Firm size, the choice of technique and technical efficiency : evidence from India's soap manufacturing industry

FIRM SIZE, TE CROICE OF TECNIQUE AND TECHNICAL EFFICIENCY: EVIDENCE FROM INDIA'S SOAP MANUFACTURING INDUSTRY By John M. Page, Jr. Princeton University Series: Studies in Employment and Rural Development No. 59 'Division: Employment and Rural Development Department: Development Economics Development Policy Staff International Bank for Reconstruction and Development This paper was prepared for the internal use of the World Bank, and may not be quoted, referred to without permission of the author or the Bank. The views expressed represent those of the author and are not necessarily those of the Bank. Washington, D. C., December 1979 TABLE OF CONTENTS Page No. 1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . 1 2. FIRM SIZE, THE CHOICE OF TECHNIQUE AND TECHNICAL EFFICIENCY . .. . ... .. .. .. . .. . ... 3 3. SOAP MANUFACTURING IN INDIA . . . . . . . . . . . . . 10 (a) Structure of the Industry . . . . . . . . . . . . 10 (b) The Process of Production . . . . . . . . . . . . 10 4. THE SAMPLE AND THE DATA . . . . . . . . . . . . . . . . 13 5. EVIDENCE ON FACTOR PROPORTIONS . . . . . . . . . . . . 17 6. A TEST FOR RELATIVE EFFICIENCY - THE PROFIT FUNCTION . 25 7. TECHNICAL EFFICIENCY - A NONPARAIETIC APPROACH . . . . 33 8. CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . 41 FOOTNOTES . . . . . . . . . . . . . . . . . . . . . . 43 REFERENCES . .. . .. . . . . .. . . . . .. . . . 45 1. Introduction This paper is the first in a series of studies of small scale enterprises in India. The analysis is largely based upon the results of a sample survey conducted during 1978 of 53 soap manufacturing firms in metropolitan Dehli. The objective of undertaking the survey was to provide a set of microeconomic data which covered unregistered firms and those employing less than ten workers, categories not normally included in industrial census returns, and to provide a sufficiently large and diverse set of firm level observations to permit econometric modelling of production relationships and statistical tests of hypotheses within a well defined product category. Nearly all previous studies of small scale enterprises have been based upon industrial census materials which are reported at a high level of aggregation, or upon microeconomic surveys which attempt to cover a large number of small enterprise types at the expense of compara- 1 bility among size classes of firms within individual industries. These studies are of limited value in addressing some of the more interesting questions concerning the role of small scale enterprises in developing countries, including the choice of technique and the relative economic efficiency of small firms. The concept of economic efficiency lies at the center of many of the controversies surrounding small industry policy. Comparisons of small and large firms in terms of their relative factor proportions describe -2- only one dimension of economic efficiency, the choice of technique. Firms employing the same technique may differ in the quantity of output which they produce using identical quantities of measurable inputs. Such differences can arise from differences in technology; one group of firms may employ machines of a newer vintage which are superior to those of an earlier era, or from differences in firms' endowments of non-measureable inputs, such as managerial ability and effort, which affect the efficiency with which measurable inputs are combined. Economic efficiency reflects both dimensions, and indeed the potential for tradeoffs between appropriate choice of technique and technical efficiency has dominated much of the discussion (although little empirical investigation) concerning the desir- ability of small enterprise promotion in less developed countries.2 This paper focuses on an empirical investigation of the rela- tionship between choice of technique, price efficiency, relative technical efficiency and firm size in India's soap manufacturing industry. Because of the strong policy emphasis in India on promotion of small scale enter- prises the conclusions have immediate policy relevance. A second paper in this series will explore ,a number of other interesting and related topics including enterprise history, background of the entrepreneur, product markets and quality, and the welfare costs of small enterprise protection on which data from the surveys also provide some insights. 2. Firm Size, the Choice of Technique and Technical Efficiency The relationship between choice of technique, technical and economic efficiency has been explored in a number of papers, largely based on the work of Michael Farrell (1957).3 In a two factor world with well behaved, linear homogenous production functions, production decisions may be characterized byapoint in input space representing the combination of factors required to produce a unit of output. The envelope of minimum input combinations required to operate at the unit level traces out a unit isoquant which defines the best practice technology actually employed in the industry. Such a unit isoquant is represented in Figure 1. Although a number of firms will be located on the frontier, for example those represented by Q and Q', the scatter of observations will also give rise to points to the northeast of the frontier isoquant such as P and P'. These observations, which employ the same techniques as Q and Q' use more of both inputs, although in the same proportions, to produce a unit of output and are therefore less technically efficient than their frontier counterparts. Technical efficiency is, thenfore, a concept which is independent of the choice of technique and of relative factor prices. In Figure 1 both Q and Q' are technically efficient, although they employ different techniques of production. The appropriateness of the technique chosen is determined by the firm's level of price (or allocative) efficiency. If MM' represents the relative factor price ratio facing all firms in the industry, the optimum input combination lies on the ray OQ'. Both Q' and P' are price efficient. K p A Mi A Figure I Technical and Price Efficiency -4- A firm such as Q fails to fulfill the first order conditions for profit maximization (cost minimization) although it is technically more efficient than P'. Economic efficiency is the product oi both price and technical efficiency. If all firms in an industry face equal relative factor prices, equal economic efficiency implies that in long run equilibrium all firms must choose the same productive technique and operate with equal levels of technical efficiency. This would lead one to believe that only one point on the unit isoquant would be observed. The empirical reality, however, seldom corresponds to such a definition of long run equilibrium. Cross section studies of production encounter substantial variation in factor proportions and in the level of technical efficiency. The literature on small enterprises suggests several factors which may explain the coexistence of establishments of different size using different techniques of production with varying degrees of efficiency. First, firms may operate at different sets of market prices. Since the decision rule on profit maximization yields actual profits as a function of input prices, it is clear that two firms of equal price efficiency may choose different techniques if they face different price regimes. Frequently, the argument is made that smaller firms face substantially higher opportunity costs for capital and, hence, lower wage rental ratios than large scale firms. Efficient substitution of labor for capital would therefore induce smaller firms to use more labor intensive techniques. Moreover, when selecting techniques firms must consider future prices. Investors may have different expectations with regard to relative price changes, leading to -5- different factor intensities despite apparently equal (static) relative prices. Second, firms may not maximize profits. Varying administratiVe and organizational structures among firms will lead to alternative decision 5 making rules. The techniques chosen under those rules need not correspond to those which would be predicted on The basis of profit maximization. If small and large firms differ systematically in their decision making criteria, these differences may be reflected in systematic differences in factor proportions. Third, all entrepreneurs may not possess knowledge of the complete range of productive techniques. If large firms have more complete knowledge of the alternative methods of production available, their factor proportions may differ from small firms even under a unified factor price regime. Differences in technical efficiency among firms may also arise for several reasons. First, firms may employ different technologies. For example if plants of markedly different vintage coexist within the sample, those firms embodying the latest generation of capital equipment may dominate all others. If technical efficiency is measured relative to the industry fron- tier, enterprises employing older technologies will appear inefficient, even if they are achieving maximum output from their given vintage of capital equipment. It is frequently argued that small scale enterprises use capital equipment which is not of the latest vintage, and that they are therefore technically inferior to larger scale firms. Second, where technologies are of the same vintage and absolute efficiency, firms may still vary in relative technical efficiency due to -6- variations in the quality and quantity of non measured inputs. Entrepreneurs and managers for example may vary in their ability, initiative and technical 6 knowledge. These qualities, which are not measured as inputs in orthodox production function analysis, will affect the efficiency with which measured