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Productivity performance of U.S. trucking in the era of deregulation Caskey, Kevin 1987

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Productivity Performance of U . S. Trucking in the Era of Deregulation K E V I N C A S K E Y B.Sc . Northeastern Universi ty M . S c . Stanford Universi ty A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F S C I E N C E (Business Administration) in T H E F A C U L T Y O F G R A D U A T E S T U D I E S (Faculty of Commerce and Business Adminis t ra t ion) We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A October 1987 © K e v i n R . Caskey, 1987 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of &e>»&0te7fc& AUf/M^isSf y>n?/»*/s*'/gTl8sfvr/&. The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date /3 &>Cr<prte:fl DE-6G/81) A B S T R A C T This paper analyzes the impact on the productivity of the U. S. interstate trucking industry of changes in the regulatory climate in 1980. Two methods of analysis are used; Total Factor Productivity (TFP) and Neo-Classical Cost Function analysis. The industry's performance in 1978 is compared to the performance in 1982. Results of the Total Factor Productivity analysis indicate the TFP of the industry in 1982, after deregulation, was lower than that of 1978. However drawing conclu-sions from this result would be unfounded. TFP analysis assumes constant returns to scale. Cost Function analyses find that the U. S. trucking industry exhibits significant economies of scale. As the trucking industry does not have constant returns to scale, TFP cannot be used to draw conclusions about its economic performance. The results of the Cost Function analyses are dependent on which model is chosen. The variable measuring the effect of deregulation is either positive or negative depending on exactly what other variables are included in the model. In none of the initial models is this variable found to be significantly different from zero. After deleting six data points which produce extreme residuals and correspond to questionable observations, this variable is found to be positive and significant, indicating increased costs in 1982. ii T A B L E O F C O N T E N T S Abstract ii Table of Contents iii List of Tables iv I Introduction 1 II The Interstate Motor Freight Industry 4 III Total Factor Productivity 7 IV Cost Function Estimation 12 V Data Sources 16 VI Generalized Least-Squares 23 and Zellner Iteration VII Results of TFP and Cost Function Analysis 29 VIII Conclusions 42 Bibliography 44 Appendix A, Results of Regressions 46 Appendix B, Indexes 61 Appendix C, Residual Plots and Histograms 82 iii L I S T O F T A B L E S Title Table Page Number Categories of Labor 5-1 17 Prices Indexes 5-2 19 Tax Rates 5-3 21 Input Factor Shares 7-1 29 Quantity Indexes for 1978 7-2 30 Quantity Indexes for 1982 7-3 30 Ratio of Index Means, 1982/1978 7-4 30 First-Order Coefficients of Cost Functions 7-5 32 (Initial Six Models) Log of Likelihood Function 7-6 34 Comparisons to Full Model 7-7 35 Own-Price and Allen-Uzawa Elasticities 7-8 36 First Order Coefficients of Cost Functions 7-9 39 (Models 4, 7, 8 and 9) iv I Introduction What effect does government regulation have on the Canadian trucking industry? This has been the subject of much debate and many studies in recent years. Some effects of legitimate concern would be service to rural areas, safety, reliability of service and the economic performance of the industry as a whole. The concern of this thesis is economic performance as measured by productivity. Productivity is a concern because higher productivity means that a given level of goods or services can be provided to society while consuming fewer resources; be they natural, human or capital resources. These saved resources are then available to be applied toward the satisfaction of other needs of the society. If government regulation adversely affects the productivity (input consumed to produce a given level of output) of a given industry, society as a whole suffers because the wasted input is unavailable for other uses. For example, if regulation imposes an awkward route structure on the trucking industry more fuel than necessary may be used to move a given tonnage of freight. Another problem may be inefficient capital utilization with the effect of higher freight prices. The approach generally taken to study the Canadian motor carrier industry has been to compare firms operating in provinces with relatively little regulation, such as Alberta, to those operating in heavily regulated provinces such as Saskatchewan. The researchers then try to control for the non-regulatory differences among the provinces. Though this method has the advantage of not having to control for temporal differences, the success of this technique depends on the ability to control for these other factors (population density, road structure, industry mix, etc.) while comparing the performance of firms in different provinces. Past studies employing this method have been inconsistent in their estimation of major effects (see Chow (1982)). A better method of study would be to compare the same firms in the same geographic area operating both with and without regulation. Though we can not perform such a study with Canadian firms, we can with firms in the United States. The U. S. started to deregulate its interstate motor carrier industry in 1977 with the major change in regulation occurring in 1980 (see II for a discussion of these changes). An added benefit to studying the U. S. experience is that the U. S. Interstate Commerce Commission keeps much more extensive data on individual firms than does Statistics Canada and these data are readily accessible. 1 This thesis uses two methods to measure the change in productivity of the set of trucking firms before and after the 1980 deregulation; Total Factor Productivity (TFP) and neoclassical cost function analysis. TFP is an index number approach which creates a ratio of a weighted average of the various outputs (in the trucking industry, tmckload haulage, less-than-truckload haulage, etc.) to a weighted average of inputs used to produce the output (labor, capital, fuel, etc.). Since TFP is a ratio analysis, statistical estimation of the change in productivity is not necessary. This allows TFP analysis to be conducted faster and cheaper than cost function analysis. The index number approach does have weaknesses, however. First, the use of index numbers implies assumptions as to economic conditions, such as marginal cost pricing and constant returns to scale. These assumptions may not be correct. Second, even though TFP can indicate a change in productivity it cannot be used to make inferences as to the sources of the change. Third, if any of the underlying economic conditions change, then the validity of the comparison of TFP at two different points in time is undermined. (Please see HI for a more detailed discussion of TFP.) To overcome the shortcomings of TFP this thesis also uses statistical estimation in the form of neoclassical cost function estimation. This method does not require the restric-tive assumptions about economic conditions. In fact by using cost estimation we can statistically test the assumptions implied in TFP. In addition cost function estimation allows the identification of the sources of productivity change, such as increased traffic density or technology improvement. The multiproduct cost function can be written as: C = /(Y,W,Z,T) (1-1) where C is total cost, Y is a vector of outputs, W is a vector of prices of the inputs used, Z is a vector of control variables related to the production of the output and T is a vector of potential technology differences. Generally, both the cost function and the various factor demand equations which can be derived from it are estimated together. In this form of statistical estimation the usual assumption made in ordinary least squares estimation as to the disturbances is potentially too restrictive. Therefore a different estimation method is used. To handle a more general set of disturbance assumptions an adaptation of Zellner's iterative method for generalized least-squares is employed leading to a more efficient set of estimates. (IV describes cost functions in greater detail. VI is a discussion of the statistics involved with the generalized disturbance covariance matrix). 2 For both the TFP and cost function methods, pursued below, a panel data set was used. That is observations were made of 136 firms in both 1978 and 1982. A panel data set is two dimensional, here those dimensions are Time and Firm. These sampled firms met the following criteria; over 75% of their revenue was derived from intercity transport of general freight, they filed annual reports with the ICC for every year from 1976 to 1982 and they were classified as general freight carriers. ( See II for a discussion of the motor freight industry.) The bulk of the data for the individual firms was obtained from annual reports that the carriers are required to file with the U.S. Interstate Commerce Commission. Among the information contained in these reports are financial and operating statistics. (V provides the source and a description of the data used.) The final sections (VII & VIII) of this thesis present the results of the analysis and the conclusions drawn as to the economic effects of the deregulation of the U.S. trucking industry. 3 n The Interstate Motor Freight Industry Before and after deregulation, the ICC classified carriers into four groups ; common, contract, private and exempt. Common carriers are available to the general business community to carry shipments between any two points within their scope of operation varying in size from parcels to full truckloads. Contract carriers, as the name implies, carry specified commodities under contract to the shipper. An example of private trucking would be a firm transporting work in process between two manufacturing facilities. Exempt carriers are involved in the transport of certain goods, such as bulk agricultural products, which were exempt from ICC regulations. These groups are further classified as Class I, II or III in order of decreasing size. Since 1980 the ICC has defined Class I carriers as those with annual operating revenues above $5 Million, previously this limit was above $3 Million. The lower limit on Class II is $1 Million while Class III includes all firms that are below $1 Million of total revenue. The ICC collects no data on private or exempt carriers, and very little on class III carriers. Class I common carriers make up the bulk of the industry, approximately 80% by revenue. Because of better data availability and total industry revenue being dominated by this class, this thesis deals with a subset of Class I common carriers. The costs and handling characteristics vary widely from a carrier of consumer goods to a bulk carrier of raw materials. The sample used in this thesis was chosen in part to obtain a somewhat homogeneous sample from an inherently heterogeneous industry. The sample was limited to Class I general commodity carriers. This set was further limited to those carriers receiving 75% or more of their revenue from intercity move-ment of general freight (known as the 127 carriers). Such carriers typically transport manufactured goods and the bulk of their business is less-than-truckload (LTL) ship-ments. The ICC requires that these carriers submit Form 127, which permits the study of revenue operations with greater detail than if this form were not present. Even with this limitation there was quite a range in total revenue and percent of shipments that were LTL. All of the firms used in this study were in existence and filed annual reports with the ICC for every year in the period 1976 through 1982. Though this thesis compares the industry in 1978 to that in 1982, the more extensive data base was necessary to develop the capital investment series needed. 4 The annual reports list a range of sources of revenue from rent of equipment to non-operating services provided to other firms. This study is concerned with only two sources of revenue; Less-than-truckload (LTL) haulage and truckload haulage. The distinction between LTL and truckload haulage is an important one. The economics of producing a ton-mile of LTL can be quite different than that of producing a ton-mile of truckload freight. Truckload freight is a contract for at least one load from a specific source to a single destination. LTL operation requires the aggregation of shipments at a terminal until enough tonnage is ready to be shipped to a destination terminal where the shipments must be disaggregated and distributed. All this requires terminals, pick-up and delivery vehicles and more labor, both as drivers and dock handlers. There are other measures which can help explain differences in performance of the carriers. Some of these are; average load, average haul and average shipment size. Average load is a measure of how well the carrier is able to fill his available capacity per trip. Average haul gives us a measure of the length of these trips. Costs per ton-mile decrease when a carrier is able to haul full trailers a greater distance because some costs are fixed and independent of trip length. Average shipment size is a measure of the amount of consolidation that must be done at the warehouse. It should be less costly to consolidate a full load made up of four shipments than one from twenty shipments. This study used the above mentioned performance characteristics and total revenues as controls in estimations of economic performance. On the one hand if the average load increased from 1978 to 1982 but output did not we could infer that firms were better able to use their equipment after deregulation. However if some of the performance measures decreased but total output decreased also then the regulatory effects would be confounded with the effect of a change in the economic environment. Regulation Issues Regulation prior to 1980 f The Motor Carrier Act of 1935 consolidated interstate trucking regulation under the federal government, specifically the Interstate Commerce Commission (the ICC). The act allowed federal control of the interstate trucking industry through regulation of entry, exit, routes, rates, mergers and safety matters. To gain entry into the market, an applicant had to prove public need for a new carrier and had to show that the new service would not harm an existing carrier's business. This was in agreement with the major goals of federal regulation: minimum dupli-5 cation of service, well organized dependable service, preservation of service to small communities, and financial stability of the trucking industry. The I.C.C. had the power to set minimum, maximum or actual rates. In practice, car-riers and shippers were involved in the rate setting process through the use of protests brought before the commission. Formal rate bureaus, made up of collectives of carri-ers, were set tip in major traffic segments. The I.C.C. permitted this form of collusion until the Supreme Court found it in violation of anti-trust laws. The Reed-Bulwinkle Act of 1948 granted the I.C.C. the power to exempt this form of price fixing from the anti-trust laws. Arguments for and against Deregulation Sentiment was by no means in agreement as to the possible benefits or problems that would be realized if the trucking industry were deregulated. Proponents of deregulation argued that rates were artificially high due to entry control and operating expenses were inflated as a result of regulation induced inefficiencies. Examples were given of carriers with limited operating authorities having high levels of empty mileage. Acceptance of this argument was not universal; this thesis tests for change in efficiency before and after deregulation. Opponents of deregulation claimed that deregulation of rates and entry would result in: increased average total costs due to excess capacity, financial instability caused by pricing below actual long-run costs, unsafe carrier operations, and loss of service to rural communities. Regulatory reform 1970's and 1980's In a climate of deregulation of many industries, regulation of the trucking industry was greatly reduced starting in the late 1970's. Entry into interstate trucking is now almost totally deregulated, only the fitness test remains. Carriers were initially permitted to change rates up to 10% a year in either direction. Later, in an effort to stimulate more activity, this range was increased to 15%. Some initial studies on the effect on service to small communities indicate little change. Allegations of conflicting evidence indicate that these findings may be premature. Button and Chow (1983) contains a thorough discussion of U. S. trucking deregulation. 