JIIIIIWIWFIFIIHHHIIIFHIIIHI . TF-“i'tim i! ‘ - a 4 _ ' ‘ ’ [v v \ . r U | , ’\ \ Lv -1 f‘ V i This is ”it? flat the dissertation entitled Fixed Effect Cobb-Douglas Production Functions . for Floor Tile Firms, Fayoum and Kalyubiya, Egypt, 1981-83 ) presented by James L. Seale, Jr. ' has been accepted towards fulfillment of the requirements for , Ph . D . degree in Agric o Econ o ( Date 1%é/f( 7 1 M30 is an Affirmative Action/Equal Opportunity Institution 0-12771 ’ MSU RETURNING MATERIALS: Place in book drop to LIBRARIES remove this checkout from —u—. your record. FI__N___ES will be charged if book is returned after the date stamped below. 911121995 .V FIXED EFFECT COBB-DOUGLAS PRODUCTION FUNCTIONS FOR FLOOR TILE FIRMS, FAYOUH AND KALYUBIYA, EGYPT, 1981-1983 BY James Lawrence Seale, Jr. A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1985 ABSTRACT FIXED EFFECT COBB-DOUGLAS PRODUCTION FUNCTIONS FOR FLOOR TILE FIRMS, FAYOUM AND KALYUBIYA, EGYPT, 1981-1983 By James Lawrence Seale, Jr. The purpose of this thesis is to develop and estimate individual, firm-specific measures of differences in production among Egyptian small- scale tileries in Fayoum and Kalyubiya governorates using a fixed-effect Cobb-Douglas system and panel data collected in Egypt under the supervision of the author. Other measures to determine if tileries are failing to maximize profit and to combine variable inputs in a least cost manner are developed and estimated. After obtaining the above measures, it is determined if certain firm or entrepreneurial characteristics are associated with these estimates. The analytical procedure ‘used :hi this thesis combines techniques developed in the econometric literature on frontier production (cost) functions and panel data estimation. Physical, stochastic production functions are fitted to the panel data allowing for differences in production among firms using a fixed-effect Cobb-Douglas model. The data sets from the two areas are pooled, and tests are constructed that indicate that effects from the production function, taken as a whole, add to the explanatory power of our production function equation and that ordinary least squares or the "within" estimator is more appropriate for estimating the model with the Egyptian tilery data. Major findings are that the tileries produce under constant returns to scale; that there are differences in production among tileries, both within and between the two areas, but these differences are generally not great from an economic point of view; that tileries on average are failing to maximize profit by employing too little capital and too little labor; and that tileries on average are not combining labor and capital efficiently as they employ too much capital relative to the amount of labor they use, though the cost of this inefficiency is small. The model performed quite well in estimating actual differences in production among the tileries. Rankings in terms of the fixed effects in the production function are quite similar to a puiori rankings made by the author based on his firsthand knowledge of the tileries over a two year period. The estimates measuring failure to maximize profit and to combine variable inputs efficiently also seem reasonable. Dedicated to my wife, Colleen Seale. ii ACKNOWLEDGEMENTS Without the guidance, assistance, and support of so many people, this dissertation could never have been completed. I particularly want to recognize Professor Peter Schmidt, my thesis advisor, for all the assistance he has given me, and Professor Glenn L. Johnson, my major professor, who has been an inspiration to me throughout my time as a graduate student. I want to recognize the contributions of the other members of my thesis committee, Professor Roy Black, whose support and advice have been crucial in my completing this work, and Professor Carl Liedholm, whose encouragement, advice, and financial support have been much appreciated. I want to thank Professors Allen Shapley and Stan Thompson for serving on my guidance committee and Professor Donald Mead and Herbert Kriesel for their support and advice in both Egypt and East Lansing. My sincere thanks goes to all the persons in Egypt who assisted me during the survey and fieldwork. Special recognition goes to the people of Cairo University at Fayoum and Zagazig University at Moshtohor for their cooperation, particularly all the enumerators of both areas, Moshira El Kamal, and Professors Ali El Bassel, Abdel Rahman Saidi, Abdel Azis Mostafa, Ragab E1 Coma, Nadia Sheikh, Mahmoud Badr. My appreciation also goes to Andy Koval and all the wonderful people at Catholic Relief Service in Egypt. iii My friend anui colleague, Stephen Davies, deserves special recognition. His support and friendship in both Egypt and at Michigan State have been invaluable. My appreciation is also extended to Anne Morris for being so generous and helpful and Pat Neumann, who typed and helped organize my tables and other materials and was instrumental in completing a final copy of the dissertation. The person that deserves the most recognition is my loving wife, Colleen. Her encouragement and full understanding in Egypt, East Lansing, and now from the University of Florida have enabled me to complete this work. For this, I am eternally grateful. iv TABLE OF CONTENTS Page LIST OF TABLESOOOOOOIOOOO0.0000000000000000...OOOOOOOOOOOOOOOCOOOOVii CHAPTER I: INTRODUCTIONOOOO...0.00.0.0...OOOOOOOOOOOOOOOOOOO00.0.1 CHAPTER II: FIELD RESEARCH AND DATA COLLECTION IN EGYPT...........5 1 Description of Study Areas..............................5 .2 Phase I Survey..........................................6 2.2.1 Questionnaire Content............................8 Industry Coverage................................8 Sampling Approach................................9 Enumeration Procedure...........................12 Card Printing and Processing Procedure..........l4 Phase I Results.................................14 2. 2 5‘. 2.3 0) II surVQYoooooooooooooooooooooooooooooo000000000019 IHdUStry and Firm saleCtionooooooooooo000000000019 Data C011€Ctionooooooooooooooooooooooooo0000000021 II IHdUStrieS: An overViEWoooooooooooo000000000023 NNNNgNN'fiNNNNN o o bbbbmwwm NNNNN o #WNHmNfi-‘CDO‘M#WN 2.4 m Labor...O...0.0.0.0...I0.0.00.00.000.0000000000028 capitalooooooooooooooooooooooooooooooooooooooooo33 MarketingOOOOOOOOOOOO00......0.0.00.00000000000036 Income-000.00.000.00.ooooooooooooooooo000000000038 CHAPTER III: THEORETICAL FRAMEWORKOOO0.0.00.00.00.000.00.00.00.00043 DeterminiStiC Non-parametric FrontierSooooooo000000000053 3.1 3.2 Deterministic Parametric Frontier Functions............56 3.3 Deterministic Statistical Frontier Functions...........58 3.4 Stochastic Frontiers...................................6l 3.5 Frontier Systems.......................................65 CHAPTER IV: ANALYSESANDRESULTSOOOOO.COO...0.0.0.00000000000000083 4 1 Statement of the Model.................................85 4 2 Data...................................................9l 4.3 Estimation Procedures..................................99 4 4 Empirical ReSUItSoooooooooooooooooooooooooooo000000000105 "Within" Analysis for Kalyubiya Firms..........106 "Within" Analysis for Fayoum Firms.............ll9 Pooling the Fayoum and Kalyubiya Data Sets.....l30 . Estimating the Model with Pooled Data..........134 4.4.5 Efficiency Measures--Variab1e Inputs...........l47 4.5 Estimation of Model II--Exogenous Output..............154 o fi‘D‘b‘D‘ b-&~&-b‘ o o o D~u1hihi V CHAPTER V: CHAPTER VI: APPENDIX A APPENDIX B APPENDIX C FIRM CHARACTERISTICS, PRODUCTION, AND EFFICIENCY.....163 Description of Fayoum Firms...........................166 Description of Kalyubiya Firms........................176 Characteristics of Entrepreneurs......................189 Size of Operation.....................................l98 Market Size and Location..............................204 Changes in Marketing and Production...................208 summarYOOOOOOOOOOOOO0.0...OOOOCOOOOOOOOOOOOOOOOOOO0.0.215 CONCLUSIONSO0.0000o.00000.0...000000.000000000000000217 Phase I QUQStionnaireooooooooooooooooooooooooooooooo00223 Towns and Villages Surveyed...........................224 0..0.0.0....0.00.0.0.0...OOOOOOOOOOOOOOOOOOOOOO0......225 BIBLIOGRAPHYOOOO000......O0......0......O...0......0.0.0.000000000230 vi \O (D \l 0‘ U1 9- U) h) F‘ IE; 10 ll 12 13 14 15 16 LIST OF TABLES PAGE Selected Characteristics of Governorates Under Study............7 Total Number of Villages and Towns in Fayoum and KaIUbiya and in the sample.0.00....OOOOOOOOOIOOOOOOOOOOOO0.0.0.11 Sampled and Estimated Total Number of Enterprises and Employees in Fayoum and KaIYUbiya - 19810000000000.0000000013 Distribution of Estimated Total of Enterprises and Employment in Fayoum and Kalyubiya by Industry - 1981..........l7 Estimated Total Employment in Fayoum and Kalyubiya by Sex and Employment Category - 1981..........................18 Industries Covered in Phase II Survey - l982...................20 Labor..........................................................29 Capital........................................................34 Marketing Patterns.............................................37 Value Added and Income.........................................39 Regression Results From Production Function - KalyUbiya Governorateoooooooooooooocoooooooooooooooooooooooooo117 Fixed Effects From Production Function - Kalyubiya GovernorateOOOOOOOOOOOOO000......OOOOOOOOOOOOOOOO0.00.00.00.00118 Regression Results From Production Function - Fayoum Governorateooooooooooooooooooooooooooo00000000000000.00126 Fixed Effects From Production Function - Fayoum GOV€tfl0t3t€oooooooooooo.coo.oooooooooooooooooooooooooooooooooo127 Regression Results From Production Function for Pooled Data -- Fayoum and Kalyubiya Governorates.....................136 Fixed Effects From the Production Function for Pooled Data -- Fayoum and Kalyubiya Governorates.....................137 vii. 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 "Within" Regression From Production Function for Pooled Data - Firm 216 (Fayoum) as conStantooooo00.000000000000000...144 "Within" Regression From Production Function for Pooled Data - Firm 306 (Kalyubiya) as Constant.......................l45 Marginal Value Products and Marginal Factor Costs - variable Inputs.OOOOOOOOOOOI...OOOOOOOOOOOOOOO0.0.0.0000...00.148 Efficiency Measures - Variable Inputs.........................150 COSt Of IUBffiCienCY ‘ Variable Inputs 00000000000000.00000000153 Entrepreneurial Characteristics (Ranked by Size of Fixed Effects From Production Function).......................194 Entrepreneurial Characteristics (Ranked by Efficiency Measures From FaCtor Share Equation).ooooooooooooooooooooo0000196 Variables Indicating Size of Tileries (Ranked by Size Of Fixed EffeCtS From PrOdUCtion FUUCtiOH)...ooooooooooooooooolgg Variables Indicating Size of Tileries (Ranked by Efficiency Measures From Factor Share Equation)...............200 Population Size of Tilery Localities and Distance From Major Urban Areas (Ranked by Size of Fixed Effects From PtOdUCtion FunCtion)ooooooooooooooooooooo00000000000000.0205 Population Size of Tilery Localities and Distance From Major Urban Areas (Ranked by Efficiency Measures From FaCtor Share Equation)oooooooooooooooooooooooooooooooooooooooozo7 Changes in Marketing Strategy (Ranked by Size of Fixed EffECtS From PrOdUCtion FunCtion)ooooooooooooo00000000000000.0210 Changes in Marketing Strategy (Ranked by Efficiency Measures From FaCtor Share Equation)...ooooooooooooooooooo000.211 Changes in Product or Production (Ranked by Size of FIXBd EffeCtS From PrOdUCtion FUDGtiOU).oooooooooooooooooo0000213 Changes in Product or Production (Ranked by Efficiency Measures From Factor Share Equation)..........................214 viii CEAPTER.I INTRODUCTION The purpose of this thesis is to develop and estimate individual, firm-specific measures of differences in production among Egyptian small-scale tileries in Fayoum and Kalyubiya governorates using a fixed-effect Cobb-Douglas system and panel data collected in Egypt under the supervision of the author. Other measures to determine if tileries are failing to maximize profit and to combine variable inputs in a least cost manner are developed and estimated. After obtaining the above measures, it is determined if certain firm or entrepreneurial characteristics (e.g., size of firm, age of firm, education and age of entrepreneur) are associated with these estimates. Finally, a statement is made based on the analyses and the author's firsthand knowledge of the tileries and their production processes as to how well the model performs and what the model's fixed effects are measuring. The major goals of the study are: a) The presentation and summarizing of new information pertaining to small-scale manufacturing firms in Egypt, particularly in Fayoum and Kalyubiya governorates, using panel data collected in Egypt under the supervision of the author. b) The collection and processing of weekly panel data for twenty-five Egyptian small-scale tileries in Fayoum and Kalyubiya governorates over a period of sixty-six weeks. c) The review and synthesis of the econometric literature on frontier production (cost) functions and panel data. 2 d) The generalization of a model developed by Koch (1962) to include individual firm measures of the failure to maximize profit and to combine variable inputs in a least cost manner. e) The estimation of a model developed by Schmidt (1984) using the Egyptian panel data. f) The systematic study of whether certain firm characteristics are associated with the fixed effects on the production function or the efficiency measures on the factor share equation. The analytical procedure used in this thesis combines techniques deveIOped in the econometric literature on frontier production (cost) functions and panel data estimation. Stochastic production functions using physical units of output and inputs are fitted to the panel data collected in Egypt for small-scale floor tileries allowing for differences in production among firms. A fixed-effect Cobb-Douglas model is chosen for the analysis. An F-test is used to determine if the structural form of the tileries' subproduction functions are the same in both governorates. When no significant differences are found in the estimated elasticities of variable inputs, the data sets from the two areas are pooled. Tests are also constructed to determine if the fixed effects from the production function, taken as a whole, add to the explanatory power of our production function equation, whether the fixed effects for different firms are the same, and whether ordinary least squares or the “within” estimator is more appropriate for estimating the model with the Egyptian tilery data. Differences in output-input relationships among firms are captured in a neutral shift in the individual firm subproduction functions. The reasoning behind this assumption is that all firms are using the same technology (i.e., all tileries have the same elasticities 3 for variable inputs in their subproduction functions), but that the subproduction function of one tilery may be above or below that of other firms. This is similar to an argument made by George Stigler (1976, p. 215) that 'in neoclassical economics, the producer is always at a production frontier, but his frontier may be above or below that of other producers.” The fixed effects from the production function will be estimated for each tilery and tested to see if individual firm measures are significantly different from each other. Tileries will be ranked in terms of the fixed effects from the production function and factor share equation in the model. Based on the authors firsthand knowledge of each tilery, the analyses of this study, and other relevant information collected in Egypt, the question as to whether these rankings seem sensible will be explored. In the past, stochastic frontier production functions have been fitted for industries, but little progress has been made in fitting intra-industry stochastic production functions. By pooling cross-sectional data, a stochastic function can be estimated for each firm. Differences in industry functions have often been attributed to I'technical" inefficencies although the issue has never been studied systematically. Thus, this research hopes to make two contributions: to measure intra-industry (firm specific) stochastic production functions, and to explore what the estimation procedure is actually measuring. The research will also look at how well the tileries are allocating inputs in the production process; whether the firms are using variable inputs such that the value of marginal product of each input is equal to its marginal factor cost. Measures to determine if tileries are 4 combining variable inputs in a least cost manner are developed and estimated for the model. From these estimates, one can learn whether the tileries are using too much or too little of each variable input and whether these variable inputs are being combined efficiently. In Chapter 2, the areas of study for the thesis are discussed as well as the Non-Farm Employment Project-Egypt, its goals