inputs are combined. Similarly the inability to construct input measures which reflect labor force skills or experience may give rise to variations in output for apparently equal input vectors. To the extent that large and small firms differ in these and similar characteristics the differences may be reflected in the relative technical efficiency of firms. Knowledge of the extent of technical and price inefficiency may be crucial for the formulation of appropriate policies. If, for example, differences in factor proportions stem from different behavioral rules among producers, rather than from variations in factor prices, inferences regarding the factor prices faced by small and large firms drawn from data on relative factor proportions may be misleading. Similarly the presence and extent of technical inefficiency is important in determining the consequences (and design) of industrial policy. If small firms employ technologies which are dominated by those of larger scale enterprises, the possibility arises of tradeoffs between labor inten- sity and economic efficiency. In Figure 1 the social opportunity cost of capital and labor are assumed given by the budget line AA! As drawn both firm Q',which is technically efficient but employs an inappropriate technique at accounting prices, and firm P which is technically inefficient but price efficient at accounting prices, have equal unit social costs of production and equal economic efficiency. If the representative small firm is to the -7- right of P along the ray OP while the representative large firm is at Q', policies designed to restrict the output of large firms and favor the expansion of small enterprises will involve an increase in the social cost of production. If increases in technical efficiency require the adoption of more capital intensive technologies by small firms, a tradeoff clearly begins to emerge between employment and output. Technical inefficiency which reflects the influence of managerial training and effort may also have important consequences for the design of public policies. Managerial extension and training programs may improve the efficiency of small firms and thus move the representative firm inward along the ray OP. Such policy initiatives can contribute simultaneously to the attainment of employment and output objectives by increasing the private and social profitability of small scale firms. -8- TABLE I Profile of the Indian Soap Manufacturing Industry Organized sectora Unorganized sectorb 1970 1976 1970 1976 Number of: Firms 43 44 4500 5400 Employees 17.8 NA 42 50 ('000) Volume of Output 232 270 544 560 (Tons Thousands) Concentration Ratio for Five Largest firms in 1970: 86.2% of organized sector production 25.8% of total production Sources: aAnnual Survey of Industries, 1970 Indian Soap and Toiletries Makers Association, The Soap Industry (Bombay, N.D.). bDevelopment Commission, Small Scale Industries, Ministry of Industrial Development. -9- TABLE 2 Distribution of Sample Firms by Number of Workers Power Non Power Sector Sector Employeesa Total Work Forceb Full-Timec Total Work Only Labor Equiva- Force lents 0 - 5 14 10 8 - -- 6 - 10 17 18 20 - 11 - 20 10 13 13 -- 21 - 50 4 4 4 - 51 - 100 3 3, .3 2 101 + 2 2 2 1 Source: Sample Survey TABLE 3 Distribution of Sample Firms by Value and Volume of Output Value of Output No. Firms Volume of Output No. Firms (Rs. 000) Tons 1 - 250 10 0 - 20 1 251 - 500 7 21 - 50 3 501 - 750 10 51 - 100 11 751 - 1000 5 101 - 300 17 1001 - 2000 6 301 - 500 10 2001 - 3000 5 501 - 1000 4 3001 - 4000 3 1001 - 5000 3 (1) 4001 + 4 (3) 5001 + 1 (2) Source: Sample Survey Notes: Power using firms in parenthesis. -10- 3. Soap Manufacturing in India (a) Structure of the Industry Table 1 provides descriptive data on the structure of India's soap manufacturing industry. Two sectors are recognized in the governments statistical coverage. The organized or large scale sector consists of firms using electrical power in the manufacturing propess. These firms are included in regular statistical coverage of industrial establishments and their installed capacity is subject to central government licensing. The unorganized sector of the soap manufacturing industry consists of "small scale" and cottage industries which do not use electrical power. These establishments are mostly uhregistered and neither comprehensive output nor employment data on them are available. From the estimates in Table 1, it is apparent that approximately two thirds of soap production by volume is undertaken in the unorganized sector. Virtually all of this ouL'ut is laundry soap. Toilet soap is produced almost exclusively in the organized sector,and accounts for approximately half of that sector's output by volume. (b) The Process of Production Soap manufacturing is an extremely simple process which involves the mixing of fatty materials with caustic soda (or caustic potash). The ensuing chemical reaction yields neat soap and a residue which contains glycerine. The traditional method of manufacturing soap is a batch process in which the fatty matter and caustic material are mixed in a cauldron. The mass is heated by burning coal or firewood and allowed to boil for a period of 4 to 6 hours. When soap is formed a brine solution is added and the mixture is allowed to boil until lye is separated from the soap. These processes have a cycle time of approximately 24 hours. The quality of the -11- boap may be improved by a series of "washings" with salt solutions, and when the neat soap has reached the desired degree of purity it is trans- ferred to iron moulds where it is allowed to cool, dry, and solidify under atmospheric conditions. Cutting and packaging are performed by hand. The entire process requires from six to seven days and is performed com- pletely without mechanical power. The processes followed in the organized sector involve varying degrees of substitution of mechanical for human power and replacement of batch processing with continuous flow processes. Saponification is achieved either by boiling in a "kettle" using open steam (the batch process) or in a sealed autoclave (the continuous process). For better recovery of glycerine and improved product quality the soap is washed several times in brine solution. The neat soap is then mixed with the required quantities of "builders" -- additives designed to improve washing quality -- "fillers" -- additives designed to increase bulk, and preservatives and cooled and dried in either tubular driers or vacuum spray devices. During the final processes the soap is milled, plodded and extruded into a continuous bar which is cut, wrapped and packaged. Because of the separability of the process stages and the existance of a number of technical alternatives at each stage, it would appear that substantial scope exists within the industry for the substitution of labor for capital. The greater labor intensity of manual, batch-type operations may be diminished somewhat by an increase in working capital requirements due to increases in process cycle time and perhaps by decreases in capacity utilization, when components are not closely coordinated, but it would not be surprising to encounter substantial variations in factor intensities among plants employing different combinations of manual and mechanical processes. -12- Public policy, however, has limited the scope for factor sub- stitution by drawing a distinction between manufacturing processes which employ electrical power and those which do not. The existing structure of excise tax legislation exempts firms which do not use electrical power from payment of excise tax. In addition the government has, through its industrial licensing policies, prohibited expansion of capacity by the power sector in laundry soap manufacturing. The quantitative restriction on incremental output is intended to provide an additional measure of protection for non-power enterprises. The consequence of this distinction based upon the use of electrical power is that although there is apparently substantial variation in techniques of production within the organized (or power using) sector, there is virtually no variation in the techniques employed in the non- power sector, since the combination of mechanical with manual operations is prohibited. The smallest and largest non-power using firms employ virtually the same processes. Increases in firm size give rise to repli- cation of the initial series of operations, and thus within the non-power sector there is no engineering relationship between firm size and capital. intensity. -13- 4. The Sample and the Data All of the observations used in this study are drawn from a 1978 sample survey of soap manufacturing enterprises in the Delhi metropolitan area. Details of the sample design and coverage are provided in Appendix The final sample contained 50 manufacturing firms in the non-power sector and three firms in the power-using sector. The distribution of firms by employment size category is given in Table 2. Three measures of employment size are presented. The first is the number of employees, including family workers, but excluding working partners. The second is the total work force of the firm including working proprietors. The third measure of employment size attempts to correct for employment of casual workers and part-time laborers by first computing total man-months of labor for the firm and then converting into full-time worker equivalents. The three distributions correspond quite closely, although as expected there is some upward shifting in the smallest two firm size categories as the definition of labor force is modified to include working proprietors and casual workers. The distribution of sample firms by value and volume of output is presented in Table 3. The boundaries of Rs. one million and 300 tons per annum correspond quite closely to the 10 employee boundary in defining a