Do unions impact efficiency?: evidence from the U.S. manufacturing sector.

I. INTRODUCTION

The relationship between labor unions and firm performance has garnered a vast amount of attention from scholars, unions, and businesses, as well as from policymakers as extensive studies have explored both the theoretical foundations and the empirical evidence regarding the impact of labor unions on productivity, as well as on other aspects of business, such as sales, profitability, investment, and employment growth (Doucouliagos and Laroche 2003). Perhaps one of the most relevant public policy questions is how unions affect productivity. Although studies have empirically investigated union productivity effects for a variety of industries and public sectors, particularly in the U.S. and European countries, empirical evidence on this question, however, is mixed.

Brown and Medoff (1978) and Freeman and Medoff (1984), in their early and influential work, argued that labor unions can raise productivity by inducing managers to adopt more efficient production methods and policies, and by providing better communication channels between workers and management. Supporting this impression, Dworkin and Ahlburg (1985) argued that opening communication channels between management and workers can result in integrative, rather than distributive, bargaining. Allen (1984) used the example of the construction industry, and cited union hiring halls, apprenticeship programs, and managerial shock effects as the reasons for union productivity improvements. In recent years, many employers have adopted new ways of organizing work that emphasize employee involvement. Empirical evidence suggests that various human resources management practices have a positive impact on firms' productivity. Black and Lynch (2001) found that unionized plants with these new approaches to organizing work had higher productivity than other similar non-union plants. Recent studies indicate that improved productivity of firms with labor unions may reflect better human resources management practices (Bloom and Van Reenen 2007; Doucouliagos and Laroche 2006; Ichniowski and Shaw 2003; Machin and Wood 2005).

However, Lewis (1963) pointed out that one of the most well-established impacts of labor unions on firms is the ability to raise wages above competitive levels. Such a monopoly power may exert adverse impacts on firm productivity by distorting the labor market. Other unfavorable effects of unions are on R&D spending and investments, since by acting as a tax on the return on investment, unions limit innovative and investment activities (Connolly, Hirsch, and Hirschey 1986; Hirsch and Link 1987; Link and Siegel 2002; Lommerud, Meland, and Straume 2006; Menezes-Filho and Van Reenen 2003). These effects can have a detrimental impact on the dynamic productivity of firms. Thus, unions can both enhance and detract from firms' productivity performance. Because of the ambiguity over the net effect of unions, an assessment of the union's effects on economic performance hinges on empirical evidence (Doucouliagos and Laroche 2003). (1)

Although most literature focuses on the performance or productivity impacts of unions, a strand of literature also looks at the channels through which unions affect measured performance/productivity. Measured productivity can be decomposed into two important components: the adopted production technologies and the efficiency of utilizing the technology. The former represents a shift in the production function and the latter shows the distance between actual production level and frontier production level for given inputs. An increase in the measured productivity may result if a firm adopts a better production technology or improves "technical efficiency" by moving production toward the frontier level of a given technology.

The arguments for or against unions regarding productivity can trace their causes to the impacts on one or both of the productivity components. For instance, the communication effect of Brown and Medoff (1978) and Freeman and Medoff (1984) results in improved efficiency in using installed technology, whereas the outcome of changing production methods, also mentioned by the same authors, amounts to choosing new production technologies. Freeman and Medoff (1984) also suggested that "union shocked" management is able to extract more output from a given amount of inputs than management, which may be because of improved information flow among workers or between workers and management (Carmichael and MacLeod 1993). This channel of effect also amounts to improved technical efficiency.

For theoretical arguments, Kuhn (1985) provided a model that explains unions' effect on firm productivity, utilizing an agency cost model to show that unions may improve firm productivity by reducing its monitoring costs. Based on the agency cost theory of Jensen and Meckling (1976), Kuhn (1985) assumed that firm managers own a of the firm, whereas outside shareholders own (1- [alpha]) of the firm. Because a < 1, the effort level of managers would be less than the optimal level required to maximize the total value of the firm. The agency problem is partially mitigated if managers' efforts can be monitored by outside shareholders. However, because shareholders may be numerous and not well organized, the cost of monitoring could be high. However, organizing the union makes monitoring much easier with lower cost. The union stewards and representatives are always in the plant and can easily observe managers' performance, enhancing managers' efforts and resulting in improved technology efficiency. Better monitoring would most likely lead to a more efficient use of current technology, that is, improving technical efficiency.

