PRODUCTION FUNCTIONS IN CONTRACT CONSTRUCTION FOR THE UNITED STATES, 1972 Dissertation for the Degree of Ph. D. MICHIGAN STATE UNIVERSITY IOHN SEWELL McCONNAUGHEY, JR. 1976 -. 4" Q‘A "I $215735”. ' a ‘ This is to certify that the thesis entitled PRODUCTION FUNCTIONS IN CONTRACT CONSTRUCTION FOR THE UNITED STATES, 1972 presented by John Sewell McConnaughey, Jr. has been accepted towards fulfillment of the requirements for P .D. . h Jegree 1n Economics WWW». Major professor Datezvgg’é/ [I {€7I/ 0-7639 1,15 57 11":"34 III _3 1293 00670 3304 ___,_—-— III III IIIIIIIIIIII II V . u ,, a ABSTRACT PRODUCTION FUNCTIONS IN CONTRACT CONSTRUCTION FOR THE UNITED STATES, 1972 By John Sewell McConnaughey, Jr. Construction is a large and important sector of the U.S. Economy. Gross construction expenditures have generally averaged about 13-14 percent of Gross National product. The sector directly employs between S to 6 percent of the labor force. But over half the jobs created by construction expenditures are indirect, occurring in those mining, manufacturing, trade and transportation industries which provide construction materials to the sector. It is generally agreed that cyclical and seasonal fluctua- tions within the sector, regional shifts in demand of output, sensitivity to monetary policy, and institutional constraints (such as the separation of design from production, restrictive build— ing codes, contractural disputes, union bargaining strength) strongly affect performance and productivity growth in the sector. Economists and policy makers have been especially concerned about the performance of the construction sector regarding unemployment and inflation. Much employment is seasonal, and even in years of high demand un- employment among construction workers is high relative to other sectors. Construction costs have risen rapidly in recent years John Sewell McConnaughey, Jr. while productivity growth in construction appears somewhat lower than for other sectors. Moreover, the complexity of the sector, the heterogeneity of the output, and poor construction statistics have greatly hindered economic investigation. The purpose of this study is to examine the Contract Con- struction Industries using new data which has recently become avail- able in the 1972 Census of Construction Industries. This census is the second since World War II, but is the first to contain data on capital inputs. No previous production function study of this type has been undertaken for the Contract Construction Industries because of the lack of appropriate statistical data. We estimate single equation Cobb-Douglas and Constant Elasticity of Substitution (CES) functions for twenty-four 4 digit Contract Construction Industries. Our models are similar to those used in production function studies in manufacturing. In Contract Construction the 4 digit industries are separated into three major groups by type of specialization. They are: SIC 15, General Build— ing Contractors; SIC 16, Heavy Construction General Contractors; and SIC 17, Special Trade Contractors. Our major empirical findings are: (l) The elasticity of substitution between capital and labor is less than one for nearly half of the special trade contractor industries, but for most of the general building contractors and heavy construction general con— tractors a value of unity seems reasonable; (2) There is evidence of increasing returns to scale for about one third of the special John Sewell McConnaughey, Jr. trade contractor industries. However these industries employ nearly two—thirds of the workers in the special trade contractor group (SIC 17); (3) There is great diversity among the 4 digit industries. Many factors, especially geographic factors, influence the construc— tion process differences in a complex way. Examples are skill composition, design, size of establishment, size of construction project, degree of urbanization, and degree of unionization. Our empirical results suggest that no single policy action for the sector as a whole is likely to have the same impact in each of the separate industries. Traditional production function models generally use value added as output, and ignore the possibility of substitu- tion between materials, other inputs. We provide evidence that substitution of materials for labor and capital occurs in construc— tion, and that this substitution may be an important source of pro- ductivity growth in the sector. In a separate chapter we develop models which allows us to explore in a tentative way substitution between materials and other inputs, especially onsite labor. We find that most evidence suggests an elasticity of substitution be- tween materials and labor of about one. But these findings are not conclusive since our efforts are hindered both by statistical problems and by limitations in the functional forms which we use to examine the multiple input production functions. PRODUCTION FUNCTIONS IN CONTRACT CONSTRUCTION FOR THE UNITED STATES, 1972 By John Sewell McConnaughey, Jr. A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Ecbnomics 1976 FOR MARGARETTA, GRETA, KATHERINE, AND REBECCA ii ACKNOWLEDGEMENTS I wish to thank all my friends and colleagues at Michigan State University who have been a source of support and encouragement during this project. I am especially grateful to Professor W. Paul Strassmann for his constant guidance and support. He instilled in me an interest in the economics of the construction sector, and gave freely of his time and ideas. His help was invaluable. My thanks go also to Professor Robert H. Rasche for his time, his problem solving, and his constructive criticism; to Professor Byron W. Brown whose guidance on production theory was particularly appreciated; and to Professor Paul B. Ginsburg who combined expedi— tious reading of the thesis with sound advice for improvement. I would also like to thank my fellow graduate students, especially Robert Pierre Henry for his friendship and moral support. Technical advice on computer applications by Jan Palmer is also much appreciated. I also wish to thank my parents for their continuous support of all my academic undertakings. This thesis is dedicated to Margaretta, Greta, Katherine, and Rebecca, who have sacrificed much.during the writing of this thesis. They make everything worthwhile. iii List of Tables TABLE OF CONTENTS Chapter I. INTRODUCTION II. THEORETICAL BACKGROUND 1. General Characteristics of the Contract Construction Industries 2. General Production Theory 3. The Cobb-Douglas Form 4. The CBS Form III. THE DATA AND THE VARIABLES 1. The 1972 Census of Construction Industries 2. The Variables 3. Detailed Characteristics of the Construction Industries a. Local Nature of Construction b. Size of Establishment c. Diversity of Operations d. Regional Influences IV. THE EMPIRICAL RESULTS 1. The Cobb-Douglas Results 2. The CBS Results 3. Aggregate Construction Sector Results a. Cobb-Douglas Results b. The CBS Results V. THE ROLE OF MATERIALS 1. Substitution in Construction 2. Cobb—Douglas and CBS Models VI. SUMMARY AND CONCLUSIONS BIBLIOGRAPHY iv Page ll 17 20 26 26 32 34 35 35 40 58 65 65 76 9O 91 93 98 98 101 113 121 Table 3.10 3.11 3.12 3.13 3.14 3.15 LIST OF TABLES U.S. Summary Statistics for the Contract Construction Industries, 1972 Distribution of Total Construction Receipts by Type of Construction, 1967 and 1972 Construction Activity Outside of Home State Size Characteristics by Industry, Including Average Number of Workers, Total Construction Receipts, and Construction Wage Per Establishment Number of Workers, Construction Workers, and Non Construction Workers, Wages, and Total Construction Receipts by Industry and Census Region Factor Payments as a Share of Total Construction Receipts for Industry 1622 Input Ratios for Industry 1622 Value Added, Payroll, Materials, Capital, and Sub- contracting Payments as a Share of Total Construc— tion Receipts, by Industry ' Percent Distribution of Onsite Manhours for Selected Types of Construction, by Occupation, Various Years Value Added, Payroll, Materials, Capital, and Sub— contracting Payments as a Share of Total Construction Receipts, by Industry and Census Region Input Ratios by Industry and Census Region Apartment Characteristics by Region, 1971 Single Family House Characteristics, by Region, 1971 Percent of Nonsupervisory Construction Workers in Firms Operating under Labor-Management Agreements, September, 1972 Skilled Labor Requirements for Public Housing, 1968 V Page 28 3O 36 38 41 45 45 47 48 50 58 59 6O 61 Table 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 5.1 5.2 5.3 5.4 5.5 Two Factor Cobb-Douglas Estimates Three Factor Cobb-Doublas Estimates Two Factor Cobb-Douglas Estimates with Regional Dummies Three Factor Cobb-Douglas Estimates with Regional Dummies Kmenta Approximation of the CES Function Kmenta Approximation of the CES Function with Regional Dummies ACMS Estimates ACMS Estimates with Regional Dummies VES Estimates VES Estimates with Regional Dummies Comparison of ACMS and VES Estimates Labor Demand Estimates Labor Demand Estimates with Regional Dummies Cobb-Douglas Estimates for the Construction Sector Estimates of the Elasticity of Substitution for the Construction Sector Results of Estimating Log Y = Const + a Log L + 8 Log FK + y Log M Results of Estimating Log Y = Const + 0 Log L + 8 Log FK + y Log M with Regional Dummies Results of Estimating Log Y = Const + a Log L + 8 Log M - Ay[Log M - Log L]2 * . Results of Estimating Log V = Const + 0 Log L + 8 Log M - y[Log M - Log Y]2 Aggregate Three Factor Cobb-Douglas Estimates vi Page 66 69 72 73 77 78 8O 81 83 84 86 88 89 94 102 104 107 108 110 CHAPTER I INTRODUCTION The main purpose of this thesis is to present cross section estimates of Cobb-Douglas and Constant Elasticity of Substitution (CES) Production Functions for twenty-four 4 digit Contract Construction Industries in the United States. No previous production function study of this type has been undertaken for the Contract Construction In— dustries because of the lack of apprOpriate statistical data. We use the 1972 Census of Construction Industries as our primary source of information. It is the second such census since World War II, but the first census to contain data on capital inputs. Construction is a large and important sector of the U.S. economy. Gross construction expenditures have generally averaged about 13-14 percent of Gross National Product. The sector directly employs between 5 to 6 percent of the labor force. But more than half the jobs created by construction expenditures are indirect, occurring in those mining, manufacturing, trade, and transportation industries which provide construction materials to the sector. Changes in con- struction expenditure or its composition can have a large impact (often regional) upon the important supplying.industries. Construction output is a large component of new capital invest- ment. A major factor in meeting national housing and social goals is the ability of the construction sector to produce low cost housing. 1 Inefficient production of capital goods or housing can lead to a "cost— push" type of inflation if the price of the factors of production in construction increase more rapidly than their productivity. Economists and policy makers have been especially concerned about the performance of the construction sector regarding unemployment and inflation. This concern was clearly expressed by the Cabinet . . . . . 1 Committee on Pr1ce Stability in 1969. Construction prices and the costs of labor and nonhuman inputs are generally believed to have been rising faster than the average in recent years, and productivity in- creases have been reported as being unusually low al- though data on these points are scarce. Unemployment among construction workers has been high relative to other sectors, even in years with high demand... Thus the construction sector contributes in several ways to the unemployment—inflation dilemma. It is generally agreed that cyclical and seasonal fluctuations within the sector, regional shifts in demand and in the composition of output, sensitivity to monetary policy, and institutional constraints (such as the separation of design from production, restrictive build— ing codes, union bargaining strength) strongly affect performance, and productivity growth in the sector. Moreover the complexity of the sector, the heterogeneity of the output, and poor construction statistics have greatly hindered economic investigation. Early investigations such as Colean and Newcombs' Stabilizing Construction; The Recq£d_and Potential (1952) or Haber and Levinsons' Lgbgg_Rglatig§§_§nd Productivity in the Building Trades (1956) con- cluded that productivity growth in the construction sector was practically non-existent.2 However more recent studies using improved price indexes to deflate construction output — Dacy (1965), Gordon (1968), Sims (1968), and Cassimates (1969) - have all found that since about 1947 output per man hour has increased at an annual rate of roughly 3 percent per year.3 This rate remains below that of the other major sectors and of the economy as a whole.4 The source of productivity growth in construction is not un— like the source of productivity growth in other sectors. Dacy pre- sents a useful list of factors which have probably affected produc- tivity growth_in construction. These are: (1) An increase in the amount of capital per worker. This is especially true where new technology has been introduced such as earthmoving and excavating equip- ment, power cranes, ready-mix concrete trucks, or small power tools; (2) A shift in construction product mix toward output which is less labor intensive or which has more rapid productivity growth; (3) A shift in the geographic distribution of output to the West where productivity is thought to be higher; (4) An increase in the corporate share of contract construction output. Since corporate firms are generally larger than single proprietorships or partnerships economies .of scale may have occurred; (5) A decline in the average age of con— struction workers following World War II; and (6) New techniques of building, and the substitution of labor saving building materials for on site labor. Our census data provides new information on the Contract Con- struction Industries, and the production function framework is well suited for examining a number of the factors which affect productivity growth. In Chapter II we develop our major Cobb—Douglas and CBS models. These are single equation models in which value added is the output measure, and labor and capital are the inputs. Our basic Cobb-Douglas model allows us to examine the relative importance of each input, and returns to scale in each of the 4 digit industries. We modify this --D .T‘ v . ...u-. ! ..., r .-‘ "'th5‘ ’ .' ..‘ ‘ci. ‘-.' A ~.,‘\ L ‘4 . O 4 . ‘-. ‘1 a,‘ -. .H N D P. ~‘u ‘ model so that we can also (partially) examine the influence of technological change and differences in the quality of labor. The CBS models are used to estimate the elasticity of sub- stitution between capital and labor (0). The elasticity of substitu- tion measures the ease with which capital can be substituted for labor. In addition, knowledge of the value of 0 provides information on how the factor shares of capital and labor change with a change in their relative factor prices. An important application of o is in eval- uating the impact of changes in payroll taxes or subsidies, and in in— vestment tax credits or capital depreciation tax policies. We end Chapter II with a brief discussion of this application as it applies to employment in construction. We might expect that production function analysis using time series data is more appropriate than cross section analysis for in- vestigating the influence of technological change, changes in labor quality, and substitution between capital and labor. However there are several major drawbacks to time series data in construction. We outline these drawbacks briefly in Chapter III. Our main purpose in this chapter is to define the variables used in the study and to pro- vide a general description of the 1972 Census of Construction In- dustries. Using the census data we describe in some detail the major characteristics of the sector and of the separate 4 digit industries. The models developed in Chapter II are basically similar to those used in production function studies of manufacturing in- dustries. This similarity allows us to compare our empirical results in the construction industries with results from similar types of studies in manufacturing. We present our main empirical results and make these manufacturing industry comparisons in Chapter IV. Our results are not fully comparable with those in manufactur- ing for several reasons. One reason is that manufacturing industries are often concentrated in a few states, while the construction in— dustries are located in every state. We discover that geographic location is an important variable in our production functions for most of the construction industries, but are unable to identify spec— ifically which geographic characteristics (such as regional differences in size of firm, wage rates, output composition, skill composition, degree of unionization, differences in work rules) are most important. The level of aggregation used may also have an important bear- ing upon our results. Our construction industries are classified in the narrower 4-digit classification while the majority of manufacturing studies are based on the broader 2—digit classification. Despite this narrower classification, we have a larger number of observations in most of our industries than the number of observations used in similar 2—digit manufacutring studies. To examine such problems of aggrega- tion (in a limited way) we also present estimates for Cobb—Douglas and CBS models for the construction sector as a whole. This also allows us to compare these aggregate estimates with time series estimates of the sector by Cassimates.5 Traditional models of production, which use value added as output ignore the possibility of substitution between materials and other inputs since the value of materials used is subtracted from both sides of the production function equation. This practice has lead Evsey Domar to remarké ("V ... ‘P‘ r<\ -" 5.... a.» ‘lxv 'vv-tl . ‘ u T ., '1“ 5| ‘1‘ \- ... it seems to me that a production function is supposed to explain a productive process, such as making potato chips from potatoes (and other ingredients), labor and capital. It must take some ingenuity to make potato chips without potatoes. I do not mean that the omission of material inputs is necessarily wrong. Rather that it is not at all obvious that it is the preferred method. In Chapter V we examine the role of materials. Models are developed and results presented in which gross output is the output measure. These models allow us to explore in a tentative way sub— stitution between materials and our other inputs, especially on—site labor. However our efforts aretfijxknxxiby both statistical problems and by limitations in the functional forms which we use to examine the multiple input production functions. Our findings and conclusions are reviewed in Chapter VI. Perhaps the most important of these are: (1) That the elasticity of substitution between capital and labor is less than one for nearly half the special trade contractors, but for general building contractors and most heavy construction contractors a value of one seems reasonable; (2) There is evidence of increasing returns to scale for about one third of the special trade contractor industries. However these in— dustries employ nearly two-thirds of all employees in the special trade contractor group (SIC l7); (3) There is great diversity in the con- struction process between the 4—digit industries, and by geographic region. No single policy action is likely to have the same impact in each of the separate industries. Another implication is that aggregate studies of the sector as a whole must be interpreted with caution. Notes to Chapter 1 Studies by the Staff of the Cabinet Committee on Price Stability, U.S. Government Printing Office, Washington, D.C., 1969, p. 103. Colean, M. and Newcomb, R., Stabilizing Construction: The Record and the Potential, McGraw—Hill, New York, 1952; and Haber, W. and Levinson, H., Labor Relations and Productivity in the Building Trades, Bureau of Industrial Relations, University of Michigan, Ann Arbor, 1956. Cassimates, Peter, Economics of the Construction Industry, The National Industrial Conference Board, Studies in Business Economics, No. 111, New York, 1969; Dacy, Douglas, "Productivity and Price Trends in Construction since 1947", Review of Economics and Statistics, November, 1965, pp. 406-411; Gordon, R.J., ” A New View of Real Investment in Structures, 1919-1966," Review of Economics and Statistics, November 1968, pp. 417-428; and Sims, Christopher, "Efficiency in the Construction Industry", in the President's Committee on Urban Housing, Technical Studies: Housing Costs, Production Efficiency, Finance, Manpower, Land, Vol. II, U.S. Government Printing Office, Washington, D.C., 1968, pp. 145-176. Cassimates, ibid., pp. 88—89. Cassimates, ibid., Chapter 5. Domar, Evsey, Comment in The Theory and Empirical Analysis of Production, Murry Brown, ed., NBER Studies in Income and Wealth, Vol. 31, Columbia University Press, New York 1967, pp. 471-472. CHAPTER II THEORETICAL BACKGROUND Before discussing the particular theoretical models and estimating methods in detail, we will begin this chapter with a brief description of those characteristics of contract construction which distinguish this sector from others. Section 2 contains a general theoretical background, summarizes the properties of produc- tion functions, and discussed the assumptions required in order to estimate these functions. As a part of this section various problems and weaknesses in our approach will be considered. The particular Cobb-Douglas and Constant Elasticity of Substitution (CES) models to be estimated are presented in sections 3 and 4. 