The impact of unionization on motor carrier costs.

Kerkviet, Joe ; McMullen, B. Starr

I. INTRODUCTION

The increasingly competitive markets fostered by the Motor Carrier Act of 1980 have forced motor carriers to focus on cost saving strategies intended to reduce operating miles, fuel consumption, and capital and labor expenses. There are two reasons unions firms may be at a competitive disadvantage in these efforts. First, although the union/nonunion wage differential has decreased following regulatory reform, Rose [1987] and Hirsch [1988] find that union firms still pay higher wages. Second, managers of unionized firms may have less flexibility in the use of inputs since union work rules restrict the activities and substitutability of drivers, terminal workers, and terminal facilities. Indeed, Harrington [1987] reports that post-1980 trucking expenses are still 40% higher for unionized motor carriers than for nonunion firms. Unionization may affect carrier cost both by increasing the price of labor and by potentially affecting cost function parameters. If union rules make labor less productive, the entire cost function will shift upwards for a given set of factor input prices. Further, Freeman and Medoff [1982] argue that work rules may be expected to result in reduced elasticities of substitution between labor and other inputs in the unionized setting. Indeed, they find that substitution between production labor and other labor in manufacturing is generally lower in unionized settings.

The impact of unionization on production has been investigated in industries such as construction, coal mining, hospitals, and the cement industry by Allen [1984; 1986a; 1986b], Byrnes et al. [1988] and Clark [1980a; 1980b]. The results have been inconclusive, with unionized firms being more productive than nonunion firms in some instances and less productive in others. Studies such as Allen [1986c] and Addison and Hirsch [1989] have utilized production function methodologies that use restrictive functional forms which impose homogeneity and identical elasticities of substitution between pairs of inputs.

Allen [1986c] examines the relative efficiency of union and nonunion firms with a translog cost function, allowing for union effects using intercept and slope parameters that vary by union status. In his study of different types of construction projects, he finds significant differences between the cost functions for union and nonunion firms, but no evidence of the inelasticity of factor substitutions as hypothesized by Medoff and Freeman. In fact, his estimates of factor demand elasticities show no discernible pattern for union versus nonunion firms, leading him to conclude that work rules do not have the anticipated impact on elasticity.

The purpose of this study is to test whether unionization impacts motor carrier costs and, if so, to determine the direction of the impact. Of particular interest is whether the work rules imposed by the Teamster's union have had a significant impact on factor substitutability in unionized firms as argued by Freeman and Medoff [1982].

Friedlaender and Spady [1981], Daughety et al. [1985], McMullen and Stanley [1988], Grimm et al. [1989] and Ying's [1990] studies of motor carrier industry costs have used translog cost functions which implicitly assume that union and nonunion cost functions arise from the same production technology. This is equivalent to accepting the hypothesis that unionization does not affect the production structure of motor carrier firms. If unionization does affect a firm's production process, the results from these studies could be biased.

Accordingly, this study uses a translog cost function to test for differences in the cost structure of union and nonunion carriers. Not only is the translog cost function standard in the motor carrier literature, permitting comparison of these results with those of previous work, it also allows the flexibility necessary to examine the differential impact of unions on cost function parameters and elasticities of substitution between factors.

However, estimates of elasticities based on nonlinear equations may be biased. In particular, Anderson and Thursby [1986] argue that inferences based on the assumption of normality may be incorrect when estimates are drawn from complex or unknown distributions that are unlikely to be normal. Previous reported estimates of elasticities of demand and substitution such as Allen [1986c] suffer from this possible bias. Accordingly, we implement a bootstrap technique suggested by Eakin et al. [1990] to obtain elasticities of demand and substitution and compare these estimates to those obtained from traditional techniques.

The results here indicate a statistically significant difference in the cost structure of union and nonunion carriers. Both groups of firms exhibit the standard technological constant returns to scale, but nonunion firms exhibit greater economies associated with increases in the average length of haul and average shipment size, two output attributes that are important determinants of cost. Calculations based on the cost function estimates indicate that cost for the average union firm is over 70% higher than for the average nonunion firm. Further, this difference cannot be attributed simply to higher factor prices and different output attributes; if union firms had nonunion factor prices and output attributes, their average costs would still be approximately 39% higher than nonunion firms. Despite evidence indicating higher overall average costs for unionized firms, estimated elasticities of substitution indicate that union work rules are ineffective in curbing substitution between labor and other factor inputs.

