A COMPARISON OF INDUSTRIAL EFFICIENCY FOR '
MEXICO, PUERTO RICO, AND THE UNITED’STATES I . , I 7 I ’

Thesis for the Degree of Ph. {3‘
MICHIGAN STATE UNIVERSITY
PAUL EDWARD SNOONIAN '
1921 '

 

 

2“.

{Th F 8' ~
LI B RA 1%. Y
Michigan State

Univcrfs: i7
Lemma-cum ”tr;

This is to certify that the

thesis entitled
A COMPARISON OF INDUSTRIAL EFFICIENCY FOR MEXICO,
PUERTO RICO, AND THE UNITED STATES

presented by

PAUL EDWARD SNOON IAN

has been accepted towards fulfillment
of the requirements for

Mdegree in ECQHOWIC}

 

0-169

ABSTRACT

A COMPARISON OF INDUSTRIAL EFFICIENCY FOR MEXICO,
PUERTO RICO, AND THE UNITED STATES

By

Paul Edward Snoonian

This study shows that Mexican and Puerto Rican
industries operating with capital intensity levels of
equivalent United States industries would not achieve labor
productivity levels of those United States industries. The
resulting difference in labor productivity is called a
"labor efficiency difference." A multiple regression
analysis reveals a significant relationship between high
capital intensity levels and high levels of labor produc-
tivity. A Cobb-Douglas production function is then used to
calculate labor efficiency differences between Mexican,
Puerto Rican, and United States industries. It is
generally found that labor efficiencies in Puerto Rico are
higher than those of Mexico because many Puerto Rican
industries produce for United States markets. Labor
efficiency differences between united States and Mexican
industries are attributed to worker and managerial ability
and economies of scale.

Puerto Rican-United States efficiency differences

 

are mainly

economies of
mentioned ea

produce for

 

are mainly due to worker and managerial ability with
economies of scale being a smaller influence since, as
mentioned earlier, a number of Puerto Rican industries

produce for United States markets.

A COMPARISON OF INDUSTRIAL EFFICIENCY FOR MEXICO,

PUERTO RICO, AND THE UNITED STATES

By

Paul Edward Snoonian

A THESIS
Submitted to
Michigan State University

in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Economics

1971

@Copyright by
PAUL EDWARD SNOONIAN
1971

This
adVice and 1
Strassmann .

Henderson 31-,

ACKNOWLEDGMENTS

This work was made considerably easier by the
advice and invaluable assistance of Professor W. Paul
Strassmann. Professors Carl Liedholm and John P.

Henderson are also thanked for their time and assistance.

ii

Cflflm
I ASSESS}

REFEF

 

 

 

CAPII
Hypot
Ger
Lin
Sele:
Prc
Em;

Em;

TABLE OF CONTENTS

CHAPTER
I ASSESSMENT OF LABOR PRODUCTIVITY STUDIES WITH
REFERENCE TO RELATIVE AND ABSOLUTE LEVELS OF
CAPITAL INTENSITY
Hypothesis and Introduction
General Statement Concerning Methodology
Limitations of the Present Study
Selected Survey of International Labor
Productivity Studies
Empirical Tests of the Hirschman Hypothesis
Empirical Production Functions and
International Labor Productivity
Comparisons
Summary
II ‘METHODOLOGY
The Equations
The Regression Function

Cobb-Douglas Procedure

iii

PAGE

22
48
51
51
51
54

 

CHAPTER

So
Se

Se?

 

 

 

 

 

 

CHAPTER PAGE

The Assumption of Increasing Returns to

Scale 57

The Data 61
Sources of Data 61
Selection of Years 61
Selection of Industries 62
The Data 63
Output 63
Capital 64
Labor 66
Summary 67
III INTERPRETATION OF THE CALCULATIONS 68
General Results and Conclusions 68
Labor Efficiency Summary Statistics 68
Summary Results for Mexico 71
Summary Results for Puerto Rico 74
General Conclusions 75
The Multiple Regression Analysis 77

Significance Tests and the Regression
Coefficients 77
Coefficients of Multiple Correlation and

Determination 79

iv

CHAPTER

 

 

 

Ze

Labo
Co
Met

Put

laI

Rei

CHAPTER PAGE
Zero Order and Partial Correlation
Coefficients 81

Labor Productivity and Labor Efficiency

Comparisons 83
Mexican-United States Industry Comparisons 83
Puerto Rican-United States Comparisons 92

Labor Productivity and Labor Efficiency
Compared under Increasing Returns 94
Relative Mexican and Relative Puerto Rican

Comparisons and Their Historical

Economic Developments 95

Conclusions 100

Summary 108

IV SUMMARY AND CONCLUSIONS 110
BIBLIOGRAPHY 117
APPENDIX 123

 

8a

LIST OF TABLES

TABLE

8a

EMPLOYMENT WEIGHTED AND UNWEIGHTED MEAN LABOR
EFFICIENCY RATIOS FOR MEXICO

EMPLOYMENT WEIGHTED AND UNWEIGHTED MEAN LABOR
EFFICIENCY RATIOS FOR PUERTO RICO

SELECTED INDUSTRIES FOR MEXICO AND THE
UNITED STATES

VALUE OF PRODUCT (V) FOR MEXICO AND THE
UNITED STATES, IN $1,000

VALUE OP FIXED CAPITAL ASSETS (K) FOR'MEXICO
AND THE UNITED STATES, IN $1,000

TOTAL EMPLOYMENT (L) FOR MEXICO AND THE
UNITED STATES

CAPITAL-LABOR.RATIOS (E) AND VALUE OF
PRODUCT PER UNIT OP LABOR (2) FOR MEXICO
AND THE UNITED STATES

RELATIVE VALUE OF PRODUCT PER UNIT OF LABOR
(Y1), RELATIVE CAPITAL-LABOR RATIOS (X2),
AND AVERAGE LEVELS OF CAPITAL INTENSITY
(X3) FOR MEXICO TO THE UNITED STATES

Y1, X2, AND X3 FOR MEXICAN AVERAGES (1961+63)
T0 UNITED STATES AVERAGES (1958+63)

SELECTED INDUSTRIES FOR PUERTO RICO AND THE
UNITED STATES

vi

PAGE

69

70

123

125

128

131

134

138

142

144

DOLE

m

H

U

U

14

U

H

H

N

M

VALUE

(K) .
FOR P

VALUE 0

(K) .
FOR

CAPITAL-
PER UT
THE Uh

RELATIVE‘

(Y1):
AND AV

(X3) F

RESULTS I
To THE‘

 

PARTIAL I
COEFFIC

RESULTS I
RICO T(

PARTIAL I
COEFFIc
STATES

COMPARISI
PRODUCf

MEXICO

TABLE PAGE

10 VALUE OF PRODUCT (V), FIXED CAPITAL ASSETS
(R), IN $1,000, AND TOTAL EMPLOYMENT (L)
FOR PUERTO RICO 145

11 VALUE OF PRODUCT (V), FIXED CAPITAL ASSETS

(R), IN $1,000, AND TOTAL EMPLOYMENT (L)

FOR THE UNITED STATES 147
12 CAPITAL-LABOR RATIOS 3%) AND VALUE OF PRODUCT

PER UNIT OF LABOR (I) FOR PUERTO RICO AND

THE UNITED STATES 149

13 RELATIVE VALUE OF PRODUCT PER UNIT OF LABOR
(Y1), RELATIVE CAPITAL-LABOR RATIOS (X2),
AND AVERAGE LEVELS OF CAPITAL INTENSITY
(X3) FOR PUERTO RICO TO THE UNITED STATES 151

14 RESULTS OF THE REGRESSION ANALYSIS: MEXICO
TO THE UNITED STATES 153

15 PARTIAL AND ZERO ORDER CORRELATION
COEFFICIENTS: MEXICO TO THE UNITED STATES 154

16 RESULTS OF THE REGRESSION ANALYSIS: PUERTO
RICO TO THE UNITED STATES 155

17 PARTIAL AND ZERO ORDER CORRELATION
COEFFICIENTS: PUERTO RICO TO THE UNITED
STATES 156

18 COMPARISON OF LABOR PRODUCTIVITY, CAPITAL
PRODUCTIVITY, CAPITALPLABOR RATIO, AND
LABOR EFFICIENCY IN SELECTED INDUSTRIES FOR
‘MEXICO, 1956, To THE UNITED STATES, 1954 157

19 COMPARISON OF LABOR PRODUCTIVITY, CAPITAL
PRODUCTIVITY, CAPITAL-LABOR RATIO, AND
LABOR EFFICIENCY IN SELECTED INDUSTRIES FOR
MEXICO, 1961, TO THE UNITED STATES, 1958 159

20 COMPARISON OF LABOR PRODUCTIVITY, CAPITAL
PRODUCTIVITY, CAPITAL-LABOR RATIO, AND
LABOR EFFICIENCY IN SELECTED INDUSTRIES FOR
MEXICO, 1961, TO THE UNITED STATES, 1963 162

vii

 

21

22

23

24

25

26

27

28

29

TABLE PAGE

21 COMPARISON OF LABOR PRODUCTIVITY, CAPITAL
PRODUCTIVITY, CAPITAL-LABOR RATIO, AND
LABOR EFFICIENCY IN SELECTED INDUSTRIES FOR
‘MEXICO, 1966, TO THE UNITED STATES, 1963 165

22 COMPARISON OF LABOR PRODUCTIVITY, CAPITAL
PRODUCTIVITY, CAPITAL-LABOR RATIO, AND
LABOR EFFICIENCY IN SELECTED INDUSTRIES FOR
MEXICAN AVERAGES (1961+63) TO UNITED STATES
AVERAGES (1958+63) 168

23 COMPARISON OF LABOR PRODUCTIVITY, CAPITAL
PRODUCTIVITY, CAPITAL-LABOR RATIO, AND
LABOR EFFICIENCY IN SELECTED INDUSTRIES FOR
PUERTO RICO, 1958, TO THE UNITED STATES,
1958 171

24 COMPARISON OF LABOR PRODUCTIVITY, CAPITAL
PRODUCTIVITY, CAPITAL-LABOR RATIO, AND
LABOR EFFICIENCY IN SELECTED INDUSTRIES FOR
PUERTO RICO, 1963, TO THE UNITED STATES,
1963 173

25 COMPARISON OF LABOR PRODUCTIVITY, CAPITAL
PRODUCTIVITY, CAPITAL-LABOR RATIO, AND
LABOR EFFICIENCY IN SELECTED INDUSTRIES FOR
PUERTO RICAN AVERAGES (1958+63) TO UNITED
STATES AVERAGES (1958+63) 175

26 CAPITAL AND LABOR WEIGHTED MEAN LABOR
PRODUCTIVITY AND MEAN LABOR EFFICIENCY
RATIOS FOR MEXICO 177

27 RELATIVE SIZE OF THE MEAN LABOR EFFICIENCY
RATIO TO THE MEAN LABOR PRODUCTIVITY
RATIO FOR MEXICO 178

28 CAPITAL AND LABOR WEIGHTED MEAN LABOR
PRODUCTIVITY AND MEAN LABOR EFFICIENCY
RATIOS FOR PUERTO RICO 179

29 RELATIVE SIZE OF THE MEAN LABOR EFFICIENCY

RATIO TO THE MEAN LABOR PRODUCTIVITY
RATIO FOR PUERTO RICO 180

viii

 

TABLE

30 RELATII
PRODI
INCRR

31 RELATII)
CAPIT
UNDER

 

 

TABLE PAGE

30 RELATIVE MEXICAN LABOR PRODUCTIVITY, CAPITAL
PRODUCTIVITY, AND LABOR EFFICIENCY UNDER
INCREASING RETURNS TO SCALE 181

31 RELATIVE PUERTO RICAN LABOR PRODUCTIVITY,

CAPITAL PRODUCTIVITY, AND LABOR EFFICIENCY
UNDER INCREASING RETURNS TO SCALE 182

ix

 

FIGURE

1 REIATI
PROD

2 0mm

LIST OF FIGURES

FIGURE PAGE

1 RELATIVE PRODUCTIVE EFFICIENCY UNDER THE CES
PRODUCTION FUNCTION 30

2 DOWNWARD BIAS IN THE REGRESSION COEFFICIENTS 41

 

ASSEE

This .
Comparison 01
entials at va
CourItries 1m
Puerto Rico w
of Comparison
in the less d
labor ratio 01'
United States,

 

CHAPTER I

ASSESSMENT OF LABOR PRODUCTIVITY STUDIES WITH
REFERENCE TO RELATIVE AND ABSOLUTE

LEVELS OF CAPITAL INTENSITY
I. HYPOTHESIS AND INTRODUCTION

This analysis is concerned with the calculation and
comparison of international labor productivity differ-
entials at various levels of capital intensity. The
countries involved are the United States, Mexico, and
Puerto Rico with the United States serving as the standard
of comparison. The hypothesis is that even if industries
in the less developed areas were equipped with the capital-
labor ratio of equivalent manufacturing industries in the
United States, labor productivity levels for the former
countries would not approach labor productivity levels of
the latter country for the greater majority of industries.
It will be shown that the hypothesis holds true regardless
of the productivity of capital in the less developed
countries and the highest plausible values assigned to the
output elasticity coefficient of capital. A related suppo-
sition is that scale of plant and integrated industrial

development with commensurate linkage effects increase the

41
i :

productivit

efficiency

General Sta

 

To C:
sectional er
from the max
are employec
certain Yea!

The calculat

(1)

(2)

2
productivity of capital and hence labor productivity and

efficiency under given levels of capital intensity.

General Statement Concerning Methodology
To test the previously mentioned hypothesis, cross
sectional empirical data for output, labor, and capital
from the manufacturing sectors of the respective countries
are employed. Productivity comparisons are made for
certain years as well as averages of some selected years.
The calculations seek to answer these questions.
(1) To what extent do capital intensity differ-
ences lead to labor productivity differences?
(2) Are labor productivity differences less for
industries of intensive capital than for
industries of intensive labor?
After establishing that relative productivity differences
in lesser developed areas are greater than their relative
capital intensity differences, an explanation must be made
as to the probable cause or causes of the further differ-
ences. Different industries in the same country are com-
pared as well as the same industry for different years.
Differences among industries in the less developed areas
are also compared within the context of their historical

economic development patterns.

 

The
advanced I
worker eff
itself. F
are less f
intensive
investment
set up an .
coordinate
be more ef:
decision me

If 1
Successful]
°apital 1m
require knc
countries u
assumptions

the Se fun: t

there 18 V1

each indiviq

previOUs em]

3

The second question (above) relates to a hypothesis
advanced by Hirschman who does not divorce managerial and
worker efficiency from the level of capital intensity
itself. Hirschman states that productivity differences
are less for capital intensive industries than for labor
intensive industries. Accordingly, capital intensive
investment projects promote operations on a large scale,
set up an atmOSphere where labor becomes more efficient,
coordinate difficult human tasks, and force management to
be more efficient thereby shortening and improving the
decision making process of the managerial hierarchy.1

If the hypotheses and questions are to be answered
successfully, productivity adjustments must be made for
capital intensity variations per worker. These adjustments
require knowledge about production functions in the
countries under investigation. Otherwise certain
assumptions must be made about the characteristics of
these functions. The latter approach is used here since
there is virtually no knowledge of production functions for
each individual industry under investigation. However,

previous empirical studies have provided production

 

1Albert Hirschman, The Strategylgf Economic Develop-
ment (New Haven and London: Yale University Press, 1959),
pp. 146-50.

functions wl
One such fur
The usual pri
regionally c
duction funo
assunption 6
try in all t

ally not be

 

data and the
CONStants he

the emPirica

 
 
    
 

TWO '2
regression f1

 

calculate rel

4
functions which could be applied to all the industries.
One such function is the Cobb-Douglas production function.
The usual procedure when productivity comparisons are made,
regionally or internationally, is to assume a single pro-
duction function for all industries again with the further
assumption that the exponents are the same for each indus-
try in all the countries. The constants need or will usu-
ally not be the same if the function is fitted to empirical
data and the equation solved for the constant. Nor do the
constants have to be the same when they are determined from
the empirical data.

Two techniques are employed in this analysis. The
first uses arithmetic and logarithmic multiple linear
regression functions while the second uses a ratio of Cobb-
Douglas production functions. The regression equations
calculate relative labor productivities for Mexico and
Puerto Rico under appropriate levels of capital intensity.
Briefly, the regression planes are used to compute the
following: (1) quantitative and directional influence of
changes in the capital-labor ratio upon the ratio of output
to labor; (2) to test the Hirschman hypothesis; and (3) to
compute the overall relative productivity of Mexican and
Pnerto Rican industries operating with the aggregate United

States capital-labor ratio for the chosen industries. The

 

second meth
functions a‘
countries.
computed £0:
with relati‘
Following tl
find Puerto i
United State
are worked c
of Substitut
under cons ta
tr198 and in
I’uerto Rican
A deta
Presented in
Elven 1n the

t0 interpretfi

latims ’ and

support which

L

%o

 

I

 

5
second method assumes that Cobb-Douglas production
functions are applicable for all industries in all
countries. Relative capital and labor productivities are
computed for Mexican and Puerto Rican industries along
with relative capital-labor ratios for each industry.
Following this, per worker labor productivities for Mexican
and Puerto Rican industries operating with the observed
United States capital-labor ratio in each similar industry
are worked out under varying values of capital elasticity
of substitution coefficients. This analysis is carried on
under constant returns to scale assumptions for all indus-
tries and increasing returns for some selected Mexican and
Puerto Rican industries.

A detailed explanation of the above calculations is
presented in Chapter II. The data and calculations are
given.in the Appendix. The remaining chapters are devoted
to interpretation, analysis, and conclusions of the calcu-
lations, and sub-hypotheses flowing from support or non-
support which the calculations give to the original suppo-

sitions.

limitations.g§ the Present Study

Apart from problems stemming from the lack and

nature of raw data, every empirical study must contend

with certai
formed calc
input-outpt
of technolo
ratio is no
tries. Th1
techniques 4
growth rate.
Products woL
are not rega
manageabilit

ence t0 labo-

   
  

capital inte
The :-
evaluates Pr

Wan-130,3

 

 

6
with certain limitations regarding the scope of the per-
formed calculations. This investigation does not construct
input-output tables nor attempt a measurement of the rate
of technological change. Also, an optimum capital-labor
ratio is not quantified for Mexican and Puerto Rican indus-
tries. This would require the specification of optimum
techniques and determination of a most favorable economic
growth rate. In turn, demand elasticities for final
products would have to be ascertained. These calculations
are not regarded as unimportant. However, for purposes of
manageability, computations are made strictly with refer-
ence to labor productivity differences at varying levels of
capital intensity.

The remainder of the present chapter reviews and
evaluates prior studies of international labor productivity
comparisons which give credence to the current analysis.
The characteristics and application of the Cobb-Douglas
production function in empirical testing is then discussed
as well as methodological problems involved for any study

using empirical production functions.

 

Ear
have raise
This write:
takes were
incomplete,
more deeply
internation
than attemp
Stress is g:

to the Press

WE

Carlo
tivity diffe

to tESt the ‘

hYP°thesis . 2

 

7
II. SELECTED SURVEY OF INTERNATIONAL

LABOR PRODUCTIVITY STUDIES

Earlier international labor productivity studies
have raised and explored some very important questions.
This writer feels however, that some methodological mis-
takes were made, that some studies were analytically
incomplete, and that some investigations could have probed
more deeply into the topics raised by the existence of
international labor productivity differentials. Rather
than attempt a complete review of the vast literature,
stress is given to studies which are especially pertinent

to the present investigation.

Empirical Igggguggughg Hirschman Hypothesis

Carlos Diaz Alejandro has compared labor produc-
tivity differences between the United States and Argentina
to test the existence and magnitude of the Hirschman
hypothesis.2 A cross section of sixty-three manufacturing
industries was chosen in both countries on the basis of
output comparability. The compared years were an average

of data for 1953 and 1957 in Argentina and the single year

 

2Carlos Diaz Alejandro, "Industrialization and Labor
Productivity Differentials," Review.gf Economics and
Statistics, Vol. 47 (May, 1965), pp. 207-14.

1

1958 for th
differences
the former <
attributed 1
absolute si:
size of firm
were represe

was used to

The terms p,
relative pro
labor intens
was“ and sa
workers to t
went; the ab:
"31an is th.
establishmem

establishmEnt

° e

helm:

8
1958 for the United States. Relative labor productivity
differences between the United States and Argentina with
the former country as the comparative yardstick were
attributed to (l) labor intensity in Argentina; (2) the
absolute size of firms in Argentina; and (3) the relative
size of firms in Argentina. These productivity differences
were represented by the following regression equation which
was used to test the Hirschman hypothesis:
P-a-bL+cS-gE.

The terms P, L, S, and E represent in turn, the average
relative productivity per worker in Argentina; the absolute
labor intensity in Argentina denoted by the portion of
wages and salaries for production and non-production
workers to total dollar value added for each establish-
ment; the absolute size of Argentine establishments where
"size" is the average number of production workers per
establishment; and E is the relative size of Argentine
establishments to comparable establishments in the United
States. The results of the regression equation are given
below:

P - 67.77 - 0.935(L) + 0.035(8) - 0.018(3).

The regression coefficient for labor intensity was
very high but the regression coefficients for the absolute

and relative size factors indicated a weak relationship

 

between t1“.
coefficien
nificantly
try, relat
industries
United Sta

0n 1
the Hirsch:
fied his ac
Argentina g
trade also
other force
but 1flag 0
(1) 111'Port =

 

9
between these factors and relative labor productivity. The
coefficient of determination (R2) was 0.523 and not sig-
nificantly high. Except for the petroleum refining indus-
try, relative labor productivities in all Argentinian
industries were lower than the equivalent industry in the
United States.

On the basis of overall results, the author accepted
the Hirschman hypothesis with some reservations. He quali-
fied his acceptance by showing that some industries in
Argentina with a comparative advantage in international
trade also possess a high degree of labor intensity.

Other forces which could affect the Hirschman hypothesis
but lying outside its analytical scope were cited such as
(1) import substitution industries in lesser developed
areas having highly capital intensive techniques and
therefore smaller labor productivity differences when com-
pared to similar industries in developed countries;

(2) tariff protection for certain industries in under-
developed areas favoring capital intensive techniques
placing those industries in a more favorable price position
than competitors in developed countries; and (3) the
narrowing of technical factor substitution possibilities as
industries become more capital intensive. Alejandro

claimed, and correctly so, that any further conclusions had

 

to be
functi
ductio
outside
given a
equatio
Approxir
unexplai
be given
also sufj
1ndf'lpende
PTOductiv;
“0t airplai
AleJandro
results Woz
was also us
SIZe “flab
relations“;
relationship

per egtélblisl

10
to be based on the characteristics of industrial production
functions in Argentina and the United States. If pro-
duction functions were known or assumed, factors which lay
outside the range of Alejandro's analysis could have been
given a meaningful interpretation. Alejandro's regression
equation could scarcely be called a production function.
Approximately 48 per cent of the output variations were
unexplained by capital intensity variations and these could
be given no meaningful analysis. The regression equation
also suffers from poor and inconsistent definitions for the
independent variables. In the first place, relative labor
productivities for Argentinian manufacturing industries are
not explained by labor intensity in Argentina alone.
Alejandro did use relative size as a variable and the
results would have been better if relative labor intensity
was also used. Secondly, Alejandro's definition of the
size variable is not able to produce a high positive
relationship with capital intensity even if such a
relationship did exist. A high average number of workers
per establishment or industry might very well indicate a
high degree of labor intensity. Consistency would require
that the size factor be used as an inverse index of capital
intensity along with the labor intensity variable given

the author's definitions. As used by Alejandro, an

 

incompatibi
size variab
the greater
their share
Therefore, t
intensity ar
greater the
the size var
level of capl
is also Corr
the low regr
the aMolute

state the t c'

was “Vaila‘;

A 311135

data in a c

I
1 |
|
|
on

|

In additiOn’

between the 8

being de fine d

 

ll
incompatibility is present between the labor intensity and
size variables which is revealed in the following manner:
the greater the number of production workers, the greater
their share of payroll in total dollar value added.
Therefore, the greater would be the level of labor
intensity and the lower the capital-labor ratio. But the
greater the number of production workers, the greater is
the size variable (S) and consequently, the greater is the
level of capital intensity. The relative size variable (E)
is also correspondingly affected. This could account for
the low regression coefficients obtained by Alejandro for
the absolute and relative size variables. Alejandro did
state that capital-labor ratios would have been better
indicators of capital intensity but that data on capital
was unavailable for Argentina.

