The Minimum Wage: Consequences for Prices and Quantities in Low-Wage Labor Markets.
by Paul Wolfson , Dale Belman Do moderate increases in the minimum wage reduce employment? lf not, do they nevertheless raise wages? To examine these questions, we apply techniques of time series analysis and systems estimation that are commonly used in macroeconomics and finance to five panels of data that contain between 11 and 34 low-wage industries. Our answers are "No" and "Yes," respectively. We find that increases in the federal minimum wage between 1947 and 1997 have raised average wages in many of these industries, especially the lowest wage ones. The effect on employment, however, is mixed and typically nonsignificant, even when average wages have risen. KEY WORDS: Employment; Systems estimation; Time series analysis; Wages. 1. INTRODUCTION The four increases in the federal minimum wage during the 1990s revived debate about the impact of a minimum wage on wages and employment. This renewed interest is reflected not only in an increased quantity of research--more than 200 articles were published in U.S. journals in the 1990s compared to 47 in the 1980s--but also in a new diversity of approaches to measuring the effects of minimum-wage increases (from EconLit[c] for U.S. journals). Before 1990, minimum-wage research was dominated by time series studies of teenagers and young adults. Surveying this literature, Brown, Gilroy, and Kohen (1982) established the oft cited consensus range for employment elasticities of -.1 to -.3. While continuing the longstanding focus on the effect of the minimum wage on employment, wages, and poverty, the new research relies on a greater variety of data sources and statistical techniques, and has produced wider variation in its outcomes (e.g., Card 1992a,b; Katz and Krueger 1992; Neumark and Wascher 1992; Card and Krueger 1994, 1995, 1997; Deere, Murphy, and Welch 1995; Kim and Taylor 1995; Currie and Fallick 1996; Hungerford 1997; Neumark, Schweitzer, and Wascher 1998; Baker, Benjamin, and Stanger 1999; Belman and Wolfson 1999; Dickens, Machin, and Manning 1999). Although much of the research supports the conclusions of Brown et al. (1982), a growing body of evidence suggests that minimum-wage increases within historic experience have no effect or even possibly a positive effect on employment. This has spurred developments in the theories of monopsony and of the market for lemons to explain the apparently positive relationship between the minimum wage and employment (Belman and Wolfson 1999; Dickens, Machin, and Manning 1999). Although most of the new research applies static models and assumes a contemporaneous relationship between changes in the minimum-wage and its impact, several studies suggest that the impact may lag implementation. Using state-by-year panels, Neumark and Wascher (1992) estimated a model in which state minimum wages can influence employment contemporaneously and with a lag. This specification yields a consistently stronger, although not always significant, negative employment effect than when the impact of the minimum wage is constrained to be strictly contemporaneous. Using similar data from Canada, Baker, Benjamin, and Stanger (1999) found an effect on teenage employment for up to 6 years following increases in provincial minimum wages. Neumark, Schweitzer, and Wascher (1998) found evidence that the initial impact of the minimum wage on wages is larger than the impact after 1 year. Each of these studies indicates that the effect of the minimum wage may not be solely contemporaneous and suggests gains to estimating impacts in a fully articulated dynamic model. With two modifications, the present research returns to the earlier approach of measuring the effect of minimum wage on wages and employment in a dynamic model using long time series. These changes involve updating the statistical techniques and shifting the focus from teens and young adults to industries in which employment is likely to be sensitive to the minimum wage. Studies of low-wage industries, those likely to be sensitive to increases in the minimum wage, form a distinct body within minimum-wage research. Brown et al. (1982, p. 514) suggested that interest in these industries is "[i]n line with the observation that such effects will be reliably detected when a significant fraction of the workers in the sample studied are directly affected by increases in the minimum wage...." Estimates of the employment effect in retail trade vary considerably between studies, with elasticities ranging from -.03 to -1.0. The estimate of Brown et al. (1982) is negative but not significant because of the small size of the sample. The effect on service industries is more marked, with a "preferred" elasticity of -.1 (Brown et al. 1982). The impact in manufacturing is larger than in retail or service, with a preferred elasticity ranging from -.24 to -.36. These estimates indicate substantial variation in the elasticities among major industries, and several studies find "notable" variation within major industries. Time series analysis has advanced considerably in the last two decades, particularly in the treatment of unit roots and co-integration. We take advantage of these developments to estimate the response of average wages and employment to the minimum wage between 1947 and 1997. The data we use are organized by industry, and we examine industries with low wages or a high proportion of young workers in their labor forces. The models incorporate controls for the time series properties of the data (i.e., seasonality and trending), for concurrent macroeconomic events, and, through inclusion of an aggregate of high-wage industries insensitive to the minimum wage, for misspecification or omitted variable bias. The model is estimated in a seemingly unrelated regresion (SUR) framework that allows for contemporaneously correlated errors within and between industries to improve the efficiency of the estimations and allow for joint tests of coefficients across industries. Because the series used in this research vary considerably in length, we calculate estimates on five panels of data, trading off sample length against number of industries. The data panel with the longest time span begins in 1947 and has 11 industries; the shortest starts in 1982 and has 33 industries. Parameters are allowed to vary by industry, and we find considerable differences in the effect of minimum wage on wages and employment across industries. Although the anticipated negative employment effect is found for some industries, the elasticities are small for most, and, as a consequence, it is often not possible to reject the null of no employment effect. In contrast, the effect of the minimum wage on the industry average wage is consistently positive and often both statistically significant and substantial. We make use of this result to further restrict our focus, limiting the investigation of the employment response to industries in which the average wage is shown to be sensitive to the minimum wage. This does not qualitatively alter our findings. 2. DATA: SOURCES AND PRELIMINARY ANALYSIS The empirical foundation for this work is data on industry employment and average production earnings collected as part of the Current Employment Statistics (CES) project of the U.S. Bureau of Labor Statistics (BLS). During the week that contains the 12th of the month, this project currently surveys roughly 400,000 business establishments, which employ nearly one-third of all payroll workers in more than 500 industries. The universe of the CES, derived from state unemployment insurance (UI) records, includes 99% of private sector employment. Several important differences exist between the establishment data of the CES and the more familiar household data of the Current Population Survey (CPS): the definition of employment, the frequency of both complete and partial revision of the sampling frame, the length of the time series, and the role of standard industrial classification (SIC) industries in the definition of the data. First, because it measures employment as jobs rather than as employed individuals, CES employment is more closely related to the definition that economists use in labor market models of the minimum wage, particularly when individuals can hold more than one job. Second, the CES sampling frame is completely revised annually and partially updated semiannually; the CPS sampling frame is completely revised each decade and partially updated annually based on building permits for residential construction. This difference in updating frequency is important in periods of unexpectedly rapid change. Third, CES time series are far longer than those that can be constructed from household data, going back to 1909 for some industries. Monthly employment data by industry are only readily available from the CPS since 1973, and monthly wage data are available only since 1979. Finally, the CES provide more precise measures of the industrial distribution of employment and month-to-month changes in industrial employment than the CPS (Greene 1969). Since at least the mid-1970s, it has been recognized that the employment estimates of the two surveys usually differ and these differences vary over time. During the 1980s, the CES estimate increased relative to the CPS estimate. One explanation for this is that the CPS was unable to capture the unusually high levels of illegal immigration and the growth in moonlighting on a timely basis. More recently, it has been noticed, not for the first time, that the (preliminary) CES employment figure rises relative to the CPS figure going into recessions. The most widely cited explanation is errors in imputing establishment births, a necessary activity for deriving the preliminary figures of the CES. These figures are revised several times, both as more of the data from each monthly survey are gathered and as the sampling frame is updated to reflect more recent UI data. Because the current analysis relies on final figures, problems with the preliminary estimates are not at issue in this research. The start dates of the series vary considerably by industry and variable. This research uses data panels that begin in 1947, 1958, 1964, 1972, and 1982, years in which earnings and employment series were initiated for many different industries. Later panels include more industries, but provide a shorter time frame for estimation. All panels end in December 1997. The data are available at http://stats.bls.gov. Using two- and three-digit SIC industries, we define low-wage industries as those for which the mean ratio of the minimum wage to the CES industry average wage is greater than one half for the period under consideration. One exception is SIC 58, Eating and Drinking Places, which has a large proportion of employees who are subject to a reduced minimum wage; the minimum wage for tipped workers is one-half that for other workers as long as their combined regular and tip income exceeds the statutory minimum. Based on this lower minimum, the ratio varies between .36 and .40 for SIC 58. An important employer of low-wage