A strand of empirical research employs the data envelopment analysis (DEA) approach, which is a mathematical programing method. Byrnes et al. (1988) used the DEA approach to estimate the effect of unions on technical efficiency using data from the U.S. mine establishments in the 1970s. They did not find evidence that unions harmed technical efficiency. Doucouliagos and Laroche (2006) also used the DEA approach to investigate the effects of human resource practices and unionization on technical efficiency of French industries. They found that while the human resource practice improves efficiency, existing unions moderated the effect. A different strand of literature uses the econometrics approach of stochastic frontier models. Cavalluzzo and Baldwin (1993) compared the productivity differential between union and non-union contractors in the United States and found a substantial union productivity premium. Dickerson et al. (1997) used the model proposed by Cornwell et al. (1990) to examine the effects of union strikes on productivity and efficiency in a sample of UK manufacturing industries in the 1970s. They found that strikes only had a negligible net impact on output in this period, and the presence of unions mitigated the effect.

This article estimates the impact of labor unions on the U.S. manufacturing sector using state-level panel data on 48 states from 1983 to 1996, focusing on technical efficiency effect of the union. The main motivation of this article stems from observing that unionization rates in the U.S. manufacturing sector at both the national and state levels have been continuously declining for the last few decades. Understanding how much these changes over time have affected efficiency or productivity of the U.S. manufacturing sector would be useful for scholars, unions, and businesses, as well as policymakers. Given this objective, using the state-level manufacturing sector as a unit of analysis would be appropriate as data on dependent and independent variables are not only available, but also provide a rich panel data set that consists of 48 states and over 14 years (672 observations). (2)

The current study adopts the econometric approach (the stochastic frontier model) in this research. Stochastic production frontiers are preferred for a number of reasons. Although the DEA approach has the advantage of not requiring the specification of any particular functional form of the underlying production process, using deterministic frontiers is based on the unrealistic assumption that total error is because of inefficiency and that there are no random errors that occur in the production process. (3) Another benefit of stochastic frontiers is that they allow inefficiency to exist in all states. In contrast, DEA identifies the frontier by assigning some of the states as operating under best practice (100% efficient) and defining the frontier in relation to these firms. With a stochastic production frontier, every state can be inefficient, although some will be more inefficient than others. Compared to the DEA method, the econometrics approach of the stochastic frontier model is more structural in specifying the relationships between variables and easily accommodates random noises in the data.

This article adds to the union-efficiency literature in several ways. First, this article employs a Tran slog stochastic production specification which is more flexible than the Cobb-Douglas specification adopted by most existing studies (Cavalluzzo and Baldwin 1993; Dickerson et al. 1997). Second, the cross-sectional nature of the data typically limits studies in the union-efficiency literature at the firm level, and the labor union measure is commonly defined with a dummy variable with a value of 1 if a union is present and 0 otherwise, because the preferred union density figures are hardly available. Not only does state-level manufacturing data enable us to cover an extended period, from 1983 to 1996, but the availability of union density also allows us to measure the effect of the continuous decline in union density in U.S. manufacturing on technical efficiency and productivity. Third, by employing the "true-fixed effect" panel stochastic frontier model of Greene (2005), econometric analysis presented in the article captures the effects of unionization rate on technical efficiency on U.S. states' manufacturing, while unmeasured attributes that are fixed over time are controlled for estimating the effect of labor unionization. To our knowledge, this is the first study that applies the true-fixed effect model to estimate union effects.

The remainder of this article is organized as follows. Section 2 discusses the empirical model and data, Section 3 presents the results, and Section 4 concludes.

II. EMPIRICAL MODEL AND DATA

The stochastic frontier model for cross-state panel data is specified as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where y (state manufacturing output) is subscripted with i (state) and t (year), [[mu].sub.i] are state-specific fixed effects and m = 1, ... M indexes inputs that affect the frontier (maximal) level of output. The input variables (xs) consist of state public capital stock (g), state private manufacturing capital stock (k), manufacturing labor (l.), and unionization rate (union). (4) Non-neutral technical change is assumed in Equation (1) by introducing t (time trend), [t.sup.2] (time trend squared), and cross-products of t and inputs to capture technical change effect. (5) [u.sub.it] is an error term which is independent and identically distributed [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and independent of [u.sub.it] which are non-negative random variables that account for technical inefficiencies in production. [u.sub.it] are assumed to be independently distributed as truncations at zero of the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]distribution where [S.sub.it]= [Z.sub.it] [delta], where zit is a vector of variables that affects the deviation of output from the frontier causing technical inefficiency and [delta] is a vector of parameters to be estimated.

