Tài liệu Research " A diserttation submitted in partial satisfacion of the requirments for the degree Doctor of Philosophy in economics " ppt

Value Added Growth, TFP Growth, and the Rate of Return, Mexican Manufacturing Sector 1984-1994 1893 firms.. ccccceecccc cece ceeseceeeseneeesssesseesecessecessseecessessessssessssesseses

UNIVERSITY OF CALIFORNIA

Los Angeles

Productivity and Profitability

in the Mexican Manufacturing Sector:

1984-1994

A dissertation submitted in partial satisfaction of the

requirements for the degree Doctor of Philosophy

Bell & Howell Information and Learning Company

300 North Zeeb Road P.O Box 1346 Ann Arbor, Mi 48106-1346

The dissertation of Leonardo Egidio Torre Cepeda is approved

Arnold Harberger, Committee Chair —-——

University of California, Los Angeles

2000

For their patience, support and love, I dedicate this dissertation to:

2.7.1 Comparing Series na 3 36

Appendix 2.1 Criteria for Cleaning the Data Q Q HH ng S2 vsrrsee 49

Appendix 2.2 TFP Growth in the Mexican Economy Q co coecccecce 50

II CONCENTRATION PATTERNS OF PRODUCTIVITY GROWTH: THE

3.2 Understanding Economic Growth: The Theorist”s View ẶQ Q22 Ssằ 53 3.3 Understanding Economic Growth: The Empirical Worker’s View 55 3.4 TFP Growth and the Nature of the Growth Process : Evidence from Aggregate and Microeconomic Data c:cccccecccessseccecsscceececcesesseceserscecesessesseesssecesseneee 60 3.4.1 Constructing Sunrise-Sunset Diagrams 0.0 000000 cccccccceeececesceeesceseeeeeee 61 3.4.2 Sunrise-Sunset Diagrams : The U.S Economy 1948-1985 2000000000000 63 3.4.3 Sunset-Sunrise Diagrams : The British Manufacturing Sector 1954-1986 .69 3.4.4 Sunset-Sunrise Diagrams : The Mexican Manufacturing Sector 1984-1994.73

Appendix 3.1 The U.S Economy, List of Industrial Sectors 87

Appendix 3.2 Bristish Manufacturing, Industries Covered by the Census of

“AI 3o n n 113

“ ' 116 4.5 Concluding Comments 0 0 0.cccccccceccceccccsscsccesssececesssecsecenseccerseerenssestsees 123

3342.125101 130

List of Tables:

2.1 Coverage of the Annual Industrial Survey 1984-1994 HH 22

2.2.a Average Rate of TFP Growth 1984-1989, Mexican Manufacturing Sector 31

2.2.b Average Rate of TFP Growth 1990-1994, Mexican Manufacturing Sector- 32

2.2.c Average Rate of TFP Growth 1984-1994, Mexican Manufacturing Sector 33

2.3 TFP Growth for Different Values of “” ng TH TT TT nay 34 2.4 Estimates of TFP Growth, Mexican Manufacturing Sector 1984-1990 38

2.5 Estimates of TFP Growth, Mexican Manufacturing Sector 1984-1990 40

2.6 Aggregate vs Weighted Estimates of TFP Growth, Mexican Manufacturing 1984- 2.7 TFP Growth in the Mexican Manufacturing Sector 1984-1994, Nine Industrial si) HH 45

2.8 Estimates of TFP Mexican Manufacturing Sector 1984-1994 Ặ5 2Q S2 ằ 48 3.1 TFP Growth for Six Countries (Annual Average Compound Growth Rates) 57

3.2 Annual Average Rates of GDP and TFP Growth, 1950-1987 (96 Countries) 58

3.3 Annual Average Rates of GDP and TFP Growth, 1950-1987 (96 Countries) 59

3.4 Sectoral Rates of TFP Growth, U.S Economy, 32 Sectors 1948-1979 68

3.5 Sectoral Rates of TFP Growth, U.K Manufacturing Sector 1954-1986 72

3.6.Differences in TFP Growth: High Productivity vs Low Productivity Firms 81

3.7 TPP Growth in the Mexican Manufacturing Sector 1984-1994 82

4.1a .Profitability in the Mexican Manufacturing Sector 1984-1989, 44 branches (%) 99

4.1b Profitability in the Mexican Manufacturing Sector 1990-1994, 44 branches (%).100

4.1c .Profitability in the Mexican Manufacturing Sector 1984-1994, 44 branches (%) 101

4.2 Distribution of Median and Mean Values of Branch Level Rates of Return, Mexican

Manufacturing Sector 1985-1984 0000.0 ccecccesceccccescesereseccecccsscessececsceeeeee 103

4.3a Profitability in the Mexican Manufacturing Sector 1985-1994, Median Rates of

Retum, 44 branches (3%) _ - HQ HH HH HH TH TH HT TT HH TT TH TT nen vay 104

4.3b Profitability in the Mexican Manufacturing Sector 1985-1994, Median Rates of

