Do Unions Increase Labor s Shares? Evidence from US Industry-Level Data

Transcription

1 Do Unions Increase Labor s Shares? Evidence from US Industry-Level Data Andrew T. Young * College of Business and Economics Division of Economics and Finance West Virginia Universy Morgantown, WV Andrew.Young@mail.wvu.edu Hernando Zuleta Department of Economics Universidad del Rosario American Universy in Bulgaria hernando.zuleta@gmail.com This Version: September 2011 JEL Codes: E25, J20, J51 Keywords: labor s share, labor share, capal share, trade unions, labor unions, income distribution, labor market instutions, labor demand We thank Brandon Brice for excellent research assistance. * Corresponding author. 1

2 Do Unions Increase Labor s Shares? Evidence from US Industry-Level Data Abstract: We explore the relationship between union densy and labor s shares using panel data on 35 industries, spanning the entire US economy, for the years 1983 through For the full sample, a standard deviation increase in union densy (membership or coverage rates) is associated wh an increase in an industry s labor s share of about one and a half standard deviations. However, for manufacturing industries the effect is much smaller: a standard deviation increase in densy is associated wh only a one half standard deviation higher labor s share. We control for capal-to-output ratios in our analysis; doing so implies the sign and magnude of the elasticy of substution between labor and capal. We find that this elasticy is less than uny in our sample but relatively high in manufacturing industries. Since the effect of unions on labor s share appears to be increasing in the elasticy of substution, our study provides support in favor of the right-to-manage model of union bargaining over the efficiency bargaining model. JEL Codes: E25, J20, J51 Keywords: labor s share, labor share, capal share, trade unions, labor unions, income distribution, labor market instutions, labor demand 2

3 The struggle of the labourer against capal [...] does exist, whatever the apologists of capal may say to the contrary. It will exist so long as a reduction of wages remains the safest and readiest means of raising profs; nay, so long as the wage system self shall exist. The very existence of Trades Unions is proof sufficient of the fact; if they are not made to fight against the encroachments of capal what are they made for? [...] The produce of the labour [...] has to be divided between both classes, and is this division about which the struggle is constantly going on. Each class tries to get as large a share as possible[.] Friedrich Engels (1881) 1. Introduction Offered by Friedrich Engels in the nineteenth century, one may ponder whether or not this raison d être for labor unions is still relevant today. How effective are unions at obtaining as large a share as possible? Though the starkness of classical capal versus labor polical economy has lost some appeal in latter days, the relationship between labor s share of income and labor organization is still an important one. In this paper we examine this relationship in the US economy using industry-level data. Figure 1 displays US union membership and labor s share from 1929 through If there is a relationship between the two variables, is not immediately apparent. The increase in unionization before 1948 and s steep decline after 1970 might correspond to similar changes in labor s share. Then again, the thirty years intervening seem to indicate a negative relationship between the two variables. We are interested in more formally exploring this relationship because, as argued by Bentolila and Saint-Paul (2006, p. 4), labor s share provides a compact way of looking at labor demand. Do unions increase the share of production paid out to labor by increasing wage rates? 3

4 Or do higher union wages [...] combine wh substantially lower employment and thus to a lower rather than a higher labor s share (Macpherson, 1990, p. 143)? 1 Also, do union workers receive higher wages at the expense of profs, or at the expense of their non-union counterparts? Labor s share captures these questions in a single variable; one that is relatively straightforward to observe. In addion to fight[ing] against the encroachments of capal economists since Freeman and Medoff (1979, 1984) have also rsuggested that unions may have a role in increasing productivy. Specifically, by providing agency services unions may increase both the supply of and demand for firm-specific human capal (Malcomson (1983), Fah and Reid (1987), and Skovsgaard and Sena (2005)). Labor s share will also reflect the part of such productivy gains that are captured in both higher wages and increased employment. Lastly, the relationship between unions and labor s share will depend on the substutabily between labor and capal. When unions put upward pressure on wages, firms may be able to easily substute capal in the place of labor. Alternatively, labor demand may be relatively inelastic if substution possibilies are poor. The elasticy of substution between capal and labor will, therefore, be a key parameter determining both the size and sign of the influence of unions on labor s share. In the empirical lerature on unions there is a consensus that unions in the US compress the structure of wages across employment types (e.g., Card (1996), DiNardo, Fortin, and Lemieux (1996) and Fortin and Lemieux (1997)). 2 However, the effect of unions on the share of income paid to employees generally is unclear. Early studies by Levinson (1951), Sultan (1954), 1 Engels, to our knowledge, did not explicly acknowledge this tradeoff; nor did his collaborator Karl Marx. 2 Rees (1967) and Reynolds (1967) are pioneering works that suggested and documented wage compression associated wh unions. 4