dividing line between small scale and medium and large scale firms. The concept of establishment size could be made operational by using any of the above measures or by using estimates of the size of the capital stock or value added. In most studies the size classification is performed by taking number of employees. The advantage of using labor force statistics as an indicator is that it permits comparability with other studies of small scale enterprises and that it provides a graphic -13a- TABLE 4 COEFFICIENTS OF CORRELATION BETWEEN INDICATORS OF ESTABLISHMENT SIZE TOTAL WORK VALUE TONS VALUE CAPITAL EMPLOYEES FORCE ADDED OUTPUT OUTPUT STOCK EMPLOYEES 1.000 TOTAL WORK FORCE .999 1.000 VALUE ADDED .977 .978 1.000 TONS OUTPUT .971 .971 .963 1.000 VALUE OUTPUT .975 .975 .970 .997 1.000 CAPITAL STOCK .952 .949 .957 .937 .947 1.000 -14- indicator of establishment size. In our sample all of the possible indicators of firm size are highly correlated. Table 4 presents zero order correlation coefficients between employment and other indicators of firm size. All of the variables.are significantly correlated at the one percent level, and throughout the remainder of the study total work force, corrected for part-time and casual labor will be employed as the primary indicator of firm size. One interesting datum which emerges from the sample is the very imperfect relationship between use of electrical power and firm size. Eighteen firms in our sample (36 percent) produce more than 300 tons per annum without the use of electrical power, and two of our non-power firms exceed one of the power using firms in both volume of output and total employment. Thus although the largest firm size categories (more than 500 employees) are exclusively the preserve of power using enterprises the existance of a significant number of large and medium scale non-power firms indicates that the special incentives provided to the non-power sector do not exclusively benefit small scale enterprises. Table 5 describes the product composition of the sample. It is immediately apparent that the overwhelming majority of firms in the non-power sector produce laundry soap. Thirty-six firms produce laundry soap exclusively and 48 firms produce more than 50 percent of their out- put in the form of laundry soap cakes or flakes. Of the two remaining firms one produces toilet soap and the other "soft" soap. In order to insure homogeneity of the sample in examining factor proportions and relative efficiency the two firms producing products other than laundry soap are excluded from the analysis. Of the three firms using electrical TABLE 5 PROPORTION OF SALES DUE TO LAUNDRY SOAP BY VALUE OF OUTPUT AND NUMBER OF WORKERS OUTPUT MEAN I COUNT I 1-250 251-500 501-750 751-1000 1001-200 2001-300 3001-400 5000+ ROW STD DEV 1 0 0 0 TOTAL S 1 2I 31 4 1 5 1 6 1 7 1 9 1 NEMPIO ---------I-----------1----------I--------- --------- I----------I----------I----------1---------- 1 1 100.00 I 100.00 I 0.00 1 0.00 1 0.00 I 0.00 1 0.00 I 0.00 1 100.00 ONE 1 2 1 1 01 01 0 1 0 O 1 01 OI 3 1 0.00 1 0.00 I 0.00 I 0.00 1 0.00 1 0.00 1 0.00 1 0.00 1 0.00 - ----------I----------I----------I----------I----------I----------I----------I----------I 3 1 100.00 I 0.00 1 0.00 1 0.00 I 0.00 I 0.00 1 0.00 I 0.00 1 100.00 THREE I 21 0 1 01 0 1 01 0 1 0 O 2 I 0.00 I 0.00 I 0.00 I 0.00 1 0.00 I 0.00 I 0.00 I 0.00 I 0.00 - ----------I----------I----------I----------I----------I----------I----------I----------I. 4 1 87.60 1 83.00 I 0.00 I 0.00 1 0.00 I 0.00 I 0.00 1 0.00 1 86.83 FOUR I 5 II 0 1 01 01 01 01 01 6 i 21.65 I 0.00 1 0.00 I 0.00 I 0.00 I 0.00 I 0.00 I 0.00 I 19.46 -I----------I----------I----------I----------I----------I----------I----------II-----------I 5 1 100.00 I 100.00 I 98.43 I 100.00 I 100.00 1 100.OO 1 0.00 I 0.00 I 99.42 5-9 I I 5 1 7 1 4 1 1 I 1 0 1 01 19 I 0.00 I 0.00 I 3.05 I 0.00 1 0.00 I 0.00 1 0.00 [ 0.00 1 1.92 -I----------I----------I----------I----------I----------I----------I----------I----------I 6 1 0.00 I 0.00 1 100.00 1 0.00 I 96.00 1 100.00 1 0.00 1 0.00 I 97.60 10-14 I 0 I 0 1 I 0 I 3 I 1 I 0 I 0 I 5 1 0.00 1 0.00 I 0,00 I 0.00 I 6.93 ' 0.00 I 0.00 I 0.00 I 5.37 -I----------I----------I----------I----------I----------I----------I----------I----------I 7 I 0.00 1 0.00 I 86.00 I io4.oo I 99.00 1 59.00 1 100.00 I 0.00 I 15-49 I 0 1 O I 1 I 1 1 2 1 1 1 3 1 01 8 I 0.00 1 0.00 I 0.00 I 0.00 I 1.41 1 0.00 I 0.00 1 0.00 I IB.RL -I----------I----------I----------I----------I----------I----------I----------I----------I 8 1 0.00 I 0.00 I 0.00 1 0.00 I 0.00 I 56.00 I 0.00 I 99.00 I 90.40 504 I 01 01 0 I O I O I 1 I 0 1 4 1 5 I 0.00 I 0.00 I 0.00 I 0.00 I 0.00 1 0.00 I 0.00 I 2.00 1 19.31 -I----------I----------I----------I----------I----------I----------I----------I----------I COLUMN TOTAL 93.80 97.57 97.22 10.00 97.67 78.75 100.00 99.00 10 7 9 5 6 4 3 4 48 15.85 6.43 4.99 ..O.0 4.80 24.57 0.00 2.00 - -15- power, two produce both toilet and laundry soap, and one produces laundry soap only. Many of the data drawn from the record of the sample survey required substantial manipulation. The particular variable definitions, on which the results are based were chosen after some experimentation with alternative measures of such central variables as output, capital and labor. Table 6 provides descriptive statistics on the major variables. Value added, which is our principal measure of output, is defined conventionally as the ex-factory value of output less total raw material consumption. The share of value added in gross output is quite low for soap manufacturing which is to be expected given the nature of the production process. The mean value of the share of value added in gross output is approximately .15 and it coefficient of variation is 43 percent. Labor inputs are measured in man-months of unskilled labor equivalents using a wage weighted linear aggregation across skill categories. The weights were derived from the sample average wage by skill category. Torking proprietors presented a problem in that the weight which should be assigned to their labor input could not be inferred from wage data. The problem is further complicated by the multiple roles played by working proprietors in firms of less than 10 employees. In these enterprises proprietors perform unskilled labor, skilled labor and managerial functions. The productivity of these three activities is obviously different and the final weight for proprietors should reflect the distribution of their effort among these tasks. The division of labor time was accomplished by using the proportion of unweighted man-months in total man-months for each skill category in firms with 10-20 employees. The weighted average thus defined was 1.56 which is approximately equal to the weight for skilled -15a- TABLE 6 TBE SAMPLE: SOME DESCRIPTIVE STATISTICS ON NON POWER USING ESTABLISHMENTS Mean Standard Deviation Number of Observations 48 Employees 19.08 33.33 Total Labor Force 21.25 33.45 Wage Weighted Man Months per Year 307.83 484.37 Capital Stock (RS'000) 569.30 920.91 Gross Output (RS'OOO) 1816.13 3594.67 Value Added (RS'000) 206.00 374.76 Tons of Output 456.80 825.25 Average Wage (RS) 200.50 62.46 Capital Stock/Labor Ratio (RS/Man Month) 29.43 17.54 Capital Service/Labor Ratio (RS/Man Month) .43 .21 Ratio of Working Capital to Total Capital .34 .14 Age of Enterprise (Years) 18.38 7.62 Average Experience of Labor Force 4.63 5.87 (Years) -16- labor and less than the weight assigned to white collar and management personnel.7 Capital inputs are measured at replacement cost and include values of land and buildings, machinery, vehicles and working capital. We have also constructed an approximate capital service variable from the available data. Based upon the inquiries made in the survey concerning the economic lifetimes of principal items of capital equipment we have assumed the following economic lives: Buildings 40 years Machinery 15 years Vehicles 5 years .Working Capital Infinite The rate of return to capital was assumed to equal 15 percent. Wage data are drawn from two sources within the sample. Implicit wages were derived from data on the total wage bill and the man-months of hired labor employed by each enterprise. In addition, the questionnaire provided firm specific data on the minimum and maximum wages paid to each skill category of labor. Output price variables were constructed in a similar fashion. This-implicit price of output was derived from quantity and value data. In many cases price data were also directly available from the questionnaire. The two estimates conformed quite closely, although there was evidence that the implicit price was systematically less than the reported unit price, indicating that firms may have understated their value of output. For this reason when the implicit price of output was less than the reported price by more than 10 percent the value of gross output was revised by taking the product of volume of output and the reported price. Use of either gross output measures does not affect the substantive conclusions of the paper. -17- 5. Evidence on Factor Proportions Examination of factor input ratios derived from the sample survey supports the contention that the principal difference in choice of technique exists between the power-using and non-power using sectors of the industry. Table 7 gives capital-labor ratios for subsets of firms in the sample. Three sets of capital-labor ratios are presented. The first is the ratio of capital stock to man-months of labor. The second is the ratio of capital services to man-months of labor, and the third is the ratio of capital services to man-months of labor in unskilled labor equivalents. The three measures of capital intensity are highly correlated and therefore provide similar results, but the capital service variable is conceptually superior to the use of capital stock.9 The use of unskilled labor equivalents