1. General Characteristics of the Contract Construction Industries Most economic research concerning the construction sector has been in labor and industrial relations.1 These studies have stressed the many characteristics of construction which distinguish the sector from others in the economy. The intent here is to list and to discuss briefly these characteristics for an overall picture of the sector. Specific information concerning the 1972 Census of Construction Industries, is presented in Chapter III. Construction differs from manufacturing (and other industries) in a number of ways. The product is generally custom designed, durable, large, expensive, immobile, assembled at a particular site, and has a long gestation period from initial design to final completion. Since much of the work is outdoors, production is dependent upon weather conditions, and in most parts of the country construction is seasonal in nature. Construction is geographically dispersed throughout the country rather than concentrated in a few geographic areas. With the exception of heavy construction it is labor and material intensive relative to capital. There is a wide variability of demand —— between regions, over the business cycle, and among private residential, private non-residential, public building, and maintenance/repair work. The firms, labor markets, and institutions which have developed are highly flexible and specialized to meet the unique requirements of the sector. Long term financing is usually involved. Construction has numerous and highly specialized firms. There are twenty—seven types of construction firms listed in the 1972 edition of the Standard Industrial Classification Manual. They are classified in three broad categories -- general building contractors (SIC 15), general heavy construction contractors (SIC l6), and special trade con- tractors (SIC 17). The firms are generally small but usually the general contractors are larger than the special trade contractors. One - two man firms outnumber larger firms, but their share in total con— struction receipts is small. With the partial exceptions of Operative builders, subdividers and developers (who engage in residential con- struction for sale on their own account) the firms operate under a set of complex contractural and subcontractural relationships. The main advantage of the subcontracting system is that it allows a high degree of flexibility in production. Construction projects lO differ in design, size, location, and skill requirements. General contractors do not have the volume of demand to continuously employ skilled workers or highly specialized equipment. In most cases they retain only some of the fixed capital investment and skilled workers needed, instead relying on subcontractors and rental equipment. Contractor specialization allows the flexibility to expand rapidly, to respond to changing product markets, and yet to use skilled workers and specialized equipment economically. A major disadvantage of the subcontracting system is that management may be loose with wide divisions in responsibility. Dis- putes can arise between the general contractor and the subcontractor about contractural obligations. Jurisdictional disputes occur be- tween unions. Such disputes can lead to work stoppages and reduce effective scheduling and coordination of the job. Disputes add un— certainty to already risky and uncertain undertakings. Many con- tractors fail. There is a large amount of entry and exit into the industry, particularly by smaller firms which have relatively low capital requirements. The product and factor markets in which contractors Operate are local in nature. There is a high degree of competition in the product market between contractors since construction work is most commonly obtained through competitive bidding. For public construction, competitive bidding is almost universal, since it is generally re— quired by law. In private construction bidding is the most common method to award construction contracts, although contracts may often be negotiated.2 In residential construction some builders (operative builders) construct residences on their own account. They act as the 11 general contractor, but subcontract the major share of the work. Com- petition is not perfect however, since the size, reputation, and union/ non union status of contractors are often considered by clients and lenders in determining the ability of the contractor to handle the job. The local nature of the market may also foster political relationships which affect the awarding of contracts. Building codes and regulations reinforce the local nature of the market. Contractors usually face fixed factor prices in their local market although larger firms often obtainquantitycdiscounts in purchasing materials. Union wage agree— ments fix wages for two or three years. There is generally a pre- vailing wage for non union workers as well, but there can be a sub— stantial differential between the union and non union wages which may differ from one local market to another. Factor prices vary sub- stantially between regions. For material inputs this probably reflects transportation costs, the size of markets, and regional preferences or climatic differences in design. Labor markets are linked somewhat so that wage increases in one region will have impacts in other areas. How- ever substantial differentials between regions exist. Wages may differ due to differences in the degree of unionization, the cost of living, regional variation in the composition of construction demand, or regional variation in demand for similarly skilled workers in industries other than construction. 2. General Production Theory The microeconomic theory of production, cost, and input demand is basic to understanding the neoclassical theory of distribution. The production function provides the framework for appraising these issues. 12 TLet the general production function Q = F(xl,x2,...,xn) (2,1) define the technical relationship between a flow of output (Q) and a flow of inputs (Xi) for a firm, where F is assumed to be a continuous twice differentiable function. The output and inputs are Ineasured in physical terms. However this study, like the vast Inajority of empirical studies of production, is based upon aggregate rather than firm data. Output is aggregated using prices and is measured in value terms. While the labor input is measured in physical terms all other inputs are measured in value terms. To apply the production function concept to aggregate data, and to specify a particular form of the production function for estimation requires a number of strong simplifying assumptions. This study involves a cross section of the 4 digit contract construction industries. The industries are the general and special trade contractors defined in the 1972 edition of the Standard Industrial Classification Manual. Observations are by state. Out- put and input data is divided by the number of establishments in each state. Each observation is assumed to be from a'representative establishment" in that state.4 We also assume that representative establishments in the same industry have the same production func- tion, and that each establishment is producing efficiently. The pro- duction function is assumed to have the prOperty of homotheticity. This means that the observations can be thought of as being observed on a single isoquant, since this property requires that the slope of 13 the isoquant (or marginal rate of substitution) is independent of scale and depends only on input proportions. Industry output is assumed to be homogeneous in each 4 digit industry. Each repre- sentative establishment is assumed to face a perfectly competitive local factor market. Different relative factor prices between local markets lead establishments to choose different factor proportions which allows identification of the production function. Although such assumptions are typical of aggregate pro- duction studies they introduce a number of weaknesses to the study.5 Some assumptions do not correspond to the actual conditions (such as the assumption of constant output prices cross-sectionally) but.Can- not be avoided because of data limitation. The best that can be done in this case is to examine the possible direction of bias. The assumption that there is a homogeneous output may be particularly Open to criticism in a study of the construction sector. Buildings and other structures are not homogeneous. They may differ from each other in design, materials used, quality, size and by many other characteristics. However this problem is minimized by the classification system which defines the industries. General con- tractors usually specialize in one or a few building types. The workers which they directly employ usually work on the structure. The rest of the work is subcontracted. The other function which general contractors usually perform is that of general supervisor and coordinator at the site. Although the design and char- acteristics of two construction projects may be dissimilar the work performed by subcontractors may be relatively homogeneous. 14 Thus the relatively narrow classification system reduces criticism of the homogeneous output assumption. In fact, our data is probably superior in this regard to many studies in manufacturing. The level of aggregation used in most manufacturing studies is a broad 2 digit classification which leaves much greater leeway for errors due to changes in the composition of output. For example, in the food processing industry (SIC 20) observations in Michigan may largely represent breakfast food production, in Florida orange juice processing, in Iowa meat packing, and in California frozen vegetable processing. There are several assumptions which can be made about the ways in which the output and inputs are defined. Aggregate studies in manufacturing use a value added measure of output. In this chapter we will also follow this practice. Value added is obtained for the construction industries studied by subtracting the value of materials and subcontracting services purchased from the value of gross output (V = Q — M - S). This value added assumption allows comparison of our results with those from similar types of studies in manufacturing. It focuses attention on the role of capital and labor. Since the value of materials and subcontracting services is subtracted from both sides Of the production function problems of estimation are reduced. For the economy as a whole it is legitimate to use value added as output since the material inputs are intermediate goods and cancel out (except imports). Similarly, for the construction sector as a whole subcontracting services may also be excluded. But for the separate general contracting and special trade contracting industries 15 analyzed in this study both materials and subcontracting services are purchased outside the 4 digit industry. They do not cancel out. Both can be substituted for labor or capital used in the industry. The level of capital and labor services used in the industry depends not only on the relative price of capital and labor, but also on the relative prices of materials and subcontracting services. In Chapter V we introduce materials as an input and develop models using a gross measure of output for this purpose. This study will use single equation production function models. To estimate a single equation model using ordinary least squares (OLS) a multiplicative disturbance, or random error is introduced. For example, a simple Cobb—Douglas model is specified as a B ui Vi = A KiLie (2.2) Traditionally, the rationalization for introducing the error term (ui) is to account for differences in entrepreneurial ability be- tween establishments. The basic assumptions necessary to use OLS require that: (l) ui is normally distributed; (2) E(ui) = O; E(ui) = 02; (3) The ui's are independent of each other, that is E(uiuj) = O; (4) That 111 is independent of the level of L and K used. That is, E(uilog Li) = E(uilog Ki) = 0. These assumptions imply that the level of output is a function only of the level of inputs chosen, and by theform of the productiOn function. Marschack and Andrews first criticized the single equation approach and presented a more comprehensive simultaneous equation system model of the firm derived from the profit max1mizing assumptlon. In their model output and input levels are jointly determined from the production 16 function and from the input demand equations. Product and factor market conditions other than perfect competition are allowed. They show that random disturbances in the input demand equations are transmitted to the production function so that assumption (4) above no longer holds, and if OLS is used to estimate the single equation (2.2) the estimates of a and B will be biased and inconsistent.7 Our rationale for using the single equation OLS approach stems from a model developed by Zellner. Kmenta and Dreze (ZKD).8 Al- though it is also a simultaneous equation model it differs from the Marschack-Andrews model by assuming: (1) that the production process is not instantaneous or deterministic; and (2) that production is viewed as a stochastic process with respect to profit maximization by the firm. Now, the random disturbance (ui in equation 2.2) repre- sents the influence of factors such as weather or other unpredictable circumstances which affect production. Production is not instantaneous and profit is uncertain. ZKD assume that establishments maximize expected profits. Output and input prices are assumed to be known with certainty; or if input prices are not known exactly decisions are based upon anticipated prices randomly distributed around the actual price. With the added assumption that ui is normally distributed ZKD are able to show that random disturbances in their input demand equations are not transmitted to the production function. This vindicates the single equation OLS approach to estimating the Cobb- Douglas function from cross section data, and the estimates from this model are asymptotically unbiased and consistent. Since conditions in the construction industries approximate the assumptions of the ZKD model the use of OLS seems appropriate. 17 In preparing bids contractors use existing or anticipated input prices. Except for "cost plus" types of contracts and cuildings build for speculation the "price" for the output which contractors receive is set in advance except for later adjustments made for specification changes which entail extra work. Profits are uncertain for many pro- jects due to the long gestation period in which unanticipated juris— dictional disputes, weather problems, soil conditions, etc. can occur. Of course we cannot push this interpretation too far, and the small sample characteristics of the OLS estimators remain unknown. Whatever the interpretation given to the data a likely and serious source of bias will be simultaneity and bias introduced due to errors in the measurement of the data — particularly capital data. While we cannot do a great deal about errors in the data specific attempts to investigate various sources of bias in both the Cobb- Douglas and CBS models reported later. 3. The Cobb-Douglas Form The main parameters of the Cobb-Douglas form which we will be concerned with are: (l) The output elasticities which indicate the relative importance of each input in the production of the output; (2) returns to scale, which tell how output responds to changes in the scale of the establishment; (3) How these prOperties vary by industry and by census region. The non stochastic Cobb-Douglas form is v = AKaLB (2.3) where a and B are the output elasticities for capital and labor defined as 18 LY a =9—I—(——— 8:.8_L__ “ V/K ’ V/L ' They provide a normalized measure of how much output changes due to a proportional change in the input. If there is perfect competition and constant returns to scale these elasticities also measure the relative factor shares of capital and labor. The sum of the output elasticities indicate returns to scale (a + B 1 imply VIIA decreasing, constant, increasing returns to scale). The parameter A can be considered an efficiency parameter since functions with identical output elasticities may have different outputs if A dif- fers. The elasticity of substitution 0, which measures the relative ease with which capital may be substituted for labor, is restricted to one. Equation 2.3, which we will call the basic Cobb-Douglas model assumes that both capital and labor inputs are homogeneous. We will modify this assumption to allow for differences in input quality. The first modification is to separate labor into con- struction (LC) and nonconstruction (LA) workers. The function to be estimated is v = AK LC LA (2.4) The basic model assumes that L and L are perfect C A substitutes, i.e., 0L L = w while this model assumes that C A 0L L = 1- A.preferable method for incorporating differences in C A the quality of labor would be to construct an index of labor quality for each industry by state. Griliches has done this in his studies of 19 9 . . . . the 2 digit manufacturing industries. On the b331s of his findings he concludes that his results ...underscore the importance of labor- . . 10 quality differences in accounting for differences in product1v1ty." However, adequate data on the occupational distribution of the labor force in construction by state, which is needed for such an index of labor quality are not available. O u A second modification to the basic model, develOped by Solow and others, attempts to adjust for the different ages - or vintages - of capital.11 Liu and Hildebrand have proposed the ratio of net to gross value of capital stock (R) as a proxy for capital vintage.12 The higher R the newer the capital. Their hypothesis is that technological change is embodied in new capital goods so that new capital is also more capital. We introduce R into the Cobb-Douglas model, augmenting capital as follows v = A(R - K)O‘L8 (2.5) This assumes that R and K have the same exponent which allows equation (2.5) to be rewritten as v = A RQKQLB (2-58) Estimating equation (2.53) will test the common exponent assumption and allows the effect of R to be estimated separately. A final modification to the basic .. y to introduce regional dummy variables. Many factors which affect construction -- such as building design, size of establishment, skill composition of labor, degree of unionization and of urbanization, climate, building materials prices, output prices, to only name a few -- vary by geographic region. If these factors have an important effect upon production in our 20 industries but are not incorporated in our models then our models are misspecified. The use Of regional dummies will reduce this specifica- tion error, but unfortunately will not identify the influence of any particular geographic factor. 4. The CBS Form A major problem associated with the Cobb—Douglas form is that the elasticity of substitution is restricted to one. In the CES form v = y[sK’p + (1 - (5)1.‘91‘V/p (2.6) l . . . 0 is the substitution parameter where o = 1:3, y 18 the eff1c1ency parameter, 5 is the distribution parameter, and v is the scale parameter. If p = 0 then 0 = l and the function reduces to the Cobb-Douglas form. Direct estimate of the CES form is difficult since it is non—linear in the parameters. However Kmenta has de— veloped a linear approximation of the CES by taking logarithms and expanding a Taylor series around 0 = 0.12 The approximation is Log V = Log Y + 5LOgK + v(1 - 5)Log L - 1 2 ‘2 D v6(1 - 5)Ilog K - log L] (2.7) In addition to providing an estimate of o, estimation of this equation provides a test of the Cobb—Douglas form. If p = 0 then a = 1 and the coefficient of the last term will not be significantly different from zero. Such a test is weak since the value of the coefficient also depends on the value of 6. Since 1/2 and the 6(1 - 0) terms are fractions the value of the coef— 21 ficient is likely to be low. Additionally o is estimated as a second order parameter since its value is derived from the value of p. To illustrate if .V = l, d = .3, (1 - 0) = .7, and p = l (o = .5) then the coefficient is quite small (equal to —.105). With a small sample size or with data containing measurement error it is likely that the standard error will be large. Another problem associated with using this approximation is that the estimate of 0 becomes worse as p departs from a value near zero. The original method of estimating the elasticity of sub- stitution introduced by Arrow, Chenery, Minhas and Solow (ACMS) provides another means of testing the Cobb—Douglas assumption. The ACMS method, which assumes constant returns to scale, is based on the marginal productivity condition derived from profit maximization. The estimating equation is Log V/L = a + b Log w/p (2.9) where b is the elasticity of substitution and w/p is the real wage. This method is also weak since it has been shown that for cross section data b may often be biased toward one.13 This is true for example, if labor quality, output price, or the efficiency parameter vary over observations. We will again use regional dummies to examine this problem. Since these sources of bias may be geographic we would expect the estimate of b to be lower when regional dummies are included. ACMS derived the CES function by first observing the strong empirical relationship between V/L and the real wage. Liu and Hildebrand have criticized this approach by arguing that V/L is 4U T» .1. 