5 and Simler (1961) all fail to find evidence that unions raise labor s share. 3 While Ahlseen (1990) is in agreement wh these early studies, other scholars find that union densy is associated wh higher labor s share in the US (e.g., Henley (1987), Macpherson (1990) and Fichtenbaum (2009 & 2011)). Of these, however, both Henley (1987) and Macpherson (1990) find the effect to be modest. 4 We follow Bentolila and Saint-Paul (2003) and Checchi and García-Peñalosa (2010) and derive a relationship between labor s share and the capal-to-output ratio. On this share-capal schedule (Bentolila and Saint-Paul (2003)) labor is paid s marginal product. Whin our empirical framework other determinants of labor s share can then be interpreted as eher shifts in the share-capal schedule (e.g., a biased technological change) or departures from the schedule (e.g., an increase in wages above competive levels). Addionally, whether the elasticy of substution between capal and labor is greater than or less than uny is implied by the slope of the share-capal schedule. The data we analyze comes from the industry-level (roughly two-dig SIC) Jorgenson (2007) KLEM database. From the KLEM we compute time series on labor s shares from 1983 through 2005 for 35 industries that span the entire US economy. Other recent studies focus only on manufacturing industries. 5 We are able to estimate union effects for both manufacturing and service industries, the latter constuting the larger part of the US economy. Furthermore, we organize the data into a panel including six (five four year; one three year) time periods. Other studies analyze annual variation in their data (Fichtenbaum (2009 & 3 Levinson (1951) examined aggregate US data while Sultan (1954) and Simler (1961) focused on manufacturing industries. 4 Fichtenbaum (2009) finds that the decline in US unionization accounts for 28 percent of the decline in the share if US income paid to production workers. 5 This includes Henley (1987), Macpherson (1990) and Fichtenbaum (2009 & 2011). Ahlseen (1990), alternatively, uses cross-sectional data (from the 1958 US Census of Manufacturers) and examines only seven 2-dig SIC industries and only for production in 28 US states. 5

6 2011)) or are purely cross-sectional studies (Henley (1987) and Macpherson (1990)). Given the nature of collective bargaining (and the persistence of s results) is unlikely that the relevant variation in union densy and labor s shares is annual. Our study is the first to explo more reasonable variation in the data over time. In our analysis, labor s shares are related to industry-level union membership and coverage rates. In doing so we include controls for biased technological change, labor adjustment costs, the volatily of the economy, and the national labor conflict rate. The last of these (which is based on the number of strikes and lockouts) is included to control for changes in the willingness and abily of unions to exert influence independent of the percent of workers represented by unions. Fixed effects OLS estimates suggest that union membership is posively and significantly associated wh labor s shares. This effect is robust to employing industry (i) injury and illness incidence rates, (ii) work stoppage days idle, and (iii) union employees as a percent of all US union employees from the 1960s and 1970s as instruments. In fact, Arellano and Bover (1995) GMM estimation increases the estimated effect by nearly an order of magnude. A standard deviation increase in union membership (about 12.5 percent) is associated wh an over 37 percent increase in labor s share; this is a 23 percentage point increase in labor s share for the mean industry in our sample. A notable contribution of this paper is that, unlike any of the above-ced US studies, we explicly address the potential endogeney of union densy by offering an identification strategy utilizing (what we argue are) plausible instruments. We defend this identification strategy by reporting evidence of instrument strength, the based on Sargan tests, the lack of evidence rejecting instrument validy. 6

7 Furthermore, we report that union effects on labor s shares are both statistically and economically significantly smaller for manufacturing industries relative to those in services. This is a surprising result given the data focused on by other studies and the general perception of unions as most relevant to the manufacturing sector. GMM estimates of the share-capal schedule also suggest that the elasticy of substution between capal and labor is larger in manufacturing industries. Combined, we argue that the effect of union membership on labor s shares is inversely related to the elasticy of substution, consistent wh the right-to-manage model of union bargaining. We now proceed to section 2 which contains the theoretical underpinnings of our basic empirical model. Section 3 then lays out that model and provides more details about the data wh which that model is estimated. Regression results are then reported in section 4. We wind up wh concluding discussion in the fifth and final section. 2. Theory The share-capal schedule that will be the basis of our empirical framework is derived independently in papers by both Bentolila and Saint-Paul (2003) and Checchi and García- Peñalosa (2010). Consider industries indexed by i where each has a constant returns to scale production function, (2.1) Y FK, A L, that is continuously differentiable wh diminishing returns to eher productive factor while holding the other factor fixed. Y, K, and L correspond conventionally to output, capal, and labor; an index of labor-augmenting technology is denoted by A. Constant returns means that we can also express the production function in s intensive form, 7