Return, 44 branches (%) 000000ccccccccessseseeeeesescccesseceecececccecececececececcecececeeeeees 105 4.4 Value Added Growth, TFP Growth, and the Rate of Return, Mexican Manufacturing Sector 1984-1994 (1893 firms) .20 000.0.cccccccccecccccceececesecessssecseeees 106

4.5 Mean and Median Rates of Return by Region, Mexican Manufacturing Sector 1984-

1994 (Wo) 00.2 ccccceecccc cece ceeseceeeseneeesssesseesecessecessseecessessessssessssesseseseesesecessnsesteceeenses 108 4.6.Raters of Return in the Mexican Manufacturing Sector 1984-1994 (Assumes 15% downward adjustment in income attributable to capital for all fims 109 4.7.Rates of Return in the Mexican Manufacturing Sector 1984-1994 (Assumes 15 % downward adjustment in income attributable to capital for firms of sizes I and II 110 4.8 Gross Profit Rates for Whole Manufacturing Sector by Country, Selected Years

List of Figures :

2.1.GDP, Net Capital Stock and PPI Deflators 1984-1990 (1980=100) 42

3.3 Sunset-Sunrise Diagrams, U.K Manufacturing 1954-1986, 130 Sub-sectors 70 3.4 TFP Growth Profile in the Mexican Manufacturing Sector 1984-1994, 1893 firms.73 3.5a TFP Growth Profile for Fast-Growing Branches, Mexican Manufacturing 1984-

3.5b TFP Growth Profile for Medium-Growing Branches, Mexican Manufacturing

bS 76

3.5c.TFP Growth Profile for Slow-Growing Branches, Mexican Manufacturing 1984-

3.6a Average Annual TFP Growth Rate, Mexican Manufacturing Sector 1984-1994, Frequency Distribution, 44 Industrial Branches .00 00 000 cccccccececccescceeeeceeeee 79

3.6b Maximum Average Annual TFP Growth (Maximum Ordinate of TFP Growth

3.6c Percentile with Positive TFP Growth, Mexican Manufacturing Sector 1984-1994, Frequency Distribution, 44 Industrial Branches 00000.00 00 ccccccccccceccceccceseseecceeceee 79 3.6d Percentile where Cum Sum TFP Contribution=100 percent, Mexican Manufacturing Sector 1984-1994, 44 Industrial Branches HH sec 80

4.1 Economic Regions in Mexico 107

ACKNOWLEDGEMENTS

I am thankful to all the committee members for their assistance in providing helpful comments and suggestions I am particularly indebted to my Committee Chair, Amold Harberger, for his patience and constant advice through all stages of this work I also thank Kenneth Sokoloff for encouraging me to finish this work

Georgina Kessel, Nicholas Oulton, Luis Rubalcava, Chely Teruel, Jesus

Amozurrutia, Juan Moreno and Nidia Tijerina provided the data I employed in this work and therefore I am thankful to them

I would also like to thank Enrique Flores, Hajime Hadeishi and Ann Rabe for his comments and invaluable help in the early stages of this work

Teaching Assistant Universidad Autonoma de Nuevo Leon

Monterrey, Mexico

Teaching Assistant University of Cincinnati M.A in Economics University of Cincinnati

Research Assistant

University of California, Los Angeles

Teaching Assistant University of California, Los Angeles

M.A in Economics

University of California, Los Angeles

C Phil in Economics University of California, Los Angeles

ABSTRACT OF THE DISSERTATION

Productivity and Profitability

in the Mexican Manufacturing Sector: 1984-1994

by

Leonardo Egidio Torre Cepeda Doctor of Philosophy in Economics University of California, Los Angeles, 2000 Professor Armmold Harberger, Chair

This dissertation consists of three essays that look at the behavior of productivity growth and investment profitability The first chapter presents a new set of productivity growth estimates for the Mexican manufacturing sector for the period 1984-1994 computed under the Two Deflator Method, and compares them with existing estimates The comparative study presented here shows that the pattems of productivity growth differ widely across different studies, but more importantly, the more recent estimates suggest that the behavior of productivity growth may not be as vigorous as it has been reported The second chapter asks whether the smooth and pervasive process of economic growth implied by neoclassical models and new neoclassical (endogenous) growth models, is consistent with the empirical evidence Employing data from the United States economy

1948-1985, the United Kingdom manufacturing sector 1954-1986, and the Mexican manufacturing sector 1984-1994, it is shown that the process of productivity growth is highly unstable and concentrated, no matter whether we look at it from an aggregate or microeconomic perspective These results support the view that new neoclassical models are an inadequate vehicle for organizing understanding about economic growth The third chapter looks at the determinants of investment profitability using data from the

microeconomic, and geographic location forces should be simultaneously considered when attempting to account for the behavior of rates of return at the microeconomic level.