2. . . . a A a VI. ..wb .. a ‘5 .Fll ‘. A .p u In W.» I” ... _ .C .v. a... .N,. .1.» a?» Wu ..3 AI» .1 ”C e a I. . . ..C u... v- 3a .uu R» v L o s ..F» F . Rh L.» It ru\ ; k u a .N . . .7. .. s . _ Ce . s ..A .L F» .fa a: I. ruk .A.U4 :- . . x . .c v . .5 n . . ... .1. e r. a.. .Q a» :3 u p. i .C e n I . .eh ~. ..s n. a .-I. uaa ... n.4,. . l. ...-s P. 3 g -I« 0.» .15 «V- .04“ s u r . .. . . . v . . . w . . s b u v . A \ .n~ .. a ...I .\. AV. ..M-s ..‘v 22 not only a function of the real wage but also of the amount of capital per worker. They estimated Log V/L =Ia + b Log(w/p) + c Log (K/L) (2-11) for 17 two digit manufacturing industries and for the majority of the industries obtained significant coefficients for c.14 This equa— tion leads to a variable elasticity of substitution (VES) form. It is beyond the scope of this study to fully develOp a VES model. However a rough estimate of the elasticity of substitution can be derived from the coefficients of equation 2.11 and data on the share of capital.15 One of the major reasons for interest in the elasticity of substitution between capital and labor is the relationship 0 has to the demand for labor. The wage elasticity of demand for labor has two components, the substitution effect which occurs as capitol is substituted for labor and the output effect which depends upon the output price elasticity of demand.16 Minasian has shown that under the ACMS assumptions 0 is the wage elasticity of demand with output held constant. When output is allowed to vary 0 represents the substitution component of the wage elasticity of demand for labor, and represents a lower bound estimate of this elasticity.l7 Thus a o < 1 not only implies that a relative wage increase will increase the labor share of output, but also that the wage elasticity of demand for labor may be inelastic. A complete study of the demand for labor in construction is again beyond the scope of this study. However, to supplement our estimates of the elasticity of substitution we will estimate a simple demand for labor 23 function. From the marginal productivity conditions on labor the demand for labor is a function Of the wage rate, output, and the price of capital. Our estimating equation modifies this by excluding the price of capital. Thus we will estimate Log L = a + b Log W + c Log V (2.12) where b is the wage elasticity of demand for labor with output held constant. 24 Notes to Chapter 11 Two excellent early studies are Colean, M., and Newcomb, R., Stabilizing Construction: The Record and Potential, McGraw— Hill, New York, 1952; and Haber, W., and Levinson, H., Labor Relations and Productivity in the Building Trades, Bureau of Industrial Relations, University of Michigan, Ann Arbor, 1956. More recent general studies are: Cassimates, Peter, Economics of the Construction Industry, The National Industrial Con- ference Board, Studies in Business Economics, No 111, New York, 1969; Dietz, Alfred, The Building Industry, prepared for the Commission on Urban Problems, Department Of Architecutre, M.I.T., Cambridge, 1968; and Rossow, Janet, and Moavenzadah, Fred, The Construction Industry, Department of Civil Engineering, M.I.T., Cambridge, 1974. The most recent comprehensive work on industrial relations is Mills, D. Quinn, Industrial Relations and Manpower in Construction, M.I.T. Press, Cambridge, 1972. For a more complete discussion of the types of contracts see Rossow and Moavenzadan, ibid., pp. 202-216. For more information on wage determination in construction see Mills, Op. cit., Chapter 6. A similar assumption is made in Liu, Ta-Chung, and Hildebrand, George, Manufacturing Production Functions in the United States, 1957, New York State School of Industrial and Labor Relations, Cornell University, Ithaca, 1965. See Liu and Hildebrand, ibid., Chapter II for a critical review of the general assumptions which are common to most aggregate production function studies. Liu and Hildebrand present their own model in Chapter III which relaxes many of these assumptions. Marschak, J. and Andrews, W., "Random Simultaneous Equations and the Theory of Production", Econometrica, July-October, 1944, pp. 143-205. For an excellent review Of the Marschack-Andrews approach as it has develOped in the literature see Bridge, J.L., Applied Econometrics, North-Holland Publishing Co., Amsterdam, 1971. For proof see Zellner, A., Kmenta, J., and Dreze, J., "Specifica- tion and Estimation of Cobb-Douglas Production Function Models", Econometrica, October 1966, pp. 784-786. See also Griliches, Zvi, and Ringstad, V., Economics of Scale and the Form of the Production Function, North Holland Publishing Co., Amsterdam, 1971, pp. 13—14. Zellner, Kmenta, and Dreze, ibid. 10. ll. 12. l3. 14. 15. 16. 17. 18. 25 See Griliches, 2., "Production Functions in Manufacturing: Some Preliminary Results" in M. Brown, ed., The Theory and Empirical Analysis of Production, NBER, Studies in Income and Wealth, Vol. 31, New York, 1967, pp. 275-322, for results using 1958 data. See Griliches, 2., "Production Functions in Manufacturing: Some Additional Results", The Southern Economic Journal, October 1968, pp. 151-156, for results using 1954, 1957, and 1963 data. Griliches, 2., "Production Functions in Manufacturing: Some Additional Results", ibid., p. 168. Solow, R.M., "A Contribution to the Theory of Economic Growth", Quarterly Journal Of Economics, February, 1956, pp. 65-94. Liu and Hildebrand, op. cit., pp. 49-50. See Kmenta, Jan, Elements of Econometrics, The Macmillan Co., New York, 1971, pp. 462-465. See Lucas, Robert E., "Substitution Between Labor and Capital in U.S. Manufacturing", unpublished doctoral dissertation, Univ. of Chicago, 1964, pp. 26-31. Also see Mayor, Thomas, "Some Theoretical Difficulties in the Estimation of the Elasticity of Substitution from Cross-Section Data", Western Economic Journal, June 1969, pp. 153-163. Liu and Hildebrand, Op. cit., pp. 33-40. = 1+0 -lpm/S where p = 1&2, m = IEE’ and SK. is the share of capital. See Nerlove, Marc, ”Recent Empirical Studies of the CBS and RElated Production Functions" in M. Brown, ed., The Theory and Empirical Analysis of Production, NBER, Studies in Income and Wealth, Vol. 31, New York, 1967, pp. 74-82. Also see Nadiri, M.Ishaq, "Some Approaches to the Theory and Measure- ment of Total Factor Productivity: A Survey", Journal of Economic Literature, December 1970, pp. 1156-1157. 0’ For a more complete discussion see Ferguson, C.E., The Neo- classical Theory of Production and Distribution, Cambridge University Press, Cambridge, England, 1969, pp. 235-239. Minasian, Jora, "Elasticities of Substitution and Constant Output Demand Curves for Labor", Journal of Political Economy, June 1961, pp. 261-270. CHAPTER III THE DATA AND THE VARIABLES In this chapter our main purpose is to define the variables and to describe the characteristics of the Contract Construction Industries in greater detail. We begin with a general description of the 1972 Census of Construction Industries (Census) and briefly compare the type of information which it provides to data from other sources. Next, in section 2 we define the variables which will be used in the study. We conclude, in section 3, with a description of how these variables differ between industries, regions, by size, and by degree of urbanization. 1. The 1972 Census of Construction Industries The 1972 Census of Construction Industries is the second such census since the end of World War II. It is superior to the pre- vious 1967 Census because it is the first census to contain data on the gross and net book value of capital assets. It also uses the new 1972 SIC industry definitions. The main advantage of these definitions over the previous 1967 SIC definitions is that the general contracting industries are now split up into a larger number of industries which correspond more closely to the type of construction which they perform. The Census also furnishes data \ 26 27 on total construction receipts, value added, payrolls, employment, the number of establishments, equipment rental, and material and sub- contracting payments. The Census is based upon information provided by all construction establishments with ten or more employees, and from a sample of smaller construction establishments with payroll. Other federal records were used to compile information on the very small "non-employer" establishments with no payroll. We have already briefly discussed in Chapter II how the 1972 SIC classification is based upon specialization within the sector. Table 3.1 lists the industries included in the Census and presents U.S. summary statistics for construction establishments with payroll.l From Table 3.1 we see that in 1972 there were approximately 437,941 construction industry establishments with payroll compared with 368,771 such establishments in 1967. Approximately 30 percent of the establishments are general building contractors, 6 percent gen- eral heavy construction contractors, 61 percent special trade con- tractors, and 2 percent subdividers and develOpers.2 Net construction amounted to over $11.2 billion, 30 percent of which went to general building contractors (including subdividers and developers), 23 per- cent to general heavy construction contractors, 47 percent to special trade contractors. Value added was nearly $68.2 billion and total pay- roll slightly over $40 billion. The census reported a total average employment of over 4.1 million workers.. Special trade contractors employed the most workers (nearly 51 percent), followed by general building contractors (28 percent), general heavy construction con- tractors (20 percent) and subdividers and develOpers (1.5 percent). The year 1972 had a boom in residential construction with approximately 1.3 million single family and 1 million multiple unit 28 TABLE 3 .1 U.S. SUMMARY STATISTICS FOR THE CONTRACT CONSTRUCTION INDUSTRIES, 1972 I977 10131 Number 01 employees hymn Receipts 0mm; yea: I Net "UNION oI . _._. -, _ I . ___._. :onwuctlon 19p uhhhsh- . I . inc-171'» ‘ MI (.ontlvuclvon . 101.11 Comluuchou . 10711 I TIIIII “C [Mushy "my Md 10011st "ms employees IOIII‘IS prIoII women: I Ittmuls LDMIHICMII code , , I mew” . . I IJV’IJICI (average) I 11.. J) I . . . __ A ' B I C D E I F G ' H T C(RiSTRIIC‘I'Im INDUSTRIES AND sunmvxurixs ‘ AND DEVELOPERS, TO’IAI ..................... 437 941 4 145 779 3 486 592 40 004 782 32 187 130 155 849 652 149 429 410 111 23.’ 17; , D16 ' 17 'CONSTRUCTIGI INDUSTRIES, TOTAI ................... 430 027 I 4 083 465 3 464 203 ‘39 528 036 32 035 697 152 721 579' I48 110 817 110 715 923’ 15 CENI‘NAI BUIIDING CONTRACTORS AND OPERATIVE I 13011117115 ..................................... 1)) 054 1 149 520 937 771 10 159 240 7 739 797 64 349 923 61 865 294I H .745 .1131 1521 01mm: CONTRACTORS--51NI£L£-FAHII.Y IIIXISES... . . . a . , 1511 OPERATIVI‘. HUIIIHHS .......................... }| 90 207 469 152 365 778 3 460 727 2 464 162 25 122 6131 23 161 742 1-0 .64 .17 1522 GENERAL CONTRACTORS- RESIDENTIAL BUILDINGS . OTHER THAN SINGLE-FAMILY ................... 7 651 112 215 94 627 977 707 771 876 6 525 513 6 407 131 3 033 312 154 CENItRAI CON‘I'RACTORSHMNRESIDENTIAI. BUILDINCS: 1541 INI)I.'\TR1A1. BUIIDINCS AND HARI'IIICRJSES ....... 9 538 173 094 I44 625 1 729 634 1 350 140 8 666 746 8 507 370 4 805 8381 1542 NONRESIDENTIAL BUILDINGS, N.£.C ........... 25 658 395 059 332 741 3 991 _172 .3 147 519 24 034 963 23 789 051 11 141 896' 16 HEAVY CONSTRUCTION GENERAL CONTRACTORS ........ 27 991 827 146 709 306 9 255 253 7 537 355 11 460 896 30 514 009 2.5 357 103' I611 HIquAY AND STREET CONSTRUCTION ........ 9 232 278 107 244 292 2 846 063 2 364 818 11 325 982 11 005 402 8 986 451, 162 HEAVY cousntucrmu, rtxcsl'r IIIItnwAY: 1622 311100;, TUNNEL, AND ELEVATED HICHHAY CONSTRUCTION .......................... 1 204 53 710 47 366 589 670 498 49 2 282 232 23 369 1 780 057! 1623 HATER, SEWER, AND UTILITY LINES ........... 9 355 209 318 184 199 2 154 000 I 798 102 6 369 576 6 227 482 6.28 010 1629 HEAVY CWSTRUCTION, N.E.C ................. 8 110 286 211 233 449 J 665 520 2 875 686 11 483 106 11 047 756‘ 8 962 585 I 17 SPEITIAI. TRADE CONTRACTORS ..................... 268 982 2 106 599 1 817 126 20 11) 543 16 758 545 56 910 760 55 711 514 52 113 507i 1711 PII‘IBINC, HI‘ATINC, AND AIR CONDITIONING ..... 53 301 456 100 171 113 4 787 958 3 809 878 15 615 468 15 321 135 13 594 125, 1721 PAINTING, PAPER HANGING, AND DECORATING ..... 29 011 136 575 125 807 1 080 729 961 201 2 405 714 2 382 301 2 290 258} 1731 ELECTRICAL HGIK .......................... 32 455 323 748 271 441 3 792 682 3 151 047 9 608 035 9 448 881 9 229 309' 174 HASONRY. PIASTERINC, AND Tm: SETTING.- 1741 msoNNY , STONI‘ SFT‘IINIZ . AN1101’111‘R STONI‘HORK 23 8% 165 580 156 195 1 310 777 1 199 012 3 104 947 3 085 759 3 978 08‘ 1742 PIASTHNING, DRY‘UAI.I., AND INSIIIAI'ION 170x10. I3 415 170 164 151 825 l 684 875 1 445 728 4 195 295 4 084 687 J 839 335 1743 TFRRAZZO. TILE, HARHIJL, AND MOSAIC HORN... 4 270 30 874 26 600 260 053 213 439 716 892 703 114 684 738 175 CARPENTERING AND “mama: 1751 LARI'ENTIIRINC ..................... . ....... 23 524 I23 910 115 464 925 144 842 225 2 355 521 2 129 145i 2 128 203 1752 11001 IAYINC AND (TIMER FLOGUORK .......... 9 052 44 262 36 402 367 077 291 384 1 209 945 l 175 846 I 132 194 . I 1761 Rom-”INC AND SHEET METAL 901K ................ IR 535 158 051 134 189 1 405 756 1 117 .‘71 3 999 967 J 940 243I J 752 108 1771 CONI'RE'I‘E Hoax ............................... 17 772 147 924 135 041 1 197 014 I 045 342 3 6'79 141 3 050 338, 3 452 348 1781 WATER WELL DRILLING ......................... 4 159 17 136 14 598 125 I47 101 967 556 965 534 171 523 128 179 MISCEIIAMJHIS SPECIAL TRADE CONTRACTORS: I I 1791 STRUCTURAL STEEL ERECTION ................. 2 760 58 137 49 983 617 949 534 094 1 496 417 1 457 836i 1 185 610 179] CIA.“ AND GIAZINI: HOT-III .................... 2 459 20 023 14 175 1‘10 447 133 41.17 657 352 593 658. 584 642 1794 EALA'JATINC AND FOIINDATION WORK ............ 15 981 104 598 92 592 923 448 786 an; 3 054 467 2 956 531 i 2 737 914 1795 UNICKINC. AND new): 1T1()N Hoax .............. 1 027 9 067 7 544 110 173 64 0711 236 678 219 412 202 581 I 1796 INSTALLING BUILDING EQUIPMENT, N.E.C...... 1 945 38 956 31 058 517 966 406 046 I 457 818 l 408 192 1 349 214 1799 SPECIAL TRADE CONTRACTORS, N.E.C. ......... 15 420 101 294 82 899 826 328 635 758 2 540 138 2 440 265 2 264 658 6552 SUBDIVTDERS AND DEVEIOI‘ERS, PLEA: ............... 7 914 _62__J.Iij 22‘189 476 746 151 4'31 3 128 07] 1 318 6791 516 256 Note: Some of the 1972 used in 1967. industry definitions are different from those Where applicable, the 1967 data shown in this table were developed by retabulating the original information to approximate the new definitions. 1Combined because of misclassification problems within these two in- dustries. See Industry Series Report C72-l-2, "General Contractors, Single-Family Houses and Operative Builders (SIC 1521/1531)." 29 selected payments." TABLE 3.1 (Continued 1972-Contmued 1967 Selected payments v.1“. added Totat Deprecreote assets Rental A11 Total Value added captm cements 101 empioyecs constructron laterals. Constmctron exam” Gross boot Net varue ngmwy recerpts ”[72 components. won 5110- f d' ‘" value at at end or :Qmmm 505 and swam: contracted an end at year year ' c e to others (“'1’ (average) 1 1 K L I N 0 P Q R 40 420 441 38 197 317 68 197 327 3 871 388 23 238 220 12 054 282 1 972 054 3 430 205 92 588 002 42 322 097 15.10 40 084 702 37 394 894 67 009 920 3 053 222 22 331 002 11 405 570 1 945 271 3 413 757 92 113 437 42 105 324 17 10 414 029 28 019 981 17 883 050 095 325 4 990 988 3 149 327 339 019 938 043 30 925 054 10 091 353 15 7 723 579 8 897 475 ’7 009 570 511 579 2 419 902 1 711 037 00 530 300 385 12 025 240 ’3 910 077 I§§I 1 509 803 3 373 819 1 501 851 03 220 400 441 270 030 40 597 01 442 2 708 839 686 370 1522 154 2 213 309 3 701 532 2 751 905 97 240 099 057 330 073 92 513 184 900 0 700 474 2 120 302 1541 4 887 278 12 047 155 6 500 530 223 278 1 479 528 780 981 105 973 385 250 15 491 101 4 174 004 1542 10 103 094 5 150 900 10 200 290 1 429 874 9 399 199 3 995 227 1 091 000 792 920 21 502 953 11 439 684 10 3 468 714 2 018 951 5 838 317 688 403 4 049 351 1 822 418 523 288 255 777 7 711 858 3 929 002 1011 . 102 858 092 453 312 970 028 01 002 508 005 223 723 57 868 50 718 1 000 553 747 446 1022 1 900 404 599 472 3 309 700 351 130 2 028 077 941 274 200 159 107 Lee 4 229 522 2 004 005 1023 3 875 004 2 085 171 s 522 251 309 273 2 15 100 1 007 812 250 351 292 945 8 015 015 4 158 771 1029 19 500 979 3 618 007 33 725 774 1 328 023 7 933 495 4 201 022 513 986 1 682 707 33 024 701 19 834 240 17 0 093 928 1 727 010 7 794 530 22 :85 1 498 811 807 105 59 520 309 131 9 932 903 4 758 230 1711 474 514 92 043 1 839 157 35 010 254 102 151 049 12 917 139 190 1 700 017 1 303 309 1721 3 591 892 219 512 s 790 631 120 739 860 171 455 230 38 028 204 900 5 891 241 3 449 512 173 174 940 345 107 077 2 050 925 00 275 357 335 209 340 24 705 144 93s 1 953 210 1 308 714 1:41 1 305 138 245 352 2 584 805 50 848 410 874 243 221 19 513 110 753 2 028 051 1 254 132 1742 279 118 18 370 419 398 8 823 70 409 30 544 1 419 32 107 555 714 324 709 1743 175 049 595 200 942 1 504 934 34 391 170 392 104 354 11 232 82 354 1 207 093 790 928 1751 510 918 43 052 049 375 14 441 90 013 51 099 735 30 459 702 005 433 240 1752 1 403 049 188 135 2 347 903 68 317 403 912 253 320 14 104 133 147 2 384 200 1 414 505 1701 1 359 862 197 990 2 141 :89 132 804 707 394 303 977 03 501 114 579 2 120 701 1 24 373 1771 220 07s 11 043 325 047 47 238 201 987 138 313 4 042 14 190 318 090 190 033 1781 . 179 411 301 72 220 1 012 890 45 797 273 928 143 352 34 134 41 515 ‘731 914 ‘551 110 1791 307 501 9 010 340 77s 9 500 0a 591 39 255 1 172 12 290 274 191 101 072 1793 032 001 233 017 2 188 240 359 4 1 814 402 930 012 173 188 77 920 1 052 031 1 213 909 1794 24 489 10 831 195 355 17 .09 as 842 as 132 18 858 10 213 101 057 144 711 1795 420 021 58 978 978 219 17 638 140 443 04 290 11 883 25 170 044 758 434 042 1790 815 172 175 007 1 549 359 04 350 370 889 200 023 23 975 05 481 1 233 133 785 867 1799 341 739 802 423 '387 401 218 100 906 544 648 700 20 783 22 508 474 505 157 373 5552 2 . I! H H H "Value added" equals "total receipts less land receipts less total "Land receipts" for SIC 1521 and SIC 1531 combined were $1,432,057(000) and for SIC 6552 were $1,596,510(000). 3Not comparable to the SIC 1521 and SIC 1531 industry report because land receipts were not taken into consideration when calculating value added for each state. In 1967 land receipts amounted to $620,935(OOO). 4Identifying code number, 1971, for this industry is the same for 1972 as 1967, but the data are not exactly comparable. tractors primarily engaged in nonbuilding construction and classified in major group 16 in 1967 are now included in the appropriate in- dustry in major group 17. Special trade con- 30 housing starts. But most categories of non-residential construction . . 3 declined in real terms from 1971. We may also see a changing com— position of demand in Table 3.2 which compares the distribution of total construction receipts by type of construction for both 1967 and 1972. Table 3.2. Distribution of Total Construction Receipts by Type of Construction, 1967 and 19721 Type of Percentage of Total Construction Receipts Construction 1967 1972 Residential building 27.5 33.1 Non-residential building 41.4 38.8 Heavy Construction 25.9 24.5 Not Classified 5.2 3.7 lSource: Same as Table 3.1. 