labor, we include SIC 58 because of the widely held view that the industry is a candidate for employment reductions in response to increases in the minimum wage. Food stores and automobile repair shops, where the ratio is also less than one-half, appear because of the large number of young employees in each industry (SICs 54 and 753, respectively). In 1989, more than 30% of employees in each of these industries was under age 25. Other industries that meet this "youth" criterion were also included under the low-wage criterion. Table 1 lists the industries that comprise each data panel and the ratio of the minimum to the industry average wage. (The age distribution of industries was calculated with CPS data.) A concern for any study is whether there are sufficient numbers of the group of interest to be reasonably assured that relationships can be detected by statistical methods. This may be of special concern here because it is not possible with the CES industry data to incorporate information about the level or variation of state minimum wages that exceed the federal minimum. Table 2 provides data from the CPS on the proportion of employees in the low-wage and youth industries who earned less than the new minimum wage in the year prior to the increase. Table 2 begins in 1973 when microdata on wages became available in the May CPS. Two patterns are apparent. First, a substantial fraction of employees in these industries earned less than the new minimum wage in the year before the increase. In 1981, for example, this fraction ranged from 8.1% (SIC 239, miscellaneous fabricated textile products) to 50.1% (SIC 533, variety stores); most fall between 9% and 27%. Only 7.3% of the labor force as a whole was bound by the minimum wage in that year. (Two figures are provided for SIC 58, eating and drinking places: the upper figures apply the minimum wage for tipped employees--one-half of the usual minimum wage; the lower figures apply the full minimum wage. We provide both figures because many, but not a majority of, workers in this industry come under the tipped employee rules.) Data for other years follow a similar pattern. The second pattern is that there is a decline in the fraction of employees below the new minimum over time, but this reverses prior to the 1996 and 1997 increases. In the 1970s and early 1980s, between 18.1% and 34.1% of employees in grocery stores earned below the new minimum. This fraction had fallen to 13.2% by the 1990 increase and 6.4% by the 1991 increase. The proportion of employees affected by the new minimum then increased to 14.7% in 1996 and 27.4% in 1997. This pattern is consistent with the declining real value of the minimum wage during the 1980s and the cumulative effect of the four increases in the 1990s. Even at the low point prior to the 1991 increase, most of our industries had a sufficient number of employees bound by the minimum wage to produce a detectable effect. Returning to the CES, total employment in the 1947 data panel, which consists of 10 manufacturing and 1 retail industry, ranged from a minimum of 1.9 million employees (July 1997) to a maximum of 2.7 million employees (December 1973). Total employment in the other four panels, each with more industries as well as a broader sectoral mix, was always at a minimum within a half year of the beginning and at a maximum in the last month, December 1997. Thus, the 1958 data panel ranged from 6.3 million employees in April 1958 to 12.0 million in December 1997. Employment in the 1964 panel varied between 8.7 million (January 1964) and 19.7 million. For the 1972 panel, the range extended from 14.3 million (February 1972) to 25.9 million; and for the 1982 panel, from 18.9 million (February 1982) to 28.9 million. Data on the minimum wage are from Kaufman (1997); the Consumer Price Index (CPI) and Unemployment Rate (UN) are from the BLS. 3. ANALYTIC FRAMEWORK We estimate the effect of the minimum wage with a Box-Jenkins forecasting model of employment and wages. Specification of the model involves testing for the presence of unit roots and cointegrating relationships, modeling of seasonal and higher frequency serial correlation, avoiding spurious correlation through appropriate controls for macroeconomic conditions, and distinguishing between the effects of legislated increases in the minimum wage and declines in the real minimum wage that occur through inflation and nominal wage increases. We discuss each of these topics after describing the system. The model consists of a system of two equations for each industry: one for the average nominal wage and one for employment. The general specifications of the wage and employment equations, respectively, are (with all variables in logs and [DELTA] indicating the first difference) (1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] The variables are | |
C the constant term (may include monthly dummies)
CPI the consumer price index
MW the nominal federal minimum wage
N employment in an industry
[N.sup.HI] employment in the composite high-wage industry
RMW the value of the minimum wage relative to industry
average wage, MW/[bar.W]
[DELTA]RM[W.sup.+] the absolute value of the (log) difference
of the relative federal minimum wage when
that is positive and zero when it is negative
[DELTA]RM[W.sup.-] the absolute value of the (log) difference
of the relative federal minimum wage when
that is negative and zero when it is positive
UN the national civilian unemployment rate
[bar.W] the industry average wage
[[bar.W].sup.HI] the average wage for the composite
high-wage industry.