L INTRODUCTION

For decades, researchers from different backgrounds and profiles have supplied innumerable attempts for shedding light on why some economies perform well and why

others do not As the literature has developed, new issues have been raised and more

specific questions have had to be addressed Today, and as a result of all these years of struggle, the economics profession is served by a complex theoretical literature that identifies channels leading to sustainable per capita output growth; and also by more sophisticated methodologies for measuring the sources of economic growth

Although researchers in the subject are possibly overwhelmed by the abundance and diversity of this theoretical and empirical literature, it is fair to say that there is still a lot of work to do in the area In particular, the wider availability of better data at the industry and firm level continuously opens the door for studying in more detail the nature

of growth process For any given country, for example, interesting lessons may be

learned by providing estimates of output and productivity growth that employ new data sets or better methodologies Additionally, there is the opportunity to contrast the implications of aggregate models of growth with what actually happens at the

microeconomic level On this point we may ask, for example, whether the growth process

is fairly widespread across an economy -as implied by neoclassical or new neoclassical models of growth-, or whether is highly concentrated across sectors or firms Additionally, we could ask whether it makes sense to study the determinants of productivity -and hence output- growth through regression analysis, specially when the data available is at the firm level.

Considering the opportunities that new theory, methodology, and data offer, in this dissertation I present three essays oriented to shed light on some of the issues raised above

In Chapter IT I employ a new data set and apply a recently developed methodology to estimate total factor productivity (TFP) growth in the Mexican manufacturing sector Although the initial idea of this essay had been simply to illustrate

the implementation of this new methodology, it turned out that the exercise provided an

interesting finding, namely, that TFP growth in the Mexican manufacturing sector during the period 1984-1994 had not been as dynamic as it had been suggested by previous studies In particular, while existing studies report that TFP in the Mexican manufacturing sector grew on average at rates in excess of 5-7 percent during the period 1984-1990, my estimates show that for that same period the average annual rate of TFP growth

fluctuated between -1.6 and -1.1 percent Moreover, when considering the whole period

1984-1994, the same trend held This is an interesting result for it suggests that structural changes during those years -trade liberalization, deregulation, privatization, etc.- did not bring about the expected gains in dynamic efficiency as suggested in other studies

Chapter HI, on the other hand, had its motivation in the differences that

theoretical economists and practitioners have had when trying to understand the growth process In particular, while theoretical economists have become increasingly satisfied

with modeling a few transmission channels that allow an economy to register sustained

positive per capita growth in the steady state -as shown in neoclassical and new neoclassical models-, some practitioners have been pressing on the difficulties that those

models face when attempting to capture essential features of the growth process This latter group argues that aggregate neoclassical and new neoclassical models convey a picture of a stable and smooth growth process, when in fact this process is much more complex, highly irregular and concentrated My essay attempts to identify features of the growth process that may be of help in this discussion In reaching this goal, I employ data

from different countries (Mexico, United Kingdom, and United States) at different levels

of aggregation (firm, industry, and sector level) during different time periods to document whether the growth process is steady and uniformly widespread, as implied by aggregate models of economic growth; or, instead, is unstable and concentrated

My examination of the concentration patterns of TFP growth in the countries studied suggests that the process of economic growth is, in fact, very unstable and

concentrated, no matter the level of aggregation, or time period we choose to look at

These findings imply, in turn, that theoretical research focused in developing models in which one or two forces lead to sustainable growth is, for the most part, misguided

Certainly, more empirical work at lower levels of aggregation -branch or firm level- is required for it is there where the forces that lead to higher productivity and output growth are located

Having established that productivity growth -and hence output growth- is the result of a complex process of competition among economic agents, in Chapter IV I shift

to study the determinants of investment profitability at the firm level using, once again, the data set from the Mexican manufacturing sector The reason for studying the rate of return to investment in a dissertation focusing on productivity and output growth is not

hard to discern since this variable plays a key role in the motivation of economic agents The search for increasing investment profitability is one of the main engines behind economic agents’ efforts to reduce costs Therefore, learning more about the behavior of the real rate of return and its determinants is essential for improving our understanding of the growth process

In the empirical implementation presented here I find that investment profitability depends on macroeconomic, microeconomic and geographic location forces In particular, my results suggest that investment profitability at the firm level is related to aggregate output growth, the real exchange rate, the inflation rate and the level of trade protection I also find that firms located in regions with better infrastructure and market conditions tend to register higher rates of return These results, which are robust to the empirical implementation adopted, reinforce several well established policy lessons about the elements that promote investment and hence growth

il PRODUCTIVITY GROWTH IN THE MEXICAN MANUFACTURING

SECTOR 1984-1994: AN APPLICATION OF THE TWO DEFLATOR METHOD

2.1 Introduction

During the 1980’s many developing countries embraced market-friendly reforms

seeking to alter the structure of payoffs in their economies and lead economic agents to respond at the microeconomic level with better and more efficient ways to engage in their

productive endeavors The freeing up of external trade, promotion of foreign direct investment, elimination of subsidies, fiscal adjustment, fight against inflation, among others, were essential elements in this international economic transformation This wave