permits us to correct to a degree for variations in technology which may not be captured in the simple factor ratios, but which are reflected in variations in the skill composition of the labor force. We use as our first indicator of capital intensity the total capital labor ratio including both directly productive capital and working capital. In our discussion of the processes of production we conjectured that more mechanized, and presumably more capital intensive production methods, could shorten the period of production and therefore reduce working capital requirements. Interpretation of the results can, therefore, be enhanced by estimating separately the working capital-labor ratio and the technical capital-labor ratio. The results thus generated make possible an examination,of the view that a systematic relationship exists between the labor intensity of the production process and working capital requirements. -17a- TABLE 7 CAPITAL LABOR RATIOS FOR POWER AND NON-POWER ESTABLISHMENTSIN THE SOAP MANUFACTURING INDUSTRY Non Power Firms Power Firms CAPITAL STOCK MEASURES Total 29.4 (17.5) 82.1 Working 10.2 ( 4.7) 37.1 -Technical 19.2 (17.7) 45.0 CAPITAL SERVICE MEASURES Unweighted Labor Input Total .429 (.207) 1.397 Working .128 (.059) .557 Technical .301 (.201) .840 Weighted Labor Input Total .350 (.169) 1.109 Working .106 (.053) .442 Technical .244 (.161) .667 Notes: Ratios are RS'000 per man month Standard deviations in parentheses -18- The difference in capital intensity between power using firms and non-power using firms in the sample is striking. The raito of the means of the total capital-labor ratio, measured either in stock or flow terms, is approximately three. Decomposition of the capital stock into technical and working capital reveals similar divergences. Indeed the ratio of means of working capital-labor ratios exceeds that for technical capital, although the small size of the power sample precludes tests for equality of the means. If there is an inverse relationship between mechani- zation and working capital requirements its effects are swamped by some other factor in our sample. One possible explanation lies in the difference in marketing arrangements made by firms in the power and non-power sectors. Firms in the organized sector perform many of their own wholesaling and delivery operations which presumably require them to maintain relatively larger stocks of finished goods than firms in the non-power sector, the majority of which sell ex-factory. We have not attempted to correct for this difference in the "thickness" of firms and the variations are presumably reflected in the factor ratios. When the evidence on factor proportions within the sample of non-power firms is examined in greater detail the picture becomes further complicated. Table 8 presents data on the relationship between firm size and factor proportions for the subset of 48 non-power using firms producing laundry soap. On the basis of the apparently limited technical possibilities for substitution of capital for labor in the non-power sector, we would expect little variation in factor proportions. Never- theless, the coefficient of variation of the total capital-labor is approximately 50 percent under any definition of capital. Thus there is substantial variation in factor proportions in the non-power sector. TABLE 8 CAPITAL SERVICE - LABOR RATIOS BY SIZE OF FIRM IN THE NcN POWER SECTOR Capital Service to Man L < 5 6 < L < 10 ll< L < 20 L > 21 Months of Labor (Weight ed) Total Capital .437 .330 .329 .343 (.302) (.138) (.122) (.126) Working Capital .075 .093 .118 .146 (.027) (.049) (.056) (.057) Technical Capital .363 .237 .211 .197 (.306) (.118) (.085) (.106) -19- Moreover although there is no systematic relationship between firm size and the total capital-labor ratio, this is the product of two offsetting movements in the working capital and technical capital components. The working capital-labor ratio is significantly and positively correlated with firm size; larger firms tend to be more working capital intensive. The technical capital-labor ratio moves in the opposite direction; small firms are the most capital intensive and larger firms the least. If one splits the sample at total employment of ten or fewer employees (corresponding to an annual output of 300 tons) differences in the means of the working capital- and technical capital-labor ratios are significant at the .01 and .10 levels respectively. The inverse correlation between firm size and the technical capital-labor ratio would be further reinforced if we abandoned the assumption of equal economic lifetimes for components of the capital stock across all size groups. Therre is some evidence from responses to the sample survey that smaller firms (those with ten or fewer employees) tend to depreciate their physical capital over a shorter period of time than larger scale firms. This would further raise the capital service measure of factor intensity. The bulk of the literature on small scale enterprises suggests that small firms face higher capital costs and, if they are profit maximizers, should be less capital intensive than larger enterprises. The working capital-labor ratios observed in our sample are consistent with this hypothesis, but the productive capital labor ratios are not. Neither nonprofit-maximizing behavior nor lack of managerial ability suggest anything specific about the behavior of these ratios. A management error could cause the input ratios to be wrong in either direction. If -20- the mean of each group is the correct ratio then the group with the larger variance will be making more errors. A test against the null hypothesis that the input ratio variances are equal is appropriate. The test shows that one cannot reject the hypothesis for working capital- labor ratios but that there are significant differences between the variances of the productive capital labor ratio. Smaller firms are making more mistakes with regard to the choize of technique. One factor which was not covered in our survey may provide an explanation for the apparent decline in capital intensity with increases firm size and for the greater variability of factor ratios for smaller firms. If there are systematic variations in capacity utilization, such that larger firms use more of their installed physical plant than smaller firms with the same engineering capital labor coefficients, smaller firms will appear to be more capital intensive. Labor inputs will adjust to the lower level of capacity utilization while physical capital will not. Since working capital requirements are presumably based on the volume of output, they should adjust more quickly to variations in capacity utilization. Thus what we may be observing is not a significant variation in techniques of production but significant differences in the utilization of plant and equipment. Evidence on relative factor prices can be of some help in supplementing and explaining the behavior of the factor input ratios. Table 9 presents some of the data from the survey concerning the markets for labor and capital in which sample firms operate. Again the striking differences occur between power and non-power firms. -20a- TABLE 9 FIRM SIZE AND FACTOR PRICES: EVIDENCE FROM THE SAMPLE SURVEY LABOR COSTS IN RS MONTH NON POWER SECTOR 0 < L < 5 6 < L < 10 11 < L < 20 21+ POWER SECTOR AVERAGE 178 213.6 199.8 193.0 830.7 WAGE (84.3) (67.6) (35.0) (64.2) AVERAGE MINIMUM 196.9 198.8 195.8 193.3 492 UNSKILLED WAGE (24.0) (26.0) (19.9) (34.8) MINIMUM UNSKILLED 180 165 175 175 270 WAGE CAPITAL COSTS AVERAGE INTEREST RATE 12.0 12.09 12.80 13.01 NA ON ALL LOANS (3.49) (2.39) (2.36) PERCENT OF RESPONDENTS 12.5 63.2 69.2 77.8 NA REPORTING LOANS PERCENT OF CAPITAL REQUIRE- 79.4 83.8 88.9 79.8 NA MENTS MET THROUGH PERSONAL (31.2) (32.4) (33.5) (35.2) SAVINGS NOTES: Standard deviations in Parentheses -21- The non-power sector which is officially considered cottage or small scale industry is exempt from a number of the labor laws which apply to registered enterprises, and applicable portions of the labor legislation do not appear to be enforced effectively. Trade union activity is nonexistant in the non-power sector, and, thus, the market for labor is highly competitive. Power using firms, on the other hand, are subject to full enforcement of labor legislation and to significant trade union activities. The differences in labor market characteristics are reflected quite strikingly in lines 2 and 3 of Table 9. These report the average and minimum starting wage for unskilled labor offered by firms in the sample. Power using firms reported average starting wages more than twice as large as those of non-power using firms, and the minimum starting wage reported by power using firms exceeds that for non-power firms by approximately fifty percent. A portion of the wage differential may represent differences in the quality of unskilled labor, particularly between average starting wages, but the difference in minimum starting wages also reflects the differing characteristics of the labor markets faced by each category of firm. Within the non-power sector there is little variation in wage rates. Minimum wage legislation in.Delhi is apparently scrupulously 11 enforced and observed. The reported minima for firms in each size class reflect the wage floor as do the average starting wages. There is little variation both within and between size classes of firms. -22- Firms in the non-power sector recruit only unskilled workers. Responses to the interviews indicated that skill formation was accomplished entirely by on-the-job training. More than half of the firms interviewed indicated that they offered a number of non-wage incentives designed to reduce turnover and increase the period of employment of their labor force. The most popular of these incentives included money bonuses, gifts at festivals and holidays, and provision of accommodations. Evidence on relative capital costs between the power and non- power sector is limited by the failure of the power-using firms to report borrowing rates of interest. Interest rates for those non-power using firms which reported borrowing a portion of their financial requirements were in the range 6-18 percent with a mean value of about 12.5 percent. Our findings on the utilization of sources of finance external to the firm are consistent with those reported in other small enterprise studies. The proportion of establishments using external sources of finance increases with firm size from approximately 12 percent of firms with five or fewer full time workers to 78 percent of firms employing more than 20. The percentage of capital requirements met through personal savings, however, is approximately 80 percent for all size categories of firms. Thus although increases in firm size apparently give rise to greater access to the financial market, they do not appreciably increase the firm's share of borrowed funds in its portfolio. The principal financial instrument employed by non-power firms was the overdraft facility provided by commercial banks. -23- Asurprising findingoorsuvyilgh of responses to other small industry surveys is an apparent lack of interest by small entrepreneurs in obtaining loans from he commercial banking system or the government. 