A subsequent article by Edmar Bacha included capital
data in a comparison of relative labor productivities
between Mexico for 1961 and the United States for 1958.3
In addition, Bacha calculated a correlation coefficient
between the size of firms and capital intensity, "size"

being defined as the number of establishments divided by the

 

3Edmar Bacha, "A Comparison of Industrial Produc-
tivity Between Mexico and the United States," §;_Trimestre
Economico, Vol. 33 (October-December, 1966), pp. 657-73.

 

number of
to an emp
were sele
bility of
computati:
amatmt of
K/L stood
United Sta
of comparig
"u" and "m"
the order 8
the capital.
Fm“ this, I
industries t
omined. N.
capital. lab 02

result Of wh

(l)
K"

The absolute

industry in b
Der unit of 1
industries wa.

tivity was en

12
number of workers. The Hirschman hypothesis was also put
to an empirical test. Forty-five manufacturing industries
were selected from both countries on the basis of compara-
bility of outputs and availability of statistics. For the
computations, the symbols K, L, and VA represented the
amount of fixed capital, labor, and value of output. Thus,
K/L stood for the level of capital per unit of labor. The
United States, as in Alejandro‘s article, was the standard
of comparison (i.e., United States - 100). The subscripts
"u" and "m" specified the United States and Mexico, each in
the order given. Bacha then computed the absolute size of
the capital-labor ratio for each industry in each country.
From this, the relative capital-labor ratio for Mexican
industries to comparable United States industries was
Obtained. Next, Bacha derived the aggregate relative
capital-labor ratio for Mexican industries, the numerical

result of which is given below:

(1) Km Lm -
Ku Lu 0°36°

The absolute value of output per unit of labor for each
industry in both countries and the relative value of output
per unit of labor for Mexico in each of the forty-five
industries was calculated. Overall relative labor produc-

tivity was ensuingly determined:

(2)

Bacha concl
for United

greater the
intensity i
being nearl
(1.0/0.36) .
Productivit;

intensity v:

(3)

Bacha
intensity d1
resulting f1|
(DP?) betwee

mung OUtpu

for removing

below:

(4)

\l

v!
BaCha

l3

(2) VAmZLm _ O 27.
VAu/Lu

Bacha concluded from the above that overall productivity
for United States industries was approximately four times
greater than Mexican industries (1.0/0.27). Capital
intensity for United States industries was computed as
being nearly three times greater than Mexican industries
(1.0/0.36). Bacha attributed 75 per cent of the overall
productivity difference to the difference in capital

intensity via the succeeding manner:

(3) o,2711,o - 0 75
0.36/1.0 ° °

Bacha proceeded to remove the effects of capital
intensity differences upon output for each industry. The
resulting figure was termed an "efficiency difference"
(DP?) between United States and Mexican industries. This
0?? was to point to the presence of other factors influ-
encing output besides capital intensity. Bacha's method
for removing capital intensity differentials is shown

below:

VAu/Lu ' Ku/Lu °

Bacha interpreted a DPP of greater than 100.0 as
the United States using a "disproportionate" amount of

capital to achieve a greater per worker product than

average 1a

 

Alternativ
factors in
advantage u
of United 5
tries. Out
less than 1
the United
Productivit
which were
The
Bacha to fu-
on relative
Mexico. The

Capital inte

(5)

The rem-.8831
“19 and th

Hirschman hyp
fashion

4p
bu

ta 10w abs
comet

14

average labor output in the equivalent Mexican industry.
Alternatively, a DPP of less than 100.0 showed that other
factors in the United States than the capital intensity
advantage were responsible for the productivity advantage
of United States industries over similar Mexican indus-
tries. Out of forty-five industries, thirty had a DPP of
less than 100.0. The conclusion was that the majority of
the United States industries under examination possessed
productivity advantages over the same Mexican industries
which were not attributed to capital intensity.

The Hirschman hypothesis was empirically tested by
Bacha to further determine the effects of capital intensity
on relative labor output of manufacturing industries in
Mexico. The regression equation, given below, depicts the
capital intensity and productivity relationship:

Km

(5) log VAm Lm E

VAu/Lu - log a + b log
The regression coefficient (b) had a positive value of
0.219 and the coefficient of correlation was 0.319, neither
one of which was significantly high. Bacha found that the
Hirschman hypothesis generally held but in a very weak
fashion. A positive value of the regression coefficient

but a low absolute value of 0.219 would indicate this to be

correct. A 1 per cent change in the capital-labor ratio by

"'1

1'

Bacha's ca
a 1 per ce
for Mexica
that the H
with cauti‘
period; (2:
data; and <
been due mc
the Possibi
intensity 1

Bach
conducted 1;
the °°ntr1b1
efficiency ,
ten the Hi]
equati‘m als
Alejandro's

0.229 respec

15
Bacha's calculations would lead only to a 0.219 per cent of
a l per cent change in the ratio of relative productivity
for Mexican industries. Apart from this, Bacha believed
that the Hirschman hypothesis would have to be accepted
with caution because (1) his data covered only a one year
period; (2) the business cycle may have influenced his
data; and (3) differences in labor productivity may have
been due more to technology than to capital intensity since
the possibilities of factor substitution narrow as capital
intensity levels rise.

Bacha's study is an improvement over the analysis
conducted by Alejandro. Bacha made an attempt to measure
the contribution of capital to productivity and isolate an
efficiency difference. Alejandro's prime concern was to
test the Hirschman hypothesis. Bacha's linear logarithmic
equation also provided a better fit to the data than
Alejandro's (the correlation coefficients were 0.319 and
0.229 respectively) although goodness of fit could scarcely
qualify a regression equation as a true production function
for the data under consideration.

Previously stated, the measurement of the contri-
bution of capital intensity and the correction of output
for differences in capital intensity by Bacha thereby iso-

lating an efficiency difference, represented an important

contribut
Once such
economic

capital 1
Bacha's a
his defin:
the same a
ratio and
relative c
to conside
75 P873 can
MEXiCan an
attributed

l6
contribution to international labor productivity studies.
Once such procedures are accomplished, the feasibility of
economic development through maximum or minimum levels of
capital intensity becomes more apparent. Nevertheless,
Bacha's adjustment method for the efficiency difference and
his definition of that term is unsatisfactory. Bacha used
the same adjustment to obtain a productivity of capital
ratio and to remove the effects of capital intensity on
relative output. To explain Bacha's error, it is necessary
to consider his method for arriving at the conclusion that
75 per cent of the overall productivity difference between
Mexican and United States manufacturing industries was
attributed to the difference in aggregate capital intensity.

His calculation technique is as follows:

 

(63

(7)

(8)

l7

(6) Wm Lm _
VAu/Lu 0'27

(7) 3.3M-
Ku/Lu 0'36

(8) VAmZLm
VAuZLu -

KmZLm
Lm

Ku/Lu

(88) VAmZ KuZLu _

VAu/Lu . Km/Lm

(8b) VAm . §g_.
VAu Km

(8c) VAm . Ku
Km VAu

(8d) VAm Km.
VAu/Ku

The absolute value of equation (8d) was 0.75 which Bacha
called the difference in productivity due to the difference
in capital intensity. However, (8d) is only an aggregate
relative productivity of capital ratio for Mexican indus-
tries compared with identical United States industries.
Moreover, Bacha also used the above procedure to adjust for
capital intensity differences calling the result a "pure
efficiency difference". In brief, the same computational
procedure was used to obtain capital productivity and to
remove the influences of differences in capital-labor
ratios on relative output. In both cases the result was a

relative productivity of capital ratio. Another

shortcomi

 

equation

labor pro
industrie;
intensity
gather Uni
choice sin
during 195
as well as

than 1958 ‘

the empiric

“53888 and

 

18

shortcoming of Bacha's investigation lies in the regression
equation used to test the Hirschman hypothesis. Relative
labor productivities between Mexican and United States
industries were determined on the basis of capital
intensity in Mexico alone. The choice of 1958 as a year to
gather United States data could not be considered a sound
choice since a recession was occurring in that country
during 1958 which could have distorted capital-labor ratios
as well as other data under consideration. If years other
than 1958 were selected along with the latter year, then
the empirical data could have better reflected true capital
usages and labor productivities.4

The previously reviewed articles provide a start but
lack analytical depth. The Cobb-Douglas function enables
this writer to examine questions and reach conclusions
which could not have been explored or drawn by Alejandro or
Bacha. The most obvious advantage possessed by the Cobb-

Douglas production function over the other regression

equations is that the exponents can'be expressed as

 

4Einar Hardin and W. Paul Strassmann, "Industrial
Productivity and Capital Intensity in Mexico and the
United States," El Trimestre Economico, Vol. 35 (January-
March, 1968), pp. —51- 62; and W. Paul Strassmann, Techno-
logical Change and Economic Development (Ithaca, New York:
Cornell University Press, 1968), p. 78.

elasticitii
inputs or ,
the factor
Douglas fm
(1) both an
to unity; .-
regression

(9)
If the x1 c
ficient a 1
exponent va
sum to unit
duction fUn
then be Wri

(10)
where the r
subsutthiQ
capital and

In a
Mexican 1nd

tl‘dty Of c

Efficienc

l9
elasticities of substitution between capital and labor
inputs or can be considered as the output elasticities of
the factor inputs. The output elasticities for the Cobb-
Douglas function have three notable characteristics:
(1) both are positive but less than unity; (2) both sum
to unity; and (3) both are constant. Consider the
regression equation:b b

l
1 x2

If the X1 coefficient is a capital input, the X2 coef-
II II

ficient a labor input, a an arbitrary constant, and the

(9) Yc - aX 2.

exponent values b1 and b2 for the capital and labor inputs

sum to unity, equation (9) becomes a Cobb-Douglas pro-
duction function. The logarithmic form of equation (9) can
then be written as:

(10) log Yc = log a + b log X + b log X

1 2 2
and b2) are the

l
where the regression coefficients (h

1
substitution elasticities or output elasticities for the
capital and labor inputs respectively.

In addition, the relative economic efficiency of
Mexican industries is not described by a relative produc-
tivity of capital ratio. The concept of economic
efficiency is elusive and deserves careful consideration

before any conclusions can be reached about investment

priorities for lesser developed areas. For example,

 

various 3
their own
Bacha's d
descripti‘
capital re
economic e

As
Production
over the p
mEitical pr
”ougIas fu:
Score. Th:
mathematics
fUHCtion ar

prOduc t 1 On

20
various analyses define economic efficiency according to
their own or given aims and purposes but in any event
Bacha's definition must be considered as not being
descriptive of anything save a relative productivity of
capital ratio. Chapter II fully elaborates the notion of
economic efficiency used in this analysis.

As stated earlier, the application of a Cobb-Douglas
production function to empirical data provides advantages
over the previously mentioned studies. However, the mathe-
matical properties and the assumptions underlying the Cobb-
Douglas function are subject to criticism on their own
score. The remainder of this chapter briefly reviews the
mathematical properties and assumptions of the Cobb-Douglas
function and some relevant studies which have employed
production functions of the CObb-Douglas type for inter-
national labor productivity comparisons. The studies to be
cited have somewhat different methodologies and purposes
from the current study but they will serve to uphold the
methodological validity used in this investigation.

The CObb-Douglas production function has the mathe-
matical property of being linear homogeneous of degree one.
This property along with constant substitution elasticities
which add to unity cause objections toward the Cobb-Douglas

function for empirical testing. To begin with, the

1:

3C

is

th

de

Pr:

tha

tha

°0u1

21
function is based upon the assumption of perfect compe-
tition in resource markets. Moreover, the assumption of
linear homogeneity of degree one requires that all firms
are operating on the minimum point of their long run aver-
age cost curves which requires in turn, that the conditions
for long run competitive equilibrium have been met.
Markets are far from perfect nationally or internationally
and since the Cobb-Douglas function was developed by obser-
vation of United States data, its usage on an international
scale is complicated by different accounting systems which
may record capital and labor inputs differently. Defi-
nitions of the market place may also be different for the
lesser developed areas. In the United States, a trans-
action is recorded in the GNP accounts if the transaction
is productive and if there is a money flow associated with
the transaction. Such may not be the case with many lesser
developed areas. What is considered productive in the
United States may not be considered productive elsewhere.
Further, many lesser developed areas typically have many
productive transactions with no commensurate money flows,
that is, at least a higher proportion of such transactions
than the United States. ‘More importantly, market imper-
fections and structural disequilibria of various sorts

could hamper output elasticities or substitution

for
asst
tour
Crea
zati
that
81th
cana

faCt

wher

tiviI
Pp.¢

22
elasticities for the lesser developed areas to a greater
extent than the United States. Narrow domestic and export
markets for the former countries leading to low sales

volume could also distort capital-labor substitution.

Empirical Production Functions and International Labor
Productivity Comparisons

An article by E. J. Heath compared labor produc-
tivity for Great Britain and Canada for 1948.5 A Cobb-
Douglas production function was fitted to empirical data
for output, capital, and labor. The same exponents were
assumed for similar industries between the different
countries. Relative horsepower per unit of output with
Great Britain as 100.0 was used as the level of mechani-
zation or capital intensity. The horsepower data suggested
that its use per unit of labor was higher in Great Britain
although output per unit of horsepower was higher in
Canada. The Cobb-Douglas function was employed for a three
factor case and written as:

(11) x - pf H’M"
where X is output; L is relative labor; H is relative

horsepower; M.is relative fuel usage; and "p" is the

 

5E. J. Heath, "British-Canadian Industrial Produc-
tivity," Economic Journal, Vol. 67 (December, 1957),
PP. 665-91.

prod

abov

elas

prod
than
that
equa

was I
tive

supe1
7 per
for h
Such

°rgan
error
made ‘

d8 ten

writtg

SUbStj

23

productivity ratio. Using a logarithmic form of (11)
above, a three variable regression was calculated and the
numerical values of "p" andor,~B , andd' , the output
elasticities, were calculated. It was found that labor
productivity in Canada was 7 per cent higher in Canada
than Great Britain. Using a Cobb-Douglas function proper,
that is by excluding'Md and reducing the regression
equation to a two factor case, labor productivity in Canada
was 55 per cent higher in Canada than Great Britain. Rela-
tive fuel usage then revealed that fuel inputs were
superior in Great Britain than Canada. The remaining
7 per cent difference in labor productivity not accounted
for by differences in capital intensity was attributed to
such factors as quality differences in horsepower, business
organization, labor and managerial effort, and statistical
errors in Heath's measurement technique. No attempt was
made by Heath to adjust productivity differences to
determine relative labor efficiencies.

Some years later, several economists, in a jointly
written article, advanced the CES (Constant Elasticity of

substitution) production function as an alternative to the

t6

wi

wh

an

rel
0f
be

tr:

(b;

24
Cobb-Douglas production function.6 Using nineteen
countries including the United States and Mexico, and
twenty-four industries within each country, the authors
tested the relationship of value added upon wage rates

with the regression equation:

(12) log % - log a +‘b log W + e

where V is value added in units of $1,000 per man year;

L is labor input in man years for units of $1,000 per value
added; W is the average wage rate in $1,000 units per man
year or total labor cost divided by the number of workers;
and "e" a random error term.

The coefficient of determination for the above
regression equation was very high showing that 85 per cent
of the variations in average labor productivity (¥5 could
be associated with variations in the average wage rate (W).

A "t" test revealed that for all twenty-four indus-
tries in the nineteen countries, the regression coefficient

(b) was significantly different from zero at the 90 per cent

level of confidence. In fourteen of twenty-four cases, the

 

6Kenneth Arrow, Hollis Chenery, Bagicha Minhas, and
Robert Solow, "Capital-Labor Substitution and Economic
Efficiency," Review‘gg Economics‘gng Statistics, Vol. 43
(May, 1961), pp. 225-47.

cc
ca
di
th
C0

C8?

dew

was

PTO

“he:
was

Cons
buti
each

whie]

Cobb.

nelty

25

"b" value was significantly different from unity at the
90 per cent confidence interval which led the authors to
reject the hypothesis that the regression coefficient (b)
could be called the elasticity of substitution between
capital and labor. If the "b" value was not significantly
different from unity at the specified confidence level,
this could have generalized the case for application of a
Cobb-Douglas production function for empirical tests con-
cerning output, labor, and capital.

Rejection of the hypothesis led Arrow, et al. to
develop an alternative to the Cobb-Douglas function. It
was called the CES (Constant Elasticity of Substitution)

production function which was written as:
I

-f’ .;P __
(13) V: V[d|< +(\-d)L_ j‘P
where V was value added per man year; K.was capital; and L
was man years of labor time. The terms V , (5 , and-P were
constants standing for an efficiency parameter, a distri-
bution parameter, and a substitution parameter each to

each. The term —1— was the elasticity of substitution

1+6
which was also a constant.
The CES function possesses similar properties to the

Cdbb-Douglas production function such as (1) linear homoge-

neity of degree one; (2) positive marginal products subject

 

Cc
re
as
on
Co
Co'
re:
cm
fur
gre
ela

fUn

Pro.
eXci
Varj

Varj

1111

26

to diminishing returns; (3) pure competition in factor
markets; and (4) constant elasticities of substitution.
With constant substitution elasticities both the CES and
Cobb-Douglas production functions have no uneconomic
regions. Graphically, uneconomic regions may be portrayed
as isoquants bending backward upon themselves or as stages
one and two in a three stage output curve. The CES and
Cobb-Douglas functions have no such regions.7 However, the
Cobb-Douglas and CES production functions differ in one
respect. While the Cobb-Douglas is constrained to a
constant elasticity of substitution of unity, the CES
function could have constant substitution elasticities
greater than zero and up to unity. In the limit, where the
elasticity of substitution is unity, the CES production
function reduces to the Cobb-Douglas form.8

Part of the article was devoted to testing the CES
production function parameters for efficiency variations due
exclusively to capital intensity variations, efficiency

variations attributable solely to changes in labor, and

variations in efficiency which affect both labor and

 

7C. E. Ferguson, Microeconomic Theory (Homewood,
Illinois: Irwin, 1966), pp. 146-48.

81bid., p. 150n.

 

 

b1
t1“.

91

27
capital in equal proportions. The countries used were the
United States, Canada, the United Kingdom, Japan and India.
Industries employed for the tests were spinning and
weaving, basic chemicals, iron and steel, and metal
products. Capital estimates, obtained from balance sheets,
were defined as net fixed assets plus land plus cash plus
working capital. An estimate of the rate of return on
capital was also required and this was defined as gross
profit from operations less depreciation. The coefficient
of variation was calculated for each parameter. Con-
clusions Pointed to a constant distribution parameter (6)
meaning that any changes in productive efficiency (Y) would
affect capital and labor in amounts proportionate to the
value of the respective exponents for the capital and labor

9 The distributive shares would thus remain

inputs.
constant and increases in output would be shared in the
ratio of the respective exponents. The Cobb-Douglas
production function thus has the property of neutral
efficiency variations between capital and labor inputs. In
brief, technical change is neutral in the CES (as well as

the Cobb-Douglas) function meaning that the output

elasticities and the distributive shares of capital and

 

9Arrow, et al., 22. cit., pp. 235-36.

 

tc

su

Ja

me:
“he
to

Sub
901-
aUtl

Won

28
labor in the national income are unaltered as technological
change occurs.

The CES production function was then used to calcu-
late relative productive efficiencies for sample manu-
facturing industries of Japan to United States industries.
The first step was to estimate distribution parameters and
the elasticity of substitution for each industry with the

latter defined as:

(K/L)u wu/ru

where K/L is the capital-labor ratio or capital intensity;
"w" is the real wage rate; "r" is the real rate of return
to capital;(7'is an exponent power of the elasticity of
substitution; and the subscripts "j" and "u" represent
Japan and the United States respectively. The weighted
median elasticity of substitution was found to be 0.93
whereas a previous analysis in the same article showed it
to be 0.87. The higher former value for the elasticity of
substitution (0.93) was attributed to the omission of
working capital from the capital intensity index. The
authors stated that the elasticity of substitution between
working capital and labor is much less than unity and since
manufacturing industries were believed to possess large

amounts of working capital relative to fixed capital, the

 

 

 

elast
unity
tal i

lower

real ‘
ductii
in Jar
States
betWee

ratio.

It

11

29

elasticity of substitution would be significantly less than
unity for those industries. The inclusion of working capi-
tal in the current calculations thus accounted for the
lower value of 0.87 compared to 0.93.10

Variations in the efficiency parameter (Y) and the
real wage rate were studied to establish relative pro-
ductive efficiencies of selected manufacturing industries
in Japan compared with similar industries in the United
States. The authors also looked for a positive correlation
between the efficiency parameter (V) and the capital-labor
ratio.

Having estimated the distribution parameters (6) and
the elasticities of substitution 1:175 for the various

\/

industries, the authors determined iso-product curves (17)

from commodity prices to generalize their concept of rela-

tive productive efficiency by using Figure 1.11

 

1
oIbid., pp. 236-39.
llIbid.

 

 

30

 

if):
C
B | GEL.
__ I D
I I
I | A (95
__ _ _| _
I |
I l . (a.
I I I
K2 K3 K1
FIGURE 1

RELATIVE PRODUCTIVE EFFICIENCY
UNDER THE CES PRODUCTION
FUNCTION

 

tt
ra
pr
Cd:
inc
was
Sta
dif.
sho]
Prod
inef

mark.

31

If point A with labor input 0L1 were selected as a

starting point, the labor input at point B or 0L2 could be

determined by:

.L
L‘[dXJ‘P+ (l—d)] ”:-

_.——_- L2[<S X3P+ (lrdq _ ‘P

where x is capital intensity. Point B on the isoquant

(15)

ll

<Q<f

shows factor combinations necessary to generate a unit of
output with factor proportions in Japanese industries at
industrial levels of efficiency in the United States.

Point C shows the actual combination of resource inputs used
in Japanese industries for the output at point B. Briefly,
the efficiency ratio used by the authors was shown by the
ray DC in Figure 1. Therefore, conclusions were that in
primary production the efficiency ratio was lower in all
cases with a range of 0.13-0.56. In Japanese manufacturing
industries except petroleum products, the efficiency ratio
was relatively lower when compared with the same United
States industries. The authors attributed the efficiency
differences to a number of factors which were (1) relative
shortages of natural resources which would hamper primary
production; (2) tariffs and transport costs protecting
inefficient Japanese industries producing for the domestic

market; and (3) differences in capital intensity and size

 

WE
pa
811
We

in

ma
ab;
Ba:
dii
in

dif
dif
of

ant

SEt

32

of plants.12
General conclusions were that the elasticity of
substitution for manufacturing industries may be less than
unity but such evidence in the case of primary production
was not nearly as strong. Especially pertinent to this
paper was the conclusion that relative efficiency differ-
ences of Japanese industries to United States industries
were less in industries of intensive capital than labor
intensive industries indicating that the Hirschman
hypothesis may be operative.13
The CES production function analysis of inter-

national relative productive efficiency improves consider-
ably upon the investigations undertaken by Alejandro and
Bacha. Alejandro had no method for isolating efficiency
differences. Bacha attempted such an isolation but failed
in that he used the same adjustment to obtain productivity
differences due to capital intensity and to correct for
differences in capital intensity. Thus, Bacha's definition
of productive efficiency could not be accepted. The

authors of the CES function proceed further because they

set forth a sound definition of relative productive

 

12Ibid.. pp. 241-46.

13Ibid., pp. 246-47.

 

 

t1

re
e1
du
“0

di

th
the
reg
Car
den
tri
s1z

Eno.

33
efficiency given their estimation of the production
function parameters. It is questionable however, whether
the CES production function has any great advantage over
the Cobb-Douglas function when both are applied to the
same empirical data. In fact, the limiting case of the CES
production function is the Cobb-Douglas form since the

elasticity of substitution in both cases is unity.

