We empirically test the effects of right-to-work legislation on employment trends by estimating a model to describe county-level industry employment as a percentage of total private employment for each of the 18 two-digit, NAICS industries for the year 2018. One advantage of examining industry employment as a percentage of total employment is that the variable is automatically adjusted for ups and downs in the business cycle. That is, both the numerator and the denominator are impacted by a downturn in the economy. Of course, economic downturns can still affect specific sectors more than others, such as housing construction during the Great Recession and restaurants and similar service sectors during the COVID-19 recession.
Control variables used in the model include various county population demographics obtained from the U.S. Census, such as total population, percentage of population in poverty, percentage of population aged 25 and older with at least a bachelor’s degree, percentage of population who are nonwhite in race, percentage of population who are female, and percentage of population aged 20 to 64. While we are interested in the effect of right-to-work legislation, we must also control for each state’s general institutional environment, as one might expect that a state which has opted for right-to-work legislation might also tend to enact certain other types of policies that may be considered “market friendly” or aim to promote economic growth. To control for such policies, we include the 2017 “economic freedom score” from the Fraser Institute’s Economic Freedom of North America report. We remove the union density (area “3Aiii”) element of the ranking and recalculate the score to reduce the likelihood that this variable measures similar policy influences as our right-to-work variables.
The direct effect of right-to-work legislation on the home county is measured through the inclusion of two binary variables. Following Newman’s (1984) finding that the effects of right-to-work tend to diminish over time, early adopters of right-to-work legislation may observe different employment patterns than those states which more recently adopted the policy. To permit such variation in the effects of right-to-work laws, we distinguish whether such a law was enacted before or after the year 2000.
The most recent right-to-work enactments prior to year 2000 include Texas in 1993, Idaho in 1985 and Louisiana in 1976. Six states enacted right-to-work legislation after 2000: Oklahoma in 2001, Indiana and Michigan in 2012, Wisconsin in 2015, West Virginia in 2016 and Kentucky in 2017. It is possible that the full effects of the most recent adopters will not appear in the 2018 data. However, we expect that counties in right-to-work states will observe higher relative employment share growth in industries traditionally represented by higher union membership regardless of the adoption year.[*]
To measure the indirect effect of a right-to-work law on nearby counties, particularly in non-right-to-work states, we interact the right-to-work binary variables with a spatial weight matrix. This interaction variable indicates for each individual county the percentage of bordering counties which have enacted right-to-work laws (pre- and post-2000 enactment). To the extent that job opportunities move toward right-to-work states, we might expect non-right-to-work counties bordering right-to-work counties to observe lower employment in traditionally high-union density sectors. However, it is also possible that right-to-work policies create regional industry economies of scale, which could spill over in nearby non-right-to-work counties, potentially leading to increased employment.
The estimation model employed for the analysis is a spatial error model. SEMs control for the influence of spatially correlated, unobservable omitted variables. Particularly in the case of county-level data, many variables, including omitted ones, will be correlated systematically across space. The spatial correlation of omitted variables can lead the estimated coefficients from a standard regression to be inconsistent — that is, the expected value of the estimated coefficient does not approach the true (though unknown) value as the sample size increases. The SEM corrects for this problem and reduces the potential damage from omitted variables. Anselin (1988) and Lesage and Pace (2009) have defined the SEM as follows:
u = λ Wu + ε,
ε ~ N (0, σ2I n),
where y represents industry employment as a percentage of total private employment, X is the vector of independent variables, β is defined as the vector of linear slope coefficients, and the error term (u) is spatially correlated when λ is nonzero. W represents the row-normalized spatial weight matrix. In this case, we use first-order contiguity to determine neighbors. OLS estimates of β are unbiased but inefficient; as such, maximum likelihood is used.
To better understand the construction of the spatial weight matrix, consider the selected Michigan counties in Figure 1. For the purposes of this discussion, we will assume that only the eight red-highlighted counties are relevant (i.e., none of the eight counties border any other relevant county). However, we include in the full analysis all counties in the contiguous U.S. for which data are available.
Graphic 4: Select Michigan Counties
The first step in creating the weight matrix is to determine the border counties for each county. Consider Clare and Midland Counties, for example. Limited to just the counties shown in red, Clare County borders Gladwin, Isabella and Midland. Midland County shares borders with all the included counties except Arenac.
Figure 2 displays the numerical representation of the contiguous neighbors (left-hand side) and the row-normalized spatial weight matrix (right-hand side). Each row is interpreted as the “home” county and each column as the contiguous neighbor. If a home county is contiguous with another county, it is coded “1” and if not, “0.” Thus, for Clare County (third row from the top), there are ones in the columns corresponding to Gladwin, Isabella and Midland. For Midland County (second to last row), there are ones in every column except those corresponding to Arenac and Midland. Since a county cannot border itself, the diagonal will only contain zeros.
To create the row-normalized weight matrix, the matrix of zeros and ones must be row normalized such that each row sums to one. Since Clare County borders three other counties, the row normalization can be accomplished by dividing each element of the Clare County row by three such that in the right-hand side of Figure 2 the Clare County row now includes only cells of value 0 and 0.33. For Midland County with six contiguous neighbors, the row normalization involves dividing all elements of the row by six such that the respective row in the weight matrix includes cells of value 0 and 0.17 only.
Graphic 5: Weight Matrix Construction Example
The row-normalized spatial weight matrix is used to minimize the econometric issues stemming from spatial correlation that is problematic for much of the prior academic literature on the effects of right-to-work laws. This is accomplished first through the use of the SEM in which the spatial weight matrix controls for spatial correlation in the error term due to spatially correlated omitted and otherwise unmeasurable variables. We further control for spatial influences specifically related to right-to-work policy by interacting the spatial weight matrix with the binary right-to-work variables. The interpretation of this interaction term is the weighted average of the county’s contiguous neighbors that are in right-to-work states (pre- or post-2000 enactment) with the elements of the row-normalized spatial weight matrix serving as the weights.
[*] Varying this watershed year should not have a significant impact on the estimated results. Selecting an earlier watershed year by up to six years would have no impact on the classification of early or late adopters, and varying the year by up to 11 years later would cause only Oklahoma to switch from a late to an early adopter.