of changes, in tum, has invited economists to gauge the effects of such reforms on output

and productivity growth at both, microeconomic and aggregate levels

The Mexican case, and particularly the experience of its manufacturing sector, has been a fertile ground for this research Recent studies report a significant impact on productivity growth from the structural reforms started in the mid 1980’s However, it is interesting to note that, despite the relevance of the subject and the well known sensitivity

of productivity growth estimates to the techniques and data sources employed, so far there are no comparative studies on productivity growth for the Mexican case This fact leaves us without answers to questions such as the following: Can we feel comfortable with the estimates of TFP growth reported in these studies? Do the same patterns of productivity improvement emerge across different estimates? Is the existing evidence strong enough to support the view that a significant improvement on TFP growth has been registered within the Mexican manufacturing sector? This chapter attempts to provide answers to these questions In this pursuit, I employ data at the establishment level for 44 industrial branches of the Mexican manufacturing sector for the period 1984-

1994 to compute an alternative set of TFP growth estimates Then, I proceed to compare these estimates with those reported in other recent studies to determine whether a consistent message emerges out of them

My work suggests that due to both methodological and data considerations, it is not possible to convey a clear picture of productivity performance within the Mexican manufacturing sector during the period in question There are important differences among TFP growth estimates In particular, while some estimates convey a rosy picture

of productivity performance, other estimates indicate the opposite The differences are significant not only in terms of the levels of TFP growth among industrial branches, but also in terms of their rankings

The chapter is organized as follows: Section 2.2 presents an overview of the Mexican economy during the period 1984-1994 Section 2.3 briefly surveys the growth accounting framework and outlines the nature of TFP growth Section 2.4 describes the Two Deflator Method for measuring total factor productivity growth, which is the framework used to obtain my estimates of TFP growth Section 2.5 presents the data employed in my estimates and section 2.6 presents the results Section 2.7 reviews recent work on TFP growth within the Mexican manufacturing sector, presents a comparison of these estimates, and discusses the potential sources of the observed differences Section 2.8 concludes.

2.2 The Path Toward Economic Liberalization in Mexico

The Mexican economy experienced a prolonged stage of sustained growth and low and stable inflation that extended from the 1950s up to the early 1970s Between

1958 and 1972 the economy grew at an average annual rate of 6.7 percent, inflation never exceeded 6 percent and the fiscal deficit was moderate However, things changed

significantly during the next few years Public expenditure would increase from 20

percent of GDP in 1971 up to 32 percent in 1976, while at the same time the inflation

rate accelerated GDP growth would experience a steady decline from 1972 up to 1976, and would be accompanied by an appreciation of the real exchange rate, stagnation of

exports, and external debt accumulation

The government responded to this environment with more protection, more spending, and more intervention in the productive sector (the number of public enterprises went from 391 up to 1,155 between 1970 and 1982) In this opportunity, the

expansionist stance of the government was fueled by more foreign lending, largely

“justified”, in the lender’s eyes, by large increases in Mexico’s proven oil reserves

However, during 1981 things changed drastically as it became clear that the

expected increase of oil export revenues was unrealistic The situation became more

complicated during 1982 as international interest rates went up and the world entered a recession The debt crisis that ensued led Mexican authorities to curtail public expenditures -mostly investment- and increase public sector prices and tariffs

During the next two years following the start of the crisis, inflation went down

slowly and the real exchange rate experienced a significant appreciation, which in turn

made inputs for the manufacturing sector either unavailable or expensive The external sector had to improve if the Mexican economy was to rebound, and therefore something different had to be attempted Hence, a trade liberalization program was initiated in 1985,

“which marked the beginnings of a fundamental reorientation in economic policy toward

a more private sector-based, market friendly economy.”' This effort would be followed in the late 1980s and early 1990s with additional reforms that included the privatization of government owned enterprises, deregulation of industry, and the liberalization of foreign investment These efforts succeeded in stabilizing the inflation rate and the fiscal deficit, and “also created a friendlier business environment, which resulted in a revival of

investment flows and increased foreign capital inflows.””

For some researchers, the structural change pushed by government authorities during the mid 1980s and early 1990s should have translated into higher rates of productivity and output growth across the economy In this study, however, I present evidence from the Mexican manufacturing industry suggesting that productivity growth in this sector may not have been as dynamic as it has been previously suggested

! World Bank (1998), p 26

2.3 The Sources of Economic Growth

Before presenting any calculations and comparisons of TFP growth estimates, it is recommendable to offer first an interpretation of it and note its significance for understanding the growth process