 

9
Both functions have identical properties of i#

(l) homogeneity of degree one or constant returns to scale;

(2) diminishing marginal product but with no uneconomic

regions of production; (3) constant substitution

elasticities; and (4) a neutral impact of changes in pro-

ductive efficiency upon capital and labor inputs which

would leave the capital and labor exponents and hence the

distributive shares unchanged.
Empirical evidence advanced by Arrow, et a1. showing

that the elasticity of substitution was substantially less

than unity is not corroborated by the present writer. The

regression coefficient (b) exhibited a value of signifi-

cantly less than unity at the 90 per cent level of confi-

dence in only fourteen of twenty-four manufacturing indus-

tries or 58.3 per cent of the cases. Given the sample

size, it is felt that this evidence is not conclusive

enough to say that the elasticity of substitution is less

s‘:

34
than one for manufacturing industries in general.

‘Moreover, the inclusion of working capital by the
authors in the index of capital would distort the true
elasticity of substitution between capital and labor. The
authors stated that the elasticity of substitution between
working capital and labor was much less than unity and con-
cluded from this that since manufacturing industries had
large amounts of working capital, the elasticity of substi-
tution would typically be less than one for those indus-
tries. Of course, the conclusion could easily be reached
that the elasticity of substitution between working capital
and labor would be less than unity or perhaps even zero.
Working capital is defined as the excess of current assets
over current liabilities. Current assets include cash,
receivables, prepaid expenses, and inventories which may be
categorized as raw materials, work in process, and finished
goods. It is hardly legitimate to believe any substi-
tutability exists between the excess of the previously
mentioned assets above current liabilities. To Obtain a
more accurate value for the elasticity of substitution only
fixed assets such as machinery, equipment, and assemblies
should be employed. An increase in inventories in no way
reflects a decrease in labor. A rise in raw materials,

goods in process or finished goods might very well

CC

fa

Wa

Pr

Ca

35
necessitate a rise in labor inputs. Inventories, in
addition, cannot be considered an input but the result of
inputs of labor and/or fixed capital. In short, this
writer agrees with Arrow, et al. that the elasticity of
substitution between working capital and labor is much
lower than unity or even close to zero but the current
writer does not agree that working capital is an input
which is substitutable for labor. When the originators of
the CES production function omitted working capital in
their definition of the capital input during a section of
their investigation, the elasticity of substitution between
capital and labor took on a higher value (0.93) than when
working capital was included as part of the capital index
(0.87).

The CES function was used in a subsequent study to
compare relative labor productivities for eleven manu-
facturing industries between the United States and Peru.14
Labor productivities were given and then the CES function
was applied to the empirical data to determine what labor
productivity in Peru would be with the United States

capital-labor ratio for the selected manufacturing

 

1['C. Clague, "An International Comparison of
Industrial Efficiency: Peru and the United States," Review
2f,Economics,ggg_§tatistics, Vol. 49 (November, 1967),

PP. 487-93.

indu
of t]
inte:

COSt

where
aside
at th

lated

36

industries. Labor efficiency was defined along the lines
of the CES study and capital inputs were defined as the
interest rate plus depreciation charges. The annual input
cost per $100 worth of capital was calculated as:

(16) p - i$100 + d
where "i" is the rate of interest and "d" is the amount set
aside from the earning stream of the asset to get back $100
at the end of the asset's life. The "d" value was calcu-

lated as:

(17) d _.__ $199...
:1 (I+i)""T

where "n" is the life of the asset. Calculation of rela-
tive efficiency was then calculated on the basis of the
average interest rate between the two countries. The aver-
age rate of interest was assumed to be 12.4 per cent and it
was further assumed that the opportunity cost of internal
financing was correctly represented by the interest rate.
The assumption of opportunity cost enabled the interest rate
to properly reflect the marginal productivity of capital.
Capital figures for Peru were converted to United States
prices by dividing the Peruvian figures by an index of one
hundred fifty. Since the value of buildings was not
available for Peru, it was assumed that the United States

share of buildings in total fixed capital also applied to

 

 

 

ran

eff

' int

Per'
How:
autl

that

rela
for

deve
coun
Sout]
Denna
1958.
desig

and t]

DECembE

37
Peru. The relative price of all fixed assets in Peru was
then computed by the formula, x(1.0) + (l-x)(l.5). After
estimating capital requirements and calculating relative
efficiencies, the author found a high positive Spearman
rank correlation coefficient (+0.71) between relative
efficiency and the United States level of capital
intensity, and that relative efficiencies for the eleven
Peruvian industries were lower than United States levels.
However, given the nature of the empirical data and the
author's method of estimating capital, this writer feels
that Clague's results were inconclusive.

Another article, by Edward J. Mitchell, examined the
relationship of average man hour output and the wage rate
for eleven developed countries and a total of seventeen
developed and underdeveloped countries.15 The developed
countries were Australia, Canada, New Zealand, Norway,
South Africa, Sweden, the United Kingdom, the United States,
Denmark, Puerto Rico, and Finland selected for the year
1958. The underdeveloped countries, chosen for 1958, were
designated as Greece, Japan, Peru, the Philippines, Turkey,

and the United Arab Republic. The following regression

 

15Edward J. Mitchell, An Econometric Stud y_ of Inter-
national and Interindustrial Differences in Labor Produc-
tivity (Santa'Monica, California: Rand Corporation,
December, 1966), 97 pp.

38

line was employed in the analysis:

(18) log % ‘ log a + b log w + e

where %.is average output per head of labor; "w" is the

"e" a residual error term.

wage rate; and

Like the authors of the CES production function,
Mitchell used his regression equation to determine whether
the "b" coefficient was significantly different from unity
and the constancy of the wage share. The developed
countries supported the hypothesis that the "b" coefficient
was not different from unity at the 5 per cent level of
significance. Therefore, the elasticity of substitution for
the developed countries assumed a value of unity. For the
developed and underdeveloped countries combined, the
hypothesis was rejected at the 5 per cent significance
level. Overall conclusions however, were that the wage
share of national income was approximately constant over a
span of time which indicated a constant unitary substi-
tution elasticity between capital and labor.

‘Mitchell also proposed a method for isolating differ-
ences in value added because of labor efficiency differences.
Variations in labor efficiency among countries were

attributed mainly to differences in the quality of labor

with average wage differentials accounting for variations

39
in labor quality. Mitchell then put forth a basic form of
the Cobb-Douglas production function:

R 1"°‘

(19) r ”CXA '1':

where "r" is the rate of return to capital or the marginal
product of capital which is assumed to be equal among
countries;cy'is the elasticity of substitution; and E is
the capital-labor ratio or level of capital intensity.

Mitchell stated that a l per cent change in the
efficiency parameter (A) would cause a 1-0tchange in value
added. Changes in technology and efficiency (the greater
the quality of labor, the greater would be the marginal
product of capital for any given capital-labor ratio) were
presumed to be reflected in l-ot. Changes in o< were
attributed to changes in capital intensity levels. His
method for isolating productive efficiency differences did
not require the collection of capital data due to his
assumption of equalization of capital rates of return made
possible by the mobility and homogeneity of international
capital movements. Productive efficiency differences then
were exclusively reflected in the quality of labor which
was assumed to have very low international mobility.

‘Mitchell did not calculate relative productive

efficiencies for the industries in the different countries.

 

 

N0!

40
He merely set forth a method for doing so. However,
Mitchell's analysis gives support to the notion that
substitution elasticities between capital and labor are
approximately unity among several countries and industries.
On that score one point should be mentioned. Puerto Rico
was used in his analysis and since Puerto Rico is used in
this present analysis as an underdeveloped country, the
case for usage of a Cobb-Douglas production function is
strengthened.

A study by Fuchs in 1963 showed that the data used
by the authors of the CES function do not support or neces-
sarily imply that the elasticity of substitution is less
than unity. Fuchs proposed that when two different groups
of countries are compared, each group could have an
elasticity of unity, but different intercepts for the
regression lines. When the lines are combined, the
regression coefficient (the elasticity of substitution) may
be subject to a downward bias. This proposition is demon-

strated in Figure 2.16

 

16Victor R. Fuchs, "Capital-Labor Substitution: A
Note," Review of Economics and Statistics, Vol. 45
(November, 1963), pp. 436-38.

log

 

41

b1 - 1.0

b - 1.0

II

I + bn = bIII<1-0

 

log W
FIGURE 2
DOWNWARD BIAS IN

THE REGRESSION
COEFFICIENTS

subsc
line
regre
is be
rate
V
1 ._
og L
downw
and I“

were |

42

The "b" terms are the regression coefficients and the
subscripts denote the respective country groupings. The
line with numeral III indicates a summation of the
regression coefficients. The relationship shown on Figure 2
is between value added per unit of labor (.E) and the wage
rate (W) and is represented by the regression equation,
log'% = log a +-b log WA+ E.

Fuchs tested the CES production function for this
downward bias using the same industries, years, countries,
and regression equation as Arrow, et al. The countries
were divided into developed and underdeveloped categories.
The authors of the CES function made no such categorization.
Fuchs concluded that the regression coefficient (b) for
both groups of countries was not significantly different
from unity indicating the elasticity of substitution to be
constant and unity. Fuchs also used a shift coefficient to
measure differences in the elasticity of substitution
between capital and labor resulting from different payroll
data and different wage accounting systems in various

countries. Again, the conclusions were that the elasticity

of substitution was constant and unity.

for
indu:
of ti
year:

line

Wher1

adde.

sign
the

valu
case
woul
Sea]
Sub:
V311

ma n.

43

C. E. Ferguson tested the elasticity of substitution
for 129 samples Obtained from 61 industry groupings.17 The
industries were selected from the four digit classification
of the United States Census 9f Manufactures. The census
years were 1947, 1954, and 1958 and the ensuing regression
line was employed:

(20) log v = log a + b log w + u
where "v", "w", and "u" respectively represented value
added per worker, the wage rate and a random error term.

The regression coefficient (b) was found not to be
significantly different from unity in more than one half of
the 129 samples. For 13 per cent of the samples, the "b"
value was between zero and one and in 16 per cent of the
cases the "b" value was greater than one. The latter value
would indicate some presence of increasing returns to
scale. Ferguson further concluded that the elasticity of
substitution has changed randomly over time shifting from
values between zero to unity and greater than unity for
many industries.

The previous critique of the CES production function

was not intended to substantiate the correctness of the

 

17C. E. Ferguson, "Cross Section Production
Functions and the Elasticity of Substitution in American
Manufacturing Industry," Review.gf Economics gngw§gg-
tistics, Vol. 45 (August, 1963), pp. 305-13.

 

Cobb-Doug

 

critical
productic
of the Co
elasticit
negation.
function
criticism
0f substi
caPital a
undertaki
Al
ass‘mptio ,
Single re g
Country an
In brief,
stud1e8 c1
establishe
or Value 0
then teste

coefficieu t

an alternat;

44
Cobb-Douglas procedure for empirical testing. Rather, the
critical evaluation was designed to show that the CES
production function is not a strong or reliable repudiation
of the Cobb-Douglas technique if empirical observations of
elasticity of substitution coefficients are the basis for
negation. The basic form of the Cobb-Douglas production
function is used in the current study. Since much of the
criticism of the function hinges on its constant elasticity
of substitution of unity, empirical justification for the
capital and labor exponent values used was a necessary
undertaking.

All the studies reviewed make essentially the same
assumption as this analysis; namely, the application of a
single regression equation for all industries within a
country and for the countries whose industries are compared.
In brief, a single regression equation is used by all the
studies cited here. ‘Many of the studies reviewed here
established the crucial relationship as between value added
or value of output per unit of labor and the wage rate and
then tested for the value of the elasticity of substitution
coefficient. The authors of the CES article also put forth
an alternative production function to the Cobb-Douglas form
for empirical testing and tested relative efficiency

differences between the United States and Japan. In

 

addition .I
efficienc
(A) and jlI
in Mitche
compared
Great Bri
efficienc
test for
Procedure
Correct fa
11'lfiol’r'ect
in this c}
Douglas pr
be drawn v
function I
Thul
applying pl
fined Inain

Inng as SL2

markets of

fundamentaj
most V1 ta 1

bility Of

 

“Berton

45
addition, Mitchell offered a procedure to isolate relative
efficiency differences by varying an efficiency parameter
(A) and judging the change in l-a. The causal relationship
in Mitchell's paper is different from this analysis. Heath
compared relative labor productivities between Canada and
Great Britain.but did not offer a method to judge an
efficiency difference. Clague used the CES function to
test for efficiency differences but was not clear on his
procedure or methodology. Bacha also offered a method to
correct for efficiency differences but was shown to be
incorrect. In any event, the studies which were mentioned
in this chapter were to establish the validity of the Cobb-
Douglas procedure and to show that useful conclusions can
be drawn with the application of a single production
function among industries and countries.

Thus far, comments regarding the shortcomings of
applying production functions to empirical data were con-
fined mainly to the mathematical properties and the under-
lying assumptions regarding the resource and product
markets of these functions. There may however, be more
fundamental criticisms than those discussed earlier. The
most vital part of any production function is the possi-
bility of technical factor substitution set forth by the

function. A high or low regression coefficient or a high

coeffici
of a pro
Douglas

bilities

not able

a product
values muII
if Physic
nature we
inputs co1
measure d.

and excess

 

BalanCe st
Costs and
assets wou
capital an
333%ng
different

natimm1 p

\

18

It!

46
coefficient of determination is not an adequate description
of a production theory. Nor does a good fit of a Cobb-
Douglas function to empirical data reflect the true possi-
bilities of capital-labor substitution. Empirical data are
not able to reflect technical factor substitution and hence
a production function. For aggregation purposes dollar
values must be used for physical inputs and outputs. Even
if physical quantities are available their heterogeneous
nature would prevent any meaningful aggregation. Labor
inputs could be represented by man hours of labor but this
measure does not reflect intensity of effort. High capital-
1abor ratios may contain a high degree of unused capital
and excess capital capacity is not shown on balance sheets.
Balance sheets in turn, show fixed assets at historical
costs and not market values. Market values for capital
assets would indicate a more accurate output indicator for
capital and therefore a truer rate of return to fixed
assets.18 All the above problems are compounded when
different accounting systems come into play with inter-

national productivity comparisons.

 

18Ibid., pp. 311-12.

r _-_..— r-“m

 

S

producti

P
of g
ever,
them
purp
is t
speci
that
the e
ships
of em
defin
macro
with 1
take
conce1
PhYSid
are n(

 

 

 

47
Solow had made further comments regarding empirical
production functions:

Production functions are best suited to the realm
of general equilibrium analysis and micro theory. How-
ever, some amount of aggregation is necessary to make
them useful (for empirical testing and predictive
purposes). At this point two tacks are possible. One
is to try to preserve the rigor of the theory by making
special assumptions and defining special aggregates so
that the underlying microeconomic relationships entail
the existence of corresponding macroeconomic relation-
ships. The other is to give up (some) rigor in favor
of empirical practicality, to use conventionally
defined aggregates and index numbers, and to construct
macroeconomic relationships more or less by analogy
with microeconomics. But it seems to me to be a mis-
take to ask deep philosophical questions of such loose
concepts. Index numbers will not behave like the
physical commodities they are supposed to mimic. They
are not trying to do so; they are empirical compromises.
They fged scrutiny, of course, but of an appropriate
kind.

This analysis is constructed along the lines of the
second approach outlined by Solow. Given the hypothesis
and purposes of this paper empirical compromises can still
yield useful predictions. Market values are indeed better
indicators of capital or fixed asset values than historical
costs. But the only way true and accurate market values
could be determined is through liquidation of plant assets.

Then the industry is no longer a going concern and

 

19Robert M. Solow, "Comment: Concepts and'Measures
of Changes in Productivity," Review 2; Economics and
Statistics, Vol. 41 (August, 1959), pp. 282-85.

ad ———-—..4 «mu——

producti‘
moreover
heteroger
specific
empirical
Douglas,

refute it

 

for the U
Upholds t

elasticit:

unity .

48
productivity comparisons are meaningless. Dollar values
moreover, provide a useful mechanism for the aggregation of
heterogeneous types of capital equipment. As far as the
specific form of the production function applied to the
empirical data in the body of this work, namely, the Cobb-
Douglas, no mandatory alternative has been offered to
refute its practicability for empirical testing. Evidence
for the United States as well as on an international scale
upholds the constancy of the wage share and a constant
elasticity of substitution between capital and labor of

unity.

III. SUMMARY

The purposes of Chapter I were to (1) set forth the
working hypothesis; (2) frame the analytical apparatus;
and (3) establish the methodological viability of the ana-
lytical framework. The hypothesis was stated and the
methodological approach for testing this hypothesis was put
forth as fitting regression equations and Cobb-Douglas
production functions to empirical data on capital, output,
and labor for a cross section of selected manufacturing
industries among selected countries. The chosen countries
were Mexico, Puerto Rico, and the united States with the

United States designated as the comparative standard. The

relative
tive levJ

measured

 

changes 1‘
capital il
labor efJ
With met

labor pro
cedural m
assmes t
Cobb‘Doug
applicatj
by examil
functIOn
c"“Clude
°°n8tant
nothing
tution .
the an:
elderEd
°°mpe11
‘43
tution

Hithir

49
relative labor outputs of Mexico and Puerto Rico at rela-
tive levels of capital intensity would be compared and
measured by the regression and Cobb-Douglas functions and
changes in value of output per labor unit to changes in
capital intensity levels would be calculated. Relative
labor efficiencies also would be determined. In connection
with methodology, some previous studies of international
labor productivity comparisons were cited and their pro-
cedural mistakes examined. Since the present analysis
assumes that all industries in all countries operate with
Cobb-Douglas production functions, justification for its
application toward empirical data was made. This was done
by examining studies which made use of empirical production
functions of the Cobb-Douglas type. At best, some studies
concluded that the elasticity of factor substitution was
constant and unity. At worst, it was concluded that
nothing could be said about elasticity of factor substi-
tution values between capital and labor. The findings of
the authors of the CES production function.were also con-
sidered inconclusive. In the absence of any mandatory or
compelling alternatives to the Cobb-Douglas approach and
the use of money values as indexes of capital-labor substi-
tution, the current methodological tack can be justified

within the light of previous studies of this type. The

belief o
preclude

C‘
Douglas :
detail.
nation of
explainec
cussed.

the end c

 

 

 

50
belief of this writer is that useful conclusions are not
precluded by such procedures.

Chapter II discusses the regression equation, Cobb-
Douglas function, and other analytical procedures in great
detail. Sources and handling of the empirical data, combi-
nation of years, and the choice of industries are also
explained. The notion of economic efficiency is then dis-
cussed. An Appendix of the calculations is presented at

the end of the thesis.

   
 

P1
ple line:
form. T}

countries

 

and uses

fOr each

Esksg
Th

CHAPTER II

METHODOLOGY

I. THE EQUATIONS

Preliminary tests of the hypothesis employ a multi-
ple linear regression function in arithmetic and logarithmic
form. The second method assumes that all industries in all
countries operate with Cobb-Douglas production functions
and uses these functions to obtain a labor efficiency ratio

for each industry in Mexico and Puerto Rico.

The Rggression Function

The initial calculations show relationships between
relative labor productivities under appropriate levels of
capital intensity (United States - 100). The regression
function is also used for testing the Hirschman hypothesis.
The dependent variable in the regression equation is the
relative output between Mexico or Puerto Rico to the United
States. The predictor or independent variables are the
relative levels of capital intensity and average levels of
capital intensity between the compared countries. The
symbols used in the regression function are defined as
follows: V is aggregate output; L is the amount of labor;
K is the quantity of capital; and "m", "p" and "u" are

51

subscrip
States r

I

regres 3 ii

h00d es tin)

0f the

 

Ha

52
subscripts representing Mexico, Puerto Rico, and the United
States respectively.
If Mexico and the United States are compared, the

regression equation in arithmetic terms is:

(21) VméLm B anm (fig .153)
Vu Lu a+b2 Ku/Lu+b3 Im+Lu

2
vm Lm . KmZLm)
where'vaéia is the relative labor productivi;:y,(Ku/Lu is
the relative capital-labor ratio; and (%E’+‘EE) is the
2

average level of capital intensity between Mexican and
United States industries.1 To make comparisons for the

"m" along

United States and Puerto Rico, "p" would replace
with the Puerto Rican output, labor, and capital figures.
If Y stands for the relative labor productivity, X2 for the
relative level of capital intensity, and X3 for the average
level of capital intensity, the regression equation can be
written as:

(22) Y - a + b2 X2 + b3 X3
and the logarithmic form of equation (22) above is:

(23) 1og Y - a +b2 log X2 +‘b3 log X3.

The equations (22) and (23) are the maximum likeli-

hood estimators for the data essentially meaning that the

sum of the squared deviations around the regression plane

 

1Hardin and Strassmann,.gp. cit., pp. 51-62.

 

will be

both the
are used
in terms
ficients
changes

intensit
Sign for
Rican im
tiVity 1.
0f the ca
a relati‘
hiSher th
PTOduct b
1ndUStry.l
the relat
per cent

erided

ficient b

capital 1

is held Co

 

53
will be minimum no matter which equation is used. However,
both the arithmetic and logarithmic forms of the function
are used to determine which equation best describes the data
in terms of higher correlation and determination coef-
ficients. The regression coefficients (b2 and b3) show how
changes in relative and absolute levels of capital
intensity affect relative labor productivity. A positive

sign for the b coefficient means that Mexican and Puerto

2
Rican industries approximate United States labor produc-

tivity levels in those industries where the relative value
of the capital-labor ratio is high. An industry which has
a relative capital-labor ratio one unit or 1 per cent

higher than another industry also has a relative value of

product b2 units or b2 per cent higher than the latter

industry. Similarly, a one unit or 1 per cent change in

the relative capital-labor ratio leads to a b2 unit or b2

per cent change in the relative output per unit of labor

provided that the b coefficient is held constant. Coef-

3

ficient b3 reveals how changes in the average level of

capital intensity affect relative labor productivity if b2

is held constant.

54

Cobb-Douglas Procedure

Labor productivity differences do not reveal labor
efficiency differences if there has been no adjustment for
differences in capital intensity between the industries
under investigation. The method used in this analysis
makes such an adjustment assuming that Cobb-Douglas pro-
duction functions are applicable for all the selected
industries in Mexico, Puerto Rico, and the United States.
The Cobb-Douglas production functions are written down for
the United States, Mexico, and Puerto Rico respectively as:

(24) Vu - CuKugLuh

(25) Vm - CmeijR

(26) Vp - CpkgL;
where V is output volume; C is a proportional constant; K
is the amount of capital; L is the amount of labor; "g" and
"h" are the capital and labor input exponents in the United
States; "j" and "k" are the capital and labor input
exponents in Mexico; and "r" an "s" are the capital and
labor input exponents in Puerto Rico.

If equation (24) is divided on both sides the aver-

age productivity of labor is obtained as:

(27) its _ C (52)3
Lu “ Lu -

If Mexico is the country being compared to the United

55
States, equation (25) is divided on both sides by Lm and

there results:

(28) £2 - Cm (%)j.

Then a ratio of the average labor productivities of beico
to the United States is taken as:

(29) Vm Lm 92 (KmZLm)j

Vu/Lu Cu (Kn/Lu)g

VmLm.. 2a..
where Vu/Lu P, and Cu 2.

A labor efficiency ratio (E) can now be stated as:

(30) E = z (I(u/Lu)‘j.g
provided that equation (29) is solved for "2".2
Equation (30) shows what Mexican labor productivity would
be in a given Mexican industry if that industry had the
same capital-labor ratio as the equivalent United States
industry assuming values for the "g" and "j" exponents. A
labor efficiency ratio (E) can also be calculated by

solving equation (29) for "z" and by substituting that

value into equation (30) resulting in:

(31) s - p (my.

Km/Lm
As long as the exponent summations for both

countries are constrained to unity and constant returns to

 

2Ibid., pp. 55-58, and Strassmann, 22. cit.,
pp. 78-81.