12Only 36 percent of the respondents identified lack of finance as the principal impediment to expansion of the enterprise, and less than ten percent of respondents identified obtaining loans from the organized financial sector as a major objective. The reason cited by virtually all of the firms for lack of interest in financial institutions was the high opportunity cost of the entrepreneurs time. The procedures involved in sanctioning any loan by public or private financial institutions were criticised as quite lenigthy and cumbersome. In addition the need for bribery and kick-backs was frequently cited as a substantial addition to the costs of borrowing from commercial banks or governmental agencies. Thus although the interest rates reported in Table 9 appear to be low in relation to those encountered in other small enterprise surveys and to the structure of interest rates in the organized sector of the economy, the real costs of borrowing from the organized financial market may be substantially greater. Our evidence on factor prices does not really provide any additional insights into the sources of variations of the working capital-labor ratio and the technical capital-labor ratio with firm size. The low variability observed in factor prices in the non-power sector is consistent with the lack of systematic variation in the total capital-labor ratio but not with its high variance. It is possible that the variations in factor intensities reflect mistakes in achieving the first order conditions for profit maximization. It is also likely, -2 4'- however, that some of the variation represents the possibility that the capital variable is measured with error. The most straightforward of these errors is undoubtedly our failure to correct the capital service variable for differences in capacity utilization. Differences in the vertical integration (thickness) of enterprises may also explain some of the variation in the working capital-labor ratio. In sum the variations in factor proportions observed in our sample, like those observed in most cross-section studies of production, are greater than those which would be predicted on the basis of conventional (static) microeconomic theory.13 -25- 6. A Test for Relative Efficiency - The Profit Function Our test for relative economic efficiency is due to Lau and Yotopolous (1971; Yotopolous and Lau, 1973) and uses a Cobb-Douglas variable profit function to test simultaneously for technical and price efficiency. Assume that the production technology for small and large firms is defined by a Cobb-Douglas production function: V - AY La i= (S,L) (1) where V = value added A = a technical constant K capital services L = labor services = the elasticity of output with respect to capital a= the elasticity of output with respect to labor. Thus the production functions for the two size classes of firms S < 10 employees and L > 10 employees differ by a constant but share common elasticities of output. 'It may then be shown that, assuming profit maxi- mization, a normalized variable profit function exists corresponding to the production function defined in (1) of the form: 7i =A iaKb (2) where i = normalized variable profit (V-wL)/p A =(A/p) [1/(1-a)] (1-a)a-a w = w/p, the normalized wage rate a =-a/(-a) b = S/(l-a) w = the nominal wage for firm i p = the price of output for firm i -26- Variable profit is a decreasing function of the normalized wage, and an increasing function of the capital service variable which is assumed to be predetermined. Thus the profit function explicitly allows for variations in factor and commodity prices in addition to allowing for variations in the firm's endowments of fixed factors. If firms are price efficient in the sense that they successfully fulfill the marginal conditions for profit maximization, differences in the A will reflect differences in technical efficiency between classes of firms. Suppose, however, that firms respond imperfectly to factor prices. One possible behavioral rule is that rather than equating the value of the marginal product of labor (the variable input) with the wage, each firm may interpose a proportional divergence: AiK'L(a-1) = ki (3) If ki 1 the firm (or class of firms) exhibits absolute price efficiency. If ki = kj 1, (iOj) the firms exhibit equal relative price efficiency, ij and if ki k the firms have different relative price efficiency. Since the k iw now represent effective prices for the variable inputs, the observed normalized variable profit function includes the constant of proportionally i k: i i wayb (4 T = A** wa where A = (A/p) (1-a/k )(k ) a i j The test A Al which may be performed by using a dummy variable to estimate A /A is a test of equal economic efficiency. To test for equal technical efficiency Ai = A , we must maintain the hypothesis k=kj in which case: A'*!A = A'/A* =A ](1-a)-1 (5) -27- Hence first we must test for equal relative price efficiency. To do this Yotopolous and Lau exploit a convenient property of the Cobb-Douglas function, the constancy of factor shares. As the wage rate varies the ratio of labor costs to variable profit should remain constant. If the firm is a profit maximizer, ki=1, and -wL/T -(-) = a (6) if k 1 1 it can be shown that i i-1 i -wL/r = a(l-a)[k (1-a/k = a(7) Thus a test of the hypothesis ki = k may be performed by testing whether or not the ratio of the observed wage bill to variable profit is significantly different for large and small firms. The relevant estimating equation is: _UL/7 = aSDS + aLDL (8) where DS = 1 for firms with 10 or fewer employees, 0 elsewhere DL = 1 for firms with more than 10 employees, 0 elsewhere The profit function is linear in logarithms and is estimated as In 1T = 1n AL + yD + a Inw + b In K (9) S L where y = In (A S/A ). Since the independent variables in equations (8) and (9) are all predetermined, ordinary least squares will yield consistent estimators of the parameters. But if the covariance of the errors of the two equations is permitted to be nonzero for each firm, and errors are assumed to be independent across firms, Zellner's (1962) method is appropriate. The efficiency of the estimation may also be improved by imposing known constraints on the coefficients of the two equations. -28- Data are drawn from the 48 non-power using firms in the sample of soap manufacturing enterprises. The capital service variable is the same as that defined above and includes both directly productive and working capital. Labor services are the wage weighted sum of man-months in unskilled labor equivalents, including hired labor, non-paid family labor, and working partners. The wage rate is the minimum nominal wage for unskilled male workers-reported by the establishment, and the price of output is the implicit price derived from the ratio of value to weight of output expressed in Rs. per ton. Variable profit is value added less the imputed wage bill. Estimtes-of the profit function and labor demand function by ordinary least squares and Zellners method of seemingly unrelated regressions are reported in Table 10. The profit functions perform quite well. The 2 R of the OLS profit equation equals .710. All coefficients have expected signs. The wage variable is significant at the five percent level and the capital service variable at the .01 level in the OLS estimates. Six hypotheses are tested successively on the data, and the results of these tests are summarized in Table 11. Hypothesis (i) states that the economic efficiency of small and large firms is equal. This hypothesis is rejected at the ten percent level on the basis of the OLS estimates and at the one percent level on the basis of the systems estimates. Large firms (those with more than 10 employees) are more economically efficient than small firms. Hypothesis (ii) maintains that small and large firms are of equal relative price efficiency -- i.e. that they succeed in equating the value of labor's marginal product to the wage to the same degree. This hypothesis cannot be rejected at the .10 level; small and large firms TABLE 10 ESTIMATED PARAMETERS OF THE COBB-DOUGLAS PROFIT FUNCTION ONE RESTRICTION TWO RESTRICTIONS PARAMETER OLS NO RESTRICTIONS b5=b b2=b5=b ___ __ __ __ __ __ ___ __ __5 6 2 5 6 1uq bo 4.977 1.444 1.457 2.980 (2.327) (1.645) (1.664) (.438) D b -.408 -.548 -.412 -.380 (.233) (.207) (.166) (.155) In WAGE b -1.219 -.255 -.278 -.658 2 (.572) (.404) (.407) (.068) In SK b .728 .678 .679 .673 G 3 (.117) (.083) (.084) (.079) I D b -.737 -.737 -.672 -.658 s 5 (.091) (.091) (.069) (.068) DL b -.589 -.589 -.672 -.658 6 (.103) (.103) (.069) (.068) TABLE 11 TESTS ON HYPOTHESES REGARDING THE RELATIVE EFFICIENCY OF LARGE AND SMALL FIRMS MAINTAINED HYPOTHESES TESTED HYPOTHESES COMPUTED F CRITICAL F Hl F.0 0 0 (F.01) b=0 F(1 90) =7.543 3.96 REJECT (6.97) b=b6 F(1 90) 1.251 3.96 ACCEPT (6.97) b =0 and F= 4.008 3.11 REJECT b=0, an(4.89) b =b. 5 6 b 2=b5 F = 1.457 3.96 ACCEPT (4.89) b =b F 2 6 (1, 90) = .069 3.96 ACCEPT (4.89) b5=b6 b2=b6 F(2 90) =1.183 3.11 ACCEPT (4.89) -29- have equal relative price efficiency. A test on the coefficients of the OLS labor demand function yields similar results. Hypothesis (iii) states that small and large firms jointly exhibit equal price and technical efficiency. This hypothesis is rejected, which is not surprising in view of the results of (i) and Hypotheses (iv) and (v) test for the absolute price efficiency of small and large firms. The maintained hypotheses are therefore equi- S L valent to k = 1 and k = 1. Both hypotheses are accepted. Small and large firms in the sample appear to fulfill the first order conditions for profit maximization. The test is not completely convincing, however, because of the relatively large standard error of the wage coefficient in the profit function. Hypothesis (vi) states that there is absolute price efficiency under the maintained hypothesis of equal relative price efficiency. This hypothesis cannot be rejected at the .10 level. 