8 (2.2) f y, l where y and l are, respectively, the output to capal ratio and effective labor (A L ) per un of capal. Assuming that inputs are paid their marginal products, so that the real wage rate is equal to the marginal product of effective labor, labor s share will be, (2.2) l l l. f f The capal-to-output ratio is, by definion, k 1 f l, and assuming that f is monotonic means 1 that is invertible and l hk f 1 / k arrive at the share-capal schedule: (2.3) k hk f hk.. If we substute this expression into (2.2) we Labor s share is a function of only the capal-to-output ratio. The slope of the share-capal schedule depends on the elasticy of substution between d K labor and capal, i d F K L F L F K K F L L l f f l l l f 1 f l li. From (2.2) and the definion of k follows that (Bentolila and Saint-Paul, 2006, p. 7), (2.4) d dk 1f l i f l l f l l f f l l l f i k l f l f l 1, 8

9 where f l f l l 0. 6 If we consider a Cobb-Douglas (σ = 1) as a baseline, the share-capal schedule has a zero slope; labor s share is a constant regardless of the value of k. Departing from the baseline, if capal and labor are more complementary (σ < 1) then an increase in the capal-to-output ratio will result in an increased labor s share. Likewise, if capal and labor are more substutable (σ > 1) then an increase in the capal-to-output ratio will decrease labor s share. The share-capal schedule, (2.3), is the basis for our empirical specifications. Of course, observed labor s shares will have addional determinants other than the capal-to-output ratio. However, the theory can guide in the selection of other variables for inclusion as well as the interpretation of their estimated effects. In particular, the derivation of the share-capal schedule assumes competive factor markets and neutral (labor-augmenting) changes to technology. Independent of changes in the capal-to-output ratio, changes in labor s share may occur due to eher departures from the share-capal schedule (when factor are not paid their marginal products) or shifts of the schedule (when there are non-neutral changes in technology). The role of unions in the determination of labor s share may be interpreted eher in terms of movements along or departures from the share-capal schedule depending on the model of bargaining assumed. According to the right-to-manage model (Nickell and Andrews, 1983) firms choose the quanty of labor employed taking the wage rates as given. The wage rates are the result of a prior bargaining process between firms and unions. Since firms are still price-takers, wages are still set equal to labor s marginal product and unions will affect labor s share by 6 Bentolila and Saint-Paul (2006) define the elasticy of substution as simply the change in the capal to labor ratio associated wh the change in the technical rate of substution rather than the negative of the ratio. This is of no import but using the negative seems more natural to us. E.g., Bentolila and Saint-Paul (2006, p. 7) refer to the Cobb- Douglas production function as having an elasticy of substution equal to negative one, while in our formulation we would say that the elasticy is simply uny. 9

10 moving firms along their share-capal schedules. Alternatively, in the efficiency bargaining model (MacDonald and Solow, 1981) bargaining takes place over wages and employment simultaneously. Wages end up set equal to a weighted average of the two threat points of employers and employees, i.e., the marginal product and the reservation wage, respectively (Christoffel and Linzert, 2010, p. 1439). This results firms operating above their share-capal schedule. Estimating the effects of unions on labor s shares may serve to discriminate between the right-to-manage and efficiency bargaining models. The latter predicts that bargaining power unambiguously places an industry above the share-capal schedule, increasing labor s share. However, the right-to-manage model implies that unions are associated wh movements along the share-capal schedule and, therefore, their effect on labor s share will be increasing if the elasticy of substution is less than uny; decreasing if this elasticy is greater than uny (Bentolila and Saint-Paul, 2003, pp ). Also, the share-capal schedule will have a negative (posive) slope when the elasticy of substution is below (above) uny. (An inspection of (2.4) confirms this to be the case.) 7 We follow Bentolila and Saint-Paul (2003, p. 19) in assuming that labor s share can be expressed in a multiplicative form, (2.4) g k, S hx, where the function g represents the share-capal schedule described above and h is uny if i operates on that schedule. S includes technological changes that may shift the schedule while X includes variables that may drive a wedge between marginal products and wage rates (leading to 7 For the Cobb-Douglas case (i.e., an elasticy of substution between labor and capal equal to one) the share capal-schedule has a zero slope; labor s share is constant as long as factor markets are competive. 10