1967 data uses 1972 SIC classification. The 1972 Census is particularly useful as a source of information about the construction sector because it provides the first complete set of disaggregated output and input data. Prior construction statistics on output are not comparable with input statistics. The Bureau of the Census collects and reports statistics on construction activity, but this measure -- value of construction put in place -— includes forced account construction, which is performed by owners who hire their own labor rather than hire firms classified in the con— tract construction industries. Employment information collected by the Bureau of Labor Statistics measures employment in contract con- struction only. When output is disaggregated it is classified by type 31 of construction (residential, commercial, highways, etc.) or by type of ownership (private residential, private nonresidential, public). Employment information is disaggregated by skill or trade (carpenters, electricians, masons, etc.). Information on capital assets (for con- struction corporations only) are available from the Internal Renevue Service, which also measures output as business receipts in contract , 4 construction. Separate output and employment data are also published by the Bureau of the Census in County Business Patterns, based primarily upon Social Security Administration information. These statistical problems have hindered economic analysis of production in the construction sector. The only previous study of U.S. construction using the production function approach is a time series study by Cassimates.S It is an aggregate study. Due to the data limitations Cassimates was only able to estimate pro- duction functions for the contract construction as a whole. Time . series data are strongly influenced by cyclical phenomenona.6 Con— struction activity is strongly cyclical. Until recently private residential construction has generally been countercyclical, rising during recessions and falling during booms. Private nonresidential construction generally moves with the business cycle. Although these two types of cycle tend to cancel out the composition of construction output is constantly changing. This changing composition of output as well as the changing physical characteristics of the various types of construction over time hav£:hindered_the development of appropriate price indexes to deflate the aggregate construction output, although some progress has been made in this area by Gordon.7 Thus the informa- tion provided by the Census is particularly useful since it lessens some 32 of these statistical problems and allows production function analysis at a disaggregate level. Of course, numerous statistical problems associated with using the Census remain. 2. The Variables The basic variables in this study are defined on a per establishment basis for the 4 digit industries listed in Table 3.1. Observations are by state, but for many industries data is not available for each state. Two 4 digit industries were excluded from the study; Industry 1799, Special Trade Contractors, not else— where classified,was excluded since it is a miscellaneous "catch all", Industry 6552, Subdividers and Deve10pers was excluded after obtaining poor results in preliminary calculations. One problem was the relatively small number of observations in this industry. More serious however, was the manner in which the census obtained value added. Value added was obtained by subtracting land receipts as well as materials and subcontracting payments from total receipts. However after this subtraction, value added is smaller than total payroll! One possible explanation for this result is that establish— ments in this industry inflated land receipts which qualify as capital gains. In addition, data for Industry 1521, General Con- tractors for Single Family Housing and Industry 1531, Operative Builders are combined. During its review of the final industry re- ports, the Census Bureau discovered that approximately 30% of the establishments classified in industry 1521 should have been classified as Operative Builders, but no reclassification was made. Both industries predominantly build single family houses including row— houses and townhouses. Operative Builders are classified separately since they engage in construction for sale on their own account 33 rather than as contractors. Speculative builders and condominium develOpers are also included in this industry. LT LC LA PW WC WA The variables and derived variables which we will use are: Total number of establishments. The Census defines construction establishment as "a relatively permanent office or other place of business at which ... usual business activities related to construction are conducted". State observations are divided by N to give a per establishment average. Average number of all employees. This is the average number of all paid employees (permanent and temporary, full—time and part—time) on the establishment payroll on the 12th of March, May, August, and November. Excluded are all salaried officers and executives of corporations, and if unincorporated the pro- prietors or partners. Average number of construction workers. This is the average of all paid construction workers including supervisors through working foremen on the establishment payroll on the 12th of March, May, August, and November. Average number of non—construction workers. Defined as LT - LC. Adjusted Labor input. This is defined as the total payroll divided by the construction worker payroll times LC. This adjustment converts non—construction workers into construction worker equivalents in order to partially allow for quality dif— ferences due to differences in the mix of construction/non— construction workers between states. Total payroll. Average construction worker wage. The ratio of the total con- struction worker payroll to LC. Average non—construction worker wage. Defined as the ratio of the difference between the total payroll and the total con— struction worker payroll to LA. Total establishment receipts. Includes receipts from non— construction activities such as land sales, rental of equipment, engineering and architecturer's fees. Total construction receipts. Includes receipts from new con— struction and from maintenance and repair. Also includes receipts from the sale of buildings less the value of land. Materials payments. Payments for the purchase of all materials, components, supplies, and fuel by the establishment. 34 S = Subcontracting payments. Payments for construction work sub— contracted to other establishments. This includes payment for all materials, supplies, and components used by the subcon- tractor . V = Value added. Defined as (Q — M — S). Y = Gross output. Defined as (V + M). GK = Gross book value of capital assets (at acquisition cost). NR = Net book value of capital assets. Defined as GK less accumulated depreciation. FK = Capital services. A proxy derived by assuming a 15% rate of depreciation on GK and a 6% rate of return to CK. Thus capital services from owned capital is 21% times GK. Rental payments for equipment and machinery is added to this amount to obtain FK. R = The ratio of net to gross value of capital stock. A proxy for capital "vintage". E,C,S,W = Regional dummy variables where E is the Northeastern, C the North Central, 8 the Southern, and W the Western Census regions.9 U = Degree of urbanization. This is the proportioncflfthe state p0pulation living in Standard MetrOpolitan Statistical Areas (SMSA) according to the 1970 Census of POpulation. For those states with no SMSA (Vermont, Wyoming, Alaska) U was set to .01. For the District of Columbia U as assigned the value 1. 3. Detailed Characteristics of the Construction Industries In this section we describe in greater detail some of the important characteristics of the 4 digit construction industries. We find that Specific characteristics such as size, or the relative importance of the different inputs vary a great deal both between industries and in the same industry for different geographic regions. 35 a. Local Nature of Construction One characteristic which was stressed in Chapter II was the local nature of construction. In 1972 only 12.7 percent of the total construction receipts for all of construction were received for work performed by establishments outside their home state, and much of that in border areas. A more detailed breakdown, by 4 digit industry, is listed in Table 3.3. The percentage of receipts obtained outside of the home state for the special trade contractors and single family con— tractors is much less than for other general building/heavy construction contractors. Receipts from outside the home state are higher for heavy contractors, and to a lesser extent the general building contractors (other than single family residences) due primarily to the size and complexity of the work being performed. The market for suppliers of the larger, more complex projects which require special skills (such as dams, utility plants, refineries, hospitals, etc.) may often encompass more than one state and for some types of conStruction (i.e. nuclear power plants) may be very large. b. Size of establishment One way to measure size of firm is to look at total receipts, while another is to look at the number of employees per establishment. Although we have already noted in Chapter II that the size of the majority of the firms in construction is small, there is a wide diversity in size for each industry. Small firms are more numerous but larger firms account for the majority of total receipts. According to the 1972 Census there were 920,806 establishments in 1972, but the majority (482,865) were "non-employers” with no pay- 36 TABLE 3.3 CONSTRUCTION ACTIVITY OUTSIDE OF HOME STATE Percent of construc- 1521/1531 tion receipts earned Single Family outside home state Houses/Operative Builders 4.0 1522 Other Residen- tial Buildings 12.6 1541 Industrial Buildings 17.1 1542 Other Non-residential Buildings 13.4 1611. Highways and _§£;§ets ' 12.0 1622 Bridge/Tunnel/Elevated Highway 24.4 1623 Water/Sewer] Jtilitv Lino: 15'9 1629 Other Heavy Construction 52.9 1711 Plumbing/Heating/ 6 1 Air Conditioning ' 1721 7 2 Painting/Pater Hanging ' 1731 6 8 Electrical Work . 1741 6 6 Masonry/Stonework . 1742 Plastering/Drywall/Insulation 8.9 1743 Tile/Marble/Mosaic Work 6.8 1751 . 4 1 Carpentering ‘ 1752 Ploorwork 5.2 1761 Roofing/Sheet Metal 7-4 1771 Concrete Work 5.1 1781’ Water Well Drilling 5.9 1791 2 Structural Steel 18.7 ‘1973 Glass 6 Glazing 4.6 1794 . Excavation/ 5.1 [Qundations 1795 Urecking/ Demolition 8'7 1796 Equipment 11.6 Installation 1In dollars; 2Based upon preliminary Census Report. 37 roll. They accounted for only 5 percent of total receipts. Al- though less than 2 percent of the establishments reported receipts over $2,500,000 in 1972 they accounted for 44 percent of receipts of all construction establishments. Various measures of establishment size by 4 digit industryare presented in Table 3.4, primarily using the number of employees and total construction receipts as proxies. Table 3.4 also presents the average construction wage for each in- dustry. Not unexpectedly, we find that the heavy contractors are largest using either size measure. General building contractors, except single family residence contractors, are next while the Special trade contractors (with a few exceptions) are smallest. Con— struction wages roughly follow the same pattern, being relatively high for heavy contractors and somewhat lower for general building contractors. Wages for workers employed by the single family residence contractors are especially low. This probably reflects both lower skill requirements and a smaller amount of unionization in this industry. There is a wide range in the construction wage for the special trade contractors with the lesser skilled trades such as carpenters or painters at the low end, and the more highly skilled trade such as equipment installers or electricians at the high end. In comparing size neither number of employees nor total construction receipts per establishment are perfect measures. This is especially true for employment by the general building contractors. A particularly high prOportion of their total construction receipts is paid out to subcontractors, thus lowering their average number of employees. 38 moods mmH.aNH mmm.o co ea xn930c0um\xnc0mcx Hana xuo3 Hmowpuoofim Hmaa coo.s NHH.Nw wo~.o om oH moawco: nooon\mcaocnnn Hmaa moatowoaocoo na< \wcHumom\wc«nE:Hm HHNH aoo.HH mMH.HmN mum.m wn mm ooN.oH cqc.wwm nmm.® mu Hm mam.ma am~.~om.a Ho~.mm on AN noooosnonooo %>mo: uocuo awos nflaaaenaxfll \umsom\uoom3 mNoH Non.m «wc.mco m~m.m~ am No 0mm.oH Nem.mmn.a nem.aq co mm >m3£wwm cmum>oam\fioccsh\owcwpm NNOH muoouum was mhw3£wwz .HHQH omo.o moo.NaH.H «NH.om no oq omo.a oms.s~o som.mH ow om nmcfioafiom Hmwucocwmoulcoz uocuo News vaa amH.m s~o.amw soo.sa mm Hm nwtanHasm Hoso Iamuwmwm Hocuo NNmH umn.c Nom.omm Ho~.n on HH wuocHfiam o>wumuoao\mom:o: saason onch Ho 0 HA moozoaoao once we OH mooaofiaao whoa no 3 H saws mucoenmaannumo OH sues mucoazmwa HmmH\H~mH how muofiouou huu Innumo mo ucouuom navcH mo unwound ezmzmmHam< ozaosaozH .smsmsazH rm muHsmHmmHoamexu mNHm e.m m4mnuxm wona NH¢.m MN¢.H¢N qu.m 00 em wcfiwmau a mmmfiu mama. mo~.oa “Nw.omo mmw.aa am we NHomum Honouuzpum Hana mwm.o nme.m~H oma.q No a mewfiawpn Ham: noun; Hmma H¢m.~ mmm.mo~ mmm.w on om 3pc: oumuucoo HNNH mneqw qwmqwam nmm.m ms nu anus: umo;m\wcHwoom Homa nooqm mqumNH omw.c mm «H xuozuoon Nmmd cmNam HHO.mm mo~.m on HH wcHuoucoaumwll Hmma «8.» «8.34 ea; no 2 ins 383133553: mama -m.o has.oom ook.~a No om nonnosnooH\HHoasno\wnanoonoam:l Nona AnwscfiucouV ¢.m mqm (4-041) 1611 Highway, & 50 .774 .258 1.032 .881 Streets (1U.196) (3.590) 1622 Bridge/Tunnel/ 27 .731 .237 .968 .320 Elevated Highwayz (4'149) (1-313) 1623 Hater/Sever] 41 .751 .271 1.022 .669 Ut111t1.1102§ (7.746) (3.020) 1629 Other Heavy 2 40 .293 .793 1.091* .945 Construction (3.262) (10,117) 1711 Plumbing/Heatins/ 51 .397 .727 1.124 .777 Air Conditioning (4.406) (7.110) 1721 - Painting/Paper 3b .414 .750 1.164 .738 Hanging, (5.648) (5.243) 1731 Electrical 45 .264 .547 1.111 .800 Work (3.355) (8.484) 1741 Masonry/Stone- 38 .465 .656 1.120 .879 work (6.148) (5.177) 1742 ‘ Plastering/Dry- 40 .263 .874 1.137 .837 wall/Insulation (2-675) (7.470) 1743 Tile/Marble/ 14 .785 .251 1.036 .577 Mosaic Work (2.900) (1.043) 1751 Carpentefingz 29 .315 .798 1.113 .880 gr 0391 (5 4021 1752 Floorwork 27 .092 . 890 .982 . 7816 (1-903) (7.891) 1761 77‘ Roofing/Sheet 32 .1418 .361 .779 .266 Metal (2.740) (2.014) 1771 Concrete2 36 .404 .766 1.170 .760 Work (4.397) (6.525) 1781 Water Well 21 .267 .740 1.007 .733 Drilling (3.277) (5.282) 1791 Structural 23 .378 .669 1.047 .620 Steel 12.500) (3.314) 1793 Class 6 17 .180 .571 .751 .663 Glazing (1.311) (2.828) 1794 Excavation! 40 .714 .339 1.053 .849 Foundationsz (6.762) (3.250) 1795 ** Wrecking] 17 .574 .715 1.289 .831 Demolition2 (5.150) (5.167) 1796 . * Equipment 20 .055 1.174 1.229 .906 Installation (.708) (8.276) 1Log V - Const + 6 Log FK + 6 Log L 2 Data from preliminary census Reports. Remainder of data from final reports. 4 Significantly different from 1 at .05 level. an Significantly different from 1 at .10 level. 67 Because FK relies in part upon a somewhat arbitrary determination of the depreciation rate and the rate of return to capital, in our pre- liminary investigation we also used net capital stock, NK, as an alternative measure of capital. For the Cobb—Douglas models the fit using either definition was close, but with few exceptions the NK specification had slightly lower coefficients of determination. The labor coefficients were somewhat larger and the capital coefficients smaller (and often not significant) for the NK specification. We also used the NK specification for the other models discussed in Chapter II, with similar results. Since NK did no better, and was often worse than the capital services definition we will only report results using the FK specification. Nearly all the coefficients of L and FK are significant (values are reported in the tables beneath the coefficient estimate). The output elasticity for labor is larger than that of capital for the majority of our industries. But there are important exceptions among the heavy contractors and for a few of the special trade con- tractors. Although the sum of the output elasticities exceed one in over two thirds of the industries, increasing returns to scale are statistically significant at the .05 percent level only in industries 1629 and 1796. The sum of the coefficients for the general building contractors appears slightly smaller than for the heavy or special trade contractor groups. Our ‘i is reasonably high, with majority of the industries about .75. However the fairly high ‘EZ is in part due to our choice of Log v rather than Log(V/L) as our dependent variable. A trans- formation to a regression using Log(V/L) as the dependent variable 68 (Log(V/L) = const + a Log(FK/L) + (1 — a - B)Log L) give the same capital output (a) and labor output (8) elasticities, but theE2 is generally lower. Although the output elasticity for labor is not given directly, this transformation is especially useful since a labor coefficient in this model (1 - a - B) which is significantly different from zero provides a direct two tail test for significant returns to scale. In table 4.2 we report the results of estimating the three factor Cobb-Douglas model (equation 2.4) which separates labor into construction and non-construction workers. Although the adjusted co— efficients of determination are slightly larger than those in table14.l the fit has not noticeably improved. There are fewer significant co- efficients, primarily due to the increased collinearity between the inputs. For most industries, excepting the heavy contractors, the capital coefficient is lower while the sum of the two labor co- efficients is higher than similar coefficients in the basic model. Moreover, the coefficient for the nonconstruction workers relative to construction workers is larger than its share of the wage bill would suggest. Griliches also obtained this type of result in a study of the 2-digit manufacturing industries for 1963.2 He suggests that errors in measurement may partially account for his result. Our data may be even more subject to such errors since the census uses number of workers rather than manhours as the basic unit of measure for labor. This choice means that part-time employees are counted with the same weight as full time employees. Varying degrees of part-time employ- ment between LA and LC could possibly account for this result. EH? TABLE 4.2 THREE FACTOR COBB-DOUGLAS ESTIMATESI’Z COEFFICIENTS or 2 LA LC SCALE E 1521/1531 ‘ Single Family Houses/Operative ~16? .405 .393 .961 .718 Builders (1.640) (5.454) (2.760) 1522 Other Residen- .172 .251 .515 .938 .676 tial Buildings (2-064) (2 692) (5.778) 15‘2 .220 .394 .395 1.008 .885 Other Non-residen- -379 ~410 .178 .967 .787 tial Buildings (“-195> (3.440) (1.289) 1611 Highways 5 .698 .342 .033 1.073 .907 Streets (9-734) (4.054) (.378) 1622 Bridge/Tunnel/ .749, -.140 .334 .943 .825 Elevated Highway ('603) ('1-337) (3.805) 1623 water/Sever/ .748 .016 .266 1.030 .866 Utility lines (7.1971, (.112) (1.839) 1629 Other Heavy .269 .223 .568 1.065 .953 Construction (3.204) (3.541) ,(5.846) 1711 Plumbing/Heating/ .260 .344 .518 1.122 .834 Air Conditioning, (3.093) (4.346) (4.880) 1721 Painting/Paper .334 .373 .388 1.095 .829 Ranging (5.538) (28.281) (2.849) 1731 Electrical .188 .548 .453 1 189 .853 ggrk (2.688) (4.891) (4.333) 1741 Masonry/Stone- .423 .100 .561 1.089 .879 work (5.327) (2.024) (4.271) 1742 Plastering/Dry- .279 .312 .506 1.097 .878 wall/Insulation (3.088) (4.481) (3.676) 1743 Tile/Marble] .366 .576 .015 .957 .783 Mosaic Work (1.560) (3-519) (.080) 1751 .315 .121 .645 1.081 .879 Ca'Pe“‘e'1“8 (3.057) (1.811) (4.189) 1752 .035 .198 .773 1.006 .803 F1°°rw°rk (.373) (1.716) (5.528) 1761 - Roofing/Sheet .076 .749 .058 .883 .605 Metal ( 587) (5.231) (.417) 1771 328 204 642 1 174 801 C n ete ' ‘ ° ' ' "grit (3.600) (2.669) (5.959) 1781 .265 .060 .722 1.047 .717 Hater Hell , Drilling (2.524) (.844) (3.930) fizztctur‘l .460 .288 .243 .991 .857 Steel (3.303) (3.323) (1.080) 1793 Glass 5 -.025 .891 .176 1.092 .788 glazing (-.198) (3.211) (.886) 1794 Excavation/ .571 .145 .330 1.046 .863 Foundations (4.789) (2.550) (3.360) 1795 Wrecking/ .620 -.118 .760 1.262 .845 Demolition (5.562) (-.992) (5.519) 1796 Equipment .367 .785 ~ .054 1.206 .909 Installation (4.469) (11.422) (.710) 1 2 Log V - Const + 6 Log FK + 8 Log LA + 9 Log LC. Number of observations and source of data same as Table 4.1. 