The inefficiency is determined by U.S. states' private manufacturing unionization rates, unemployment rates, wage index, U.S. unemployment rates, and time trend. The primary variable of interest is U.S. states' private manufacturing unionization rate. To disentangle the union effect from other effects, several variables are included in the inefficiency function. U.S. states' unemployment rate and U.S.'s unemployment rate are included to account for cyclical changes in unutilized capital and hoarded labor that are likely to hinder a state from reaching the production frontier (Munnell 1990). We also controlled for worker quality by including the wage index in the equation. The quality of union and non-union workers may be different because unions encourage their members to stay longer in the firm and thus their skill levels may be higher because of average longer job tenure. Given the fact that workers are generally paid according to their performance, the wage index obtained by dividing the gross earnings of all employees on the payroll of operating manufacturing establishments by the number of employees is used as a proxy for labor quality. (6) Finally, this study includes time trend, commonly employed in the frontier production literature, to capture other time-related factors. Following Battese and Corra (1977), we replace [[[sigma].sup.2].sub.v] and [[[sigma].sup.2].sub.u] and [[sigma].sup.2] = [[[sigma].sup.2].sub.v] + [[[sigma].sup.2].sub.u] and [gamma] = [[[sigma].sup.2].sub.u]/([[[sigma].sup.2].sub.v]+[[[sigma].sup.2].sub.u]). The maximum-likelihood estimator (MLE) (7) estimates the model parameters ([theta], [delta], [[sigma].sup.2], and [gamma]).

The above-specified model allows the production function (frontier) to have state-specific fixed effects ([[mu].sub.i]). That is, instead of assuming a single U.S. frontier function for all the states, we allow heterogeneity via state-specific intercepts in the frontier production function (the "true-fixed effect" panel stochastic frontier model by Greene 2005). This effectively eliminates biases in the parameter estimates that arise from omitting unobserved time-invariant variables correlated with included explanatory variables. As emphasized in theoretical and empirical studies by Kumbhakar (1991) and Greene (2005) respectively, failure to include individual-specific effects in a panel stochastic model is likely to bias the estimate of the one-sided error, [u.sub.it], which is one of the most important estimation elements. In a recent study, Kumbhakar and Wang (2005) provided evidence of heterogeneity in the production functions, for both the translog and Cobb-Douglas specifications, across countries.

The data covered 48 contiguous states observed for the period 1983-1996. (8) The primary independent variable of interest was the U.S. private manufacturing unionization rates, defined as the percent of employed workers covered by a collective bargaining agreement obtained from unionstats.com. (9) The state-level data on manufacturing output (million dollars), labor quantities, wage index, state-level manufacturing private capital stock, and public capital stock were obtained from Cohen and Morrison Paul (2004). (10) Manufacturing output was deflated by manufacturing the Gross State Product deflators for each state. The perpetual inventory method was applied to the data on state-level new capital expenditures (Annual Survey of Manufactures) as well as to the state-level public infrastructure investment data to obtain private manufacturing capital stock and public capital stock estimates. (11) U.S. and U.S states' unemployment rates were obtained through the U.S. Bureau of Labor Statistics. Table 1 provides summary statistics.

TABLE 1

Summary Statistics

Variables                         Mean   Standard    Min     Max
                                         Deviation

Panel (a)
  Manufacturing                  62,998     63.858  2.229  368,329
  outputs

  Private                        19.894     20.758    645  105.892
  manufacturing capital stock

  Public capital stock           15.495     13.410  2.108   78.105

  Manufacturing                  13,488     14,862    186   79,339
  labors

  Private                         21.34      10.02   2.70    50.00
  manufacturing unionization
  rate (%)

  States' unemployment rate (%)    6.25       2.00   2.30    17.40

  U.S. unemployment rate (%)       6.59       1.14   5.30     9.60

  Wage index                       0.81       0.12   0.54        1

Year         Observation        State-Averaged Private
                            Manufacturing Unionization Rate (%)

Panel (b)

  1983                48                                27.19

  1984                48                                25.88

  1985                48                                24.99

  1986                48                                23.86

  1987                48                                22.22

  1988                48                                21.75

  1989                48                                20.91

  1990                48                                20.60

  1991                48                                20.56

  1992                48                                19.49

  1993                48                                18.81

  1994                48                                18.30

  1995                48                                17.18

  1996                48                                16.96

Sources: (a) Cohen and Morrison Paul (2004), U.S. Bureau of Labor
Statistics, Statistical Abstract of the United States (various issues)
and www.unionstats.com and (b) www.unionstats.com.