11 departures of an industry from the share-capal schedule). If we addionally assume that both g and h are multiplicative, a linear regression analysis can be justified by taking logs of (2.4). 3. Empirical Model and Data We start by considering the following empirical model motivated by Bentolila and Saint-Paul (1999, 2003): (3.1) ln 0 1UNION 2 lnk 3 lnoilt EMP _ CHANGE UNCERT CONFLICT t, where UNION is eher the union membership (MEM ) or coverage (COV ). The coefficient, β 1, is the parameter of primary interest in (3.1). In addion to union membership or coverage (which is industry specific) we also control the labor CONFLICT rate economy-wide (i.e., the number of strikes and lockouts divided by the number of employees). The capal-to-output ratio (k ) controls for the share-capal schedule. (Given our industry-level data, in practice these are capal-to-value-added ratios.) We would expect the sign of β 2 to be posive (negative) if the elasticy of substution between labor and capal (σ) is less than (greater than) uny. We also control for the real world price of oil (OIL ), the growth rate of an industry s labor input (EMP_CHANGE ), and a measure of uncertainty: the sample standard deviation of an industry s value-added (UNCERT ). The former of these (OIL ) may be correlated wh biased technical changes and shifts in the share-capal schedule. EMP_CHANGE and UNCERT proxy for current labor-adjustment costs and expected future adjustment costs, respectively, that may be associated wh departures from the share-capal schedule. We also consider an alternative model where sector-specific union effects and sharecapal schedules are allowed for both manufacturing and services: 11

12 (3.2) ln UNION d lnunion lnk d lnk 3 ln 0 OIL EMP _ CHANGE UNCERT CONFLICT t 1,0 4 i 1, i 2,0 i 2, i i M, S im, S, 5 6 t where d M and d S are dummy variables that take values of 1 for, respectively, manufacturing and service industries in our sample (and values of zero otherwise). Young (2011) presents evidence that the services sector σ is greater than that of manufacturing. The right-to-manage model of bargaining then suggests that union effects on labor s shares will be larger in the manufacturing sector than in services. 3.1 Labor s Shares, Union Membership and Coverage, and Other Controls Our labor s share and capal-to-output variables come from the Jorgenson (2007) KLEM data based on 35 US industries. This is an input-output database and is described in Jorgenson et al. (1987) and Jorgenson and Stiroh (2000). The industry classification is roughly at the two-dig standard industrial classification (SIC) level. For our purposes, the database provides the prices and quanties are productive factors capal and labor, in particular as well as sectoral valueadded. The data are annual wh observations from 1960 to Variables include the quanty of output (Q ) and the price of output (P Q, ); the quanty and price of capal services (Q K, and P K, ); the quanty and price of qualy-adjusted labor inputs (Q L, and P L, ); the quanty and price of energy inputs (Q E, and P E, ); and the quanty and price of materials inputs (Q M, and P M, ). Dividing service values by prices yields the quanties K, E, and M. Value added is computed as VA = Q P Q, V E, V M,i. Labor's share in value-added is computed as = S L, (1 12

13 S M, S E, ) where S X, = V X,ti Q P Q, for X = L, M, and E. The capal-to-output ratio is the real quanty of capal as a fraction of real value-added K /(VA /P Q, ). 8 For our union variables, we start wh the US industry-level union membership and coverage data that is described in Hirsch and Macpherson (2003) and is available from 1983 through 2009 at the Hirsch and Macpherson (2011) unionstat webse. These data are compiled from the US Bureau of Labor Statistics (BLS) Current Population Survey (CPS) and are reported for CPS industry classifications. Since the unionstat and KLEM industry classification systems are different, we aggregate and match the former to the latter. 9 This results in labor s shares, capal-to-output ratios, and union membership and coverage rates for 35 roughly 2-dig SIC industries from 1983 through Since we are not interested in cyclical and other short-term variation in our data, we break the sample into six time periods ( , , , , , and ). Average values of the above variables are calculated for each time period. This provides the basis for a panel wh 35 cross-sections and a time dimension of six. Regarding our remaining controls, EMP_CHANGE is the growth rate of labor input, from the KLEM data. Our uncertainty measure (UNCERT ) also comes from the KLEM data; is the sample standard deviation of an industry s value-added over each time period. OIL t is from the US Energy Information Administration. The data for CONFLICT t come from the Comparative Polical Data Set described in Armingeon et al. (2008a, 2008b). The conflict rate is the number of strikes and lockouts as a percent of all US employees (from the BLS) and we take 8 Since our theory is based on a production function wh only capal and labor arguments, value-added is the appropriate denominator rather than gross output. Technically the variable we use is the capal services-to-output ratio. This is the most appropriate measure given the production function framework. However, means that the values will most often be less than uny, which is not typically the case when using a capal stock-to-output measure. 9 Details are provided in an appendix at the end of this paper. 13