The paper is organized as follows. Section II discusses how unionization may be expected to influence motor carrier costs. The econometric model is introduced in section III and the data are described in section IV. Empirical results are presented and interpreted in section V. The final section summarizes major findings and identifies questions for further research.

II. UNIONIZATION AND MOTOR CARRIER COSTS

The labor literature contains competing views of the impact unionization may have on a firm's cost and production structure. The monopoly view of unions is that work rules and higher wages cause unionized firms to alter their use of inputs, resulting in the adoption of less efficient technologies than used by their nonunion counterparts. According to this hypothesis, unionized firms can be expected to have lower elasticities of substitution between factors and higher average costs than nonunion firms. Alternatively, Freeman and Medoff [1984] offer the collective voice view of unions. They suggest that unions may raise productivity by improving worker performance and adopting better methods of internal organization. According to this hypothesis, union firms may actually exhibit lower overall costs due to productivity enhancing activities.

Motor carrier labor is represented primarily by the Teamster's Union. Harrington [1987] reports that managers of unionized carriers believe that union work rules prevent the optimal use of labor and owned and rented equipment. As an example, the 1985 Teamster's Master Freight Agreement prohibited the use of either intermodal or owner-operator transportation as a substitute for owned capital and union labor, except to move overflow freight. Given McMullen's [1991] finding that the use of intermodal transport can lower firms' costs, this restriction may place union firms at a cost disadvantage relative to nonunion firms that are free to use the least expensive means available to transport commodities.

However, there is evidence that the national union rules may not actually have much of an impact on a firm's costs. According to the U.S. Department of Labor [1988], the union failed to strengthen these provisions in the 1988 Master Freight Agreement and many companies have departed from the national leadership, signing less restrictive individual contracts. Horn [1990] finds no union/nonunion differences in implementing work measurement standards. However, Shultz [1989] finds lower worker turnover rates for unionized trucking firms. This finding would be compatible with the collective voice hypothesis if the low turnover were due to higher levels of worker satisfaction, resulting in higher productivity. It is possible, however, that the lower turnover in union firms is due to union protection of less efficient drivers that prevents firms from firing a unionized worker. Therefore, lower turnover rates alone do not provide unambiguous support for either the monopoly or collective voice views of unionization.

Informal discussions with trucking industry managers suggest that union/nonunion differences may be the result of aggressive cost cutting strategies adopted by nonunion firms. Union films may either be unaware of these strategies or unable to engage in them due to union rules. For instance, one nonunionized firm pays drivers different amounts depending on shipment-specific factors such as the weather or road conditions. Another nonunion firm encourages efficiency enhancing cooperation between drivers, terminal workers, and management by paying monthly bonuses based on the overall performance of individual terminals. This "teamwork" approach may not be possible in unionized settings where unions often survive by maintaining distance between labor and management.

To determine the impact of unionization on motor carrier firms requires more extensive information on differences in union/nonunion cost structures, factor substitutability, and overall average costs. Evidence that the elasticities of demand and substitution are affected by unionization in the manner suggested above would support the monopoly view of unions. If the elasticity differences are not consistent with those expected from statutory work rules, the collective voice view would be supported only if union firms are more cost efficient. If the "teamwork" strategy of nonunion firms is successful, nonunion firms would be expected to have lower overall average costs than union firms. The cost model presented below provides an explanation of the techniques used to provide a preliminary test of how unionization influences costs for less-than-truckload general freight motor carriers in the U.S.

III. THE MODEL

A cost function approach is used here to examine the production structure of union and nonunion trucking firms. Following McMullen and Stanley [1988], the cost function is specified as

(1) C = C(Q, P, X)

where Q is firm output, P is a 1 x N vector of factor prices, and X is a 1 x K vector of output attributes which control for the heterogeneity of output across firms. As Diewert [1974] notes, the translog function provides a second-order approximation to any arbitrary, twice-differentiable cost function and is used here to approximate (1).

To allow for union/nonunion differences in the parameters of the cost function, equation (1) is respecified as

(2) [Mathematical Expression Omitted],

i,j = 1, ..., N, k, h = 1, ..., K, d = 1,0.