6 i n Total Factor Productivity As stated in the Introduction, Total Factor Productivity, TFP, is a relative measure. Of interest is the change in productivity of a firm over time or a comparison of different firms in the same time period and over time. One value of TFP taken alone is not of interest. Development of Quantity Indexes for Inputs and Outputs In order to make these comparisons, the various input and output data for each firm in each year must be aggregated. It is common practice first to aggregate the data into a small number of input and possibly output categories. For example, all of the various expenditures for labor (ie. managerial, clerical, direct labor, etc.) will first be combined into a single measure of labor input, a labor quantity index. Then the broad input quantity indexes are weighted and combined to produce the "aggregate input" quantity index. In the case of a multiproduct industry, there will also be different output categories. For example, in the trucking industry a firm may have both less-than-truckload and truckload output. Again these are weighted and combined to produce the "aggregate output" quantity index. The ratio of aggregate output to aggregate input is then formed. This single statistic, TFP, representing the relative performance of a given firm in a single year, can then be compared to other firms or years. Another advantage of first creating input and output quantity indexes before the cal-culation of TFP is that the change in a given quantity index can also be observed. For example, one may observe that the total use of labor has decreased for a given firm over time. Development of TFP index Research in economic theory has shown that index number formulas can be derived explicitly from particular aggregator functions (see Caves, Christensen and Diewert (1982)). An index so derived is referred to as 'exact' for the underlying aggregator function. Diewert (1976) limits the selection of aggregator functions to those which can provide second order approximations of arbitrary aggregator functions. Functions with this property are known as 'flexible'. Diewert then terms index numbers that are exact for flexible aggregator functions as 'superlative'. 7 The index used in this research is a generalization of the Tornqvist-Theil-translog index: \TLTkl = Y,(Su + Ski)\ii(Zki/Zu) (3-1) i where T is the index comparing time (or firm) k to 1, i corresponds to the values being aggregated, the S's are the share weights of these economic entities being compared, and the Z's are the corresponding prices or quantities. Diewert (1976) has shown this index to be exact for the homogeneous translog aggregator function (see Christensen, Jorgensen and Lau, (1971, 1973)), a flexible form widely used in economic research. When more than two entities are being compared a conflict in criteria arises. Fisher (1922) termed the following test 'circularity ': hi = hi/In (3-2) where I is the index and i j,k are firms (or time periods for the same firm). Others refer to this property as transitivity. Dreschler (1973) uses the term 'characteristicity' to describe to what degree the weights are specific to the individual comparison being made. Dreschler states that these two properties are always in conflict. Caves and Christensen (1980) proposed the following formula as a compromise between characteristicity and transitivity ( see Caves, Christensen and Tretheway, 1981) in binary comparisons. l n r F P f c - l n r F P , = ^ ^ ^ ^ (3-3) i i i i where a bar over a variable indicates an arithmetic mean and a tilde indicates a geomet-ric mean, k and 1 are adjacent periods, Yi3- are output indexes, Xij are input indexes, Rij are output revenue shares and Wij are input cost shares. This multilateral TFP formula maintains a high degree of characteristicity while being transitive. The use of revenue shares as weights implicitly assumes constant returns to scale and marginal cost pricing of outputs (Caves et. al., 1980). The validity of these assumptions will be examined by the use of cost function analysis, discussed in (IV) below. 8 As stated above, the individual input indexes are also aggregations and are built up in a similar manner. As an example, let us look at labor input. Some of the various cate-gories of labor are; management, clerical, drivers and helpers, and warehouse workers. Equation 3-3 is adapted as follows: In Lk - m L, = £ W i k ~ W i HUk/Li) - £ W « + W * l n ^ / L * ) (3-4) i i where Lij is the number of employees in the ith category for the jth firm and Wij are the compensation shares. Input Index for Capital The input index for Capital is not so straightforward in that the costs for various capital categories are not found in the annual reports. The book values in the annual reports reflect the peculiarities of accounting and tax law more faithfully than they reflect the economic concept of capital input. The development of the capital index follows the work of Christensen and Jorgensen (1969). The development involves two factors; a measure of quantity of capital, the capital stock, and then a price per unit for the use of that capital, the service price. First, a measure of capital stock for each type of capital service (eg. structures, land, trucks, etc.) must be developed. For this the perpetual inventory method is used. A discrete time representation of this method is: Kit = la + (1 - ln)Kiyt-1 (3-5) Kit is stock at the end of period t, la is investment in period t, and /i» is the rate of replacement, all for capital category t. All investment data must be in constant dollars. As this is a recursive process, a starting value for each category, a benchmark, must be given. In this paper the book value of each category in the year 1974 is used as a benchmark. The double declining balance method is used for the capital depreciation rate, /x; /z» = 2/Ni where Ni is the mean service life of capital stock t. The above series gives us a measure of the amount of capital in use in period t. We now need to develop the capital service price, which is the cost of using one unit of an asset for a fixed period of time, usually a year. The service price, P5 t , involves more than just the cost of buying the capital items, (which is the asset price). PSt takes into consideration the effects of taxation; both income and property, the cost of replacement, and the opportunity cost of foregoing the chance to invest elsewhere. The 9 asset price, qt, tracks the cost of a given asset in different years. Usually a base year value is set to 100 to represent the cost of a group of capital items in the base year. Then, if the next year the same group of capital items cost 10% more, the value of qt+i would be 110. The service price formula differs depending on the type of capital good involved; land, structures or producers durables, due to differing effects of taxation. The formula for the service price of producers durable equipment is: P S t = (1 " 1*-^ Kt)(qt-lTt + q t f i ~ ( g t ~ + q t t t ( 3 _ 6 ) where r t is the rate of return on corporate property, tt is the effective property tax rate, lit is the effective corporate profits tax rate, Zt (expanded below) is the present value of a dollars worth of depreciation deductions, fx is the rate of replacement for producers durables that was derived above, Kt is the investment tax credit, and qt is the asset price of capital. In the above equation the first term has two factors. The first factor is an adjustment for the effect of corporate income tax including depreciation. The second factor contains three terms: the cost of capital, the current cost of replacement and the cost of capital loss. The second term in (3-6) reflects the cost of the tax on corporate property. The equation for the present value of a dollar's worth of depreciation deductions, Zt, where L is the lifetime of the capital stock, and rt is again the rate of return on corporate property. Zt takes into account depreciation of an asset occurs over the lifetime of the asset in declining amounts which gives equation (3-7) the form of a present value calculation of an investment series. The service price for structures is: PSt = ) ( ? t - i r * + M ~ fat - qt-i)) + qttt (3-8) where the indexes and rates are for corporate structures. Here the income taxation effect factor is somewhat simpler with the lack of an investment tax credit. is: (3-7) 10 The service price for land is simpler still, as land is not depreciated: PSt = r ^ — (fc-ii-t - {qt ~ + qttt (3-9) 1 — {it again the rates and indexes are those appropriate for corporate land. The annual cost of capital used to develop the capital input index is then the capital stock of each category multiplied by the appropriate service price. The capital index is then developed analogously to the labor index. Comparing Individual T F P Values To create the TFP index, the individual input indexes are then aggregated and com-pared to the output or outputs using the the single output or multilateral TFP index formula as appropriate. Because we are working with a panel data set comparisons can be made in various ways. The TFP index for firms in a given year can then be compared to the TFP of the same firms in another year to detect a change in TFP for the individual firm or, by aggregating these comparisons, the industry across time. The TFP of different firms can also be compared to other firms within the same time period to detect a relationship of some other firm characteristic (eg., region) to TFP. In this thesis the mean TFP (weighted by total cost) of the sample of trucking firms in 1978 will be compared to that of the same sample of firms in 1982. Also the number of firms that either increase or decrease their TFP will be observed. The various data will then be used as input for the cost function models to be discussed in (TV) next. 11 r v Cost Function Estimation Background In the introduction it was stated that neoclassical cost function analysis would be used for a more general economic analysis of the trucking industry. Cost function analysis allows the testing of both the economic assumptions of TFP, discussed in III, and the examination of the sources of change in productivity such as the effect of change in the performance statistics mentioned in II. An example of a change in such a statistic would be a increase in average haul. The technology of a firm can be described by either a cost or production function. Indeed by Shephard's (1953) Lemma it is generally accepted that a duality exists be-tween these two functions, with the assumption that the firms minimize cost. The cost function where Y is aggregate output, W is an m dimensional vector of input prices and T is a vector of technology variables is said to be the dual of the production function where X is an m dimensional vector of input levels. For the duality to hold, certain regularity conditions must be met. These conditions are: C must be nonnegative, real valued, nondecreasing, strictly positive for nonzero Y, and linearly homogeneous and concave in W for Y. To estimate equation 4-1 a specific cost functional form must be adopted. Translog Cost Function In this study the translog functional form proposed by Christensen, Jorgenson and Lau (1973) is used. This form has been widely used in recent econometric studies. This form is flexible in the sense that it provides a second-order approximation to an unknown cost function. In the initial models in this study a dummy term for year and terms for three technology variables ( average load, average shipment size and percent of revenue from less-than-truckload operations) are included. In later models average C = <7(r,W,T) (4-1) T = /(y,X,T) (4-2) 12 shipment size was deleted and replaced with average haul. The full model used is : n InC = a 0 + aS2h2 + ay lnF + £ ^ f t In Wi + ^ <f>t lnT i-i t + Uyy (ln Y)2 + i £ £ 7 i y ln Wi In W> + I £ £ ^ ln 2J ln Ty (4-3) i 3 i j + pYi In y ln Wi + ^ 2 fiYi In YlnTi + X) E A*'ln Wi 1x1 ^  i i i 3 where I&2 is an indicator variable for observations from the year 1982. Because a cost function must be homogeneous of degree one in input prices, the fol-lowing restrictions are implied: E» fa = li Hi = Hi* 2y ftf = 0 f o r a 1 1 *' IC* Pr. = 0 and = 0f o r a 1 1 J-By Shephard's Lemma the input share (of total cost) is equal to the logarithmic partial derivative of the cost function with respect to input prices. The share equation for the tth input is: S; = ft + £ H i l n Wi + PYilnY + AyZnTy (4-4) 3 3 with the restriction that E* = 1 The estimation of 4-3 together with 4-4 allows for more efficient estimation of the regression parameters as will be discussed in V I . The trucking industry is a multiproduct industry. Among the products of interest are truckload haulage, less-than-truckload haulage and other revenue producing opera-tions. The translog model can be expanded to handle multiple outputs. The following extension from Caves, Christensen and Tretheway (1980) meets the multiproduct re-quirement for a model with m outputs and without technology control variables: i n n - m m In C = ao + £ on \nY<• + £ ft ln W< + - £ £ ft,- ln y< ln Y3-i i i 3 + \ E E W ^ Wi ln Wi + \ f; £ In Yt In W3- (4-5) i i i j T F P Data used as Cost Model Data TFP analysis preceded cost function analysis in this study. Using some of the data collected for the TFP models reduces the effort involved in developing the input data 13 for the cost models. Specifically, using equation (4-4), output Y was represented by the output index developed in the TFP study (see III) and the factor prices were represented by dividing the total cost of an individual factor by that factor's index. For example, Price of Labor was set equal to total dollars spent on labor divided by the labor quantity index used in the TFP study, this is referred to as a "dual" price index. By using the aggregate output index as input to equation 4-3 rather than using the multiproduct model (4-5) fewer parameters need be estimated but the ability to examine the effects of the individual outputs on the cost function is lost. This was deemed