as does Diaz Alejandro for his P denominator), the result should be very close to 1 if the two measurable labor classifications W and O W are congruent for the U.S. and Argentina. Column 1 of the Appendix shows that this does not seem to be the case.

T h e corrected P = (peso wages and saIaries)/(W” + OW’j divided by k ($ wages and salaries)/(W + OW) and is shown €or 49 industries in Column 3 of the Appendix.

‘“On the assumption that wage rates are roughly the same in all industries, the share of wages and salaries paid in cash in total value added by each industry in Argentina has been taken as the index of labor intensity [i.e., LI” [I, p. 2081.

’ m e fulfillment of the wage equality assumption implies that all labor is equally productive or that labor’s return does not reflect its productivity level. Hence, the factor return weights used by Diaz Alejandro to calculate P are not necessarily correct in either of these instances.

”Travis, in an incisive criticism of Basevi, suggests that direct labor requirements per $1,000 of US. value added be used as a measure of labor intensity. Doing the same for Argentina would make P an index of relative labor intensity in Travis’ terms [31.

HUMPHREY: CAPITAL INTENSITY 417

In our opinion, so poor are these results that, if one accepts our pro- cedures, it can reasonably be concluded that Diat Alejandro's support of the modified Hirschman hypothesis on statistical grounds is misguided.I3 These resiilts further imply that Hirschman's hypothesis can be deleted as a strong absolute consideration among investment criteria, for its effect, at least in Argentina, appears insignificant. But, obviously, more research needs to be performed-especialiy in other semi-industrialized nations.

'The negative sign before E is explainable by the fsct that multicollineari~:y exists between E and S-the simple correlation between them is R = 9 2 . When S is deleted, the a prior; reasoning of a positive relationship between the corrected P and E is borne out. The correlation coefficient becomes .10 and the significance level of L rises to 53% while that of E falls to to 2OoJo. -Of course, it is equally plausible that variables important to the hypothesis have not yet been

adequately measured.

APPENDIX

W'/(W' + OW') W / I W + O W )

Edible oils Soft drinks Rice milling Cane sugar Prepared meats

Poultry dressing plants Meat packing Breweries Chocolate and cocoa products Macaroni and spaghetti

Canned and dehydrated fruits and vegetables

Biscuits and crackers Flour and prepared flour Ice cream Cereal preparations and elaborations

Distilled liquors Dairy products, except ice cream Bread & bakery products Fish or frozen packaged fish Wine

Other foodstuffs Cigarettes Other tobacco Textiles Apparel Lumber & wood products Furniture fixtures Pa erboard containers & boxes d ' p mills Other paper & allied products

cli 1.16 1.84 1.09 1.13 1.05

.96 1.05 1.26 1.06 1.14

.95 1.05 1.04 .51 1.12

.91 1.66 1.28 .92 1.02

1.02 .90 1.04 .98 .88

1.03 1.08 1.15 1.14 1.06

Arnornt of wages

and salaries in pesos

(W' + OW') ( 2 )

20.6 16.4 14.3 19.3 15.0

19.5 19.9 21.1 15.2 14.7

14.7 12.2 19.9 9.5 20.1

21.3 15.9 13.6 14.8 18.6

16.2 20.5 12.1 18.2 19.6

10.7 13.8 13.1 21.4 19.9

Corrected P

( 3 )

32.4% 29.8 28.4 29.3 23.2

- 28.7 25.9 24.8 27.2

29.8 16.3 32.0

32.4 26.2

45.8 28.9

22.6

37.1 30.9 41.5 48.0

23.4 25.8 -

418 WESTERN ECONOMIC JOURNAL

Newspapers & magazines Other printing & publishing Paints & varnishes Cleaning & toilet goods

Explosives Printing ink Other chmical & allied products Petroleum refining Other petroleum & coal products

Rubber footwear Tires & inner tubes Dther rubber products Leather footwear Transmission belts (leather)

Leather tanning & finishing Other leather products Lime Portland cement Glass & glass products

Other stone, clay & glass products Metals, excl. machinery Elevators & moving stairways Motorcycles, bicycles & parts Other vehicles & machinery,

Drugs

exd. electrical

Radio and television Other electrical machinery Matches Toys Musical instruments

Brooms, brushes, etc. Billboards & signs Other misc. products

W’/ f W’ + 0 W’) W / f W + O W )

(1)

.98 1.10 1.24 1.15 1.16

1.22 .97 1.18 1.06 1.09

1.07 1.04 1.14 .96 1.16

1 .oo .89 1.04 1.06 1.06

1.08 1.07 1.37 .90

1.19

.92 1.14 1.11 1 .oo 1.15

1.01 .98 1.12

Sowces: Same as Diaz Alejandro’s Appendix C1, p. 2121.

REFERENCES

Amovnt of wages

and salaries in pesor

fW‘ f OW’) ( 2 )

25.3 18.6 22.0 19.5 20.6

21.3 24.7 17.5 31.4 20.4

15.8 24.6 16.3 18.1 16.0

19.8 13.6 14.0 21.7 19.3

14.9 18.7 18.6 13.4

18.6

19.7 20.6 14.8 11.2 13.4

8.3 16.5 15.4

Corrected P

( 3 )

30.6% 29.0 - - 27.7

30.2 33.2

37.1) 29.4

28.6 32.2 26.3 43.9 25.6

33.3 31.5 23.2 31.9 29.6

-

- 26.3 24.4 22.7

- - 27.3 23.3 21.6

16.5 26.1 22.3

1. C. F. Diaz Alejandro, “Industrialization and Labor Productivity Differentials,” Rev. Econ. Stat., May 196S, 47, 207-14.

2. A. 0. Hinchman, The Strategy of Economic Development. New Haven, 1958. 3. W. P. Travis, Does the American Tariff Protect Labor?. Working Paper # 244-67, A. P.

Sloan School of Management, M.I.T., March 1967.