The binary variable, d, is equal to one for firms employing nonunion labor and equal to zero for unionized firms. Thus, any nonunion coefficient is the sum of the estimated union coefficient and the associated coefficient estimate for d. For example, the union coefficient for the ith first-order price term is [[Alpha].sub.i], while the corresponding nonunion term is [[Alpha].sub.i] + [[Alpha].sub.n,i].

The specification in (2) easily allows testing of the hypothesis that all cost function parameters are equal across union and nonunion firms. This is accomplished by testing whether all of the coefficients subscripted with "n" are simultaneously zero. Failure to accept the null hypothesis indicates that pooling of union and nonunion firm data may introduce bias into the cost estimation. It is this sort of test that has been performed in past studies of union/nonunion cost function differences such as Allen [1984; 1986a; 1986b; 1986c] and Clark [1980a; 1980b].

Unfortunately, the test described above sheds little light on the sources of the union/nonunion differences. More definitive tests of union/nonunion differences are possible by using equation (2) to impose restrictions on appropriate subsets of the nonunion parameters. For example, the hypothesis that scale economies are the same for union and nonunion can be tested by imposing the restrictions:

(3) [[Alpha].sub.n,Q] = [[Gamma].sub.n,iQ] = [[Gamma].sub.n,kQ] = 0

i = 1, ..., N, k = 1, ..., K.

The procedure used in this study is to conduct independent tests for differences in the effects of output level, attributes, and factor prices using the general method described in equation (3). With the accepted equality restrictions imposed, (2) is re-estimated. The results are used to calculate union/nonunion differences in average costs, elasticities of substitution, and factor demands.

Throughout this analysis, linear homogeneity of the cost function is imposed. This requires

(4) [Mathematical Expression Omitted]

i,j = 1, ..., N, k = 1, ..., K d = 0,1.

Applying Shephard's lemma to (4) yields an expression for the factor shares of total cost:

(5) [Mathematical Expression Omitted],

i = 1, ..., N d = 0,1.

The own-price elasticities of demand for the ith input are given by

(6) [[Xi].sub.ii] = ([Delta][x.sub.i]/[Delta][p.sub.i])([p.sub.i]/[x.sub.i]) = [[M.sub.i]([M.sub.i] - 1) + ([[Gamma].sub.ii] + [[Gamma].sub.d,ii]*d)]/[M.sub.i],

and the cross-price elasticities of demand between the ith and jth inputs are given by

(7) [[Xi].sub.ij] = ([Delta][x.sub.i]/[Delta][p.sub.j])([p.sub.j]/[x.sub.i]) = [[M.sub.i][M.sub.j] + ([[Gamma].sub.ij] + [[Gamma.sub.n,ij]*d)]/[M.sub.i].

Finally, the Allen-Uzawa elasticities of substitution between inputs are given by

(8) [[Sigma].sub.ij] = (1/[M.sub.j])[[Xi].sub.ij] = 1 + ([[Gamma].sub.ij] + [[Gamma].sub.n,ij]*d)/[M.sub.i][M.sub.j].

Factor shares are estimated simultaneously to increase statistical efficiency. Since the factor shares sum to unity, one of the factor share equations is dropped from the system and the results are invariant to the share dropped. The equation system is estimated by Full Information Maximum Likelihood.

IV. THE DATA

The data are from the American Trucking Association's 1988 Motor Carrier Annual Report. The sample includes all Section 27 carriers with complete data.(1) Section 27 carriers are Class I and II motor carriers which have an average of at least 75% of annual revenue derived from intercity general commodity freight over the preceding three years.

Table I gives variable definitions and descriptive statistics for union and nonunion firms. Capital, labor, fuel, and purchased transportation are the factors of production, with prices PK, PL, PF, and PR. Appendix 1 contains further details on the definitions and construction of input prices.

Firm output (Q) is measured as total annual tonmiles. This variable does not provide a homogeneous measure of output. Two firms with identical tonmiles may differ substantially with regard to the commodity carried, the weight of the load, and the distance traveled. The cost equation (1) contains a vector of attributes to control for this heterogeneity. Following previous studies by Friedlaender and Spady [1981], Daughety, Vigdor and Nelson [1985], McMullen [1987], and McMullen and Stanley [1988], the output attributes are defreed as average length of haul (ALH), average load (ALOAD), average shipment size (ASIZE) and average insurance per tonmile (INS).