III. RESULTS

We estimated two versions of Equation (1), and Tables 2 and 3 report the results. Model 1 in Table 2 assumes no state-specific fixed effects (i.e., [[mu].sub.i) = 0, [for all] i) and Model 2 in Table 3 allows for the full set of fixed effects. Before discussing the individual coefficients, we note that the absence of the inefficiency effects of the generalized likelihood-ratio tests of the null hypothesis are strongly rejected in both models. (12) Because each individual coefficient of the inputs (and interaction terms of inputs) of a translog model does not convey interpretable information, we calculated output elasticities for the inputs and the results are reported in Table 4.

TABLE 2

The Translog Model without State-specific Fixed Effects (Model 1)

Frontier Function         Coefficient  Standard  Inefficiency
                                       Error     Function

[[theta].sub.0]           -7.269 ***   0.921     [[delta].sub.0]
[[theta].sub.g]           1.603 ***    0.355     [[delta].sub.w]
[[theta].sub.k]           -1.157 ***   0.351     [[delta].sub.t]
[[theta].sub.l]           2.053 ***    0.332     [[delta].sub.un]
[[theta].sub.kk]          0.071        0.126     [[delta].sub.un2]
[[theta].sub.ll]          -0.014       0.039     [[delta].sub.union]
[[theta].sub.gg]          (-0.051)     0.110
[[theta].sub.kl]          0.040        0.108
[[theta].sub.kg]          0.227 ***    0.080
[[theta].sub.gl]          -0.347 ***   0.063
[[theta].sub.t]           0.097 ***    0.028
[[theta].sub.tt]          0.004        0.001
[[theta].sub.kt]          -0.028       0.008
[[theta].sub.gt]          -0.011       0.005
[[theta].sub.lt]               0.029   0.007
[[theta].sub.union]        0.947 ***   0.213
[[theta].sub.unionunion]   0.140 ***   0.052
[[theta].sub. unionk]     -0.446 ***   0.067
[[theta].sub. uniong]          0.033   0.036
[[theta].sub. unionl]     0.383 ***    0.061
[[theta].sub. uniont]        -0.006    0.005

Frontier Function         Coefficient  Coefficient  Marginal
                                                    Efficient

[[theta].sub.0]           4.283         4.283                ***
[[theta].sub.g]           -8.996       -8.996       (-1.101) ***
[[theta].sub.k]            0.254        0.254        (0.031) ***
[[theta].sub.l]            0.190        0.190        (0.023) ***
[[theta].sub.kk]          -0.039       -0.039           (-0.005)
[[theta].sub.ll]          -0.029       -0.029       (-0.004) ***
[[theta].sub.gg]
[[theta].sub.kl]
[[theta].sub.kg]
[[theta].sub.gl]
[[theta].sub.t]
[[theta].sub.tt]
[[theta].sub.kt]
[[theta].sub.gt]
[[theta].sub.lt]
[[theta].sub.union]
[[theta].sub.unionunion]
[[theta].sub. unionk]
[[theta].sub. uniong]
[[theta].sub. unionl]
[[theta].sub. uniont]

Frontier Function         Standard
                          Error

[[theta].sub.0]           1.198
[[theta].sub.g]           2.459
[[theta].sub.k]           0.070
[[theta].sub.l]           0.044
[[theta].sub.kk]          0.028
[[theta].sub.ll]          0.007
[[theta].sub.gg]
[[theta].sub.kl]
[[theta].sub.kg]
[[theta].sub.gl]
[[theta].sub.t]
[[theta].sub.tt]
[[theta].sub.kt]
[[theta].sub.gt]
[[theta].sub.lt]
[[theta].sub.union]
[[theta].sub.unionunion]
[[theta].sub. unionk]
[[theta].sub. uniong]
[[theta].sub. unionl]
[[theta].sub. uniont]

Other Parameters

                 coefficient  Standard Error

[[sigma].sup.2]  0.094*       0.015
[gamma]          0.0823*      0.027

Model Statistics

Log-likelihood               300.58
LR test of one-sided error  134.265

Notes: Subscripts of the symbols indicate the variable or variables,
where g is the public capital, k the private capital, the labor.
the time trend, union the union rate, iv the wage index, un the state
unemployment rate, and un2 the U.S. unemployment rate.