70 We also estimated those models which use R, the ratio of net to gross value of capital as a proxy for capital vintage. Our results do not support Liu and Hildebrands' hypothesis that R is a good proxy for the vintage of technology. The coefficient of determination for the capitol augmenting model (equation 2.5, V = R-FK)aL8) was roughly similar to the basic model. For practically all industries the labor coefficient increased and the coefficient of (R-FK) decreased - in several cases so that it was no longer significant. In our alternative model (equation 2.5a) which allows the effect of R to be estimated separately (Log V = const + 0 Log R + chog FK + 8 Log L) there were significant coefficients for R in two industries, but they were negative — i.e. the wrong sign. In fact, for over two-thirds of our industries, the simple correla— tion between R and value added was negative. Griliches has also tested Liu and Hildebrands' hypothesis. He found no support in his study of the manufacturing industries in 1958 but in a later study "... trace of 'embodiment' in 1963, industries with "younger" 3 found a capital stock having somewhat higher productivity levels..." Griliches suggests two reasons why R may not be a good proxy for cap- ital vintage. The first reason is that R may differ more due to dif- ferent depreciation policies than due to different ages of capital stock. The other reason is thathistoric costs rather than current or constant prices are used to report capital data. Although newer capital may be "more" capital under the embodiment hypothesis, it may also be "less" capital due to changes in the price of capital goods. It is likely that these effects may cancel out.4 71 In the final set of Cobb-Douglas estimates which we will present regional dummy variables are introduced. Table 4.3 contains estimates for the basic model with the regional dummies, using the Eastern census region is the reference region. A comparison of these results to those of the basic model using the F test indicates that the addition of the regional dummies as explanatory variables is significant for over half of the industries estimated. For nearly all industries the output elasticity for capital has decreased while the output elasticity for labor has increased. Of special interest is that in this model we now have 7 industries in which increasing returns to scale are significant at the .05 percent level. In table 4.4 we report similar results for our three factor Cobb-Douglas model. When we include regional dummies as explanatory variables, their addition is significant in 14 of the industries. Comparing these coefficient estimates to earlier estimates, we see that the coefficient for construction workers has increased and the coefficient for capital services decreased in practically all of the industries. The output elasticity for nonconstruction workers has not changed as systematically, although for the majority of industries this coefficient declined. We have significant increasing returns to scale in nearly one fourth of the industries. Since the LA and LC coefficients with regional dummies in more closely correspond to their wage.bill shares, the use of the regional dummies appears to have helped by reducing some of the specification error without seriously affecting the significance level of these coefficients. Even though the estimates with dummies in 723 146Lr 4.3 Two FACTOR COBB—DOUGLAS ESTIMATES WITH REGIONAL DUMMIEsl'Z cutrric16nis 0F —2 (K L (LxTRAL SOUTH wssr R SCALE 1521/1531 | Single Family .222 .861 .080 -.125 .188 .696 1.083 ”0useS/0Pe‘ative (2.049) (4.838) (.808) (—1.102) (1.885) ggnilders 1522 O‘he' Res‘éen‘ -309 .834 -.019 -.308 -.126 .5301 Buildmgs (2.582) (7.678) (-.171) -2.676) —1.177) .673 1.043 1542 .257 .775 —.119 —.240 -.067 .862 1.012 -;g2;5tr131 BU11dings (2.404) (7.161) (—1.409) (-2.446) (-.724) Other Non-residen— -590 366 -.049 -.115 -.029 736 1.000 tial Buildings (4-042) (3 730) (-.514) (-1.177) (-.308) 1611 Highway, 5 .635 436 .008 -. 49 .021 .893 1.071 szfeets (6.475) (4.760) (.1099) ( 1.940) (.251) 1622 Bridge/Tunnel/ -037 .337 -.345 -.474 -.098 .897 .964 Elevated Highwar3 (4.546) (2.202) (-2.700) (-4.o38) (-.578) 1623 water/Sewer/3 .610 .455 -.095 —.234 .012 .903 1.065 Utility lines (9.332) (4.669) (-1.239) (-3.179) (.151) 1629 . Other Heavy .319 .780 .066 - 166 .078 .960 1.098 Construction' (4.055) (11.006) (.738) (-1.929) (.857) 1711 3 Plumbing/Heating/ .235 .976 -.007 -.275 —.028 .859 1.211 Air Conditioning (2.883) (10.322 (-.107) (-4.540) (-.438) 1721 3 . fl Painting/Paper .427 1.027 .041 -.226 .127 .837 1.254 Hanging, (2.968) (8.083) (.506) (-2.943) (1.236) 1731 ' t Electrical} .118 1.104 -.049 - 320 -.003 .898 1.272 Work (1.854) (13.311) (-.780) (-5.118) (-.049) 1741 3 , Hasonry/Stone- 222 .922 -.O3O -.298 -.084 .923 1.145 work (2 636) (7.645) (-.471) (-4.424) (—1.275) 1742 3 %* PIastering/Dry- 231 .900 -.024 —.229 -.l76 .892 1.132 gall/Insulation (2.272) (7.997) (—.334) (-3.550) (—2.241) 1743 Tile/Marble/ 332 .513 .092 -.328 -.138 .784 .040 Mosaic Work (1.366) (2.640) (.708) (-2.836) (-1.034) 1751 - 030 1.230 .005 -.392 -.161 936 1 200 Carpenterins (- 294) (8.748) (.064) (-4.200) (-1,736) 1752 089 .972 -.010 -.311 - 047 .876 1 .63 F1°°’“°'k (1.147) (10.889) (-.116) (-3.464) (- 530) 1761 3 Roofing/Sheet 254 .732 -.O70 -.300 -.147 “30 >07 Metal (1 339) (3.721) (-.649) (-2.968) ( 1.323) 1771 Concrete .3J3 1.064 “.032 "'.358 "‘ 059 .861 1.38/ Work (4.388) (9.754) (-.472) (-4.589) (- 724) 1781 3 ”ate, 0.11 .231 .856 .152 -.117 .091 .854 1.087 Drilling (3.253) (6.769) (2.112) (-1.501) (1.223) 1791 f ‘ Structura13 .405 .582 —.061 -.264 -.046 .888 .987 Steel (3 214) (3.551) (-.708 (-3.499) (-.444) 1793 5183, 5 .152 .761 -.164 -.128 .145 742 915 Glazing (1.178) (3.661) (-1.54) (-1.207) (1.127) 1794 _ Excavation] -028 .459 .010 -.085 .049 .859 1.088 Foundations (5.800) (4.039) (.175) (-l.633) (.775) 1795 4 w,eck1n8, .450 .984 .045 -.277 .198 .885 1.433 Demolition (9.393) (6.060) (.397) (”2.361) (1.246) 1796 . . ** Equ1pment -.052 1.244 .087 —.142 -.175 .930 1.192 Installation (“-617) (9.962) (1.005) (-1.243) (-1.174) 1Number of observations and source of 2 Log V - const + 6 Log FK + 8 Log L + 3 Log c + 6 Log 8 + c Log W. data same as Table 4.1. 3Significantly different at .05 level from estimate in Table 4.1. * Significantly different from 1 at .05 level. TABLE 4.4 THREE FACTOR 73 COEFFICIENTS OF COBB—DOUGLAS ESTIMATES WITH 1 REGIONAL DUMMIES ’ 2 88. LA LC CENIRAL $0018 gas: 82 SCALE 1521/1531 . Single Family - 008 .504 .538 -.015 -.200 .163 .834 1.034 Houses/Operative (-.084) (8.011) (3.916) (-.200) (-2.381) (2.175) Builders 1522 Other Residen- .166 .231 .601 -.010 -.251 -.099 .708 1.059 tial Buildings (2.096) (2.567) (6.450) (-.095) -(2.313) (-.894) 1542 3 .078 .475 .529 -.146 -.252 .001 3141.082 Industrial Buildings (.837) (5.556) (6.502) (-2.176) (-3.263) (.019) 1342 Other Non-residen- .320 .422 254 -.077 -.104 -.019 .781 .996 tial Buildings (2.989) (3.384) (1 482) (-.880) (-1.160) (-.2l5) 1611 Highways a .567 .332 .165 .024 -.065 .078 .921 1.064 Streets (6.092) (3.821) (1.504) (.374) (-.897) (1.001) 1622 Bridge/Tunnel] .651 -.060 .344 -.339 -.457 -.122 895 .936 Elevated Highway3 (9.184) (-.409) (2.279) (-2.024) (-3.850) (-.b95) 1623 Hater/Sewer] .059 .008 .429 -.097 -.219 .007 .596 1.072 Utilitx_}ines (6.154) (.065) (3.123) (-1.215) (-2.907) (.087) 1629 . . Other Heavy .-95 .164 .625 .070 -.138 .084 .964 1.084 Construction (3.886) (2.741) (7.114) (.815) (-1.632) (.964) 1711 t Plumbing/Heating/ .101 .234 .788 “.024 “.218 ”.020 .675 1.204 Air Conditioning} (2.278) (3.120) (6.961) (-.402) (-3.571) (-.336) 1721 - painting/paper .218 .269 .688 .057 -.124 .114 .852 1.175 Hanging (2.913) (3.490) (4.027) (.731) (-1.480) (1.158) 1731 . * Electrical3 .101 .324 .836 -.049 -.265 —.019 .911 1.261 work (1.692) (3.822) (8.078) (—.834) (-4.424) (—.324) 1741 it Hasonry/Stone-3 .252 .041 .849 -.038 -.281 -.106 .910 1.143 work (2.834) (.906) (6.011) (-.559) (-3.625) (-1.506) 1742 Plastering/Dty- .150 .270 .669 -.043 -.223 -.083 .918 1.089 wallllnsulation (1.616) (3.515) (5.264) (-.697) (—3.926) (-1.058) 1743 rile/Marble! .211 .360 .307 .077 -.219 -.074 .826 .878 Mosaic work (.903) (2.059) (1.416) (.653) (-1.861) (-.593) 1751 - 034 .118 1.108; -.058 - 432 -.223 .936 1.192 Carpenterlns (-.325) (2.236) (7.606) (- 714) (-4.466) (-2.318) £Z52 k .034 .211 .824 -.024 -.295 -.032 .888 1.068 °°’"°' (.414) (2.380) (7.427) (- 286) (-3.470) (- 376) 1761 ‘*—'—*’ Roofing/Sheet .102 .648 .200 -.o44 -.103 —.073 .578 .950 Metal (.600) (3.641) ( 982) (-.478) (-1.057) (-.734) 1771 8 Concrete .309 .139 .904 -.027 -.305 -.039 .874 1.351 work (4.192) (2.229) (8.561) (—.423) (-4.036) (- 496) 1781 3 water well .205 .046 .857 .158 —.112 .084 .642 1.108 Drilling (2.149) (.806) (5.169) (2.025) (-1.273) (1.057) 1791 Structural .450 .180 .340 -.061 -.224 —.055 .893 .969 Steel (3.295) (2.119) (1.603) (-.679) (-2.791) (-.546) 1793 Class 5 -.060 1.059 .089 -.251 -.113 -.o77 .861 1.088 Glazing3 (-.524) (3.763) (.378) (-2.897) (-1.441) (-.680) 1794 Excavation, .3“) .226 .532 .020 “.137 .066 .90“ 1.101 pound3t10n33 (3.009) (4.399) (5.494) (.425) (-3 067) (1.250) 1795 4 * wrecking/ .497 —.019 .954 .102 -.196 .207 .873 1.432 Demolition (4.318) (-.158) (6.319) (.831) (-l.603) (1.157) 1796 Equipment -.031 .390 .807. .100 -.103 -.107 .925 1.166 Installation (-.334) (2.256) (3.752) (1.056) (-.809) (—.691) 1Number of observations and source of data same as Table 4.1. 2 Log V - const + 0 Log PK + 8 Log LA + y Log LC + Regional Dummies. 3Significantly different at .05 level from estimates in Table 4.2. 0 Significantly different from 1 at .05 level. 74 more closely correspond to our a priori expectations we must be cautious in interpreting these results since we cannot separate specific characteristics which vary by region. A particularly interesting result is the finding of increas- ing returns to scale for a number of our industries - especially the special trade contractors. Previous studies have found that there are economies of scale for certain building types. Increasing re— turns to scale and economies of scale are related, but somewhat dif- ferent concepts. Returns to scale is a production function concept which indicates how much output responds to changes in the scale of the establishment. Economies of scale is a cost function concept which indicates how unit costs respond to changes in the scale of the establishment. Sherman Maisel, in Housebuilding in Transition found in the 1950's that medium-sized builders sold houses (excluding land) at a price 3 percent below the price for similar houses built by small builders. Large builders (over 100 houses per year) sold houses 6 percent lower than similar houses built by small builders.5 Cassimates obtained similar results in the 1960's but also found some evidence of diseconomies of scale for builders with a volume of more than 500 houses per year.6 Fleming found somewhat different results in Northern Ireland where medium sized firms (79—120 workers) priced houses 11.5 percent less than similar-houses build by either larger or smaller firms.7 Fleming makes a useful distinction by pointing out that for homebuilding economies of scale may be associated both with the size of the builder and with the number of units built in 75 one project. This distinction was also made recently in a study of multiple family housing construction by Barbara Stevens. She found evidence of economies of scale in single site construction of multiple family projects.8 Over her entire sample (which consisted of projects in Massachusetts and New Jersey having between 12 and 600 units per project) unit costs declined about 10 percent when the number of units in the project doubled. The Bureau of Labor Statistics has also showed that economies of scale are associated with larger public housing projects.10 Although the sum of the output elasticities generally exceeds one in tables 4.1 to 4.4 for the general residential building contractor industries 1521/31, and 1522, increasing returns to scale are not statistically significant. Combining operative builders with single family residence contractors may have affected these results. Operative builders, who build on their own accounts, employ a larger number of nonconstruction workers (such as salesmen) than the general building contractors. Land receipts are important for Operative builders, and we suspect that like Subdividers and Developers (In- dustry 6552) they may be inflated for tax purposes. Since land receipts are also subtracted from gross receipts to obtain value added, value added may be somewhat smaller than it otherwise would be. But our findings of increasing returns to scale for many of the special trade contractors complements findings of economies of scale in the literature. Such a result is not surprising since theory suggests that economies of scale stem from both specialization of labor and technological factors. Special trade contractors may achieve 76 economies of scale by performing the same specialized type of job on different projects. There is probably greater opportunity in the building trades for such economies in the more urbanized areas. It is also likely that the larger subcontractors work on the larger building projects. We provided some evidence in Chapter III that project size varies regionally. The major technological factor is that the subcontracting system allows the special trade contractors to use more specialized construction equipment at a high rate of utilization. 2. The CBS Results Our results for estimating the Kmenta linear approximation of the CES function are given in table 4.5. Compared to our basic Cobb-Douglas results in table 4.1, our fit has not appreciably improved nor are there as many significant labor or capital co- efficients.11 Recall that this model provides a test of the Cobb- Douglas form, by examining the significance of the coefficient of the squared term . In only one industry (1796 - Building Equipment Installers) is this coefficient significantly different from zero. Even this result is questionable since 0 < —l and the elasticity of substitution implies is infinite. The other estimates of the elasticity of substitution differ from one in both directions but are not statistically significant. Thus this test provides no evidence to reject the Cobb—Douglas hypothesis that o = 1. As we see in table 4.6 the addition of regional dummies to the Kmenta model does not change our conclusions concerning the value of 0. However the Kmenta model is a weak test of the Cobb—Douglas hypothesis, 717 TABLE 4.5 KMENTA APPROXIMATION OF THE CES FUNCTIONI'Z COEFFICIENTS or PK L (FK/L)2 SCALE 3 ‘2 1521/1531 . Single Family .383 .671 -.251 1.054 .327 .622 Houses/Operative (3.444) (4.591) (-l.312) Builders 1522 Other “caiden' .332 .583 - 160 .915 .398 .635 ‘131 3°11dinss (3.053) (5.830) (-1 570) 1542 .526 .489 — 235 1.016 .350 .850 Industrial Buildings (.315) (3_553) (-l.lO6) 1542 Other Non-residen- .700 .352 — 280 1.052 .295 .750 tial Buildings (4.225) (2.472) (—1.439) 1611 Highways 8 .317 .688 130 1.005 a .880 Streets (.593) (1.368) (.864) 1622 Bridge/Tunnel/ —1.423 2.319 .902 .896 .671 .836 Elevated Highway (—1. 196) (2.014) (1.828) 1623 water/Sewer/ .554 .461 .089 1.080 .049 .866 Utility lines (.763) (.678) (.282) 1629 ** Other Heavy -.268 1.349 .235 1.080 .416 .949 Construction (—.o99) (4.056) (1.967) 1711 ' Plumbing/Heating/ .381 .744 -.181 1.125 .410 .775 Air Conditioning (4.079) (7.036) (-.700) 1721 Painting/Paper .430 .714 .027 1.152 .249 .732 Hanging (4.066) (3.789) (.299) 1731 Electrical .174 .972 -.181 1.146 .290 .802 Work (1.621) (6.808) (-1.221) 1741 Masonry/Stone— .256 .856 -.179 1.112 .355 .879 work (1.218) (3.787) (—1.068) 1742 ,, Plastering/Dry- .068 1.075 -.132 1.1410 .195 .833 wall/Insulation (.146) (2.207) (-.427) 1743 Tile/Marble/ 1.1616 ”.168 .306 . 996 .893 .5103 Mosaic Work (1.281) (-.170) (.439) 1751 .882 .243 .215 1.125 e .880 Carpentefins (1.478) (.408) (.965) 1752 .319 .679 .196 .998 . 786 Floorvork (1.349) (2.976) (1.064) - 1761 Roofing/Sheet .009 .782 -.564 .791 .008 201 Metal (.024) (2.078) (-l.268) 1771 Concrete .325 . 44 .113 1.169 .142 .756 work (2.236) (5.218) (.705) 1781 . water "all .260 .759 .007 1.019 .078 .717 Drillingfi (.632) (1.631) (.042) 1791 , Structural .947 .103 -.716 1.050 .061 .822 Steel (1.853) (.196) (-1.164) $1238 a _‘ .244 .513 .275 .757fl e .661 Glazing (1.594) (2.423) (.955) éizzvation/ 1.603 - 550 —.284 1.053 .109 .848 Foundations (1.529) (-.525) (- 852) 1795 “4' 4 5 4 30 7* 590 825 wrecking/ .8 063 .16190 —.1287 1. 9 . . Demolition (2' ) ( ' ) (-' ) 1796 ‘ 4 Equipment .185 1.043 .282 1 228 e .923 Installation (1.999) (7.336) (2.157) 1Number of observations and source of data same as Table 4.1. 2 Log V - const + 0 Log FK + 8 Log L + y(Log FK/L)2. 0 SEC to 00 where o < -1. 0 Significantly different from 1 at .05 level. 4* Significantly different from 1 at .10 level. TABLE 4.6 KHENTA APPROXIMATION OF THE CES FUN 753 COEFFICIENTS OF CTION NITH REGIONAL DUMMIPQI‘Z L PK (PK/112 CENTRAL 50018 wasr SCALE 1521/1531 . Single Family .855 .266 -.218 .062 -.129 .182 1.121 Houses/Operative (4.836) (2.355) (-1.267) (.623) (-l.145) (1.834) Builders éfiir Residen_ .776 .264 -.079 -.044 -.291 -.139 1.040 tial Buildings (3 690) (2.331) <--713> (- 389) (~2.464) (-1.728) 1542 d .655 .402 -.210 -.134 -.236. —.210 1.057 igggstrial ”“11 1n85(4.054) (2.224) 1-.994) (-1.559) (—2.3941 1.-9941 Other Non-residen‘ .446 .628 —.252 —.045 -.085 -.004 1.072 1611 Buildings (2.443) (3.2881 (-1 195) {—-474) (— 844) g, 0451 Highways 6 1.168 -.147 .215 .029 -.148 .039 1.021 Streets 12 341) (- 27511111 491) ( 4111 42-1 9511, ( AhQ) 1622 Bridge/Tunnel/ .702 .251 .159 -.328 —.452 -.083 .953 Elevated Highwaz ( 669) I 53]) I 532) ‘ 2 36]) I 3 335) ‘ (IE) 1623 water/Sever, .378 .690 ".036 “.095 -.235 .011 1.068 utility lines (-641) (1.127) (-.l32) (-1.223) (-3.121) (.139) * 1629 1.119 -.027 .142 .085 -.136 .084 1.092 Other Heavy (4.096) (- 096) (1.289) (.943) (-1.533) (.929) Construction 1711 * Plumbing/Heating/ .970 .243 .134 -.006 —.284 -.031 1.231 Air Conditioning (10.155) (2.924) (.623) {-.087) (-4.5331 1- 473) 1721 911 304 099 066 I 226 142 1 215** Painting/Paper ' " ° - . -- . . _ . Hanging (6.015) (3.220) (1.357) (.609) (-2.981) (1.395) 1731 ., . * Electrical 1.220 .033 -.171 —.062 -.323 -.005 1.253 work (11.289) (.408) (-1.624) (.408) (-.994) (-5.266) * $741 [St _ .951 .193 -.027 -.027 -.294 -.081 1.143 as:“" °“e (4.885) (1.069) (—.189) (-4.16) (-4.118) (-1.202) U01" 1742 it Plastering/Dry- .727 .400 .110 -.023 -.231 -.185 1.127 wall/Insulation (1.667) (.947) (4 12) (-.325) (—3.526) (~2.245) 1743 Tile/Marble/ -.037 .842 .407 .117 —.319 - 115 1.212 Mosaic work (-.051) (1.235) (.803) (.857) (—2.677) (— 828) 1751 .497 .722 .287 .012 — 397 -.172 1.219 Carpentering (1.189) (1.725) (1.849) (.164) (-4.473) (-1.943) 1752 .846 .228 .120 .006 -.297 -.062 1.120 Floorwork (4.278) (1.085) (.713) (.069) (-3.204) (—.664) 1761 Roofing/Sheet .730 .257 .004 .070 .300 -.147 .987 Natal (2.090) (.703) (.009) (.703) (-.634) (~2.696) 1771 Concrete 1.357 .074 .350 .006 “.398 “.079 1.431 work (9.766) (.698) (2.969) (.098) (-5.592) (-.948) 1781 gate, "211 1.035 .066 .063 .147 -.128 .084 1.102 Drilling» (2.840) (.206) (.526) (1.972) (-1.550) (1.083) 1791 , Structural -.482 1.467 -1.321 —.051 -.292 -.031 .986 Steel (-1.276) (4.008) (3.037) (-.688) (—4.474) (-.357) 1793 Glass 5 .717 .210 .233 -.127 -.108 .177 .927 Glazing (3.301) (1.421) (.890) (—1.072) (-.977) (1.307) 179“ 420 1 508 280 014 O76 063 1 087 Excavation] " . ' —' ,, ' " ' ° Foundations (-‘“00) (1'436) (“'8“2) (-244) (‘1-435) (.950) 1795 , 7 * wrecking] .636 .849 -.155 .113 -.253 .227 1.484 ) _ _ Demolition (1.837) (2.27-) ( 1.110) (.886) ( 2.135) (1.423) giggpment 1.140 .064 .208 .086 -.107 -.152 1.204‘ Installation (8‘679) ('612) (1'733) (1-055) (--937) (-l.033) 1Number of observations and source of data same as Table 6.1. 2 , Log V - const + 8 Log FK + 0 Log L + y(Log FK/L)2 + Dummies. 0 set to m p<-l. * Significantly different from 1 at .05 level. 0 3 E2 .380 .701 355 .668 .307 .862 2.929 .738 3.557 .896 v .892 .772 .900 .089 .961 m .857 7.619 .841 .086 .903 .748 .919 6.785 .889 031 .775 w 942 w .873 1.044 408 m .888 m .847 m .917 w .735 25~704.858 .504.888 w 939 79 as we have already mentioned. Our poor results in estimating 0 using the Kmenta method are similar to Griliches and Ringstad's findings in their study of Norwegian manufacturing. In that study they showed that the estimate of the coefficient for the squared term had only about l/7th of the precision of the estimate for the capital coef— ficient.12 In this light our results are not surprising. Our findings on returns to scale using the Kmenta model agree with the Cobb-Douglas models. And, the addition of regional dummies as explanatory variables in the Kmenta model has almost the same effect upon the scale parameter. This is an encouraging result since Maddala and Kadone, in a Monte Carlo study of Kmenta type equations have shown that the Kmenta method provides a reliable estimate of returns to scale even though the estimate for o is poor. Two alternative sets of estimates for o are given in tables 4.7 and 4.8. The first set is the traditional ACMS (Arrow, Chenery, Minhas, Solow) method while the second adds our regional dummies to the ACMS equation. We use WC as our wage variable. . None of our sample ACMS estimates are significantly above unity while there are seven industries with an estimate significantly below unity at the .05 percent level. This is an unusual result in comparison with cross sectional studies of the manufacturing industries. Griliches, who surveyed a number of studies of the manufacturing industries, points out that generally 0 clusters around 1 in cross section studies but time series estimates are significantly below 1.14 It is well known that is biased towards l for the ACMS model using cross section data if labor quality, output price, or the efficiency parameter vary over observations.15 80 TABLE 4.7 ACMS ESTIMATES 1521/1531 Single Family 1 .085 . 