| | The division of the industry equations into nominal (wage) and real (employment) is carried into the specification of explanatory variables: average wages are a function of nominal variables; employment is a function of real variables. This division, which is characteristic of macroeconomic time series, excludes nominal variables, such as the inflation rate, from the real equation and excludes real variables, such as the unemployment rate, from the nominal equation. This model may be estimated under different assumptions about the interequation error structure: without intra- or interindustry correlation in contemporaneous errors, in a SUR framework with contemporaneous correlation between wage and employment equations within industries but no interindustry correlation, or a SUR framework with contemporaneous correlation of the error terms between all equations in a panel. We focus on the latter because it is the most efficient and there are only modest differences in the point estimates among these specifications. 3.1 Unit Roots and Cointegration Use of time series data suggests both a Box-Jenkins framework, which stresses the importance of serial and seasonal correlation in the dependent variables, and testing for the presence of unit roots and cointegration. Conventional unit roots tests take the presence of a unit root as the null hypothesis, which may result in finding unit roots too frequently. We adopt Leybourne and McCabe's (1994) test, in which the null hypothesis is that the series is instead stationary. For each industry in each panel this null is rejected at the .01 level for the logarithms of employment and the industry average (nominal) wage. It is also rejected for the relative minimum wage in most industries at the .01 level and for all industries at the .1 level, with the exception of SIC 533 (variety stores) in the 1964 panel. Given the large number of tests, we chose to ignore this one nonrejection of a unit root. Having found unit roots, it is possible that cointegrating relationships exist between the minimum wage and either employment or wages in some industries. Engle-Granger tests uniformly reject cointegration in all industries between the nominal minimum wage and between the industry average wage, and between the relative minimum wage and employment, at a test size of. 1. Consequently, all variables are in differenced form and no error correction term is included in the equations. 3.2 Short Term Serial Correlation and Seasonal Correlation Box-Jenkins modeling is a nonstructural approach to analyzing an industry's internal dynamics and response to external factors. Its advantage is its focus on issues of immediate import, in this case measurement of the minimum-wage effect on employment and wages, without requiring construction of a comprehensive structural model. Equations (1) and (2) include two sets of lagged dependent variables: the first, [[summation of].sup.a.sub.i=1] [a.sub.i] [DELTA][Y.sub.t-i]], allows for short term serial correlation in the dependent variable; the second, [[summation of].sup.P.sub.i=1] [r.sub.i] [DELTA][Y.sub.t-12i]], allows for seasonality at a lag of 12 months. We judged the adequacy of the serial correlation specification using Durbin's alternative h statistic, a test for serial correlation at any lag. The lag structure varies for each series across both industry and dependent variable (wage and employment). Except for the 1972 and 1982 data panels, where the short sample periods require a lag structure specific to each panel, the own-lag structure for each series remains constant over all panels that contain the industry. 3.3 Maeroeconomic Controls Spurious correlation between either the minimum wage and employment or the minimum wage and the industry average wage may arise when events occur contemporaneously with a minimum-wage increase. Prior research on employment suggests that improved wage and employment forecasts result from accounting for macroeconomic conditions, specifically the unemployment and inflation rates (Brown et el. 1982). We further control for broad economic trends by including a wage and employment series for a composite high-wage industry. These series are constructed from several of the highest-wage industries with complete information for the period under consideration: for example, petroleum refining, carpentry, and railroad equipment (see Table 3). The employment series is the average of employment for the series used; the wage series is an employment weighted average. Granger tests for a relationship from the minimum wage either to employment or to the industry average wage reject the hypotheses that changes in the minimum wage affect these industries. 