14 the average over each time period. 10 The national conflict rate may help to control for trends in the strength of unions that are not captured in the extensive margins of membership and coverage and we control for here. 11 Table 1 contains summary statistics for the variables included in (3.1) and (3.2). When variables enter in logged form, summary statistics are provided for the variable in both logged and non-logged form. Table 2 provides addional summary statistics for MEM, α, and k for each individual industry separately. (To conserve space, COV is not reported on in table 2. However, the correlation between membership and coverage rates in our sample is ) 3.2 Instruments We report on estimations of (3.1) and (3.2) based on both fixed (industry) effects OLS and GMM using the Arellano and Bover s (1995) system estimator. This estimator is based on a model in both levels and first-differences simultaneously. Its virtue lies in directly incorporating the information in variable changes over time whout discarding the also-valuable information contained in the levels. We treat both UNION (MEM or COV ) and k as endogenous variables. 12 For instruments we first turn to 1960s and 1970s values of variables reported in the US Census volumes of the Statistical Abstract of the Uned States that are likely to be correlated wh the prevalence of unions from 1983 to These variables are occupational injuries and illnesses per 100 full time employees in an industry (IIR ) for the years 1965, 1967, 1968, 1974, 10 This data is not available at the industry level. 11 Bentolila and Saint-Paul (2003) find that the effect of the labor conflict rate on labor s shares in OECD countries is actually negative. 12 It is also likely that EMP_CHANGE is endogenous. However, while we include this variable as a control for labor-adjustment costs, we are not particularly interested in s partial effect on labor s shares. Therefore we are not concerned wh potential bias in regards to that particular estimate. Also, given our instrument set, by treating only our variables of direct interest as endogenous (UNION and k ) we preserve an addional overidentifying restriction wh which to assess instrument validy. 14

15 1975, and 1978; man-days idle per production worker during work stoppages in an industry (DAYS_IDLE ) for the years 1960, 1965, 1968, 1972, 1974, and 1978; and the percent of all US union workers in a given industry (PERC_MEM ) for the years 1964, 1968, 1970, 1972, 1974, and We view IIR and DAYS_IDLE as plausible determinants of workers demands for union representation. Workers in in jobs wh higher chances of on-the-job injury and/or stoppages over other unsatisfactory condions in the 1960s and 1970s were more likely to express higher demand for union representation, leading to higher union membership and coverage during our sample period. PERC_MEM expresses relative historical pattern of union membership and is also likely correlated wh union membership patterns during our sample period. 13 While is plausible that these three instruments are also correlated wh the other endogenous variable in our analysis, k, we also employ 1960, 1964, 1968, 1972, 1976, and 1980 values of the capal-to-value-added ratio as an instrument. The capal intensy of given industries is likely to be persistent over time. However, only the share-capal schedule during our sample period will directly determine labor s shares. Since k enters our regressions in log form, we also take logs of the lagged values for the instrument (LN_K_IV ). IIR, DAYS_IDLE, and PERC_MEM are not available for agriculture, so our GMM estimates will be only for the non-agricultural US economy. (Agriculture s value-added share is less than 2.4 percent over our sample period.) 13 UNION is taken from the Statistical Abstract of the Uned States years 1967 (table 351), 1970 (table 357), 1974 (table 590), 1976 (table 620), and 1980 (table 716). IIR is taken from years 1970 (table 354), 1976 (table 627), 1980 (table 723). DAYS_IDLE is constructed using days idle from years 1967 (table 355), 1976 (table 624), 1970 (table 363) and1980 (table 720); and using production workers from years 1970 (table 329), 1976 (table 597), and 1980 (table 692). For some variables and/or some years, industries in our sample were not available separately. For example, for UNION motor vehicles and transportation equipment & ordinances were reported in one industry category. In another example, IIR government enterprises was not available for years 1974, 1975, and In cases like the former, the numbers for the enveloping industry classification were recorded for both KLME industries. In cases like the latter, the last available number (in the example above, 1968) was used for the remaining years. (Full details of all these cases are available from the authors upon request.) 15