56
scale are assumed, equation (31) can be used to show labor
productivity in a Mexican industry which operates with the
United States capital intensity level for that same indus-
try. Equation (31) is superior to equation (30) in that
equation (31) requires an assumption about the capital
input exponent of the Mexican industry alone.3 In brief,
the inverse of the observed relative capital-labor ratio
between Mexico and the United States is raised by an
exponent power of the capital intensity level for a given
Mexican industry. The resulting figure is then multiplied
over the relative labor productivity for the selected
industry. A labor efficiency ratio (E) is thus obtained.
The procedure dictated by equation (31) is used in this
analysis under the assumption of constant returns to scale.
Of course, if Puerto Rico is taken into account rather than
Mexico, the same analysis is followed with equation (26)
substituting for equation (25).

The results of the calculations from equation (31)
are shown in the Appendix under varying values for the
capital elasticity of substitution coefficient. The
elasticity values assumed here are the two extreme values

0.9 and 0.1 with intermediate values of 0.7, 0.4, and 0.3.

 

3 id.

57
After calculating the labor efficiency ratios, the
weighted mean values of the labor productivity and

efficiency ratios are calculated with the mean statistic:

(32)

“1X1

[f]:

Lal-
I
H

 

pd
I

W

[V]:

i

(.1-
H

where "w" is a weight representing capital (K) or labor

(L); and i is mean labor productivity (P) or mean labor

efficiency (E).

The Assumption‘gf Increasing Returns.£g Scalg

If increasing returns are assumed, equation (31) is
unsatisfactory for computing a labor efficiency ratio
because only the capital input exponent is known. Both
capital and labor exponents must be included to incorporate
the effect of increasing returns into the analysis. How-
ever, by writing an unrestricted Cobb-Douglas production
function, that is, by allowing the exponent powers to sum
to greater than unity and by rewriting equations (27) and
(28), the analysis can incorporate the influence of

increasing returns to scale. Equation (27) now becomes:

(33) '2? - Cu(Kug).
Lu

58
Equation (28) is also rewritten as:
(34) Vm a Cm( j)
I}? K” °
m
Taking a ratio of equations (33) and (34) there obtains:

(35) Vm/Lmk Kg
- z —- O
Vu/LB

 

R
u

Equation (35) is solved for "z" and its value substituted
into equation (36) to Obtain a labor efficiency ratio which
is:

(36) E = z (Ku/Lu)j-g.
Equation (36) is the same as equation (30) and is appropri-
ate for calculating a labor efficiency ratio under
increasing returns. Since an assumption must be made about
the value of all the exponents for both the United States
and Mexico, the problem is now to pick plausible values for
those exponents. A study made by welters has revealed some
insights into the problem of choice of exponents under
increasing returns.“ Welters criticized Solow's assumption

of constant returns to scale in the aggregate production

 

4A. A.'Wa1ters, "A Note on Economies of Scale,"

Review‘g§_Economics‘ggg Statistics, Vol. 45 (November,
1963), pp. 425-27.

59

5 and then proceeded to fit a Cobb-Douglas function

function
with an exponential trend to Solow's data to calculate
elasticity of substitution values. In three separate
tests, Walters found that the sum of the elasticity of
substitution coefficients was 1.353, 1.265, and 1.375. The
capital input exponents in each case were 0.125, 0.187, and
0.151 and in all of the tests Walters found that the
elasticity of substitution coefficients were greater than
unity. He concluded that 27 to 35 per cent of the increase
in aggregate output over the years studied by Solow was due
to economies of scale.

A previous article by welters made a comprehensive
survey of the literature concerning production functions.6
Among the topics discussed were estimation and identity
prdblems and the value of the exponents in the Cobb-Douglas
production function. The author found some evidence that
the elasticity of substitution was not unity but the more
general case was that the elasticity of substitution was

approximately unity for industries in various countries as

well as the United States. welters concluded however, that

 

SRobert‘M. Solow, "Technical Change and the Aggre-
gate Production Function," Rexiew,g§ Economics and Sta-
tistics, Vol. 39 (August, 1957), pp. 317-20.

6A. A. Walters. "Production and 3°“ Functim‘s’"

Econometrica, Vol. 31 (January-April, 1963), pp. 1-66.

60
nothing conclusive could be said about economies of scale.
He said those industries which concluded that the
elasticity of substitution was approximately unity used
inputs as a measure of the variation in plant size. Hence,
the result was a proportionate change in value added,
which, in turn, led to a constant elasticity of substi-
tution between capital and labor.

This current study incorporates Walter's findings
concerning Solow's data and uses a value of 1.3 as the
summation of the exponent powers indicating increasing
returns. This is approximately the average for all three
of the tests conducted by welters. Ten industries are
selected for the United States and Mexico and five indus-
' tries are chosen for the United States and Puerto Rico.
Three cases are subsequently examined.

(1) The compared countries both operate under

increasing returns with the same exponents.

(2) Mexico and Puerto Rico operate under increasing

returns with the united States under constant
returns and the capital input exponent for
Mexico or Puerto Rico is greater than the
capital input exponent for the United States.
(3) The United States works under increasing

returns with Mexico and Puerto Rico exhibiting

61
constant returns. The capital input exponent
for the United States is greater than the
corresponding capital input exponent for

Mexico or Puerto Rico.

II. THE DATA

The following section defines the sources and
treatment of the data to which the equations are applied.
Definitions of output, capital, and labor are also dis-

cussed.

Sources 9_f 293;;

For the United States, output and employment figures
were obtained from the gggggg‘gijanufacturgs for 1958 and
1963. Capital figures were provided by the Angus; Sgrggy
of Manufactures for 1964. The Puerto Rican Census 2;;
‘Manufagtures for 1958 and 1963 yielded data on output,
labor, and capital. Mexican figures on output, labor, and
capital were derived from the Industrial 929229. 2; gig-1:339

for 1956, 1961, and 1966.

Selection,g§ Ygars

The combinations of years selected for comparison
are apparent from the tables showing the calculations. The

choice of years was dictated by availability of good census

62
information concerning the data. Comparisons were made on
the basis of proximity of years for both countries. When-
ever averages of years were compared it was not the aver-
ages of the capital-labor or value of product per unit of
labor ratios but the averages of the raw data subsequently

converted to the proper ratios.

Selection 9f Industries

Industries were chosen on the basis of product homo-
geneity and availability of statistics. The criterion of
product homogeneity is considered especially important
since, without that criterion, comparisons would be
meaningless. Of course, availability of statistics is
always the final factor in the selection of any industry.
For instance, many industries in Puerto Rico could not be
chosen because of a lack of capital data or information
with which a reasonable capital estimate could be made.
The Puerto Rican census only reveals capital data for
industries with ten or more employees. Also, much capital
reporting is not given in order that individual company
totals are not disclosed.

In most cases the four digit industrial classi-
fication.was used because Mexico had only four digit

classifications except for power companies and petroleum

63
and to avoid double counting in the output value for the
United States and Puerto Rico. Some three digit classi-
fications were used and some four digit classifications
were added for any country when it was necessary to obtain

output comparability.

The Data

 

Most of the data was directly obtainable from the
various censuses but some capital estimates were necessary.
All output and capital figures are shown in dollar values
by converting Mexican pesos at the appropriate rate of

exchange.

.922222. This figure was directly obtained from all
censuses and is defined here as the dollar value of net
sales. This definition is consistent for all countries.
Value added of output may have been a better measure to use
but the Mexican census provided no figures for value added.
In the case of the United States and Puerto Rico, "value of
shipments" is synonomous with the definition of output
used here and there is some possibility of double counting
when value of shipments is used rather than value added.
The Qgggg§,g§ Manufactures does reveal however, that double
counting is negligible when the four digit classification

is used. No mention of double counting was made in the

64
Mexican census but it can be assumed that double counting
is negligible for Mexico in the value of output figures
since four digit classifications were used there also. The
important consideration however, is not so much that value
added or value of product be used but that the definitions

be consistent among countries.

Capital. The gross book value of fixed assets
defines capital. Fixed assets are plant and equipment,
machinery, tools, and buildings. ‘Working capital, for
reasons discussed in Chapter I, was excluded from the defi-
nition of capital. The Mexican censuses for 1956 and 1961
did provide total fixed capital figures but the 1966 census
only provided total capital (fixed plus working capital).
Total fixed capital was estimated during 1966 by taking the
proportion of fixed to total capital during 1961 for each
Mexican industry and assuming this rate was applicable to
the same industry during 1966. By multiplying the
appropriate rate over total capital for each industry,
total fixed capital was derived industry by industry.

The Annual _S_u3_v_e1 of Manufactures of the United
States for 1964 provided total fixed asset figures as well
as the rental value of fixed capital equipment and

machinery for 1964, 1963, 1962, and 1957. Thus 1963

65
capital figures were directly obtained for the United
States industries. The fixed capital figures for 1954 and
1958 were estimated by obtaining an index of capital growth
of each year to each succeeding year.7 An average index of
fixed capital growth was obtained over the seven year
period, 1957-64, for each industry. The average index was
divided into the 1963 fixed capital figure plus rentals and
into each consequently lower figure until the required
capital figures were reached in each industry for 1958 and
1954. If the 1958 figure was lower than the 1957 fixed
capital book value, the 1957 book value was adjusted upward
by the index of growth for that industry. A check was then
made to determine the accuracy of the estimates. Since all
industries for 1958 showed higher fixed capital figures
than 1957, net investment should have occurred for 1958.

8 and

In fact, total net investment for 1958 was $18 billion
thus the accuracy of the estimates is corroborated in the
total sense.

For Puerto Rico, only net investment and expenditures

 

71f the years represent the figures, the indexes were
computed as 1964 x 100, 1963 x 100, and 1962 x 100.
1963 1962 1957

8Board of Governors, "Financial and Business Sta-
tistics, 0.3.," Federal Reserve Bulletin, Vol. 50 (January,
1964), PP. 104-5.

66

on consumed plant and equipment were provided. To estimate
total fixed capital for Puerto Rican industries, the ratio
of expenditures of used plant and equipment to total fixed
capital was calculated for comparable industries in the
united States. This rate was then divided into the expendi-
tures on used plant and equipment for the same Puerto Rican.
industry. Net investment was added to that figure to
obtain total fixed capital for each industry in Puerto Rico
during 1958 and 1963. This procedure assumed that each
Puerto Rican industry was replacing fixed assets at the same
rate as the comparable United States industry.

To the extent that rental values do not reflect the
true book value of assets which are rented, the capital
data for the United States may be underestimated. Since
rental values are not known for Puerto Rico and Mexico,
capital figures for those industries may also be under-

estimated.

Lgbgg. Employment figures were defined as pro-
duction and non-production workers and, for the Mexican
case, any worker who was not permanently attached to the
industry but who may have contributed to production during
the year. These figures were directly obtained from all

of the censuses. The justification for including all

67
workers rather than just production workers is that any
workers may contribute to production whether directly or
indirectly involved in the manufacturing process. The
Hirschman hypothesis also lends justification to including

workers directly or indirectly involved in production.

III. SUMMARY

This chapter described the regression equation used
in the analysis and the Cobb-Douglas procedure used to test
the hypothesis. The Cobb-Douglas production function was
also applied to selected industries assuming the sum of the
exponents showed increasing returns to scale. The empirical
data was also analyzed in terms of its sources and years,
definitions, and estimation methods.

Chapter III presents a summary and detailed dis-
cussion concerning the initially introduced hypothesis and
the calculations which support that hypothesis. The first
part of the chapter presents overall results and con-
clusions for purposes of brevity and clarity. There follows

a detailed explanation for completeness and conciseness.

CHAPTER III
INTERPRETATION OF THE CALCULATIONS
I. GENERAL RESULTS AND CONCLUSIONS

L922; Efficiency Summary Statistics

The arithmetic mean values of the labor efficiency
ratios are presented for Mexico and Puerto Rico on the
following pages. Table 1 summarizes the results for Mexico
and Table 2 gives the summary results for Puerto Rico.
Column (3) shows the employment weighted arithmetic means
of the labor efficiency ratios while column (4) contains
the unweighted labor efficiency means of the Cobb-Douglas

"a"

results. Column (5), or antilog , shows the labor

efficiency ratios when the exponent values for capital and
labor inputs are the same for the compared countries.
Column (5) was computed using the simple logarithmic linear
regression:

(37) log Y - a + b log X

2 2

where Y’-‘%E§%E, or relative output value for Mexico; and
x-£n:.[_12

2 Ku/Lu’
The subscript "p" replaces

or the relative capital labor ratio for Mexico.
"m" when Puerto Rico is compared
to the United States. The antilog of the constant term "a"

is the ratio of the two constant terms in the two

68

9
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71
Cobb-Douglas production functions one representing Mexico
or Puerto Rico and one representing the United States in
equation (37). Then antilog "a" shows overall labor
efficiency for either Mexico or Puerto Rico when the capi-
tal and labor input exponents are the same as the United

States.1

Summary Results for, Mexico

Table 1 reveals that Mexican labor efficiencies for
all years and columns are lower than United States levels
except for the 1956-54 comparison in column (4) under the
0.9 exponent. Column (5) follows the same general trend
as both the weighted and unweighted Cobb-Douglas results and
corresponds most generally to the exponent values of 0.3 and
0.4. It should be mentioned that a 0.9 capital input
exponent is an extreme assumption for a Cobb-Douglas
function. This means that a 100 per cent change in labor
inputs leads to a 10 per cent output change (holding capi-
tal constant). Further, the term "labor efficiency" not
only applies to worker characteristics but to all factors
affecting output per unit of labor after capital stock

adjustments are made. This becomes apparent as the analysis

1Hardin and Strassmann,‘22. cit., pp. 55-62, and
Strassmann,,gp.‘g;§., pp. 78-81.

72
continues.

There is little difference in the values of the
weighted and unweighted means in Table l and, as expected,
both vary-directly with the assumed capital exponent power.
The 1956-58 comparisons yield increasing labor efficiencies
over 1956-54 for the weighted means but decreasing efficien-
cies in the unweighted columns. This is a result of higher
labor weights being associated with higher labor efficien-
cies thereby raising weighted averages over the years,
1956-54. Reliance must be placed on the unweighted means
for 1956-58 since United States capital-labor ratios
increased along with relative output values from 1956 to
1958. The overall productivity of capital fell for Mexico
in 1956-58 (1.35-l.21).

Generally, except for 1956-54, and the average year
comparisons, both the weighted and unweighted means increase
or decrease in the same manner under all exponents for all
the compared years. For 1961-58, labor efficiencies have
fallen from the previous relative year (1956-58) in the
upper regions of the capital input exponent (0.9 and 0.7 in
column 3 and 0.9 in column 4) while rising for the lower
exponent regions. Exactly the reverse is true when 1961-63
is compared to 1961-58. Labor efficiencies have risen for

the weighted and unweighted calculations (0.9-0.7) but have

73
fallen in all other regions. A recession occurred during
1958 in the United States and what capital was utilized was
employed efficiently. The relative productivity of capital
was higher for the United States in 1961-58 (0.99) but fell
in 1961-63 (1.17), while the relative capital-labor ratio
fell for Mexico during those years (O.52-0.43).

It is not surprising to find the relative capital
productivity and the relative capital-labor ratio moving in
opposite directions. Further, the relative productivity of
capital is a more important factor in changing labor
efficiency at higher capital exponent powers (0.9-0.7) while
the relative capital intensity is a more important determi-
nant in lower elasticity regions (0.4-0.1). Where capital
productivity and its output elasticity are high, further
increases in capital significantly affect labor efficiency
regardless of the original capital intensity. Relative
capital productivity loses influence as its output
elasticity falls and the level of capital intensity is a
controlling factor in changing labor efficiency as massive
doses of capital are needed to increase labor efficiency.

The above discussion is supported by comparing labor
efficiency changes between the relative years 1961-63 and
1966-63. Labor efficiencies for 1966-63 fell for both the

unweighted and weighted means for the 0.9 and 0.7 exponents

74
but rose for the 0.4-0.1 exponents. The relative produc-
tivity of capital also fell during 1966-63 (l.l7-0.93) while

the relative capital-labor ratio rose (0.43-0.51).

Summary Results fig; 2.1.1.922 £99

Puerto Rican labor efficiencies (Table 2) are higher
than those of Mexico in all columns. The Puerto Rican
unweighted means are higher than the weighted means and
overall labor efficiencies in column (5) correspond closely
to the means obtained for an exponent value of 0.1.

Unweighted and weighted labor efficiencies for
Puerto Rico increased between 1958-63 but overall efficiency
remained the same for both years (0.55). The weighted
results do not increase by as much as the unweighted means.
Puerto Rican employment figures for 1958 are very low in
many cases between about 20-50 for many industries in the
three digit classification. They do increase for 1963 but
the low initial employment followed by sharp increases
could affect the weighted results. ‘Moreover, the overall
relative capital-labor ratio fell for Puerto Rico from
1958-63 (1.38-0.86) while the relative productivity of
capital changed upward (1.31-2.08). These offsetting
changes may have kept the overall result in column (5) the

same between years but the tremendous jump in capital

75
productivity may have offset the fall in relative capital
intensity so that the weighted and unweighted means were
pulled upward for all the exponents between the compared

years.

General Conclusions

Given the assumptions, including those concerning
the Cobb-Douglas production function, Mexican and Puerto
Rican industries would have to use much greater levels of
capital intensity than equivalent United States industries
to achieve the same labor productivity as the latter. This
result is suggested by the summary results in Table l and
Table 2 and by examination of individual industries in the
relevant tables in the Appendix. There were also signifi-
cant regressions obtained under the multiple regression
analysis suggesting that higher levels of labor productivity
are associated with higher capital-labor ratios. Then labor
productivity differences are less for industries of
intensive capital than industries of intensive labor.

The remaining productivity gap in Mexican and Puerto
Rican industries after adjustment for United States capital
stock levels (the labor efficiency difference) could theo-
retically be attributed to five factors: (1) social,

cultural, and political hindrances in Mexico and Puerto Rico

76
regarding work and capital formation; (2) the superiority
of fuel and resource-related inputs in the United States;
(3) newer capital stock in the United States; (4) differ-
ences in worker and managerial ability; and (5) economies
of scale in favor of the United States. The first three
reasons were rejected or not explored.

Mexican-United States labor efficiency differences
were attributed to differences in worker and managerial
ability and greater economies of scale for united States
industries as demonstrated by their market size for final
output. This is also demonstrated by Mexican-Puerto Rican
comparisons. Wage rates are generally higher for Puerto
Rico than Mexico thereby dictating more capital intensity
for Puerto Rico. Puerto Rican labor efficiencies are also
higher than the Mexican indicating more scale economies for
Puerto Rico since many Puerto Rican industries produce for
the United States market. For this reason, labor
efficiency differences between United States and Puerto
Rican industries are probably not mainly due to scale
differences. The labor efficiency difference is probably
due to superior workers, managers, and decision makers in

the United States.

77

II. THE MULTIPLE REGRESSION ANALYSIS

Significance igggg and the Regression Coefficients

Since the capital-labor ratio of United States indus-
tries is substituted for capital intensity levels of the
same Mexican or Puerto Rican industries, it was necessary
to determine whether a significant relationship existed in
the population for the given years. If there was no linear
relationship among the variables, the raising of labor
productivity for Mexican and Puerto Rican industries by
substituting the pertinent United States capital-labor
ratios would have little meaning apart from being an exer-
cise in mathematical mechanics. The null hypothesis stated
that there was no relationship in the population between
value of output per unit of labor and relative and absolute
levels of capital intensity. A "t" test was conducted at
the .0005 significance level for both the arithmetic and
logarithmic regression coefficients for Mexican and Puerto
Rican comparisons to the United States. The appropriate
degrees of freedom were used in each case and the null
hypothesis was rejected for all years for both the
arithmetic and logarithmic coefficients. Thus, it can be
concluded, and especially for the very low significance

level of .0005, that there is a significant relationship in

78

the population for the compared variables. An examination
of Table 14 and Table 16 (Mexico and Puerto Rico
respectively) reveals very low standard errors of the
regression coefficients relative to the size of the coef-
ficients. The null hypothesis could be rejected for most
commonly used significance levels by visual inspection.
The standard errors of the regression coefficients are
shown in parentheses directly below the coefficients.

Referring to Table 14 and Table 16, the regression
coefficients all show positive signs and high numerical
values. For Mexico (Table 14), the arithmetic b2 coef-
ficients range from 1.14-1.62 and the arithmetic b3 coef-
ficients are 1.0 for all comparisons. The logarithmic b2
coefficients have values of 1.31-1.57 and the logarithmic
b3 coefficients have a range of 1.05-1.10. Thus, in the
case of Mexico, the arithmetic and logarithmic regression
coefficients show that a one unit or 1 per cent change in
the relative and average values of capital intensity induce
an equivalent or greater change, in units or per cents, in
the relative value of output per unit of labor.

For Puerto Rico (Table 16) the b2 coefficients in
the arithmetic case range from 1.02-1.60 and the arithmetic
b coefficients are unity for all years as well as the 1958

3
and 1963 average. The logarithmic regression coefficients

 

79
for Puerto Rico range from values slightly less to slightly
greater than unity. The signs of the coefficients are
again positive. Therefore, for both the Puerto Rican and
‘Mexican cases and given all the previous information, higher’
capital-labor ratios are definitely associated with higher

labor productivities.

ngffigients. g Multiple Correlation 22g Determination

Mexican and United States correlation coefficients
(R) are neither exceptionally high or low and are shown in
Table 14 along with the coefficients of multiple determi-
nation (R2) and the unbiased coefficients of multiple
determination (R2). The comparison of the years 1956-54
shows the lowest values for R, R2, and R2. The correlation
and determination coefficients for Puerto Rico compared to
the United States (Table 16) are noticeably lower than
Mexican-United States comparisons.

2 ‘2

The coefficients R and R are of special importance

to this analysis. Interpretation is made here with refer-
ence to‘R2 since the unbiased coefficient of determination
is adjusted for degrees of freedom thereby yielding more
accurate results. With the exception of the arithmetic
result for the comparison of 1956-54, the arithmetic

unbiased determination coefficients provide a better fit to

80
the data than the logarithmic determination coefficients
for Mexican-United States comparisons. For Puerto Rico,
the unbiased determination coefficients in arithmetic terms
are negative for 1958 and for 1963. For averages of those
years,‘R2 is very low showing a value of 0.10. The loga-
rithmic unbiased determination coefficients are also very
low.

Table 14 and Table 16 reveal that for both the
arithmetic and logarithmic cases a large amount of vari-
ations are left unexplained by the regression planes. The
unexplained variations are much larger for Puerto Rico than
for'Mexico. Hence, the analysis shows very high regression
coefficients with a large scatter of unexplained points
around the regression planes for all the comparisons. Geo-
metrically, this situation is represented by a steeply
sloped regression plane with a wide scatter of points

around the plane.2

The predictor variables (X2 and X3) are
very strong but the large amount of unexplained variations
around the regression plane reveals that factors other than

capital intensity affect relative output to a large degree.

 

20n the other hand, there may also be low regression
coefficients along with high determination coefficients.
This is shown geometrically by a relatively flat regression
plane with a small scatter of points around the plane.

81
ggggmgyggy‘ggg Partial Correlation Coefficients
To determine the individual correlations of each of
the predictor variables with the dependent variable and to
determine the correlation between the predictor variables,
the zero order and partial correlation coefficients were

3 The results are summarized in Table 15 for

calculated.
Mexico and Table 17 for Puerto Rico. For Mexican-United
States comparisons, the correlations between the predictor
variables are very low under both the logarithmic and
arithmetic calculations. This holds true for both the zero
order (R23) and partial correlation coefficients (R23.l)‘
When the Puerto Rican analysis is undertaken, the
arithmetic and logarithmic correlations between X2 and x3
are larger for both the zero order and partial correlation

coefficients than those for the Mexican analysis but not

exceptionally large. If extremely large correlations or

 

3For example, the term R1 is the zero order or
simple correlation coefficient of relative value added and
the relative capital-labor ratio. However, in the case of
the simple correlation coefficient, the effect of the vari-
able X could enter into the correlation between Y and X
(R1 ). The partial correlation coefficient (R12 ) removes
the influence of X upon the correlation between' and X .
The first two subscripts for the simple and partial corre-
lation coefficients denote the correlated variables. The
last subscripts attached to R for the partial correlation
coefficients show the variables whose effects have been
removed from the correlations of the first two variables.