and the findings from its research. In Chapter 3, the econometric literature pertinent to this study is reviewed, and the theoretical underpinnings of this thesis are developed. In Chapter 4, a fixed-effect Cobb-Douglas system is presented and generalized to include individual, firm-specific measures of differences in production and inefficiencies in allocating variable inputs. Alternative estimation procedures are described and discussed, and the panel data used in the analyses are discribed. Results from estimating the model are presented in Chapter 4, and, finally, a fixed effect Cobb-Douglas model deve10ped by Schmidt (1984) is estimated using the Egyptian panel data. In Chapter 5, a description of all tileries in our sample is presented, and, following this, firm characteristics that are associated with the measures obtained in Chapter 4 are identified. -Conclusions are given in Chapter 6. CHAPTER II FIELD RESEARCH AND DATA COLLECTION IN EGYPT 2.1 Description of Study Areas The two governorates selected for study are different in a number of important ways. Kalyubiya is immediately adjacent to the greater Cairo urban area; in the new regionalization of the country, for planning purposes, the governorate as a whole is treated as a part of that metropolitan area. The biggest city in the governorate--Shubra E1 Khayma, with a p0pulation of about four hundred thousand--is just north of Cairo and is essentially an extension of that city. The governorate lies astride the main highway from Cairo to Alexandria; transportion and communication links to the outside are good. The situation with regard to Fayoum is quite different. It is essentially a large oasis located 60 kilometers southeast of Cairo and is separated from the Nile river valley by 10-30 kilometers of desert. There are two main roads entering the Fayoum, one from Cairo and one from Beni Suef, and a railway system that connects the three largest towns in Fayoum to the Nile river valley. The oasis is irrigated by a canal, the Bahr Yousef, which brings water into the depression from the Nile. Although the transportation network within the Fayoum is poor, there is a good network between Fayoum City and Cairo; buses, taxis and trucks make that run frequently over a reasonably good road. 5 6 Table 1 provides comparative statistics on the two governorates. The pOpulation figures for Kalyubiya include the city of Shubra El Khayma, which is not covered in this study; excluding that city, the population is virtually the same (1.1-1.3 million) in each of the two governorate under study. Line 4 makes clear that Kalyubiya is far more developed than Fayoum in terms of private, larger scale manufacturing employment; on a per capita basis, the figure for Kalyubiya is some 4.5 times the level for Fayoum. 0n the other hand, population density is over 2.5 times as high in Kalyubiya (line 2). Line 3 shows that Kalyubiya is considerably more urbanized than Fayoum, reflecting in part the inclusion of Shubra El Khayma in these statistics for Kalyubiya. Lines 5 and 6 give some measures of welfare of the population of each governorate; they show that Kalyubiya has a higher literacy rate and a more extensive piped water supply. These figures suggest that, while the size of the total population under study is approximately the same in the two governorates, the level of urbanization, industrialization, and population density are all higher in Kalyubiya. 2.2 Phase I Survey1 The Phase I Survey had two major goals. The first was to provide comprehensive data concerning the extent and basic characteristics of small enterprises in the areas under study. The second was to provide the sample frame for the selection of particular industries and enterprises for the more detailed analysis in Phase II of the study. 1Much of this section is taken from Badr, Seale, Mostafa, Sheikh, Davies, and Saidi (1982). TABLE 1 Selected Characteristics of Governorates Under Study Fayoum Kalyubiya 1. Estimated Total Population, 1979 (000) 1,140 1,674 2. Population Density: Population per 557 1,439 Square Kilometer 3. Rural Population as 96 of Total 76 59 4. Private Manufacturing Employment, Firms With Ten or More Employees (1970/71) 1,727 11,511 5. Literacy Rate 26 46 6. Availability of Piped Water 12 20 Sources and Definitions: CAPMAS estimates 1976 Population Census 1976 Population Census CAPMAS estimates Percentage of the total population of the governorate recorded as literarte, in 1976 populaton census. Percentage of the total population of the governorate with piped water in the building where they reside, as recorded in 1976 housing census. U‘PNNH o o o o o S" 2.2.1 Questionnaire Content The survey instrument comprised the two sides of one mark-sense computer card. After identifying the respondent (name, location, primary and secondary products produced), nine questions were asked: the form of ownership of the firm; the sex of the owner; the location of the workshop and the type of building in which it is housed; the work force; the number of machines in use, value of the most sophisticated machine, the total value of all machines and tools, and the use of power; and the seasonality of production. A more detailed paraphrasing of the questionnaire is provided in Appendix A. 2.2.2 Industry Coverage The central focus of the survey was on small manufacturing firms. Small was defined as any firm with 50 or less employees; larger establishments were not enumerated. Mobile or itinerant producers--those without any fixed place of work--were also excluded from the survey. Manufacturing was defined to include all industry groups covered in the International Standard Industrial Classification of All Economic Activities (ISIC) codes 31-39, a somewhat restricted definition of manufacturing; in addition, the coverage was extended to cover ISIC code 951, relating to the repair of manufactured goods. It was felt that, in the Egyptian context, such repair shops are often engaged in manufacturing activities as well. This classification scheme is also consistent with the system that has been used in most published Egyptian censuses. The enumeration also covered laundries, barber and beauty shOps, photographic studios, painters, and construction enterprises, although information from these five industries are not included in any of the tables except in the addendum to Table 2. Similarly, it was 9 decided after some discussion to include producers of £001 and taaliya in the survey; these enterprises could be considered as either producers of food products (manufacturers) or as restaurants (producers of services). Again, these producers are shown separately in the addendum to Table 2 below, but are excluded from all other tables. 2.2.3 Sampling Approach The basic sampling approach was one of stratified random sampling within clusters. The clustering was done by villages and towns, and the strata were defined in terms of the population of the various villages or towns. This basic approach was applied somewhat differently in the two governorates. In the Fayoum governorate, a distinction was made in sampling among towns (defined as any place which is a seat of government at a district, governorate, or national level) and villages (all other locations). Fayoum has five towns, ranging in pOpulation from 19,671 to 166,910. All five of these towns were enumerated. With regard to villages, it became evident during the familiarization phase of the study that certain villages were specialized in producing one main nonagricultural commodity. In these villages, a significantly larger percentage of the working population is involved in small-scale manufacturing than in those villages which are not specialized. Drawing upon the local knowledge of team members and others, all Fayoum villages were classified as either specialized or nonspecialized. The villages were then further stratified by population size. From the 156 total villages in the Fayoum Governorate, 143 villages were classified as nonspecialized and thirteen were classified as specialized. All of the specialized villages were enumerated. The 10 nonspecialized villages were further stratified by pOpulation size. Within each stratum, villages were selected randomly, and the stratum sampling fractions were increased as population size increased, reflecting the general finding that small villages are rather homogeneous while differences among villages within stratum increase as population size increases. In Kalyubiya, the sampling approach was somewhat different. Executives of village councils were asked to fill out a brief questionnaire providing information about the extent of nonfarm activities in their jurisdictions. The results of this questionnaire showed no clear need for the treatment of certain villages as specialized. Also, while it was clear that commercial activities and services increased in the towns, it was not clear that manufacturing would differ between towns and large villages. The Kalyubiya survey, then, stratified all localities--villages as well as towns--by population. The last locality drawn in the random sample in each of two strata in Kalyubiya (3,000-5,999 and 12,000-19,999) was replaced by a locality of similar size known to have had substantial government efforts directed at small enterprises through cooperatives. The survey results suggest that these efforts were neither particularly large nor particularly effective. On the other hand, Shubra El Khayma, a large and highly industrialized area on the northern border of Cairo containing both large and small firms, was excluded from the sample frame and from the survey. Table 2 shows the resulting pattern of localities selected for sampling. Within any locality selected--village or town--100t of the 11 TABLE 2 Total Number of Villages and Towns in Fayoum and Kalubiya and in the Sample Size of Locality (Population) 0- 3000- 6000- 12000- 20000- 2999 5999 11999 19999 29999 400004- Total w Specialized Villages: Total No. of Villages 0 5 4 4 0 0 13 Villages Selected O 5 4 4 0 O 13 Sampling Percentage - 10096 10096 10096 - - 10096 Non-Specialized Villages: Total No. of Villages 51 48 34 9 1 0 143 Villages Selected 5 5 5 3 1 O 19 Sampling Percentage 10% 1096 1596 3396 10096 - 1396 Towns: Total No. of Towns 0 0 0 l 2 2 5 Towns Selected - - - 1 2 2 10096 Sampling Percentage - - - 10096 10096 10096 10096 Total, Villages at Towns: Total No. 51 53 38 14 3 2 161 No. Selected 5 10 9 8 3 2 37 Sampling Percentage 10% 1996 2496 5796 10096 10096 2396 KALYUBIYA Total, Villages and Towns: Total No. 60 60 47 16 8 2 193 No. Selected 12 12 10 6 4 2 46 Sampling Percentage 2096 2096 2196 4096 5096 10096 2496 Source: Survey Data, Phase I. 12 small-scale enterprises were enumerated. In Fayoum City and most of the towns of Kalyubiya, this involved having the enumerator walk down each street or lane, asking about small enterprises if he had reason to suspect their existence. In the villages of both governorates and in all the towns of Fayoum except Fayoum City, the enumerators approached each household asking whether any manufacturing activities were taking place there. Phase I survey results have been ”blown up" using the inverse of these sampling proportions, so they reflect the whole governorate (or in the case of Kalyubiya, the whole governorate excluding Shubra El Khayma). The actual number of enterprises sampled by stratum and the sampling preportion inverses are presented in Table 3 below. The names of the villages selected in the Phase I Survey and their populations are reported in Appendix B. 2-2.4 Enumeration Procedure The enumeration began in early April, 1981, and was completed in late July of that year. The enumerators for the Phase I survey included both high school and college graduates, both male and female. They were carefully trained and took part in both pre-testing of the questionnaire and in field trials of the final survey instrument which was administered to peOple not in the Phase I sample. In general, the enumerators were a *well motivated and well trained group. In both governorates, before enumerating a village or town, the cnmda.(meyor) or the local council members were contacted and informed of the purpose of the survey and introduced to the professional staff and the enumerators. Their support, which was offered freely in almost every case, gave credibility to our project and facilitated our work. TABLE 3 l3 Sampled and Estimated Total Number of Enterprises and Employees in Fayoum and Kalyubiya - 1981 Sampled Estimated Enterprises Enterprises No. of Sampling No. of Employ- Emp./ Enter— Employ- Proportion Enter- Employ- ment per 100 prises ment Inverse prises ment Enter Pop. Province and Location Size FAYOUM: 0- 2,999 772 891 10.13 7,891 8,472 1.1 10 3,000- 5,999 3,452 3,869 4.76 16,429 17,586 1.1 8 6,000- 11,999 5,385 6,396 2.58 13,916 16,955 1.2 6 12,000- 19,999 9,054 11,229 1.39 12,544 15,671 1.2 10 20,000- 39,000 3,686 4,948 1.00 3,686 4,948 1.3 6 40,000+ 2,818 7,487 1.00 2,818 7,487 2.7 4 TOTAL 25,167 34,820 2.27 57,212 71,119 1.2 7 KALYUBIYA: 0- 2,999 1,624 2,752 4.76 7,730 13,152 1.7 11 3,000- 5,999 1,981 3,076 5.10 10,108 15,356 1.5 6 6,000- 11,999 1,738 3,1 11 4.76 8,273 14,809 1.8 3 12,000- 19,999 2,880 4,798 2.50 7,220 12,078 1.7 5 20,000- 39,999 1,364 3,429 2.00 2,728 6,858 2.5 3 40,000+ 1,064 3,900 1.00 1,064 3,900 3.7 2 TOTAL 10,651 21,066 3.49 37,123 66,153 1.8 5 GRAND TOTAL 35,818 55,886 2.63 94,335 137,272 1.5 6 Source: Survey mta, Phase 1. 14 2.2.5 Card Printing and Processing Procedure After the questionnaires had been tested in the field and then revised, they were sent to East Lansing, Michigan for printing. When the original number proved inadequate, a second printing was done in Cairo, with sufficiently satisfactory results to be able to read the information recorded on the cards into the microcomputer. The original processing of the survey results was done largely by hand, as the delayed arrival of the card reader, microcomputer and printer all precluded processing rapidly enough to keep the following stages of project work on schedule. Subsequently, however, all Phase I survey results were processed through the project's microcomputer in Egypt; all the compilation, cross-tabulations and adjustments to move from sample to population universe figures were estimated making use of that equipment. 2.2.6 Phase I Results The first phase of our study, undertaken between April and July of 1981, was designed to provide an overview of small enterprises in the two governorates under examination. Tables 3-5 summarize the major findings in terms of numbers of enterprises and employment by locality size, by industry group, and by employment categories. Among the major findings of this first phase of the study are the following: a) The numbers involved are large: 94,000 establishments, employing nearly 140,000 people, in the two governorates combined. Approximately one person in fifteen in the total population of the governorates--men, women, and children--is involved at least on a part-time basis in small manufacturing activities. 15 As indicated in Table 3, these activities are widely dispersed in different-sized localities. On a per capita basis, they are most heavily concentrated in smaller communities. The industry composition differs widely by locality size: in smaller villages, the main activities are household-based (e.g., dairy products, knitting of hats, embroidery, making baskets), while in larger locations they are more sophisticated, often with hired workers and more capital invested. Even within one industry, product lines change as one goes from smaller to larger localities: in smaller villages, tailors and dressmakers make the same traditional outfits year after year, while urban firms make more modern clothes, with annual style changes. b) The average firm size is small: 1.5 workers per establishment, including owners and family members. Nearly sixty percent of all establishments had only one worker; less than one percent had ten or more workers. Again, this differed somewhat by location and even more clearly by industry type, but the overwhelming characteristic is one of many small, privately owned firms. Over ninety-nine percent of all firms with less than forty-nine workers are privately owned. c) The composition of small-scale industries is detailed in Table 4. Perhaps the most striking feature is the dominant role of makers of dairy production; in each of the two governorates, over 506 of all reported employment is in this activity, generally involving the making of butter and cheese in villages, partly for own consumption, partly for sale. Aside from dairy products, over 40% of all small enterprise employment is in textiles, broadly defined: tailors and dressmakers, needlework and knitting, spinning, the making of mats, rugs, fish nets, and a variety of related activities. The third largest group, 16 with 20 percent of total employment excluding dairy products, is wood products: crates, baskets made from henna branches, furniture, doors and windows. This is followed by other food products (primarily butchers and bakers). Other activities are smaller in the aggregate, although they may be quite important either in particular locations (e.g., bricks), in terms of their backward and forward linkages (e.g., blacksmiths and welders, essential oils), or in terms of their growth potential (e.g., cement floor tiles, machine shops, repairs). d) Women constitute a significant part of the small-scale industry labor force in the two governorates. The labor force data in Table 5 again show the preponderance of workers in dairy enterprises, where most of the work connected with the production and sale of dairy products is done by females. Women are important in other industry groups as well, making up over 30% of the work force in all industries other than dairy products. WOmen comprise nearly 50% of the work force in the textile subsectors and are important in Fayoum in the production of a variety of palm products included in the wood products category. From a different perspective, family members dominate the labor profile. Virtually all workers in the dairy products industry, for example, are family members. Aside from that subsector, family members comprise nearly sixty-five percent of the total work force; just over a quarter are hired workers, with the remaining nine percent being apprentices. Both hired workers and apprentices are more heavily concentrated in particular industries: textiles, wood products, tiles, and other food products. These highlighted findings as well as other aspects of the Phase I survey results are discussed in more detail in Badr, Seale, Mostafa, Sheikh, Davies, and Saidi (1982). 