'The result is anticipated by the results of (ii) .and (iv) or (v). If a hypothesis was not rejected we proceeded to compute estimates of the parameters of the profit function incorporating the restriction. The restricted estimates are reported in Table Indirect estimates of the Cobb-Douglass production function coefficients can be obtained from the parameters of the profit function. These estimates, together with direct OLS estimates of the production function parameters, are presented in Table 12. The indirect estimates have the virtue of being statistically consistent while those estimated directly by ordinary least squares suffer from simultaneous equations bias. -29a- TABLE 12 COMPARISON OF DIRECT AND INDIRECT ESTIMATES OF INPUT ELASTICITIES OF THE PRODUCTION FUNCTION Parameter of Direct Estimate OLS One Restrictiona Two Restr- Three ictionsb Restrictions Capital .233 .342 .531 .406 .520 Labor .840 .530 .218 .397 .480 Notes: a: equal relative price efficiency b: equal absolute price efficiency c: constant returns to scale -30- The computed elasticities appear reasonable in comparison with the OLS estimates. Although there is a striking shift in the magnitude of the labor coefficient between the direct and indirect estimates, the direction of change is consistent with the elimination of simultaneous equation bias in the direct estimates. The sum of the elasticities derived from the profit functions are less than one except for the final restriction to constant returns. Our results indicate that large firms are more economically efficient than their smaller counterparts in India's soap manufacturing industry. These differences arise from the lower level of technical efficiency of small scale firms, since both classes of firm apparently succeed in maxi- mizing profits to the same degree. In an effort to explore possible sources of the superior technical efficiency of large firms we modify the profit function to test for the presence of learning by doing. Data from the sample survey include the age of the enterprise and a frequency distribution of the duration of employment of workers in the firm from which an average duration of employment was estimated. These two variables are incorporated into the Cobb-Douglas production function in the following manner: V = Be K La (10) where eXT is an efficiency factor representing the accumulation of experience, and X is the rate of increase in output due to an increase in experience T. We employ both age of the enterprise and average duration of employment as proxies for experience. It is reasonable to expect that there will be decreasing returns to experience beyond some level of age of enterprise or duration of employment. In order to incorporate this type of decrease in the effective- ness of experience we employ two alternate specifications of the production -31- functions: i [AT + 1T2 a V =Be KL (11) V= Bi TK La (12) where p is expected to be negative. Plotting log V against T -- holding other factors of production constant -- the specification in (11) yields a curve with slope equal to X initially, decreasing continuously with T until it becomes equal to zero at -X/2p years. The parameter 6 in equation (12) is obviously the elasticity of output with respect to the level of experience. Variable profit functions derived from the production functions in (10), (11) and (12) yield the following estimating equations. L S ln r = lnB + cT + yD + a lnw + b In K (13) L 2 S In v = InB + cT + dT + yD + a Ir + b ln K (14) L S ln w = InB + lnT + yD + a ln + b In K (15) L S Assuming that k =K these functions may be jointly estimated with the pooled labor demand equation: -WL/7 = a. (16) The estimated coefficients using both OLS and Zellner's method appear in Table 13. The two measures of experience perform relatively well in explaining variations in the efficiency of firms. All coefficients are of expected sign, although the power function form appears to perform somewhat better than the exponential form, and average experience of the labor force performs somewhat better than age of the enterprise as a measure of experience. TABLE 13 ESTIMATED PARAMETERS OF PROFIT FUNCTION INCORPORATING EXPERIENCE OLS NO RESTRICTIONS ONE RESTRICTION In B* 5.656 6.573 6.801 2.135 2.473 2.955 2.832 2.821 2.752 (2.413) (2.478) (2.351) (1.692) (1.831) (1.682) (.433) (.445) (.420) D -.390 -.352 -.317 -.392 -.386 -.344 -.373 -.372 -.340 (.233) (.233) (.225) (.163) (.171) (.161) (.152) (.155) (.145) In w -1.423 -1.695 -1.774 -.489 -.582 -.729 -.665 -.666 -.670 (.605) (.633) (.595) (.424) (.465) (.426) (.067) (.067) (.067) In SK .741 .726 .736 .692 .693 .686 .689 .688 .679 (.118) (.117) (.112) (.082) (.086) (.080) (.078) (.080) (.074) EXPER .017 .076 .019 .027 .022 .028 (.016) (.047) (.011) (.034) (.010) (.029) 2 [EXPER] -.002 -.0002 -.0002 (.001) (.0008) (.0008) In EXPER .251 .188 .185 (.108) (.077) (.065) a -.672 -.672 -.665 -.666 -.670 (.068) (.068) (.067) (.067) (.067) t TABLE 13 (CONTINUED, ESTIMATED PARAMETERS OF PROFIT FUNCTION INCORPORATING AGE OF ENTERPRISE OLS NO RESTRICTIONS ONE RESTRICTION L In B 4.722 5.166 4.582 8.914 1.084 .796 2.741 2.654 2.414 (2.365) (2.390) (2.366) (1.655) (1.740) (1.652) (.450) (.517) (.515) D -.399 -.375 -.392 -.397 -.395 -.391 -.359 -.358 -.356 S (.234) (.235) (.234) (.164) (.170) (.163) (.153) (.155) (.152) In w -1.191 -1.417 -1.223 -.195 -.251 -.250 -.655 -.658 -.657 (.577) (.609) (.573) (.403) (.443) (.399) (.067) (.067) (.067) In SK .724 .729 .725 .669 .672 .673 .663 .645 .667 (.118) (.117) (.117) (.082) (.086) (.082) (.078) (.079) (.077) AGE .009 .069 .014 .017 .014 .026 (.012) (.054) (.008) (.039) (.008) (.035) AGESQ -.002 -.0001 -.0004 (.002) (.001) (.001) In AGE .150 .202 .206 (.158) (.111) (.104) a -.672 -.672 -.655 -.658 -.657 (.068) (.068) (.067) (.067) (.067) -32- In the power function form the coefficient of average experience is significant at the .05 level or better in all regressions. The indirect estimate of the elasticity of output with respect to average experience derived from the restricted estimate of the profit function is .111. Thus a ten percent increase in the average experience of the firms labor force would give rise to about a one percent increase in output without an increase in other productive factors. Age of the enterprise yields an indirect elasticity of .124 which is to be expected since the two measures are highly correlated. The evidence indicates that learning by doing is an important phenomenon in India's soap manufacturing industry. For this reason it is perhaps not surprising to learn that firms are willing to provide wage and other incentives to increase stability of their labor force and reduce turnover. Controlling for experience (or age of enterprise), capital and variation in wages and prices does ot eliminate the significant differences in the technical efficiency of large and small enterprises, however. Test statistics on the hypothesis that y = 0 are reported in Table 13. The maintained hypothesis is rejected at the .05 level in all cases. Learning by doing explains a portion of the relative variation in technical efficiency among enterprises, but it cannot explain it all. -33- 7. Technical Efficiency - A Ronparametic Approach The preceeding analysis of relative efficiency indicated that on average firms with a total labor force of ten or fewer employees were less economically efficient than those of larger scale. The difference in economic efficiency was attributed to relative technical inefficiency, the failure to achieve maximum output for a given endowment of variable and fixed factors of production, rather than to relative inability to meet the conditions.for profit maximization (price inefficiency). In this section we turn to a more detailed examination of the technical efficiency of individual firms, employing Farrell's (1957) method. Consider each of the firms as a separate activity producing a unit of output through the input of m factors of production. The jth activity is then completely described by a vector of m+l elements, and f.. represents the quantity of factor i used in the unit activity j. The objective is to determine the location of each firm relative to the origin and an envelope of all firms in the sample. Given all activities and the jth list of inputs it is possible to estimate the maximum amount of output which can be produced. Since by definition the jth activity produces one unit of output, if some combination of activities can