82
almost perfect correlations prevailed between the predictor
variables, the partial regression coefficients would be
severely affected although the overall prediction yielded
by the regression lines would not be hampered. That is,
the interpretation of b2 with b3 constant would be severely‘
limited since large variations in b3 would enter into the
b2 variations and conversely.

The strongest zero order and partial correlations for
Mexico are between relative value added per unit of labor
and relative capital intensity for both the arithmetic and
logarithmic equations (R12 and R12.3). The highest zero
order and partial correlations for Puerto Rico are between
relative and average levels of capital intensity for the
arithmetic and logarithmic calculations (R23 and R23.l)
although not high enough to affect the partial regression
coefficients.

The next part of the current chapter compares rela-
tive labor productivities for Mexico and Puerto Rico to
relative labor efficiencies. The comparisons are shown in
Tables 18-22 for'Mexican-United States comparisons and

Tables 23-25 for Puerto Rican-United States comparisons.

83

III. LABOR PRODUCTIVITY AND LABOR EFFICIENCY COMPARISONS

Mexican-United States Industry Comparisons

Tables 18-22 reveal that relative labor produc-
tivities and relative capital-labor ratios are lower in
Mexico for almost all industries. Labor efficiencies are
also lower in the greater majority of cases. The greater
the capital input exponent or the power of the capital
intensity ratio, the greater is the relative labor
efficiency. Labor efficiencies are greatest under a 0.9
capital input exponent and lowest when a value of 0.1 is
assumed for the capital intensity ratio since the exponent
power is the output elasticity of capital (the percentage
change in output with respect to the percentage change in
capital). Raising a given capital-labor ratio by a rela-
tively greater elasticity exponent increases output by a
greater amount than if the capital-labor ratio was raised
by a lower elasticity coefficient.

For Table 18, which compares Mexico, 1956, to the
United States, 1954, only twelve of thirty-nine Mexican
industries show greater labor efficiencies than United
States industries under a capital input exponent of 0.9.
These industries are Dairy Products, Wines and Grape

Liquors, Cigars and Cigarettes, Cotton Spinning and weaving,

84

Pharmaceuticals and Medicines, Gypsum, Lime, Pottery and
Related Products, Metal Doors, Sash, and Trim, Metal Drums
and Containers, Cutlery, and Dental Equipment. When the
exponent value is 0.7 the number of Mexican industries
showing greater labor efficiencies than the similar United
States industries decreases sharply to Dairy Products,
Gypsum, Pottery and Related Products, and Metal Drums and
Containers (four of thirty-nine industries). At an
exponent value of 0.4, only the Gypsum industry in Mexico
has a higher labor efficiency than the Gypsum industry in
the United States.

Table 19 compares Mexico, 1961, to the United States,
1958. Under the 0.9 capital input exponent, nine of sixty
industries in Mexico (Leather Tanning and Finishing, Organic
Chemicals, Fertilizers, Lubricating Oils and Greases,
Hydraulic Cement, Gypsum, Lime, Tires and Inner Tubes, and
Motor Vehicles and Parts) are more efficient under a capital
intensity power of 0.4 than the similar United States
industries. Apparently a recession during 1958 in the
united States did not affect labor productivities or
capital-labor ratios as shown by their comparisons to Mexi-
can industries.

When Mexico, 1961, is compared to the United States,

1963, in Table 20, thirteen of sixty industries in Mexico

85

show greater labor efficiencies than the same industries for
the United States (0.9). The industries are Chewing Gum,
Soft Drinks, venetian Blinds and Shades, Leather Tanning and
Finishing, Organic Chemicals, Fertilizers, Pharmaceuticals
and Medicines, Lubricating Oils and Greases, Hydraulic
Cement, Gypsum, Lime, Tires and Inner Tubes, and Motor Vehi-
cles and Parts. Of these industries only Leather Tanning
and Finishing, Fertilizers, and Tires and Inner Tubes show
a greater labor efficiency than United States counterparts
when the 0.7 exponent is used. For a capital input exponent
of 0.4 a single industry alone, Leather Tanning and
Finishing, possesses a higher labor efficiency for Mexico.

For 1966-63 comparisons (Table 21), the number of
Mexican industries showing higher labor efficiencies is
greater than any other year rising to seventeen out of
fifty-nine industries given a 0.9 exponent (Bakery Products,
Chewing Gum, Shortening and Cooking Oils, Manufactured Ice,
Venetian Blinds and Shades, Leather Tanning and Finishing,
Plastics, Pharmaceuticals and Medicines, Lubricating Oils
and Greases, Hydraulic Cement, Gypsum, Lime, Pottery and
Related Products, Cutlery, Motors and Generators, etc.,
Storage and wet and Dry Batteries, and Tires and Inner
Tubes). For a capital input exponent of 0.7 the industries

in Mexico with greater relative efficiencies than

86
United States industries are five out of fifty-nine (Leather
Tanning and Finishing, Hydraulic Cement, Gypsum, Pottery and
Related Products, and Tires and Inner Tubes). Relative
Mexican labor efficiencies are lower in all industries
under an exponent value of 0.4.

When the averages of years for'Mexico and the United
States are compared (Table 22), thirteen of fifty-nine
Mexican industries reveal higher labor efficiencies than
comparable United States industries (Bakery Products,
Chewing Gum, Shortening and Cooking Oils, Soft Drinks,
Leather Tanning and Finishing, Pharmaceuticals and Medi-
cines, Lubricating Oils and Greases, Hydraulic Cement,
Gypsum, Lime, Pottery and Related Products, Storage and wet
and Dry Batteries, and Tires and Inner Tubes). Merely two
of fifty-nine industries (Leather Tanning and Finishing and
Lubricating Oils and Greases) have higher labor efficiencies
for Mexico than the United States. Again, Mexican labor
efficiencies are lower in every single industry for a capi-
tal intensity power of 0.4.

The preceding discussion proves that the productivity
gap between the less developed countries and the United
States goes well beyond differences in capital intensity.
This holds true for all ranges of output elasticity coef-

ficients for capital under a Gobb-Douglas function. The

87
question arises as to which capital input exponent best
fits Mexican-United States comparisons. Hardin and
Strassmann use a capital input exponent of 0.4 and 0.3 when.
comparing labor efficiencies between Mexican and United

States industries.4

Douglas, in his study of manufacturing
industries for a twenty-two year period ending in 1924,
found the capital input exponent to be 0.25.5 welters
calculated the capital input exponent using two tests (one
of which employed an autocorrelation function) and found

six capital input exponent values ranging from approximately'

o.12-o.23.6

Given the above information the pertinent
capital input exponent for this study could be 0.3 or
certainly a value no higher than 0.4. Under these exponents
the hypothesis is very strongly supported.

To expand the original hypothesis, industries were
arranged by ascending order of labor productivity for each
of the relative years and by ascending order of relative

years for the same industry. Labor productivity groupings

show that the same level of relative labor productivity can

 

4Hardin and Strassmann, op, cit., p. 58, and

Strassmann, 92. cit., pp. 80-81.

sPaul Douglas, Theory'gf wages (New Yerk: Macmillan,
1934), p. 133.

6Walters, "A Note on Economies of Scale," 22. cit.,
P. 427.

88
be achieved by a high relative capital productivity ratio
accompanied by a low relative capital-labor ratio and con-
versely. In brief, for a constant level of relative labor
productivity the higher the relative capital productivity
ratio the lower is the relative capital-labor ratio. This
is as could be expected. A high capital productivity
implies little capital usage per unit of labor to achieve
a given level of labor productivity. What is significant
is that the higher the relative capital productivity ratio,
the higher is the labor efficiency ratio which results from
the same level of relative labor productivity.

The labor efficiency differences for different capi-
tal productivities or capital-labor ratios are only large
at the upper regions of the capital output elasticity coef-
ficient (0.9-0.7). As the output elasticity coefficient of
capital falls, the labor efficiency differences become less
such that for a coefficient of 0.3 the differences are
slight and for a coefficient of 0.1 the differences are
practically non-existent. Thus for a given level of labor
productivity, regardless of the absolute value of that
productivity, the capital productivity ratio is a strong
influence on labor efficiency differences only at the upper
regions of the capital output elasticity coefficient. At

lower coefficient regions neither the relative capital

89
productivity ratio or the relative capital-labor ratio has
an influence on relative labor efficiency.

Differences in relative labor productivities and
labor efficiencies among industries are caused by differ-
ences in relative productivities of capital and relative
capital-labor ratios. The higher the relative capital
productivities and relative capital-labor ratios the higher
the relative labor productivities and efficiencies. The
regression coefficients (b1 and b2) also bear out this
relationship. Previous comparisons have shown that changes
in labor efficiency are very responsive to the relative
productivity of capital ratio at the upper regions of the
capital output elasticity coefficient. The relative capi-
tal-labor ratio is a more important determinant of changes
in labor efficiency at the lower regions of the output
elasticity coefficient for capital. For example, the
figures reveal that industries with different relative capi-
tal productivities and different relative capital-labor
ratios have the same labor efficiencies for a capital
output elasticity coefficient of 0.9. Beyond that coef-
ficient at the lower capital exponent ranges of 0.4-0.1,
the industries with the relatively lower capital produc-
tivities and relatively higher capital-labor ratios have

greater labor efficiencies.

90

The grouping by relative years for the same industry
shows that almost all industries in Mexico are becoming
capital intensive with the exception of Dehydrated, Frozen
Fruits and Vegetables, Seafood, Confectionery Products, and
Soft Drinks. A few other industries became less capital
intensive but the falls in capital intensity were negligi-
ble. The size of fixed capital assets is increasing almost
without exception for all years. This would indicate that
industries which became less capital intensive mechanized
rather than instrumentized their operations, the former
requiring more labor and the latter less labor. It is not
difficult to suppose that the foodstuff industries mecha-
nized the preparation of canned or frozen foods. Variations
in relative capital productivities and relative capital-
labor ratios as well as variations in the absolute value of
those ratios for Mexico show capital-labor substitution and
the absence of fixed technical coefficients. value of
product per unit of labor and value of product figures are
increasing almost without exception. The increases in
product values for the greater majority of industries are
almost doubling and tripling between years indicating a
widening of markets. If market extension is indicative of
returns to scale, then a scale factor could be present for

Mexican industries.

91

As expected, variations in relative labor produc-
tivities and labor efficiencies between years for the same
industry are caused by variations in relative capital
productivities and relative capital-labor ratios. Whenever
relative capital productivities and relative capital-labor
ratios increase together between years, relative labor
productivities and labor efficiencies rise without exception
for those years. If both relative capital productivities
and capital-labor ratios fall between given years, then
relative labor productivities and labor efficiencies also
fall. If either the relative capital productivity or the
relative capital-labor ratio falls while the other
increases, then labor productivities and efficiencies can
move in opposite directions. A rise in relative produc-
tivities of capital increase labor productivities even
though relative capital-labor ratios have fallen. Thus,
increases in capital productivities can increase labor
productivities by offsetting falls in capital-labor ratios.
In this situation labor efficiencies increase for every
single output elasticity of capital coefficient. If rela-
tive productivities of capital fall but relative capital-
labor ratios rise labor productivities again increase.
Labor efficiencies will decrease for the capital input

exponent 0.9 and for some values of 0.7 while all other

92
labor efficiencies rise. Further, given increases in rela-
tive capital-labor ratios, falls in relative capital produc-
tivities, and falls in relative labor productivities, labor
efficiencies fall for the lower ranges of the capital input
exponent (0.4-0.1) but rise in most cases for the higher
exponent values (0.9-0.7). Therefore, labor efficiencies
and relative labor productivities move in opposite
directions whenever relative capital productivities and
capital-labor ratios move in opposite directions. The labor
efficiencies and productivities move in the same direction
when capital-labor and productivity ratios move in the same
direction. Again, the productivity of capital is a more
important determinant of labor efficiency increases in the
upper ranges of the capital input exponent while the capi-
tal-labor ratio is more influential concerning increases in

labor efficiency at the lower input exponent values.

Pugrto Rican-United States Comparisons

The data presented in Tables 23-25 reveal that rela-
tive labor productivities are generally higher for Puerto
Rican industries than Mexican-United States comparisons.

In many industries Puerto Rican capital-labor ratios are
higher than comparable United States industries.

In the 1958 comparisons (Table 23), five of

93

twenty-two industries have higher labor efficiency ratios
for Puerto Rico than the United States given the capital
exponent of 0.9. For 1963 comparisons (Table 24) and given
the capital input exponent 0.9, fifteen of thirty-three
industries in Puerto Rico show higher labor efficiencies
than similar United States industries. Again under the 0.9
exponent, twelve of twenty-two Puerto Rican industries in
Table 25 have greater labor efficiencies than the same
industries in the United States. The industries which have
greater labor efficiencies are not listed here as they were
in the Mexican analysis because the tables and industries
for Puerto Rico are not as numerous as they are for Mexico
and hence these industries are more easily discernible by ’
an inspection of Tables 23-25.

Predictably, when the capital-labor ratio in a Puerto
Rican industry is greater than the capital-labor ratio for
the same United States industry, labor productivity in the
Puerto Rican industry falls as the lower United States
capital-labor ratio is substituted for the higher Puerto
Rican capital-labor ratio. However, labor efficiencies
rise as the capital output elasticity coefficient falls.
This is to be expected. A lower capital-labor ratio results
in a lower labor productivity. Then, as the output

elasticity of capital falls, labor productivity (efficiency)

94

rises since the lower capital-labor ratio has a lesser
influence on the level of output as the capital output
elasticity coefficient falls. This situation is also true
for Mexico. When industries for Puerto Rico are grouped
by labor productivity and by year for the same industry,
the same conclusions are reached as in the Mexican
industrial groupings.
.LEEQE Productivity gag L329; Efficiency Compared Qgggg
Increasing Returns

When Mexican and United States industries are com-
pared under increasing returns assuming identical capital
and labor input exponents (Table 30), Mexican labor
efficiencies rise beyond United States levels in four of
ten industries (Plastics, Inorganic Chemicals, Hydraulic
Cement, and Tires and Inner Tubes). For Puerto Rican
industries (Table 31) labor efficiencies are greater than
United States industries in three of five observations
under identical capital and labor input exponents. These
industries are‘Millwork and Related Products, Concrete
Block and Brick, and Concrete Products. In some industries,
labor efficiencies fall below original labor productivity
levels when the same input exponents are used. This occurs
for Meat and Dairy Products, Veneer and Plywood Plants, and

Petroleum Refining in Mexico and for Canned Fruits and

9S
Vegetables in Puerto Rico.

Under increasing returns to the United States and
constant returns to Mexico (Table 30), labor efficiencies
are greater for all Mexican industries except Petroleum
Refining. Given the identical assumptions for Puerto Rican-
United States comparisons, all industries in Puerto Rico
have greater labor efficiencies than their United States
counterparts (Table 31). Where Mexican and Puerto Rican
industries Operate under increasing returns and United
States industries exhibit constant returns, all industries
in Mexico and Puerto Rico show lower labor efficiencies
than their original labor productivity levels.
Relative‘Mexican‘ppngelative Pugrto‘gippp Comparisons
‘ppgnzppi; Historical Economic Developments

The previous sections have shown that most Mexican
and Puerto Rican industries have productive deficiencies
exceeding their capital deficiencies when compared to simi-
lar United States industries. Labor productivity and
efficiency differences and fluctuations in these values
were attributed to have the same causes for both countries.
There are however, some notable differences in the data
between Mexican and Puerto Rican industries. Relative capi-
tal-labor ratios are generally much higher for Puerto Rican

industries as well as labor efficiencies. A higher

96

percentage of industries in Puerto Rico have greater labor
efficiencies than similar United States industries than is
the case for Mexico. These greater labor efficiencies in
Puerto Rico extend in many cases into the exponent values
of 0.3-0.1. In Mexican comparisons, no industry in any of
the compared years has a labor efficiency which is greater
than the United States level when the capital intensity
powers are 0.3-0.1. Also the number of industries which
have greater labor efficiencies in Puerto Rico compared to
the United States under a 0.7 exponent does not fall as
sharply as Mexican cases, remaining the same as the 0.9
exponent in Table 23, and falling to thirteen out of thirty-
three in Table 25. Under a 0.4 exponent further declines
for Puerto Rican efficiencies are witnessed but not as
severe as Mexican-United States comparisons. Then why do
these differences in Mexican and Puerto Rican industries
exist? What were the patterns in economic development
which have led to similarities or dissimilarities in labor
productivities and efficiencies for Mexico and Puerto Rico?

'Mexico and Puerto Rico have experienced similar
economic development patterns. Both countries could
scarcely be underdeveloped in the sense of traditional
economies stagnating in low level equilibrium traps and

vicious circles of poverty. Both countries experienced

97

breakdowns of social and cultural barriers to capital
accumulation and technological change before 1940 and from
1940-65 the rate of industrialization was heavy for the two
economies. Further, Mexico and Puerto Rico possess rela-
tive ease of access to United States technology and the two
countries have good export markets and tourist trades which
alleviate inflationary pressures during the course of
development.7

As early as 1900, in Mexico, foreign enterprises had
set up mining, railroads, and electric power industries.
Also at that time beer, glass, cigarettes, match, soap,
cloth, cement, and steel establishments had been set up by
foreign and domestic manufacturers. During the years
1935-40 a stable political process was established, and
schools, roads, and irrigation systems were built. Urban
industries also arose.8 Investment in social overhead capi-
tal was made and combined with the backward and forward
linkage effects of the cement and steel industry, economic
development became an on-going process during the early
1940's. From 1945-60 the heavy rate of industrial growth

was achieved largely through tariff protection, credit

 

7Strassmann, pp. gi§., pp. 279-80.

8Ibid., p. 282.

98

manipulation in the capital market by the government which
encouraged banks to lend on easy terms to industry, tax
exemptions, and fast depreciation writeoffs were granted to
new and necessary industries (e.g., steel) by the govern-
ment. There were elements of government planning in the
industries of steel, cement, food, transport, and petroleum
but hardly anything proceeding along socialistic lines.
Unequal income distribution in favor of corporate profits
was also tolerated.9

In Puerto Rico social overhead capital was formed
through the United States New Deal administration during
the 1930's. Schools, roads, hydroelectric plants, and
cement plants were built. Unlike Mexico, Puerto Rico is a
United States territory and provides special tax exemptions
to industries. ‘More importantly, unlike Mexico, Puerto
Rico had some planning for an integrated industrial
structure. Huge direct financial assistance was given to
core industries. Core industries were defined as those
using Puerto Rican minerals and plant inputs or industries
which import and process crude raw materials to be used by
other industries. Essentially core industries were those

which supply or buy from many other industries. Thus core

 

9Ibid., pp. 286-98.

99
industries imply industries with significant backward and
forward linkages. There is one other important difference
between Mexican and Puerto Rican industrial development.
There are more economies of scale evident in Puerto Rico

10 The data

since Puerto Rico produces for a larger market.
appear to show that Puerto Rican labor productivities, capi-
tal productivities, capital-labor ratios, and labor
efficiencies are higher than those of Mexico. value of
product figures are larger for Puerto Rican establishments
in general than for Mexican establishments. Value of
product figures would indicate or serve as a proxy for
market size. Capital figures per establishment could serve
as a proxy for scale of plant. Given the data on capital
and value of product figures along with the historical
development pattern of the two countries it must be con-
cluded that differences in labor productivity and efficiency
between Mexico and Puerto Rico are attributable to

(l) economies of scale; and (2) planning or integrating

economic development along the lines of backward and

forward linkage.

 

10
Ibid.. PP. 298-315.

100

IV. CONCLUSIONS

The hypothesis of this analysis states that
industrial labor productivity in less developed areas would
be less than industrial labor productivity in the United
States even if industries in the less developed areas had
the same capital-labor ratios as similar United States
industries. The hypothesis is stated for all plausible
values of the capital output elasticity coefficient which
can be assumed for a Cobb-Douglas Production function.
Given the results of the regression analysis and the labor
efficiency calculations assuming a Cobb-Douglas production
function for industries in all three countries, the
hypothesis is accepted. Industry comparisons between
Mexico and the United States strongly support the hypothe-
sis, and Puerto Rican-United States industrial comparisons
also support the hypothesis but not as strongly as in the
‘Mexican case. Even under the greatest capital exponent
power, labor efficiencies for the compared industries in
Mexico and Puerto Rico are lower than United States produc-
tivity levels for the majority of industries. As the
exponent power of capital falls, the number of Mexican and
Puerto Rican industries with greater labor efficiencies

than similar United States industries decreases sharply

101
thereby strengthening the hypothesis.

Thus, the capital input exponent is of prime
importance in determining labor efficiency levels of Mexi-
can and Puerto Rican industries. walters has cited studies
in his article which have determined the empirical value of
the capital input exponent to range from 0.1 to approxi-
mately 0.3 for countries such as Australia, Great Britain,
New Zealand, the United States, and India.11 The Western
developed nations cited in Walters' article have perhaps a
higher capital output elasticity than.Mexico or Puerto Rico.
Reviewing the historical development pattern of Mexico and
Puerto Rico, they could scarcely be called underdeveloped
in the same sense as India. It could be inferred that the
output elasticity of capital for Mexican and Puerto Rican
industries is generally higher than that of Indian indus-
tries but certainly not higher for most industries in the
western world. Also, given the relative capital produc-
tivity figures and labor productivity figures for Mexico and
Puerto Rico, the latter country's capital output elastici-
ties for the majority of industries could be considered
higher than Mexico. But certainly for both Mexico and

Puerto Rico capital output elasticities in most cases could

 

1Walters, "A Note on Economies of Scale," pp, cit.,
pp. 425-27. ‘

102
not be considered higher than the United States. A best
compromise for a common output elasticity for capital in
this study given all previous information would be 0.3.
With a value of 0.3 Mexican and Puerto Rican industries
would require much greater capital-labor ratios than United
States industries to achieve the same level of labor produc-
tivity. However, it would appear that policies which pro-
vide Mexican and Puerto Rican industries with greater capi-
tal-labor ratios than United States industries are both
capital and labor wasting. Some industries could realize
capital and labor shortages while others absorb dispro-
portionate amounts of capital and labor.

It should be mentioned at this point that the
results under increasing returns are not reliable enough to
support or reject the hypothesis. In both Tables 30 and
31, estimated capital productivities and labor efficiencies
are equal when the same capital and labor input exponents
are assumed for the compared countries. under identical
exponents for capital and labor for the compared countries
the labor efficiency ratio thus reduces to the productivity
of capital ratio. This however, is precisely the criticism
of Bacha's technique stated in Chapter I. It is seen that
the combinations and values of exponents severely affect

the outcomes. Tables 30 and 31 show that labor efficiency

103
levels achieved by Mexican and Puerto Rican industries are
lower under certain assumed exponent values than their
original labor productivity levels when capital-labor
ratios of similar United States industries are used. This
result is plausible if the United States capital-labor
ratio is lower than the Mexican or Puerto Rican capital-
1abor ratio. However, in the cases of Tables 30 and 31 the
lower labor efficiency results are due to the assumed
values and combinations of exponent values chosen for the
capital input.

The regression analysis pointed to a strong relation-
ship between the predictor variables and relative value of
output. Nevertheless, the wide scatter of points around
the regression plane indicated that factors other than
capital intensity strongly affect the relative value of
output. Some of these factors are managerial skill and
decision making, health and educational levels of workers,
and perhaps even elements like the quality of mail service
provided for the country in question. It has already been
shown that relative labor productivity differences in
Mexico and Puerto Rico are not eliminated when their capi-
tal intensity differences are eliminated. Then the
additional productivity gaps must be examined and explained.

As outlined earlier, the residual productivity

104
differences for Mexican and Puerto Rican industries could
in theory be attributed to five categories of factors:
(1) social, cultural, and political barriers affecting
attitudes toward work and capital accumulation; (2) differ-
ences in fuel and other material resource-related inputs;
(3) differences in the ages of capital stock; (4) differ-
ences in worker and managerial ability; and (5) differ-
ences in economies of scale as evidenced by output volume
and market size.

In the cases of Mexico and Puerto Rico social and
cultural barriers as a hindrance to economic development
can probably be dismissed. An unstable political process
is also not a hindrance. This view was supported by an
examination of the history of economic development for both
countries. Moreover, an examination of the data shows that
almost all industries are becoming capital intensive or at
least that net capital formation is occurring for almost all
the years examined. This situation is not likely to occur
in an underdeveloped economy where tradition remained
strong or where the political structure were highly
unstable.