The variable ALH is defined as tonmiles divided by tons. Carriers serving longer distances usually experience a decrease in unit cost as the fixed costs associated with terminal and handling expenses are distributed over more units of output. Holding tonmiles and all other prices and attributes constant, an increase in ALH is expected to result in lower costs.

The variable ALOAD is defined as total tonmiles divided by total miles.(2) ALOAD is an indicator of route density, and denser routes should have lower unit costs, suggesting a negative relationship between cost and ALOAD. Average shipment size is total tons divided by the total number of shipments. ASIZE is included to capture the transactions, handling, and coordination savings associated with larger shipment size. For a given output, transactions and handling costs will be smaller for a few large shipments than for many small shipments. The effect of ASIZE on cost is expected to be negative.

The variable INS controls for differences in the value of the commodities transported by a carrier. Higher valued commodities require both more insurance against loss and damage and more handling costs. It is also possible that higher valued commodities may require a higher quality service. In particular, the value of time in transit will be higher for more valuable commodities, thus making their shippers prefer more frequent, faster service. [TABULAR DATA FOR TABLE I OMITTED] Thus, the INS is expected to have a positive effect on costs.

Summary statistics presented in Table I indicate differences in both union/nonunion attributes and factor prices. Nonunion firms tend to be smaller than union firms with an average annual output that is only 55% of union firm output. On average, nonunion firms have a significantly larger ALH than union firms, suggesting that nonunion firms have a more extensive network system than unionized firms. The longer ALH length for nonunion firms may be the result of union work rules that place mileage and/or time restrictions on union drivers. ASIZE and ALOAD are slightly greater for nonunion firms, but the difference is not statistically significant. There also appears to be little difference in INS between firm types, indicating a similar mix of commodities carried by the two types of firms.

As expected, the price of labor is significantly higher for union firms. An unanticipated result is that all other factor prices were higher for union firms. The average union/nonunion difference in factor prices is statistically significant for fuel and labor, with the price of union labor approximately 15% higher and fuel price 10% higher than for nonunionized firms. The higher union price for fuel may reflect a unionized driver's lack of incentive to seek out the lowest price when purchasing fuel. Nonunion drivers, on the other hand, often engage in a variety of profit-sharing schemes with their employer, possibly making them more cost conscious.

V. EMPIRICAL RESULTS

The first step in the analysis is to test for differences in the overall cost functions for union and nonunion firms. To test whether a set of parameters in the union cost function is identical to the corresponding set of parameters for nonunion firms, a likelihood ratio test is used. The test statistic is [[Chi].sup.2] = -2([L.sub.1] - [L.sub.2]), where [L.sub.1] is the maximized log of the likelihood function from estimating (2) and (5) with equality restrictions imposed and [L.sub.2] is the maximized value without equality restrictions. For each test the degrees of freedom equals the number of equality restrictions.

Test results are reported in the first row of Table II. The hypothesis that all the parameters [TABULAR DATA FOR TABLE II OMITTED] of (2) are equal for the two types of firms is rejected with a [[Chi].sup.2] = 200.95 and a probability-value of effectively zero. This indicates differences in the overall cost/production structures of unionized and nonunionized firms, a finding consistent with results in Allen [1984; 1986a; 1986b] and Clark [1980a].

The second step is to test whether subsets of parameters corresponding to output, individual attributes, and factor prices as a group differ significantly between union and nonunion firms. These tests provide evidence regarding the source of cost structure differences. If some of the equality restrictions are accepted, they can be imposed when estimating equation (2), thus increasing the efficiency of the estimation. Table II summarizes the results of these tests.(3)

The hypothesis of parameter equality cannot be rejected for output (Q) or the INS. However, results show statistically significant differences in coefficients between union and nonunion firms for ALH, ALOAD, ASIZE, and factor prices. ASIZE, ALH and ALOAD are attributes that relate to network structure and type of operations, suggesting that union and nonunion firms have different network structures and/or specialize in different sorts of operations. For instance, lower ALOAD and ASIZE may indicate that a carrier offers greater service frequency, a dimension of service quality.