produce more than one unit of output while using the same vector of resources, activity j is in- efficient. Its index of inefficiency is defined as the reciprocal of maximum output.14 If m=2 the technique is easily handled geometrically. Figure 2 shows the input combination of capital services and labor services required to produce a unit of output for each sample firm. The envelope of linear combinations ABCDE defines the frontier isoquant, since no firm is able to produce a unit of output with a combination of inputs to the southwest of the frontier. Tm K/VA D, L/VA Figure 2 Relative Technical Efficiency in the Farrell Diagram -34- Farrell's method measures each firmis technical efficiency relative to this achieved efficiency locus. Thus in Figure 2/firm B and C are equally technically efficient; Firm F is inefficient and its index of technical efficiency is the ratio OD/OF < 1. The method is generalizable to any number of inputs using linear programming techniques, but with more than two, or possibly three, inputs it becomes difficult to visualize the production surface. The technique has several advantages for the study of technical efficiency. First, the envelope generated by the most efficient combination of activities corresponds more closely to the theoretical notion of a production function than "average" production functions fitted by statistical 15 methods. Second, it is free of functional form. Third, it can accommodate a sample of establishments using heterogenous technologies, and finally it yields a firm-specific index of technical efficiency which permits further analysis of the sources of inefficiency of firms in the sample. A number of theoretical and empirical limitations of the method exist, however. In particular since the frontier is deterministic it is defined by the extreme observations of the data set. The number of observations included in the efficiency frontier is relatively small, regardless of the size of the sample, and the presence of an observation on the frontier will depend on the number and definition of inputs. Thus the position of the frontier is strongly sensitive to errors of observation, and suffers from two offsetting sources of bias: (a) measurement errors may bias the frontier in an optimistic fashion; (b) since the estimated unit isoquant depends only on actual observations a larger sample cannot contract it, but may move it closer to the origin. The extent to which either of these biases is dominant is unknown and presumably varies with each sample. -35- As the two dimensional case makes clear, the technique also introduces the implicit assumptions that the productive processes exhibit the proportionality property (that they can be operated at any level) and that they are subject to constant returns to scale. These limitations can be obviated to some extent by estimating efficiency frontiers for several size groupings of establishments, and observing their relative positions. To estimate relative technical efficiency for the soap manu- facturing industry a unit isoquant in value added was constructed in capital labor space. Definitions of capital services and labor services (wage weighted) are identical to those employed in the preceeding section. Labor is expressed in man-months per unit of value added and capital in Rs. per unit of value added. Figure 3 presents a mapping of the unit production points for the 48 non-power firms and the 3 power using firms in the sample. Each point corresponds to a single observation on a firm. The cross sectional mapping confirms our prior observations con- cerning the high degree of variation in factor intensities, and the relative capital intensity of the power using manufacturing process. Two sets of production frontiers are drawn in Figure 3. The first re- presents the envelope of all observations, including power using plants. The second efficiency frontier represents the envelope of non-power using observations only. In order to reduce the possibility of optimistic bias in the production frontier a second consecutive unit isoquant, determined by the envelope of all establishments excluding those in the first production frontier, was estimated for each set of observations. K/VA Figure 3 Efficiency Frontiers for - &32j ¥ Soap Manufacturing (First and Second Frontiers) r7 å 4 1.~//- 3 * -st i All 2nd All st 4 1 Non Power nd 2 Non Power . 4 / 4- 5.0 *• L/VA :4* 4 4 t i, n*ý4*.-14r++ * 4 4 4* * 4¥*4 +4+- ++‡4++***-f**¥f -* 44*4 4 +** 44 44++4 4¥ .. /22 *b -1 1 1. -36- The unit isoquants effectively illustrate the influence of pessimistic bias on the efficiency frontier. Addition of one highly efficient power using firm extends the first efficiency frontier sub- stantially to the northwest. The three remaining efficiency frontiers lie quite close together. In particular the first and second set of efficient points for the non-power sub-sample are nearly coincident at high levels of labor intensity. Table 14 illustrates the wide range, but relatively high level of technical efficiency among firms in the sample. Using the first efficiency frontier for the non-power sample as the standard of reference, 68.8 percent of all firms have relative technical efficiency indices greater than .50. Less than ten percent of the observations have co- efficients less than one-third. Notwithstanding the small number of observations, comparison of the power sector sample with its frontier firm shows an interesting variation in the relative levels of technical efficiency. The three ob- servations are widely dispersed in input space. It is frequently argued that because larger firms use more modern (capital intensive) technologies than small enterprises, the techniques of production which they employ dominate the earlier technologies absolutely. Evidence from our sample does not support such a conclusion in soap manu- facturing. Although two of the power-using units define efficient capital intensive facets of the production surface, they do not dominate efficient non-power firms. Indeed, the most efficient of the power using firms has fewer than 100 employees and is smaller than a number of the non-power using firms in the sample. The results help to point up the limitations of inferences concerning the relative efficiency of production -36a- TABLE 14 RELATIVE EFFICIENCY OF ESTABLISHMENTS IN THE SOAP MANUFACTURING INDUSTRY RANGE OF EFFICIENCY INDICES 1.00-.85 .84-.70 .69-.50 .49-.35 .34-0.00 Number of Firms 10 9 14 11 4 Relative Percentages .208 .188 .292 .229 .083 TABLE 15 RELATIVE EFFICIENCY BY ESTABLISHMENT SIZE GROUP 1.00-.85 .84-.70 .69-.50 .49-.35 .34-0.00 0 < L < 5 1 (.143) 2 (.286) 0 3 (,.429) 1 (.143) 6 < L < 10 3 (.150) 3 (.150) 9 (.450) 3 (.150) 2 (.100) 10 < L < 20 3 (.250) 2 (.167) 4 (.333) 3 (.250) 0 L > 21 3 (.333) 2 (.222) 1 (.111) 2 (.222) 1 (.111) Note: Relative percentages of establishments within each size group in parentheses. -37- processes based on engineering data alone. High levels of potential engineering efficiency are compatible with low managerial, and hence, technical efficiency in a given economic environment. The relatively high overall levels of technical efficiency in the sample are probably the result of the highly competitive environment in which soap manufacturing firms operate.16 The large number of producers, ease of entry and exit and compact spatial distribution of firms in the population make it likely that highly inefficient producers are driven from the industry. The relationship between the efficiency frontiers for firms in rarious size groupings is illustrated in Figure 4. No definite pattern of behavior emerges from the sample. The efficiency frontiers for the different size categories cross each other so that no single group of efficient firms dominates the industry. Thus it cannot be established empirically that one size group of establishments is technically more efficient than another in soap manufacturing. The estimated efficiency frontiers do not provide a picture of the average efficiency of firms by size group.. Thus, our finding that the representative small firm is less efficient than its larger counter- part is not inconsistent with the finding that the most efficient firms in each size category are of approximately equal relative efficiency. Table 15 presents the distribution of firms by size category and level of technical efficiency relative to the first production frontier (excluding power using establishments). Again no striking pattern emerges to indicate that smaller firms are markedly less efficient than large scale enterprises, although the distribution of indices within size groups does suggest that there is a tendency for average efficiency to improve with size. K/VA Figure 4 - Efficiency Frontiers för Firms of Different Size 4 1 i +11-20 4 20+ 6-10 O-5 :44 1 .e 4 o4. L/VA 9 -70 4-91>1 ,Yr ý > -9 1-11ý+ 4 494 skf4* 44 1 4 z 4 4 4 W 4 4L 4, 4 & *L4~-+ u -38- The percentage of establishments with the lowest efficiency indices declines somewhat as size increases, while the percentage of firms with indices exceeding .70 increases with size of firm. Splitting the sample at ten workers and performing a test for equality of the mean indices of technical efficiency does not yield statistically significant differences. There is, however, apparently a significant relationship between firm size and the efficiency index. Table 16 presents zero order correlation coefficients between the index of technical efficiency and a number of attributes. Firm size measured either in terms of physical output or value added is significantly correlated with the efficiency index. Larger firms tend to be more efficient. Our efforts to establish the sources of technical efficiency from characteristics of the labor force and managers have not been highly successful. Neither experience nor age of the enterprise appear to be significantly correlated with the efficiency index. This is somewhat surprising considering the results of the preceeding section but may reflect our failure to specify a learning function characterized by decreasing returns. Among the characteristics of the entrepreneur analysed, the only variable which appears to have any promise is the total experience of the principal manager. Splitting the sample into groups by level of education and computing the mean index revealed an interesting pattern of means, rising with educational level up to middle school graduate and then declining above that level but differences in the means were not significant at conventional levels. -38a- TABLE 16 CORRELATIONS BETWEEN TECHNICAL EFFICIENCY SCORES AND OTHER ATTRIBUTES CORRELATION WITH EFFICIENCY INDEX Firm Size Indicators Employment .173 Tons Output .221* Value Added .257* Factor Intensity Indicators Capital Service/Labor Ratio -.331* Technical Capital Labor Ratio -.497* Ratio of Working Capital to Total Capital .557* Labor Force Attributes Experience .087 Skill Ratio -.166 Age of Enterprise .090 Proprietors Characteristics Experience in Firm .087 Years of Prior Experience .117 Total Experience .164 Notes: *Significant at P > .10 -39- The most striking results were obtained when the efficiency index was correlated with the capital-labor ratio. The tot..