686 Houses/Operative (10.289) Builders 1522 Other Residen- .917 _ tial Buildings (7_393) '379 1542 _533k* 014 Industrial Buildings (5.14;) 1542 Other Non-residen- 1_033 .742 tial Buildings (12.026) 1611 Highways G .870* .785 Streets (13.397) 1622 Bridge/Tunnel/ 1.043 713 Elevated Highway (8.095) 1623 Nater/Sewer/ 1.013 .889 gtility lines (18.176) 1629 * Other Heavy .569 .438 Construction (5.603) 1711 Plumbing/Heating] .902** .844 Air Conditioning (16.492) 1721 Painting/Paper .934 -917 flaming (20.284) 1731 Electrical .914 .840 werk (15.227) 1741 Masonry/Stone- .942 373 work (16.363) 1742 Plastering/Dry- -395* ~869 wall/Insulation (lb-109) 1743 Tile/Marble/ ~961 '692 Mosaic Work (10°399) 1751 * Carpentering '765 '820 _._ (11.341) 1752 .668* .643 Floorwork (6 ' 9U9) 1761 Roofing/Sheet '6?5** ‘878 Metal (14.997) - 1771 .890** 654 Concrete , - work (1%.lbl) 1781 .514* .221 Water Well (2 583) Drilling ' :Zgictural '887 .835 Steel (11.947) 1293 1.229 .622 Class 6 (5.231) GlazingL :izgvation/ '711* 7““ Eggndations (10.697) ___'_’_“ 1795 .852 .804 Wrecking/ (5.152) Demolition 1796 .760 389 Equipment (3.621) Installation 1Number of observations and source of data same as Table 4.1. Log V/L I Const + 0 Log WC. 2 *Significantly different from 1 at .05 level. '"Significantly different from 1 at .10 level. TABLE 4.8 ACMS ESTIMATES E31 WITH REGIONAL DUMMIES Installation 1 Number of observations and source of data same 2Log V/L - Const + 0 Log BC + Regional Dummies. “Significantly different from 1 at .05 level. i ' Significantly different from 1 at .10 level. as Table 6.1. —~ £1:me SOUTH 1.11151 1521/1531 . Single Family 1.050 .015 .044 .143 715 "OUSCS/OPerative (8.386) (.241) (.699) (2.412) Builders 1522 Other RPS‘den' .927 -.014 -.033 -.128 .571 [‘81 Buildings (4.943) (-.156) (-.295) (-1.310) 1542 .7336 -.113 -.127 —.635 .632 Industrial Buildings (3.501) (—1.736) (_1.729) (_.454) 1547 Other Non-residcn- 1.024 -.011 —.000 .043 .711 _tial Buildings (10.126) (—.174) (-.003) ( 717) 1611 Highways 6 .787* .063 .041 .157 .310 §L£09ts (8.836) (1.546) (.672) (7 943) 1622 Bridge/Tunne1/ 1.061 -.O96 .012 110 _724 Elevated Highyay (5.622 (-.903) (.088) ( 832) 1623 Water/Sewer/ 1.169** .017 .126 .056 _397 utilitx_1incs (12.976) (.365) (2.160) (1.204) 1629 Other Heavy .550* .155 .075 .147 .462 Construction (4.633) (1.849) (.857) (1.777) 1711 _ Plumbing/Heating/ .835* -.035 -.060 .005 .850 gir Conditioning (11.819) (-1.003) (-1.650) (.160) 1721 ,, Painting/Paper .858* —.044 -.050 .062 '93“ flinging (13.579) (-1.200) (-1.508) (1.989) 1731 Electrical .77&* —.014 -.085 .035 .874 Qgrk (11.712) (-.421) (-2.264) (1.032) 1741 Masonry/Stone- .813* .014 —.078 .057 _599 work (10.056) (.365) (-1.469) (1.431) 1742 Plastering/Dry- .810* -.016 -.039 .021 .876 Bfljl/Insulation (12.479) (— 517) (—1.134) (.614) 1743 Tile/Harble/ .869 .035 —.044 .011 .363 Megaic Work (4.645) (.402) (-.436) (.125) 1751 Carpentering .706* - 117 -.174 -.132 .836 (6.946) (-2.550) (—4.020) (-2.800) 1752 .5346 .006 —.154 .037 765 Floorwork (5.934) (.119) (-2.516) (.646) 1761 - , , Roofing/Sheet .80/* .01“ -.0-44 .019 878 Metal (9.646) (.313) (-.632) (.410) $771 .863** —.053 -.045 —.016 -850 ,oncrete ,r . _ york (11.435) (-1.309) (-.931) (.369) 1781 267* 123 13’ , Water Well ' , '099, -' “ ' 7 '437 grilling (1.005) (1.155) (-.960) (1.351) gigictural .820*' - 093 - 067 -.015 .335 Steel (9.83)) (-2.195) (-1.945) (-.271) 613:3 6 1.110 -.l33 -.025 .044‘ .669 Glgzing_ (3.595) (—1.727) (.303) (.506) :Zzivation/ .778* .013 068 .154 _804 ‘ ‘ ‘ (10.516) (.353) (1.726) (3.552) Egundations 1795 .957 .159 .157 .201 .816 "'OCking/ (6.154) (1.700) (1.178) (1.677) gomolition 1’96 .479* .045 . -.123 -.122 .443 Equ‘Pm°"t (1.965) (.544) (—1.376) (- 633) 82 If these sources of bias are geographic then the use of regional dummies may reduce bias due to misspecification. Such would appear to be the case since our estimates of o for the ACMS with dummies is, with few exceptions, smaller than the simple ACMS estimates. Moreover, there are now 15 industries in which 0 is significantly lower than one. Our final set of estimates are based upon the Variable Elasticity of Substitution production function, which allows us to teust whether 0 ‘varies with respect to the capital—labor ratio. We estimate equation (2.11) which for our variables is: log V/L = log a + blogW + clogFK/L + u (4.1) C The elasticity of substitution is g = ““l‘a; (4.2) 1 + p ——‘— Sk Where p = $812- , m = 11C? , and SK the share of capital, computed as the residual 1 minus the share of labor. Table 4.9 gives estimates for the VES model while table 4,10 gives estimates of the same model Where regional dummies have been added as eXplanatory variables. In table 4.9 we see that in fourteen industries the coefficient of the capital-labor ratio is significant. It is not significant for the majority of the general building contractors as one might expect, but is aIWays significant for the heavy contractors where capital is more important. The estimate of o is less than unity only for some of the special trade contractors. Adding regional dummies acts to reduCe the variation in the capital-labor ratio between states, and t he tumber of industries with significant FK/L coefficients drops £33 TABLE 4.9 VES ESTIMATESI' COEFFICIENTS OF _ _2 / KC FKIL SK 0 1521 1531 . Single Family 1.143 —.061 503 1.301 .683 Houses/Operative (8.850) (-.788). Builders 1522 Other Residen- .769 .101 375 1.080 .597 tial Buildings (5.476) (1.639) 1542 .686 .170 .395 1.204 .658 Industrial Buildings (6.193) (2.472) 1542 Other Non-residen- 947 .099 .389 1.270 .746 tial Buildings (8.422) (1.320) 1611 Highways 6 567 .401 .529 2.343 .892 Streets (8.962) (6.982) 1622 Bridge/Tunnel/ .858 .303 .400 3.538 .755 Elevated Highway (5.977) (2.295) 1623 . Water/Sewer/ .875 .152 .452 1.318 .898 Utility lines (10.183) (2.068) 1629 Other Heavy .639 .273 .401 2.001 .679 Construction (3.211) (3.941) 1711 Plumbing/Heating/ .867 .051 .392 .997 .8145 Air Conditioning; (13.863) (1.142) 1721 . Painting/Paper . 88‘. .063 . [011 1.0164 .922 flinginjL (14.593) (1.755) 1731 Electrical .662 .115 .356 1.273 .876 work (15.879) (3.780) 1741 Hasonry/Stone- .796 .148 .360 1.352 .905 work (11.879) (3.354) 1742 Plastering/Dry- .812 .110 .350 1.184 .893 wall/Insulation (16'778) (3'123) 1743 Tile/Marble] .825 .239 .386 2.166 .904 Mosaic work (8.292) (2.283) 1751 .702 .103 .377 .966 .836 Carpenterins (9.669) (1.886) 1752 .659 .070 .460 .777 .652 Floorvork (6.888) (1.307) 1761 .808 .135 .385 1.244 894 Roofing/Sheet , ' Metal (12.578) (2.346) gzzirete .801 .167 .457 1.262 .913 Work (16.301) (5.006) 1781 .495 .267 .614 .876 .586 Hater Well Drilling, (3.415) (4.218) $791 t 1 .853 .069 .358 1.057 .834 truc “‘3 (10.330) (.948) Steel $193 a ‘ 1.203 .116 .437 1.638 .639 618::n87 ' (5.215) (1.304) (I :79“ 1 / .534 .327 .605 1.162 .823 XC‘V‘t °“ (7.694) (4.223) Foundations 1795 wrecking/ .674 .194 .603 .994 .855 Demolition (5.903) (2.518) 1796 . Equipment .720 .037 .462 .783 .363 Installation (3.168) (.515) 1Number of observations and source of data 2 Log V/L - const + a Log WC + 6 Log FK/L. same as Table 4.1. E34 1 2 TABLE 4.10 VES ESTIMATES WITH REGIONAL DUMMIES ' COEFFICIENTS or _ _2 3.1L FK/l- CENTRAL SOUTH 111-151 11 1521/1531 . Single Family 1.079 -.035 .008 .035 .136 1.009 709 “OUSQS/OPerative (7.620) (-.446) (.127) (.526) (2.196) Builders 1522 Other Residen- .009 .095 —.030 —.()39 -.125 1.083 586 tial Buildings (4.035) (1.497) (—.338) (-.360) (—1.312) 1542 .662 .157 -.063 -.063 -.020 1.132 661 IndUStrial Buildings (5.515) (2.047) (-l.626) (-.811) (—.287) 1542 Other Non-residen- .957 .086 -.010 .010 .030 1.229 .732 tial Buildings (6.000) (1.038) (—.156) (.162) (.484) 1611 Highways 6 .600 .377 .044 .065 .076 2.089 .895 Streets (8.192) (6.105) (1.094) (1.437) (1.856) 1622 Bridge/Tunnel/ .759 .355 —.175 -.110 .044 6.747 .785 Elevated Highway (3.650) (2.692) (-1.776) (-.832) (.369) 1623 Water/Sewer/ 1.013 .142 —.008 .096 .046 .1477 .904 Utility lines (6.427) (1.684) (—.169) (1.650) (1.014) 1629 Other Heavy .591 .261 .066 -.001 .062 1.693 .684 Construction (6.462) (5.0514) (1.306) (-.017) (.947) 1711 Plumbing/Heating/ .819 .037 -.040 -.059 - 001 .904 .849 Air Conditioning (11.111) (.793) (-1.108) (-1.591) (—.039) 1721 - Painting/Paper .835 .033 -.048 -.052 .046 .908 .933 Hanging (12.248) (.697) (-1.300) (-1 554) (1.024) 1731 Electrical .772 .083 -.024 —.075 .009 1.007 .869 work (12.479) (2.568) (-.742) (-2.121) (.263) 1741 Masonry/Stone— .751 .106 -.001 -.052 .034 1.064 .909 work (9.171) (2.157) (—.037) (~1.138) (.899) 1742 Plastering/Dry- .756 .105 -.032 0.040 “.021 1.123 .090 wall/Insulation (12.677) (2.333) (-1.040) (-1.248) (-.573) 1743 Tile/Marble, .728 .255 .053 -.038 —.018 2.145 .900 Mosaic work (4.204) (2.099) (.710) (-.443) (-.242) 1751 .704 .025 -.115 -.161 -.130 .754 .682 Carpentering (6.745) (.460) (-2.468) (-3.108) (-2.706) 1752 .530 .059 -.004 —.156 .030 .608 .775 Floorwork (5.992) (1.329) (- 084) (-2.603) (.540) 1761 2 3 4 884 Roofing/Sheet .761 .1 2 -.015 -.03 —.009 1 1 3 . Metal (9.432) (1.605) (-.325) (-.638) (-.179) 1771 ,_ Concrete .603 .170 -.021 .001 .026 1.279 .910 Work (13.442) (4.787) (-.670) (.029) (.678) 178 Hatir Well .496 .271 .166 .078 .164 .891 .735 Drilliqz (2.619) (4.354) (3.015) (.780) (2.390) :791 .776 .061 - 082 -.093 -.013 .935 .653 "”°t“'“1 (7 656) ( 769) ( 1 815) (-2 049) ( 247) steel 0 a - I I -. 1793 Glass 6 1.137 —.124 .019 .070 .156 .886 .728 Glazing (4.063) (—1.763)(.245) (.872) (1.909) 1794 Excavation/ .676 .277 -.002 .057 .118 1.251 .861 Foundations (6.586) (3 911) (-.071) (1.710) (3.135) 1795 Wrecking/ .813 .162 .113 .147 .148 1 112 .650 Demolition (5.122) (1.940) (1.296) (1.223) (1.329) 1796 Equipment .469 -.055 .038 . -.163 -.127 .419 .426 Installation (1.885) (-.643) (.448) (4.474) (-.643) 1Number of observations and source of data same as Table 4.1. 2 Log V/L - const + 8 Log WC + b Log FK/L + Regional Dummies. 85 to eleven. Like our ACMS estimates, the addition of the regional dummies to the VES model also lowers the estimate of 8. Note that the VES estimates of'g are generally larger than the ACMS estimates of (where o = 1370' This follows from our definition of E-in equation 4.2. When c is significant it is positive. SK is also positive so the relationship between 0 and 0 depends on the value of 0. When 0 is greater (less) than zero, - l 0 is greater (less) than 0. The capital share which we use is much larger than the alternative definition FK/V. A smaller value for S increases the value of 8‘ when the coefficient c is K positive. Thus the estimates of 0' which we present represent a lower bound of this elasticity. Unfortunately we are not able to test the hypothesis that .8 differs from one. Despite the diversity between the various ACMS and VES estimates we have a reasonably good idea of value of the elasticity of substitution in nearly two thirds of our industries. Table 4.11 summarizes these results. Where the coefficient of the capital-labor is not significant we accept the ACMS results. Mostewidence Sfllggests that the elasticity of substitution is unity for general bLuilding contractors. And if we believe our VES estimates, 0 is By contrast, un:ity or possibly greater for heavy contractors. théare are six special trade c0utractor industries for which 0 iAs less than one (Plumbing, Heating and Air Conditioning; Painting, PaIDGBr Hanging, and Decorating; Carpentering; Floor Laying; Water lkLlfll Drilling; and Equipment Installation Subcontractors). Of the r“—‘TT‘Iaining special trade contractors, o is at least unity for Terrazo, Tile, and Marble Work; Concrete Work; Glass and Glazing Work; and wrecking and Demolition Subcontractors. TABLE 4.11 86 ACMS + ACMS DUMMIES VES COMPARISON OF ACMS AND VES ESTIMATES VES + PROBABL DUMMIES OF E VALUE 0 1521/1531 Single Family Houses/Operative Builders 1522 Other Residen- tial Buildings T542 Industrial Buildings 1542 Other Non-residen— tial Buildings 1611 Highways 8 Streets 1622 Bridge/Tunnel/ Elevated Highway 1623 Water/Sewer/ Utility lines 1629 Other Heavy Construction 1711 Plumbing/Heating/ Air Conditioning 1721 Painting/Paper Hanging 1731 Electrical Work 1741 Masonry/Stone- work 1742 Plastering/Dry- wall/Insulation 1743 Tile/Marble/ Mosaic Work 1751 Carpentering or > 1 or > 1 or > 1 1752 Floorwork 1761 Roofing/Sheet 89:81 1771 Concrete Work 1781 Water Well Drilling 1791 Structural Steel 1793 Glass 6 Glazing 1794 Excavation/ Foundations 1795 Wrecking/ Demolition 1796 Equipment Installation 4 Significantly different from 1 at .05 level. it Significnatly different from 1 at .10 level. aVES term not significant. H 1... or > 1 or < 1 or > 1 87 Knowledge of the elasticity of substitution is important in evaluating the effects of wage taxes/subsidies, and investment tax credits. Variations in 0 between industries can lead to changes in factor shares and the distribution of employment. Since we have evidence of differences in the elasticity of substitution and the functional form (Cobb-Douglas, CES, VES) for the 4 digit construc- tion industries policies designed for the whole sector will have differing impacts in the different industries. For example a policy which increases the wage relative to the price of capital - such as an investment tax credit or approval of regulations which improve union bargaining strength - will have a greater impact on employ- ment for the general building and heavy contractors (where capital is more easily substituted for labor) than for those special trade contractors where o < 1. But labor productivity (V/L) will not in- crease as much for industries in which 0 < 1. These findings underscore both the complexity of the sector and the difficulty of lnaking policy decisions concerning the sector. . In Chapter II we summarized the relationship between the eliasticity of substitution and the demand for labor. Our estimates 0f the demand for labor are given in table 4.12. Although the wage elasticity is less than unity in twenty industries the difference is Siéznificant in only five industries. In table 4.13, where we report reSults including regional dummies as explanatory variables, the “UTDIJer of industries with wage elasticities significantly less than LmJLtiy rises to eight. Nearly all of the industries having inelastic denléind.elasticities are special trade contractors, which are less 88 COEFFICIENTS OF TABLE 4.12 LABOR DEMAND ESTIHATESI’2 11 no 112 1521/1531 Single Family .785 -.892 .822 Houses/Operative (14.818) (-8.654) Builders 1522 Other Residen- .875 -.899 .819 tial Buildings (11.726) (-7 392) 1542 1.057 -.864 .923 Industrial Buildings (22.084) (-3,154) 1542 Other Non-residen- .905 -,953 .859 tial Buildings (17.498) (—9.745) 1611 * Highways 8 .952 -.850 .913 Streets (21.570) (-12.597) 1622 . Bridge/Tunnel/ .943 -l.003 .906 Elevated Highway (15.628) (-7.383) 1623 water/Sewer, .996 -1.012 .961 Utilityglinea (30 600) (-17.177) 1629 Other Heavy 1.096 -.801 .962 Construction (24'744) (‘5'538) 1711 Plumbing/Heating/ -998 -.900 .931 Air ConditioninggAg (25.826) (—13.019) 1721 Painting/Paper .987 -.939 .900 Hanging (17.996) (-12.097) I731 Electrical , 1.008 -.979 .945 Work (26.505) (-12.265) 1741 Hasonry/Stone- 1.016 .967 .931 work (19.624) (-9.658) 1742 , , Plastering/Dry- 1-063 --937 .964 wall/Insulation (30'117) (”12'859) 1743 Tile/Marble! 1.101 —1.035 .907 Mosaic Work (11.094) (-8.801) 1751 ** Carpentering 1.025 - 804 .949 (19.739) (-7.581) 1752 1.042 -.707 915 Floorwork (16.528) (-6.213) 1761 Roofing/Sheet .961 -.862 .814 Metal (10.702) (—10.747) 1771 Concrete 1.009 -.900 .915 Work (19.717) (-10.880) 1781 Water Well .783 -.368* .636 Drilling (6.020) (-1.761) 1791 Structural 1.004 “.893 .943 Steel (20.455) (-8.722) 1793 Glass 6 .~ .855 -l.242 .882 Glagigg, (9.299) (-5.538) 1794 * Excavation] 1.042 -.743 .901 Foundations (18.918) (-9.479) 1795 wrecking] .983 *.835 .856 Demolition (9.796) (-5.783) 1796 * Equipment .780 -.228 .908 Installation (10.076) ("-885) 1Number of observations and source of data same as Table 4.1. 2 Log L - const + 0 Log V + 8 Log WC. * Significantly different from 1 at .05 level. 89 l 2 TABLE 4.13 LABOR DEMAND ESTIMATES WITH REGIONAL DUMMIES ’ COEFFICIENTS 0F v 90 CENTRAL SOUTH WEST 82 1521/1531 4 Single Family .774 -.748 .001 .069 -.052 .831 Houses/operative (12.257) (-5.359) (.016) (1.085) (-.888) Builders 1522 Other Residen- .844 -.779 -.020 .097 .112 .819 _tial Buildings (10.001) (-3-929) (-.226) (.656) (1.161) 1542 1.027 —.776 .111 :109 .036 .924 §;2;9t’1‘1 B"11“"88 (17.682) (-4.946) (1.689) (1.299) (.502) Other "on‘residen- 682 -.874 .004 .033 - 050 .657 tlal Buildings (15.671) (-7.238) ( 069) (.531) (-.664) 1611 ** Highways 5 1.022 - 806 -.093 -.059 - 174 .921 Streets (17.365) —7 828) (- 1546 (—.750) (-2.502) 1622 Bridge/Tunnel/ 941 -l.024 .048 -.030 —.166 .906 Elevated Highway (12.856) (—4.962 (.390)47 (-.208) (-1.104) igizr/5euer/ 1.019 -1.195 —.012 -.133 - 051 .964 ”(111:1 lines (29.461) (-11.689) (-.261) (—2.209) (-1.070) 1629 Other Heavy 1.083 - 794 -.139 -.102 -.115 .96: construction (21.859) (-4.270) (—1 697) (1.165) (-1.385) 1711 * Plumbing/Heating/ .969 —.782 .032 .072 -.003 .934 Air Conditioning, (21.960) (-7.635) (.899) (1.786) (-.099) 1721 Painting/Paper 1.093 -.862 .045 -.049 -,062 920 Hanging (16.665) (-6.266) (1.178) (1.322) (-1.452) 1731 Electrical .979 —.733 .014 .094 -.034 .955 Work (22.391) (-6.792) (.401) (2.213) (-.995) 1741 Masonry/Stone— 1.012 -.838 -.014 .066 -.060 .943 work (18.799) (—6.047) (—.375) (1.266) (-1.399) 1742 PlaStering/DTY‘ 1.077 — 952 .034 .030 -.026 .966 :gig/lnsulation 4’3 anlllgl—ln 2771 11 0701 (-912) (—-7691 Tile/Marble, 1.133 -.917 -.022 .085 .032 .664 Mosaic Work (9.096) (—4.602) (—.250) (.600) (.336) 1751 .971 -.645' .111 .184 .139 .968 Carpenterlns (20.277) (-5.043) (2.356) (3.924) (2.829) 1752 * Floorvork 1.026 -.566 —.002 .149 -.041 .944 (16.725) (—5.066) (-.045) (2.387) (-.704) . 1761 i ‘77—“—"‘—’ Roofins/Sheet .929 -.751 -.005 .060 -.009 .615 Metal (9.63111 [—6-629] (3102) (1.037) b-1881 1771 Concrete 1.006 -.874 053 .041 .016 .112 Hork 11117971 1—5-3071 (1.291) (.576) (.306) 1781 * Vatet Well .752 -.126 -.074 .125 -.149 .776 Drilling (7.162) (-.533) (—.972) (1.108) (-l.70()) 1791 Structural 1.062 -.905 110 .094 .003 .353 5...) (21.061) (-8 423) (2 498) (2.135) (.051) 1793 Class 8 .864 -1.063 107 .025 -.078 .096 Glazing, (9.506) (-3.597) (1 419) (.317) (-.904) ilzgvation/ 1.108, -.910 001 -.101 -.161 .931 Foundations (20.639) (-9.417) ( 033) (-2.438) (-3.876) 1795 Wrecking/ .933 -.642 157 -.105 -.215 .665 genolition (6.567) (—2.870) ( 1.623) (—.601) (-1.688) 1796 4 . Equipment .771 -.043 -.088 .033 .147 922 Installation (9.771) (~-179) (-1-278) (.417) 1Number of observations and source of data same as Table 4.1. 2 Log L - const + 0 Log V + m Log WC + Regional Dummies. * Significantly different from 1 at .05 level. *1 Significantly different from 1 at .10 level. 9O likely to use unskilled labor which can be more easily replaced by ‘mechanization. And, it is basically these industries in which estimates of are significantly less than one in our ACMS models, as we expect from theory. We must regard these estimates of labor demand in the con- struction industries as only a first step in examining employment in construction. More complete models separating labor into construc- tion, non-construction worker categories, or including the price of capital as an explanatory variable would prove useful. 3. Aggregate Construction Sector Results Until now we have put our main emphasis upon examining the 4 digit construction industries. However, it may also be interesting to examine aggregate production functions for the sector as a whole so we can compare our results with Cassimates' time series estimates. We have two sets of estimates. In the first set we use total con- struction activity information summing all the 4 digit construction industries, including Subdividers and Developers for each state. Our observations are the fifty states plus the District of Columbia. We are not able to subtract data on Subdividers and Developers from our state totals since this information is not reported by the census due to disclosure rules. In the second set, each 4 digit industry is summed for a U.S. total. Our observations are the twenty-four 4 digit industry totals plus the total for industry 1799 - Special Trade Contractors not elsewhere classified. We have excluded Subdividers and Developers. Our variables are defined as before. For the in- dustry aggregation we introduce dummy variables for the major 91 a. Cobb-Douglas Results Table 4.14 summarizes all of our Cobb—Douglas results. What is immediately obvious is the lack of agreement between the two types of aggregation. The models with observations aggregated by state, which is analogous to a 2-digit cross section study, give the poorest results, both in terms of fit and in the credibility of the estimates. We suspect that a major reason for these poor results stem from the fact that the subcontractor and develOper industry is included in state totals. Recall that in this industry total payroll exceeds value added on due to the subtraction of land receipts from gross output. Another unusual characteristic of this industry is that nearly two-thirds of all workers are nonconstruction workers. This last factor may be one reason for the insignificant coefficient for construction workers in equation 5 of table 4.14. This industry also has regional concentrations, being large in a few States (California and Florida) and relatively small in most other States. A second reason for the relatively poor results is that aggregation makes a changing composition of output and inputs by States. Each State total sums data from industries having different output elasticities, returns to scale, and elasticities of sub- stitution. Given these fairly large differences among 4 digit in- dustries and also between regions in size, capital intensity, etc., which we established in chapter Ill, it is not likely that the out- PUt and inputs are homogeneous, as the model requires. Our estimates based upon observations by industry appear much better. In fact the simple Cobb—Douglas estimate (line 2 of 92 .Hm>ma ucmuumm mo. um H Eoum ucmumMMHv xauchflmflcwwm yo Amwz.mv zoom.ov Akzw.av now oz ems. «moa.a fizz. Hem. owe. zoonooez .m Amok.mv Amms.mv Ammo.NV oz no» New. emoN.H ems. owe. mom. oooom .k Amoz.ev AsH~.mv Aokm.wv oz oz aka. mmo.a mma. saw. mNo. snonoocz .e Ammo.sv Amok.kv Aeee.v . oz oz mam. oza.z moo. Nam. who. oonom .m Ammm.ov Azoe.mHv now oz mam. isoz.z sea. was. znooooeH .6 Aokk.ov Aesm.zzv oz wow wow. eaom.z mmo. wee. monom .n Aokm.mv Aozm.zav oz oz mom. eoo.z mez. Hos. sponsocz .N Akoo.mv Aszm.mv oz oz mms. ramm.z omm. omk. oonom .a mmHEEDQ mmfiEEDQ ¢ 0 muumsvcH mumum mm. mamom 2m A A A Houumm cowuusuumcoo use now mmumEHumm mwawsoalnnou mo mucmwuwmwooo .qH.q manme coaummmuwwfi mo maze 93 table 4.14) agrees closely to the only prior production function 17 study of contract construction. Cassimates estimated a Cobb— Douglas production function for contract construction using time series data from l929~64. His estimate, which incorporates a time trend to account for technological change, gives a capital coef- ficient of .178 and a labor coefficient of .846. Our other Cobb— Douglas models also appear to have a more reasonable set of estimates. When dummies are included for our major industry classifications there is evidence of increasing returns to scale. Despite these seemingly good results we do not place as much weight on these estimates as we do those for the separate 4 digit industries which we reported earlier in this chapter. Our primary reason again relates to differences which we have observed between industries. Our estimates for the sector as a whole assume that all observations are from the same production function. Yet even when we restrict ourselves to the Cobb—Douglas results in our 4—digit estimates we find large differences between industries in the value of the Capital and labor coefficients. Moreover our estimates suggest that both a and the form of the production function also differ among tile 4 digit industries. 