acceptable for the purposes of this work because the sample is limited to firms with a high percentage of revenue coming from LTL operations and because percent of revenue from LTL operations is used as a technology control variable. Modifications of the Translog Cost Function The translog cost function contains many second-order and interaction terms. At sample points far from the mean these second-order terms may dominate the results. This would limit the inference that could be drawn from the first-order terms. As a check on this domination, equation 4-3 was estimated with all the second-order terms set to zero. This reduces 4-3 to the Cobb-Douglas Total Cost Function: ln C = a0 + a 8 2 i 8 2 + ay lnT + /?»ln Wi + 0t log Tt (4-6) i t There appeared to be a strong correlation among the various technology variables. Because of this correlation, the first and second order models were estimated with three, one (average load), and none of these variables included in the model. The three technology variables initially were average load, average shipment size and percent LTL. Because of a suspected correlation between average shipment size and percent LTL, the models are also estimated with average haul replacing average shipment size. With a strong correlation it is possible for the coefficients representing other variables to change drastically in value or even change sign. If this does not occur the model can be said to be robust. Economic Interpretation of the Regression Coefficients First-Order Coefficients. By using a logarithmic functional form, the regression parameters have a direct eco-nomic interpretation. Because the of the logarithmic form and because the total cost 14 and all the regressors have been normalized, the first-order coefficients represent the cost elasticities at the sample arithmetic mean. With respect to input factor prices these elasticities are equivalent to factor shares of total cost. Thus Piabor hi equation 4-3 represents the amount of total cost attributed to labor, ftoutpvt relates total cost to output and gives a measure of returns to scale. If /?outp«* = -85 then a 1% increase in output would increase total costs by .85% . The inverse of this parameter represents returns to scale; RTS = 1/Poutput' If RTS > 1 a firm is said to have positive returns to scale. Second-Order Coefficients. The own-price elasticities and elasticities of substitution are functions involving the second-order coefficients. Own price elasticity, the change in demand of an input due a change in its own price, is; ELASi = Si — 1 + Pa/Si, where S»- is the cost share of input factor t. This value should be negative. A small absolute value of ELASi indicates inelastic demand. The Allen-Uzawa cross elasticities of substitution relate the demands of factor i to factor j. They are represented by; AUELij = (Jij/SiSj + 1 . Positive values of ELASit- indicate substitutes, negative values indicate complements. Dummys Used to Measure Technological Change. The use of a dummy to measure the change between sets of observations implies certain economic assumptions. The principal assumption is that of Hicks neutral technical change which is standard in economic literature. Here a change in technology is assumed not to be biased toward any one factor of production or any particular output. Technical change is assumed to be cost saving and not directed toward any one factor, as would be the case if it were exclusively labor saving, for example. The neoclassical cost model used in this thesis, and explicitly specified with the translog functional form, already incorporates shifts in technology due to changes in input prices, output levels or service characteristics. For example, if fuel prices tripled from one time period to another, the model will indicate how cost will change, including cost changes due to fuel saving technology induced by the price rise. Further analysis could examine whether technological change is factor or output specific. 15 Data Sources Introduction This section discusses the collection of the data used in the study on the effects on productivity of trucking deregulation. These data were principally collected from an-nual reports filed with the U. S. Interstate Commerce Commission. The annual reports include financial, accounting and operating data as requested by the ICC. The reports include data both for the respondent only and for the respondent and affiliated com-panies. In this study the respondent only data were used. These data were received on magnetic tape from the Interstate Commerce Commission. Of the greater than 600 carriers included on the tapes, this study is limited to only those which are common carriers receiving more than 75 percent of their revenue from intercity shipment of general freight, known as 127 carriers. Also, only firms that were in operation for the duration of the study period, 1974 to 1982 were included to allow for the development of the capital stock series. First the data used to develop input indexes will be discussed, followed by data used to develop the output index for the total factor productivity ratio- Finally, the data used as measures of the technology of the trucking industry will be discussed. Input Quantity Indexes The inputs have been separated into five categories: • Labor • Purchased Transportation • Revenue Equipment (trucks, tractors and trailers) • Materials and Expenses (fuel, parts, tires and tubes, other materials and expenses) • Capital other than revenue equipment. For each of these categories both a measure of physical input (e.g. hours, miles etc.) and a measure of cost is needed. Each of the given inputs will be discussed below. The schedule numbers in the annual reports were changed starting with the reports for 1977. Throughout the body of this paper, when referring to a schedule number, the 1977-1982 number will be given as earlier data are only used to develop the investment series. 16 Labor. The annual reports contain various sources of data on labor input. The most descriptive source is schedule 800. This schedule reports the average number of employees as well as the total hours worked and salary or wages received for most of the labor categories listed. Line-haul drivers and helpers are an exception; their measure of input is in miles not dollars. For the purpose of comparison we have assumed a rate of 40 miles per hour for line-haul drivers. This figure was agreed upon after conversations with industry representatives. See Table 5-1 for the labor categories used . Table 5-1 Categories of Labor Labor Category 1 Officers (upper management) 2 Terminal, Department and Division Managers 3 Supervisory and Administrative Personnel 4 Clerical and Administrative Aids 5 Drivers and Helpers; line-haul mileage 6 Drivers and Helpers; other basis 7 Cargo Handlers 8 Vehicle Repair and Service 9 Other Labor In addition this schedule contains two categories for owner-operators. However, such labor input is treated as a separate input category: Purchased Transportation. The number of hours worked by salaried personnel has been computed from the number of working days times eight as schedule 800 lists the input in this category as days. Though these data were collected in the above categories, not all the firms had positive entries for all the categories. The indexing procedure uses natural logs and this requires that each "type" of labor input have nonzero entries. To avoid eliminating many firms the following aggregation was done to create labor types which had nonzero entries for all firms. • Category 1 alone • Category 2 and Category 3 • Category 5 and Category 6 • Categories 4, 7, 8 and 9 together In addition to the compensation found above, the schedules contain a total fringe 17 benefits paid category. This includes payroll taxes, insurance, pensions and other fringe benefits. The total for this category is found on schedule 560. This amount was added into the total labor cost for use in the calculation of Total Factor Productivity. Purchased Transportation. This category includes transportation of goods using other modes of transport (rail, water, air etc.) or other carriers. Also included is the use of owner-operators in the operations of the respondent carrier. The categories are: • Owner-Operator; mileage basis • Owner-Operator; other basis • Purchased Transportation; with driver • Purchased Transportation without driver • Purchased Transportation; other transport modes The data for the owner-operator variables, total miles or hours and total cost were found on schedule 800. The mileage data for the other items were found in the supplemental statistics schedule 720. Because of the variety of contracts between the respondent firm and the lessors, these data can be recorded in many ways. The contract can be for the vehicle complete with a driver on the lessor's payroll in which case the total expense, vehicle and driver, is listed as Purchased Transportation; with driver on schedule 560. The vehicle and driver can be contracted separately (as in the case of owner-operators) in which case the vehicle portion appears in schedule 560 and the labor portion as Owner-Operator; mileage basis or Owner-Operator; other basis (percent of revenue etc.) on schedule 800. For the above categories other than Owner-Operators the total expenses were found on schedule 560. The total hours variable for Owner-Operators; other basis was first multiplied by 40 to conform to the mileage variables used as input quantities for the other items. This input category suffered from poor reporting to the ICC on the part of the reporting firms. Frequently only the dollar amount spent was recorded with no corresponding mileage or hours. Consolidation of categories did not eliminate this problem. To avoid eliminating this input category input quantities for the non-reporting firms were taken as the average (weighted by total cost) of the reporting firms for a given year. Where data were available for one of the two years the above average was adjusted by the 18 ratio of reporting year index divided by reporting year average index. Though this is a crude assumption the finding that the mean percent of total cost due to Purchased Transportation was only 6% kept the impact of this averaging low. Materials and.Expenses. This category is divided into four sub-groups: • fuel • tires and tubes • parts • other materials and expenses. With each of these categories the total dollar amounts spent on each for the year is used. The input quantity is derived by dividing this dollar figure by the price index for the category (fuel, tires, parts, materials) found in the Bureau of Labor Statistics price indexes. Table 5-2 contains the various price indexes. Table 5-2 Price Indexes YEAR PRICE INDICIES Struct Durables Motor Fuel Tires Vehicles & Tubes 1970 88.2 110.4 108.7 101.0 109.0 1971 99.0 114.0 112.2 110.2 109.8 1972 110.0 119.1 115.7 119.5 110.6 1973 121.0 134.7 119.2 128.7 111.4 1974 132.0 160.1 129.2 223.4 133.4 1975 144.8 174.9 144.6 257.5 148.5 1976 149.0 183.0 153.8 276.6 161.5 1977 159.4 194.2 163.7 308.2 169.6 1978 176.4 209.3 176.0 321.0 179.2 1979 200.2 235.6 190.5 444.8 205.9 1980 227.4 268.8 208.8 674.7 236.9 1981 254.2 293.4 237.6 805.9 250.6 1982 265.8 299.3 251.3 761.2 255.2 source: BLS Producers Price Indexes, Table No. 803 19 Revenue Equipment Owned. Revenue equipment includes: • trucks • tractors • semitrailers • trailers. This category is a capital input therefore some method of accounting for the use of a capital resource must be used. The schedules found in the annual report contain some of the needed data, however as was discussed in III the capital cost data found in the reports is more faithful to accounting conventions than to a true measure of capital input. The costs of capital goods are calculated using the method proposed by Christensen and Jorgenson (1969). In this method first a capital investment series is computed using equation 3-6: Kt = (l — n)Kt-i + It with all amounts in real dollars. Kt is the capital stock in year t and It is new investment in year t, (i, the rate of physical depreciation, is 2 divided by the service life of the capital good being considered. These capital stock amounts are then multiplied by a service price to derive the implicit rent for each category in each year. Section III discusses both the development of the capital stock series and the service prices of capital for the given capital categories in each year. In order to use equation 3-6 a starting value or benchmark is needed for each series as well as a series of new investments in each year. Both of these must be expressed in real dollars. Schedule 740 lists number on hand and the dollar amounts for the types of equipment mentioned above. This schedule lists the numbers on hand at both the beginning and end of the year and the number of each type purchased during the year as well as the book values and amount spent on new aquisitions. The book value, expressed in real dollars, of each type of equipment for the year 1973 was used as the benchmark for the capital stock series. By starting with a benchmark 5 years before the first year of the analysis it is hoped that the inaccuracy of using accounting data for econometric purposes will have been attenuated. The new investment, /, in 3-1 was represented by the dollar amounts of new investment listed in schedule 740, again expressed in real dollars. Table 5-3 lists the tax rates used for the service price formulae in m. 20 Table 5-3 Tax Rates YEAR INTRST PRPRTY INCOME INVEST RATE TAX TAX TAX RATE RATE CREDIT 1970 .0940 .0208 .4495 .0174 1971 .0876 .0212 .4524 .0310 1972 .0823 .0210 .4635 .0501 1973 .0824 .0207 .5182 .0525 1974 .0948 .0205 .5876 .0532 1975 .1055 .0190 .4228 .0845 1976 .0982 .0184 .5112 .1046 1977 .0887 .0182 .5078 .1009 1978 .0960 .0182 .4800 .1000 1979 .1029 .0182 .4800 .1000 1980 .1267 .0182 .4800 .1000 1981 .1617 .0182 .4800 .1000 1982 .1680 .0182 .4800 .1000 source: Tretheway and Windle (1983) extended to include 1982 rates after conversation with Carl Degen of Christensen Associates Capital. The annual reports list the amount in current dollars spent in new capital equipment and the book value. The same method is used to derive the capital investment series here as was used for Revenue Equipment. Two series were computed for this input category: • Structures • Other Capital Equipment. In the case of structures the assumption that the firms hold capital goods for their entire useful life was relaxed. For this series structures sold was subtracted from structures purchased in the J term in 3-1. Land, which constitutes approximately 5% of non-revenue equipment capital, was not included because of the lack of a Land Price Index. Output Quantity Index This thesis is concerned with two categories of output; ton-miles of less than truckload (LTL) intercity freight and ton-miles of Truckload intercity freight. As was stated in 21 in the introduction, the sample has been limited to firms with at least 75% of their total revenue from intercity transport of general freight. In actuality the average firm in this sample receives approximately 95% of its total revenue from intercity operations. Because the sample has been limited to this set of firms, more data are available than would be if a wider class of reporting firms was used. The 127 carriers must file schedule 720. This schedule contains information on; Total Tons, Revenue, and Number of Shipments