-- capital labor ratio is negatively correlated with the index of technical efficiency at the .05 level and the technical capital labor ratio is negatively correlated with the index at the .01 level. Capital intensive firms are apparently less technically efficient. This supports the argument that what we may be observing via the capital labor ratio are in fact variations in capacity utilization. Firms which use relatively less of their installed capacity will appear to be relatively inefficient compared to the industry frontier. The significant positive correlation between the share of working capital in the capital stock and the efficiency index lends some additional support to this argument. Those firms with low levels of working capital relative io their capital stock may be those with the lowest levels of capacity utilization, if our arguments concerning short term adjustment of the level of working capital to the level of capacity utilization are correct. In an effort to examine the interrelatedness of a number of the attributes employed in the analysis of efficiency we have experimented with a technique of multivariate analysis known as multidimensional scaling (MDS). MDS is a method which has very recently received some attention in the economics literature and therefore requires a brief introduction.17 If we consider a matrix of correlation coefficients, interpretation of the relationships among all of the variables is difficult unless they are very stark. NDS attempts to provide a pictorial representation of the relationships among attributes by providing a plot of each of the characteristics in two dimensional space. The scaling algorithm attempts -40- to plot the points such that the distance between points corresponds to the relative correlation between characteristics. Thus if a pair of points lies in close proximity the two attributes represented are more closely correlated than more distant pairings. It is then possible to look for clusters of points which imply groupings of similar characteristics. Because it is not generally possible to insure that the relative distances perfectly mirror relative correlations, MDS minimizes an index which measures the discrepancies between the relative distances and correlations. Figure 5 is a scaling diagram for the correlation matrix of the attributes examined in the analysis of efficiency. Several interpretations of Figure 5 present themselves and tend to confirm the analysis above: (a) the single variable most closely correlated with all others (as measured by the proximity to the centroid) is age of the enterprise; (b) the indicators of firm size are quite closely grouped and show greater proximity to age of enterprise and our proxy for capacity utilization (the working capital ratio) than to total factor intensity or the index of efficiency, (c) the characteristics most highly correlated with technical efficiency (age of enterprise, total experience of the manager, capacity utilization) form a grouping which is diametrically opposed to the characteristics of factor intensity represented by the capital-labor and skill ratios. t Value added ratio Figure 5- Multidimensional Scaling of Some Attributes of Enterprises AIndex of i TechnicaliEfficiency- iProprietorl s' Experience Age of Enterprise F Workin Capital I. Ratio o FISkil] Ratio o E 0 0 o a. E Capital Labor Ratio 8. Conclusions This paper has addressed two major issues arising out of small industry policy in India -- the relationship between firm size and labor intensity and the relationship between scale and technical efficiency. We summarize our major findings as follows: 1. The principal dimension of the choice of technique in the soap manufacturing industry is the decision to use electrical power. Because public policies discriminate against firms which would employ only a limited number of mechanized processes, techniques of production have been dichotomized into relatively capital intensive power using technologies and traditional, labor intensive methods. Intermediate combinations of mechanized and hand techniques are not observed. 2. Within the non-power sector of the industry there is no relationship between firm size and capital intensity, when capital is defined to con- sist of both technical and working capital. There is a positive relation- ship between working capital-labor ratios and firm size and a negative relationship between the technical capital-labor ratio and firm size. These relationships taken together suggest that there may be a systematic relationship between size of firm and the level of capacity utilization, with larger firms using more of their installed capacity. 3. There appears to be very little variation in wage rates among firms in the non-power sector. Wages in the organized (power using) sector are about' 1.5-2 times the level in the non-power sector. Utilization of commercial or government credit and, perhaps access, appears to be positively correlated with firm size. Although interest rates on loans are modest in comparison with other studies of small enterprises, non-interest costs of borrowing appear to be substantial. -42- 4. Firms employing ten or fewer workers are on average less economic efficient than larger enterprises. The differences arise from differences in technical efficiency rather than from failure to fulfill the conditions for profit maximization. 5. Experience of the labor force, measured either in terms of the average total experience of workers or the age of the enterprise, is an important factor in explaining differences in the relative profitability of firms. There are diminishing returns to experience, however, and differences in levels of experience do not fully explain differences in the relative technical efficiency of small and large firms. 6. Best practice firms in each size category appear to be of equal technical efficiency. Power using techniques do not dominate non-power techniques absolutely, and there is apparently no systematic relationship between firm size and best practice technology. 7. Several attributes of managers, including education and experience, appear to-be related to the level of technical efficiency of the enterprise but our data provide few significant correlations. 8. A major determinant of relative efficiency as measured in our sample may be the level of capacity utilization which appears to vary positively with firm size. -43- FOOTNOTES 1See for example the studies cited in Morawitz (1974), White (1978), and Page (1979). 2See for example Child (1978), Steel (1977) and White (1978). 3Important contributions are those of Timmer (1971), Lau and Yotopolous (1971), Aigner Lovell & Schmidt (1978) and Schmidt and Lovell (1979). 4Evidence is presented in Griliches and Ringstadt (1971) and Heller (1976). 5Work on small holder agriculture (Sen [1966]) suggests that household enterprises may maximize utility-not profits. Martin (1978) explores the consequences of such a model for the level of X efficiency of the enterprise. 6 See the work of Shapiro and Mueller (1977) and Page (1980) for empirical tests of the relationship between managerial attributes and technical efficiency. 7In an experiment to determine the effect of treating working proprietors as labor inputs we have estimated an alternative set of profit functions with proprietors time as an additional explanatory variable. The results which will be reported in a subsequent paper do not overturn the conclusions reached in the present paper. 8fBased on responses to the sample survey and evidence on the costs of capital in the agricultural sector. See Bhalla (1979). 9See the discussion in Jorgenson and Griliches (1967) and Griliches and Ringstadt (1971). -44- 10The appropriate test statistic is from Mood and Graybill (1963), page 307. 11The minimum wage exclusive of benefits is RS 2100 per annum. 12Contrast the surveys reviewed in Page (1979). 13See for example Meller (1976), Griliches and Ringstadt (1971). 14Formally there are n distinct linear programming problems in which the n productive activities form a constant coefficient matrix, A, and each of the activities in turn furnishes the coefficients of the right hand side. Let V be an MxI vector of ones. The jth linear programming problem is then: MAX X0 VIX X > 0 AX < P. rfI P= j = quantity of factor i employee to produce f2j one unit of output in activity j.. For additional discussion see Timmer (1970). 15There is recent work on stochastic frontier production functions estimatedby maximum likelihood methods. 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