13. The CBS results Table 4.15 summarized our various estimates of the elasticity C>fsubstitution. Looking first at our estimate of 0 we find that, w'ith exception of the Kmenta model without dummies, o is higher in m(Ddels in which we aggregate by state rather than industry. Our ACMS all‘ld.lm uoc o Amo~.ko + Ammo.ev z\zz fizz. 0: mme. u0w mooam> u .Ho>ma somouoa OH. one um H Eouw ucmumwwflp mauomoflmficwwmea .Epmu vmumscm Eoum pmcflsumumv 0 mo Hm>ma muomUflmwcwfimH .Ho>mH ucmouoa mo. um H Eoum uomummwflo zausmUHWchfimn "mum mpwuoEmuma mo mmumeumm Hmsuo< mm» oz mam. HmH.H Nmm> zuumsnsH .NH Ammw.ov + Aqu.H~v z\zz mas. u: was. "mum muouoemuwa we mmumEHumm Hmouo< oz mm» Hmm. oqm.a Nmm> mumum .HH Ammm.mv + mmNn.qv A\Mm mma. 3 mom. ”sum muouoeoumm mo mmumswumo Hmsuu< oz oz «mm. own. Nmm> zuumsch .oH Aooq.mv Awmm.qmv . + a\zz nos. 03 won. "ope mumumEmuma mo moumeumo Hmouo< oz 02 moo. coq.a Nmm> mumum .9 Au ~qa.~ n umuosmpma mamum mo» oz mmo. cow. Housmaz zuumovoH .w 04 *wmm.H u pmqumuma wamom .Hu 9 a p0w .6 cu gym 0 oz mow mmw. «*8 Hmuomez uumum .m mq3.H u amusemuma mamum oz oz coo. Nam. Hmucmez zpumspoH .o «me.H n umumeuma mamum oz oz 3mm. mww. Hmuomez wuwum .m Amam.mv mmz oz Nam. krone. m20< xuumsvcH .q Aaaw.mav oz mow mom. «mow. m20< mumum .n Ammm.m, oz oz Noe. *«Noe. m20< zeonooez .N Awqm.wav oz 02 mm». moo. m20< mumum .H DooEEoo mmHEE:Q mmeEJQ Mm 0 Hope: newummmumMW zhumnch mumum .l we mqkfi No “RAH HOume COHUUJMUMCOU Qzu how COfiuDUHumDDm MO kquHummHm mzu we mmumefiemm mH.q maan 9S Cobb-Douglas form from these results. These results are consistent with the Cassimates estimate which is also not significantly dif— ferent from one.18 For all the VES estimates the coefficient of the capital labor ratio is significant. The industry dummies appear to be important, increasing both the 'R2 and the estimate of the elasticity of substitution. The very importance of the industry dummies however brings us back to our prior conclusion that the 4 digit estimates are preferred to those presented in this section. In this chapter we have presented our Cobb-Douglas and CBS estimates. These estimates reflect numerous differences among the 4 digit industries. The results using regional dummies suggest that the geographic differences which we described in Chapter III are important in examining the construction process. Using regional dummies we find evidence of increasing returns to scale in about one fourth of the industries, primarily among special trade contractors. We have also presented evidence that the elasticity of substitution is less than one for at least six special trade subcontractors, but appears to be unity for the general building on heavy contractors. Cobb-Douglas and CBS estimates using data at levels of higher aggrega— tion were also presented. Due to the differences between 4 digit in- dustries, and due to changing regional output mix the 4 digit estimates are preferred. 10. 11. 12. 13. 14. 15. 96 Notes to Chapter IV Data from preliminary census reports were obtained from Pre- liminary Report 1972 Census of Construction Industriesl_in: dustry Series CC72(P), U.S. Department of Commerce, Bureau of the Census, Washington, D.C., 1974. Final reports were obtained from 1972 Census of Construction Industries, Final Industry Report, Indusggy Series CC72-l, U.S. Department of Commerce, Bureau of the Census, Washington, D.C., 1975. Griliches, Z., "Production Functions in Manufacturing: Some Additional Results", Southern Economic Journal, October, 1968, pp. 155-156. ‘ Ibid. For a more detailed discussion see Griliches, Z., Review of G.H. Hildebrand and T.C. Liu, Manufacturing Production Functions in the U.S., 1957," Journal of Political Economy, Vol. 74, No. 1, 1965. Maisel, Sherman, Housebuildingiin Transition, Berkeley: Univer- sity of California Press, 1953, Chapter 8. Cassimates, op. cit., p. 66. Fleming, M.C., "Conventional Housebuilding and the Scale of Operations: A Study of Price", Bulletin of the Oxford Institute of Economics and Statistics, May 1967, pp. 109-137. Stevens, Barbara, "Single-Site Economies in the Construction of Multi—Family Housing", Land Economics, February 1975, pp. 50-57. Ibid. BLS bulletin 1821, ibid. We can no longer interpret the labor and capitol coefficients as output elasticities since in the CES function output elasticities are not constant. However, the sum of these coefficients is still a measure of returns to scale. Griliches and Ringstad, op, cit., pp. 77—80. Also see Appendix C. Maddala, G. and Kadane, J., "Estimation of Returns to Scale and the Elasticity of Substitution," Econometrica, July- October, 1967, pp. 419-423. Griliches, Z., "Production Functions in Manufacturing: Some Preliminary Results", 22, cit., pp. 286-290. See either Lucas, op. cit., pp. 26-31 or Mayor, op, cit., pp. 153- 163. 97 16. See Nadiri, 22, cit., pp. 1156-1157. 17. Cassimates, op, cit., pp. 73—75. 18. Ibid., p. 96. CHAPTER V THE ROLE OF MATERIALS In Chapter II we indicated that in the 4 digit industries which we are examining, subcontracting services and building materials are purchased outside the industry and should be considered as inputs. The level of capital and labor services chosen by the contractor will depend in part upon the relative price of materials and subcontracting as well as the relative price of capital and labor. We also pointed out that substitution of materials for on—site labor has been identified as one of the potential sources of productivity growth in construction. In section 1 we review the various types of substitution which occur in construction. We concentrate primarily upon substitution between building materials and labor. Our goal in section 2 is to examine the elasticity of substitution between materials and the other inputs. Several models are developed and results reported. 1. Substitution in Construction On the microeconomic level it is easy to find examples of many types of substitution in construction. In some cases substitution of materials for on-site labor is fairly obvious —- for example wallboard has been substituted for plaster thereby reducing the requirement for plasterers. But in other cases a relatively complex set of substitutions can take place for reasons which are difficult to isolate. Consider for example the substitution over 98 99 time of reinforced concrete for brick as the main structural material. This type of substitution might occur for a number of reasons such as: (l) A change in design due to changing tastes; (2) An increase in the price of bricks relative to concrete; (3) An increase in the wage rates of masons relative to concrete workers; (4) Increased mechaniza— tion or use of specialized equipment to mix, transport, or pump con- crete; and (5) The use of metal or fiberglass formwork, which reduces on site carpentry and concrete finishing costs. Note that when one material is substituted for another one effect can be to change skill requirements either from one skill to another (i.e. concrete workers for masons) or from skilled to unskilled worker. Mechanization or the introduction of new building techniques may increase capital require- ments but at the same time may also increase the speed of construction which changes financial costs. An excellent study which illustrates the complexity of sub- stitution in homebuilding is Sara Behmans' Productivity Change for Carpenters and Other Occupations in the Building of Single-Family Dwellings and Related Policy Issues.1 One of her main objectives is to determine to what extent new building techniques influenced the employment of carpenters, and other trades over time. She compared, in the San Francisco area, single family houses constructed by small builders in 1930 using "cut and fit" method to houses constructed in 1965 which used a large number of prefabricated components. She found for carpenters and other selected on site workers that average physical labor productivity increased at a rate of 3.2 percent per year over the 35 year period. Productivity grew at a rate of 2.5 percent per year for skilled workers but at a higher rate of 6.2 100 per cent for unskilled workers.2 One of her major findings was that "The advance in average physical labor productivity occurred in large part from the substitution of material for on—site labor".3 Wall- board, aluminum windows, precut studs, prefabricated cabinets are examples of the type of substitutions being made. Other factors which influenced productivity growth were: (1) A change in the structure of the homebuilding industry toward "merchant builders" which promoted economies of scale through labor specialization and the purchase of materials in volume at a discount; and (2) Quality changes in both the materials and in the house.4 The pattern of substitution appears to be somewhat different in heavy construction. A Bureau of Labor Statistics study has reported that manhour requirements for highway construction per $1000 expenditure _in constant 1967 dollars fell 30 percent between 1958 and 1970.5 During the same period the wage share of contract costs increased slightly from 25.5 percent to 29.4 percent, the materials share de- clined from 50.6 percent to 45 percent, while the share of overhead and profits (which includes equipment, off site wage, financing, and inven- tory costs) increased from 25.5 percent to 29.4 percent.6 These changes are primarily attributed to major advances in equipment and machinery (such as the slip form paving machine which reduced the requirement for both carpenters and wood) which changed both the skill and materials mix. The trend in highway construction has been toward more skilled workers in order to operate heavier, more expensive equipment. The study notes that this is different from the trend n .. in building construction, where skilled workers apparently are contributing a declining share and unskilled workers an increasing 101 share of all work performed at the site. The increasing use of pre— fabricated components in building construction primarily accounts for this ... by shifting skilled jobs from the site to material manufacturing plants..."7 From the above examples and studies it is clear not only that substitution between labor, capital and materials is occurring, but also that the process can be relatively complex, differing from one type of construction to another. In this light generalizations about substitution patterns for the sector as a whole should be treated with caution. Having issued this cavaet let us briefly mention material share trends for the SGCtOf. Both Cassimates and Sims have computed the ratio of value added to gross construction output in constant dollars. Although both admit that the price indexes they used are not totally appropriate. they found that the ratio of value added to gross construction output has declined since 1947.8 This implies that the real share of materials in gross output has risen, probably due to an increase in the use of more highly fabricated, or prefabricated materials which has replaced some onsite construction operations. In current dollars, construction materials maintained a relatively con- stant share (57-58 percent) of total construction activity in both the 1957 and the 1963 input-output tables.9 This implies that the elasticity of substitution between materials and value added is unity. 2. Cobb-Douglas and CBS Models The models in this section are primarily traditional Cobb- Douglas and CBS types. Estimates for a three factor Cobb-Douglas model (equation 5.1) are reported in table 5.1. 1(323 TABLE 5.1 RESULTS or ESTIMATING Log r - Const + 6 Log L + 8 Log PK + Y Log M COEFFICIENTS OF L PK 8 i2 SCALE 1521/1531 Single Family .162 .146 .786 .876 1.094 Houses/Operative (1.820) (3.021) (8726) Builders 1522. Other Residen- .106 .098 .748 .923 .953 tial Buildings (1.324) (2.472) (9.596) 15“2 .257 .196 .545 .954 .997 32235‘Y‘31 ””11d1“85 (2.793) (3.745) (5.694) Other Non—reside“- .162 .264 .597 .883 1.033 tial Buildings (1.496) (5.009) (4.837) 1611 Highways 5 .059 .508 .465 .953 1.032 Streets (.954) (10.714) (9.420) 1622 Bridge/Tunnel/ .029 .382 .574 .944 .985 Elevated Highway ( 196) (3.995) (4.718) 1623 Water/Sewer/ '227 '510 -295 .917 1.031 Utility lines (3.600) (7.050) (4.260) 1629 460 169 ‘415 977 l 064 Other Hea ' ' . . - Constructzzn (5.708) (3.110) (6.135) 1711 133 140 6 2 2 * Plumbing/Heating] ' ' ' 3 '9 6 1-105 Air Conditioning, (1.353) (2.724) (6.977) 1721 . .181 .150 .692 .878 1.024 Egigiigglpaper (1.246) (2.244) (5.424) 17 ' * Elzitrical .347 .090 .643 .924 1.0805 Work (4.252) (1.698) (6.832) 1741 Masonry/Stone- .283 .183 .556 .958 1.023 work (3.155) (3.007) (7.893) 1742 Plastering/Dry- .202 .084 .758 .948 1.043 wall/Insulation (1.779) (1-444) (7-305) 1743 Tile/Marble] -.122 .219 .933 .899 1.011 Mosaic Work (-.860) (1.466) (5.326) 1751 Carpenterlng .333 .141 .601 .967 1.076 (3 7061* (2 530; (9 811) 1752 .303 .021 .643 .944 .968 F1°°r"°'k (3.039) (.382) (7.530) 1761 Roofing/Sheet -045 ~101 .661 .761 .808 ”9,81 (3.63) ( 969) (6.103) 1771 Concrete .235 .138 .6I40 .936 1.013 Work (2.625) (2.393) (6.801) 1781 Water Well .380 .172 .444 .910 .996 Drilling (2.013) (3.352) (3.437) 1791 Structural .505 .245 .306 .923 1.055 17 01:23 5 .227 .033 .663 .914 1.008 Glazing (1.990) (.423) (5.161) 1794 .114 .470 .425 .927 .923 E t1 riiiZitiiflfi (1.277) (5.876) (6.373) bizzkinsl .662 ..521 .067 .836 1.250 Demolition (4.973) (4.634) (.455) at égzipment .877 .030 .254 .925 1.160 Installation (5.808) (.449) (3.037) 1Number of observations and source of data same as Table 4.1. .Significantly different from 1 at .05 level. as Significantly different from 1 at .10 level. 103 Log Y = const + 0 Log L + 8 Log FK + y Log M (5.1) Our results for this model, adding regional dummies as explanatory variables, are reported in table 5.2. Both sets estimates may be compared to our results using value added as the dependent variable, which we reported in tables 4.1 and 4.3 in Chapter IV. The coefficient for materials is significant in every industry except (as we would expect) Wrecking and Demolition Subcontractors. Materials appear most important relative to labor and capital for general building contractors. For a number of special trade con- tractors, the capital coefficient is significant in the value added models but not significant when materials are included as an input. In table 5.1 there are only eight industries in which all coefficients are significant. Adding regional dummies increase the number of industries in which all coefficients are significant to ten. Like the value added models, adding regional dummies raises the number of industries having increasing returns to scale. In- terestingly, increasing returns to scale become significant for the general building contractor of single family houses/Operative builders industry. We also notice the same pattern here as in Chapter IV. Adding regional dummies has generally raised the labor coefficient, and in this case lowered both the capital and materials coefficient. In tables 5.1 and 5.2 the number of industries in which all co— efficients are significant is much lower than for our value added estimates. Several factors probably account for these results. Materials usage may often be so closely associated with fluctuations in gross output that when materials are included as an input the effect of TABLE 5.2 RESULTS OF ESTIMATING Log Y - const + 0 1(14 L08 L + 8 Log PK 1Number of observations and source of 4 Significantly differentfron l at .05 level. 4* Significantly different from 1 at .10 level. data same as Table 4.1. + Y L08 H WITH REGIONAL DUMMIES L FK M CENTRAL SOUTH WEST SCALE?2 1521/1531 Single Family .258 .084 .794 -.026 -.092 .059 1.135 .904 Houses/Operative (2.666) (1.678) (8.841) (- 516) (1-739) (1.257) .Euilders 1522 Other Residen- .223 .094 .704 .009 —.118 -.029 ' 1 021 .930 tial Buildings (2.501) (2.459) (9.054), (.167) (-2.102) (-.518) 1542 .311 .140 .569 - 091 -.l31 -.058 1.021 .958 ¥9dgstria1 Buildings (2.843) (2.437) (5.783) (-1.847) (-2.479) (-l.136) 54 Other Non_residen_ .184 .221 .648 -.058 - 087 -.o35 1.053 .882, _.ial Buildings (1.494) (3.505) (4.946) (-l.045) (-1.534) (- 638) 1611 Highways a .161 .390 .487 .003 -.084 .051 1.038 .960 Streets (2 376) (6 459) (10 109)( 059) (-l.805) (.997) 8:383e/Tunnel/ .133 .334 .513 -.204 -.258 -.045 .980 .971 Elevated Highway (1.093) (4.740) (5.443) (-3.127) (-4.145) (-.511) égfzr/Seuer/ .368 .420 .256 -.074 -.177 .003 1.044 .943 Utilitlglines (5.539) (6.293) (4.396) (-1.454) (-3.578) (.067) 65(2. Heavy .459 .214 .396 .026 -.129 .024 1.066 .983 Construction (6.099) (4.033) (6.384) (.443) (-2.254) ( 387) * éliibing/Heating/ .334 .094 .708 -.017 —.140 -.028 l 137 .949 Air Conditioning (3.507) (2.085) (6.766) (-.503) (-4.387) (-.829) 1721 Painting/Paper .522 .121 .495 .003 -.159 .043 1.139 .907 Hanging (3.244) (1.920) (3.858) (.056) (-2.767) (.536) 1731 7 Electrical .576 .055 .503 -.029 -.184 - 012 1.134 .958 Egrk (7.429) (1.358) (6.403) (-.795) (-4.903) (- 315) 1741 ; Masonry/Stone- .469 .132 .456 .031 -.157 — 081 1.058 .966 work (3.803) (2.224) (5.359) (-.718) (-2.878) (-1.730) ’ 1742 - Plastering/Dry- .277 .087 .682 .035 -.136 "' 109 1.046 .965 .311/Insulation (2.709) (1.490) (7.769) (-.884) (-3.840) (-2.523) 1743 Tile/Marble] .056 .067 .773 .007 -.l66 - 116 .916 .941 Mosaic work (.382) (.669) (4.700) (-.101) (-2.835) (—1.747) t 1751 .601 .005 .526 .001 -.165 - 129 1.131 .979 Carpenterins (5.791) (.098) (9.320) (-.021) (-3 217) (-2.444) 1752 Floorwork .404 .029 .583 .001 -.158 - 035 1.016 .966 76 (4.905) (.678) (8.308) (.021) (-3.220) (- 714) 1 l Roofing/sheet .024 .076 .818 — 064 -.123 - 199 .916 .832 89591 - — - 1771 ** Concrete .442 .125 .561 -.064 -.189 -.o37 1.127 .957 Egrk (4.243) .12.389) (7.5731 (-1.536) (-4.1141H(:-791) 1781 Water well .403 .140 .493 .091 -.060 .076 1.036 .950 Drilling (2.740) (3.170) (4.512) (2 049) (-l.242) (1.506) 1791 Structural .458 .310 .263 -.o41 -.199 -.053 1.030 .950 Steel (3.614) (3.009) (6.197) (-.041) (-3.210) (-.657) 1793 Glass 6 .372 .041 .567 -.o75 -.o78 .059 .980 .927 Clazing_ (2.954) (.481) (3.953) (-1.3o7) (-l.376)(.800) 1794 Excavation/ .193 .441 .395 .002 -.o34 .045 1.029 .927 Foundations (1.780) (5.357) (5.439) (.052) (-.847) (.959) 1795 * Wrecking] .895 .413 .063. .032 -.244 .168 1.371 .881 Demolition (6.206) (3.942) (.504) (.297) (-2.170) (1.107) 1796 Equipment .921 -.o48 .260 .071 -.110 -.120 1.134 .940 Installation (6.679) (-.619) (3.296) (.946) (-.994) (-.943) 105 materials is so dominant that the role of the other inputs is obscured. This would appear to be the case for a number of our industries. In both the general and heavy contractors, and in most of those special trade contractors in which capital is important, it is primarily the labor coefficient which is not significant. The reverse is the case for those of the special trade Contractors in which capital is not very important. Increased multicollinearity between the inputs is also a factor in reduCing the significance level of the coefficients. Finally, if short run fluctuations in demand influence material usage more than capital or labor usage then materials are more endogeneous than labor or capital. Using materials as an independent variable may lead to greater simultaneous equation bias.10 For those industries in tables 5.1 and 5.2 having constant returns to scale we attempted to improve our results using a model in which the sum of the output elasticities is constrained to equal unity. We estimated: Log Y - Log n = const + a[Log L — Log M] + B[Log FK L Log M] (5.2) This transformation constrains the coefficient of Log M in equation 5.1 to be (1 — a w 8). Unfortunately, this model either with or without regional dummies, did not improve our previous estimates. Although the value of the coefficients changed slightly due to the constraint, we were not able to add to the number of industries having significant coefficients for all three‘inputs. Our investigation of CES models is limited since the only input price available is the construction wage, thus we rely on the Kmenta type of linearization 106 of the CES function. The simplest model is analogous to the estimating equation used to estimate the elasticity of substitution between capital and labor. We use: Log Y = Log y + v6 Log M + v(l—5)Log L (5.3) 1 2 _-§ pv0(l-0)[log M - log L] :‘c We also used V (gross output less capital service) as a dependent variable. Our estimates are presented in tables 5.3 and 5.4. For the majority of industries the coefficient of the squared term is not significant so we cannot reject the Cobb-Douglas hypothesis that OML = 1. Where this coefficient is significant either the labor or material coefficient is negative - the wrong Sign. Moreover, in al- most every industry at least one coefficient is not significant. Since the value of OML relies upon the significance levels of these coefficients our estimates of UML are not likely to be very accurate. We also experimented with more complex Kmenta models of_a type suggested by Griliches and Ringstad.ll For example we assumed that materials and labor together formed a composite input. We then formed what Griliches and Ringstad term the "nested” CES function: _ B -o -o -v/o Y — AK [0M + (l - 6)L ] (5.4) By expanding around 0 = 0 we could derive a Kmenta type estimating equation involving [log M - log L]2. However these results, and re- sults involving a similar function having a [log M - log FK]2 term were both unsuccessful. We suspect that this lack of success is due to primarily to errors in measurement of variables used in the non—linear approximations. In the case of simple regression such errors will tend 107 TABLE 5.3 RESULTS OF ESTIMATING Log v - const + 6 Log L + 8 Log H - AyILog M - Log L]2 L n (M/L)2 82 °HL 1521/1531 Single Family -1.798 2.889 —.388 .857 1.195 Houses/Operative (-1-128) (1.806) (-1.298) Builders 1522 Other Res‘den' —l.094 1.965 -.230 .912 1.229 tial Buildings £_ 352) I] 537; (_ 915) 1542 .225 .706 -.023 .936 .788 Industrial 81111011383 (-095) (.299) (’1048) 1542 Other "°“'”931de“‘ 3.614 -2 813 .745 .834 .878 tial B“ildi"Ss (2.045) {-1.4971 (1.895) 1611 Highways ‘ -2.350 -1 456 .440 .849 .813 Streets (2 4041 (—l-5021 (2.054) 1622 . Bridge/Tunnel/ .538 .405 .041 .905 1.550 Elevated Highway (-132) (-0991 (-0541 1623 Water/Sewer/ 1.199 -.262 .189 .832 .470 Utilitxllines (4-027) (.801) (2.3501 1629 Other Heavy 1.542 -.546 .224 .972 .654 ConStruction (2.332) (-.810) (1.499) 1711 Plumbing/Heating/ 3.764 -2.673 .723 .917 .864 Air Conditioning (1.316) (-.935) (1.281) 1721 . Painting/Paper .254 .715 .074 .860 .857 Hanging, (.410) (1.190) (.302) 1731 Electrical -2.315 3.418 -.531 .931 1.047 Work (-2 305) (3.362) (-2.651) ;:::nry/Stone_ -.209 1.221 -.l60 .948 62 (-.355) (2.126) (-.920) work 1742 Plastering/Dry- —2697 1.720 -.227 .945 1.632 gall/Insulation (-.346) (.858) (-.453) 1743 3.581 -2.635 .863 .891 .852 Tile/Marble/ Mosaic Work (1.068) (-.783) (1.104) 1751 .076 1.033 - 122 .959 .225 CarP°nte“"8 (.163) (2.164) (—.823) . 