It is understood that the growth of an economy, an industry, or a firm is determined by both investment and total factor productivity Investment is the commitment of current resources in the expectation of future returns and it can take either a tangible (investment in machinery and equipment) or an intangible form (accumulation of human capital) The mechanism by which investment translates into economic growth is very well known For example, “an investor in a new industrial facility adds to the supply of assets and generates a stream of rental income This income stream can be divided into two components: the increase in capital input (Ak;), and the marginal product of capital or rate of return (r;) Thus, the increase in capital contributes

to output growth in proportion to the marginal product (r; Ak;) Similarly, an individual who completes a course of education and enters the labor force for the first time adds to the supply of people with higher qualifications or skills The resulting income stream can

be decomposed into a rise in labor input (AL;) and the marginal product of labor or wage rate (wi) Consequently, the increase in labor contributes to output growth in proportion

to the marginal product (w;AL;).”°

* World Bank (1998), p 27

> Jorgenson (1995), p xvi

TFP growth, on the other hand, is that fraction of output increase that is not

explained by the increases in inputs or, in other words, it is a measure of the overall

efficiency of the inputs used in the production process “It is meant to provide an index of

the rate of expansion of an economy’s (or some productive unit’s) capacity to produce,

over and above the portion attributable just to expansion in its inputs quantities.”°

Alternatively, TFP growth can also be seen as the broadest available measure of change in productive efficiency associated with a net saving in the use of factor inputs per unit of output over time Thus, TFP growth is simply “the opposite side of the cost reduction coin When total factor productivity rises, real factor costs per unit of output fall If input prices remained constant, output prices would fall in proportion to the productivity advance.”*

This last interpretation of TFP growth can be more clearly understood within the

context of the traditional growth accounting framework According to this approach, the

derivation of TFP growth takes as a point of departure the “adding-up” identity between the value of output and the value of inputs:

Starting from this definition, the growth equation can be written as follows:

(2) Ri=PAy - wAAN, - rAk, = k,An + NiAw, - y,AP,,

or, expressing (2) in terms of growth rates:

(2) R/y.i=(Ayyei} s(ANƯN¿v)<s(Ák, (Ket) = 5 (At/te-1) + Sp (Awd w 1)- (APY/P,.1),

where:

SL = WiNVP›y, = actual (observed) share of labor in total output

Ss = 1,k/Py, = actual (observed) share of capital in total output

In 2’, R/y is the residual growth rate of output not explained by the share

weighted growth rate of the inputs, and is interpreted as the growth rate of output per unit of input The right hand side of 2’ also implies that R/y is equal to the (negative) growth rate of output price not explained by the share-weighted growth rates of the input prices In other words, the expression for R/y in terms of changes in output and input quantities is the dual of the expression for R/y in terms of changes in output and input

prices.®

° There is disagreement about whether to use gToss or net value added Growth theorists, for example, sustain that it is more adequate to exclude depreciation of fixed capital because “this is an intermediate cost that, like the consumption of raw materials and semi-finished goods, is excluded from the measure

of final output However, others, particularly those looking at the issue from the standpoint of production theory, prefer the gross measure because for them depreciation is part of the measure of the services of the primary factor -capital.” (In W Baumol and K McLennan, 1985, p 30.) I chose the gross value added measure based on the former argument

"If “y” were net value added, “r” would be the net rate of return to capital

* “This estimate is based only on Prices and quantities and is thus a pure index number -nothing is said about parameters of an underlying technology or even the existence of such technology” (Hulten, 1990,

p.4.) However, Solow (1957) and Diewert (1976) show that there is a fundamental unity between the

parametric and the index number approach, in the sense that both can be derived from the production

function

Finally, if we look at the right hand side of 2’ (assuming R/y>0) and ask the following questions: “What makes it possible for firms to pay more for inputs while keeping the prices of outputs the same? Or to lower the prices of their outputs while paying the same price as before for their inputs? The answer then suggests itself, and is

the same in both cases: real cost reduction is the key that makes it possible to pay (or

reap, in the case of one’s own equity) higher rewards while keeping prices constant, or to lower prices while keeping factor rewards constant.”? Thus, TFP growth is not exclusively technological advance, but a composite of the many things that businessmen

do to reduce costs and improve efficiency, such as the adoption of new technology; the

reorganization of production lines; etc

2.4 Real Cost Reductions and the Two Deflator Method

For years economists have debated about the concept of productivity growth and its measurement As a result of this perennial discussion, two main approaches for

estimating TFP growth have emerged One of them is the “parametric approach”, which

involves the specification of technology, either through the specification of a production

or a cost function The alternative is the “non-parametric approach”, which does not involve any functional specification of the technology or econometric analysis in the estimation of TFP

The estimation procedure employed in this work, called the Two Deflator Method

(TDM), falls within the second category This method, which is an extension of the project evaluation methodology to the analysis of economic growth, allows us to obtain

estimates of TFP growth which can be more closely associated with the concept of “real cost reductions” To see how this method operates, consider the following

When evaluating a project, one costs capital and labor at their relevant opportunity costs, and then subtracts them from the benefits of the project Any net benefit that appears after performing this operation is considered as a contribution to the net profitability of the project Something similar can be done when analyzing the growth

experience of a firm, or an industrial sector In doing so, we would first take the series of

value added of the relevant economic unit, and express it in real terms for each year,