Accordingly, the next step is to estimate (2) and (5) after imposing the accepted equality restrictions from Table II. In the cases where the null hypothesis was rejected, coefficient estimates were allowed to differ between union and nonunion firms. Estimation of equation (2) yields first-order parameters shown in Table III. These estimates can be interpreted as cost elasticities evaluated at the mean of the data. The estimates for all the parameters are in Appendix 2.

In order for our estimates to be consistent with cost-minimizing behavior, the estimated cost functions must be monotonically increasing and strictly quasi-concave in input prices. Monotonicity holds if the estimated input shares are positive, while quasi-concavity holds if the matrix of substitution elasticities is negative semi-definite. Although these conditions cannot be imposed globally for the translog function estimated here, they can be checked at the point of approximation (the sample mean) and for each individual observation by using the estimated coefficients and the price and attribute data to compute the fitted values.

For the estimates reported here, the fitted values indicate that monotonicity holds at the point of approximation, at both union and nonunion means, and for all but three observations. Quasi-concavity holds at the point of approximation, at both the union and nonunion means, and for 152 observations, while at least one quasi-concavity condition was violated for the 62 remaining observations. Overall, these results indicate that the data are generally consistent with cost-minimizing behavior on the part of trucking firms. Further, the generalized [R.sup.2] is calculated to be .99, indicating that the equation has a reasonably good fit.(4)

TABLE III

First-order Parameter Estimates

 Union Nonunion
Variable Coefficient Coefficient Difference

Q(*) 1.05763 1.05763 -
 (12.24) (12.24)

ALOAD(**) -1.175 -.629 .544
 (4.92) (2.14) (2.22)

ALH -.3278 -.558 -.230
 (1.74) (3.46) (1.79)

INS(*) .1397 .1397 -
 (.689) (.689)

ASIZE -.1682 -.2627 -.094
 (1.776) (2.16) (1.01)

PK .3540 .3425 -.0114
 (10.79) (9.79) (.343)

PR(**) .1419 .2387 .096
 (2.89) (5.235) (2.51)

PF(**) .0549 .0407 -.014
 (6.71) (5.96) (2.44)

PL(**) .4492 .3781 .711
 (10.38) (9.27) (4.21)

Notes: Absolute values of asymptotic t-ratios are in parentheses.

* Indicates that equality of the coefficient for union and nonunion
firms is imposed.

** Indicates that the difference in the first-order estimates is
significant at the .05 level.

The results in Table III are consistent with those reported in previous motor carrier industry cost studies. The elasticity of cost with respect to output at the sample mean is 1.057 and not significantly different from one, indicating constant returns to scale. Since scale economies are identical for union and nonunion firms, they cannot be used to explain the observed industry restructuring along union/nonunion lines.

For all attributes except INS, there are significant differences in union/nonunion coefficient estimates that may help explain differences in the two firm types. As expected, costs decline with increases in ALH, ALOAD, and ASIZE and increase with INS. However, cost elasticities with respect to ALH and ASIZE are nearly twice as large for nonunion firms. This suggests that nonunion firms have stronger incentives to expand their network systems to achieve lower costs. Union firms may not be able to achieve these cost economies due to union restrictions.

Unlike ASIZE and ALH, the absolute elasticity of cost with respect to ALOAD is nearly twice as large for union firms. This means that union firms have stronger incentives to achieve cost savings by pursuing denser routes, reducing service qualities such as frequency of service, or increasing backhaul traffic.

To determine the extent to which differences in prices and attributes can explain union/nonunion cost differences, the antilog of (2) is evaluated using parameter estimates and mean variable values. Dividing by output Q yields fitted values for average costs. Union average costs are found to be $0.31 per ton mile, 72% higher than nonunion average costs of $0.18. Some of the higher union costs may be attributed to higher prices and some to differences in output attributes. To estimate the relative importance of these effects, fitted average costs were calculated for several possible situations. The results are summarized in Table IV.(5)