17 TABLE 4 Distribution of Estimated Total of Enterprises and Employment in Fayoum and Kalyubiya by Industry - 1981 Fayoum Kalyubiya Number of Number of Subsectors Enterprises Employment Enterprises Employment Food: Dairy Products 36,555 37.622 23.415 34,519 Bakeries 133 1,042 165 1,213 Butchers 986 1,477 7806 1,466 Flour and Rice Mills 84 313 90 345 Other Food Products 160 311 623 1,575 TOTAL 37,918 40,765 25,099 39,118 Textiles, Leather, and Hearing Apparel: Tailors, Dressmakers 4,095 5.568 4,594 7,831 Clothmaking 196 280 176 776 Knitting by Machines 22 22 109 272 Needlework. Hand Knitting 2,131 2,320 552 716 Spinning, including Ropes 2,560 2,832 305 711 Rugs 34 192 259 1,193 Mats 832 1,705 341 1,020 Shoemaking, Repair 293 459 506 799 Fish Nets 673 1,417 O O Other Textiles B4 152 113 248 TOTAL 10,920 14,938 6.955 13.566 Hood Products: Furniture 642 1,659 422 1,084 Doors and Windows 403 701 671 1,254 Agricultural Tools 174 290 62 25 Baskets. Crates and Rafia Hats 4,314 5,079 364 1,539 Other Wood Products 54 150 224 990 TOTAL 5.589 7.879 1.743 4,962 Paper and Printing: TOTAL 30 146 32 92 Chemicals: Essential Oils 62 693 4 116 Other 96 179 11 53 TOTAL 158 872 15 169 Non-metallic Minerals: Tiles 22 154 130 742 Mud Bricks 740 1.025 112 155 Red Bricks 29 663 51 774 Other 535 1,720 155 352 TOTAL 1.326 3,562 448 2,023 Metal Products: Blacksmiths and welders 192 579 544 1.376 Machine Shops 38 131 84 247 Other 141 250 360 602 TOTAL 371 960 988 ' 2,225 Other Manufactures: TOTAL 62 126 9 17 Repairs: Electric Appliances 254 463 252 324 Automobiles 250 714 667 2,065 Bicycles 146 281 263 517 Other 188 413 652 1,075 TOTAL 838 1.871 1.834 3.981 GRAND TOTAL 57,212 71,119 37,123 66,153 Addendum: ' Other Services 1,308 1,711 2,814 5,246 Fool and Ta'miya 658 926 672 1,469 Source: Survey Data, Phase I 118 H omega .uaao ao>eam "oucaom oaa.m ama.a. ass.m_. ~a~.km_ saa.oa mm~.ee massacre ac_aa meets—ac. sme.m com.ap maa._e .ma.mo _am.m_ oem.m. massacre ar..a a=_u=_uxm mmuza>oaa zaom .So2a ~m~.n ”Na.op am¢.a. ana..m moo.“ .ma.s~ scans aese=_uxa ._.uoua=m mmm cm~.. amp.~ .ma.m _~ oaa.m message m c 3 2 c : nah-33:5: .859 ~_~ .om Nap.. m-.~ am _o~.~ massacre pass: as. kam.p can mwo.~ ~_P __a.F m_~ta=.: u_p_asas-=oz m am_ sN as. 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Cowoumo «coanEEm can xom .3 9033.33. ecu 8:23.". 5 «coEonEm .30... ovumEflwm n.mnuaurrr 19 2.3 Phase II Survey The goals of the Phase II survey are four: 1) to determine the ”big picture” of small enterprises in selected locations in Egypt: the number of firms, the levels of employment, and some basic enterprise characteristics by industry group; 2) to examine in more detail a sample of firms in selected industries in order to determine their production and distribution patterns, their economic viability, their constraints, and their potential for future growth; 3) to suggest to the Government of the Arab Republic of Egypt and to the United States Agency for International Development the types of policies, programs, and projects that might effectively support the development of small enterprises in these areas; 4) to collect longitudinal data in order to estimate production functions and to perform other empirical analyses. 2.3.1 Industry and Firm Selection The Phase I survey provided an overview of small enterprises in the two governorates under study. In order to understand the production and marketing patterns, the economic viability, as well as the problems and growth potential of these producters, a sample of firms and industries was selected for more detailed analysis. To make this selection on an informed basis, the researchers on the project undertook preliminary interviews with assorted producers and merchants in a number of different industries to determine which industries to include in the more detailed Phase II study. Following discussion among the researchers and with informed outsiders, thirteen industries were selected for Industries Covered in Phase 11 Survey - 1982 20 TABLE 6 Fayou- kalyuoiya Total Number of Total Number of Enterprises Total Enterprises Total Employment Employment Abbreviation in in in in Project in in Governorate Governorate in Governorate Governorate Code Subsequent Phase 11 (from Phase (from Phase Phase II (from Phase (from Phase Number Industry Tables Main Products or Activities Sample 1 Survey) 1 Survey) Sample 1 Survey) 1 Survey) 1 Rugs Ru Tied (not woven) rugs 5 34 192 13 259 1.193 2 Tiles Ti Cement floor tiles 8 22 154 13 130 742 Dairy 3 Products 0a Butter and cheese 32 36.555 37.622 19 23.415 34.519 5 Embroidery Em ‘Embroidered gannents 10 939 1.078 6 107 267 6 Hats No Need mats 16 832 1.705 16 341 1.020 7 Tailors Ta Gallabiyas. Suits. Shirts 15 1.420 2.551 31 1,739 3,509 Dress- 8 makers Dr Dresses 13 2.675 3.017 34 2.855 4.322 Assembly of shoe parts; 9 Shoes Sh making. repair 16 293 459 33 506 799 Living room. dining room. 10 Furniture Fu bedroom furniture 21 642 1.659 19 422 1.084 12 Hats Ha knitted farmers‘_hats (taiyas) 22 1.191 1.243 0 0 0 Reed (Fayom) or henna (kal- a a 13 Baskets Ba yubiyo) baskets 24 3.681 3.874 15 293 1.218 Machine Repair. making of metal parts 14 Shops NS and products 11 38 131 19 64 247 Agricul- Metal and wooden parts of 15 tural A1 hoes. plows. waterwheels. 9 174 290 6 62 95 Implements etc. Total. 13 industries 202 48.496 53.975 224 30.213 49.015 Total. all industries 57.212 71.119 37.123 66.153 Notes: aThe figures reflect all basket nroducers in Fayoum. The Phase 11 sample. however. only included the Favouni baskets. which represented 11 percent of the total. Source: Survey data. Phase I and Phase 11 21 further analysis. As indicated in Table 6, these industries account for approximately seventy-five percent of all employment in small enterprises in the two governorates, as reported in the Phase I survey. The selection of particular firms to be included in the Phase II study was done by a process of random sampling, using the Phase I sample as universe. There were some minor departures from purely random sampling. In Fayoum, a few isolated villages were eliminated from the sample frame, to reduce logistical problems. In Kalyubiya, since household dairy producers are widespread and are thought to be relatively homogeneous, they were selected last, from the universe of producers in villages where other producers had already been selected in the sample (thus avoiding the need for enumerators to go to any village solely to interview dairy producers). In both governorates, a few larger dairy products producers were nonrandomly selected and added to the sample to ensure a more complete picture of this industry. 2.3.2 Data Collection Three types of information were collected from the thirteen industries chosen for detailed study in Phase II. They were as follows: a) A regular longitudinal questionnaire was administered to each of 430 sample firms, either once or twice a week over one full year, from December 1981 to December 1982. The questionnaire used for this purpose included information on production and sales, current inputs purchased, and labor use. Information was collected and processed making use of :markrsense cards, a Chatsworth card reader, and a Radio Shack TRS-BO iflodel II microcomputer. Data collection involved approximately twenty r.» Pr. ou unc' 22 enumerators and two supervisors in each governorate, working full-time over the full period of the survey. This extensive longitudinal collection of flow data was necessitated by the lack of reliable information concerning the seasonality of production over the course of the year, the virtual nonexistence of records among small producers, and the limited accuracy of their memory recall. These three factors together meant that one-shot surveys could provide only limited information of uncertain validity concerning production, employment and income flows over the course of a full year. b) A second set of two questionnaires--approximately ten pages each-- was administered to these firms, during the period September-December 1982. These two special questionnairescovered information concerning the organization, management, and history of the enterprise; the owner/manager; the capital stock; market links and marketing patterns; the labor force and labor contracts; the producers' contacts with government and financial institutions; and problems and future prospects of the firm, as perceived by the owner. c) With minor exceptions, each of the thirteen industries being studied in Phase II was the responsibility of one of the researchers lassociated with the project. This meant that in principle he was responsible for the supervision of the enumerators working in that industry, as well as for participating in both the regular interviewing process and in supplementary discussions with producers (both in and (mutside the sample) and with other knowledgeable people, to gain an understanding of the dynamics of that particular industry. While the depth of this understanding has varied from case to case, the result has 23 been to provide a firmer grasp of the nature of the sector than could be gained simply by an analysis of statistics emerging from processed survey data. 2.4 Phase II Industries: An Overview1 This section will synthesize the findings on individual industries from the Phase II survey by classifying the studied industries into two main categories, household enterprises and micro enterprises, which will be defined below. Readers interested in a more detailed presentation of the Phase II results should see Davies, Seale, Mead, Badr, El Sheikh, and Saidi, ”Small Enterprises in Egypt: A Study of Two Governorates”, (1984). Household enterprises have two defining characteristics: minimal uses of machinery and equipment, and skill levels of workers which are low or widely available. For working purposes, L.E. 50 per firm2 (current replacement cost of machinery, equipment, and tools) has been used as a cut-off point for the first aspect: the specification in terms of skill levels must be less precise. With regard to micro enterprises, these are set apart from household enterprises by their more complex production patterns, making use of more machinery and equipment (i.e., more than L.E 50) or (usually, and) a higher level of skills among the work force. The aspect which differentiates them from larger, more advanced and more complex organizational forms is their simple marketing system. In general, this 1Much of the following material is from Head, Davies, and Seale (1984). 2The currency units throughout this thesis are Egyptian pounds (L.E.). Since the exchange rate during this period was approximately L.E. 1 - US $1, they can also be thought of as US dollars. 24 is based on an arrangement whereby final consumers contact producers directly to place orders; production then takes place in response to these orders. From these basic defining charactistics of the two producer types, several features follow. First, a summary of the result is given, but will subsequently be supported by data. With regard to household enterprises, the most important characteristics are the following: a) Production in household enterprises relies primarily on family workers, most of whom are women, although in some industries men predominate. The work may be either on a part-time or a full-time basis, but is generally low-skilled, and uses virtually no capital. The work generally takes place within the home. Firms are small (in most cases, 'only one worker), with little or no specialization by task. b) With these simple production technologies, the products made are generally correspondingly simple and of low quality. c) With low and easily learned skills and only limited capital, there is easy entry into these product lines; partly as a result, returns to labor are quite low. d) With low returns to labor, simple raw materials available from local sources, and virtually no capital, production costs are low; competition among producers means that product prices are correspondingly low. e) Low—quality, low-price products are suitable for mass markets among low-income consumers. The result is that large quantities of these products are made and sold, supplying a significant portion of the consumption needs of low-income consumers. Markets may be segmented by location, but are extensive in the aggregate. 25 f) Large markets and labor-intensive production technologies mean that many people are involved in these production processes. While incomes per person or per hour are low, many people participate. g) The markets in which household enterprises sell are threatened by increasing penetration of modern, factory-made goods. Improved transportation, the develOpment of lower-cost, mass-produced products, and the increasing availability of such products throughout the country mean that the simpler products made by household enterprises have a hard time maintaining their market position. h) Low levels of production skills, limited use of capital, and limited experience in marketing or production management mean that household enterprises have little capacity to adapt, modify or upgrade their product lines. Easy access to these production lines among large numbers of peeple with few employment options and limited job flexibility means stiff competition for problematic markets, which in turn means a threat of stagnant or falling returns per hour worked. The prognosis for micro enterprises is substantially different. The primary characteristics of this group of producers include the following. a) With few exceptions (particularly for dressmakers), the entrepreneurs in these enterprises are men. In the aggregate, nearly a third of the labor hours are supplied by hired workers: these as well as the family members involved work an average of about forty-two hours per week. Most firms have more than one worker for at least part of the year: the average is two or more workers in six of the ten micro enterprise industries studied.’ 