* 10% significance level, ** 5% significance level, and *** 1%
significance level.

TABLE 3

The Translog Model with State-specific Fixed Effects (Model 2)

Frontier Function          Coefficient    SE     Inefficiency Function

[[theta].sub.0]             20.128 ***  3.667        [[delta].sub.0]
[[theta].sub.g]             -5.501 ***  0.804        [[delta].sub.0]
[[theta].sub.k]              2.378 ***  0.755        [[delta].sub.0]
[[theta].sub.l]                  0.097  0.633        [[delta].sub.0]
[[theta].sub.kk]                -0.004  0.217        [[delta].sub.w]
[[theta].sub.ll]                 0.013  0.126        [[delta].sub.t]
[[theta].sub.gg]             0.807 ***  0.152       [[delta].sub.un]
[[theta].sub.kl]                 0.036  0.163      [[delta].sub.un2]
[[theta].sub.kg]              -0.216 *  0.126    [[delta].sub.union]
[[theta].sub.gl]                -0.018  0.108
[[theta].sub.t]              0.139 ***  0.029
[[theta].sub.tt]             0.004 ***  0.001
[[theta].sub.kt]                -0.011  0.005
[[theta].sub.gt]            -0.025 ***  0.005
[[theta].sub.lt]             0.025 ***  0.004
[[theta].sub.union]              0.048  0.028
[[theta].sub. unionunion]    0.143 ***  0.046
[[theta].sub. unionk]         0.146 **  0.064
[[theta].sub. uniong]            0.064   0.05
[[theta].sub.l]               0.125 **  0.054
[[theta].sub.t]              -0.01 ***  0.003

Frontier Function          Coefficient    (Marginal       SE
                                           Efficient)

[[theta].sub.0]                  2.694           ***  0.301
[[theta].sub.g]                 -7.257      (-0.533)  0.456
[[theta].sub.k]                  0.212   (0.016) ***  0.017
[[theta].sub.l]                  0.162   (0.012) ***  0.011
[[theta].sub.kk]                 0.022       (0.002)  0.019
[[theta].sub.ll]                -0.024  (-0.002) ***  0.004
[[theta].sub.gg]
[[theta].sub.kl]
[[theta].sub.kg]
[[theta].sub.gl]
[[theta].sub.t]
[[theta].sub.tt]
[[theta].sub.kt]
[[theta].sub.gt]
[[theta].sub.lt]
[[theta].sub.union]
[[theta].sub. unionunion]
[[theta].sub. unionk]
[[theta].sub. uniong]
[[theta].sub.l]
[[theta].sub.t]

Other Parameters

                 cofficient  Standart Error

[[sigma].sup.2]   0.062 ***           0.009
[gamma]           0.937 ***           0.007

Model Statistics

Log-likelihood               838.01
LR test of one-sided error  309.882

Notes: Slate-specific fixed effects are not reported. Subscripts of
the symbols indicate the variable or variables, where g is the public
capital, k the private capital, / the labor, / the time trend, union
the union rate, w the wage index, un the state unemployment rate,
and un2 the U.S. unemployment rate.

* 10% significance level, ** 5% significance level, and *** 1%
significance level.

TABLE 4

Output Elasticities and Returns to Scale

Model 1                           Model 2

              Coefficient  SE                   Coefficient  SE

Output                                  Output
elasticities                      elasticities

G               0.193 ***  0.024             G       -0.142  0.099

K               0.464 ***  0.034             K     0.128 **  0.052

L               0.402 ***  0.033             L    0.938 ***  0.050

union               0.032  0.029         union   -0.099 ***  0.024

T               0.010 ***  0.003             t    0.018 ***  0.003

Returns to      1.058 ***  0.013    Returns to    0.924 ***  0.113
scale                                    scale
(g, k l)                             (g, k, l)

Notes: Coefficients are evaluated at the mean, and the associated
standard errors are computed using the Delta method. Subscripts of
the symbols indicate the variable or variables, where g is (he public
capital, k (he private capital. / the labor. / the time trend, and
union the union rate.