TABLE IV

Average Costs per Tonmile for Union Firms

 Input Prices
 Union Nonunion

 Union .314 .274
Attributes
 Nonunion .261 .227

First, if union firms face the same input prices as the mean nonunion firm, estimated union costs per tonmile fall by about 13% to $0.27. If union firms face union prices but have nonunion output attributes, costs per tonmile decline from an estimated $.31 to $.26. If union firms face both nonunion factor prices and output attributes, estimated average cost per tonmile falls to $0.23. However, $.23 per tonmile is still 29% higher than the $.18 per tonmile for nonunion firms. This suggests that it is something in the production structure itself that is causing the high union costs and not simply lower factor prices and different output characteristics.(6)

Union costs can be expected to be higher if union work rules or institutions constrain substitution between inputs. This possibility can be explored by using the parameter estimates to evaluate (6), (7), and (8) at both the union and nonunion sample means to obtain elasticities of factor demand and substitution. Own- and cross-price elasticities of demand are shown in Table V under the column labelled "Traditional." Similarly, "Traditional" estimated elasticities of substitution are shown in Table VI. As explained in Anderson and Thursby [1986], these estimates are so labelled because their standard errors are computed using the traditional method of approximating the variance formula using a first-order Taylor series. However, these standard errors may be inaccurate due to the non-linearity of equations (6), (7), and (8). Anderson and Thursby [1986] show that the elasticity estimates themselves are drawn from complex or unknown distributions and are not likely to be normal. Thus, inferences based on the assumption of normality may be inaccurate.

To avoid this potential pitfall, we follow Eakin et al. [1990] and use the bootstrap resampling technique to estimate the elasticities and their standard errors. Under the "Bootstrap" column, Table V reports the means and standard deviations obtained from 200 bootstrap estimates of the elasticities of demand. Similarly, Table VI provides the means and standard deviations for the elasticities of substitution obtained from bootstrapping. Note that all standard errors are smaller with the bootstrapping technique.

Using both techniques, all the own-price elasticities in Table V are negative, as expected. While the own-price elasticity of demand for labor in union firms is smaller than for nonunion firms (-.497 versus -.759) using the traditional method, the bootstrapped union [TABULAR DATA FOR TABLE V OMITTED] and nonunion elasticities of demand for labor appear to be very close in magnitude (-.346 versus -.334). The traditional result supports the hypothesis that unionization decreases the elasticity of demand for union labor. This argument has also been coupled with the suggestion that unions may be attracted to industries with a less elastic demand for labor (Freeman and Medoff [1982]). Since we are dealing with a single industry here, however, there is no reason to expect the elasticity of demand for labor to differ between individual firms due to technological factors. The bootstrapped results support this.

While own-price elasticities for capital are similar for union and nonunion firms, union firms seem to have a slightly more elastic demand for rented capital. The cross-price elasticities for labor and rented capital are of particular interest given union rules inhibiting substitution between these factors. The elasticity of demand for labor with respect to the price of rented capital is nearly twice as large for union ([[Epsilon].sub.LR] = .0998) compared to nonunion firms ([[Epsilon].sub.LR] = .0522). Rented capital use is five times more responsive to increases in union wages ([[Epsilon].sub.RL] = .3158) than to changes in non-union wages ([[Epsilon].sub.RL] = .0615). Bootstrap estimates yield similar results. These findings suggest that union rules limiting the substitution of rented capital for owned capital (and thus union labor) have not been successful in preventing substitution of rented transportation services and labor.

TABLE VI

Elasticities of Substitution

Parameter Union Nonunion
 Traditional Bootstrap Traditional Bootstrap

[[Sigma].sub.LF] .0553 -.0374 .1082 .3312
 (.2756) (.1789) (.8113) (.3235)

[[Sigma].sub.LK] .8762 .8837 .9231 .9283
 (.0876) (.0549) (.2687) (.0874)

[[Sigma].sub.LR] .7031 .7139 .1626 .1603
 (.4228) (.2193) (.7156) (.1339)

[[Sigma].sub.FK] .7107 .5639 .2027 .2421
 (.2465) (.1714) (.4080) (.2436)

[[Sigma].sub.FR] .9276 .8649 1.0300 1.011
 (.6853) (.5688) (1.0970) (.3307)

[[Sigma].sub.KR] .9840 .9647 1.3145 1.409
 (.4172) (.2847) (.3293) (.1758)

Standard errors are in parentheses.

he elasticities of demand depend on the factor shares and on the elasticities of substitution as shown by Chi [1989]. These, in turn, are estimated using the first- and second-order price coefficients from the translog cost function. The estimates suggest differences in both components of the elasticity estimates. For example, at their respective means, labor's estimated share of cost is .45 for union and .37 for nonunion firms, while the rented capital shares are. 14 for union and .24 for nonunion firms. The second-order price terms show the same pattern of statistically significant differences between the union and nonunion coefficient estimates.