26 b) There is a substantial investment in machinery, equipment, and tools. Beyond this, firms in some micro industries hold substantial amounts of inventories, particularly of raw materials and semi-finished products. Production generally takes place in a workshop separate from the home. c) Returns to the producer per hour or per year are substantially higher than for household enterprises. d) The products made are more diverse than those produced by household enterprises. Some items, such as the products of village tailors, dressmakers, and shoemakers, continue to be consumed primarily by lower-income groups; others, such as furniture, cement floor tiles and machine shOps, are designed primarily for higher-income consumers. The income elasticity of demand for these products varies from case to case, but on the whole it is generallly well above the level for products of household enterprises. e) If the demand characteristics of these industries are more favorable that those of household enterprises, so also are the production conditions, particularly in terms of their capacity to respond to shifts in tastes and to new marketing opportunities. With somewhat higher levels of education and skills both in production and in management, many producers from this group have a substantially greater chance of taking advantage of and benefiting from any growth dynamic which exists in the country, being carried along by it rather than being swept aside. f) For most micro enterprises, on the other hand, the marketing system remains quite simple. Most sell directly to a limited range of final consumers, often restricted to those in the immediate neighborhood of the producer. Often this marketing system is further simplified--but A /— 27 further restricted as well--by the fact that production takes place only on the basis of orders previously placed by final consumers. These characteristics should be thought of as referring to individual firms or producers. Subsequent discussion--in particular, the data in the tables--focuses not on individual enterprises, but on industry averages. In most cases, the range within each industry is narrow enough so industry averages are a good reflection of the characteristics of individual firms within that industry; not only industry averages, then, but the great majority of the individual producers within each industry fit quite cleanly into one of the two categories. There are three partial exceptions. a) In two industries studied--dairy products and embroidery--the sample included producers of two distinctly different types. One of these clearly fits the definition of household producers, while the other group uses substantially more capital and skills, and so should be considered as micro enterprises. In subsequent discussion and tables, we have divided these two industries into two components, to reflect this dichotomy. b) There are two industries where the individual producers are reasonably homogenous within the industry, but where the industry averages might make them candidates for an intermediate or borderline category. Instead of creating an intermediate category, one should recognize that one of these (mats) is in many respects at the upper end of the household enterprise category, while another (dressmaking) is at the lower end of the micro enterprise category. c) The small-scale floor tileries, which is the focus of this dissertation, represents a borderline case of a different type, being at 28 the top end of the micro enterprise category. Particularly in terms of specialization of management, tile producers might be considered to be in a class by themselves among the Phase II sample of producers;1 yet their other production and marketing characteristics are similar enough to other micro enterprises so that it is felt to be reasonable to include them with that group. With this background, we will now examine in more detail the characteristic of these enterprises. In particular, we will look at questions of labor use (Section 2.4.1); capital (Section 2.4.2); marketing (Section 2.4.3); and income earned (Section 2.4.4). 2.4.1 Labor 0f the considerable information collected in the original study concerning labor use, we report here on six aspects: the sex of the owner/entrepreneur in the enterprise; the average number of workers per firm; the breakdown of labor time between family and hired workers; the extent to which the work is a part-time or full-time activity for the work force; the level of education of the owner/entrepreneur; and the total employment in these industries in the two governorates. Information is presented in Table 7. The first column of the table makes clear that there is considerable concentration by sex of owner/operators in the two industry groups. Except for mats, household enterprises are largely in the hands of women; except for dressmakers, micro enterprises are virtually all 1Family members in the floor tileries spent only 188 of their reported working time in production activities (as opposed to marketing, input procurement, supervision, repair, and other). For all other micro enterprises taken together, by contrast, an average of 80‘ of all working time is spent in production activities. 229 —UHOh\-m “flag .~_ omega .ouoo xo>cam ”oucaom \MONm.~_ o.m m.mm n.~e m.~¢ —.m m.¢~ m.o~ o.” «.mo amaso>< mwc n.p m.~p o.oe ~.mm e.~ m.m~ ~.cu m.— ~.vm mucosa—as. possu—:u_co< mow ~.m m.mp m.co ~.~c _.m ~.on m..m o.~ o.oo~ macaw oe_=ua: «mo m.~ o.mm c.mv “.me ~._ m.ns o.m~ m.c ~.mm mo—_h 2 a.” 2 2 2. n: 92 :— 2 us as. ~e¢.~ e.e ~.~m m.me o.—m m.~p m.mn m.oo m.~ o.co— usausccau m——.— o.m -- o.ue «.mv -- P.o_ o.nm v._ “.ma meoxueoogm mac.» o.— m.m~ m.on “.mm w.m e.~p m.~m —.— m.m msoxusmmoga m—n.o p.e m.me ~._e p.5e o.~ m.~m m.mm o.~ o.co— «to...» ma. o.m -- ~.~e o.~m -- m.~_ ~.~m m._ o.oop Acme—organ cocoa: a. m.~p -- ~.mv a.m~ -- ~.p~ m.w~ m.~ o.oop mt.~o caveat mommumuoucu ecu—t \meao.~m ~.o m.~e m.mv m.m~ p.o o.p m.mm m.o ~.m_ caucu>< mwu m.o -- o.me m.m— -- ~.o m.oo 0.0 o Agoowoanu o~m.~c ~.o -- -- ~.n~ -- ~.o m.om m.o m.e— mausooca aye-a w~o m.o -- -- v.mn -- _.o «.mm o.o m.~ muoxmom _o_.— e._ -- -- m.oe -- -- c.co_ 0.. 0 mac: mmc.~ m.o m.~e m.me v.oe o.v m.Np o.- _.~ w.mo mun: mommcduouco v—ogomao: mousse: Laococaocuco ouwucocaa< coup: a—msod wu_ucocang vote: x..smu omwcduouco Amopus av -to>oc emu do can cavemen .oo>_o>c. covuouaoo xoor Lon ooxcoa mousse: -ocuco\tocro o_aooa co meow» newton Lon meson Peace co noose: co xom co cones: co census vogue: meson co co oucgo>< .32. ounce: .345: acorn; 6633.... a LODMJ nwmu-unqcru. 30 run by men. This division clearly reflects the low levels of skills, mobility, and access to investible funds among women in provincial towns and villages of Egypt. Turning to questions of firm size and breakdown of labor supply between family and hired workers, mats again are something of an exception among household enterprises; except for that industry, the average firm size is one or less persons,1 with virtually exclusive reliance on family labor. Mat production requires two people to work larger looms, so the average firm size is somewhat larger; while more than three quarters of the labor time in this industry is still supplied by family members, there is also some hiring of workers and apprentices from outside the family. In the case of micro enterprises, the average firm employs 1.6 workers.2 There is considerable variation around that average, ranging from 1.1 workers for dressmakers to 4.5 for cement floor tiles. In the smaller micro enterprise industries (those averaging less that two workers per firm), family workers supplied 70-90 percent of the labor time; among those averaging two or more workers, family members supplied 25-60 percent of the labor force. The survey information indicates that among enterprises with more than one worker, the second (or third) worker is frequently also a family member rather than simply someone hired from 1The average is calculated as the number of workers reported each week, summed and divided by the number of weeks of the survey. Thus an average of one worker could mean either two workers for half the year and zero for the rest, or one person working each week for fifty-two weeks. 2In this and other cases in these tables, the averages by industry type (e.g., for all household enterprises taken together) are weighted averages, where the weights are estimated total numbers of producers (enterprises, or firms) in a particular industry in the two governorates. 31 the outsidel. This is confirmed by responses to a separate question (not reported on here) which indicate that a substantial share of the workers in micro enterprises are family members of the owner/entrepreneur. The next set of columns of Table 7 makes clear that there is considerable diversity concerning the extent to which these are full-time, as opposed to part-time activities. Among the household enterprises, mats, hats, and basket making might be considered as full-time occupations, while dairy products and embroidery are done on a part-time basis, in between other household chores. Hired workers in mat production seem to match the full-time work of the family members along side whom they work. There is considerable diversity in length of work among family members in micro enterprises. For some (e.g., agricultural implements), the shorter work week may reflect a limited demand for the product. In other cases, the primary explanation may be the involvement of the entrepreneur in other activities, either of a household nature (for dressmakers) or in other business activities (e.g., for modern dairy producers, many of whom operate urban grocery stores, so making dairy products is only a part of their total economic activity). In the case of hired workers, in every case but dressmakers these people work an average of at least forty-eight hours per week; in six of the ten micro industries listed, they work longer hours than the family members, often substantially so. Assuming a six-day work week, which is common among all small producers in Egypt, one finds that family members in furniture making have the longest average work day, at 8 l/2 hours per day; for 1For modern embroidery, for example, the information in the table concerning total employment, share of total working time supplied by family members, and average hours worked per week by each implies an average of 1.6 family members and 0.2 hired workers per enterprise. 32 micro enterprises as a whole, seven hours per day for family members and hired workers alike does not reflect sunup-to-sundown hours. Of course these are averages, but as such they do not suggest excessively long hours of work. We have no satisfactory direct measure of skill levels in these industries. Imperfect and indirect measures include estimates of earnings (discussed below) and our own direct observations of the production processes and the skills which they require. A further indicator is the level of education of the entrepreneur. The next-to-last column of Table 8 shows that, among household enterprises, the entrepreneurs have an average of only 0.2 years of schooling. Among micro enterprises, there is considerable diversity, but the average is more than ten times this high. Education is only a partial indicator of skill levels, but it is consistent with other indicators which suggest a significantly higher skill level among micro enterprises than among household producers. The last column of Table 7 gives an indication of the numbers of people engaged in small enterprise production among all establishments in these industries in the two governorates under study. The total population of the two governorates amounts to about 2.4 million persons (excluding Shubra El Khayma, which is not covered in the study), which suggests that nearly three percent of the total papulation of the two governorates—~men, women, and children--are engaged at least part-time in small enterprise production in these thirteen industries. Over two-thirds of these people are women, reflecting the overwhelming dominance of dairy products producers, followed by micro enterprise dressmakers and producers in other household enterprises. 33 2.4.2 Capital There are three dimensions of capital use which are of interest here: the location of the work place itself; the level of investment in machinery, equipment, and tools; and the level of inventories. Summary data are presented in Table 8. With regard to the location of the work place, it is not surprising that with few exceptions the household enterprises are located in the home.1 In the case of micro enterprises, only for dressmaking and rugs are the majority of producers located in the home. For the rest, the greatest number are in rented quarters. Only among producers of tiles, rugs, and dairy products are there significant numbers of micro enterprises in owned premises which are separate from the home. Rent control regulations are widespread in Egypt but are unevenly enforced, especially in rural areas. Where they are enforced, they have the effect of providing a subsidy to currently existing enterprises operating out of rent-controlled premises, but of making it more difficult for firms to move to larger or more suitable locations. It is hard to know what would happen to rental rates in an unregualted market. Our impression is that on balance the control regulations are hurting the small enterprises as a group, since the decreased mobility resulting from a reduced supply of rental space is more significant than the price subsidies enjoyed by by those who currently have access to such space.2 1Note that this is not a part of the definition of household enterprises--despite the name!--but is something which emerges from the data. 2For further discussion of this issue, see Davies, Liedholm, Mead, Seale, and Strassman, ”Choice of Location Among Small Enterprises in Egypt: Tailors and Shoemakers in Fayoum and Kalyubiya,“ April 1984 (mimeo) . 34 TABLE 8 Capital Location of work_place Current replace- ment cost of Inven- In the Separate machinery, equip- tories home Rented Owned ment and tools (96 of all producers) (Avg. per producer, in LE.) Household enterprises Mats 94.2 5.8 0 48 35 Hats 100.0 0 0 5 0 Baskets 99.5 0.5 0 6 1 Dairy products 100.0 0 0 l3 2 Embroidery 100.0 0 O 6 9 Average 99.9 0.1 0 13 2.5 Micro enterprises Modern dairy 14.3 57.1 28.6 671 649 Modern embroidery 0 100.0 0 1050 O Tailors 20.2 75.4 4.9 339 17 Dressmakers 94.7 5.3 0 222 16 Shoemakers 10.1 82.9 7.0 221 225 Furniture 2.0 90.6 7.4 625 891 Rugs 65.5 13.3 20.2 1164 588 Tiles 7.9 60.2 32.0 2845 963 Machine shops 0 93.1 6.9 2555 6 Agricultural implements 45.4 46.5 8.1 464 105 Average 54.8 41.6 3.7 389 141 Source: Survey, Phase 11. 35 Turning to the use of machinery, equipment, and tools among small producers, the gap between household and micro enterprises is striking and clear. Part of the definition of household enterprises is that they have, on average, less than L.E. 50 of machinery, equipment and tools; as the table makes clear, all but mats are well below this cut-off point. Among the micro enterprises, by contrast, the level of investment is many times this level. From the sample of 267 micro enterprise firms covered in the survey, eleven had machinery and equipment of over L.E. 4,000 (current replacement cost), while an additional twenty-five firms had investments of L.E. 2,000 or more. Cement floor tileries and machine shops were at the top of this list in terms of industry averages, while some individual furniture producers had comparably substantial investments in machinery and equipment. The patern of inventory holding is significant as an indicator of the extent to which small enterprises need working capital for their operations. Table 8 reflects considerable diversity in this regard. Some enterprises such as floor tileries, furniture, modern dairy, and rugs reportedly hold quite substantial inventories, particularly of raw materials and semi-finished products, reflecting among other things the uncertainties and lack of assured availability of input supplies in these industries. The small inventories of tailors and dressmakers reflect the fact that these producers generally do not keep either raw materials or finished products in stock; the customer brings the cloth when he or she places an order and picks up the garment when it is completed. Diverse inventory levels in other industries are primarily a reflection of the varying extent to which this pattern is followed in other sectors. 36 2.4.3 larketing Table 9 indicates that marketing patterns for household enterprises are rather diverse. Some households produce primarily or exclusively on order, while others Operate this way only rarely. Orders are received either from merchants or from final consumers. In some cases the customer supplies raw materials, but this practice is limited to certain industries among the household enterprise category. Among firms in the micro enterprise group, there is considerably more homogeneity. The first column of Table 9 indicates that most industries in this category produce mostly in response to orders. The second section of the table makes clear that while some of these orders are placed by merchants (particularly for rugs and embroidery), by far the largest source of orders is the final consumer of the product. On the average, this source of demand accounts for fully ninety percent of the orders received by this group of producers. The striking change in marketing patterns, from diversity in the household industries too much greater homogeneity in the micro enterprises, may be explained in terms of differences in the types of products made. If firms are not producing for a known customer who has placed an order, they must be producing for inventory for later sale to currently unknown customers. The reason why one method of marketing is chosen over the other lies primarily in the characteristics of the goods and the resulting effect on the inventories that must be maintained by the merchant in order to be able to sell to unknown customers. Products from household industries are generally more homogeneous (and simple) in terms of units of quantity, informal grading, the number of characteristics embodied in the good, and the range of styles. 37 .2 3a.... .38 >623 ”3.58 to 5K ad mg: 5.“ 93 m6 New o; Em m.~m omega; mucosa—as. o «.3 5.3 o N.» «.3 o 53 m.... o mdm 3.53323 0.5 pg... m.- ad 9m «6 ad mam cg o “do 393 2:55. _.~_ «.3 ~13 fie— ..m o c 98 T? a 9mm 3.2. o mdm new o o 98 o mén o 78 Tom was. a c.~ 9: «.mu o.~ ad a 93 o 1m 93 9.3.5:... ad ogw Tam 7o» ~.m o.~ a6 98 o.~ o 93 23835 93 e...” in a; m.~_ 98 ad— pdm o o ads €32.33: m; a... ~.: Wm o «.3 o; mdm o o o.~m 93:3 c «.8 o o ~.$ o «.3 o ~.S «.2 13 showered Educ: ode— o o o o c 0.8— o o o o .958 E38. 