* 10% significance level, ** 5% significance level, and *** 1%
significance level.

Overall, the estimates of the frontier production functions are different between models with and without state-specific fixed effects. Take, for example, the union effect, which is the main focus of our study. Without the fixed effects, Model 1 shows an insignificant output elasticity, but the elasticity of union becomes significantly negative when the fixed-effect specification is used in Model 2. The negative impact of the union on the production frontier indicates that the union may hinder the adoption or progress of production technology, which may occur if the union limits the firms' ability to invest in R&D and other types of innovative activities (Connolly, Hirsch, and Hirschey 1986; Hirsch and Link 1987; Link and Siegel 2002; Menezes-Filho and Van Reenen 2003). Our union model exerts its influence on productivity through both the technology channel (shift of the frontier function) and the efficiency channel (distance between the actual production and frontier production). This article discusses the effects from the second channel in a later section.

The output elasticities of other production inputs also show noticeable differences between Models 1 and 2. The elasticities of both public and private capitals decrease when the fixed effects are included, whereas the labor elasticity increases from 0.402 (Model 1) to 0.938 (Model 2) with fixed effects. Technology progress (effect of t) also increases horn 1% to about 2% per year after controlling for fixed effects, and the later figure is consistent with the literature's findings of U.S. industries (Kumb-hakar and Wang 2006). The result sheds light on the impacts of individual heterogeneity on estimates.

Because Model 1 nests within Model 2, we conducted the likelihood-ratio (LR) test on the joint significance of state-specific fixed effects. The LR statistics are 1074.86. Given the degree of freedom equal to 47, the test overwhelmingly rejects the hypothesis that fixed effects are jointly insignificant. Therefore, the data provide evidence of heterogeneity captured via the state-specific fixed dummies in the production functions of the U.S. manufacturing sector. The results reinforce the finding of Kumbhakar and Wang (2005).

In terms of technical inefficiency determinants, Tables 2 and 3 report the estimated effects. Because the exogenous determinants of inefficiency enter the inefficiency function in a nonlinear way, we reported not only the coefficients of determinants, but also their marginal effects defined as [alpha] E ([alpha] / [Z.sub.it)). The marginal effects were calculated using the formula given in Wang (2002). Qualitatively, the marginal effects of the various exogenous determinants were similar between the two models. In particular, findings revealed that labor unions reduce technical inefficiency (increase technical efficiency). The marginal effects are -0.004 in Model 1 and -0.002 in Model 2, and both are statistically significant. A figure of -0.004 (-0.002) implies that the output can be improved by 0.4% (0.2%) if the existing technology and resources are used more efficiently. The finding that unions improve technical efficiency is consistent with the communication effect of Brown and Medoff (1978), the union shocked management hypothesis of Freedman and Medoff (1984) and Carmichael and MacLeod (1993), and the agency cost story of Kuhn (1985).

Findings for other variables show that although the U.S. unemployment rate does not have significant effects on technical inefficiency, the state-level unemployment rate is detrimental to manufacturing sectors' technical efficiency (increases inefficiency). A plausible explanation is that the unemployment rate positively correlates with firms' excess capacity (because of fixed capitals and labor hoarding). Therefore, production potentials are not fully realized when the unemployment rate is up, resulting in increased technical inefficiency. Finally, as expected, wage increases, which is a proxy for labor quality, have significantly positive effects in improving technical efficiency (reducing inefficiency).

Table 5 reports the efficiency index defined as E (exp (-[u.sub.it]) | [u.sub.it] - [u.sub.it]), which measures the percentage by which the potential production is achieved. The results show that the sample mean of the index is about 91% (Model 1) to 94% (Model 2), indicating fairly high efficiency levels. The efficiency index of Model 1 is expectedly lower than that of Model 2, because Model 1 may incorrectly capture some of the time-invariant and state-specific effects as inefficiency.

TABLE 5

Efficiency Indexes

Model  Mean    25%    50%    75%

1      0.908  0.892  0.930  0.951
2      0.940  0.928  0.958  0.973

Note: The efficiency index is E (exp (-[u.sub.it] | [u.sub.it] -
[u.sub.it]) based on Battese and Coelli (1988).