16 Table 3 reports the results of OLS regressions of our endogenous variables on the instrument set: IIR, DAYS_IDLE, PERC_MEM, and LN_K_IV. For both MEM and COV, each instrument is a statistically significant (at the one percent level) correlate. The F-statistics from Wald tests of joint significance of the instruments are both greater than 14, indicating rejection of the null at the one percent significance level. In the case of ln(k ), the instrument, PERC_MEM, is not a statistically significant correlate by self, but each of the remaining instruments are at the 10 percent level or better. The F-statistic is so joint significance of the instrument set cannot be rejected. 3.3 A Preliminary Look at the Data Before proceeding to the results of regression analyses, figure 2 provide a cursory look at labor s shares in our sample in relation to union membership and coverage rates. In eher case, the raw correlation of the union variable and labor s shares is very weak ( for MEM and for COV ). Fted OLS regression lines have negative slopes but, in addion to not being statistically significant, these slopes are not economically large. Figure 3 provides a scatter plot of labor s shares and capal-to-value-added ratios. A steep, negative relationship is evident. (The slope from an OLS regression is and significant at the one percent level.) This suggests a negative share-capal schedule for our full US sample. A negative share-capal schedule is consistent wh an elasticy of substution between capal and labor that is less than uny. This is consistent wh several recent studies using US data (e.g., Antràs (2004), Chirinko et al. (2007), Klump et al. (2007), and Young (2011)) See Chirinko (2008) for a survey of the empirical lerature on this elasticy: the evidence rather strongly rejects the Cobb-Douglas assumption of σ equal to one (p. 683). 16

17 The weak reduced-form relationship between labor s shares and unions, along wh labor s shares strong relationship to capal intensies, highlights the importance of analyzing the former in a framework founded on production theory. Our empirical analysis will control for and estimate share-capal schedules. The remaining variation in labor s shares is then related to the cross-sectional and time variation in the prevalence of unions. 4. Estimation Results Estimation results based on (3.1) are reported in table 4. We begin wh some preliminary OLS results. The results are produced whout addressing issues of endogeney. However, they get us started wh a preliminary look at the raw partial correlations in the data. 4.1 OLS Results Columns (1) and (2) contain pooled OLS results of the baseline specification using MEM and COV respectively. In both cases, union densy is posively and significantly (at the 5 percent level or better) related to labor s share in an industry. Also in both cases, the coefficient on ln(k ) is negative and significant at the 1 percent level. This suggests that the typical industrylevel elasticy of substution is less than uny. The only other significant coefficient estimates in columns (1) and (2) are associated wh UNCERT. An industry s value-added volatily is negatively related to s labor s share. However, the statistical significance of UNCERT disappears once industry fixed effects are included in the estimation. 17

18 Column (3) reports OLS fixed effects results using MEM as the dependent variable. 15 Again, union memberships are statistically significantly (at the 1 percent level) associated wh higher labor s shares. A standard deviation increase in an industry s union membership is associated wh a 7 percent increase in s labor s share. The mean of labor s shares is Relative to this mean value, a 7 percent increase corresponds to about 4.2 percentage points. Whether or not this is a large effect is somewhat subjective. The (sample) standard deviation of industry labor s shares is about 18 percentage points, relative to which 4.2 percentage points is fairly small. However, if employment is held constant, increasing an average laborer s income by 4.2 percentage points seems non-negligible. This estimated effect of union memberships on labor s shares is essentially the same when macroeconomic volatily (UNCERT_RGDP) and growth (RGDP_CHANGE) are controlled for; also when a time trend is included. (See columns (4) and (5), respectively, of table 4.) Separate time trends for manufacturing and services industries are allowed for in generating the column (6) estimates. Again, MEM is statistically significant at the 1 percent level and the magnude of the effect is virtually unchanged. 4.2 GMM Results Our regressors of interest the union densy measures and capal-to-output ratios are likely endogenous. Columns (7) and (8) of table 4 report results from estimation of our baseline specification using Arellano and Bover s (1995) GMM variant. The virtue of this approach is 15 To conserve space, the remaining OLS results (columns (3), (4), (5), and (6) of table 4) are all based on the dependent variable MEM. OLS results using union coverage are virtually identical and available from the authors upon request. However, GMM results, starting wh column (7) of table 4 and continuing in subsequent tables, are all reported for both MEM and COV. 18

19 that estimation is that utilizes information contained in both the levels and the first-differences of the data. We report evidence on the strength of our instruments above in table 3. We assume two endogenous variables in any regression (MEM or COV; and ln(k)) and this provides us wh two over-identifying restrictions. Columns (7) and (8) both report the J-statistics associated wh a Sargan test. The p-values are both around There is no evidence suggesting that our instruments are invalid. However, recall that our instruments were not available for the agriculture industry, so all GMM results reported below are based on data for the remaining 34 industries only. Whether considering union membership or coverage, the GMM estimate of the effect on labor s share in an industry is posive and significant at the 5 percent level. In the case of union membership, the GMM estimate is an order of magnude larger than the OLS fixed effects estimate. A standard deviation increase in MEM is associated wh about a 38 percent increase in an industry s labor s share. Starting from the mean labor s share value of 0.614, this is an increase of 23 percentage points (or 129 percent of a standard deviation.) The point estimate of the effect is slightly larger when union coverage is used (coefficient equal to rather than 0.030) though the column (7) and (8) estimates are not statistically distinguishable from one another. The GMM coefficient estimates on ln(k) in table 4 are both negative (consistent wh an elasticy of substution less than uny). However, they are not statistically significant. On the other hand, the labor conflict rate becomes negative and statistically significant (at the 1 percent level) in both the column (7) and column (8) regressions. A standard deviation increase in CONFLICT, when union membership (coverage) is also controlled for, is associated wh about a 19