33.33:... 9.3: Two .ém m.~ ~.o ad «4 ode 12. To 06 «2: mafia: m.e~ c o o.m Tom can mém 5.3 o c was Eugene“ 5.2 9.3 ed a o o.~ NS adv o o.~ oé. 3269... 2.8 Tan 5v o mg... o a; was ad ad 93 T: 387.8 o o o o o 92: o adv o 9mm 92: 3o: 9:” man arm a; N: am 98 Tom c Tue 5m... 3m: mom_uauou:o v—ozomao: 7...: :a .o a. .6... z. .o t 28.3 o» uncommo. «to “:25... mam—Son 32.32 £2..an manage 9. guesmcou 3:298... 3.2.95... 5 :33 P... o: .853 :38 53 :38 58 3a.. 9.75 :9. 9.75 265° 2...: 2.3.6... 2.0 1.3.... was .95 o .26.. o a... o as 5 8 Sewage... 3 .363: «8.22.3 .2 :3: meta... roam—omen.” $8.8 co 8.53 .293... =- o. Cob... 5:. 3:82.52: 2 m a 2.0th mains—.82 a mafia. 38 Because of this homogeneity, any amount of product may be sold in the central market by anyone who can find a place to sit down. The amount of working capital required for producing in this way is modest, and can be expanded incrementally. In contrast, trying to sell from inventory the more heterogeneous and complicated goods that are produced by micro enterprises requires a substantially larger investment in inventories in order to make one sale. The entire array of possible products must be available to the customer so that he can make a choice. The fact that most micro enterprises sell on order is consistent with the idea that there is a systematic difference in the complexity of the goods between these two groups of producers, and that micro enterprise producers respond to this increasing complexity by utilizing an efficient, risk-adverse business strategy. The final section of Table 9 indicates that for several of the micro enterprises, customers either supply raw materials (tailors, dressmakers, rugs, agricultural implements) or make a down payment when the order is placed (furniture; to a lesser extent, shoemakers and floor tileries). This pattern of input procurement can be quite helpful in meeting the working capital needs of small producers. 2.4.4 Income Table 10 presents information concerning the value of production, value added, and income earned among small producers. The returns to the family are derived by deducting from the value of production all purchases of raw materials and intermediate inputs (including purchased services), wages paid to nonfamily workers, and an imputed cost of 39 .= 03...... .33 avian «00.58 ammo. nod mad mod and 32 Rn _ wonw oaa.o>< 93 3... R... a... R... S... 3.: Son 3552...... .m5::u_..m< wan 2.0 and .56 Ed 82 aaon anmn 30:» 0:285. .52 :5 an... -- 3... n2... 5...: 83.3 .2: ac No.0 .2. 26 m: a: a: a: «and KS 25 and 2.0 wad Sun aaan iua 9.3.0.5". R E S 36 aod an .o Nan _ 32 an _ n n.0meoocm 33 no.0 n _.o .i o~.o 2n .an R: onmEmmo..D :8 mod n _ .o 3.0 G. a :— ama. 33 30:2. «a u- 26 i .o 36 Now aaa aao— €030..on 0.0002 a. I 26 .... an; $2 onmu 3am .330 c.0002 manteouco 0.022 33 8... 2... 8... 8... R 8 2n case... a -- -- I .5... 2 a R Excess ”an -- -- -- 8... 2 an ”am 3026... £8 a N. E i I aod a2 a: aw... 30x30 5 3 u- 8. No.0 an an an 3m: N 3 :0. 2. no. :6 a; Sn 2...: 322 33.93:.» 205.020: Soc .va 3...: 13> tom E..."— ..od .m...c 35.05300 30: 29:03 23:85. 2:0: too azEmm 0a 0023. c0302. 03% 6023* scoao< 00...: bran... combo 3.30m «02 o=_m> .05 «0 33> .20... Bad .om .m...c 02m> .50: .2. 83. can? 0:50.: 0.... coco... 02m> S mug—9:. 40 capital for machinery, equipment, and tools.1 Data limitations make it impossible to make a similar deduction for inputed costs of land and buildings, so these are included along with estimated labor income under the heading, returns to family. Looking first at household enterprises, it is clear that mat production supplies a fairly substantial income to mat-producing families. The L.E. 413 average may be put in perspective by indicating that a university graduate starting out in government service would earn a beginning salary of about L.E 420 (L.E. 35 per month). The low returns per hour in the next column for mat production, on the other hand, remind us that this substantial annual family income requires work by an average of 1.6 members, each working an average of forty-six hours per week throughout the year. In fact, average returns to the family per hour of work are strikingly low for all household enterprises, ranging from L.E. 0.03 to 0.11 per hour. Because these activities require little capital and minimal skills, there is considerable ease of entry into these industries; competition among producers keeps returns exceedingly low. For comparative purposes, the wage rate of an unskilled agricultural laborer was L.E. 0.20-0.25 during this period (Hansen and Radwan, 1982); among household enterprises, only mat production approached even half that level. It is interesting to find that the hourly pay of hired workers in mat production is approximately equal to the net return to family members in the industry. In the case of dairy products, while net 1Costs of capital are calculated using a capital recovery factor, R - rv/(l-(l+r)-n) where v is the value of the asset, r is the discount rate, and n is the useful life of the asset in years. For the calculations reported here, r is taken to be 10%, n is assumed to be 15 years for machinery and equipment, and 7 years for tools. 41 returns per family per year and per hour are both quite low, the fact that so many households are engaged in this type of work means that over L.E. three million was earned by dairy producers in these two governorates, quite an important supplement to the income of rural households, particularly to rural women. It is clear that micro enterprises generate substantially higher returns than household producers. Overall average returns per family (or per producer) per year for micro enterprises are some twenty times as high as for household enterprises. Even dressmakers, who make the least returns per family hour of work among the micro enterprises, have average net returns of L.E. 0.20 per family hour of work, almost twice as high as for mats which has the highest hourly return per family hour worked among the household enterprises. One reason for the higher returns among micro enterprises may be the skill or capital requirements, which impose barriers to entry into these enterprises. Competition is still there, in varying degrees, but the barriers d0 prevent an influx of pe0ple sufficient to drive incomes down to the levels earned in household industries. Even in the borderline case of dressmaking, in spite of the widespread availability of required production skills and limited requirements in terms of marketing abilities, the need for L.E. 100 or more for a sewing machine has kept returns well above what could be earned in making hats or household embroidery, for example, where skill levels are comparable, but capital requirements are much lower. With regard to wage rates for hired workers, it is interesting to find that in almost every case paid family members earn returns well below those earned by hired workers. This could reflect ”self- exploitation"; it could reflect the fact that family members also share 42 in the family's net returns (they get room and board at the family table); or it could indicate that family members who are paid a wage are young people, who are less skilled than hired outsiders. Wages for nonfamily hired workers in micro enterprises fall into two groups. For "modern" dairy, embroidery, tailors, and dressmakers, wages are low: L.E. 0.10-0.17 per hour, on the average. While these wages are above the range of returns for household enterprises, they are still well below the wage rates for unskilled agricultural workers. Low wages in these industries reflect the low skill levels of the workers, as well as (particularly for dressmaking and embroidery) the fact that the industry itself yields only low returns, even to the entrepreneurs. The rest of the micro enterprises pay substantially higher wages, averaging L.E. 0.26-0.39 per hour. For all in this group except cement floor tile, hourly returns of hired workers are just under half the level earned by family members working in the industry. Among this group of micro enterprises, wage rates are about four times the average earning of family members in household enterprises. The last column of Table 10 gives an estimate of total value added in these industries, among all producers in the two governorates under study. The figures make clear that although there are fewer pe0ple involved, micro enterprises contribute substantially more to the aggregate income of people in these governorates than household enterprises. Tailors, furniture, tiles, and dressmakers are each particularly important; the total for all firms in the ten micro enterprise industries in the two governorates is nearly L.E. 17 million. CHAPTER.III THEORETICIJ.IWUHHHKNUK There has been much interest in the measurement of frontier production functions since the pioneering work by Farrell (1957). Instead of measuring an ”average" production function, many have felt that the frontier production function is closer to the theoretical concept of production in neoclassical economics, that is, each firm operates on the production function which allows the maximum amount of output from given quantities of productive inputs. As Stigler (1976,p. 214) points out, the above assertion is ”a simple corollary of profit or utility maximization." When a researcher estimates an “average“ production function (e.g., estimation by ordinary least squares (OLS)), the implicit assumption is that all firms in the sample are producing on one function, the average function, and any deviation from this average function is due only to “noise" or random events not controllable by the firm. There are several reasons why the above may not be the case. If, for example, firms are using the same technology (i.e., the elasticities of the variable inputs are the same for every firm when the production function is a Cobb-Douglas function) but for some reason one firm's subproduction function is above or below another firm's, then measurement of an ”average" production function by 0L8 may give biased results (Mundlak, 1961). Although not known as a proponent of frontier production function 43 44 analysis, Stigler (1976, p. 215) has asserted that ”in neoclassical economics, the producer is always at a production frontier, but his frontier may be above or below that of other producers." Whether firms are producing on subproduction functions identical except for a neutral disembodied productivity differential is, in principle, a testable hypothesis. One problem in the past with testing this hypothesis has been due to the use of mathematical programming techniques that do not allow statistical tests; another has been due to the use of stochastic models that do not allow estimation of individual firm measures. This study generalizes earlier models used in estimating frontier production functions and enables one to estimate ”individual“ firm subproduction functions that are the same for each firm (the elasticities of variable inputs are the same) except that subproduction functions of firms may be above or below that of other firms (a firm's intercept term from the production function can be different from that of other firms). If firm differences in production are found, then the obvious question to ask is what the causes or sources of these differences are. Many explanations can be given as to why one firm seems to produce more output than another firm from an apparently similar set of variable inputs. Advocates of frontier production analysis generally attribute differences among firms to differences in "technical” inefficiencies due to such factors as information deficiencies, adjustment cost, lags, and differences in management skill, effort, and will. Shapiro and Mueller (1977) have asserted that measured "technical“ inefficiencies are due to misspecification of the model by leaving out relevant productive inputs such as information. Stigler (1976, p. 215) makes a similar argument 45 stating that “the effects of these variation [technical inefficiencies] in output are all attributed to specific inputs... [sometimes] chiefly due to the differences in entrepreneurial capacity...Neoclasical economics...allocates the foregone product to some factor, so in turn the owner of that factor will be incited to allocate it correctly." Recently, Johnson (1985a) has stated that frontier function advocates view the production frontier as the surface of a solid. According to Johnson, there are three views of the production function, none of which are comparable to a frontier function. These three views are as follows: 1. A production function is deterministic and stable and is viewed as a surface; the stability of nature insures that there can be no variation in output from identical sets of rigorously controlled inputs. 2. A production function can be stochastic with all differences in output from a rigorously specified set of inputs being the consequences of uncontrolled inputs varying at random; thus, all variation in output from its expected value is devoid of any efficiency meaning, whether technical or allocative. 3. A production function allows for observed “wild card" inliers and outliers because of gross nonrandom (1) input or output aggregation errors or (ii) failure of observed instances to conform to the specifications as to which inputs are fixed at what levels. View one is what is used in economic theory; however, it is not generally appr0priate for empirical analysis since the production process, in fact, is stochastic. View two is what an empiricist is striving for as an ideal when he is specifying a production function for empirical estimation. A rigorously specified subproduction function under the second view would indicate which factors of production are variable, which are fixed and at what level, and which are varying randomly with an 46 expected value of zero. This rigorously specified subfunction will have both outliers and inliers that are due to randomness only; thus, it does not allow for systematic differences among firms. The third view allows for systematic differences among firms, but only because of mistakes made by the researcher in specifying the subfunction or in aggregating output or inputs. Johnson holds that, except for stochastic variations, all firms in a panel should be rigorously specified as a part of a larger function. This larger function, view one, can be expressed as Y . £(x1,x2,.....,xt) where Y is output and the X's are all possible inputs, both fixed and unfixed, known and unknown, discovered and undiscovered. As Johnson points out, this function is probably unknown and unknowable. One possible subfunction of the above production function which corresponds to view two would be Y = £(x1,...,xn) + u where x ,...,xn are variable 1 factors of production and u = g(xn+1,...,xt) with xn+1,...,xt being randomly distrubuted about 51, i - n+l,...,t, such that E(u) a 0. Another specified subfunction of the overall production function is Y - £(xl,...,xg/x ,...,xn=Cn) + u where Y is output, x1.....x g+lgcg+l g are the known variable inputs, xg+1,...,xn are unknown inputs fixed at C1 where C1 is the same for each firm, u = g(xn+1,...,xt), and xn+1,...,xt are variables randomly distrubuted about their means, £1, for i - n+1,...,t, such that E(u) a 0 and allowing for the possibility that for some i = n+1,...,t, xi may be equal to xj - E(xj)for j - g+1,...,n. One can also envision the case where the subfunction is identical to the second subfunction above, except that Ci for i - g+l,...,n can be fixed at different levels for different firms. Johnson (1985b) allows for the Ci's to differ among firms, but says the differences are due to SEC L'te 47 the fact that the firms "do not conform stochastically to the specification of what factors are fixed at what levels, i.e., inputs which are specified to be fixed may actually vary nonstochastically from [firm to firm].' Firms with more than the specified amounts of the so-called fixed variables are outliers and those with less than the specified amounts will be inliers. To correct for this, Johnson says we should (1) only use those firms that adhere to our specifications in estimating a subproduction function and eliminate those that do not or (2) identify the offending inputs and treat them as variable inputs. b b For the Cobb-Douglas function, view one is y - axll...xtt. The first subproduction function as presented above that conforms to the b b 1 second view of the production function is Y = axl "'xnn as now E(u) . 