As discussed earlier, unions may affect productivity through both the technology frontier and the technical inefficiency channel. Here we calculate the union's overall effect on productivity using the results of Model 2. The effect is calculated by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Because we used the log of unionization rate (In [union.sub.it)) in the translog specification of the frontier equation (i.e., the f (.) function) and the rate level in the inefficiency function (i.e., the u (.) function), the first term on the right-hand-side of the equation may be transformed using the following approximation equation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

As shown, union elasticity on the technology frontier is--0.099 and union marginal effect on technical inefficiency is--0.002. Given that the sample mean of the unionization rate is 21.34, the overall effect measured at the mean is equal to -0.0026 (=-0.099/21.34 + 0.002). The technology channel dominates the inefficiency channel. Interestingly, the conclusion would have reversed if we based our analysis on Model 1, which ignores time-invariant and state-specific fixed effects.

The unionization rate declined in the sample period from 1983 to 1996. Given the findings that unionization increases technical efficiency but reduces overall productivity, it would be interesting to see the impact on production efficiency and productivity had the unionization rate remained at the higher level of 1983. To this end, we conducted two sets of counterfactual simulations. First, we used the estimated parameters of Model 2 to recalculate the efficiency index for the year 1996 assuming the unionization rate in each state was at the 1983 level. The result yields a mean efficiency index of 0.975. If the actual data is used, the mean efficiency index in 1996 is 0.951. Therefore, declined unionization rate impairs the technical efficiency by about 2.4 percentage points.

Second, we used the results of Model 2 to compute the (conditional) expected level of log-output with and without the unionization rate fixed at the 1983 level.

The expected level of output is defined as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where E ([v.sub.it] | In x, z) is zero and the formula of E ([u.sub.it] | In x, z) is given in Wang (2002). Results show that the expected log-output in 1996 is 10.704 using the actual data, and the figure would reduce to 10.630 had the unionization rate been fixed at the 1983 level. This indicates an industry gain of 7.4% of output owing to the declining unionization rate.

This section shows that the unionization helps improve the technical efficiency of firms but hampers their technology adoption. The results provide important policy implications. As the long-term trend of the declining unionization rate continues in many of the U.S. states, efforts should focus on implementing efficiency-improving measures where there are less union stewards and representatives in the plants to monitor managements and help communications between workers and managers. One of the possible measures is to improve the quality of workers, which is shown to be positively correlated with technical efficiency, through better human resource management practices such as training, incentive compensation plans, employee monitoring, profit sharing, and information sharing. However, for a few states which show signs of increasing unionization rates in the recent years (e.g., California and Colorado), the policy should be designed to mitigate the union's negative impacts on firms' technology adoptions. Lowering the cost of R&D and providing more incentives for adopting new technologies are among the possible actions.

IV. CONCLUSION

This article investigates channels through which unions affect measured performance/productivity. Utilizing state-level panel data on 48 states from 1983 to 1996, we estimate the impact of labor unions on the U.S. manufacturing sector, focusing on the technical efficiency effect of the union. Employing the "true-fixed effect" panel stochastic frontier model, the results indicate that while labor unions reduce firms' technical progress, they improve the technical efficiency by which firms utilize existing technology. The fall of the unionization rate in the 1983-1996 period thus impaired firms' technical efficiency by 2.4 percentage points. However, because the effect on technical progress dominates the effect on technical efficiency, the overall result of the declining unionization increases the manufacturing output by 7.4% in the sample period.

Although the use of state-level manufacturing sector as the unit of analysis enables us to investigate the impact of labor unions on technical efficiency of the U.S. manufacturing sector, the data does not allow for the investigation of union effects at the less aggregate levels such as industry level. As noted by Kuhn (1998), the union effects may be different among industries within the manufacturing sector because of different management approaches, production methods, and other industry-specific characteristics. In addition, most decisions affecting technical efficiency are made by the firm and, therefore, are likely affected more by union activities at the firm level than by those at the aggregate level. Thus future studies at the industry and firm levels would be nice complements to the current study.