all divided into Truckload and LTL operations. In addition this schedule contains listings for total Ton-miles. This statistic, Ton-miles, is the measure of physical output needed for this analysis. Unfortunately, the Ton-miles entries are not sub-divided into Truckload and LTL operations. This made it necessary to estimate the division of Ton-miles into that from Truckload and that from LTL. This estimate was made by multiplying the Ton-miles listed by the percentage each firm listed for total tons of Truckload or LTL. The assumption here is that the average haul is the same for Truckload and LTL operations, an assumption deemed reasonable by industry representatives. To examine the effect of this assumption, percent of revenue from LTL operations was introduced as a technology variable in the models using such control variables. Technology Variables The translog functional form allows the introduction of control variables to measure the effect of differences in operation among the sample firms. The initial full models discussed in section IV contain three such variables; average load, average shipment size, and percent of revenue from less than truckload (LTL) operations. Later models drop average shipment size and add average haul. Average shipment size and percent LTL may measure the same effect, thus having both in the model could make neither appear significant. Average shipment size is dropped because percent LTL is desired for reasons mentioned in IV. The importance of these variables was discussed in section II. The data to calculate these measures are all available in schedule 720. The values of these variables used are listed in Appendix B. 22 VI Generalized Least-Squares and Zellner Iteration Multiple Equations for Cost Estimation Section (IV) states that the cost equation (4-3) is estimated together with the input share equations (4-4), with one of the share equations deleted to avoid singularity. The share equations are included because the form of these equations is known from Shep-hard's Lemma and their dependent variables, input factor shares, can be observed. By estimating the system of equations together we are better able to extract any infor-mation contained in the data. However, the relationship among the equations requires a generalization of the least-squares method to handle the fact that the disturbance terms for the cost equation and its share equations may have non-zero correlations for any one firm in a given year. The generalized least-squares method and the correlations among equations will be discussed below. Introduction to Generalized Least-Squares. As was stated in section (TV) describing the cost function model, estimating the cost function together with the factor share equations allows for an estimation method that can be asymptotically more efficient than ordinary least squares. This method is designed for models where there may be some relationship among the equations. Specifically, for any one firm in any given year the set of cost and share equations contain some of the same coefficients and variables and may have correlated disturbances. A more efficient estimation procedure allows more of the information contained in the data to be used in the model and less allotted to the error terms. This permits statistical inference with tighter confidence. The following description follows Johnston (1972) and Zellner(1962). The ordinary least-squares model: y = X £ + u (6-1) has a variance-covariance structure represented by the second order expectation: £(uu<) = CT21 (6-2) where y and u are vectors of length n and X and I are n by n matrices. Equation 6-2 corresponds to the assumptions that the disturbance term has constant variance and 23 is not autocorrelated. For the ordinary least squares model, equation (6-3): POLS = ( X t X ) _ 1 X t y (6-3) provides a minimum variance unbiased estimator for p. Here the superscript t indicates the transpose of the matrix. Generalized least-squares retains the assumption that E(u) = 0 but relaxes equation 6-2 to: E{aut)=a3n (6-4) where a2 is unknown but ft is a known positive definite matrix of order ra. Equation 6-4 can also be written as S = 2?(uu*) = V . Here V is assumed to be a known, symmetric, positive- definite matrix. For the generalized least squares model equation 6-3 is no longer a minimum variance linear unbiased estimator. A generalization of equation 6-3 with these properties is: PGLS = (x tn-1x) ^ n ^ y (6-5) Grouping the Cost and Factor Share Equations Let us group the cost equation with m — 1 factor share equations then Zellner shows that estimating the group of equations: y<=X<ft+u, i = l , . . . , m (6-6) will be asymptotically more efficient than estimating each of the m equations in turn using ordinary least-squares. The vectors y and u in 6-6 are of length ra, the matrix, X is ra by p, and P is p by 1. A set of cost and share equations could be written as in (6-7). For readability the equations have only two inputs, L and K, and no technology or dummy variables. r C i ShL1 ShK1 Cn ShLn ShKn j = [A] a PY PL VK PYY PLL PLK PYL PYK* + (6-7) 24 where A = •1 Yi Lx Kx LLX KKx LKx YLx YKX 0 0 1 0 0 Lx 0 Kx Yx 0 0 0 0 1 0 0 Ki Lx 0 n 1 Yn L n Kn YYn LLn KKn LKn YLn YKn 0 0 1 0 0 L n 0 Kn Yn 0 .0 0 0 1 0 0 if* L n 0 A is an 3n by p matrix, where p is the number of parameters. In this model there are cross equation restrictions on the parameters. The same pa-rameter, /?£,, appears in both the cost and labor share equations. In addition, there are restrictions on the parameters due to homogeneity of degree one in input prices. Some of the equations (in this case, the share equations) have identical regressors, although a given regressor will have different a coefficient in each equation. How the model in (TV) fits this model will be discussed below. Equation (6-7) can be rearranged as follows: where ' Cx • " a ' ~uCx' '. PY cn PL SHLX PK = [B] PYY + " ShLn PKK PLK UK I PYL • -ShKn. IPYKI 1 Yx Lx Kx YYX LLt KKX LKt YLx YKx 1 Yn L n Kn YYn LLn KKn LKn YLn YKn 0 0 1 0 0 Lx 0 Kx Yx 0 B 0 0 1 0 0 0 0 0 1 0 L n 0 0 Kx K Lx n Yn .0 0 0 1 0 0 Kn L n 0 0 0 Yx Yn J 25 The variance-covariance matrix for the disturbance term, u, is: E{xm*) = E = £(u cu* c) E { u a u * L ) E ( u c u K ) E{vLL-a*a) E{uLu*L) E { u L u K ) EiuKii*,) EixiKul) E { u K U K ) (6-8) The dimensionality of the above matrix is 3n by 3n as there are ra observations of each of m equations, where m = 3 in this example. It is assumed that the terms in 6-8 have the following form: E(mvi}) = a,* (i,j = C , L , K ) (6-9) Here each vector u» of length n, corresponds to the n disturbances from one of the m = 3 equations. Note that in 6-9, o~i3- can be different for each ij pair. With i = j in 6-9 the assumption states that u in any one set of equations is homoscedastic and non-autocorrelated. With i ^ j the assumption 6-9 states that there is a non-zero correlation between the disturbances corresponding to a given firm in a given period but zero correlations among all disturbances relating different firms or time periods. This variance-covaxiance matrix fits the generalized least squares model. If we compare (6-7) to the cost equation (4-3) and the share equations (4-4) together with the homogeneity restrictions we find for the simplified case as in (6-7): InC = <X + PY InY + 0L]nWL + p K l n W K + i /? y r ( lnY) 2 + \ p L L ( l n L ) 2 + ± p K K ( l n K ) 2 PLK In WL ln WK + p Y L ln Y ln WL + p Y K ln Y + p Y K l n Y l n K and the share equation for labor is: S h L = p L + p L L \ n W L + p L K \ n W K + p Y L l n Y As stated above there are restrictions on the parameters in this model. The homogene-ity restrictions require PL + PK = 1 , PLK = PKL , PLK + PLL = 0 , PLK + PKK = 0 and PYL + PYK — 0. These restrictions would involve more parameters in models with five share equations, as in (IV), rather than the two presented here. A further observation is that the sum of the share equations is one. Because of this, to estimate this system of equations one of the share equations is dropped. The following implications to the share and cost equations are implied (6-9). Each submatrix is allowed to have a different a^. This states that each group of equations 26 (eg. cost) can have a different variance and that the the terms representing the rela-tionship of one set of equations to another can also have individual values of a. It is reasonable to expect the variance for the cost equations to be different from those of any of the share equations. When i equals j the Labor share, Capital share or Cost equations taken alone are assumed homoscedastic and non-autocorrelated. As there are over 100 firms but only two years, the non-autocorrelation assumption seems rea-sonable. The assumption of homoscedasicity also is acceptable since larger firms would not have larger shares of input factors and the cost equations involve the log of cost which would tend to minimize any large firm effect. With » not equal to / , (6-9) implies that for a given firm in a given year the disturbance terms in the cost and share equations may be correlated. As the inputs are either substitutes or complements it can very well be that a firm overspending on one input may over- or underspend on another input. Also the share and cost equations are related. For example, a firm overspending on labor, which is about 60% of total cost, will almost certainly have higher costs overall. Zeros in the off-diagonal terms in (6-9) with i unequal to j imply that there is not a correlation among different firms or years. Estimating the parameters 6-8 and 6-9 yield the variance-covariance matrix when the number of different equa-tions is expanded to m: E = < 7 n <7i2 ... (Jim 0 2 1 0 2 2 ••• 0 2 m <g> I = E c ® I (6-10) . 0 m l 0 m l • • • 0 m m J where ® indicates Kronecker multiplication of matrices. The inverse of 6-10 is: E _ 1 = E ; 1 ® I (6-11) The application of Aitkens generalized least-squares to 6-7 yields the best linear unbi-ased estimator: b = ( X ' E ^ X ^ X ' E - V (6-12) As E is unknown, 6-12 can not be used directly to estimate 6-7. Zellner proposed using ordinary least-squares to estimate each of the m equations in turn and using the residuals of this estimation to estimate the a»y in 6-10. This estimation procedure is 27 viable as while ordinary least squares is not efficient it is a consistent estimator for b and hence u. The results of the first stage, A = pQXi)"lXjy< (6-13) allow an to be estimated by: < B.(yi - x A ) W x < A ) ( 6_ 1 4 ) (n - ki) and Oij to be estimated by: ( y ^ x ^ y ^ - x ^ 3 {n-ki)1/2{n-k3)l/2 K } These estimates are then substituted for E„ in 6-11, and 6-12 can then be used. Zellner (1962) contains a proof of the gain in efficiency provided by this method. 28 VII Results of TFP and Cost Function Analysis The results of the Total Factor Productivity and Cost Function Analysis will be ex-amined in turn. A rather brief examination of the results of the TFP analysis will be followed by a more extensive examination of the results of the cost function regressions. TFP Results The total factor productivity was calculated for the entire sample and for 1978 and 1982 separately. Before the comparison of the two years is made it is useful to observe the relative factor shares of the five input categories. Table 7-1 lists these data: TABLE 7-1 Input Factor Shares Input Factor Shares Mean Std Dev Minimum Maximum Labor 0.60 0.07 0.35 0.74 Expenses 0.23 0.03 0.15 0.42 Rev. Equ. 0.08 0.04 5.81D-04 0.23 Pur. Iran. 0.06 0.06 0.00 0.36 Capital 0.03 0.03 6.12D-03 0.20 From Table 7-1 it is easy to see that labor is the largest single input factor, comprising 60% of total input. The next largest input factor is annual expenses. This category contains fuel, parts, tires and tubes as well as other non-capital expenses. Capital, Revenue Equipment and Purchased Transportation make up much smaller percents of total input for the mean firm, though there exist firms using a significant amount of each of these inputs. Table 7-2 and 7-3 present means, weighted by total cost, and deviations for the Total Factor Productivity (TFP) , the output index and the five input indexes. 1978 indexes are presented in Table 7-2 and 1982 indexes in Table 7-3. 29 TABLE 7-2 TFP, Output, and Input Quantity Indexes for 1978 Mean Std Dev Minimum Maximum TFP 1.62 0.58 0.30 3.46 Output Index 19.55 20.28 0.13 57.80 Tot Inp Index 8.37 7.95 0.10 24.22 Labor Index 10.99 4.77 0.07 32.93 RevEq Index 14.13 12.93 0.03 40.80 Expense Index 9.30 8.86 0.15 25.53 PurTran Index 2.84 0.78 0.39 5.44 Capital Index 8.40 8.61 0.05 23.93 TABLE 7-3 TFP, Output, and Input Quantity Indexes for 1982 Mean Std Dev Minimum Maximum TFP 1.43 0.49 0.25 5.60 Output Index 19.11 19.66 0.10 54.00 Tot Inp Index 9.19 8.36 0.04 23.33 Labor Index 10.16 9.19 0.01 26.89 RevEq Index 17.53 17.52 0.01 52.53 Expense Index 13.56 12.50 0.04 35.20 PurTran Index 2.87 0.69 0.36 3.89 Capital Index 26.08 27.05 0.17 75.75 TABLE 7-4 Ratio of Index Means, 1982/1978 INDEX Mean Ratio TFP 0.88 Output Index 0.98 Tot Inp Index 1.10 Labor Index 0.92 RevEq Index 1.24 Expense Index 1.46 PurTran Index 1.01 Capital Index 3.11 Table 7-4 shows that the TFP index fell by about 12% for the mean firm between 1978 and 1982. This drop was a broad effect, not only did the TFP index fall for the mean 30 firm but out of 116 firms with enough data to calculate the measure, the TFP index fell in 89, rose for only 23 and was unchanged in 4. This change in the TFP index is a result of a 10% rise in total inputs while total output dropped slightly. The large change in the capital (other than revenue equipment) index, can be explained by a large increase in the service prices for capital from 1978 to 1982. These were: Capital Service Price Structures Other 1978 .1305 .2595 1982 .3241 .5474 Most of this increase can be attributed to an increase in the corporate interest rate from .0960 in 1978 to .1680 in 1982. Section III gave the equation used to calculate the service price of capital. The results of the next analysis are critical to the interpretation of the above Total Factor Productivity results. Because one of the assumptions of TFP analysis is constant returns to scale, to draw any valid conclusions from the above change in the TFP index the cost function analysis must indicate an absence of scale economies. In the presence of scale economies, change in TFP is not a measure only of change in efficiency or productivity. With economies (or diseconomies) of scale, TFP is affected by both changes in efficiency and returns to scale. Initial Cost Function Results The total cost function for the U . S. trucking industry was estimated using the six models described in IV and the prices for the five input categories and output index discussed above, together with three measures of technology; average load, average shipment size and percent of revenue from less-than-truckload operations. The im-portance of these technology variables was discussed in TJ. The number of parameters being estimated in these models varies widely from only 7 in the first order model with no technology variables to 46 in the full second order model with all three technology variables. Table 7-5 presents the first order coefficients of the six models. The complete regression results for all six models are contained in Appendix A. These models are: 31 Model [1] Second Order Model with no Technology Variables. Model [2] First Order Model with no Technology Variables. Model [3] First Order Model with three Technology Variables. Model [4] Second Order Model with three Technology Variables. Model [5] First Order Model with Average Load and Second Order Terms for Output Average Load and their cross-product. Model [6] Second Order Model with only one technology variable; Average Load. T A B L E 7-5 First-Order Coefficients of Cost Functions Standard Errors in Parentheses Initial Six Models (1) (2) (3) (4) (5) (6) Output .767 .740 .828 .837 .850 .843 (.017) (.019) (.017) (.021) (.020) (.021) Labor .592 .594 .591 .593 .591 .593 (.004) (.004) (.004) (.004) (.004) (.004) Revenue .0836 .0838 .0840 .0842 .0840 .0841 Equipment (.002) (.002) (.002) (.002) (.002) (.002) Expenses .226 .227 .227 .227 .227 .227 (.002) (.002) (.002) (002) (.002) (.002) Purchased .0629 .0606 .0629 .0610 .0630 .0607 Transport (.004) (.003) (.004) (.003) (.004) (.003) Capital .0349 .0349 .0347 .034 .035 .035 (.002) (.002) (.002) (.002) (.002) (.002) Average — — -.636 -.682 -.821 -.824 Load — — (.077) (.105) (.094) (.098) Average — — -.019 -.027 — — Shipment — — (.053) (.089) — — Percent — — -.086 .264 — — LTL — - (.164) (.284) — — Dummy .0654 .0611 -.005 -.015 -.015 .021 for 1982 (.047) (.044) (.046) (.044) (.042) (.040) 32 Interpretation of Regression Coefficients Because all the regressors and total cost are expressed as logarithms and have been normalized, the first-order coefficients have a direct economic interpretation: they are the cost elasticities taken at the sample mean. The input factor elasticities indicate how much of total cost is attributable to the given input. Here we see that Labor makes up almost 60% of total costs and Expenses (fuel, tires and tubes, parts etc.) make up approximately another 27%. As can be seen from the standard errors, all of these were found to be statistically highly significant. These share values correspond to those presented in Table 7-1, the shares found in TFP. The share values also correspond with the cost study of Friedlander, Spady and Wang Chaing (1981) for labor and purchased transportation. Their research defines the other inputs differently, therefore their percentages would be expected to be different. This paper will be referred to as F,S and WC for the rest of this section. The relationship between total cost and output is an important one, the regression coefficient indicates by what percent total costs increase for a 1% increase in output. A value of 1 for this regression coefficient indicates constant returns to scale, a value greater than 1 indicates negative returns to scale as a value less than one indicates positive returns. In the models with no technology variables the coefficient for output is approximately 0.75 and significantly different from unity, indicating strong returns to scale. In the models including one or more technology variables this value is approx-imately 0.84, still indicating strong but less extreme returns to scale. In all models this value is highly significant leading to the rejection of the hypothesis of constant returns to scale. In the models including technology variables, the only one found to be significantly nonzero was average load. This coefficient being negative indicates as average load increases while holding ton-miles constant, costs decrease, which is to be expected. For a 1% increase in average load costs decrease by between 0.64 and 0.82% depending on which model is being used. In the models including average load the returns to scale, as found above, appear less dramatic. This follows the assumption that larger firms also were able to maintain higher load factors. The effect of average shipment size is in the direction expected, costs decrease with an increase in average shipment size, however this statistic was not significantly nonzero. It may be that as most of the firms in this sample had a very large percentage of LTL business consolidating a load from 20 shipments is not noticeably more costly than consolidating from 10 shipments. The 33 coefficient of LTL percentage itself changes sign between the two models containing it and in neither model is it significantly nonzero. Average shipment size and percent LTL are related measures. As a firm increases its percent of revenue from LTL operations it would be expected that more shipments were required to make up the average load. Below one of these technology variables, average shipment size, will be dropped in later models to test whether LTL percent becomes significant. Percent LTL was chosen to remain in the model because it was desired for the single output form as stated in (IV). The dummy for the difference between 1982 and 1978 is always quite small, changes sign depending on what other variables are included in the model, and is not found to be significantly nonzero in any of these initial six models. Comparing the models Before the analysis involving second order terms can be done it is necessary to decide which of the six models to use for estimating the total cost of the U. S. trucking industry. The test statistic used to compare model i with model j is: 2(ln(Likelihood)i - ^ (Likelihood)}) = Test (7 - 1) which is compared to the x2 statistic for the desired confidence level and (Parameters)i — (Parameters), degrees of freedom. If Test is greater than the x2 value, then the hypothesis that all of the terms set to zero in the second model are indeed zero is rejected. A comparison of the likelihood functions vs. the number of regression coefficients to be estimated is made. The log of the likelihood functions for the six models appears in table 7-6. TABLE 7-6 Log of Likelihood Function Model Log of likelihood No. of Parameters Full 3 Tech 1811.09 46 Full 1 Tech 1791.31 29 Full Model Simple 1777.03 22 1st Order /w TY Cross 1660.01 11 1st Order 3 Tech 1653.55 10 1st Order Simple 1643.53 7 34 Making these comparisons for the six models above, in no case does the reduction in degrees of freedom offset the drop in log of likelihood therefore the largest model is used for the rest of this analysis. For example, comparing the full model with three technology variables against the model with only average load as a technology variable the comparison is: 2(1811.09 - 1791.31) = 39.56 > 27.59 = x29s,i7 The results of these comparisons are: TABLE 7-7 Comparisons to Full Model Alternative Change in D.F. Test Stat. Chi Squared Full 1 Tech 17 39.56 27.59 Full Model Simple 24 68.12 36.41 1st Order w/ YT cross 35 302.16 49.80 1st Order 3 Tech 36 315.08 51.00 1st Order Simple 39 335.12 54.57 The full second-order model with three technology variables will be used for the rest of this section. Second Order Elasticities As was mentioned in IV, the own-price elasticities and the Allen-Uzawa elasticities of substitution involve the second-order coefficients. Table 7-8 contains estimates of these own-price and Allen-Uzawa elasticities computed at the sample mean: 35 TABLE 7-8 Own-Price and Allen-Uzawa Elasticities Right-Hand Estimated Standard T-Variables Coefficient Error Statistic Own Price Elasticities Labor -.371811 .140659E-01 -26.4334 Revenue Equipment -.645020 .671539E-01 -9.60509 Expenses -.568242 .276512 -2.05504 Purchased Transport -.410636 .385944E-01 -10.6398 Elasticities of Substitution Labor - Revenue Equipment .833268 .953431E-01 8.73967 Labor - Expenses .963934 .409247E-01 23.5539 Labor - Purchased Transport .348396 .779181E-01 4.47131 Revenue Equip - Expenses .529197 .299463 1.76715 Revenue Equip - Pur Tran -.549605 .320952 -1.71242 Expenses - Pur Tran .868223 .119434 7.26951 All of the own-price elasticities have the expected sign, are significantly nonzero, and indicate a strong degree of elasticity. The Allen-Uzawa cross elasticities indicate that for all combinations other than Revenue Equipment-Purchased Transportation the input factors are substitutes. The sign of the cross elasticity of Revenue Equipment versus Purchased Transportation is not expected but is not highly significant with respect to the standard error. The elasticities for capital were not included because capital makes up a very small percentage of input. Comparing the elasticity results discussed above with those F,S and WC obtained for interregional carriers we find similar results for all the own-price elasticities and for all elasticities of substitution except those involving purchased transportation. They do not find labor-purchased transportation to be significantly non-zero, where Table 7-8 reports this to be significant. They find the cross-price elasticity of purchased transportation with revenue equipment (in their model; Capital) to be positive and significantly non-zero. Table 7-8 shows this elasticity to be negative and insignificant. As purchased transportation was a missing data problem in this work and that the results here are different from expectations and previous work, inferences involving purchased transportation will be suspect. 36 Effect of the Second-order Terms It is possible with a model such as the full model ([4] in Table 7-5) with many second-order and cross-product terms for the first-order effects to be dominated by the second-order terms. This effect is especially a problem at samples far from the sample mean. By estimating the cost model with the second-order terms set to zero and observing the change in the first-order coefficients the robustness of the first-order terms can be assessed. This restricted model is model [4]. Table 7-5, column (3) and (4) contain the first-order terms for the restricted and full model, respectively. The terms for Output and the input factors have almost no change and are all highly significant. The coefficient for average load increases slightly in ab-solute value and is significant. The terms for Average Shipment Size, Percent LTL, and the 1982 dummy are all statistically insignificant in both the restricted and unre-stricted model. Thus the model can be said to be robust with regard to a substantial simplification ( The elimination of 36 parameters). Results Adding Average Haul to Model. Previous work has found that the inclusion of average haul in cost models decreases or eliminates any returns to scale in the trucking industry. Because of these earlier results, model [4] (three technology variables) was changed to include average haul and drop average shipment size. It was decided to drop one of the other technology variables rather than just to add average haul in order not to increase the already large number of parameters to be estimated by 11. Average shipment size was dropped because it was not found to be significantly non-zero in either model in which it was included and because its effect may be adequately represented by percent LTL. As was stated above, it is assumed that as the percent of business that is LTL increases so would the number of shipments needed to make up a load. Table 7-9 includes the first order terms from model [4] and: Model [7]. Model [4] with average haul replacing average shipment size Model [8], Model [7] with all average haul coefficients restricted to zero Model [9], Model [7] with six outlier observations removed from the sample Model [9] will be discussed below. A comparison of model [7] (with average haul) to model [4] (with average shipment 37 size) should find that if average haul is significantly non-zero it will also be a better predictor of costs in the trucking industry. This is found to be the case. Models [4] and [7] have the same sample size and the same number of regressors therefore an increase in the log-likelihood function (from 1811 to 1855) indicates a better model. A second result of the change in technology variables is that percent LTL becomes sig-nificant and positive. This indicates that costs increase as more of the business is made up of LTL operations. Since truckload operations require less terminal consolidation, this result is as expected. In earlier models ( [3] and [4]) this effect was spread across two technology variables, average load and percent LTL, causing neither to appear significantly non-zero. 38 T A B L E 7-9 First-Order Coefficients of Cost Functions Standard Errors in Parentheses Models 4, 7, 8, and 9 (4) (7) (8) (9) Output .837 .950 .835 .951 (.021) (.035) (.020) (.017) Labor .593 .593 .593 .596 (.004) (.004) (.038) (.004) Revenue .0842 .084 .084 .084 Equipment (.002) (.002) (.002) (.002) Expenses .227 .227 .227 .227 (.002) (.002) (.002) (002) Purchased .0610 .061 .061 .058 Transport (.003) (.002) (.003) (.003) Capital .034 .035 — .035 (.002) (.002) — (.002) Average -.682 -.164 -.691 -.137 Load (.105) (.121) (.103) (.091) Average — -.486 — -.503 Haul — (.060) — (.044) Percent .264 .480 .347 .534 LTL (.284) (.140) (158) (.101) Dummy -.015 .068 -.020 .101 for 1982 (.0434) (.039) (.042) (.029) Model [8] tests the hypothesis that all the terms corresponding to average haul are zero by restricting all of these terms to be zero. To compare these models and test the hypothesis the log-likelihood test is again used. Twice the difference in log-likelihood is compared to the appropriate Chi squared statistic. 2(// 7-// 8)=96 > X?.95,0) = 16.9 From this result the null hypothesis is rejected indicating at least one of the average haul terms is non-zero. In model [7] the coefficient representing output is .95 and is significantly non-zero. This indicates that the inclusion of average haul decreases observed economies of scale but 39 that these economies are still present. F,S and WC find a coefficient of -.38 for average haul (compared to -.49 in model [7]) and an output coefficient of .90 in their model of interregional carriers. However their models of Northeastern and regional carriers find -.51 and -.62 for the average haul parameter and 1.09 and 1.07 for the output coefficient. Thus they find a stronger effect of average haul for regional carriers and that only interregional carriers have positive returns to scale. The results of model [7] agree with their findings of returns to scale for interregional carriers, but the model [7] result for average haul falls between their interregional and regional result. This may be an outcome of the sample in this study including both interregional and regional firms. In model [7] the dummy for 1982 becomes positive indicating greater costs in 1982 but this coefficient is not significantly non-zero. The elasticities calculated from this model are not noticeably different from those from model [4]. Checking Models for Normality and Fit As a check on the appropriateness of the models, the actual versus fitted values of the dependent variables of the cost and share equations for model [7] were plotted. These plots indicated that in general the fitted and actual values were were quite close but occasionally these two values were quite far apart, causing some concern about, the normality of the residuals. To check the normality, normal quantile (Q-Q) plots were obtained of the residuals of the cost, labor share and revenue share equations. Normally distributed residuals should yield a normal bell-shaped histogram and a linear Q-Q plot. Appendix C contains the histogram and Q-Q plot of the cost equation residuals. The residuals to the input share equations for the two largest inputs (labor and revenue equipment) looked normal but the plot of the cost equation residuals indicated more observations in the tail farthest from zero than expected for a normal distribution. In an attempt to get the Q-Q plot to reflect a distribution closer to normal, the farthest outliers were removed recursively. After removing 5 outliers from the large values and one from the small values the Q-Q plot appeared normal (see the second set of histograms and Q-Q plots in Appendix C). Model [9] represents model [7] with these six observations producing the outliers removed. The six removed observations were then examined to see if there was any reason to suspect their validity. All six observations had total costs at most one fifth of average but there are many other firms that are also this much smaller than average. Five of the observations had a price of labor between 3 and 7 times that of the average 40 price of labor, and thus their data were suspect. Looking at the individual firms the following was found. Budig Trucking appeared twice, once for 1978 and again its 1982 observation. This firm was reclassified by the ICC and is no longer a 127 carrier. Crouse Cartage, Fareway Express and Motor Cargo are all smaller firms with a large percent of their business devoted to interline haulage, shipping either from or to another operator. This may have affected the manner in which they reported their operating statistics. These firms also were heavily involved in leasing, a practice known to alter operating statistics. The last carrier, R.M. Sullivan, had no noticeable peculiarities. As all but one of these outliers is indeed explainable, the six observations were dropped because of questionable data. Model [9] becomes the preferred model. Most of the first-order coefficients in model [9] are about the same as in model [7] and the significance of these coefficients did not change. The elasticities calculated from model [9] are also similar to those of the earlier models. The major change between model [7] and [9] is the dummy for 1982. In model [9] this coefficient is positive, has increased in magnitude, and has become significant ( t statistic = 3.5). As was stated above, a positive value for this coefficient is contrary to what was expected for deregulation in general. However some writers in the transport field thought that ease of entry, one of the outcomes of deregulation, would decrease the average utilization of revenue equipment, adversely affecting productivity. 