Estimated elasticities of substitution are shown in Table VI. Union firms seem more able to substitute rented capital for labor as is indicated by a union elasticity of substitution between labor and rented capital that is four times as large for union firms for both traditional and bootstrap results (.7031 for union versus .1626 for nonunion firms using traditional estimates; .7139 versus. 1603 for bootstrap results). Further, these differences in union/nonunion elasticities of substitution between labor and rented capital are statistically significant using a 95% confidence interval.(7) Accordingly, the differences in the elasticity of substitution between labor and rented capital appear to be an important source of the observed differences in their cross elasticities of demand. However, with this single exception, none of the differences between union and nonunion elasticities of substitution estimates are statistically significant using a 95% confidence interval.

These results suggests that union work rules regarding the substitution of rented services for services provided by union labor are largely ineffective. Further, it appears that unionized firms have an incentive to substitute rented capital for labor. A possible explanation is that nonunionized firms have a sufficiently low wage structure that there is little to gain from renting the services of the less expensive owner-operators. Conversely, the higher wages earned by unionized labor in trucking may be the impetus driving unionized firms to substitute rented capital for labor. Allen [1986c] suggests that unions "shock" managements into looking for innovative and efficient ways of doing business. The substitution of rented capital for labor may be an example of such an innovation.

VI. CONCLUSIONS

This study estimates the impact of unions on costs and input use for U.S. motor carriers. A translog cost function is specified so that parameters can vary systematically by union status and independent tests can be made for differences in the effects of input prices and output attributes.

Overall, union and nonunion cost functions were found to be significantly different. Significant union/nonunion differences are found in the effects of factor prices and three output attributes, but not scale or shipment value effects. The differences suggest that nonunion firms are able to reduce costs through changing attributes and achieving networking economies to a greater extent than union firms. Union firms were found to have the greatest potential for cost reduction by increasing ALOAD. Increasing ALOAD can be achieved either through increasing route density or filling empty backhauls. The direct evidence on the impact of union work rules on input substitutions does not support the view that union work rules inhibit input substitution. Elasticity estimates obtained using both traditional and bootstrap methods are, with one exception, not found to be statistically different. The union labor/rented capital cross-price elasticity was found to be twice as large as the nonunion, suggesting more substitution between rented capital and labor for union firms. Higher wages paid by union versus nonunion firms may provide the incentive for union firms to engage in such substitution when there is an increase in the price of labor. This evidence implies that union work rules are ineffective.

Evidence presented here indicates that union firms are at a competitive disadvantage, with average costs about 70% higher than nonunion costs. Although part of the higher cost is due to higher factor prices and different output attributes, a 30% difference remains after controlling for these effects. This could be partially attributable to union work rule restrictions on factor substitution that the current data set is unable to capture.

The "teamwork" observed in nonunion firms suggests that substitution between management, drivers, and terminal workers may allow nonunion firms to achieve cost savings unavailable to union firms due to inflexibility imposed by union rules. Unfortunately, the data set used here was not detailed enough to allow computation of substitution elasticities between different types of labor.

An alternative explanation for higher union costs is that union firms may provide more expensive, higher quality service. Once again, there is no direct measure of service quality. Higher service quality, however, is usually associated with the transportation of higher valued commodities. Shippers of higher valued commodities place greater value on transit time, thus preferring higher service frequency that is more expensive to produce. Insurance per tonmile is a standard measure of commodity value and the statistical tests here indicate no significant difference in commodity value between union and nonunion firms. Thus, the cost differential cannot be attributed to differences in the value of the commodity.