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ABBREVIATIONS

DEA: Data Envelopment Analysis

LR: Likelihood Ratio

(1.) As noted by Kuhn (1998), a fair summary of the literature suggests that not only are both positive and negative effects conceivable, but both may well exist in different industries and situations. Supporting this impression, Hoxby (1996) used district-level data to find a negative effect of unions on productivity of U.S. public elementary schools. Black and Lynch (2001) found that unions' productivity effects depend on other aspects of the human resources environment, which tends to be negative when unions maintain more traditional labor management relations, but positive when unions adopt new or "transformed" industrial relations practices that promote joint decision making coupled with incentive based compensation. A recent meta-analysis by Doucouliagos and Laroche (2003) on 73 studies shows negative association between unions and productivity for the United Kingdom, whereas a positive association for the United States in general and for U.S. manufacturing.

(2.) While there is substantial intra-industry variation in union coverage in the United States, at least at the two-digit SIC-level, 75 of 82 census industry codes (three-digit CIC) in the U.S. manufacturing sector have experienced declining unionization rate, on average 13%, from 1983 to 1996 (www.unionstats.com). This study also found a similar decline in state-level unionization rate for the manufacturing sector as a whole (Table 1).

(3.) It should be noted that here we employed a translog specification on the stochastic frontier model which is considered more flexible than the Cobb-Douglas specification.

(4.) In Equation (1), we allow unionization to affect the frontier by including the union variable into the production function as suggested by empirical evidence on unions and technology change. For example, Link and Siegel (2002) investigated the relationship between unions and implementing new technologies by utilizing a qualitative analysis (field-based methods) in the U.S. coal mining industry. The findings suggest that unions constitute an obstacle in adopting and using new technologies. Menezes-Filho and Van Reenen (2003) focused on surveying recent microeconometric results in the areas of R&D, innovation, technological diffusion, and productivity growth. Empirical evidence shows consistently strong and negative impacts of unions on R&D in North American studies.

(5.) Non-neutral technical change has been widely used in studying stochastic frontier models (Heshmati, Kumb-hakar, and Hjalmarsson 1995). In addition, recent empirical evidence on aggregation production (Henderson and Russell 2005) suggests that the production function shifted in a non-neutral way.

(6.) Cohen and Morrison Paul (2004) used a similar strategy to determine the price of labor at the state-level manufacturing sector.

(7.) The likelihood function can be found in the appendix of Battese and Coelli (1993).

(8.) The data excluded the states of Alaska and Hawaii and the District of Columbia. The data coverage was jointly determined by the availability of all variables used in the model. While data on some variables were available to date, the others were limited to preserve data consistency. Because the U.S. Bureau of Economic Analysis does not construct state-level private capital in the manufacturing sector, we relied on the dataset constructed by Cohen and Morrison Paul (2004), considered the most recent and refined state-level data estimate for private capital stock in manufacturing. However, the availability of data was limited to 1996 because of the change of SIC industry definitions (before 1997) to NAICS industry definitions (after 1997). This discontinuity results from many sources, including differences in source data and different estimation methodologies that may affect estimates for state-level private capital stock. Although the data employed in this article might appear out-dated, the empirical evidence found herein proves to be relevant and useful as several studies on union efficiency/productivity in the United States employed similar period data. Therefore, this paper's results can serve as a comparison (Doucouliagos and Laroche 2003, Table 1).

(9.) Workers are counted as covered by a collective bargaining agreement if they are union members or if they are not members, but are covered by a union contract. For greater details, see Hirsch and Macpherson (2003). The database also provides union membership, which is the percent of employed workers who are union members. Using union membership, instead, does not change the findings of the paper.

(10.) Researchers have often used state-level manufacturing private capital stock data when dealing with U.S. capital stock (Henderson and Kumbhakar 2006).

(11.) See Cohen and Morrison Paul (2004) for more details. The author is grateful to Daniel J. Henderson for making the data available.

(12.) LR test of one-side error with the null hypothesis of [gamma] = [[delta].sub.o] = [[delta].sub.us] = [[delta].sub.i] = [[delta].sub.un2] = [[delta].sub.union] = 0.

doi: 10.1111/j.1465-7287.2010.00228.x

Chintrakarn: Lecturer, Business Administration Division. Mahidol University International College (MUIC), Salaya, Nakornpathom, Thailand. Phone [phone]#1238. Fax [phone], E-mail [e-mail]

Chen: Assistant Professor, Department of Economics, Tamkang University, Tamsui 251, Taiwan. Phone [phone] #2862, Fax [phone], E-mail [e-mail]