3.4 Specification of the Minimum-Wage Measures The specification of the minimum-wage term differs in the wage and employment equations. Except for the constant term and the monthly dummies, all variables in the wage equations refer to nominal quantities. There is only one minimum-wage term, the contemporaneous minimum wage. This reflects the assumption that the direct effect of an increase in the minimum wage on the industry average wage is immediate. Further change in the industry average wage would be an indirect response to a minimum wage increase, most likely due to the time series dynamics of wages and employment. All variables in the employment equation refer to real quantities except for the various constants. Minimum-wage effects on employment are driven by lagged values of the relative minimum wage (RMW), defined as the ratio of the legislated minimum wage to the average industry wage. The equation contains six terms of RMW: three for increases in the relative minimum wage and three for decreases. Changes are split to avoid imposing the restriction that employment responds symmetrically to increases and decreases, thus allowing for a distinction between the effects of legislated increases (the only time when the minimum wage increases) and other changes in the RMW. The lag structure allows for convexity in the costs of varying the size of the labor force in low-wage industries. As a compromise between the assumption of instantaneous adjustment, common to earlier time series models, and a lag structure that requires estimation of many terms, the specification adopted for this work has three lags for the RMW term, permitting the direct employment response to be spread over 3 months. Nearly all increases in the minimum wage have taken effect earlier in the month than the data to which the CES refer. When this is not the case, we change the date of the increase to the following month. Thus, the apparently contemporaneous minimum-wage term in both equations is an artifact of the timing of minimum-wage increases and data collection. The coverage of the minimum-wage provisions of the Fair Labor Standards Act (FLSA) has changed substantially over the period under consideration. The original act applied mainly to manufacturing, and only a small proportion of workers in retail trade and service industries were covered. The 1961 amendments greatly expanded the scope of the FLSA in retail trade by extending coverage to enterprises with sales exceeding $1,000,000, along with coverage of local transit, construction, and gasoline service station employees. Congress further broadened coverage with the 1966 amendments by lowering the enterprise sales test to $500,000 in 1967 and to $250,000 in 1969, as well as extending coverage to service and retail trades previously exempted. Newly covered industries and firms were initially subject to a lower minimum wage. We allow for the changes in coverage, where possible, by setting the value of the minimum wage to zero for the period in which industries were not covered by the minimum wage and to the industry-specific value of the minimum wage when this deviated from the national minimum wage. For instance, the value of the minimum wage for eating and drinking places was set at one-half the national minimum wage. Given the nature of the CES data, it is not possible to fully control for the reduction in the minimum revenue requirements in the earlier data panels. This is not an issue in the later panels which postdate these changes. 3.5 Feasible Generalized Least Squares To this point, the system defined by (1) and (2) allows for no relationship between these equations nor are the estimates related across industries. Although ordinary least squares (OLS) would provide consistent estimates of the parameters, the existence of contemporaneous events that are not explicitly modeled suggests that joint estimation would be more efficient. Joint estimation is also suggested by the recurrence of common and closely related variables across the equations. Finally, tests of cross-equation hypotheses require joint estimation. SUR provides an obvious approach to obtaining efficient estimates. The conventional SUR estimator is difficult to apply to this model because of the number of parameters in each system. For example, in the longest three data panels, the wage equation for SIC 56 requires 13 terms for seasonal behavior, including monthly dummies, another 9 for short term serial correlation, and 7 more for inflation, wage change in high-wage industries, and the minimum wage [see (1)]. The employment equation has 23 terms for seasonal behavior, another 8 lags for short term serial correlation, and another 12 for national unemployment, employment growth in high-wage industries, and increases and decreases in the RMW [see (2)]. Thus, more than 70 parameters need to be estimated in the two equations for SIC 56 over a sample, in the 1947 panel, of 575 monthly observations. The smallest panel, for 11 industries beginning in 1947, has 22 equations and 620 parameters (see Table 4 for details about each panel). The size of the matrices to be inverted in a conventional SUR approach, essentially generalized least squares (GLS) of the stacked equations to account for simultaneity of error terms, renders such an approach impractical if not infeasible. One way to reduce the dimensionality of the system is to impose restrictions on parameter values across equations, for example, to require that the effect of changes in lagged industry employment or in the relative minimum wage be identical across industries. Statistical testing suggest this is overly restrictive, and we instead adapt Telser's (1964) iterative SUR procedure to our problem (see the Appendix). A concern with SUR is that, although the restrictions on the covariance matrix may increase efficiency, they may also result in inconsistent estimates. We have estimated less restrictive systems for the 1947 and 1972 panels, both with contemporaneous correlation of errors only within industries and without contemporaneous correlation of errors across any equations. The point estimates from these efforts (available from the authors) are qualitatively similar to those of the system with full contemporaneous correlation. 