These conclusions suggest that union firms may continue to lose business to nonunion firms unless efforts are made to lower their costs, enabling them to compete more effectively in a virtually deregulated market environment. It is important to note that the higher union costs found here do not arise simply because of higher labor costs or different network attributes. Unions may wish to study the successful cooperative and flexible arrangements being used in nonunion firms to formulate cost reduction strategies essential to the long-run survival of unionized motor carriers. A re-evaluation of union labor policy is particularly timely given the new Teamster's leadership and the trend towards local, rather than national, union decision making.

APPENDIX 1

All data for the computation of cost and factor prices are from the 1988 Motor Carrier Annual Report. Total cost (C) is calculated to include a 12% return to capital:

C = TOE + .12(NOPE + WC).

A real value for net operating property and equipment is obtained by deflating the 1988 dollar values using a ten-year average of the producer's durable equipment implicit price deflator for trucks.

The price of labor (PL) is the firm's total employee compensation divided by the total number of employees. The price of rented capital (PR) is total expenditures on purchased transportation divided by the total number of rented vehicle miles. The price of owned capital (PK) is computed by dividing residual expenses (obtained by subtracting total fuel, labor, and purchased capital expenditures from total cost) by net operating property and equipment plus working capital.

Finally, PF is calculated as total fuel and oil expense divided by an estimate of the number of gallons of fuel used. We assume that trucks average five miles per gallon and estimate gallons by dividing [TABULAR DATA FOR APPENDIX 2 OMITTED] total vehicle miles by five. For those firms not reporting purchased transportation or fuel expenses, regional averages were used as proxies for their PF and PR. Firms are assigned to regions according to the state in which the firm is located. Although there are 267 Section 27 firms listed, only 214 firms had all the data required for this analysis, of which 142 are union firms and the remainder are nonunion.

ABBREVIATIONS

ALH: Average length of haul ALOAD: Average load ASIZE: Average shipment size C: Cost INS: Average insurance per tonmile LTL: Less-than-truckload NOPE: Net Operating Property and Equipment PF: Price of fuel PK: Price of owned capital PL: Price of labor PR: Price of rented capital Q: Annual tonmiles TOE: Total Operating Expenses TONMI: Tonmiles WC: Working Capital

1. The original sample contained 267 observations. After deleting observations which did not have data on ALH, ALOAD, number of shipments (needed to calculate ASIZE), or TONMl, there were 214 firms left in the sample. For firms that reported zero expenditures on purchased transportation services or fuel, the average regional factor price was used as a proxy for the market price. The average regional factor price thus serves as a proxy for the factor price faced by the firm in its decision making process.

2. ALOAD is a weighted average load for the firm just as ALH gives a weighted average distance. Note that ALOAD times ALH does not result in TONMI.

3. It is not possible to test for differences in individual factor price coefficients because of the homogeneity restrictions imposed. The test performed is whether there are any differences in all factor price coefficients.

4. The generalized [R.sup.2] is calculated as

1 - exp[2([L.sub.1] - [L.sub.2]) / T],

where [L.sub.1] is the maximum value of the likelihood function when the coefficients of all the right-hand variables are constrained to equal zero, and [L.sub.2] is the maximum when these coefficients are included in the model. T is the number of observations. Berndt and Khaled [1979] show that the "generalized" [R.sup.2] is related to the likelihood ratio test that all coefficients are equal to zero.

5. The calculation of average union and nonunion costs can also be done by calculating each individual firm's cost using that firm's factor prices and attributes, and then taking the average. This method still yields higher average costs for union firms ($.55 versus $.41). However, later in this section, calculations are made putting union factor prices and attributes in the nonunion cost function and vice versa to see how firms would operate in a different institutional setting. For this analysis, it is impossible to tell exactly what union prices and attributes would be for any individual nonunion firm since these are not observed. To allow comparison with the existing situation, the union/nonunion average cost figures are calculated using the average prices and attributes for union and nonunion firms.

6. It also appears that nonunion firms could produce output with union prices and attributes with lower costs than union firms. The fitted average cost for a nonunion firm assumed to pay nonunion prices and producing with union attributes is $0.23. This compares to $0.27 for a union firm facing the same prices and attributes. Similarly, if the nonunion firms are assumed to face union prices and produce with union attributes, their average costs are $0.27 compared to union average costs of $0.31.

7. The 95% confidence interval for the elasticities of substitution was obtained using the percentile method described in Eakin et al. [1990].

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