1; the second subfunction which conforms to view two as presented above is Y b b b b l 9 +1 AX1 ...x§ where A an+l ...Cn as E(u) l and Ci is the same for all firms. The first production function is not for i a g+l,...,n estimable, but the other two are estimable with ordinary least squares (OLS). When one makes allowances for the fact that the Ci's may differ among firms, we have potentially more than one subproduction function, up to as many as the number of firms in our panel data. This author would suggest that, in empirical estimation, the possibility of not being able to specify the subproduction exactly, so that no systematic differences remain among firms, is quite common. For example, if differences in fact do remain among firms, then to specify the subproduction function as if those differences do not exist may (but not always) cause our estimates to be biased. If we are unwilling to throw out those firms that do not adhere to our specifications of the fixed variables being fixed at the same levels for all firms or are 48 unable to identify the I'offending" inputs to the point that we can consider them variable inputs, then an estimator such as the 'within' estimator, which will be used in this dissertation for estimation purposed, may improve our estimates over those of OLS. As misspecification is always a possibility, when one has panel data it will often be reasonable to specify and estimate one's subproduction function according to both views: there are no systematic differences among firms (the Ci's are the same for all firms), and there are systematic differences among firms (the 01's may be different among firms). The first view is actually a restricted form of the second function, and one can construct an F-test to determine if allowing for differences among firms as to the explanatory power of our production function. Also, by using a Hausman (1978) test, one can determine whether the assumptions necessary to make OLS efficient are met (no specification errors) or whether the assumptions for the unrestricted view are more appropriate for the data being used in estimation. The unrestricted specification, that systematic differences among firms may exists, is used in this dissertation when estimating subproduction functions for Egyptian small-scale tileries. If one interprets xg+l""'xn to be factors that affect ”technical“ inefficiency, then the specification is a composed error model similar to Aigner, Lovell, and Schmidt (1977) for cross-section data. For panel data, when one believes these variables to be fixed at nonzero levels (or correlated with the other regressors, x1....,xg), a fixed-effects model should be used in estimation;1 if one believes these variables to be 11t is recognized that, if correlation exists between the fixed variables and those that are included in the model, the elasticity estimates will be imprecise (the larger the correlation, the more imprecise), but this problem also exists for the specification that does 49 random with nonzero means and to be uncorrelated with the other regressors in the model, a random effects model should be used. Our assumptions about what xk+1,...,xn are does not change the correct estimation procedure, but only the interpretation of the model and the results. All the above arguments have more to do with the interpretation of the model and the results from estimating the model than with the construction of the model. Improved methods of measuring firm differences in output may bring us closer to understanding what these measured differences are and what causes the differences, especially if, as firm-specific measures are refined, research is directed toward explaining these differences. ‘For example, according to the view that all firm differences in production must be due to aggregation errors, specification errors, or fixed factors being fixed at differenct levels for different firms, it should be possible in practice to estimate a subproduction function under view three and then to return to the firms and continue studying their production processes until one discovers the omitted variables or sources of error. Once this is done, one can enter these new variables into the subproduction function as specified in view two or make the necessary corrections for aggregation or measurement error and, if the specification is correct, all firm differences except those due to stochastic variations should disappear. Before leaving this section, another point should be discussed. Some (though not all) advocates of frontier analysis assert that a firm can move from the interior of the production surface to the frontier not allow for systematic differences among firms as well as the problem of the estimates being biased. 50 without any cost to the firm. For example, Bagi and Huang (1983) in a study of farms in Tennessee found that, on average, the farms were approximately twenty-three percent ”technically” inefficient in the cases of both cr0p and mixed farms. From these results, they wrongly assert that ”through the efficient use of existing inputs the farm output can be increased by almost 23 percent without any additional cost to the farmers." Johnson suggests that if a firm's subproduction function is different from that of another firm's, it must invest in more fixed inputs to shift upward or disinvest to shift its subproduction function downward. Whether a firm should shift upward or downward depends on the costs and benefits of making such shifts. If the firm is investing, acquisition prices are the appropriate prices to use in making the decision; if it is disinvesting, salvage prices are the appr0priate prices to use. In some cases, it will pay the firm to shift its subproduction function while in others it does not.1 This author feels that the views of "technical" efficiency advocates and nonadvocates are reconcilable. Both these views allow the output levels of the production process to differ by firms using the same measured bundle of variable inputs, though they attribute the variation to different causes. One view is that differences are due to "technical" efficiency; another is that it is due to fixed factors being fixed at different levels for different firms. If the management skills of the entrepreneur affect the production process and two firms have different skill levels of management, the differences in output given the same 1See Edwards (1958) for a more complete exposition of this theory. 51 bundle of variable inputs are attributed to “technical” efficiency by the "technical" efficiency advocates and to fixed factors (management skill) being fixed at different levels by the fixed variables advocates. One almost feels that the differences are more semantic than substantive. What is more crucial is whether these differences can be "corrected" freely as some "technical" efficiency advocates suggest, or whether there is a cost involved on the part of the firm in removing these differences. Johnson points out that free correction is usually unrealistic. Shifts among subproduction functions are not ordinarily "free". He states that, since prices and costs must be considered when deciding whether a shift among subproduction functions pays (benefits outweigh costs), the ”distinction between technical and price or allocative efficiency evaporates as price allocation is clearly involved in the case of so-called technical efficiency.” This author would differ slightly and claim there may be two sources of "inefficiency”: one where a firm is allocating itS‘variable inputs wrongly given its prices for these inputs; the other due to fixed factors being fixed at different levels for different firms, factors such as management skill, technological "know-how” (learned from experience), and information. For example, for a complex production process, the entrepreneur with more education than other entrepreneurs may have an advantage in assimilating and using the necessary technology and, from the same bundle of measured variable inputs, can produce more measured output than other firms. The more educated entrepreneur may also have an advantage in searching for, learning, and using information which can make the firm more productive. 52 Also, an entrepreneur with more experience than another entrepreneur may have learned ways to speed up the production process. In the production of tiles, the experienced entrepreneur may have learned that by relocating tiles stacking racks two steps closer to the tile presses, one can increase the hourly production of tiles in his firm by a square meter, or, by monitoring the weather closely, he can make decisions to shorten the soaking or drying step in producing tiles by several hours to a full day. As an entrepreneur gains more experience, he may be able to more often mix raw materials such as sand, water, and cement in the optimal manner to minimize waste and production of the wrong tile type. Adjustment lags in allocating factors (both fixed and variable) in response to changes in relative prices, changes in the demand for the product or product types, or changes necessary to correct past mistakes may also be of differing lengths among firms and cause some firms to produce more measured output from the same set of measured variable inputs. Once the above inefficiencies have been identified, the decision to "correct” for them is an allocative decision: however, the distinction among sources of inefficiencies should remain. The remaining sections of this chapter will survey the development of deterministic non-parametric frontiers, deterministic parametric frontiers, stochastic frontiers, and frontier systems which attempt to estimate "technical" as contrasted to "allocative" efficiency. In reviewing this literature, the author is not expousing the view of ”technical” efficiency, but presents this literature more for its contribution to econometric estimation, since the two models to be estimated in this thesis are an outgrowth of this literature as well as the econometric literature on panel data. 53 3.1 Deterministic Ion-parametric Frontiers Although earlier authors have develOped models to measure “technical” inefficiency (Marschak and Andrews, 1944; Roch, 1955), Farrell (1957) is considered to be the first researcher to measure "technical” inefficiency relative to a frontier production function (or a frontier unit isoquant). In Farrell's well-known procedure, he hypothesizes that efficiency can be divided into two components, "technical” efficiency and "price” efficiency, and that these components can be summed into overall ”productive" efficiency. Farrell uses linear programing to construct a frontier unit isoquant by constraining all observations to lie on or above the unit isoquant. The distance that an observation is from the unit isoquant is attributed to ”technical” inefficiency and can be measured by drawing a straight line from the axis to the observation and then by dividing the distance from the axis to the unit isoquant by the distance from the axis to the observation. "Price” efficiency is assumed to be independent of ”technical" efficiency and is the ability to allocate productive inputs according to their opportunity costs. Given relative factor prices, an isocost line can be constructed that is tangent to the unit isoquant line and intersects a line from the axis to an observation. Price efficiency for a particular observation can be measured by dividing the distance from the axis to the intersection of the isocost line with the line from the axis to the observation by the distance from the axis to the unit isoquant line along the same straight ray. Overall productive efficiency is measured by dividing the distance from the axis to the intersection of the isocost line with the straight line from the axis to the observation by the distance along the ray from the axis to the observation. 54 Although Farrell's technique has the advantage of not imposing a functional form on the data and the ability to calculate ”technical" efficiency measures for individual observations (firms), it is still considered by many production frontier advocates to be overly restrictive. Assumptions that must be maintained are constant returns to scale, free disposability of inputs, and all variations in output being attributed to ”technical” inefficiency. There is no relationship among observations except that they must lie within a frontier isoquant and, as the method does not use the entire sample to compute the frontier, it is highly sensitive to extreme observations and measurement error. Another major weakness is that the efficiency measures are not statistical in the sense that no standard errors or t-ratios can be computed: thus, hypotheses about the measures can not be tested statistically. The ”data envelopment analysis” (DEA) technique deve10ped by Charnes, Cooper, Rhodes and their colleagues as well as by Fare and his colleagues is a further refinement of Farrell's pure programming technique. This approach essentially uses a sequence of linear programs to construct a transformation frontier and to compute “technical" (primal) and "allocative" (dual) efficiency 51a Farrell relative to the frontier.1 The first of the three steps in the procedure is to construct an input set which satisfies necessary conditions to ensure a ”well-behaved" technology. Often further restrictions, strong input and output disposibility, are imposed on the input set. The second step is to solve the Farrell “technical” efficiency measure for each production unit in the sample by solving a minimizing programming problem. The 1See Lovell and Schmidt (1983) for an excellent and more detailed summary of DEA. 55 third step is to compute the minimum cost for each production unit in the sample by solving another minimizing programming problem. This third step computes measures of what Farrell called "price” efficiency and "economic” efficiency, the latter a composite measure of ”technical" and “price“ efficiency. The input set constructed above will be nonparametric, and the data set is enveloped or bounded by a convex weak-disposal hull made up of a series of facets. It contains the smallest input set that includes all the observations from the sample and satisfy the conditions for a “well-behaved” technology. This "smallest" input set provides an upper bound of the “actual” efficiencies, but does not provide a corresponding lower bound. Varian (1983) has shown necessary and sufficient conditions for an input set that "rationalizes' the data in that the data could have been generated by cost-minimizing behavior for that given input set. Further, he derives the tightest possible inner and outer bounds for any input set that 'rationalizes' the data and finds that his inner bound is identical to the input set constructed by DEA. Banker and Maindiratta (1983) extend Varian's analysis to the case where the all the data in the sample could not have been generated from cost-minimizing behavior and then show how to identify the subset of data that does obey the conditions for rationalizability. As they show, the input set constructed by DEA ”rationalizes' this subset of data, though this input set is not unique in the sense that it is not the only input set that can rationalize the subset of data; however, what has yet to be shown is the outer bounds for all input sets that rationalize the rationalizable data subset. 56 One of the most appealing aspects of DEA is that it constructs the input set that is the smallest well-behaved set containing all the data and is piecewise linear. Aside from certain technical problems with DEA that have to do with the radial nature of the Farrell measure of ”technical" efficiency (as opposed to some type of nonradial measure), the technique does have major deficiencies. The entire deviation of an observation from the frontier is attributed to ”technical” efficiency, taking no account of the possibility that the deviations, at least in part, may be the result of random shocks, measurement error, omitted variables (specification error), or fixed factors being fixed at different levels for different firms. In addition, since the technique is nonstatistical, it is not possible to make probabilistic statements about the shape or position of the frontier, nor can one construct statistical tests concerning the individual efficiency measures. 3.2 Deterministic Parametric Frontier Functions Farrell proposed a method of computing a parametric convex hull of the observed input-output ratios, but it is Aigner and Chu (1968) who first use this method. Aigner and Chu specify a Cobb-Douglas functional form and require all observations to lie on or beneath the frontier production function by constraining each residual to be less than or equal to zero. Two estimation techniques are proposed: linear programming, which minimizes the sum of the absolute values of the residuals subject to the constraint that all residuals be nonpositive; and quadratic programming, which minimizes the sum of squared residuals subject to the constraint that all residuals be nonpositive. Although this method imposes a functional form on the data, it has the ability to handle non-constant returns to scale, and it is still S7 able to estimate individual efficiency measures for each observation (firm). Disadvantages to the approach are that it limits the number of observations that can be efficient to the number of parameters being estimated, that it only uses a subset of the data to measure the frontier which causes the estimated frontier to be highly sensitive to extreme observations and measurement error, that it attributes all variations among observations in output given a set of inputs to "technical" efficiency (including any measurement errors or random errors to output), and that the approach is nonstatistical in the sense that no standard errors or t-ratios are computed. Recognizing the sensitivity of the estimated frontier function to extreme observations and measurement error, Aigner and Chu (1968) suggest and Timmer (1971) inplements an approach to 'desensitize' the estimation. Timmer uses linear programming to estimate the frontier which is specified as a Cobb-Douglas function with the constraint that all residuals be nonpositive. Timmer proposes first estimating the frontier with one hundred per cent of the sample and then to reestimate the frontier with (lOO-P) per cent of the sample, with P prespecified. Alternatively, Timmer suggests dropping the most efficient observations, one at a time, until the resulting estimated coefficients of the function stabilize. Criticisms to these methods are that the selection of P is arbitrary, that observations must be thrown out of the sample, that only as many efficient firms as there are parameters in the production function are allowed by this method, that the parameter estimates are still nonstatistical, and that the method is sensitive to outliers. 