“using some numeraire price level such as the GDP deflator or the consumer price index Second, we would construct a time series of net capital stock (expressed in real terms, ideally by the use of the same deflator as was used for value added) Next, we would deflate the wage cost series, also by the same deflator, and subtract them from value added”.'° Then, we would estimate the rate of return to capital for a given year by subtracting wage costs from value added, and dividing this difference by the entering capital stock for each year The cost of capital would then be given by the product of the rate of retum computed in this manner, and the stock of capital for the period Finally, we would subtract the real wages bill and the cost of capital from value added in order to get

'° Harberger (1993), p 13

a benefit attributable to each year This net benefit is precisely the residual or TFP change Furthermore, and although not obvious at this point, the residual obtained in this

fashion is precisely the estimate of TFP growth yielded by applying the TDM to growth accounting

In the discussion above, notice that only one deflator (either the GDP deflator or

the CPI) was suggested for expressing the nominal data into real terms This is in marked contrast to what is usually done in cases where TFP growth is estimated with methodologies that ignore the connection between capital theory (project evaluation) and the breakdown of economic growth In those cases, it is customary to use different deflators for the series of investment, and sometimes even two deflators for estimating real value added How can the use of only one deflator be justified to express all nominal figures in real terms? To answer this question, imagine an entrepreneur who just bought five different machines to start his business (all of them required for the production process of only one good), a project which he hopes will produce a stream of benefits The entrepreneur, in order to evaluate the net benefits of his project, would certainly not express the nominal value of those machines in real terms using a different price deflator for each capital asset, and then compare these costs with the present value of the flow of benefits that the project is expected to generate, where these benefits have been expressed in real terms with a price index of consumer goods'' What the entrepreneur is more likely to do, however, is to express those costs and benefits in terms of comparable baskets In other words, the entrepreneur, when making his calculations of costs and

benefits, is probably thinking in terms of how many baskets he must sacrifice today in order to obtain a certain number of baskets in the future The natural numeraires which come to mind for performing such calculations are either the CPI, which measures the cost of a typical consumption basket; or the GDP deflator, which measures the cost of a typical production basket

The second deflator, on the other hand, is the one which allows us to obtain a

“quality inclusive” measure of labor.'? In other words, the second deflator is the key for solving the problem of sending to the residual a fraction of growth that in fact corresponds to labor In understanding this point, notice that when the traditional analysis

of growth is carried out empirically, a subtle problem arises when accounting for the contribution of labor to growth In particular, the traditional analysis of growth implicitly assumes that the quality of labor remains constant through time when it assigns to new increments in the number of workers (AN) an average wage (w’) equal to the average wage of the existing labor force:

(3) R/y = (Ay/y) - [Ww N/y](AN/N) - s(Ak/k)

Under this formulation, if an upgrading of the labor force takes place (due to education, experience, training, reallocation of workers from low productivity to high productivity activities, etc.), the results of such an improvement are measured not as a part of the labor contribution, which is the right thing to do, but as a part of the residual

To see why this happens, assume that in a given year the number of workers and the

'! This is what is usually done in other analyses of productivity growth

stock of capital in some establishment remains constant, and that during that period all

workers receive some special training which allows them to produce 30% more output

per hour, and receive, say, a wage 30% higher than before Under these assumptions,

sL(AN/N) = sx(Ak/k) = 0, since the number of workers and capital did not change;

however, (Ay/y)>0 because output is higher Consequently, we have a positive residual

due solely to the improvement in the quality of labor

The TDM corrects for this problem in a simple fashion The first step in this strategy consists in choosing a “basic labor unit” (say an average primary school graduate, 30-40 years old, and employed) which receives an average wage “Wa” With this basic wage measure, we can express other people’s labor in terms of units of the chosen basic wage Thus, if we divide the total wage bill Zw;.Nj: (wj1 = wage in industry

“7°; Nj: = number of workers in industry “j”) by wo:, we obtain a precise measure of the

total contribution of the labor force at time “t’”, measured in basic labor units:

(4) L}: = (ZwjNj)/Wa-

The expression in (4) implies that total labor earnings at time “t” (>w;,N;.), can be expressed as wu,L;: With this at hand, we just have to apply it to the breakdown of growth itself, with s.(AN/N) being replaced by (Wo, AL’},)/yj,-1, so that:

(5) (R Yjt-1) = (Ay/ Yis-1) - (Wot AL}/ Yja-1 7 Su(Ak/kj,.-1)

'? For expository purposes, the discussion is presented in terms of the traditional approach to growth

Notice that in the previous example and under this new formulation'”, N;:=N;¿= Nj; however (Zw¿:N¡: - ZW¡uiN¡¡ )> 0, since this period the more productive workers are paid higher wages, and consequently w„ AL”;;>0