The second possible reason for differences in labor
productivity in Mexico and Puerto Rico after removal of the

capital gap, namely the superiority of fuel and other

105
resource-related inputs used in the United States, is
outside of the scope of this study. The Cobb-Douglas
function is a two factor case and no allowance has been
made for differences in material inputs.

The third reason for productivity differences for
Mexico and Puerto Rico could be differences in the quality
of capital as measured by the age of their capital stocks.
If Mexican or Puerto Rican industries employ machinery and
equipment which are much older than United States indus-
tries, this could explain part of the labor efficiency
differences. However, there is reason to believe that the
capital stock is newer in Mexican and Puerto Rican indus-
tries than in United States industries. As previously
stated, Mexican and Puerto Rican industries with very few
exceptions are also becoming more capital intensive. Net
investment in almost all industries has been rising since
1956 for Mexico and since 1958 for Puerto Rico. There is
one qualification to this statement. Relatively lower
volumes in Mexico and Puerto Rico can lead to different
ages and qualities in capital machinery and equipment
employed by'Mexican and Puerto Rican industries.

There remain two other explanations of the causes of
labor productivity and efficiency differences for Mexico

and Puerto Rico: (4) differences in worker and managerial

106

ability; and (S) differences in market size or economies of
scale. When relative Mexican data are compared to relative
Puerto Rican data, capital-labor ratios and labor efficien-
cies are generally higher for the latter country. The
development pattern of both countries suggests that the
differences in the raw and calculated data point to greater
economies of scale for Puerto Rican industries because of
greater market size and production volume. Many Puerto
Rican industries also produce for the United States market
and therefore realize significant scale economies and more
organized marketing outlets for large production volume.

With the elimination of causes of labor efficiency
differences between Mexico and the United States and
differences in value of product and capital figures, it
must be concluded that economies of scale, managerial
ability, and worker capacity account for the labor
efficiency gap in Mexico. For instance, in Mexico, for
many industries "lack of volume and unpredictable demand
levels prevent gains from external economies by checking
internal economies. Production runs are too short and
demand levels unpredictable. Metal fabricators complain
about large volumes they have to buy from steel mills and
steel mills say that demand for special steel is too low

to make production worthwhile. It is also possible that

107

short production runs keep a worker low on the learning
curve."12 This prevents workers from solving breakdown and
maintenance problems. The supply of competent managers is
therefore hindered because promotion through the ranks is
not possible. Vocational training by private or govern-
mental means becomes especially important. Lack of good
managers can further lead to procurement problems, internal
supply bottlenecks, and poorly set up marketing channels
for distribution of final output. This last factor further
aggravates the situation of small markets for final output.

In Puerto Rican-United States comparisons, labor
efficiency differences are much narrower for the Puerto
Rican industries. From the data and previous discussions
it could be inferred that economies of scale are strong in
Puerto Rico and therefore account for higher labor
efficiencies. The labor efficiency differences which do
exist in Puerto Rico must then be due to managerial and
worker ability. There may perhaps be some scale economy
advantages for United States industries where Puerto Rican

industries produce only for the island market.

 

12Strassmann,.pp,_c__i_§_., pp. 162-65.

108

V. SUMMARY

Important results of the calculations were discussed
in this chapter. It was stated that the regression coef-
ficients showed strong relationships between relative and
average levels of capital intensity and relative value
added for the compared countries. Significant relationships
between the compared variables were also found in the popu-
lation according to "t" tests conducted for the sample
regression coefficients. Nevertheless, the unbiased coef-
ficient of determination revealed that factors other than
capital intensity play a strong role in determining labor
productivity. The maintained hypothesis was therefore
accepted. Labor and capital productivity differences were
discussed along with labor efficiency and capital intensity
differences among industries in the same country and
between years for the same country for'Mexico and Puerto
Rico. The causes of labor efficiency differences between
Mexico and Puerto Rico and the United States were examined
and it was found that the efficiency differences were due
to differences in (1) capital intensity; (2) worker and
managerial ability; and (3) economies of scale as indicated
by the size of the market for manufacturing output. How-

ever, economies of scale as a reason for efficiency

 

109
differences between Puerto Rican and United States indus-
tries were not considered an important factor since many

Puerto Rican industries produce for United States markets.

CHAPTER IV

SUMMARY AND CONCLUSIONS

This investigation began with a statement of the
hypothesis and general procedures for testing this hypothe-
sis. The hypothesis was that labor productivity levels for
less developed areas would not be as great as labor produc-
tivity levels in United States industries even if the
former countries worked with United States levels of capi-
tal intensity. Underdeveloped areas would necessarily
have to increase capital intensity levels by greater
amounts than United States levels to achieve the same
amount of product per unit of labor. The countries chosen
for the analysis were'Mexico, Puerto Rico, and the United
States. The United States served as the comparative
standard. The analysis used a multiple linear regression
equation and a Cobb-Douglas production function to test the
hypothesis. The remainder of Chapter I cited previous
international labor productivity comparisons discussing
their methodology and mathematical techniques. The
validity of the Cobb-Douglas procedure was also established.

Chapter II was specifically concerned with the
methodology of this investigation. The first part of this

chapter discussed the statistical procedures for testing

110

111
the hypothesis. The multiple regression equation was set
forth in arithmetic and logarithmic form and the terms in
the equation were discussed in great detail. The behavior
of the regression coefficients was then interpreted. Then
the procedures for calculating labor efficiencies were
explained under the Cobb-Douglas production function
assuming constant returns to scale. An explanation of the
calculation of labor efficiencies under increasing returns
by way of modification of the Cobb-Douglas technique was
also put forth. The second part of Chapter II was concerned
with the nature of the empirical data itself. The sources
of data, selection of years, and selection of industries
were enumerated. The terms output, capital, and labor were
defined and methods for estimating capital figures for some
years in Mexico and Puerto Rico were given. The Appendix
presents tables concerning the raw data and calculations
which result from applications of the equations to the
data.

The presentation in Chapter III was involved with
interpretation of the regression results and calculations
of the labor efficiencies under constant and increasing
returns. The regression function in the logarithmic and
arithmetic case showed that the b and b regression coef-

2 3
ficients were very high in all years for both Mexican-

112
United States and Puerto Rican-United States comparisons.
These coefficients also verified the Hirschman hypothesis.
Significant relationships were also found in the population
at the .0005 significance level for the variables used in
the regression function. The multiple correlation, determi-
nation, and unbiased determination coefficients showed a
wide scatter of points around the regression plane indi-
cating that factors other than relative and average levels
of capital intensity strongly affect relative labor produc-
tivity. The calculation of labor efficiencies showed that
in the majority of cases for all exponents, labor efficien-
cies in Mexican and Puerto Rican industries were not as
high as similar United States industries. Given the
results of the regression analysis and the calculation of
labor efficiencies, the hypothesis presented in Chapter I
was accepted for all plausible values of the output
elasticity of capital which could be assumed under a Cobb-
Douglas production function.

Several other results were proven other than the
original hypothesis. It was found that for a given level
of labor productivity, fluctuations in labor efficiency
come about because of changes in capital productivity
and/or changes in the capital-labor ratio. Under a constant

level of labor productivity among Mexican and Puerto Rican

113
industries, the higher the capital productivity ratio the
lower is the capital-labor ratio. The greater the capital
productivity ratio the greater is the level of labor
efficiency at the upper values of the capital output
elasticity value (0.9-0.7). At the lower values of the
capital exponent (0.4-0.1) there is virtually no difference
among labor efficiencies for industries with the same labor
productivities regardless of differences in capital produc-
tivities or capital-labor ratios. However, higher labor
productivities and efficiencies are caused by higher capi-
tal productivity ratios and higher capital-labor ratios in
general. An examination of differences among years for the
same industry shows further that differences in labor
productivities and efficiencies are caused by capital
productivity and capital-labor ratio differences. If capi-
tal productivities and capital-labor ratios both increase
between successive years, labor productivities and
efficiencies also increase. Decreases in capital-labor
ratios which are offset by increases in capital produc-
tivities do not affect labor productivity and efficiency
increases. Both labor productivities and labor efficien-
cies increase when a rise in capital productivity offsets
a fall in capital intensity. If the rise in capital

productivity does not offset a fall in the capital-labor

 

114
ratio, labor productivities fall in all cases. However,
in the majority of cases, labor efficiencies do not fall at
the capital exponent of 0.9-0.7 but fall nevertheless for
the lower exponent values of 0.4-0.1. If a fall in the
productivity of capital is offset by a rise in the capital- _5
labor ratio, labor productivities rise and so do labor
efficiencies except for the capital exponent values of 0.9-

0.7. For those values, labor efficiencies decrease. It

 

was thus concluded that changes in relative capital produc-
tivities were more important determinants of labor
efficiencies at the upper ranges of the capital exponent
(0.9-0.7) and that changes in relative capital-labor ratios
were a more important determinant of labor efficiencies at
the lower ranges of the capital exponent (0.4-0.1). The
figures further reveal that almost all Mexican and Puerto
Rican industries are becoming more capital intensive and
that net investment is occurring in nearly every single
industry. Employment figures are also rising in every
single case for Mexican and Puerto Rican industries along
with value of shipment figures, the latter indicating an
expansion of market size.

Relative Mexican and relative Puerto Rican data were
compared to each other and it was found that in most cases

for Puerto Rico (1) labor productivity is higher;

115

(2) capital productivity is higher; (3) the capital-labor
ratio is higher; and (4) labor efficiency is higher for all
exponent values of capital. Both countries have followed
similar economic development lines except that Puerto Rico
has had greater economies of scale as evidenced by the
larger markets for which Puerto Rican industries produce
and has had a somewhat more integrated economic development
in terms of planning for backward and forward linkages.
The data on market size here is taken to be value of
product or value of product per unit of labor and supports
the historical evidence of more economies of scale for
Puerto Rico.

It was previously stated that after Mexican and
Puerto Rican industries are equipped with the same capital-
labor ratio of similar United States industries, the Mexi-
can or Puerto Rican industries fall short of United States
productivity levels. An explanation of the productivity
gap exceeding the capital intensity gap was then under-
taken. The differences in labor productivity other than
capital intensity differences were stated as differences in
(1) superiority of fuel inputs; (2) ages of capital stock;
(3) worker and managerial ability; and (4) economies of
scale. Differences attributed to superiority of fuel

inputs and capital stock ages were eliminated because of

116
the nature of the data and the historical economic develop-
ment pattern of Mexico and Puerto Rico. It was thus con-
cluded that labor efficiency differences between Mexican
and Puerto Rican industries and United States industries
were due to worker and managerial ability and economies of
scale as United States industries produce for larger
markets. The scale factor as a cause of a labor efficiency
difference between the United States and Puerto Rico was
considered to be strong only when Puerto Rican industries

produced for the island markets.

Vina: .

 

BIBLIOGRAPHY

 

B IBLIOGRAPHY

Alejandro, Carlos Diaz. "Industrialization and Labor
Productivity Differentials," Review‘pf Economics and
Statistics, Vol. 47 (May, 1965), pp. 207-14.

Arrow, Kenneth, Hollis Chenery, Bagicha Minhas, and
Robert Solow. "Capital-Labor Substitution and Economic

Vol. 43 (May, 1961), pp. 225-47.

Bacha, Edmar. "A Comparison of Industrial Productivity
Between Mexico and the United States," §;,Trimestre
Economico, Vol. 33 (October-December, 1966), pp. 657-73.

Bator, Francis. "On Capital Productivity, Input Allocation,
and Growth," Quarterly Journal.p§ Economics, Vol. 71
(February, 1957), pp. 86-106.

Bentzel, R. "On the Aggregation of Production Functions,"
International Economic Pa ers, No. 8. New York:
Macmillan, 1958, pp. 74-90.

Board of Governors. "Financial and Business Statistics,
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APPENDIX

APPENDIX

TABLE 3

SELECTED INDUSTRIES FOR MEXICO AND THE UNITED STATES

 

 

Meat Products

Dairy Products

Dehydrated Frozen Fruits, and vegetables
Rice‘Milling

Canned, Dehydrated, Frozen, and Fresh Seafood
Bakery Products

Cane and Beet Sugar

Confectionery Products

Chocolate and Related Products

. Chewing Gum

Shortening and Cooking Oils

. ‘Manufactured Ice

Breweries

. Wines and Grape Liquors

15. Soft Drinks

P‘P‘F‘P‘F‘
$‘U’B3F‘C>¢>GD\IO\U|¢‘U)BDF‘

16. Animal Foods

17. Cigars

18. Cigarettes

19. Cigars and Cigarettes

20. Cotton Spinning and Weaving

21. ‘Men's, Women's, and Children's Underclothing
22. Sawmills

23. Wooden Containers

24. ‘Miscellaneous Wood Products

25. veneer and Plywood Plants

26. Wooden Furniture

27. Metal Furniture

28. venetian Blinds and Shades

29. Book Publishing and Printing

30. Commercial Printing, Lithography, and Book Binding
31. Leather Tanning and Finishing

123

32.
33.
34.
35.
36.
37.
38.
39.
4o.
41.
42.
43.
44.
45.
46.
47.
43.
49.
so.
51.
52.
53.
54.
55.
56.
57.
58.

59.
60.
61.
62.
63.
64.
65.
66.
67.

124
TABLE 3 (cont'd.)

Plastics

Organic Chemicals

Inorganic Chemicals

Fertilizers

Insecticides

Paints and varnishes

Pharmaceuticals and Medicines

Soaps and Detergents

Perfumes and Toilet Articles

Petroleum Refining

Paving Mixtures, Blocks, Asphalt Felts, and Coatings

Lubricating Oils and Greases

Hydraulic Cement

Gypsum

Lime

Iron and Steel Foundries

Pottery and Related Products

Steel Pipes and Tubes

Metal Doors, Sash, and Trim

Metal Engraving

Metal Drums and Containers

Cutlery

Bolts, Nuts, Rivets, and Washers

Boilers and Boiler Shop Products

Farm‘Machinery and Equipment

Office Equipment and Machines

Motors, Generators, Electrical Transformers,
Measurers, and Switchboards

Storage and Wet and Dry Batteries

Ship and Boat Building and Repairing

Locomotives and Parts

Tires and Inner Tubes

Motorcycles, Bicycles and Parts

‘Motor vehicles and Parts

Opthalmic Instruments and Lenses

Dental Equipment

‘Musical Instruments

 

 

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000x02 d, 0000»
mowuucpoo

0.0.us660 0 00000

133

 

 

 

 

 

 

 

 

000.00 000.00 000 000 .00
000.0 00 .00

000.00 000.00 000.00 000.0 000 000 .00
000.000 000.000 000.00 000.00 .00
000.0 000.0 000.0 000.0 .00
000.00 000.00 000.0 000.0 .00
000.00 000.00 000.0 000.0 .00
000.000 000.000 000.0 000 .00
000.00 000.00 000.0 000.0 .00
000.000 000.000 000.00 000.0 .00
000.000 000.000 000.0 000 .00
000.000 000.000 000.0 000.0 .00
000.00 000.00 000.0 000.0 .00
000.00 000.00 000.0 000.0 .00
000.00 000.00 000.00 000.0 000 00 .00
000.00 00 .00

000.00 00 .00

000.00 000.00 000.00 000.00 000.0 00 .00
000.00 000.00 000.0 000.0 .00
000.00 000.00 000.00 000.0 000.0 00 .00
mmfihu 9.60:.

0000 0000 000: 0000 0000 0000 0000M

. mwumum UNUSED 00.3002 uflflhugou

A. V. UGOOV 0 Waugh.

TABLE 7

)0

>lr-l

MEXICO AND THE UNITED STATES

CAPITAL-LABOR RATIOS (15") AND VALUE OF PRODUCT PER UNIT OF LABOR (

 

 

United States

beico

 

L

NA

1963

“Ir-l

i>MA

1958

nap:

 

“In-J

>I—‘l

1966

MIA

>|Fl

1961

MIA

>lu—‘l

 

1953f?

MIu-l

 

Y are

Indus-
tries

134

HORMONNO‘CMOQOMNOM
O O O O O O O C O C O O O O O O O
\OMOGNCO‘NlflowI-INOOHN
“QMO‘NNONWQOHM‘DNBH

QCN‘QHHGQNHNONM

nowfifioonédwofim
HHNHNr-l

10.3
12.7
3.3

ONONHQNU‘HNNMOQ’HVSH

JQI‘JO‘DI‘JGNO‘OBQOJN
“MNQNHQHMMO‘HNQHVSH

GNOMNQO‘NNNOQCQQNG

df‘ONMQHQO‘hQONI-ONQH
H N Flo—l

”HI-l HOWN cue-noon

O O O O O O O I O O. I O

meow menu-c oaomnmax

N H mv—nn as urn-net

nnh {\me wonoooo
. O O O C .0. O O

«can moons HNMNNH
H N H

O‘
OQMOV‘QO‘MO‘OO‘MOOQMH
I O O O O O O O O O O O O O O O O
NMMGQNQMHMBMQMOVNN
HF! NHN HI-i N

H
osmhoonnhaucoonmrdmms'r
NmHMNOethnmasONero

QOQQQMQNMMOOONNNQ

comerNoqu-cooougonna

G
fi‘OHQ‘DflMMMv-IQQOQMI‘:

NMNHNOIflv-IINNGNI‘ONMO

 

In
”0% HQWN ”ONONQ'
O O O O O O O O O O. O 0
{NC ONMI-l SHMHO‘O
H“ I"! HN Ifi
Mhl‘ HNQH ONHMQQ
O C O C O O O . O O. O 0
N00 003°C MNNOOO

HNMfiMONQO‘OHNMQmON
HHHHHHHH

TABLE 7 (cont'd.)

Un ted States

beico

 

 

 

Countries
Years

1963

1954

1966

1961

1956

4.953

r

 

>lv-l

MIA

>Ir-l

MIH

>Ir—1

#401

>lu-l

m0:

adv:

hflrl

>Io—l

MIA

 

Indus-
tries

63.8 11.6 74.7

7.8

16.2

3.4

12.8

3.9

0‘0
0 o
@0‘

NV}
0 O
«101

Nln

NH

7

('1
FIG

0
me

@3055

0H0
HHI—O

m
O‘HO
. .

omen

no
0.

moo
v-l

moo

ouxqootxq’om 00
O O O O O 0 O O O O O O O
~7H~O~OOMON CO
HHHHNHNN «m
wnmomfimvx Inn
¢N¢0§mn¢a~ hm
(fir-I
N (DOM <f~D
O O O O O O Q
0‘ mme cm H
HH HH an
o
m «hoax «1H
0 O O O O O
O va-i MN

Inc-4

mno
a o
@616!

\O
NM‘O
HHO

ONO:
MNH

Q x?
4‘50

OHO

d‘r-l

I-lr-l

O I

135

20.2
13.6
18.6
18.7
25.1
15.8
24.1
25.2

ND.I\I-C\DMI—lr-IH

fiq.w¢"'\.l-ion u—I
O

m 0
o o o o o o o o
NOP‘OInI-‘HN

wd’ONOWNOBv-fiw
o o o o o 0 o o o o o

N‘I’HMNQNQMQ‘O:

a:
NnNMNMOG®Nm
O
MOHOHHOH.N€M
B N
x? HMO‘ ON?
C O O O O O
H 0H0 NH
0 ma
h NnN no
0 O O O O O O O O
o GHQ 00

moo
\ONWQONN: Ofi‘
MN

0
coax

{CG
MMQ‘

h-c>0a
O O
I~\o¢n
H

NOH
C O

;963

 

1958

United States

1954

1966

"f

TABLE 7 (cont'd.)

 

1961

Mexico

1956

 

 

Countries
Years

136

 

oivw¢<mcocao¢0\h~¢<3 owcxocud30\<wor~
O O O O O O O O. 0 O O O O O
>|H NooounmvannHmo MHHmooovxx-ro
usg3aauswurwoopardwuo¢ 0:040:010404oarawv
«O‘NHNHOHsoHN. mqoonquq
O I O O O O O O O O O O
MIH \owmovxmmooxolnx-r. nowhoooooqo
(DuHoH\O¢ficfl F‘
OONNHNNMMOG Nm¢mmHomn
O O O O O O O O O O O O O O O O O O O O
NH @GHNQHQNGNN momNmono
mommNMHH NH HHHNHHNHN
omocnoNHNww dmeHthw
0 I O O O O O O O O O I O 0 0 O O O O O
mH mqmwwmmhnmm «wqhonomw
mHHMNH
m nOH H Hon
O O O O O O O O O
NH m 05¢ m mme
N NNH H H
m @HN w ONwm
O O O O O O 0 O 0
MH N 05¢ m QNNN
q NHH
@0fiO.¢Nwthh wm¢OHonm
O O O O O I I O O
NH omooMMNomOH NmnomomHn
HH NH
o m
mqmeH¢mmmn 00mmNNONm
O O O O O 0 O O 0
MH NonnhHHHNNo ONNNHHNmm
<1 H H H
HMNHQOONGOM #NmeHMOO
. O O O O O. O O O 0 O 0 O O O O O O O
NH mangoMNwwwH NMHMN¢€NH
n o H
momNoMNNmmm mNnomNnnn
mH OOHMSH.H0mmO ONNNQHHNO
no G h
H Nwm m nmoo
O O O O 0 O O
NH m Noo o OOHH
mm m hm¢N
d th o OBHH
O O O O O O I O O
mH 3 N00 0 oooo
I
3»
"ON-Q o o o O O o o o o o e o o o o o o o e o o 0
an OHNm¢nohmeHNm¢mohmeH
Hu ¢¢¢¢¢¢<¢¢¢mmmmmmmmmmoo

 

. .
. . . -
I . O
¢ - . . o
1 I
o . D n o c u
- x u v u . , . . . .
o . n . a . . n a
' ¢ 0 u . - .
_ o
. - D o O

‘+- 1W -‘

 

137

 

 

 

 

 

 

 

 

 

 

 

o.mH q.m M.¢M M.m m.m M.H N.M oq.o .Mo
M.HH n.~ o.M HM.o .om
m.q~ H.m M.HH m.¢ ¢.w m.m ~.m H.M ¢.H wo.o ~.H oq.o .no
M.mm ¢.NH H.mm M.HH ~.mH m.m m.~M M.M .qo
o.o~ M.n o.oH m.¢ m.¢ m.M H.q m.~ .mc
o.qm ~.oM w.w~ N.oa «.oN H.M m.ma m.q .No
mwfihu
-mscca
..._. m m. m m. m m m m m m m
> M > M > .nnyM >V M > M > M
moma mmma.lix an M [moMH HMMM onmfi mung»
muuuum v3.2.5 00.33: moan—“.550

A.v.ufl00v H. and“.

138

 

 

 

m.w om.o mm.o m.0 mq.o M~.o ~.m ¢~.o MN.o 0H
m.0 M~.o mo.o M.m om.o mm.o m.0 N~.o o~.o .mH
m.~M Mm.o o~.o M.MH mm.o «N.o m.qH mm.o MH.o .MH
M.mH oq.o mq.o m.~M m¢.o Mq.o M.¢H nm.o nm.o .MM
o.o~ m~.o ¢~.o 0.0 -.o m~.o N.m nH.o w~.o .NH
$.MH m~.o am.o ¢,qH o~.o Hu.o M.mH wH.o M~.o .HM
o.M mN.o qm.o M.« m~.o Hm.o o.m aH.o mN.o .oM
m.oM mm.o mm.o o.o q~.o ofi.o o.m MM.o oH.o .m
m.q Mm.o «M.o m.~ Hm.o m~.o n.m ¢~.o ma.o .m
o.MM o~.o Mo.o o.m~ q~.o MH.o ¢.MM MH.o Mo.o .M
m.m wo.o «M.o m.~ NM.o «H.o m.m mo.o HM.o .o
m.m Mo.o ON.o ~.m oM.o «m.o ¢.m no.0 w~.o .n
M.w w~.o 0H.o ¢.o MH.o mo.o m.M oH.o mo.o .e
o.m H~.o MH.o m.m mm.o MM.o ~.n MN.o mM.o .m
o.M mm.o Mm.o q.n on.o m~.o m.0 om.o «M.o .N
~.q mm.o om.o M.m ~m.o MM.o o.q o«.o oM.o .H
mmfimw.
I mflvGH
mM NM HM mM NM MM mM MM HM «M «M HM
moak}¢m¢u¢um mmMH ”mmuwum moofi "mmumum «mm» "mwumum
umUMao vegan: vegans nuggaa
coma "ooMMmz Momg "oOMMoz MoMM “oofixoz omMM "ooMMmz

 

 

mfifim 852: Sr... 8. ooHMM: Mom AmMV Emzflza 43.8% mo 3E5 @592 $2
.ANMV moHM<M.Mom<a-g<aHm<o M>HM<AMM .AHMV MoMMM mo 9H2: Mum sosooMm Mo mp4<>.m>~a<guM

m mHmflH.