58 Recently, Kopp (1981) has shown that Farrell's input-based measures of “technical" efficiency can be generalized to deterministic parametric functions. He calculates, in addition to multiple-factor efficiencies, single-factor efficiency. Although recognizing that the same weaknesses of the method remain as discussed above, Kopp proposes this method whenever the researcher is interested in estimating individual efficiency measures as he believes that estimation of individual efficiency measures from stochastic frontier models are generally impossible. 3.3 Deterministic Statistical Frontier Functions Afriat (1972) extends the model proposed by Aigner and Chu (1968) by assuming a distribution for the nonpositive residuals (which he calls efficiencies). This allows the model to be statistical in the sense that by explicitly assuming a distribution for the residuals the possibility of calculating standard errors and t-ratios exits. As a result, the estimated parameters of the model can at least be potentially tested by the usual statistical tests for significance. Afriat proposes a two parameter (mean and variance) beta distribution for the efficiencies (residuals) and suggests estimation by a maximum likelihood method. In addition to assuming a beta distribution for the residuals, Afriat also suggests assuming a gamma or an exponential distribution. Richmond (1974) considers the model assuming a gamma distribution and shows that, by transforming the model slightly (subtracting the expected value of the error term from the intercept term and adding the expected value of the error term to the error term), OLS will give unbiased and consistent estimates of the slope coefficients as well as the mean of the residuals. Consider the model where 59 K hi and ut - exp(-zt) and the zt's are assumed to be a random sample from a Gamma distribution. Then it can be shown that w -n (2) E(u) - fexp(-z)G(z;n)dx = 2 o where E(zt)-n, Var(zt)=n, and Cov(zt,zs)=0, sat. Writing the model in logs, we have K = + . . - a Z blx 2t (3) Y i=1 1t t where ytalnYt, xt=lnxt, a=lnA, and 2t is defined as above. Now letting bO-a-n and vt=n-zt, we have a model that can be estimated by OLS; that is, x (4) Yt 8 b0 + ifabixit + vit where E(vt)-0, E(v:)-n, and E(vt,v8)-0, sfit. By also assuming E(v/X)-0, where v'-(v1,...,vT) and x=(xit), it can be shown that an unbiased estimate of n is - T - x - 2 (5) n - 1 2 (y - b - 22b.x. ) . T - K - 1 t=l t 0 i-n 1 1t 60 From the above, it follows that E(b0)=a-n, E(bi)-bi, and E(n)=n for (i-l,...,K). It also follows that b0 + n is an unbiased estimate 0 Q of a, that exp(bo+n) is an upward biased but consistent estimator of of A, and that E(u)=E(2-fi) is an upward biased but consistent estimator of E(u)-Z-n. The estimate of the last term, E(u), gives us an estimate of the average level of efficiency for the population being estimated. Schmidt (1976) shows that, by assuming the residuals are distributed exponentially, Aigner and Chu's linear programming technique is maximum likelihood, and that, by assuming the residuals are distributed half-normally, their quadratic programming technique is maximum likelihood. In addition, Schmidt shows that OLS gives unbiased and consistent estimates of the sloPe coefficients, but that the OLS estimate of the constant term is biased and inconsistent in a statistical sense; however, it should be noted that using corrected OLS (COLS) as suggested by Richmond will give consistent estimates of the intercept term. Problems have been encountered when trying to estimate the statistical properties of the estimated parameters with maximum likelihood methods. Schmidt (1976) points out that the range of the dependent variable depends on the parameters being estimated, thus violating the usual conditions used in proving the consistency and efficiency of maximum likelihood estimates. Greene (1980a) shows that by assuming a gamma distribution for the residuals the usual asymptotic pr0perties of the maximum likelihood estimators can be derived; however, distributions such as the truncated normal or the exponential distributions do not allow such calculations. The reason, as is shown by Greene, is that in order for the usual desirable asymptotic properties of 61 maximum likelihood to hold, the density of u, the error term, must equal zero at zero and the derivative of the density of u with respect to its parameters must approach zero as u approaches zero. Since different distributional assumptions for the residuals lead to different estimates for the maximum likelihood estimators, the restriction on choice of distributional assumptions for the residuals is not a trivial matter. Also, these estimates are highly sensitive to outliers as are the previously discussed deterministic models. Of course, COLS as proposed by Richmond (1974) can be used as an alternative to maximum likelihood estimators. However, even after correction for the OLS estimates, residuals may have the wrong sign (positive for a production frontier and negative for a cost frontier). Also, the correction for the OLS intercept is not independent of the distribution of the residuals, and different distributional assumptions lead to different estimates of average ”technical” efficiency. Greene (1980a) suggests a remedy to the above problems by shifting the OLS constant term upward until all observations lie on or below the production frontier. This ensures that all residuals have the ”correct" sign and does not allow distributional assumptions for the residuals to change the estimate of average ”technical” efficiency. The problem of sensitivity to outliers, however, is not removed by using COLS ala Richmond or Greene. 3.4 Stochastic Frontiers Much criticism has been leveled against deterministic frontier functions. Most economists have difficulty in believing that all variations in a firm's output given its input set are attributable to ”technical" efficiency. After all, we live in a world full of 62 uncertainty, and the luxury of knowing production processes exactly is not possible. Weather, unpredictable machinery breakdowns, and luck are just a few of the many factors that are not controllable by the firm. In addition, whenever empirical work is done, there is always the possibility of measurement error as well as specification error. Also, since these models constrain all observations to lie on or below the production frontier, they are highly sensitive to outliers. To lump all random and uncontrollable exogenous shocks to the firm's production process (as well as measurement error and specification error) under the heading of ”technical" efficiency is not desirable. Aigner, Amemiya, and Poirer (1976) address the above issues by proposing a weighting scheme to weight positive residuals less than negative residuals, specifically e*i if e*. > o 1 - e 1 (6) e1 = . i = 1,...,n e*i if e*. < o 1 ._ e where e*i is independently normally distributed with mean zero and variance 0? for 0 < 0 <1 , but is either negative or positive truncated normal for C>= l or C>- 0, repectively. Their justification for the above specification is that differences among firms in their production of output given productive inputs may be due to the inability of all firms to use the "best practice” technology which would call for a one-sided error distribution or may be due to either symmetric measurement error in output or the influence of an additive random and symmetric input which could cause the error term to be above or below 63 zero. The term 6 is interpreted to be a measure of the relative variability of observations above or below zero. When 9 = l, the model becomes the deterministic parametric statistical frontier or ”full frontier", and when G = 1/2, it becomes the average function case. A more direct and seemingly more reasonable approach to the above issues is taken by Aigner, Lovell, and Schmidt (1977) and Meeusen and van den Broeck (1977). Both groups of authors explicitly acknowledge the possibility of shocks and other random factors outside the firm's control as well as the inability of some firms to produce on the frontier function because of factors that are controllable by the firm. Consider the following production model, (7) Y1 = f(Xi;B)+ei (i = l,....,n) where Yi is the maximum amount of output obtainable from Xi, a vector of nonstochastic productive inputs for the 1th firm, and B is a vector of unknown parameters to be estimated. In addition we note that (8) e. = vi + u. i = l,....,n where vi is the error component representing symmetric disturbances distributed normally with zero mean and variance qfi. The error component ui representing ”technical" inefficiency is assumed to be independently distributed from V1 and less than or equal to zero. If 0:,- 0, then the model collapses to the deterministic frontier model. If 0: = 0, then we have the stochastic production function proposed by Zellner, Kmenta, and Dreze (1966). 64 The composed error model can be estimated by assuming distributions for both ui and vi and applying a maximum likelihood method. Both Aigner, Lovell, and Schmidt (1977) and Meeusen and van den Broeck (1977) estimate the model by assuming that V1 is normal with mean zero and variance 0: and that ui is distributed exponentially. In addition, Aigner, Lovell, and Schmidt estimate the model assuming that ui is distributed as a negative half-normal with mean zero and variance<3:. Stevenson (1980) estimates the model assuming a negative half-normal distribution for ui, but allows the mean of ui to differ from zero. This model has the desirable feature that statistical properties of the estimated parameters can be calculated and that all variation in output given a set of inputs is not attributed to ”technical" efficiency. The major weakness of the model is its difficulty in estimating individual efficiency measures for each observation (firm) although average efficiency for the population is readily available from estimation by Maximum likelihood methods or COLS. Until recently it was felt that to decompose the individual residuals into their two components was impossible (Forsund, Lovell, and Schmidt (1980); Kopp (1981)). However, Jondrow, Lovell, Materov, and Schmidt (1982) show that by assuming V1 is normal, ui is negative half-normal, vi and ui are independent, and that inefficiency is independent of the regressorsl then an estimate of the individual inefficiencies for each observation (firm) can be obtained, though not consistently. The estimate for ui is based on the conditional mean of ui given ei, that is 65 t f eix’/O ei = O — (9) E(Ui/ei) . a H? (e1A /0 ) 0 * t where f and F represent the standard normal density and distribution 2 2 2 2 2 2 . . (5 ‘ 0'0 62 (fl - o o l o 0 function, respectively, and . u v/ , u + v' and - u/ v' By replacing ei with its estimate, e , and 0', O , Aby their estimates, i Ui can be estimated. Bagi and Huang (1983) estimate individual efficiency measures for 193 farms in Tennessee using this method, and, more recently, Huang (1984) developes an EM (expected-maximization) algorithm as an alternative to the two-step procedure proposed by Jondow, Lovell, Materov, and Schmidt to estimate individual efficiency measures for 151 farms in India. 3.5 Frontier Systems In addition to measuring 'technical' efficiency, a researcher may also be interested in measuring "allocative” efficiency, that is, whether or not a firm is producing off its least cost expansion path, and, if so, by how much. The duality between a production function and its associated cost function has been recognized by economist for quite some time, either function uniquely defining the firm's technology. If the necessary conditions for duality are met, then knowledge of the production (cost) function will allow derivation of the cost (production) function, provided that the functional form of the production (cost) function is tractible. Thus, if we are able to measure technical (allocative) efficiency from the production (cost) function, we can then, in principle, derive measures for allocative (technical) efficiency from the parameters in the production (cost) function. 66 The stochastic frontier model has been extended by Schmidt and Lovell (1979) to allow measurement of average "technical" efficiency for the population and allocative efficiency for each observation (firm). The system of equations to be estimated are the production function as specified in Aigner, Lovell, and Schmidt (1977) plus K-l factor share equations derived from the first-order conditions for cost minimization, K being equal to the number of productive inputs into the production process. The behavioral assumption is made that firms choose to minimize cost given their desired level of output (i.e., that output is exogenous and inputs are endogenous). A firm is defined to be technically inefficient if it is producing output below that of the most technically efficient firm for a given set of productive inputs: a firm is allocatively inefficient if it is operating off its least cost expansion path. In addition to being able to derive K-l stochastic factor demand equations, the cost function can be derived, and, from it, allocative efficiency measures for each observation (firm) can be estimated. The model is estimated using cross-sectional data for a sample of US steam-electric plants under three different assumptions: firstly, firms are allocatively efficient, but may be technically inefficient; secondly, firms may be both allocatively and technically inefficient but without any systmatic tendency to over (under) utilize any input relative to any other input: and thirdly, firms may be both allocatively and technically inefficient and may tend to over (under) utilize any input relative to any other input. In all three cases, ”technical“ and “allocative” inefficiencies are assumed to be uncorrelated. This assumption is relaxed in Schmidt and Lovell (1980), and a test is constructed to test for the presence of such correlation. 67 Greene (1980) develops a similar model, but assumes that the error term for the production function is one-sided and has a gamma distribution. Unlike Schmidt and Lovell who specify a Cobb-Douglas. functional form, Greene specifies a translog cost function and derives its corresponding factor share equations using Shephard's (1953) Lemma. Alternatively, as an example, Greene specifies a translog production function with its associated share equations and measures average ”technical“ efficiency. From the residuals on the share equations, he is able to obtain allocative efficiency measures for each firm. The translog functional form is more flexible than a Cobb-Douglas function, but does not allow explicit solution for the production function (cost function) corresponding to the translog cost function (production function); thus, it is difficult to know how an error in one function relates exactly to the corresponding quantity in the other function. 3.6 Stochastic Frontiers and Panel Data The problem of estimating individual ”technical“ efficiency measures from stochastic frontier functions with cross-sectional data is due to a lack in degrees of freedom. If we have n firms, we have n equations from which to estimate k+n parameters, k slope parameters and n ”technical" efficiency parameters (one for each firm); thus, we use up all of our degrees of freedom plus some. Jondrow, Lovell, Materov, and Schmidt (1982) show that one can obtain individual measures of ”technical” efficiency (ui) conditional on the estimated residuals from the stochastic frontier (ei = vi - ui); however, this measure is inconsistent. 