Therefore, “whereas the traditional calculation of TFP incorporates changes in the quality of labor, and also changes due to shifts of labor from lower-paying to higher-

paying jobs for whatever reason (e.g., shifts among industries or among regions with

different pay scales for similar labor), the present method includes the results of these

movements as part of the labor contribution.”'* But how should we define the basic wage

for an empirical implementation? In this regard, a number of different definitions for the basic wage could be initially suggested, such as the average wage of textile workers, or the wages of individual industries and/or individual occupations However, these wages

“have a volatility that detracts from their suitability as a deflator It is somewhat analogous to using a highly volatile price measure to show how the real national income

of a country changes through time, or how the real wages of workers move over a decade If one used such a deflator, the resulting series would have large swings that

had nothing to do with the concept being measured, but that only reflected the volatility

One alternative to attenuate these problems would be to use a specified fraction (say 2/3) of the per-capita real GDP of the country in question, the reasoning behind this metric being that: “a) in just about every country one will find significant numbers of workers whose annual full-time earnings are around 2/3 of per capita GDP of that country, b) in every case, such workers tend to be very much at the low end of the labor- quality spectrum, thus justifying our attribution of wa as applying to basic labor, and c) the volatility of this measure is very low as compared to competing series from specific Occupations.”!6

Summarizing, the TDM proposes two changes when implementing a growth

accounting exercise First, use only one deflator (the CPI or the GDP deflator) to

estimate the stock of physical capital And second, use a “basic wage” to obtain a correct estimate of the contribution of labor to output growth These two steps allow one to obtain a residual component of growth which can be more closely associated with real cost reductions

'® The use of the basic wage allows to divide total earnings (WaL;,) into basic labor component (WaN;,), and a human capital component, w (L,,- Nj) This implies, in turn, that the total contribution of labor can be broken down into a fraction due to the increment of basic labor, (w ANj,.), and another due to the

increment in human capital, [wa (AL” ¿t* ÂN, )] Furthermore, ít is possible to obtain an even finer

breakdown of the increment in human capital [wo (AL” jr- 4N,)]- A first component of this breakdown is

{(WoWy,, )[(ŒL- N}/N] AN,.?, which can be interpreted as the increase in human capital contribution

required to endow the new units of basic labor with the pre-existing average endowment of human

capital per worker The second element, (Wa/Y;.)[ AL”;;- (Ly Nw AN;,J, can be seen as a quality change component and captures how the contribution of human capital (the excess of each worker’s wage over

the basic wage) changes under several circumstances For example, the change in the excess of each

worker’s wage over the basic wage will be positive (negative) if (a) the demand for a particular skill rises (falls) when holding the supply of skill constant; or (b) if the supply for skill rises (falls) when holding demand constant; or (c) if there an upgrading (downgrading) of the average skill of the labor force See

2.5 Data for Estimating TFP Growth in the Mexican Manufacturing Sector

Once outlined the methodology I plan to use in my calculations, it is now the turn

to speak about the data There are two main data sets that have been employed to

estimate TFP growth in the Mexican manufacturing sector The first set consists of the output, wages, and employment series estimated by the Instituto Nacional de Estadistica,

Geografia e Informatica (INEGI), and the net fixed capital stock series estimated by

Banco de Mexico for 47 industrial branches (2 digit SIC level) At the early stages of this

work, however, I was able to identify significant consistency problems with this data set,

the most troublesome being that the ratio of capital stock to value added was in almost all industrial branches lower than one, figures that implied average annual rates of return above one hundred percent for most of the industrial branches Given the implausibility of such results, this data set was discarded

A second set available to compute TFP growth estimates consists of establishment

level data from the Annual Industrial Survey (AIS) collected by INEGI since 1984 The

survey is not random in the sense that it is biased towards collecting information of

establishments of larger size, with size being defined in terms of the number of people employed (Table 2.1) The original data set contains information on more than 40

variables for more than 3200 industrial establishments!’ classified in 9 sub-divisions and

'” In the AIS survey, an "establishment" is defined as every “economic unit that in a unique location,

delimited by buildings and fixed infrastructure, combines resources under one owner or control, to

develop on their own account, activities of assembly, processing, and total or partial transformation of raw materials that result in the production of goods and services, contained within a unique class of economic activity." In my work I will refer to industrial establishments as firms, even though I do not have information for identifying which establishments belong to the same firm

47 branches during the period 1984-1994.'* After cleaning the data set, however, only

1893 establishments from 44 industrial branches were kept.'? Since the number of manufacturing establishments in the 1985 Industrial Census (IC) is 9,254, the establishments kept represent about 20 percent of that total

Table 2.1: Coverage of the Annual Industrial Survey 1984-1994

Sources: Industrial Census INEGI (1985) and AIS 1984-1994

The coverage of the survey differs among the different sub-divisions For

example, employment in the survey represents more than 60 percent of the employment

reported in the 1985 IC for division VII; between 35 and 45 percent in sub-divisions L,