IABLE 8 (cont'd.)

1961 Mexico: 1966

Mexico:

1961

Mexico:

1956

Mexico:

United

United

United

United

1963

States:

 

1958

States:

.-

1963

States:

1954

States:

 

o o o o o o s o o o o o o o o o o
o o o o o s o o o o o o o s o o o
00 COO 00900000 00 OD
HN MHN NHmHMNNN mm ”N
o o o e o o o o o o I o o o o o 0
CO COO 09000000 00 00
NO‘ 0*” ommwwmmmNQo \Da‘
0 o o o o o o o s o o e o s o s o
o o o o o o o o o o s o s so 0 o 0
QC 000 ooooooooooo oo
HN NHH ”HHHNHNHHNq NH
0 o o o o s o o o s o o 0 as o o 0
CO COO OOOOOOOOOOO 0°

0“!) Ha‘o O‘ONOONHON‘OM HM
o o o o s o o o o o s o o o o
NHI—l

o o o o o o o o o o o o o o o o o o
CO COO OOOOOOOOOOO 00
Q“ «Inn VCOQQNOQ’QQQ 0‘0
0"" NHH NHHHHHNHOHM HH
0 o s o o o o o e o o o o o o o o 0
CO 000 ooooooooooo CO
on HMH ”01-4 OH \ONOO

o o o o o o o o o o o a o o
no ”RN HNH ~O¢ thinmm

e o o o o o o o o o o o o 0
CO 000 COO CC 0000

H BOO NCO OHM”

OH OHH OHO HO NHHO

o o o o o o o o o o o o o o

 

Indus-
tries

140

 

 

 

 

 

A.o.u:oov a mqn<y

 

 

 

 

 

N.N NN.o oN.o N.m mo.o “H.o n.N Mn.o «H.o .oo
M.m MN.o mm.o M.q NN.o MN.o M.¢ mfi.o 9N.o .Nn
N.¢. MN.o mm.o N.m NN.o 0N.o N.N NN.c MN.o .Nn
o.m NN.o mN.o N.o No.N MN.o N.N ow.o oM.o .Nn
H.m mm.o 0N.o m.¢ MN.o nN.o M.q MN.o «N.o .on
m.n om.o mN.o N.N Mn.o oN.o m.n Hm.o No.o .nm
N.o Mm.o MN.o n.m NN.o MN.o N.n NN.o nN.o .en
o.¢ No.0 NN.o N.N NN.o 0N.o H.¢ NN.o OM.o N.M no.o mo.o .nn
o.q No.0 NN.o .Nm
n.N em.o qo.o .Nm
e.N NH.o No.o N.N n~.o No.o o.N NN.o No.0 o.N No.0 wo.o .on
N.NN Nw.o oN.o M.m nw.o MN.o N.NH nn.o mN.o .ae
m.q mm.o oq.o N.n No.N «N.o o.o Mm.o oN.o o.N No.o NN.o .Nq
o.oH m.N N.N N.» q¢.M no.0 N.N oN.N Nm.o .Ne
N.NH no.0 NN.o N.oH oo.o MN.o N.NN no.o No.o N.N No.0 No.0 .oq
N.NN No.o No.0 N.NN $0.0 ON.o N.NN «o.o mo.o N.» No.o No.o .me
N.Nq mN.o o¢.o N.¢N Nm.o Nm.o «.mm MN.o MN.o N.¢N oN.o MN.o .ee
o.NN om.o Nq.o N.m 0N.o oe.o o.oN MN.o Mm.o .Ns
0M.o Mm.o m.0 N.N NN.o ON.o m.» 0N.o no.0 .Nq
N.mo mn.o «N.o o.NN mn.o NM.o o.Nm em.o No.0 N.NN NN.o NM.c .Nq
q.q om.o oN.o m.N NM.o «N.o o.m «N.o oa.o .oe
N.NN «N.o MN.o N.M NN.o «N.o N.oH MN.o MN.o N.< NM.o NN.o .mm
asap»
unavau
mM NM NM mM NM NM mM NM NM nM NM NM

momN ”magnum wan “magnum mme “muuaum emNN “nouuum

nouNas couNaa uuuNpa vuuNca

cemN "ooNMmz NoNM “ouNMuz_ HoaN "ooMMoz onafi "ooNMmz

~ - I ~ . — o a
. ‘ Q C I Q 4 I
. . . . - . - - s

. . . o A . . o o .
o . n g . - u , o » l l .

o v u o ‘ u - A . v

. , t . ‘ c o a O
c - . 0 c 9 n n I - . .

- v r , . -

I ‘ O C ‘ .
~ -

 

 

     

 

 

141

m.N Nm.o HN.o H.N NH.o mo.o m.H ¢H.o wo.o .Nw

 

 

 

 

 

 

 

 

 

N.N co.o mo.o .oe
M.m NN.o NN.o N.N «N.o SN.o o.N mN.o NN.o c.N NN.o NM.o .no
N.m Nm.o «N.o N.o «N.o mm.o N.N «N.o NN.o .qo
m.m mm.o «N.o q.m Mm.o 0N.o N.N m«.o NN.o .Ne
N.NM ¢¢.o oo.o N.N N¢.o N¢.o N.oN MN.o oq.o .No
N.N Mm.o 0N.o w.¢ mo.o «0.0 e.n No.o mo.o .No
muHHu
unsvcH
mM NM MM NM NM NM mM NM MM mM NM NM
NomN “mmmem mnmN “magnum momfi “mmuaum «mofi "muumum
umuNca wouNca nouNaa wouNap
eemN nonfixmz NomN ”oONMuz NemN “ooqux onmN “oONMmz

A.u.u:oov a man<s

142

TABLE 8a

Y1, x2, AND x3 FOR MEXICAN AVERAGES (1961+63) TO
UNITED STATES AVERAGES (1958+63)

 

 

Industr es

 

92563926392ANAN3755—I.

365a-h32538558.4unv.5./.1...O.

1.. 1..
35577078279361.4297
542161144212432413
O O O O O O O O O O O O O O O O O O
000000000000000000
653644979495964 31..
221021032322423412
O O O O C O O O O O O O O O O O
000000000000000300

L2345¢°.78.9 0.11.2
1.11

14.
15.
16.
17.
18.

19.
20.

199

1.31.

0.71
0.2
0.2

21.
22.
23

24:

367..1...0.nu.4..9...
AHLBZthuhu—I.

93322318
42319211
0 o o o o o o 0
00000000
17643450
31213222
0 o o o o o o 0
00000000

25.
26.
27.
28.
29.
30.
31.
32.

33.
34.
35

0.30
0.47

9

00

36.
37.

5.7

0.34

0.31

143

TABLE 83 (cont'd.)

Industries

 

7

o o o o o o . o o . o o .
7033802519410
1 5 1311 1..
1235232004586
0 o o . o o o o o o o . o
0000000001000
. o o o o o o o o o o o o
0000000000000
. o o o o o o . o o o 0
8901234567890
3344444444445

51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.

6958476585400
0 O O O O O O O O O O O 0
35444343693m3

0.24
0.30
0.43
0,32
0.22
0.30
0.24
0.75
0.41
0.44
0.42

.0.65

0.14
0.25
0.20
0.25
0.16
0.35
0.29
0.12
0.18
0.55
0.25
0.27
0.20

62.
63.
64.
65.

0.19

66.
67.

2.2

0.26

0.17

 

 

144
TABLE 9

SELECTED INDUSTRIES FOR PUERTO RICO AND THE UNITED STATES

 

 

Fluid'Milk

Canned Fruits and Vegetables
Grain Mills

Bread and Related Products

Raw Cane Sugar

Distilled Liquor Except Brandy
Macaroni and Spaghetti

Knit Outerwear Mills

Throwing and Winding Mills
Women's and Children's Underwear
Corsets and Allied Garments
Fabric Dress and Work Gloves
13. Pleating and Stitching

. Millwork and Related Products
15. Wood Furniture Not Upholstered
16. ‘Metal Household Furniture

17. Corrugated Shipping Containers
l8. Pharmaceuticals and Medicines
l9. Perfumes and Toilet Preparations
20. Shoes Except Rubber

21. Luggage

22. leather Gloves

23. Purses and Small Leather Goods
24. Concrete Block and Brick

25. Concrete Products

26. Ready Mixed Concrete

27. Metal Doors, Sash, and Trim
28. Sheet Metal Work

29. Special Industry Machinery

30. Lighting and Wiring Devices
31. Electronic Components

32. Sporting and Athletic Goods
33. Costume Jewelry and Notions

Hudrd
NHOOQVO‘UIL‘WNH

H
b

 

 

145

 

 

 

 

 

“RN sod omo.~ .HN
wow.~ mom.H on~.afi nsn.H mo~.~ one.» .ON
mam «sm «Ho.e mod «on nmn.a .oH
coo mam.oa omo.h~ «on ooe.~ o~o.m .mH
omo.H mqm.mH mqo.m .sfi
mas hem ano.¢ aha wo~ Hue.~ .oH
mmm.~ omm.- ~q¢.~fi nH~.H cow.o~ ¢m~.m .nH
own ~so.~ m-.m nos mm“ noo.~ .sH
own was nfiq.~ .mH
NaH.H NNN «OH.o NBa an Naa.m .NH
Hmo.m s-.m «mm.qn mam.s oom.~ mwo.~u .HH
mmm.m qu.H~ aHH.- .oH
«a "as -n.~ .a
am¢.~ mam.n Nm~.mfl mmo.~ NNH.¢ wn~.- .m
mma “an oqm.H “Ha mss mho.a .5
om~.H moo.oH omo.sn mmo.H mam.- Hum.qfi .o
oom.o moo.~qm o~a.onfi mo~.~ «Nn.mo~ “Ho.-H .n
ems.“ ~m~.nfi «mm.wfi sna.~ me.~H osm.m~ .s
own mao.H omm.om .m
mmN.H m-.m omw.o~ mHa Hmm.~ msm.a .N
Non.H amn.~H mgo.ws ”HH.H o-.m~ ~eo.o~ .fi
mQHHu mafia—H
A x > a u >
moms wmmfi mummy

 

 

o." ”Ania

oon oemmsm mom any azmzwoamzu a<soa 92¢
.ooo.~» 2H .Auv mammm< A¢HHm<o amxam .A>V yuanomm so m=a<5

146

 

 

 

 

 

 

 

 

 

 

Hum H¢H.H wow.“ .mm
men.H omm.~ Nna.m .Nn
BHH.H emu mwN.sH an“ mus wam.< .Hm
Hmn ~m~.mH mcH.oH coo oam.a mmm.m .om
fine Huo.H ~m~.o “on mow aoH.n .aw
mmu ¢m~.~ me.m .mu
sac ems «Ho.ma «we won emu.“ .NN
an“ mm~.H on~.nH .o~
msm.H aeo.H mam.oH HN¢.H Heb o~m.¢ .mN
own nqo.H ooo.o NHn we“ mmo.~ .«N
ooq.H mos ~H~.m we~.s use an .nu
mm« and mqa.a .NN
mflflhu mfifiGH
a x > A u >

mama mnaa «any»

A.v.u:00v OH man<fi

147

 

 

 

 

mos.o~ mmw.sm mom.oH~ .HN
no~.NHN was.s- u-.-m.~ mmm.o- mam.o- NHo.HoH.N .ON
mmm.sm aHm.mH~ Noo.~mn.a «os.m~ omn.oeH «0H.amo.fi .oa
~H~.mm «mo.omm.fi mmm.efim.m N¢~.Nm ouo.mnm “HH.qu.~ .mfi
m-.mm Hs~.mmn hmfi.ooH.N .NH
osm.mN ~mm.~m nom.s~n mmm.om emfi.o~ hqfi.ooq .GH
Nwm.osH omm.n~q ~mm.~mw.~ aHo.n~H qwm.onn mo~.~mm.H .ma
sq~.~qfl wsm.non www.mflo.m m~o.nma ~m~.msn Hom.Hm~.~ .sH
mmm.oH mqm.~H me.OMH .nH
H-.~H «mm.¢fi mon.mqfi fiso.ma Noo.m mq~.mHH .NH
qu.~m omn.om mHo.mam mom.nm can.sq qu.~oe .HH
m-.o~ ms5.~ma moH.ohm .oH
amn.mH aNo.on Nn~.aam .m
osm.mo omo.o- o~¢.nso.fi omn.oo oom.mHH “an.mfim .m
o-.~ omm.o~ nsm.N- www.o oH~.~m omH.omH .5
moo.mH oqo.mmm Nos.omo.H m~n.o~ mm~.a- NHm.Hso .o
mom.m mqh.o~m 0Hh.m~m “mm.“ oso.~s~ ofio.waa .m
«mo.cm~ hso.~om.fi mom.mom.s oqw.sm~ noo.mmo.~ Nam.woo.s .q
moa.mHH s~w.~ao.~ oofi.HoH.m .m
wwm.~o~ nmo.me awn.mqu.~ s~q.wo~ o-.~mm nmw.mmm.~ .N
omo.mmH Nmo.mfie.fi Nmm.n~o.n me.NHN Hoe.sow.H mmm.-¢.o .H
w Oahu mDVGH
A x > a x >
momfl wmma mummy

 

 

Ha ".39;

mmu<wm ameHzn Mme mom Adv azmzwoamzm q<yoa oz<
.ooo.Hw zH .Auv mammm<bg<ymm<o omxam .A>v aopaomm mo u=g<>

148

 

 

 

 

 

 

nme.HN o~q.qq w~¢.ow~ .mm
mum.oq Noo.smH ma~.so~ .Nm
n~m.mm~ mam.omm.fi Nah.moa.m oHa.amH oos.~w~ oma.ms~.~ .Hm
swa.~mH mw~.mao «mo.a~m.N wHN.sNH mmn.nsq wNH.anH.~ .om
wNm.HnH om~.maH.H oo~.mom.m NoN.NoH e¢~.ooa osm.-s.~ .mN
Hnm.Ho oqo.h~m o~o.mom.fi .mN
oa~.~o mn~.qo~ sfim.mm~.d hmm.un “mo.¢H~ Hum.~mo.fl .nu
mmm.an ~N~.ooo.fi «on.~aa.~ .mm
um~.~m oww.ofis “he.m~m mmN.eq moo.om~ HHH.o- .nN
omn.m~ som.o- smfi.mom co~.- omo.on oho.mfic .qm
owa.om mqm.mm onm.omq wmo.nm wme.s~ ~o~.omm .mN
mHn.~ mum.o oso.ow .NN
m oak» mflvfiH
A u > a u >

mama mmmfl mummw

A.v.u:00v Ha mam<fi

TABLE 12

.15

(

CAPITAL-LABOR RATIOS

) AND VALUE OF PRODUCT PER UNIT

FOR PUERTO RICO AND THE UNITED STATES

L

or LABOR ({J

l963

United States

1958

1963

Puerto Rico

 

1958

 

 

 

 

C unt ies
Y ars

:>|.4

Mm

>lo-I

IKhJ

=flr4

MIA

:>m

MIA

 

ndu

nonnmommm

QQNWO‘QONU‘
I-I (fir-4H

Nln O‘MO‘QQ
O O O O O O O
OH In¢InIO€fl
MN HNQNH

coco NwIOInO
O O

Ind’ \TMMQN
(fir-I

wawman'rh
. o o o o o o o o

HNHI‘O‘NQNO‘
r-I QI-I

ea VIOJF~Ol¢I

O O O O C O

ouc> \or~aao\a>
,4 .4.4

[\In IDOGDIDO

O C O O I O

HO! Inl‘r-IMN
Flu-l

O
HNMfi'InIDNmGS

ONHV‘NO‘OQ
O O O

\Ov-IONOMUNVDI-n

r4p4

(VHF-INN

co
Inf-I'liNoman‘

HHOMMMO‘:

so.

N”
H

m
<V~3
O O

HO

BOG

\DHQ
r-II—II-I

31.7

moon H

O O

MNN O
H

Hofid'x'fd'ltln
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\T

In" In
MHHO‘lil-nNIn
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ION
{In

90
#0
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raoam
r4F4H

~¢r4«) «D
0

«Drum» en
a:

«>630: «a
HOP-l O
o:

O O O O O
~¢n \or\cn
FIH FIFIF4

TABLE 12 (cont'd.)

r

United States

Puerto Rico

1963

123:8

 

1963

 

1958

 

Countr
Year

 

>lp—I

MIA

>Ir—J

MIA

>Iu-I

MIA

>I—l

MIA

52.2
11.2

12.8

10.4

150

11.9
15,0

17.7

32.1
20.0
21.1
19.2
21.3
13.6
17.4

12.6

N
QMHwI—‘II‘O‘I—INMONOMO
o o o o o o o o o o O o 0

Own «one o ocm
O O O O O O O C 0
mm oaom h InINv-I
m HHH H HHH
N ox

OCh \DNN co OVDO
. O O O C C

no 0000 m somcr

HINInOO‘NNd’IOO‘QInwlfiIn

Honqdhhmmoonmnn

N

NHHHHH

NGQO‘

ON

0 IO
“MMMNMNQNBIONIDMN

 

Industries

NOOOOI-IOu—IOO‘HIOOI—IH
N

mm mHm N con
0 O O O O O O O O
«m onq o wHo
H H N
m o m m 5
mm MMN m «on
C O O . C O O O 0
no 0H0 o NHo
In
0 O O O C O O O O O O O O O 0
¢0HmnenonmmOH~m
HNNNNNNNNNNmmmm

 

 

TABLE 13

RELATIVE VALUE OF PRODUCT PER UNIT OF LABOR (Y1), RELATIVE CAPITAL-LABOR RATIOS (X2),

AND AVERAGE LEVELS OF CAPITAL INTENSITY (X3) FOR PUERTO RICO TO THE UNITED STATES

 

 

Averages

Puerto Rico
United States

1958+1963

1963
: 19S;

Puerto Rico:
United States

1958

Puerto Rico
United States:

1958+1963

I:

f

1958

1

 

Industries

 

151

on H
mm mHHO\N Chq NNw
O O O O O O O O O
ChN 0503061 00 MGH
m NNNH O‘N O‘d'ln
ION MHNQO NH ("INN
O O O 0 C O C C 0 O
HO HHOOH CO ONO
NH WGWNIn 0‘0 mcoox
com @mmmm mo ddd’
. O C O O O O O O O C O
CO 000°C CO 000

cod-x?
c>vsa3a3h~u><rvsvah~oxu>osu:o~o~<r

ommognvxmvmeOOc-nx-rHco

\OH NOON mm \0 NO
MMHGNOQO‘QMNHQMNHHN

HOOHHOOOHMOOHONOC

HO O‘NO‘NO‘InIDwInoowNw
oo~o.<r<1;~1'~om<r.<rmmo.cqc<r.<rH

OOHOOOOOHOOOOHOOOO

“In

”N Osx‘I'NNO ”N 0‘00‘
0 o o o o o o o 0
com émgou 00 NQH

€00me Hq \O m
on mowfl'o ql—I «and
o o o o o o a o o
No HHOOH CO ONO
Nq «I‘mmc MID “Q“
o o o o o o o o o o o 0
CO 00090 CO 000

o o o o
HHI—Ir—Ir—IHHg—I

TABLE 13 (cont'd.)

1958+1963

Averages

Puerto Rico
United States

1963

Puerto Rico:
United States

1958

Puerto Rico
United States

1958+1963

1963

1958

1

1‘

T

:-

 

Industries

1

 

152

\O 0
once 0000 In N<rm
O O O O O O O I O O
mqo 0mm N QmN
F4 F4
oxo InQH N cxxo<r
<r<run MHH H NMH
O O O O O O 0 0 O 0
H00 000 0 one
mmo NQO m OQH
OQQ 0mm 0‘ InO\€D
0 O O O O O O O O 0
H00 000 0 000
H CO

NIanIONInQONInMNIOQO

SQOHOOIDQGDNNQU‘NNH

O‘OQOIOHOMIn m QInC
HMQNQNHHHHQNOHHQIO

HOOOOOOOOOHOInOOO

OOO‘QNHQMMNQNQMO
NQOWMMMQNO‘InIanNMIO

HOOOOOOOOOOOOOOO

co co

wa InHIn m NIOQ
I O C O O O O O O O
InQO 0mm N Q36!
00 NNN O O Q
ON” WHH N QMH
O O O O O C O O O 0
N00 000 0 0:0
O‘Nln QQH H hoop
IOQIn IONC'I O‘ InNIn
O O O O O O O O O 0
GOO COD 0 GHQ

18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
32.
33.

31.