1752 1.030 -.065 .147 .944 .191 Floorwnrk (.668) (—.043) (.470) 1761 ““ “" “"“ ' Roofing/Sheet —2.645 3.401 -.607 .777 1.114 Metal (-1.740) (2.224) (-l.754) 1771 Concrete 2.365 -l.422 .539 .938 .766 Egrk (2.898) (-1.746) (2.657) 1781 Water Well 2.547 -1.640 .419 .856 1.222 Drill,n&g_i (.914) (- 590) (.768) 1791 2 Structural 1.004 .008 .106 .919 w 5.091 (5.214) ( 038) (1.594) 1793 “““ Glass 5 1.576 -.625 .247 .915 .677 c1nzjng (.567) (-.229) (.483) 1794 . Excavation, 1.041 -.165 .213 .859 .265 qugdations (1.021) (—.160) (.707) __-- $Zkain8/ .450 .744 -.272 .572 .606 Demolition (.608) (.821) (.466) Edzgpmcnt 2.864 -1.741 .415 .957 .643 Installation (5.055) (-3.011) (3.451) 1Number of observations and source of data same as Table 4.1. 201‘“. set to W when p < -1. - YILOg H - Log 212 1(363 n , * .ABLE 5.4 RESULTS or ESTIMATING Log v - const + 9 Log L + 8 L08 8 1 11 (Mildz E2 om‘ 1521/1531 Single Family -1.766 2.862 -.377 .858 1.195 Houses/operative (-1.105) (1.785) (-1.261) Builders 1522 Other Residen- -.804 1.712 —.l77 .911 1.305 tial Buildings (.600) (1.283) (-.689) 154? .612 .335 .056 .940 1.119 Industrial Buildings (.260) (.143) (.117) ’ 1542 Other Non-residen- 3.851 —2.578 .754 .836 .838 tial Buildings (2.100) (-1 547) (1.952) 1611 Highways 6 2.100 -1.170 .398 .879 .768 Streets (2.314) (—1.300) (2.001) 1622 , Bridge/Tunnel/ .419 .522 .028 .905 1.317 Elevated Highway (.103) (.127) (.038) 1623 Water/Sewer/ 1.196 -.255 .191 .834 .459 Utility lines (4.036) (-.763) (2.380) 1629 Other Heavy 1.421 -.387 .194 .973 576 ggnstruction (2.117) (-.567) (1 277) 1711 Plumbing/Heating/ 3.610 -2.511 .690 .917 .857 Air Conditioning (1.254) (—.873) (1.215) 1721 . Painting/Paper .085 .892 -.007 .858 .847 HanginL (.136) (1.477) (-.028) 1731 Electrical -2.342 3.450 -.538 .930 1.173 gork (-2.304) (3.353) (-2.655) 1741 2 Magonry/Stone— -.164 1.177 ”.147 .948 W work ' (-.278) (2.047) (- 844) 1742 plastering/Dry- -.802 1.829 -.253 .945 1.549 wall/Insulation (-.394) (.906) (-.502) 1743 Tile/Marble/ 3.567 -2.615 .860 .891 .851 Mosaic Work (1.058) (- 772) (1.095) 1751 Carpentering .078 1.031 -.119 .960 .246 (.167) (2.171) (-.810) 1752 2 Floorwork .925 .048 .125 .945 m (.589) (L931) (.380) 1761 . -*-‘-—* -—"' Roofing/Sheet -2.687 3.457 —.620 .773 1.115 natal (-1.727) (2.20g), (+1.747) 1771 2.155 ~1.164 .476 .937 .727 ggtirete (2.544) (-1.369) (2.27) ;:E:r Well 1.544 -.566 .215’ .898 675 ggglling (.622) (-.229) (.442) ézgictural 1.001 .007 .111 .916 42 $5891 (5.009) (.033) (1.609) 1793 ‘"'“" Class & 1.455 -.513 .224 .910 .578 Glazing, (.515) (-.184) (.430) 1794 g 2 Excavation/ .727 .193 .128 .865 6 Foundations (-692) (.182) ' (.413) 1795 “‘ ‘ Wrecking] .697 .536 -.162 .631 .483 Demolition (.970) (.609) (-.286) 1796 Equipment 2.864 '1.765 .418 .956 .845 Installation (5.041) (“3.009) (3.468) 1Number of observations and source of data same as Table 4.1. 20 set to KL a when p < -1. 109 to bias the coefficients toward zero. Griliches and Ringstad have in- vestigated the degree of bias possible for non—linear estimating pro- cedures such as the Kmenta method and have concluded that "... errors in variables are bad enough in linear models. They are likely to be disastrous to any attempts to estimate additional non—linearity or curvature parameters." In conclusion, in section 1 of this chapter we were able to demonstrate that substitution of materials for other inputs in con- struction is complex, has occurred, and differs by type of construction. For the sector as a whole the elasticity of substitution between materials and value added appears to be greater than unity. Our find- ings in section 2 of this chapter are inconclusive. The three factor Cobb-Douglas results suggest that in at least eight and possibly ten of our industries that we can not reject the hypothesis that the elasticity of substitution between materials and the other inputs is one. The Kmenta results reported in tables 5.3 and 5.4 also suggest this result. Certainly one factor which is probably affecting our results is the relatively narrow classification of our 4 digit industries. But as we suggest in Chapter IV aggregation for the sector as a whole is not likely to resolve the problem. It does not. We will only report a few results. For example, our three factor Cobb-Douglas results are: 110 Table 5.5. Aggregate Three Factor Cobb-Douglas Estimates Type Aggregation Coefficient of L FR M 112 State .133 .240 .775 .921 (1.460) (4.736) (8.127) Industry .586 .114 .317 .984 (6.763) (3.814) (6.530) In the State aggregation our labor coefficient is small and not significant. When regional dummies are added the coefficient is significant at the .05 percent level but its value remains small (.286). The industry aggregation results appear better, but our criticism of the industry aggregation in Chapter IV also holds here. Our 4 digit industry estimates reported in this chapter reflect large differences in the construction process among the 4 digit industries. Thus it is not likely that the same homogeneous production function holds for all industries. Our estimates of the elasticity of substitution between materials and labor (OML) using the Kmenta type model (equation 5.3) appear to have reasonable values using either Log Y or Log V* as the dependent variable for either type of aggregation. For the state aggregation OML is .871 using Log Y as the dependent variable and .785 using Log V* as the dependent variable. For the industry aggregation CML is .667 using 'Log Y as the dependent‘variable and .583 using Log V*. The squared term is not significant for the State aggregation, but significant for the Industry aggregation. Thus for our CBS estimates the State aggregation, which has a value of OML closer to unity, I!“ (all I.Illr All 111 appears better than the industry aggregation since the weight of our prior evidence suggests a value of 0 around unity. Neither the ML State nor the Industry aggregation estimates are likely to be accurate however, since for both sets of regressions the coefficient of Log M is not significant and is negative — the wrong sign. Given our evidence of substitution in section 1, our results in section 2 are rather discouraging. Our problems stem from limitations in both our construction data and in the models which we have employed. In order to better questions concerning substituta- bility, better data and more appropriate models are needed. In our concluding chapter we will briefly address these issues. {lo-712917. 10. 11. 12. 112 Notes to Chapter V Behman, Sara, Productivity Change for Carpenters and Other Occupations in the Buildinggof Single-Family Dwellings and Re- lated Policyglssues, Center for Labor Research and Education, Institute of Industrial Relations, University of California, Berkeley, California, 1971. Ibid., pp. xv - xvi. Ibid., p. xvii. Ibid., p. 103. Ball, Robert, "Labor and Materials required for Highway Con- struction", Monthly Labor Review, June 1973, pp. 42—45. Ibid., p. 43. Ibid., p. 42. Cassimates, 9p cit., pp. 103-104 and Sims, 92, cit. p. 159. Sims also has a particularly good discussion of the problems associated Wlth deriving an appropriate price indices in construction. Kingie, George, "Construction Input—Output Profile", Construction Review, August 1970, pp. 4—8. See Griliches and Ringstad, Economies of Scale and the Form of the Production Function, op. cit. pp. 108-109, for more detail on this topic. Ibid., p. 119-121. Ibid., p. 199. CHAPTER V1 SUMMARY AND CONCLUSIONS Our objective in this thesis has been to examine the Contract Construction Industries using Cobb-Douglas and CBS production functions to analyze new data on contract construction which has recently be- come available in the 1972 Census of Construction Industries. In Chapter II we explained the theoretical models used. In a produc- tion function framework a number of strongly simplifying assumptions are necessary. We asserted that the relatively narrow 4 digit classification in the Contract Construction Industries and the fairly large number of observations make our data superior to that used in manufacturing studies. We also showed that there was a considerable regional variation in wage rates and input ratios, which is important for identifying the production function cross sectionally. However, our data is less satisfactory than most manufacturing data for examining differences in the skill level or quality of labor and for examining technological change. A set of interrelated factors influences construction, such as skill composition, design, size of establishment, degree of unioniza- tion, degree of urbanization, and size.of construction project, all of which may vary regionally. We describe these factors in Chapter III, but we are not able to specify these factors as variables in 113 114 the production function. Instead, we introduce regional dummy variables to reduce error due to misspecification. We presented our estimates in Chapter IV. We had some dif- ficulty in estimating all of the parameters of interest. We were not able to estimate the effects of changes in capital vintage and had only limited success in examining the separate influence of con- struction and nonconstruction workers. Our estimates of 0 using the Kmenta, ACMS and VES models often differed. Despite these estimation difficulties we were able to learn a great deal about the structure of the construction industries. The following paragraphs summarize the more important conclusions. Our findings suggest that the elasticity of substitution be- tween capital and labor is less than one for nearly half of the special trade contractors. In contrast for most of the general build" ing contractors and for heavy construction contractors we cannot reject the hypothesis that o is unity. Differences in o be- tween industries imply that over time if wage rates inerease faster than the price of capital that factor shares and the distribution of employment will change. Our findings suggest that since capital is less easily substituted for labor by special trade contractors that employment within the sector should increase for special trade con- tractors relative to general building and heavy construction contrac- tors. This indeed has been the case. Mills has computed the change in the distribution of employment between the 1939 and the 1967 Census of Construction Industries. Employment declined from 28.4 to 25.7 percent for general building contractors, and from 27.6 to 25.6 percent for heavy contractors. Employment increased from 42.1 to 115 46.7 percent for special trade contractors.1 We computed the change in the distribution of employment between the 1967 and the 1972 census (using the 1972 SIC classification). Employment increased slightly from 27.3 to 27.7 percent for general building contractors, declined from 23.1 to 20.0 percent for heavy contractors, and in- creased from 49.0to 50.8 percent for special trade contractors. Although these figures are also influenced to a certain extent by differences in the composition of total construction output in the census years, the shift in the distribution of employment toward special trade contractors is clearly evident. There has been an opposite trend in construction receipts over time. Between 1939 and 1957 Mills showed that the general building contractor share of net construction receipts increased from 26 to 36 percent while the special trade contractor share de- clined from 44.3 to 34.3 percent. The heavy contractors share de- clined from 27.3 to 25.3 percent. These trends lead Mills to con— clude "... that certain elements of nonresidential building con- struction (that branch of the industry in which general contracting is most prevalent) have shown high rates of productivity growth since 1939."3 Our findings imply that one source of this productivity growth has been the ability of the general building contractors to sdbstitute capital for labor more easily than the special trade contractors . A second major finding of our study is that there are probably increasing returns to scale for a number of the special trade contractors. These findings depend upon accepting our 116 estimates including regional dummies as explanatory variables. We have cited evidence from other studies of economies of scale in single, and multiple family residential construction. Cassimates, using the survivorship technique was not able to detect economies of scale for corporate firms in construction between the years 1954 - 64.4 He attributes the lack of economies of scale as an institutional problem associated with the subcontracting system. Deu to the bidding system the working relationship between the sub- contractor and the general building contractor often terminates with the end of the construction project. Thus it is more difficult for general contractors to maintain or develop organizational efficiency from one project to the next.5 We attribute our findings of in- creasing returns to scale in the subcontracting industries to more economical use of skilled labor and greater utilization of complicated and specialized construction equipment. Our findings do not con- tradict Cassimates. Rather the benefits of increasing.returns to scale in the subcontracting industries may be in part dissipated by institutional factors. A frequently made policy suggestion is for the government to take action to stabilize construction demand. This policy would promote a more stable employment of both workers and equipment in Contract Construction and in major supplying industries. Our findings suggest that such a policy might also promote economies of scale in construction. Policies which expand the local market (such as elimination of conflicting building codes in nearby commu- nities) or changes in the contractural system which encourage closer 117 coordination between general contractors and subcontractors would also allow greater opportunity for further economies of scale. Our third major finding concerns the great diversity within the construction sector between the 4 digit industries and by geo- graphic region. Of course our finding of diversity is not new. For example, Mills has stated "... construction is less a single industry than a complex and shifting conglomeration of many dif- ferent specialities - each with its own employment and industrial relations policies."6 But our production function framework ~allows us to examine such diversity in a slightly different light. Different elasticities of substitution for our 4-digit industries imply that tax policies which influence wages or the price of capital will have different impacts in different industries. In Chapter IV we briefly investigated the demand for labor in our 4-digit industries. We have also contrasted the 4-digit industry estimates, and estimates based on higher levels of aggregation. These results suggest that more aggregate studies of the construc- tion sector as a whole - such as time series by Cassimates must be interpreted with caution. In Chapter V we provided evidence that substitution of materials for labor and capital occurs, often in a complex way which differs from one process to another. But we were not very successful using our production function techniques to shed much light concern- ing the value of the elasticity of substitution between materials and the other inputs. It would appear that o differs between ML industries although for many we cannot reject the hypothesis that 118 it is unity. For the sector as a whole 0 is probably one. MV But these "findings" are more like suspicions than conclusions. Better data and better models are needed to more appropriately answer these questions. More comparable construction data is necessary. The Bureau of Labor Statistics Bulletins on labor and material requirements for specific building types are especially valuable. More than one per year should be issued and their scope expanded in several ways. For example, more complete information should be collected on the degree of unionization in the sample. More detail concerning the types of prefabrication would also be helpful. These surveys, along with Bureau of the Census information on building characteristics should be used to develop both hedonic price indices on types of construction and regional materials price and wage indices for specific types of construction. A new type of production function model which appears promising for use in construction is the translog production func- tion.8 It is a multi-factor function which allows estimation of Allen partial elasticies of substitution between inputs. However like other production functions some strong simplifying assumptions are required. Constant returns to scale are assumed, and estimation uses the condition that factor shares add to one. The parameters of the function are estimated from a set of semi-logarithmic equations which require data on physical inputs and factor shares. The share of capital is taken as a residual. This may pose a special problem in construction since we have noted that the share of capital in 119 valued added computed as a residual appears much larger than it should be. Thus construction data may be no more appropriate for this type of function than the ones which we have used. Despite these potential problems the translog function may turn out to be a good vehicle for examining substitution of materials with other inputs. 120 Notes to Chapter VI Mills, D. Quinn, Industrial Relations and Manpower in Construction, .gp. cit., pp. 10-12. .ibid. .ibid., p. 10. Cassimates, pp. 58-60. _ibid., p. 68. Mills, p. 141. Sims, gp, cit., has an excellent discussion of other statistical needs in construction. For a discussion of this function which summarizes its major pro- perties see, Berndt, Ernst R., and Christensen, Laurits R., "The Translog Function and the Substitution of Equipment, Structures, and Labor in U.S. Manufacturing 1929-68", Journal of Econometrics, l (1973), pp. 81—114. BIBLIOGRAPHY BIBLIOGRAPHY Ball, Robert, "Labor and Material Requirements for Apartment Con- struction", Monthly_Labor Review, January 1975, pp. 70-73. Ball, Robert, "Labor and Materials Required for Highway Construction", Monthly Labor Review, June 1973, pp. 42-45. Behman, Sara, Productivity Change for Carpenters and Other Occupations in the Building of Single-Family Dwellings and Related Policy Issues, Center for Labor Research and Education, Institute of Industrial Relations, University of California, Berkeley, California, 1971. 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