20 9.2 percent (12.8 percent) decrease in industry labor s shares. These estimated effects are sizeable. However, the labor conflict is rate is an economy-wide (rather than industry-level) variable in our data. Interpreting the effects at face value assumes that they are the same (at least qualatively) across industries. Given this caveat, one interpretation is that unions are generally effective at negotiating larger income shares for laborers, but that their activies can become counterproductive if they are too disruptive. While collective bargaining may be a fruful activy, strikes and lockouts may antagonize ownership and management, or may simply cause disruptions of production that are ultimately borne (at least primarily) by laborers. 4.3 Allowing for Separate Manufacturing and Services Sector Effects The effects of unions on labor s shares might well be heterogeneous across industries. In particular, if the right-to-manage model is a reasonable approximation to labor-capal relations in the US economy, then differences in elasticies of substution across industries can translate into different union effects on labor s shares. For example, Young (2011) presents evidence that the elasticy of substution in the US manufacturing sector is less than that of the services sector. If this is true then the right-to-manage model suggests that unions will have a stronger (weaker) effect on labor s shares in services (manufacturing) industries. Table 5 reports GMM estimates when separate union densy (MEM or COV) and capal-to-output ratio effects are allowed for in manufacturing and service industries. This is accomplished by including interaction terms based on the dummies variables, DM and DS, that take the value of 1 for a manufacturing or services industry, respectively, and 0 otherwise. Referring back to table 2, manufacturing includes industries 7 through 27 while services includes industries 32 through

21 Columns (1) and (2) report results for the baseline specification amended wh the 4 interaction terms. Regardless of whether MEM or COV is used, union densy again posively and significantly (at the 1 percent level) associated wh labor s share. In eher case, a standard deviation increase in union densy is associated wh more than a percent increase in labor s share. Starting from the mean of 0.614, this is more than a standard deviation (18 percentage points) increase in labor s share. While the interaction of DS and union densy is never statistically significant, the interaction of DM and union densy is negative and significant (at least at the 5 percent level) for eher MEM or COV. The results reported here suggest that unions have a significantly smaller effect on labor s share in manufacturing industries. The effect in manufacturing industries is still posive and significant, but only at the 10 percent level for MEM. (For COV the joint effect is significant at the 5 percent level. The F-stats are reported in table 5.) Also, the estimated joint effects are both roughly one third of the coefficient estimates on MEM and COV alone in the table 4 GMM results (0.012 and versus and 0.035, respectively). In a manufacturing industry, roughly, a standard deviation increase in union densy is associated wh an increase in labor s share of only one half of a standard deviation. This is remarkable given that unions are tradionally associated wh manufacturing industries. Most of the recent studies on union effects on labor s shares in the US evidence this by their exclusive focus on manufacturing sector data (e.g., Henley (1987), Macpherson (1990), and Fichtenbaum (2009 & 2011). Furthermore, the average manufacturing industry in our sample have about a 20 percent union membership rates while the percent is about 8 for the average services industry. (See table 2.) It is precisely where unions are more prevalent that they appear to have a smaller effect on the distribution of income across factors. 21

22 Not only are union effects estimated to be significantly lower for manufacturing industries, but the elasticy of substution is in manufacturing industries is estimated to be significantly higher. The interaction term, ln(k)dm, is posive and significant (though only at the 10 percent level) in both regressions. This is consistent wh the empirical findings of Young (2011). It is also consistent wh the right-to-manage model of union bargaining (Nickell and Andrews, 1983). Recall that, based on this model, union effects are interpreted as movements along the share-capal schedule. The slope of that schedule is a function of the elasticy of substution between labor and capal. A higher elasticy of substution implies that firms can more easily substute capal for labor when pressured by unions. This decreases unions abily to capture a higher labor s share. The point estimates on ln(k)dm are large enough to imply a posive point estimate of the joint effect and an elasticy of substution greater than uny. (Recall equation (2.4) above.) A greater-than-uny substution elasticy would, in the context of the right-to-manage model, suggest that union effects on labor s share are actually negative However, the joint effect of ln(k) and ln(k)dm is never statistically distinguishable from zero. (F-stats are reported in table 5.) Columns (3) and (4) of table 5 report the results of reintroducing macroeconomic growth and uncertainty (RGDP_CHANGE and UNCERT_RGDP) as a robustness check. The only notable change is that, for the regression including MEM, joint insignificance of MEM and MEMDM can no longer be rejected wh 90 percent confidence or better. (The p-value is about ) 4.4 Biased Technical Change; Lagged Oil Prices 22