II, IV, V, VI, and VII; while for division II, it only covers 11 percent

Since the AIS data collects information on basic variables, some steps are required in order to construct the variables needed for estimating TFP growth The construction of variables such as value added, capital stocks, and basic units of labor, is outlined next

'8 The sub-divisions are: (I) Food, Beverages, and Tobacco, (I) Textiles, Apparel, and Leather, (III)

Wood and its products, (IV) Printing and Editing, (V) Chemicals and Oil, (VI) Non-metallic Minerals, (VIT) Basic Minerals, (VIII) Metallic Products, Machinery and Equipment, and (9) Other Manufacturing '? See Appendix 2.1 for the criteria adopted to clean the data set Most of the establishments excluded were those with a number of workers lower than 50 The criteria employed to construct the data set, I

() Ky =Vig+ Kf - Di, + Invi,

where:

Kj , = net capital stock at the end of period “t”

K‘ ,-1 = net fixed capital stock at the beginning of period “t”

Dj = SKE 4.1, + (1/2) STi, = depreciation during year "t"

5 = rate of depreciation of the fixed capital stock

Inv; , = value of inventories of outputs and inputs at the end of period “t.”

I‘, , = gross fixed capital formation during period “t.”

“4” refers either to an establishment or to a 4 digit industry

In turn, gross fixed capital formation was estimated as follows:

2) Vy = AFit + APiy + AMi,- AVig

where:

AE; ¡ = yearly asset acquisition

APi, = capital assets which are produced internally during period “t”

*° Hulten and Wykoff (1981) suggest that geometric decay is a good approximation for the pattern of total depreciation

AM, ¡ = value of improvements on the same assets during period “t”

AV; ¡ = sales of fxed assets during period “t”

The steps above were applied for each type of capital asset, and different depreciation rates were applied to each of them: machinery (7.5%), office equipment

(5%), transport equipment (8%), installations (2%), and other assets (5%)

Gross Value Added The AIS provides annual information on gross output (ye.) and intermediate inputs (cii,; = material costs + electricity costs) Thus, gross value added

(¥i1) was computed simply as:

3) _y,, = 8, - cil,

Income attributable to Capital, and Income attributable to Labor To estimate the

income accruing to capital (r.,k,,) Í need first to subtract the income attributable to labor

(W%otL ˆ,„) #om gross value added (y, ):

(4) 1 Kịt C Víi - woL is

An initial estimate of the income attributable to labor can be computed from the AIS data as follows:

(5) WBo= blue collar wages + white collar wages + social security contributions +

other non-wage benefits + profit sharing

Hence, an initial estimate of the income attributable to capital (IKo, ,) is given by:

(6) IKo,, = yi, - WBois

In general, this last estimate is being somewhat overstated This is so since the wage bill of blue and white collar workers in WBO (a) does not include the remuneration

to independent workers, (b) does not consider the value of the work put into the establishment by relatives and partners working in the establishment but who do not

perceive a remuneration and (c) it does not take into account the salaries of the executives One possibility to account for this problem -which becomes crucial for

computing the share of capital income in value added, or the rates of return-, is to adjust

Iko;: downwards by some fraction “2”, and assign this fraction to labor income This

latter adjustment will be referred here as the apportionment to labor income

Thus, taking into account this adjustment, the income attributable to capital will

be given by:

(7) fie Kin = Tkoje - pt Tkojy,

and the income attributable to labor by:

(8) Wo, Lia = W,.L= WBo;, + p Ikoj,

It must be recognized, however, that the required adjustment is far from uniform across establishments It depends, among other things, on the size of the establishment and on the industry to which it belongs However, since I do not have accurate information about the precise adjustment required for each establishment, I will estimate TFP growth rates for different values of “y” and then look at how sensitive the results are to these adjustments

The Rate of Return to Capital The rate of return to capital is computed as the ratio of that part of gross value added which accrues to capital during the year, to the value of the capital stock at the beginning of the year, both expressed in terms of prices of the same year:

(9) rị= Œko;,- H lko;¿ V kits

The Basic Wage The basic wage (Wo) is defined as 2/3 of real per capita GDP

Statistics.”

Labor expressed in basic units The units of basic labor are defined simply as the ratio

of the adjusted income attributable to labor to the basic wage:

“It is worth mentioning that the choice of 2/3 is irrelevant for determining the total contribution of labor

to value added growth This can be easily shown as follows:

Let the basic wage Wo, = 7YPS, (YPC, = income per-capita, and 1>4>0) , and substitute it into AL*;¢- AL* ig = (Wy Ly / AYP, )~ (Wey Lyg /AYPC Ly ) = (AICW, Ly / YPC )- (Wyy Ly 7 YP) DI:

Then: (woyKAL TY I)= AYPL ) (1/2) Ly / YPC, = (Weg Lyey “YPC DI:

= CYP, ) (CW, Ly / YPC, )- (Wye Ly / YP%.1 DI,

so, 4 cancels out when measuring the contribution of labor to growth What is truly relevant is the

behavior of per capita GDP