41 v m Conclusions Total Factor Productivity analysis indicated a 12% drop in the TFP index. However, cost function analysis showed that the U. S. trucking industry exhibits significant re-turns to scale ( R T S = 1.06, in the preferred model, model [9]). This finding of other than constant returns to scale violates one of the assumptions implicit to TFP analysis. Because of this, valid conclusions cannot be drawn from the TFP results. Cost function analysis allows the effects combined in the TFP index to be sorted out. With the returns to scale being indicated by the output coefficient, the 1982 dummy reports the effect of changes in efficiency between the two years. In the full model with average haul and all observations this value is negative indicating costs fell in 1982, however this value is small and insignificant. In some other models it is positive. In the preferred model ( model [9]) this value is positive and significantly non-zero. This indicates increased costs in 1982, holding other variables constant. Even though the assumptions df TFP are not found to be valid, the TFP results do agree with this cost function result. The models produce values for the technology variables that are consistent with earlier work and with a priori expectations. As firms are able to carry a load farther costs decrease (an average haul coefficient about -.5). As the amount being hauled increases, costs per ton-mile decrease (average load coefficient about -.14). However, this result is not nearly as strong as found by F,S and WC. They find the average load coefficient ranging between -.28 and -.57. Also as the amount of total revenue that is derived from LTL operations increase so do costs (percent LTL coefficient about .5). This result differs from F,S and WC but, as was reported above, this coefficient is affected when average shipment size is also a technology variable in the model, as is the case with F,S and WC. In the model where six large residual producing observations were dropped the coeffi-cient for the 1982 dummy is positive and becomes significantly non-zero. Johnson and Wichern (1982, p.315) state that when the number of observations is large minor de-viations from normality will not greatly affect inferences about the model parameters. The elimination of these six observations did affect one of the important coefficients in the model leading to the conclusion that these deviations are not minor. In most industries the finding of a positive value for a deregulation dummy would not be expected, though some writers did expect it in the transport industry. They felt 42 that in the short run ease of entry would create a surplus of capacity. The effect of deregulation is thought to either reduce costs or to have no effect. The effect of normal technological change also generally implies a negative value for this dummy. Other studies have found an increase in costs from one year to the next when the later years are part of an economic downturn (see, for example: Caves, Christensen and Tretheway, 1983). 1982 was the bottom of an economic cycle while 1978 was near the peak of that cycle. In a down year, firms may be reluctant to lay-off workers or to sell under-used equipment. This reluctance would have a negative effect on productivity in that inputs to production would not be fully used to produce output. The translog cost model may fail to reflect this effect. This analysis still does not indicate the effect of deregulation. The 1982 dummy includes both the deregulation effect and the effect of, so called normal, technological change (for example: more fuel efficient vehicles). It is possible for the dummy to have been affected in one direction by deregulation and in the other by technological change. It will be necessary to expand the time horizon of the model to include more years of data to solve this problem. By expanding the time horizon the effect of normal technological change could be observed over a longer period. The inclusion of complete economic cycles would permit the observation of the trucking industry in previous years near the bottom of an economic cycle. With this information the dummy for 1982 could possibly be broken down into a technological improvement effect, economic cycle effect and the effect of deregulation. 43 Bibliography [I] Button K., and Chow G.,"Road Haulage Regulation: a Comparison of the Canadian, British and American Approaches." Transport Reviews, Vol 3 No. 3 (July-Sep 1983), pp. 237-264. [2] Caves D.W., Christensen L.R., And Diewert W.E. "Multilateral Comparisons of Out-put, Input, and Productivity Using Superlative Index Numbers." The Economic Jour-nal, Vol. 92 (March 1982), pp. 73-86. [3] , , Swanson J.A. And Tretheway M.W. "Economic Performance of U. S. and Canadian Railroads: The Significance of Ownership and the Regulatory Environment." in W. T. Stanbury and F. Thompson, eds., Managing Public Enterprises, Montreal: Praeger, 1982. [4] , , and Tretheway M. W., "Flexible Cost Functions for Multiproduct Firms." The Review of Economics and Statistics, Vol. 62 (August, 1980), pp. 477-81. [5] , ,and , "U. S. Trunk Air Carriers, 1972-1977: A Multilateral Com-parison of Total Factor Productivity." in T. Cowing and R. Stevenson, eds., Produc-tivity Measurement in Regulated Industries, New York: Academic Press, 1981. [6] , , and , "Productivity Performance of U. S. Trunk and Local Service Airlines in the Era of Deregulation." Economic Inquiry, Vol. 21 (July 1983), pp 312-324. [7] , , And , "Economies of Density versus Economies of Scale: Why Trunk and Local Service Airline Costs Differ." Hand Journal of Economics, Vol. 15 No. 4 (Winter 1984), pp. 471-489. [8] Chow, G. "Rate and Cost Analysis of For-Hire Trucking." Reasearch Monograph No. 13, Consumer and Corporate Affairs, Canada (1982). [9] Christensen, L. R. "Concepts and Measurement of Agricultural Productivity." Ameri-can Journal of Agricultural Economics, (December 1975), pp. 910-15. [10] Christensen L. R., and Jorgenson D. W., "The Measurement of Real Capital Input, 1929-1967." 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The Making of Index Numbers, Boston: Houghton- Mifflin, 1922. [17] Friedlander A. F., Spady R. H., and Wang Chaing S. J., "Regulation and the Struc-ture of Technology in the Trucking Industry." in T. Cowing and R. Stevenson eds., Productivity Measurement in Regulated Industries, New York: Academic Press, 1981. [18] Hall R. E., and Jorgenson D. W., "Tax Policy and Investment Behavior." The American Economic Review, Vol. 57 (June 1967). [19] Johnson, R.A. and Wichern, D.W., Applied Multivariate Statistical Analysis, Englee-wood Cliffs, N.J.: Prentice-Hall,1982. [20] Johnston J., Econometric Methods, 2nd. Edition, New York: McGraw-Hill, 1972. [21] Shephard, R. W., Cost and Production Functions. Princeton: Princeton University Press, 1953. [22] Spady R. H., and Friedlander A. F., "Hedonic Cost Functions for the Regulated Truck-ing Industry." The Bell Journal of Economics, Vol. 9 No. 1 (1978), pp. 159-179. [23] Theil H. Principles of Econometrics, New York: Wiley, 1871. [24] Tretheway M. W., and Windle R. J., "U. S; Airline Cross Section, Source of Data." unpublished working paper, Department of Economics, University of Wisconsin, July 1, 1983. [25] Zellner, A., "An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias." Journal of the American Statistical Association, Vol. 58 (December 1962), pp. 977-992. 45 Appendix A Results of Regressions The results of the nine models described in TV and VII are contained here. Each model will be listed with its name from Table 7-5 or Table 7-9. To better understand the result lists, the parameter naming convention will first be described. List of Parameters AO is the intercept term in all models, ar> The B terms are first-order terms for the following variables: Y (Output), L (Labor price), Q (Revenue Equipment price), E (Expenses price), P (Purchased Transportation price), K (Capital price), D (Average Load), S (Average Shipment Size), T (Percent Less-Than-Truckload Revenue), H (Average Haul) and 82 (an index variable for 1982 observations), for example in equation (4- -3) these correspond to a82, cty, fit and so on. The C terms are second-order terms for the above output, input prices and technology variables. These terms are the squared terms such as for Output-Output.. Again from (4-3) these are terms such as: Syy, and tpi3-The D terms are cross products for the interaction of the above variables. For example^  DYL is the parameter representing the impact on total cost of the interaction of output with labor price. In (4-3) these axe terms such as: pyi and A»-y. 46 Model [1], Second-Order Model with no Technology Variables RIGHT-HAND ESTIMATED STANDARD T-VARIABLE COEFFICIENT ERROR STATISTIC AO 17.3889 .370957E-01 468.758 BY .749496 .188221E-01 39.8200 BL .594177 .386810E-02 153.610 BQ .837729E-01 .219301E-02 38.1999 BE .226583 .226265E-02 100.141 BP .605979E-01 .274242E-02 22.0965 BK .348699E-01 .172686E-02 20.1926 B82 .610703E-01 .439455E-01 1.38968 CYY .537793E-01 .159641E-01 3.36876 CLL .254229E-01 .776711E-02 3.27314 CQQ .292176E-01 .538583E-02 5.42491 CEE .382659E-01 .625730E-01 .611541 CPP .335826E-01 .184587E-02 18.1934 CKK -.401712E-02 .611026E-01 -.657439E-01 DYL .203910E-01 .362340E-02 5.62759 DYQ .119242E-01 .214341E-02 5.56316 DYE -.636668E-03 .222410E-02 -.286259 DYP -.296740E-01 .260448E-02 -11.3935 DYK -.200444E-02 .169469E-02 -1.18277 DLQ -.106278E-01 .461507E-02 -2.30285 DLE -.419882E-02 .539270E-02 -.778611 DLP -.251472E-01 .249417E-02 -10.0824 DQE -.127632E-01 .537321E-02 -2.37533 DLK .145510E-01 .411350E-02 3.53738 DQP -.753300E-02 .156469E-02 -4.81438 DQK .170635E-02 .410619E-02 .415555 DEP -.196818E-02 .161320E-02 -1.22005 DEK -.193358E-01 .616682E-01 -.313545 DPK .106576E-02 .122593E-02 .869352 47 Model [2], First-Order Model with no Technology Variables RIGHT-HAND ESTIMATED STANDARD T-VARIABLE COEFFICIENT ERROR STATISTIC AO 17.4455 .346469E-01 503.524 BY .767439 .166498E-01 46.0931 BL .592108 .444451E-02 133.222 BQ .836380E-01 .242172E-02 34.5366 BE .226436 .228368E-02 99.1536 BP .629155E-01 .397495E-02 15.8280 BK .349030E-01 .172086E-02 20.2823 B82 .654083E-01 .469184E-01 1.39409 48 Model [3], First-Order Model with 3 Technology Variables RIGHT-HAND ESTIMATED STANDARD T-VARIABLE COEFFICIENT ERROR STATISTIC AO 17.4803 .319138E-01 547.734 BY .828029 .168840E-01 49.0421 BL .591428 .444582E-02 133.030 BQ .839698E-01 .244864E-02 34.2925 BE .226910 .230283E-02 98.5354 BP .629184E-01 .399695E-02 15.7416 BK .347737E-01 .172699E-02 20.1354 BD -.636969 .768989E-01 -8.28319 BS -.193398E-01 .526152E-01 -.367571 BT -.865116E-01 .164238 -.526744 B82 -.594930E-02 .450284E-01 -.132123 49 Model [4], Second-Order Model with 3 Technology Variables RIGHT-HAND ESTIMATED STANDARD T-VARIABLE COEFFICIENT ERROR STATISTIC AO 17.3990 .371212E-01 468.709 BY .837037 .206733E-01 40.4888 BL .592873 .380735E-02 155.718 BQ .842007E-01 .220059E-02 38.2629 BE .227088 .228434E-02 99.4106 BP .610433E-01 .268711E-02 22.7171 BK .347949E-01 .174069E-02 19.9892 BD -.682426 .104651 -6.52098 BS -.271699E-01 .882836E-01 -.307757 BT .263935 .283876 .929755 B82 -.153996E-01 .434193E-01 -.354672 CYY .774873E-01 .181503E-01 4.26921 CLL .209377E-01 .804548E-02 2.60242 CQQ .227998E-01 .563883E-02 4.04337 CEE .464781E-01 .627924E-01 .740187 CPP .322505E-01 .193077E-02 16.7034 CKK -.418074E-02 .616439E-01 -.678208E-01 CDD .188064 .276709 .679645 CSS .527813E-01 .730830E-01 .722211 CTT -.547565 1.19003 -.460126 DYL .218351E-01 .409324E-02 5.33443 DYQ .110641E-0I .241546E-02 4.58053 DYE -.102454E-02 .250964E-02 -.408243 DYP -.303058E-0I .293128E-02 -10.3388 DYK -.156886E-02 .190755E-02 -.822449 DYD -.159709 .777246E-01 -2.05480 DYS .394781E-01 .661417E-01 .596871 DYT .243178 .166041 1.46457 DLQ -.832334E-02 .475485E-02 -1.75050 DLE -.485567E-02 .550985E-02 -.881272 DLP -.235822E-01 .261296E-02 -9.02508 50 DLK .158235E-01 .415767E-02 3.80587 DLD -.103814E-01 .142939E-01 -.726279 DLS .136797E-01 .964846E-02 1.41781 DLT .834719E-01 .293461E-01 2.84439 DQE -.900221E-02 .572274E-02 -1.57306 DQP -.796481E-02 .160842E-02 -4.95193 DQK .249051E-02 .433879E-02 .574010 DQD .664718E-02 .826577E-02 .804182 DQS .681661E-03 .566226E-02 .120387 DQT -.299890E-01 .169101E-01 -1.77344 DEP -.182672E-02 .165641E-02 -1.10282 DEK -.307935E-01 .617280E-01 -.498858 DED -.127688E-02 .858944E-02 -.148657 DES -.927139E-02 .590964E-02 -1.56886 DET -.162605E-02 .175779E-01 -.925056E-01 DPK .829875E-02 .617729E-02 1.34343 DPD .917353E-02 .100491E-01 .912873 DPS -.197157E-02 .679343E-02 -.290218 DPT -.617662E-01 .205548E-01 -3.00496 DDK -.416246E-02 .654703E-02 -.635779 DDS -.356633 .231928 -1.53769 DDT -1.80005 .597693 -3.01167 DSK -.311837E-02 .449427E-02 -.693854 DST -.124005 .214939 -.576934 DTK .990931E-02 .133981E-01 .739607 51 Model [5], Model with Average Load Variable and 2nd-Order terms for: Output, Average Load and Cross-product Output-AveLoad RIGHT-HAND ESTIMATED STANDARD T-VARIABLE COEFFICIENT ERROR STATISTIC AO 17.4547 .339551E-01 514.053 BY .848935 .201120E-01 42.2104 BL .591176 .443912E-02 133.174 BQ .840419E-01 .244959E-02 34.3085 BE .226978 .230361E-02 98.5315 BP .629808E-01 .398428E-02 15.8073 BK .348231E-01 .172779E-02 20.1547 