 

 

153

 

 

 

Aho.oV Aao.0v “moo.oV Awe.0v
mm.o wN.o Hm.o OH.H mn.H mm.o n~.o m~.o oo.H N¢.H m¢+wnma
o» oo+HomH
you mowmuo><
Amo.oV AoH.oV “moo.ov “mo.ov
mm.o ou.o m~.o oo.~ hm.H No.o om.o om.o oo.~ No.H mood on coma
“$0.0v Amo.oV “Hoo.ov Aeo.oV
me.o 0H.o aa.o mo.H mm.H om.o w~.o Hm.o co.” mm.H mama cu Hood
Amo.oV Amo.oV Amoo.ov Aoo.ov
Nm.o «N.o m~.o ao.~ n¢.H om.o m~.o Hm.o oo.H om.H wnoa cu Hmma
Ama.oV Amo.oV a~o.0v “No.0V
sq.o mH.o Nm.o mo.H Hm.H 0m.0 mo.o mo.o oo.H «H.H «mofl ou ommfi
m Na Na ma Np m «a mg mp Np mmumum conga:
can on oonmz
oHenuHumwoa 0HumE£uHu<

 

 

mMH<Hm anHZD mmh OH OUHNmzvumHmha<z< onmmmMumm NEH ho mBHDmmm

«H uHm<H

154

TABLE 15

PARTIAL AND ZERO ORDER CORRELATION COEFFICIENTS:

MEXICO TO THE UNITED STATES

 

 

 

 

 

Arithmetic

Mexico to the Partial Zero Order
United States R12.3 R13.2 R23.1 R12 R13 R23
1956 to 1954 0.30 0.03 0.03 0.30 0.04 0.04
1961 to 1958 0.56 0.06 0.01 0.56 0.09 0.06
1961 to 1963 0.56 -0.03 0.05 0.55 0.04
1966 to 1963 0.62 -0.008 0.06 0.62 0.04 0.07
Averages for

l961+66 to

l958+63 0.52 0.08 0.005 0.52 0.10 0.06

Logarithmic

Mexico to the Partial Zero Order
united States R12.3 R13.2 R23.1 R12 R13 R23
1956 to 1954 0.46 0.11 -0.04 0.46 0.11 0.02
1961 to 1958 0.50 0.12 -0.01 0.51 0.13 0.06
1961 to 1963 0.43 0.07 -0.004 0.43 0.08 0.03
1966 to 1963 0.52 0.13 -0.008 0.52 0.14 0.07
Averages for

1961+66 to

1958+63 0.54 0.18 -O.12 0.53 0.14 -0.03

 

 

155

 

 

Ame.0v Ame.0v Anoo.0v Amo.ov

 

mm.o 00.0 mH.o 3m.o 0H.H ¢¢.o oH.o aH.o oo.H mo.H mo+mmmH
ou mc+mmmH
you mowmuo><
Amo.0v Awo.ov Ahoo.oV Amo.oV
oN.o No.0 mo.o mH.H «m.0 wH.o mo.ou no.0 oo.H No.H momH ou momH
Aoo.ov Amo.oV Anoo.0v Aho.ov
mm.o wH.o n~.o mw.o 0N.H m~.o wo.on no.0 oo.H oo.H wmmH ou wan
m m m ma Np m m m mp Np muumum gouge:
NI N NI N 05”
oHasuHHmwoA oHuoazuHu< ou oowm cuumam

 

 

mmH<Hm DNHHZD NEH OH OUHM OHMMDA "mHmMH<z< onmmmmwmm HEB ho mHHDmmm

0H mHm<H

156

TABLE 17

PARTIAL AND ZERO ORDER CORRELATION COEFFICIENTS:
PUERTO RICO TO THE UNITED STATES

 

 

 

 

 

Puerto Rico to Arithmetic
the Partial Zero Order
United States R12.3 R13.2 R23.1 R12 R13 R23
1958 to 1958 0.19 0.09 0.36 0.24 0.17 0.38
1963 to 1963 0.08 0.13 0.27 0.12 0.16 0.29
Averages for
l958+63 to
l958+63 0.40 0.01 0.36 0.44 0.18 0.40
Puerto Rico to Logarithmic
the Partial Zero Order
united States R12.3 R13.2 R23.1 R12 R13 R23
1958 to 1958 0.45 -0.48 0.62 0.22 -0.29 0.52
1963 to 1963 -0.14 0.29 0.36 -0.03 0.26 0.34
Averages for
1958+63 to
1958+63 0.39 -0.17 0.54 0.36 0.06 0.53

 

 

157

 

 

 

00.0 0H.0 NH.0 nn.0 Hn.0 HH.0 «m.0 50.0 .0N
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nH.0 BH.0 0H.0 n~.0 su.0 50.0 0n.0 0H.0 .nN
~H.0 nH.0 n~.0 nn.0 sn.0 no.0 nH.H 00.0 .NN
0m.0 mn.0 00.0 0m.0 s~.H 0H.0 on.H nH.0 .0N
HH.0 0m.0 n~.0 no.0 0~.H no.0 00.H no.0 .mH
no.0 no.0 0H.0 nH.0 m~.0 HH.0 0n.0 «0.0 .0H
nH.0 n~.0 nn.0 on.0 nn.0 0H.0 ~0.H nH.0 .nH
NH.0 «m.0 0n.0 nn.o 0n.H no.0 on.H 00.0 .¢H
NH.0 «m.0 0n.0 0n.0 nn.0 nH.0 nw.0 <H.0 .nH
0m.0 nn.0 nn.0 ~n.0 00.0 Hn.0 0m.0 n~.0 .NH
nH.0 N~.0 n~.0 no.0 05.0 0H.0 on.0 NH.0 .HH
no.0 00.0 0H.0 Hn.0 no.0 No.0 00.H No.0 .0
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no.0 ~H.0 nH.0 nN.0 0n.0 nH.0 00.0 50.0 .s
no.0 00.0 0H.0 n~.0 50.0 n0.0 no.0 No.0 .0
«0.0 00.0 no.0 nH.0 nH.0 nH.0 nN.0 no.0 .n
no.0 00.0 «m.0 00.H ~0.~ HH.0 0n.n nn.o .N
5H.0 0~.0 H~.0 0N.0 o~.0 Hn.0 Hn.0 nH.0 .H
onuumscaH
H.o m.0 s.o 5.0 a.o magnum mufi>nu sua>au
unocoaxm usacH HmuHomu o£u mo mwsHm> Honda uoavoum nonmonm
0085mm< noon: mocoHonmmm uonma amonmz uHmuHamo Hmunamo uonqu
cmowxmz amonxm: amonxmz

 

 

can .mmH<Hm QMHHZD mmh OH .man .oonm:.mom mmHMHmDnzH nmhomamm 2H MUZMHUHhhm

mom<g az< .oae<m mom<a-q<aHm<o .wa~>~aooaomm A<9Hm<o .»HH>Hao=aomm woman no zomHm<mzoo

wH MHm<H

158

 

 

 

 

 

NH.0 «m.0 nn.0 nn.0 N0.H 00.0 n~.~ no.0 .nn
nH.0 on.0 on.0 on.0 nn.0 nH.0 00.H nH.0 .nn
NH.0 nn.0 on.0 nn.0 nn.H no.0 0n.H 00.0 .nn
nH.0 on.0 nn.0 nw.H no.0 No.0 00.0 ~H.0 .nn
00.0 00.0 00.0 00.0 HH.0 on.0 ~H.0 00.0 .Hn
no.0 nH.0 on.0 no.0 n0.~ No.0 00.n no.0 .0n
nH.0 on.0 nn.0 nn.H 00.0 No.0 00.0 NH.0 .nq
0H.0 on.0 nn.0 Hn.0 eo.H no.0 nn.~ no.0 .nw
on.0 00.0 0~.H 0H.~ 0~.N H0.0 00.n no.0 .nc
0H.0 «m.0 nn.0 nn.0 nn.0 0H.0 0H.H HH.0 .00
nH.0 nH.0 nH.0 nn.0 on.0 n~.0 H¢.0 HH.0 .Hq
nH.0 nn.0 nn.0 nn.0 Hn.0 ~H.0 00.H ~H.0 .0n
HH.0 nn.0 nn.0 no.0 nn.H no.0 ~0.N no.0 .nn
nH.0 on.0 on.0 on.0 nn.0 nH.0 00.H nH.0 .nn
NH.0 nH.0 NH.0 nn.0 nn.0 nn.0 Hn.0 HH.0 .nn
nn.0 nn.0 on.0 No.0 nn.0 nn.0 nn.0 0m.0 .nn
0H.0 0H.0 nH.0 nn.0 nq.0 «H.0 nn.0 no.0 .nn
0H.0 H~.0 nn.0 no.0 No.0 nH.0 nn.0 NH.0 .Hn
no.0 ~H.0 nH.0 nn.0 00.0 HH.0 nn.0 00.0 .nn
HH.0 nH.0 0H.0 nH.0 «m.0 No.0 0m.0 0H.0 .nn
monuumsoau

H.o m.0 «.0 5.9 o.o magnum Aufi>au Aua>flu

unocooxm unocH HmuHamo osu mo mosHm> Honma uosmoum nonooum

moaamm< wows: hoaoqoammm Hanna :monoz nHmunomo Hmonomo Honda
amonxgz confine: sundae:

A.0.ucouv wH mam<fi

. .
l D c O I a

a - o . - . I

" o i a n o
A l . l > I .

u . . . .

 

159

 

 

 

nn.0 nn.0 nn.0 nn.0 5n.0 on.0 00.0 0m.0 .nH
0H.0 nH.0 0m.0 on.0 nn.0 nn.0 no.0 NH.0 .5H
on.0 nn.0 nn.0 m¢.0 5n.0 no.0 nn.0 5n.0 .nH
nn.0 No.0 n¢.0 nn.0 nn.0 on.0 0H.H nn.0 .nH
«m.0 nn.0 nn.0 nn.0 5n.0 nn.0 5N.0 «m.0 .qH
Hn.0 00.0 no.0 nn.0 no.0 no.0 00.H 50.0 .nH
nn.0 on.0 nn.0 nn.0 05.0 nn.0 on.0 0H.0 .NH
nn.0 qn.0 00.0 no.0 on.0 0m.0 n0.H H~.0 .HH
nn.0 no.0 Hn.0 «5.0 «m.0 on.0 00.0 Hn.0 .0H
nH.0 nn.0 on.0 n¢.0 nn.0 «m.0 50.0 nH.0 .0
on.0 nn.0 5n.0 nn.0 00.0 Hn.0 «5.0 nn.0 .n
nH.0 5H.0 0m.0 on.0 00.0 «m.0 00.0 HH.0 .5
5H.0 nn.0 nn.0 No.0 «0.0 NH.0 5H.H «H.0 .0
nn.0 nn.0 5n.0 Hq.0 00.0 05.0 00.0 nn.0 .n
00.0 00.0 50.0 0H.0 nn.0 HH.0 5n.0 no.0 .0
nH.0 nn.0 0m.0 nn.0 00.0 nn.0 00.0 5H.0 .n
0H.0 «m.0 0m.0 on.0 qn.0 on.0 nn.0 nH.0 .N
nH.0 Hn.0 nn.0 5n.0 Hn.0 nn.0 nn.0 5H.0 .H
moHuumzmcH
H.o m.o s.o 5.o o.o magnum sua>ou mua>flu
ucmcoaxm usaaH Hmuwomo «nu mo mmsHm> Momma nonvoum nosvoum
omesmm< nova: noCmHonwm uonmq :monoz uHmuHomo HmuHamo Honda
fimonmz cmoaxoz. cmonoz

 

 

mama .mma<am ameuza use on .HomH .oo~xmx.mom mmnmampnzu nuaomgmm 2H wuzmaoammu

mom<a nz< .oHa<m mom<a-a<yum<o .»HH>Hso=aomm q<y~m<u .wau>uao=aomm mon<u mo zOmHm<mzoo

0H Mdmsh

160

 

 

 

nH.0 nn.0 Hn.0 ~5.0 0~.H 00.0 50.H 0H.o .nq
00.0 Hn.0 5n.0 on.0 H0.H nn.0 nH.H on.0 .00
nn.0 00.0 05.0 nH.H nn.H nn.0 55.H no.0 .nq
NH.0 nH.0 nn.0 00.0 5n.0 ~H.0 nn.0 0H.0 .Nq
0H.0 nH.0 5H.0 0m.0 nn.0 nn.0 nn.0 nH.0 .Hq
5H.0 «m.0 nn.0 n¢.0 on.0 5H.0 nn.0 0H.0 .00
nn.0 nn.0 00.0 on.0 0m.0 N~.0 mo.H 0m.0 .mn
nn.0 nn.0 00.0 on.0 no.0 nH.0 0H.H nH.0 .nn
5n.0 0n.0 nn.0 on.0 on.0 Hn.0 55.0 ¢~.0 .5n
on.0 no.0 05.0 0H.H nq.H 5n.0 nn.H «0.0 .nn
nn.0 on.0 nn.0 nn.0 05.0 nn.0 on.0 0m.0 .0n
nH.0 nn.0 nn.0 05.0 5H.H no.0 0n.H NH.0 .nn
nH.0 on.0 on.0 00.0 no.0 on.0 on.0 nH.0 .nn
nn.0 n5.0 nH.H H5.n HH.n No.0 00.~H 0N.0 .Hn
-.0 on.0 nn.0 nn.0 H5.0 nn.0 nn.0 nH.0 .0n
«m.0 nn.0 on.0 nn.0 n¢.0 n¢.0 00.0 nn.0 .0n
nH.0 5n.0 nn.0 nn.0 05.0 5H.0 «m.0 nH.0 .nn
0m.0 nn.0 on.0 «0.0 5n.0 nn.0 00.0 nH.0 .5N
0H.o nH.0 nn.0 on.0 00.0 Hn.0 5n.0 NH.0 .0n
nn.0 nn.0 nn.0 No.0 00.0 50.0 n¢.0 nn.0 .nn
Hn.0 on.0 0n.0 on.0 n5.0 Hn.0 nn.0 nH.0 .nn
Hn.0 5~.0 on.0 Hq.0 nn.0 nn.0 nn.0 nH.0 .-
on.0 nn.0 nn.0 nn.0 nn.0 50.0 00.0 nn.0 .HN
mowuumsmcn

H.o n.o «.0 ~.o a.o mofiuqm Aun>fiu mua>au

ucoaoaxm uaaaH Hmuwamo «nu mo nopHm> Honda uuavoum nusooum

0035mm< nova: nocuwoammm henna amoaxuz uHmuwoao Hmuaamu Honda
saunas: amonxoz. confine:

A.u.u=ouo a” ugm<y

161

 

 

 

0H.0 nH.0 nH.0 nn.0 0n.0 NH.0 50.0 00.0 .50
nH.0 on.0 nn.0 n0.0 0m.0 0H.0 0H.H 0H.0 .n0
00.0 on.0 m5.0 Hn.H 00.H 0H.0 0n.n nn.0 .00
nn.0 nn.0 0n.0 Nq.0 00.0 Hn.0 Hn.0 0m.0 .n0
nn.0 «0.0 00.0 00.0 no.H Nc.0 0H.H 00.0 .N0
no.0 00.0 Hn.0 nn.0 on.0 00.0 on.0 00.0 .H0
0H.0 nH.0 nH.0 nn.0 0m.0 00.0 «m.0 nH.0 .00
«m.0 nn.0 nn.0 H0.0 nn.0 nn.0 no.0 Hn.0 .0n
on.0 00.0 00.0 n5.0 no.0 nn.0 nH.H 0N.0 .nn
0H.0 0H.0 0H.0 nH.0 nH.0 50.H nH.0 <H.0 .5n
nn.0 0n.0 H0.0 00.0 05.0 on.0 0m.0 nn.0 .0n
HH.0 NH.0 nH.0 0H.0 nH.0 Hn.0 0m.0 0H.0 .nn
nn.0 on.0 nn.0 on.0 00.0 nn.0 05.0 nH.0 .0n
5H.0 nn.0 on.0 00.0 n0.o nn.0 n5.0 0H.0 .nn
no.0 NH.0 nH.0 0m.0 on.0 nH.0 50.0 50.0 .on
nn.0 nn.0 on.0 Hn.0 Hn.0 nn.0 nn.0 5n.0 .00
00.0 no.0 no.0 no.0 no.0 ~0.H no.0 00.0 .00
00.0 H0.0 on.0 nn.0 00.0 0¢.H 50.0 00.0 .50
NH.0 0m.0 0n.0 m5.0 an.H 00.0 nn.H HH.0 .00
umwnumnwaH

0.0 0.0 «.0 “.0 0.0 000000 sua>qu sua>00

unocooxm unacH Hmuwamo wnu mo moan> Honda nonvoum nosnoum

coesmm< nova: hocofiowmmw uonmq amuwxsz -Hauwauo Hmunouu Honda
amonxmz cuuuxoz_ swanky:

A.v.u:ooV 0H MHQ<H

162

 

 

 

0H.0 «m.0 0~.o 0n.0 n0.0 «n.o on.0 5H.0 .nH
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0~.0 on.0 qn.0 on.0 00.0 0m.0 m5.0 Hn.0 .0H
on.0 H¢.0 00.0 n5.0 ~0.H nn.0 nH.H 0m.0 .nH
0H.0 nn.0 n~.o nn.0 nn.0 nn.0 0n.0 0H.0 .qH
0n.0 00.0 nn.0 n5.0 00.0 nn.0 00.H nn.0 .nH
«m.0 nn.0 nn.0 00.0 00.0 nH.0 0N.H 0H.0 .NH
n~.0 nn.0 ~0.0 05.0 00.0 nH.0 5H.H Hn.0 .HH
on.0 H¢.0 00.0 00.0 HH.H 0H.0 mn.H nn.0 .0H
0H.0 5n.0 nn.0 nn.0 05.0 5H.0 00.0 0H.0 .0
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00.0 NH.0 0H.0 0m.0 0m.0 5H.0 H0.0 50.0 .5
0H.0 nn.0 0m.0 0n.0 00.0 00.0 «0.0 HH.0 .0
0m.0 nn.0 0n.0 0n.0 n<.0 n0.0 00.0 nn.0 .n
00.0 00.0 no.0 nH.0 on.0 0H.0 on.0 no.0 .0
nH.0 Hn.0 ¢~.0 0m.0 nn.0 Hn.0 N0.0 nH.0 .n
0H.0 0H.0 Hn.0 0m.0 nn.0 0n.0 0m.0 0H.0 .N
5H.0 0m.0 -.0 nn.0 nn.0 00.0 nn.0 0H.0 .H
mmHuumsvcH
0.0 0.0 «.0 0.0 0.0 000000 000>00 000>00
unocoaxm usacH Haunomo «nu mo mosHm> uonma nonvoum nonvoum
vmasmm< noon: 50cmnonmmm uonmq amonxwz -Hmunamo Hauqomo uoqu
cmoaxoz_ amowxmz amonxmz

 

 

0000 .000000 000020 000 00 .0000 .00000:.000 0000000020 00000000 20 0020000000

00000 020 .00000 00000-0000000 .000>00000000 0090000 .000>00000000 00000 00 2000000200

0N mHm<H

163

 

 

 

HH.0 Hn.0 0m.0 05.0 n¢.H 00.0 00.N 00.0 .n0
nn.0 00.0 5n.0 50.0 nn.H 5H.0 n0.H nn.0 .00
0m.0 00.0 0n.0 00.0 NH.H 0~.0 0N.H Hn.0 .n0
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00.0 nH.0 0H.0 00.0 0m.0 0m.0 0~.0 00.0 .H0
NH.0 0H.0 ~N.0 00.0 0n.0 00.0 0n.0 0H.0 .00
nn.0 nn.0 0n.0 00.0 00.0 5H.0 ~H.H 0H.0 .0n
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0.0 0.0 «.0 0.0 0.0 000000 000>00 000>00

unmcoaxm usanH Hau0awo 0:» mo muaHm> uonqa nonuoum unavonm

omBSmm< 000:: mocowoammm Honda coonxoz aHuuwamo HuUHauo uonqa
awoaxuz. cuoaxoz. cuowxmz

0.0.00000 00 00000

164

 

 

 

 

 

0H.0 0H.0 nH.0 nn.0 00.0 0H.0 5n.0 00.0 .50
0H.0 0m.0 0m.0 0n.0 nn.0 nH.0 00.H nH.0 .n0
5n.0 00.0 00.0 50.0 0N.H 0H.0 5n.H nn.0 .00
nn.0 5n.0 0m.0 5n.0 n¢.0 n0.0 50.0 Hn.0 .n0
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mo0uumsccH

0.0 0.0 «.0 0.0 0.0 000000 000>00 000>00

unocoaxm uaoaH HmuHQmo can no mman> uonug nonvoum nonvoum

coeamm< 000:: 00:600000m hogan amouxoz. aHuu0ouo Huuaaoo Honda
cwoaxmz awowxmz_ cuonxmz

A.v.u:oov 0N mgm<9

165

 

 

00.0 n¢.0 n0.0 on.0 nn.0 H5.0 nn.0 0n.0 .HN
nH.0 nn.0 nn.0 nn.0 Hn.0 NH.0 00.H NH.0 .5H
00.0 00.0 ~n.0 05.0 00.0 0m.0 ~0.0 0n.0 .0H
00.0 no.0 00.0 00.0 NH.0 Hn.0 0H.0 no.0 .nH
0m.0 5n.0 ~0.0 0n.0 05.0 Hn.0 00.0 0m.0 .qH
nn.0 ~0.0 50.0 00.0 00.0 00.0 00.H 00.0 .nH
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0n.0 00.0 0n.0 n0.0 0N.H 0H.0 nn.H 0m.0 .HH
0n.0 nn.0 0n.0 00.0 nH.H nn.0 0n.H 0n.o .0H
~0.0 50.0 on.0 H0.0 00.0 nn.0 05.0 0n.0 .0
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no.0 NH.0 nH.0 nn.0 0m.0 0H.0 00.0 50.0 .5
nH.0 on.0 nn.0 nn.0 0n.H no.0 n5.H 0H.0 .0
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HH.0 nH.0 50.0 0~.0 Hn.0 nn.0 0n.0 0H.0 .0
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0n.0 00.0 n0.0 00.0 «5.0 0m.0 05.0 Hn.0 .N
nn.0 0m.0 0n.0 50.0 nn.0 nn.0 5n.0 on.0 .H
mm0uumavcH
0.0 0.0 «.0 0.0 0.0 000000 000>00 000000
ucmcooxm uaacH Hmuaamo onu mo muaHm> Honda tosvoum nonvoum
cmBSmm< 000:: mocm0owwmm 00000 :mo0xmz_ -0000000 Hmuaamo 00000
awo0xmz_ £00000: cmo0xmz

 

 

n00H 0mm8<8m anHZD mmh OH .000H .oonmz.mOh muHMHmDDzH amsomamm 2H VUZMHUHhhm

mom<H nz< 00H9<m mom<HaH<HHm<o 0>9H>HHUDQOMM H<HHm<o .MHH>HHUDQOMM mom<H ho ZOmHm<mzco

HN mania

166

 

 

 

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mmwuumavcn

0.0 «.0 0.o ~.o a.o 000000 >00>00 h0030

uamcoaxm uamcH Hmuaamo mnu mo uoaHu> henna nonvoum soavoum

coBSmm< umvab hufiuwowmmm Honda aquaxuz. -Huuwauu Hangman Honda

auouxmz auoaxmz auowxmz

A.u.0aoov H~ mgm<a

167

 

 

 

 

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0.0 m.o q.o ~.o 0.0 00000« >00>00 kn0:30

ucmcoaxm unaaH kuuamu 0:» mo m05~w> Magma uunvoum uoavoum

noabmm< nova: Aocuuowmmu hogan cuowxuz_ -Huuaauo Hauaauo Honda
caviar: squeal: cuowxmz

A.o.0coov HN man<a

168

 

 

 

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0.o m.0 0.o ~.o 0.0 000000 000>00 h00>00

ucmcoaxm unacH kuwawo «nu mo mmnam> henna uuavoum unavoum

0masmm< umvco hocmaowmwm Henna cwouxm: -Hmuwamu Hmuwawo Henna

cmoaxmz cmoaxmz amoaxmz

 

 

Am0+wmofiv mmu<mm>< mme<em amaaza ca
Am0+0om~v muu<mm>< z<ouxmz_mom mmHmemaazH auaomamm 2H.»pzmHonmm

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NN NAM<H

169

 

 

 

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0.0 m.0 0.0 0.0 0.0 000000 h00>00 >00>00

ucwcoaxm unacH kuwamo onu mo mm5~a> Honug nonvoum nonooum

cmBSmm< 000:0 zocowowmmm Honda amouxmz_ -kuwawo kuaamo Henna
amuqxoz. cuowxmz nuoaxoz

A.v.u600v NN mam<fi

170

 

 

 

 

 

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ucwcoaxm unaaH Hmuaamu m£u mo mmus> Honwa nosvoum nonvoum

0masmm< 060a: muamuoammm Hanna cwouxwz_ -Huuaamo kuuawo uonua

cwouxcz cmuwxuz :uowuuz

“.0.u=00v NN mum<9

171

 

 

 

mm.0 00.0 nn.0 00.0 00.H 5H.0 00.H 0m.0 .0N
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00.0 00.0 nn.0 0m.0 mm.0 nn.0 Hn.0 H0.0 .0
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00.0 00.0 00.0 00.0 ~0.0 00.~ 00.0 05.0 .H
mmwuumavcu
0.0 0.0 0.0 0.0 0.0 000000 000>00 000>00
uamcoaxm usaau Hauwawo Honwa nonvoum nonvoum
0:0 00 00500> 008500< 000:: ufimuwmwo awuaauo Hanna
hoamwowmwm Henna cwuam ouumam caudm c0000 cuuwm
000000 000000 ouuusm

 

 

0000 .000000 000020 000 00 .0000 .0000 000000 000 0000000000 00000000 20 0020000000
00000 az< .00000 00000-0<HH0<0 .000>00000000 00000<0 .0HH>00000000 00000 00 00000<0zo0

MN mania

172

 

 

 

 

 

Hn.0 no.0 n~.0 om.~ oq.m 00.0 00.0 ww.o .0n
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0.0.00000 00 00000

173

 

 

 

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mocmwowmwm 00900 60000 000050 6000M 00000 60000
ouuwnm ouumsm ouuusm

 

 

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174

 

 

 

 

 

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175

 

 

 

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176

 

 

 

 

 

mm.o oq.H mn.H H~.m mn.¢ «H.o mn.n Hn.0 .Hm
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178

 

 

 

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uuunmaaz yoga;

woucwfimz Hauaaao

uzu cu coaxmz

 

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179

 

 

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mzu mo mmsau> vmasmm¢ nova: moaumm hoamwowwmm Honda awmz hufi>wuosvoum ooflm ouumam

uonwa cum:

 

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180

 

 

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181

 

 

 

 

 

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on mania

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182

 

 

 

 

 

mucmcoaxm w>qumcu~ua<

nuns: uocwwoawwm
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autocomxm u>wuwaumua< Haws:

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