23 Besides including time trends both for the full sample and for manufacturing and services separately; see table 4 our control for the effects of biased technical change is the real world price of oil. (ln(oil)). Higher (lower) oil prices raise (lower) the cost of capal inputs relative to labor. These changes in relative costs can induce innovations that are biased towards one factor or the other. 16 However, may take considerable time for innovative efforts to bear fru. Table 6 checks the robustness of our GMM results to controlling for oil prices from the lagged four year period. Results are reported for the baseline specification (columns (1) and (2)) and for specifications including separate manufacturing and services effects (columns (3) and (4)). The most notable change is that statistically significant estimates of share-capal schedules (ln(k)) nowhere to be found. A straightforward possibily is that, consistent wh induced innovation, lagged oil prices are collinear wh capal-to-output ratios. This would account for inflated standard errors and lack of statistical significance. (Note that the estimated effect of lagged ln(oil) is never statistically significant eher.) The estimated effects on unions on labor s shares remain largely unchanged. Both qualatively and quantatively, most of the table 6 estimates of MEM and COV coefficients are virtually identical to those reported in tables 4 and 5. The notable exception in in column (2) where COV is no longer statistically significant (p-value = 0.176) though the coefficient point estimate is larger than in column (8) of table 4 (0.053 versus 0.035). On the other hand, both COV and COVDM are statistically significant in column (4) of table 6. While noting the column (2) exception, table 6 tells largely the same story in terms of union effects on labor s 16 The idea of induced innovation was popularized by a series of authors including Kennedy (1964, 1973), Samuelson (1965), Ahmad (1966), Drandakis and Phelps (1966), Weizsäcker (1966) and Binswanger (1974). The theory of induced innovations has been recently revised by several authors including Zeira (1998), Acemoglu (2002), Boldrin and Levine (2002), Funk (2002), Zuleta (2008) and Zuleta and Young (2010). 23

24 shares as tables 4 and 5: a standard deviation increase in union densy in an industry is associated wh somewhere between a one and one and a half standard deviation increase in labor s share. Also, the effect in manufacturing industries is significantly smaller. 5. Concluding Discussion Are unions effective in [t]he struggle of the labourer against capal (Engels, 1881)? Do their activies lead to labor obtaining a larger share of economic output relative to capal? We provide tentative answers to the above questions for the US economy using data from 35 US industries for the years 1983 through We relate industries labor s shares to their union densies while controlling for other determinants of the distribution of income across factors. These other determinants include capal-to-output ratios, labor adjustment costs, and biased technical change. While other researchers have addressed these questions, ours is the first study to (i) analyze industry-level data spanning the entire US economy and (ii) organize a panel of fouryear periods rather than focusing on (arguably irrelevant) year-by-year variation in the data. Collective bargaining is an on-going, time-consuming process. We explo the longer-run variation in the data that is more likely to identify the effects of unions on labor s shares. While previous researchers have focused exclusively on manufacturing data, we are able to explore union effects in services industries as well. Across the US economy, union densy is posively and significantly associated wh labor s share in an industry. Furthermore, the estimated effect is que large. A standard deviation increase in a given industry s union membership or coverage is associated wh a nearly one and 24

25 a half standard deviation increase in s labor s share. Starting from the mean industry labor s share, this amounts to about a 30 percentage point increase! However, unions are tradionally associated wh the manufacturing (rather than the services) sector. The average manufacturing industry has a union membership rate of about 20 percent; compared to the average services industry where the rate is about 8 percent. We find that the effect of unions on labor s share is statistically and economically significantly smaller in manufacturing than in the services sector. For a manufacturing industry, a standard deviation increase in union densy is associated wh only an increase of about one half of a standard deviation in labor s share. If unions have a relatively small effect in industries where they are most prevalent and identified wh, then this raises the question of whether gains in terms of labor s shares makeup for potential losses in terms of total income. 17 (Are larger pie slices more than offset by a smaller pie; or by a more slowly growing pie?) Our results also imply that the elasticy of substution between labor and capal in our sample is less than uny. Furthermore, is higher in manufacturing relative to other industries in the sample. Since the effect of unions on labor s share seems to be decreasing in the elasticy of substution, our findings support to right-to-manage model of union bargaining over the efficiency bargaining model. 17 For example, see the survey of empirical studies by Hirsch (1997 & 2007). 25

26 26

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