BD -.820762 .943562E-01 -8.69854 B82 -.146572E-01 .415302E-01 -.352929 CYY .579163E-01 .170324E-01 3.40036 CDD .300279 .191312 1.56958 DYD -.209724 .694300E-01 -3.02066 52 Model [6], Second-Order Model with Average Load Variable RIGHT-HAND ESTIMATED STANDARD T-VARIABLE COEFFICIENT ERROR STATISTIC AO 17.4243 .333667E-01 522.206 BY .843248 .207789E-01 40.5820 BL .593296 .385383E-02 153.950 BQ .841559E-01 .220764E-02 38.1203 BE .227090 .228225E-02 99.5029 BP .606804E-01 .273764E-02 22.1652 BK .347777E-01 .173524E-02 20.0420 BD -.823958 .975552E-01 -8.44606 B82 -.213563E-01 .398292E-01 -.536198 CYY .873402E-01 .166502E-01 5.24559 CLL .232420E-01 .779403E-02 2.98203 CQQ .280250E-01 .541915E-02 5.17147 CEE .399542E-01 .623668E-01 .640632 CPP .332984E-01 .188392E-02 17.6750 CKK .579618E-02 .614837E-01 .942720E-01 CDD .316812 .181378 1.74669 DYL .225111E-01 .400226E-02 5.62459 DYQ .100041E-01 .236832E-02 4.22415 DYE .246940E-03 .245611E-02 .100541 DYP -.315672E-01 .288660E-02 -10.9358 DYK -.119493E-02 .186182E-02 -.641806 DYD -.210940 .664349E-01 -3.17514 DLQ -.104037E-01 .463157E-02 -2.24626 DLE -.372839E-02 .542898E-02 -.686756 DLP -.248449E-01 .253821E-02 -9.78835 DLK .157350E-01 .409806E-02 3.83962 DLD -.225399E-01 .134412E-01 -1.67692 DQE -.119232E-01 .542545E-02 -2.19763 DQP -.711869E-02 .158298E-02 -4.49701 DQK .142054E-02 .410617E-02 .345952 DQD .133096E-01 .774704E-02 1.71803 53 DEP -.235496E-02 .162886E-02 -1.44577 DEK -.219476E-01 .614242E-01 -.357313 DED -.553056E-02 .802005E-02 -.689592 DPK .105883E-01 .592704E-02 1.78644 DPD .226459E-01 .952693E-02 2.37704 DKD -.788498E-02 .609744E-02 -1.29316 54 Model [7], Second-Order 3 Tech Model with Average Haul Variable RIGHT-HAND ESTIMATED STANDARD T-VARIABLE COEFFICIENT ERROR STATIS1 AO 17.3240 .354694E-01 488.422 BY .950443 .229190E-01 41.4696 BL .593292 .358572E-02 165.460 BQ .842453E-01 .220131E-02 38.2706 BE .227076 .217649E-02 104.331 BP .605854E-01 .265626E-02 22.8086 BK .348011E-01 .172399E-02 20.1864 BD -.163829 .121011 -1.35384 BH -.486259 .603068E-01 -8.06308 BT .480036 .140155 3.42505 B82 .676441E-01 .392963E-01 1.72139 CYY .132000 .248845E-01 5.30448 CLL .240774E-01 .772656E-02 3.11619 CQQ .230425E-01 .553049E-02 4.16645 CEE .516596E-01 .646514E-01 .799048 CPP .316730E-01 .191459E-02 16.5430 CKK -.906903E-02 .635129E-01 -.142790 CDD -.969527E-01 .388226 -.249733 CHH .286418 .182135 1.57256 CTT .602574 .717944 .839305 DYL .363136E-01 .487363E-02 7.45103 DYQ .107087E-01 .297680E-02 3.59738 DYE -.907051E-02 .299405E-02 -3.02951 DYP -.342791E-01 .354817E-02 -9.66106 DYK -.367265E-02 .236745E-02 -1.55131 DYD .861680E-01 .100489 .857486 DYH -.154848 .619896E-01 -2.49797 DYT .406515 .116261 3.49658 DLQ -.695643E-02 .477118E-02 -1.45801 DLE -.696044E-02 .542716E-02 -1.28252 DLP -.235853E-01 .251792E-02 -9.36699 55 DLK .134247E-01 .426859E-02 3.14500 DLD .332105E-01 .154483E-01 2.14978 DLH -.555528E-01 .101882E-01 -5.45267 DLT .734277E-01 .214307E-01 3.42629 DQE -.964656E-02 .549973E-02 -1.75401 DQP -.789731E-02 .160892E-02 -4.90847 DQK .145777E-02 .428071E-02 .340545 DQD .500357E-02 .953745E-02 .524623 DQH .146109E-Q2 .625857E-02 .233454 DQT -.311638E-01 .133017E-01 -2.34284 DEP -.164485E-02 .161117E-02 -1.02091 DEK -.334077E-01 .635942E-01 -.525326 DED -.256001E-01 .943682E-02 -2.71279 DEH .306737E-01 .624353E-02 4.91288 DET .733444E-02 .131678E-01 .556999 DPK .945618E-02 .592371E-02 1.59633 DPD -.320090E-02 .114260E-01 -.280142 DPH .163661E-01 .741225E-02 2.20798 DPT -.642298E-01 .155847E-01 -4.12134 DDK -.941304E-02 .747443E-02 -1.25937 DHK .705190E-02 .495364E-02 1.42358 DTK .146315E-01 •104281E-01 1.40308 DDE -.105949 .281127 -.376873 DDT -1.06348 .541966 -1.96226 DHT -.644358 .285015 -2.26079 56 Model [8], Second-Order Model with Average Haul Variables set to zero RIGHT-HAND ESTIMATED STANDARD T-VARIABLE COEFFICIENT ERROR STATISTIC AO 17.4080 .359478E-01 484.258 BY .835216 .204267E-01 40.8884 BL .592894 .380843E-02 155.680 BQ .841812E-01 .219359E-02 38.3760 BE .227092 .229038E-02 99.1501 BP .610439E-01 .267694E-02 22.8036 BD -.691329 .103567 -6.67517 BT .347469 .158409 2.19350 B82 -.198310E-01 .415789E-01 -.476948 CYY .758566E-01 .177305E-01 4.27831 CLL .212164E-01 .805104E-02 2.63523 CQQ .237482E-01 .550612E-02 4.31306 CEE .506199E-01 .625564E-01 .809189 CPP .322334E-01 .191785E-02 16.8071 CDD -.605146E-01 .228893 -.264379 CTT .173464 .750338 .231181 DYL .208811E-01 .404236E-02 5.16557 DYQ .111459E-01 .238508E-02 4.67317 DYE -.513612E-03 .248864E-02 -.206382 DYP -.301447E-01 .288531E-02 -10.4476 DYD -.132263 .749076E-01 -1.76568 DYT .202891 .102443 1.98053 DLQ -.699820E-02. .472059E-02 -1.48249 DLE -.581503E-02 .549993E-02 -1.05729 DLP -.235092E-01 .260497E-02 -9.02474 DLD -.946589E-02 .142848E-01 -.662654 DLT .569623E-01 .225865E-01 2.52196 DQE -.109993E-01 .552753E-02 -1.98992 DQP -.802037E-02 .160187E-02 -5.00689 DQD .624572E-02 .823574E-02 .758368 DQT -.312276E-01 .131801E-01 -2.36929 DEP -.180887E-02 .165445E-02 -1.09334 57 DED -.151766E-02 .860905E-02 -.176287 DET .158498E-01 .137160E-01 1.15557 DPD .900762E-02 .100056E-01 .900261 DPT -.577188E-01 .155678E-01 -3.70758 DDT -1.34733 .521244 -2.58483 Note: values for capital were not computed for this model i 58 Model [9], Model with Average Haul Variables (6 observations deleted) RIGHT-HAND ESTIMATED STANDARD T-VARIABLE COEFFICIENT ERROR STATISTIC AO 17.3687 .258063E-01 673.040 BY .951750 .166715E-01 57.0884 BL .595813 .352573E-02 168.990 BQ .843015E-01 •217726E-02 38.7191 BE .227027 .223900E-02 101.397 BP .581287E-01 .253506E-02 22.9299 BK .347296E-01 .175304E-02 19.8111 BD -.136799 .907258E-01 -1.50782 BH -.503857 .438392E-01 -11.4933 BT .534298 .101211 5.27903 B82 .101456 .289592E-01 3.50340 CYY .412818E-01 .214656E-01 1.92316 CLL .431711E-01 .111468E-01 3.87297 CQQ .310120E-01 •584441E-02 5.30627 CEE .723112E-01 .652134E-01 1.10884 CPP .322095E-01 .192262E-02 16.7529 CKK -.134041E-01 .628815E-01 -.213164 CDD .126623 .281006 .450604 CHH .167372 .131157 1.27612 CTT 1.04931 .513801 2.04226 DYL .390890E-01 .495620E-02 7.88688 DYQ .106692E-01 .304826E-02 3.50011 DYE -.864168E-02 .316702E-02 -2.72865 DYP -.352227E-01 .355146E-02 -9.91780 DYK -.589386E-02 .246264E-02 -2.39331 DYD .174018 .790933E-01 2.20016 DYH -.306439E-01 .459917E-01 -.666292 DYT .205018 .876583E-01 2.33883 DLQ -.206745E-01 .617157E-02 -3.34996 DLE -.182974E-01 .817424E-02 -2.23843 DLP -.238426E-01 .260825E-02 -9.14121 DLK .196435E-01 .650711E-02 3.01877 59 DLD .336922E-01 •153385E-01 2.19658 DLH -.629057E-01 .101086E-01 -6.22301 DLT •654631E-01 .211661E-01 3.09283 DQE -.680021E-02 .567280E-02 -1.19874 DQP -.847187E-02 .163337E-02 -5.18675 DQK .493455E-02 .433961E-02 1.13710 DQD .469092E-02 .953312E-02 .492066 DQH .350431E-02 .621060E-02 .564247 DQT -.266869E-01 .132126E-01 -2.01982 DEP -.232619E-02 .168007E-02 -1.38458 DEK -.448873E-01 .634471E-01 -.707477 DED -.282480E-01 .983307E-02 -2.87276 DEH .327065E-01 .648838E-02 5.04079 DET .858658E-02 .135441E-01 .633973 DPK .690523E-02 .616358E-02 1.12033 DPD -.272517E-02 .109032E-01 -.249942 DPH .186217E-01 .711050E-02 2.61891 DPT -.618087E-01 .147514E-01 -4.19004 DDK -.740994E-02 .770033E-02 -.962289 DHK .807315E-02 .509448E-02 1.58469 DTK .144459E-01 •105992E-01 1.36293 DDH -.333365 .207155 -1.60925 DDT -.173125 .401495 -.431201 DHT -.481879 .206371 -2.33501 60 Appendix B Indexes The indexes used to produce the Total Factor Productivity index are listed below. For each index the 1978 index will be displayed side-by-side with the 1982 index. Tables of Indexes FIRM INPIND INPIND OUTTND OUTIND TFP TFP 1978 1982 1978 1982 1978 1982 1 3.88 3.51 7.66 6.23 1.61 1.45 2 6.83 8.38 14.20 13.70 1.70 1.34 3 0.48 0.41 0.73 0.63 1.24 1.27 4 0.34 0.25 0.32 0.16 0.76 0.52 5 0.54 0.44 0.58 0.84 0.88 1.55 6 0.32 0.4.1 0.34 0.29 0.87 0.59 7 0.33 0.25 0.42 0.24 1.05 0.79 8 3.46 4.64 4.96 6.52 1.17 1.15 9 0.00 0.00 0.86 2.36 0.00 0.00 10 0.18 0.24 0.45 0.24 2.07 0.80 11 0.66 0.55 0.86 0.61 1.07 0.90 12 24.22 23.33 52.90 51.30 1.78 1.80 13 0.00 0.00 3.56 3.10 0.00 0.00 14 1.13 0.88 1.28 0.85 0.92 0.78 15 4.78 6.02 8.95 10.10 1.53 1.37 16 0.85 1.03 0.95 0.94 0.91 0.74 17 8.06 9.67 23.90 23.90 2.42 2.02 18 0.94 0.70 1.09 0.64 0.95 0.75 19 0.53 0.42 0.68 0.24 1.05 0.47 20 0.78 0.79 0.86 0.69 0.90 0.71 21 1.11 0.98 0.55 0.43 0.41 0.36 22 1.28 1.24 0.96 0.78 0.62 0.52 23 1.14 1.49 1.57 1.76 1.13 0.96 24 0.00 0.00 0.88 0.16 0.00 0.00 25 3.72 3.27 6.11 4.59 1.34 1.15 26 2.87 1.83 1.98 1.49 0.56 0.66 27 1.44 1.26 1.15 0.95 0.65 0.61 28 0.23 0.16 0.19 0.10 0.67 0.53 29 0.87 1.07 0.52 0.87 0.49 0.67 30 0.00 0.00 2.73 1.51 0.00 0.00 31 0.19 0.07 0.46 0.47 1.92 5.60 32 1.62 1.97 0.71 0.78 0.36 0.32 33 0.71 0.97 0.50 0.61 0.58 0.51 34 0.54 0.39 0.52 0.27 0.78 0.57 35 0.28 0.31 1.18 0.19 3.46 0.50 61 FIRM INPLND LNPIND OUTLND OUTLND TFP TFP 1978 1982 1978 1982 1978 1982 36 3.99 6.83 9.00 13.90 1.84 1.66 37 1.42 1.34 1.16 0.83 0.67 0.50 38 1.99 1.10 3.09 1.63 1.27 1.22 39 4.98 5.39 4.47 3.77 0.73 0.57 40 11.72 11.01 26.00 21.70 1.81 1.61 41 0.22 0.20 0.14 0.82 0.51 3.43 42 0.40 0.51 0.34 0.39 0.69 0.63 43 0.00 0.00 0.10 0.57 0.00 0.00 44 3.96 3.16 10.90 7.27 2.25 1.88 45 4.21 1.46 11.50 1.69 2.23 0.94 46 5.22 4.71 10.90 8.75 1.71 1.52 47 0.71 0.48 1.03 0.81 1.18 1.40 48 0.49 0.34 0.59 0.36 1.00 0.86 49 0.24 0.21 0.39 0.15 1.31 0.57 50 0.79 0.70 0.67 0.43 0.69 0.50 51 19.72 21.99 57.80 54.00 2.39 2.01 52 0.00 0.00 0.00 0.00 0.00 0.00 53 0.83 0.61 0.98 0.53 0.96 0.71 54 1.34 1.71 2.44 2.31 1.49 1.10 55 0.59 0.58 0.97 0.62 1.34 0.88 56 2.45 1.73 7.48 4.55 2.50 2.15 57 0.54 0.77 0.43 0.44 0.66 0.46 58 1.70 1.55 1.55 1.92 0.75 1.01 59 1.00 1.39 1.57 1.48 1.28 0.87 60 3.48 3.35 2.76 4.64 0.65 1.13 61 1.88 2.35 4.80 5.32 2.09 1.85 62 0.62 0.24 0.58 0.28 0.77 0.96 63 0.00 0.00 0.18 0.20 0.00 0.00 64 1.52 1.88 2.28 4.14 1.23 1.80 65 0.00 0.00 0.16 0.27 0.00 0.00 66 1.81 2.34 1.97 1.35 0.89 0.47 67 1.07 1.34 1.14 1.24 0.87 0.76 68 4.10 3.08 9.18 5.55 1.83 1.47 69 0.90 0.74 1.09 0.86 0.99 0.95 70 0.10 0.26 0.19 0.13 1.54 0.41 62 FIRM INPIND INPIND OUTIND OUTIND TFP TFP 1978 1982 1978 1982 1978 1982 71 0.50 0.64 0.40 0.51 0.66 0.65 72 0.56 0.51 0.20 0.16 0.30 0.25 73 3.13 3.39 8.08 6.19 2.11 1.49 74 5.33 4.95 12.30 9.69 1.89 1.60 75 0.00 0.00 0.53 0.29 0.00 0.00 76 0.25 0.17 0.19 0.14 0.63 0.67 77 1.17 1.47 0.74 0.73 0.52 0.41 78 1.13 0.92 1.22 0.61 0.88 0.54 79 0.22 0.12 0.13 0.58 0.48 3.87 80 0.72 0.72 0.86 0.72 0.98 0.82 81 0.31 0.24 0.16 0.12 0.42 0.42 82 0.00 0.00 0.00 0.00 0.00 0.00 83 2.30 5.33 2.45 6.05 0.87 0.93 84 0.62 0.56 0.69 0.44 0.90 0.65 85 3.33 3.76 3.94 4.82 0.97 1.05 86 0.00 0.00 0.00 0.00 0.00 0.00 87 0.94 1.07 0.87 0.92 0.76 0.70 88 1.98 1.97 3.97 3.35 1.64 1.39 89 0.40 0.45 0.19 0.21 0.38 0.38 90 0.40 0.41 0.58 0.35 1.18 0.70 91 0.14 0.04 0.32 0.22 1.89 4.13 92 0.56 0.38 0.54 0.39 0.79 0.85 93 0.74 0.77 0.58 0.92 0.64 0.98 94 0.37 0.28 0.15 0.13 0.32 0.39 95 0.61 1.19 1.03 0.97 1.39 0.66 96 0.00 0.00 0.88 1.39 0.00 0.00 97 0.00 0.00 0.00 0.00 0.00 0.00 98 0.00 0.00 0.00 0.00 0.00 0.00 99 3.31 3.16 7.47 5.59 1.85 1.45 100 1.44 1.32 1.24 1.06 0.70 0.65 101 0.53 0.42 0.87 0.51 1.34 1.00 102 2.34 1.66 2.26 2.12 0.79 1.04 103 0.47 0.28 0.47 0.45 0.75 1.35 104 2.91 2.85 4.49 3.80 1.26 1.09 105 0.00 0.00 0.98 0.60 0.00 0.00 63 FIRM INPIND INPIND OUTIND OUTIND TFP TFP 1978 1982 1978 1982 1978 1982 106 0.63 0.84 0.60 0.69 0.78 0.67 107 0.47 0.34 0.37 0.25 0.65 0.60 108 0.47 0.67 0.70 0.89 1.22 1.10 109 0.00 0.00 0.49 0.38 0.00 0.00 110 0.66 0.58 0.83 0.58 1.03 0.82 111 2.69 3.30 2.22 2.84 0.67 0.70 112 1.05 1.08 0.94 0.96 0.73 0.73 113 0.54 0.66 0.83 1.02 1.26 1.26 114 1.15 0.89 1.52 1.00 1.08 0.92 115 2.12 1.62 3.29 2.68 1.27 1.35 116 1.10 1.00 1.25 0.88 0.93 0.72 117 6.63 5.46 19.10 13.20 2.36 1.97 118 0.00 0.00 0.42 0.16 0.00 0.00 119 7.13 7.29 13.00 11.50 1.49 1.29 120 1.69 2.35 3.29 4.19 1.59 1.46 121 0.24 0.28 0.25 0.47 0.83 1.38 122 2.36 1.67 3.89 2.75 1.34 1.35 123 0.20 0.23 0.28 0.25 1.14 0.87 124 0.61 0.64 0.88 0.72 1.19 0.92 125 1.48 1.52 1.28 1.14 0.71 0.61 126 0.00 0.00 0.34 0.23 0.00 0.00 127 18.00 20.50 43.40 41.20 1.97 1.64 128 0.78 0.34 1.50 0.65 1.56 1.55 129 0.26 0.18 0.30 0.63 0.96 2.82 130 0.00 0.00 3.14 2.50 0.00 0.00 131 0.29 0.30 0.27 0.22 0.75 0.61 132 0.62 0.78 1.02 0.75 1.34 0.78 133 0.25 0.25 0.21 0.15 0.67 0.50 134 0.29 0.78 0.89 1.38 2.50 1.45 135 0.39 0.41 0.69 0.58 1.47 1.15 136 0.00 0.00 0.14 0.54 0.00 0.00 64 FIRM LABIND LABIND EXPIND EXPIND REQIND REQIND 1978 1982 1978 1982 1978 1982 1 4.90 3.77 3.61 4.55 7.16 7.06 2 9.06 9.15 8.75 13.62 19.50 19.97 3 0.57 0.38 0.43 0.53 0.53 0.24 4 0.37 0.23 0.28 0.29 0.88 0.54 5 0.61 0.43 0.55 0.54 0.81 0.69 6 0.40 0.45 0.21 0.37 0.29 0.35 7 0.37 0.24 0.32 0.32 0.51 0.38 8 5.05 5.27 3.77 6.49 3.33 7.99 9 0.49 1.60 0.21 2.20 4.26D-03 1.73D-03 10 0.22 0.27 0.16 0.31 0.12 0.12 11 0.78 0.54 0.54 0.64 0.97 0.81 12 32.93 26.89 25.53 35.20 31.78 27.2 13 2.88 2.69 2.06 3.41 0.00 0.00 14 1.31 0.88 0.82 0.81 2.80 1.77 15 6.22 7.20 5.78 7.63 5.59 7.82 16 1.00 1.09 0.92 1.49 0.94 0.77 17 11.76 11.17 10.60 17.40 22.43 35.63 18 1.19 0.75 0.79 0.78 1.12 1.05 19 0.61 0.43 0.60 0.60 0.45 0.25 20 0.94 0.80 0.51 0.85 1.48 1.76 21 1.23v 0.96 1.08 1.14 2.67 2.29 22 1.61 1.33 0.99 1.40 1.93 1.12 23 1.36 1.63 1.08 1.91 1.63 1.55 24 0.00 0.00 0.27 0.07 0.51 0.20 25 4.18 3.34 3.88 4.66 11.53 7.61 26 3.88 1.91 2.29 2.08 3.26 2.19 27 1.87 1.44 1.47 1.66 0.86 0.51 28 0.25 0.14 0.22 0.19 0.40 0.30 29 1.06 1.20 0.69 1.27 1.40 1.01 30 0.61 0.46 0.00 0.00 0.00 0.00 31 0.17 0.04 0.21 0.04 0.42 0.18 32 1.76 1.83 1.37 2.33 6.55 6.24 33 0.93 1.13 0.44 0.97 1.09 0.87 34 0.61 0.42 0.47 0.43 0.29 0.11 35 0.28 0.25 0.22 0.33 0.38 0.47 65 FIRM LABIND LABIND EXPIND EXPIND REQIND REQI 1978 1982 1978 1982 1978 1982 36 4.38 7.29 3.89 10.69 12.39 19.36 37 1.71 1.42 1.42 1.70 2.45 2.73 38 2.55 1.04 2.35 1.45 2.40 1.31 39 6.92 6.56 3.56 5.49 8.04 3.77 40 15.84 12.71 13.07 16.16 11.91 12.72 41 0.26 0.21 0.17 0.21 0.12 0.04 42 0.49 0.55 0.33 0.68 0.36 0.44 43 0.00 0.00 0.17 0.09 0.28 0.13 44 5.00 3.39 5.20 5.09 5.71 4.01 45 5.43 1.12 5.28 1.61 6.09 3.25 46 6.81 5.36 6.16 7.30 8.65 6.49 47 0.79 0.49 0.47 0.44 1.93 0.87 48 0.54 0.33 0.57 0.48 0.12 0.13 49 0.30 0.16 0.21 0.27 0.16 0.14 50 0.91 0.74 0.72 0.74 1.55 1.41 51 25.49 23.36 23.46 32.88 28.74 45.17 52 0.00 0.00 0.46 0.19 0.37 0.15 53 0.89 0.62 1.04 0.75 1.06 0.60 54 1.68 1.72 1.29 2.21 1.42 4.18 55 0.65 0.60 0.40 0.59 1.50 0.91 56 3.08 1.52 2.48 3.21 4.21 1.95 57 0.75 1.01 0.43 1.03 0.03 0.01 58 1.87 1.41 1.70 2.25 4.98 4.15 59 1.11 1.48 0.88 1.59 2.28 2.16 60 4.57 4.06 3.67 4.29 4.00 4.87 61 2.64 3.00 1.85 3.75 3.00 3.04 62 0.71 0.16 0.63 0.47 0.80 0.34 63 0.00 0.00 0.20 0.55 0.57 0.90 64 2.09 2.25 1.37 2.68 1.66 1.97 65 0.21 0.12 0.22 0.25 0.00 0.00 66 2.11 2.45 1.46 2.44 3.98 4.13 67 1.25 1.42 1.00 1.67 1.79 1.85 68 5.58 3.28 4.60 4.88 8.35 5.40 69 1.05 0.72 0.81 0.98 1.59 0.98 70 0.07 0.23 0.17 0.23 0.29 0.35 66 FIRM LABIND LABIND EXPIND EXPIND REQIND REQ] 1978 1982 1978 1982 1978 1982 71 0.63 0.70 0.41 0.74 0.65 0.94 72 0.70 0.53 0.41 0.60 0.84 0.52 73 3.91 4.01 3.85 5.36 4.38 2.98 74 6.58 5.36 5.44 7.12 11.58 10.85 75 0.51 0.29 0.00 0.00 0.00 0.00 76 0.31 0.19 0.20 0.17 0.21 0.09 77 1.48 1.41 0.83 1.15 1.86 5.82 78 1.33 0.88 1.17 1.06 1.56 1.79 79 0.27 0.11 0.15 0.14 0.13 0.08 80 0.88 0.80 0.51 0.70 1.42 1.33 81 0.39 0.24 0.22 0.25 0.39 0.24 82 0.00 0.00 0.00 0.00 0.17 0.08 83 2.54 6.17 2.67 6.82 4.71 8.13 84 0.76 0.59 0.64 0.75 0.41 0.47 85 4.51 5.03 2.77 5.05 5.33 4.75 86 0.09 0.04 1.34 1.06 0.92 0.63 87 1.04 1.05 0.83 1.15 2.20 2.64 88 2.46 2.14 2.13 2.66 2.32 2.29 