68 An obvious extension of cross-sectional estimation of stochastic frontiers is to estimate the frontiers using panel data. The use of panel data to estimate individual and statistically validated measures of ”technical" efficiency for each observation (firm) seems to have been first applied by Hoch (1955; 1962), although he normalizes his measures relative to the “average” and not the "frontier“ firm.1 Hoch assumes that entrepreneurs maximize "anticipated” profits and, making this assumption, makes output endogenous and inputs exogenous, enabling him to obtain unbiased estimates for the model from OLS.2 Hoch's assumption implies that entrepreneurs are able to sell any amount of output that they produce without influencing the market. Output prices are known as are input prices: thus, the maximization problem for the entrepreneur is to produce the amount of output that maximizes expected profits. Production is assumed to be captured by a Cobb—Douglas function. Let N equal the number of firms, K equal the number of inputs, and t equal the time period. Following Hoch (1962) but using our notation, his model can be written as follows: K a. v. (10) Y. = D.D H X.J.e 1t Production Function 1t 1 t. it] J=1 K .n. = - Z a . (11) it PYit j=1 wjxitj Profit Funct1on 1 Mundlak (1961) uses the same technique, but specifies his model to measure slope coefficients free of "management bias". 2Zellner, Kmenta, and Dreze (1966) make a similar assumption that entrepreneurs maximize "expected” profit, or the mathematical expectation of profit. Although using different terminology than Zellner, Kmenta, and Dreze (1966), Hoch, when he operationalizes his model, makes it clear that he is also speaking of maximizing the mathematical expectation of profit. 69 32('" ) (12) it = 0 Maximizing conditions 3 xitj where Yit is the amount of output for firm i at time t, xitj is the amount of input j for firm i at time t, P is the price per unit of output, Wj is the price per unit for input j, ’"it is the profit for firm i at time t, E(') is the expectations Operator, and vit is a random error term. The aj's are the parameters of the Cobb-Douglas production function, and Di and D are the fixed effects for the firm and the time t period, respectively, where i=1,...,N is the firm and t=l,...,T is the time period. From the system above, we can solve for the expected profit maximization conditions of the form 2. . (13) P( 3E(Yit))= R.W.e 1t] (i=1'eeo'n; j=llooe'K; (axitj> 3 3 t=l,....,T) where Rjal for exact profit maximization, Rj is less than or greater than one when profit maximization is not exact, and zitj is a random error term; thus, Rj is a measure of the average deviation from Optimality, and firm variations around this average in Hoch's model are treated as part of zitj' These equations can be rewritten as K factor demand equations and, when combined with the production function, give us an estimable system of K+1 equations. The logarithmic form of the system is 70 K (l4.A) yit = di + dt + jfl ajxitj + vit (14.3) xitj = ln(ajP/ijj) + 1n(E(Yit)) + zitj (i=1,...,n; jglpooo'K; t‘lpeoo'T) where y slnY. x. .=lnX ., d.=lnD., and the other variables are as it 1 1 1 t' it) itj defined above. The equations above are estimated by Hoch (1962) for a sample of sixty-three Minnesota farms over a six-year period, from 1946 through 1951. Individual firm "technical" efficiency measures, the d 's, are 1 obtained, but RJ, the deviation from optimality for input j, is measured as an average for the population and is not made firm specific. The fixed effects, elasticities, marginal returns, and returns to scale are estimated, and several tests concerning the statistical significance of these estimates are made. Results from this unrestricted model are compared with the results from a restricted version of the model which assumes that di-O and dt-O for all i and t. The di's and the dt's when taken jointly are found to be significantly different from zero, and the di's when converted to antilogs range from 1.4 to 0.7.. It should be noted that two-thirds of the firms had firm effects less than seventy percent as large as the largest firm effect and approximately ten percent of the firms had firm effects less than half the size of the largest. The restricted model (estimated by ordinary least squares (OLS)) indicates constant returns to scale; however, the unrestricted model which allows the di's and the dt's to differ from zero indicates diminishing returns to scale. The estimated measure of the R 's from the :l unrestricted model indicate that too much labor is being allocated to the 71 production process and too little nonhuman inputs. Hoch ends his paper by showing that the di's (which he calls firm measures of "technical“ efficiency) are related to firm size. More recently, Pitt and Lee (1981) use panel data (three years only) to estimate individual ”technical” efficiency measures from a sample of fifty Indonesian weaving establishment. Pitt and Lee generalize the composed error model deve10ped by Aigner, Lovell, and Schmidt (1977) to allow for estimation with panel data. Pitt and Lee's model is essentially a variance components model of the following form: (15) y. = x1 1t 8 + ui + V. i=1'000'N; tglpeeo'T t t it where yit=lnYi and represents output, xitalnxi and represent inputs, t t the uit's are less than or equal to zero and represent "technical” efficiency, the vit's are a stochastic variable representing uncontrollable random shocks in the production process, 1 represents the . h . . th . . 1 production unit, and t represents the t time period. By making different assumptions concerning u. it , Pitt and and vit Lee have three models which they estimate and compare with each other. The first model assumes uit is time invariant, thus becoming ui, and is estimated by maximum likelihood and analysis of covariance (the ”within" estimator). The second model assumes that for all trt', E(u )-0 for ituit' all i and E(uituit,)=0 for all 173; that is, none of the firms' inefficiencies stays with them over time. This second model is essentially the same model set forth by Aigner, Lovell, and Schmidt (1977) when t=l and is estimated with maximum likelihood. The third =' I :2 ' a: model assumes that for t t , 8(uituit') Oit' for all 1 and E(u ) 0 ituit' for all iij. This model allows some firm inefficiencies to remain with 72 the firm over time and some which do not and is estimated by generalized least squares (GLS) much as a random effects model is estimated. The model specifications are tested with a procedure developed by Joreskog and Goldberger (1972). Support for the third model over the other two models is found, though the maximum likelihood estimates for the first model and the GLS estimates for the third model are quite close. Another, perhaps questionable, procedure carried out by Pitt and Lee is that they estimate the first model with analysis of covariance (”within' estimator) and then regress the individual firm effects on type of ownership (foreign or domesticly owned), the age of the firm, and the size of the firm. Finding a correlation between these variables and the firm effects, they introduce these variables directly into the production function and estimate the third model and reestimate the first. Schmidt and Sickles (1984) use panel data (35 quarters) to measure individual ”technical” efficiency measures for twelve airline companies. Their model is essentially the same Pitt and Lee's (1981) general model (Equation 15 above) with the additional assumption that firms are maximizing expected profit as discussed by Zellner, Kmenta, and Dreze (1966). Schmidt and Sickles give an excellent review of panel data estimation procedures and discuss under what assumptions one should use the different estimation techniques to estimate their model.1 Ruling out estimation of the model by OLS, Schmidt and Sickles choose the "within" estimator, the GLS estimator, and the maximum likelihood estimator (MLE); the results are quite similar for all three 1A detailed discussion of estimation procedures for panel data under different assumptions concerning the fixed effects and the error term is presented in Chapter 4. 73 estimation procedures. Increasing returns to scale are found in all three cases with 1.12 from the ”within“ estimator, 1.13 from GLS, and 1.18 from MLE. Using a Hausman-type test, they find no correlation between the effects and the regressors. (This is as expected since the results from estimating with the “within" and GLS estimators are so similar.) In addition, a joint hypothesis, effects and regressors being uncorrelated and correct distributional assumption (i.e.,normal v, half-normal u), is tested by comparing the "within” estimates with the maximum likelihood estimates and support for this hypothesis is found. More recently Schmidt (1984) deve10ps a model which generalizes the model presented in Schmidt and Lovell (1979) by allowing estimation of that model with panel data. It is also similar to the model above except that the model is no longer a single equation model, but a system of factor share equations combined with the production function; it is also similar to and is a generalization of the model presented by Hoch (1962). One essential difference between Hoch's model and Schmidt's model is their assumptions concerning output and inputs. Hoch assumes that entrepreneurs maximize "anticipated" profits. By making this assumption, Hoch makes output endogenous and inputs exogenous and can obtain unbiased estimates for the model using the "within” estimator. Schmidt assumes, as in Schmidt and Lovell (1979), that entrepreneurs are minimizing the cost of producing for a given amount of output: that is, output is exogenous and inputs are endogenous. Schmidt, as does Hoch, also assumes that output and input prices are exogenous and known. Under the assumption of cost minimization for a given amount of output, output is not a decision variable for the entrepreneur but is decided by demand factors outside the control of the firm. Examples of 74 industries producing under this assumption have generally been natural gas and power plants. The problem for the entrepreneur under this assumption is to minimize the cost of producing a given amount of output. Schmidt's model is as follows: K (16.A) y = Z a.x. + di + v. it jgl J itj it (i=l,...,N; t=1,...,T; j'2,...,K) (16°b) xitl ‘ xitj 3 Bitj + gij + uitj where di is the individual fixed effect measuring "technical“ efficiency, gij is the individual fixed effect measuring allocative efficiency, and v. and u. . are random error terms. B. . is made up of a.'s and prices it it] it] 3 and is not an additional parameter: (17) B. . = ani - an. + lna - lna. it] 1 J tj t1 1 ‘nhere Wi is the price of the jth input at time t for the ith firm and ti j=2,...,l<. Schmidt assumes independence across firms and time; that is, temporal dependence at the firm level is picked up by the fixed effects. Iklso, v and the u.'s are assumed to be independent, v is iid N(0'(Kf)' iixid the vectors (u2,...,uK)' are iid N(0, Q ). It should be noted that ‘Zlie form of the conditional MLE's as derived by Schmidt depends on rlcarmality, but the consistency of the resulting estimator does not since jLts consistency only depends on the first two moments. 75 The fact that Yit’ output, is now considered to be exogenous complicates the estimation procedure considerably. If OLS is applied to the model, biased and inconsistent regression coefficients will result. This is because OLS requires the variables to the right of the equal sign to be exogenous, and this condition is violated in the production function. The ”within" estimator could be applied to the model, but again the estimated coefficients will be biased for the same reason they are when estimated by OLS. This condition will also generally apply to the restricted GLSE. The problem of obtaining consistent and unbiased estimates of the coefficients is not irreconcilable. Following Chamberlain (1980), Schmidt derives the conditional MLE's for the model by conditioning on sufficient statistics for the individual effects which are assumed to be fixed and can be correlated with the regressors. In order to derive the conditional MLE's, the following assumptions are made: i. v 8 (vi l,...,vi22)' is independent of = I u2 (uil 2'°"'“122 2) ' ii. di and 912 are fixed individual effects, iii. individuals are independent of each other and over time, iv. v is iid N( 0,03) and uj is iid N(o,o§). Under the above assumptions, Schmidt (1984) shows that the logarithmic likelihood function is of the form: 76 (18) L - constant + NT 1n r - NT/2(ln<3: - NT/2(1nH7|) 2 2 ’ 1/2‘3v1 § E(Yit ' ? ajxitj ' di) 1 1t 3 - 1/2( 2 z z ' 9‘12 ) . it it 1 t where, in our case, i=l,...,N, t=l,...,T, j=l,...,K, and (19) r = X a. j 3 xiti'xitz'Bitz'giz (20) zit = . . iti'xitz'Bitz'giz X The likelihood function can then be decomposed into two parts, the "within" and the ”between" variation of the data; from this, it can be shown that only the "between" variation depends on the individual effects, di and gij' and that the MLE's for the effects are K (21) d. =1. - )3 a.x.. i i j=l j ij T 22 .. a Z . . T ( ) gij tslgltj/ Where i‘lpoo'N; jglpooo'K; t=1'000'T; and (23) gitj s xitl - xitj + witl - witj + ln(aj) - ln(a1) 77 and T (24) y. a 2 y. i t=1 it T (25) x.. = Z x. ./T It can also be shown that, at the point of maximization for the likelihood function, the "between” variation equals zero when we insert Equations 21 and 22 into Equation 18; thus, the MLE's of a,<3:, and S7 come from maximization of the “within" variation only. The joint MLE's of all the parameters will have desired characteristics (consistency and asymptotic efficiency) when T-+<» for fixed N, but not when N-+«>for fixed T; in this latter case, the estimates of the individual effects will not be consistent and, due to their pressence, the MLE's of the other parameters of the model may not be consistent. The problem is caused by the fact that the number of parameters to be estimated increases as N increases and is discussed by Chamberlain (1980); however, by deriving conditional MLE's for the parameters based on sufficient statistics for the individual effects, consistent and unbiased estimates of all the parameters of the model can be obtained as either N or T-*<”. Schmidt shows that the sufficient statistic for (di,g12,....,gix)' is )Eil'-§iz’°"‘§ix)' and that the conditional likelihood function is 78 (26) LC a constant + N(T-l) 1n r - N(T-l) ln|$2| 2 2 2 .. a .. t - 1/2 VIE E (Y it E ajx itj di) 1 - 1/2( X X 2*it' Q-lz*it) i t * a - * g - * . where y it yit. xit' x itj xitj iitj' and 2 it is a vector of the following form: xit1 : xit2 --§il +.312 ' B*it2_ (27) 2*it = : : xitl ' xitK "-511 +-§ix ' B*itK L- -—d and (28) 8*itj 3 witj " "iji ' 1ij + iii By concentrating the likelihood function over(3: andgl, where 2 2 (29) 0 = 1 z z (y*. - 2 a.x*. .) N(T-1) i t It j 3 1t] (30) 52 = 1 z z 2* 2*. ' N(T-1) i t 1t It the concentrated conditional likelihood function can be obtained which depends only on a = (a1, a2,..., aK)' and is maximized by the conditional MLE of a as shown below. 79 (31) L*C = constant + N(T-l) ln r|52| - N(T-l) 1n 1 Z E(y"it - Z a.x*it.)2 2 N(T-l) i t j 3 3 - N(t-1) ln 1 Z >3 2*. 2*! 2 N(T-1) i t 1t it As can easily be seen from above, z*it does not depend on a, so that the last term does not enter into the calculation of the conditional MLE of a; thus, none of the parameters in the production function (a, di' and<3:) depend on the input prices, though the estimates of S? and gij do. From differentiating the concentrated conditional likelihood function with respect to a = (a1 a2)' and setting the result equal to zero gives the following: (32) a = 3 + SSE(x*'x*)-1e f where , -1 03> s= (x. x.> m. (34) SSE = (y. - x*a)'(y* - x*5) (35) f = e'a = Z aj and (36) regressing y* on x* by OLS. Y. L 80 ”11‘ -"*111, . . ”1.911; Y*iT x* = x”'1'1'1:...,::c*1,m( Y*Nl x*Nll;...,x*N1K Y*NT_ L. x1"11'1'1: . . . ,;*NTK_ Notice that a is the "within" estimator which is obtained from Further, Schmidt shows that the conditional MLE's of the model can be obtained from a ”within" transformation on the data plus correction factors that account for the fact that output is assumed to be exogenous and inputs endogenous; that is, (37) (38) (39) (40) (41) (42) a ‘ 2 + (ass/y ' e l f = e'& = £_+ D SSE/5 SSE = (y, - x*5)'(y* - xii) = SSE + D SSEZAE? 13' B.. = -13 P.. .X.. 3‘1) U. = 511 - x.. - B 81 where a, E' SSE, and D are all derived from OLS of y* on x* so that (43) .E = e'a (44) SSE = (y, - x‘3)'(y* - xta) (45) D = e'(x*'x*)-1e and a is given above in Equation 33, and e is a le vector of ones. In addition, the asymptotic variances of the estimators are derived from the information matrix and have the following form: In summary, we have the interesting conclusion that in this fixed-effects model, the conditional MLE's are obtained by making a simple correction to the ”within" estimator. Although distributional assumptions must be made concerning the residual terms in order to calculate the conditional MLE's, the consistency of the derived estimates does not depend on the distributional assumptions; their consistency depends only on the first two moments of the residuals. It should also be noted that the above discussion skirts the difficult distributional issues that evolve if one normalizes the individual effects for the production function as done in Schmidt and Sickle (1984). One still obtains consistent estimates of the individual effects and can make comparisions across firms as T-+