89 0.49 0.49 0.38 0.50 0.42 0.43 90 0.40 0.36 0.41 0.40 0.67 0.37 91 0.09 0.01 0.44 0.36 0.30 0.33 92 0.68 0.20 0.48 1.12 0.80 0.83 93 0.87 0.63 0.51 0.63 1.47 2.33 94 0.46 0.29 0.31 0.35 0.37 0.15 95 0.46 1.24 0.94 1.80 2.79 1.30 96 0.73 0.89 0.81 1.40 0.00 0.00 97 0.00 0.00 0.00 0.00 0.11 0.05 98 0.00 0.00 0.00 0.00 0.27 0.28 99 4.73 3.76 4.22 4.87 5.67 5.42 100 2.00 1.38 0.95 1.52 2.65 3.00 101 0.58 0.40 0.60 0.61 0.73 0.44 102 3.12 1.64 2.33 2.22 2.28 3.82 103 0.55 0.16 0.36 0.62 0.76 0.74 104 3.81 3.23 2.77 3.63 6.09 6.63 105 0.00 0.00 0.44 0.32 1.00 0.40 67 FIRM LABIND LABIND EXPIND EXPIND REQIND REQI 1978 1982 1978 1982 1978 1982 106 0.73 0.86 0.62 1.19 0.76 0.55 107 0.58 0.36 0.43 0.38 0.55 0.50 108 0.55 0.63 0.41 0.85 0.51 0.64 109 0.62 0.61 0.48 0.73 0.00 0.00 110 0.83 0.54 0.58 0.86 0.78 0.48 111 3.65 4.22 2.67 4.56 2.03 1.08 112 1.24 1.19 1.02 1.38 1.44 0.59 113 0.65 0.63 0.71 1.48 0.78 0.82 114 1.49 0.98 1.12 1.14 0.98 0.65 115 2.67 1.80 2.73 2.88 2.64 2.86 116 1.31 1.04 1.12 1.25 1.14 0.67 117 8.18 6.03 7.83 9.73 9.94 5.38 118 0.26 0.23 0.00 0.00 0.00 0.00 119 8.60 8.12 5.92 7.82 20.23 17.31 120 2.14 2.23 1.61 3.45 2.09 3.42 121 0.25 0.22 0.27 0.38 0.19 0.26 122 3.37 1.95 2.32 2.68 2.79 2.00 123 0.17 0.22 0.27 0.35 0.27 0.18 124 0.65 0.62 0.64 0.70 1.19 1.80 125 1.84 1.76 1.03 1.56 3.43 2.16 126 0.00 0.00 0.30 0.44 0.05 0.02 127 22.63 21.64 20.18 28.69 40.80 52.53 128 0.99 0.29 0.70 0.48 1.02 0.67 129 0.27 0.06 0.22 0.67 0.28 1.14 130 0.00 0.00 0.72 1.22 0.80 0.44 131 0.36 0.32 0.25 0.31 0.38 0.44 132 0.76 0.84 0.70 1.03 0.17 0.70 133 0.28 0.22 0.22 0.23 0.25 0.24 134 0.16 0.73 0.65 1.18 1.09 0.66 135 0.39 0.37 0.34 0.55 0.93 0.94 136 0.25 0.19 0.22 0.19 0.23 0.12 68 FIRM PURIND PURLND KAPIND KAPIND 1978 1982 1978 1982 1 2.93 2.81 1.76 5.61 2 2.74 2.76 3.91 15.51 3 2.93 2.81 0.19 0.35 4 2.93 2.81 0.21 0.43 5 2.93 2.81 0.28 0.62 6 2.93 2.81 0.43 1.05 7 2.93 2.81 0.14 0.25 8 1.21 2.16 3.68 12.86 9 1.94 2.42 0.00 0.00 10 2.93 2.81 0.09 0.33 11 2.93 2.81 0.73 1.54 12 2.93 2.81 23.93 64.96 13 2.93 2.81 2.29 4.60 14 2.93 2.81 1.67 3.74 15 2.93 2.81 6.65 18.51 16 2.93 2.81 0.67 2.07 17 2.93 2.81 7.22 24.66 18 2.93 2.81 0.49 0.91 19 2.93 2.81 0.38 0.91 20 2.93 2.81 0.62 1.43 21 2.93 2.81 0.93 2.42 22 2.93 2.81 1.79 4.65 23 2.93 2.81 1.06 2.95 24 2.93 2.81 0.10 0.20 25 2.93 2.81 2.43 5.33 26 2.93 2.81 3.93 8.34 27 2.93 2.81 1.91 3.37 28 2.93 2.81 0.17 0.31 29 2.93 2.81 0.69 1.71 30 2.93 2.81 0.13 0.27 31 2.93 2.81 0.24 0.50 32 2.93 2.81 1.75 6.73 33 2.93 2.81 0.95 2.28 34 2.93 2.81 0.83 1.58 35 2.93 2.81 0.07 0.26 69 FIRMPURIND PURIND KAPIND KAPIND 1978 1982 1978 1982 36 2.93 2.81 1.90 4.67 37 2.93 2.81 0.55 1.40 38 2.93 2.81 1.74 4.93 39 2.93 2.81 9.47 25.54 40 2.91 3.15 13.76 34.03 41 2.93 2.81 0.09 0.17 42 2.93 2.81 0.20 0.43 43 2.93 2.81 0.21 0.37 44 2.93 2.81 2.82 5.36 45 1.83 1.76 6.33 13.05 46 5.44 3.34 3.67 7.65 47 2.93 2.81 0.57 1.12 48 2.93 2.81 0.39 0.89 49 2.93 2.81 0.11 0.19 50 2.93 2.81 0.60 1.10 51 4.05 3.89 20.87 75.75 52 2.93 2.81 0.17 0.29 53 2.93 2.81 0.92 1.85 54 2.93 2.81 1.36 4.15 55 2.93 2.81 0.57 1.15 56 2.93 2.81 3.70 7.93 57 2.93 2.81 0.67 1.75 58 2.93 2.81 1.13 2.97 59 2.93 2.81 0.99 3.62 60 2.93 2.81 1.08 3.32 61 2.93 2.81 2.45 6.86 62 2.93 2.81 0.46 0.93 63 2.93 2.81 0.13 0.33 64 2.93 2.81 1.16 4.08 65 2.93 2.81 0.16 0.35 66 2.93 2.81 2.34 8.09 67 2.93 2.81 0.79 2.52 68 2.93 2.81 3.17 7.23 69 2.93 2.81 0.80 1.47 70 2.93 2.81 0.14 0.36 FIRM PURIND PURIND KAPIND KAPIND 1978 1982 1978 1982 71 2.93 2.81 0.24 0.64 72 2.93 2.81 0.25 0.60 73 2.93 2.81 1.77 5.24 74 1.27 1.22 5.70 13.29 75 2.93 2.81 0.24 0.40 76 2.93 2.81 0.13 0.24 77 2.93 2.81 2.18 5.61 78 2.93 2.81 0.93 3.06 79 2.93 2.81 0.17 0.31 80 2.93 2.81 0.35 0.80 81 2.93 2.81 0.09 0.17 82 2.93 2.81 0.18 0.42 83 2.93 2.81 2.22 6.42 84 2.93 2.81 0.28 0.68 85 3.11 0.52 2.54 8.07 86 2.93 2.81 0.77 1.52 87 2.93 2.81 0.90 2.87 88 2.93 2.81 1.25 3.15 89 2.93 2.81 0.18 0.45 90 2.93 2.81 0.83 2.22 91 2.93 2.81 0.28 0.74 92 2.93 2.81 0.36 0.93 93 2.93 2.81 1.58 3.36 94 2.93 2.81 0.20 0.42 95 2.93 2.81 0.45 1.05 96 2.93 2.81 0.55 2.31 97 2.93 2.81 0.06 0.20 98 2.93 2.81 0.31 0.68 99 1.11 1.07 3.34 9.50 100 2.93 2.81 0.47 1.34 101 2.93 2.81 0.33 0.89 102 2.93 2.81 0.93 1.50 103 2.93 2.81 0.40 0.99 104 2.93 2.81 2.22 5.37 71 FIRM PURIND PURIND KAPIND KAPIND 1978 1982 1978 1982 105 2.93 2.81 0.43 0.88 106 2.93 2.81 0.68 2.04 107 2.93 2.81 0.17 0.37 108 2.93 2.81 0.82 2.65 109 2.93 2.81 0.31 0.66 110 2.93 2.81 0.35 0.87 111 2.93 2.81 0.90 5.71 112 2.93 2.81 1.16 2.50 113 0.39 0.36 0.34 0.78 114 2.93 2.81 0.68 1.52 115 0.68 0.66 1.94 4.22 116 2.93 2.81 1.71 3.84 117 2.93 2.81 5.28 12.41 118 2.93 2.81 0.39 0.89 119 2.93 2.81 3.53 12.44 120 2.93 2.81 3.06 14.45 121 2.93 2.81 0.05 0.19 122 1.31 0.71 1.41 3.17 123 2.93 2.81 0.13 0.27 124 2.93 2.81 0.29 0.71 125 2.93 2.81 1.01 2.47 126 2.93 2.81 0.15 0.28 127 1.72 3.82 21.01 62.38 128 2.93 2.81 0.26 0.43 129 2.93 2.81 0.07 0.89 130 2.93 2.81 1.16 2.29 131 2.93 2.81 0.14 0.32 132 2.93 2.81 0.29 0.76 133 2.93 2.81 0.22 0.73 134 2.93 2.81 0.32 1.87 135 2.93 2.81 0.14 0.48 136 2.93 2.81 0.00 0.00 The following data represent the values for the technology variables. As was discussed above firms with missing data were eliminated from the sample and will not be repre-sented below. 1978 Firm AveHaul AveShipment AveLoad PctLTL (Miles) (Tons) (Tons) 1 694.75 .5764 15.471 .7377 2 622.23 1.9186 15.488 .5485 3 403.28 .6671 13.639 .7297 4 240.71 .7885 10.663 .6991 5 196.30 1.5108 7.0573 .7255 6 163.84 .7161 11.026 .7699 7 242.63 4.2809 10.883 .3819 8 293.29 .9515 12.459 .6950 9 430.88 1.3545 15.098 .6309 10 178.60 1.2619 10.872 .7430 11 342.01 .4819 8.9636 .8242 12 911.29 .5915 14.037 .7559 13 302.00 .5988 12.504 .7884 14 220.03 1.5181 14.468 .5868 15 637.40 1.1584 12.628 .6151 16 248.52 .9032 13.205 .6517 17 681.54 1.7182 14.710 .4651 18 232.54 .8056 12.076 .7313 19 219.94 1.3057 11.674 .3299 20 180.17 2.5777 9.8678 .6456 21 158.50 .4716 9.1733 .8757 22 104.24 2.5834 8.5964 .5239 23 350.88 .9321 12.513 .6297 24 548.82 17.263 17.077 .0950 25 406.12 1.4049 12.084 .6600 27 146.02 1.0870 10.062 .7085 28 134.50 1.3623 13.128 .6100 29 102.26 1.3738 11.366 .6821 30 136.36 3.0001 10.129 .4547 31 433.80 .8421 14.915 .7017 32 130.00 .3449 10.599 .9241 33 121.10 .6471 7.8220 .8158 34 208.51 1.7833 12.044 .6600 35 739.24 2.1544 52.300 .6318 1978 Continued Finn AveHaul AveShipment AveLoad PctLTL (Miles) (Tons) (Tons) 36 784.00 1.3762 15.628 .5260 37 164.89 .8466 6.3430 .7221 38 206.78 1.3301 10.598 .3758 39 165.77 .7692 9.5647 .7277 40 779.15 .8255 14.381 .6521 41 89.999 2.1608 10.357 .6053 43 90.539 .5229 3.7701 .8550 44 1272.0 .8324 14.620 .6295 45 1304.9 1.4286 15.420 .4851 46 533.60 1.6548 14.912 .4762 47 320.63 1.4898 9.6046 .7119 48 162.03 5.6616 10.028 .3628 49 204.99 .7406 10.526 .7297 50 183.67 .8174 6.9902 .7899 51 1405.1 .6209 16.363 .7456 53 206.52 1.4382 13.010 .5910 54 413.45 .6443 15.564 .7500 55 311.32 2.2605 15.559 .4973 56 1116.6 .8909 15.746 .5812 57 120.00 .5496 6.1535 .8005 58 274.17 .7052 8.5987 .7119 59 316.46 .8434 11.392 .6775 60 309.45 .4819 12.290 .9072 61 431.00 1.3471 14.096 .5056 62 146.11 1.3819 12.525 .6033 64 168.29 .7157 8.7222 .7320 65 74.789 2.8975 8.8716 .5541 66 310.14 .7231 17.702 .4387 67 201.76 1.0318 11.119 .6972 68 565.46 1.6896 14.837 .4865 69 343.19 .4627 10.729 .8165 70 190.00 .4524 9.9124 .8407 71 188.00 .3811 7.6255 .8562 74 1978 Continued Firm AveHaul AveShipment AveLoad PctLTL (Miles) (Tons) (Tons) 72 99.549 .7458 3.8746 .8172 73 680.76 1.0038 13.782 .5987 74 1222.2 .8507 15.559 .6425 75 247.02 .8112 11.474 .7113 76 162.15 1.1846 15.405 .6209 77 161.06 .5299 12.700 .8039 78 283.38 1.5447 12.512 .5760 79 83.970 1.3307 10.819 .6752 80 247.23 .6640 14.563 .7517 81 111.35 .6664 6.9518 .7319 82 231.28 .6192 12.617 .8733 83 225.78 1.5252 10.039 .5366 84 194.24 .5806 10.373 .8394 85 221.45 1.1285 11.316 .6931 86 261.68 6.9816 14.146 .2550 87 225.33 1.0871 9.1228 .6214 88 613.25 1.0893 13.357 .5695 89 103.32 1.0909 4.2673 .7335 90 264.45 1.4117 13.888 .5955 91 363.39 1.2584 20.889 .5309 92 170.00 .6201 10.836 .7874 93 172.26 .6139 10.405 .7163 94 55.133 1.3402 8.4471 .7059 95 308.42 1.6054 16.288 .4817 96 210.78 1.1824 16.660 .6108 97 215.08 .7860 11.107 .7981 98 195.70 .7508 10.115 .6711 99 563.00 1.5599 13.758 .4669 100 195.36 .6639 8.3889 .7626 101 586.54 .4623 10.942 .8372 102 614.21 .5554 17.399 .7722 103 125.37 .6229 11.841 .7910 104 412.47 1.1361 12.535 .5580 105 217.86 .6253 9.4077 .7471 106 226.42 .9380 12.714 .7141 1978 Continued Firm AveHaul AveShipment AveLoad PctLTL (Miles) (Tons) (Tons) 107 169.77 .7509 7.5355 .7407 108 360.44 .6625 12.710 .7729 109 164.28 1.2060 12.020 .5782 110 303.52 .7168 12.804 .7502 111 223.80 .4180 8.3901 .8740 112 232.13 1.0064 9.2507 .7103 113 317.42 .6028 11.553 .7641 114 276.63 1.0568 12.084 .6563 115 372.48 .8771 12.275 .6686 116 251.51 .6993 10.069 .8133 117 1590.4 1.0877 16.496 .5737 118 177.25 .6682 9.0495 .7988 119 660.99 .9825 14.147 .6059 120 373.27 1.0503 13.557 .5938 121 209.00 .5810 8.7904 .7620 122 344.26 2.1870 15.460 .4906 123 318.95 1.0587 11.286 .6034 124 332.77 .9086 13.930 .6552 125 205.73 .7421 7.5787 .7362 126 139.00 2.3072 6.8339 .4428 127 1103.3 .9322 15.477 .6243 128 586.00 1.4398 14.554 .5006 129 262.03 1.4836 15.320 .5334 130 958.97 2.3379 16.305 .3524 131 175.07 .7702 13.399 .7194 132 307.79 .8268 12.886 .6639 133 122.55 .9545 10.974 .7087 134 187.64 1.1617 7.0203 .5877 135 430.01 .8042 13.869 .7299 136 102.30 .7755 8.6874 .7036 1982 Firm AveHaul AveLoad AveShipment PctLTL (Miles) (Tons) (Tons) 1 631.33 15.471 .5341 .8029 2 741.23 15.488 1.3643 .6742 3 521.98 13.639 .6184 .7484 4 216.28 10.663 .6122 .7499 5 284.60 7.0573 2.5013 .6555 6 176.65 11.026 .6447 .8607 7 231.74 10.883 3.2637 .4899 8 380.97 12.459 .9340 .7153 9 657.92 15.098 .6087 .7791 10 173.72 10.872 .7748 .8386 11 348.62 8.9636 .4566 .8854 12 1090.1 14.037 .4873 .8548 13 343.34 12.504 .6076 .8036 14 284.07 14.468 1.2086 .7185 15 624.05 12.628 .7629 .7829 16 242.23 13.205 .6619 .7885 17 694.06 14.710 1.4653 .6133 18 224.91 12.076 28.206 .8287 19 148.75 11.674 1.1965 .6997 20 171.30 9.8678 1.9981 .6684 21 184.49 9.1733 .4080 .9266 22 120.98 8.5964 2.0475 .6280 23 402.71 12.513 .6538 .8236 24 573.23 17.077 18.866 .0110 25 459.89 12.084 1.1895 .7724 27 161.52 10.062 .9188 .7752 28 152.08 13.128 1.1996 .7410 29 169.54 11.366 .7971 .8148 30 80.077 10.129 2.8272 .5099 31 378.68 14.915 .8278 .7582 32 166.10 10.599 .3368 .9149 33 141.85 7.8220 .6405 .8263 34 280.10 12.044 .8192 .7437 35 141.92 52.300 1.6621 .6258 36 958.59 15.628 .8956 .6948 77 1982 continued Firm AveHaul AveLoad AveShip PctLTL (Miles) (Tons) Tons) 37 152.20 6.3430 .6767 .7777 38 174.79 10.598 1.6479 .5022 39 174.11 9.5647 .6746 .7893 40 936.49 14.381 .6128 .7826 41 90.000 10.357 1.1614 .7527 43 75.000 3.7701 .5085 .8826 44 1302.2 14.620 .7450 .7393 45 887.64 15.420 1.3921 .5622 46 603.23 14.912 1.2779 .6256 47 392.77 9.6046 1.6105 .7567 48 201.07 10.028 4.5543 .3493 49 205.00 10.526 1.2165 .6060 50 182.55 6.9902 .6128 .8502 51 1340.5 16.363 .5865 .8125 53 232.96 13.010 1.3725 .6565 55 341.10 15.559 2.2408 .5085 56 987.11 15.746 .8311 .6686 57 119.99 6.1535 .5809 .8484 58 356.00 8.5987 .4581 .8798 59 267.77 11.392 .6041 .8269 60 431.86 12.290 .5683 .8487 61 431.00 14.096 1.3628 .5810 62 145.78 12.525 1.3076 .6559 64 341.13 8.7222 .7702 .7446 65 228.25 8.8716 3.3926 .3635 66 200.00 17.702 .5906 .8369 67 234.64 11.119 .7700 .8209 68 554.31 14.837 1.3039 .6225 69 459.86 10.729 .5028 .8294; 78 1982 Continued Firm AveHaul AveLoad AveShipment PctLTL (Miles) (Tons) (Tons) 70 153.27 9.9124 .5292 .6822 71 272.54 7.6255 .3745 .8367 72 91.759 3.8746 .4873 .9475 73 584.28 13.782 .7256 .7738 74 1126.9 15.559 .9464 .6725 75 , 254.91 11.474 1.1098 .6932 76 206.10 15.405 1.4180 .5853 77 181.50 12.700 .4552 .8634 78 226.22 12.512 1.0131 .7119 79 88.292 10.819 1.7428 .6432 80 288.41 14.563 .5784 .8172 81 154.08 6.9518 .4914 .8506 82 236.96 12.617 .5131 .9200 83 418.21 10.039 .9100 .7084 84 192.20 10.373 .6452 .8699 85 265.49 11.316 .7900 .7926 86 263.83 14.146 6.2172 .2842 87 228.64 9.1228 .7958 .7926 88 629.15 13.357 .8321 .7372 89 126.44 4.2673 .7574 .8272 90 202.48 13.888 1.1772 .7171 91 221.08 20.889 .8627 .7590 92 162.87 10.836 .7004 .7698 93 536.77 10.405 .5831 .6076 94 75.562 8.4471 1.3252 .7718 95 268.33 16.288 .8181 .7067 96 316.61 16.660 .8253 .7598 97 197.35 11.107 1.0317 .5984 98 190.66 10.115 .4992 .7896 99 584.28 13.758 1.2112 .6000 100 190.00 8.3889 .5817 .8262 101 588.57 10.942 .3534 .9210 102 589.24 17.399 .5172 .8392 103 159.83 11.841 .6269 .8468 104 418.24 12.535 1.1428 .5967 1978 Continued Firm AveHaul AveLoad AveShipment PctLTL (Miles) (Tons) (Tons) 105 300.60 9.4077 .7449 .7614 106 224.98 12.714 .9020 .7430 107 212.32 7.5355 .6954 .7911 108 432.62 12.710 .5999 .8310 109 206.66 12.020 1.2481 .5800 110 296.32 12.804 .9696 .6949 111 225.60 8.3901 .3940 .8400 112 265.40 9.2507 .6654 .8483 113 401.32 11.553 .4510 .9023 114 304.29 12.084 .8059 .7832 115 485.90 12.275 .8281 .7430 116 293.80 10.069 .6057 .8634 117 1239.1 16.496 .8925 .6866 118 158.65 9.0495 .5160 .8959 119 699.81 14.147 .7393 .7709 120 398.14 13.557 .9062 .7200 121 571.40 8.7904 .4407 .8600 122 398.40 15.460 1.4653 .6347 123 317.69 11.286 .8077 .7152 124 333.85 13.930 .6360 .8005 125 189.67 7.5787 .5628 .8453 126 143.49 6.8339 2.2265 .5411 127 1176.8 15.477 .6063 .7935 128 535.00 14.554 1.3308 .7251 129 459.30 15.320 .7799 .7309 130 650.79 16.305 1.8965 .5124 131 178.49 13.399 .7358 .7729 132 269.95 12.886 .7100 .7951 133 131.85 10.974 1.5992 .5862 134 416.28 7.0203 .7674 .7014 135 455.55 13.869 .6323 .8510 136 82.942 8.6874 .5238 .8795 80 Note: Treatment of Missing Data Because of the size of the sample and the source of the data, it would be very difficult to discover the cause for each missing data point. Because of this sample firms with a zero for any index were simply eliminated from the study. The exception to this practice was the Purchased Transportation Index. The majority of firms had a zero for this index. These zeros were replaced with the average of the non-zero entries in each year. 81 APPENDIX C Residual Plots and Histograms Histogram of Residuals to Cost Equation EACH * REPRESENTS 5 OBSERVATIONS MIDDLE OF NUMBER OF INTERVAL OBSERVATIONS -1.8 1 * -1.6 0 -1.4 0 -1.2 1 * -1.0 3 * -0.8 1 * -0.6 1 * -0.4 10 ** -0.2 36 ******** -0.0 104 ********************* 0.2 56 ************ 0.4 12 *** 0.6 1 * 0.8 1 * 1.0 1 * Description S t a t i s t i c s of Residuals N 228 MEAN -0.001 MEDIAN 0.023 TMEAN 0.016 STDEV 0.275 SEMEAN 0.018 MAX 0.951 MIN -1.762 Q3 0.136 Ql -0.095 Normal Quantile Plot of Cost Equation Residuals 1.00+ * - * - * 23322 3++97762 .00+ 4++++++++ 67797 334 - * - * -1.00+ *2 - * -2.00+ + + + + + + -3.00 -1.50 .00 1.50 3.00 4.50 82 Residual Plots and Histograms a f t e r d e l e t i n g s i x o u t l i e r s Histogram of Residuals (without 6 observations) EACH * REPRESENTS 5 OBSERVATIONS MIDDLE OF NUMBER OF INTERVAL OBSERVATIONS -0.8 1 * -0.6 1 * -0.4 10 ** -0.2 36 ******** 0.0 104 ********* * * ********** 0.2 56 ************ 0.4 12 *** 0.6 1 * 0.8 1 * Description S t a t i s t i c s of Residuals N; 222 MEAN 0 .021 MEDIAN 0 .028 TMEAN 0 .025 STDEV 0 .200 SEMEAN 0 .013 MAX 0 .778 MIN -0 .787 Q3 0 .137 Ql -0 .084 Normal Quantile Plot of Cost Equation Residuals (without s i x observations) 1.30+ .60+ 22** - 4442 *++977* ++++++ -.10+ 59+++ *4572 *23 _ **2* -.80+ * -3.00 -1.50 .00 1.50 3.00 4.50 83 

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