4. RESULTS These SUR estimates allow us to test whether including information about the federal minimum wage improves (in-sample) forecasts of industry wages and employment. We begin with a brief discussion of estimated coefficients for variables other than the minimum wage, and then touch on several tests of the effect of the minimum wage across industries as well as testing two constraints on the minimum-wage estimates, which, if appropriate, reduce the computational burden of the model. We then consider industry-specific estimates for all industries for each of our five panels. Finally, we consider the employment effect for those industries in which minimum-wage increases are shown to be binding by the average wage estimates. 4.1 Preliminary Examination Consider first the estimated relationship between inflation and the average industry wage, and between the unemployment rate and industry employment. These relationships are not of central interest, but examination of these estimates can inform us about consistency between the models and our expectations. In general, we expect that increases in inflation will be associated with increases in the nominal wage and this is supported in the estimates. The average estimated elasticity is .25 (both mean and median) and the range is from -.347 to .955. Only 15 of the 132 estimates over all industries and all panels are less than zero. Two-thirds of these are from the 1982 panel, covering a period in which inflation was low and not only the real, but sometimes the nominal, earnings of production workers declined (Mishel, Bernstein, and Schmidt 2001). The employment response to the unemployment rate (business cycle) is almost always as we would expect (negative), but smaller in magnitude than the response of the wage to the inflation rate. The average estimated employment response is -.01 (both mean and median), with a range of .005 to -.058. Only six estimates are positive. The small magnitude of the elasticity is partially due to the relationship between unemployment and employment, and partially due to the industries under study. When the unemployment rate rises from 5.0% to 5.1%, the increase is on the order of 2% (of the unemployment rate). The corresponding reduction in jobs (assuming no moonlighting), from 95% to 94.9% of the labor force, would be -.1% of employment. The elasticity of employment with respect to unemployment would then be -.05. The point estimates range from close to this to very close to zero. The industries being studied are in less cyclically sensitive sectors of the economy, nondurable goods and the service sector, and this may also explain the attenuation of the unemployment-employment relationship. When estimating with OLS, it is good practice to check the F statistic before closely examining individual coefficients. In this context, we first consider some likelihood ratio (LR) statistics for the full model before looking at individual elasticities. Table 5 summarizes the test statistics for various zero constraints on the wage and employment coefficients. The first row displays results of LR tests of [H.sub.0]: All minimum-wage terms in all wage and employment equations are equal to zero ([e.sub.0j] = [u.sub.ij] = [v.sub.ij] = 0, i = 0, 1, 2, j = SIC value). This hypothesis can be rejected at extremely low levels of significance in all five panels, as can the hypothesis, tested in the second row, which examines the response of the average wage to changes in the nominal minimum wage: [H.sub.0]: The minimum-wage term in all wage equations is equal to zero ([e.sub.0j] = 0, j = SIC value). The hypothesis shown in the third row of Table 5, [H.sub.0]: The minimum-wage terms in all employment equations equal zero ([u.sub.ij] = [v.sub.ij] = 0, i = 0, 1, 2, j = SIC), can also be firmly rejected, although the p values are not zero to three significant digits. Finally, the last row of Table 5 displays results for tests that concern the net effect in all industries over the quarter following changes in the relative minimum wage: [H.sub.0]: Each set of minimum-wage terms in each employment equation sums to zero ([[summation of.sub.i] [u.sub.ij] = [[summation of.sub.i] [v.sub.ij] = 0, i = 0, 1, 2, j = SIC value). Here, the results are more mixed. The 1947, 1972, and 1982 panels strongly reject the null. In contrast, the null can be rejected only at the 10% level in the 1958 and 1964 panels. Two patterns, which will also characterize the industry-specific estimates, emerge from these cross-industry results. First, the minimum wage has a more marked effect on wages than employment. Second, the minimum wage influences employment, but the magnitudes and direction vary. We have tried to avoid arbitrary constraints on parameters; for example, the elasticities in the employment equation are not constrained to be symmetric for increases and decreases in the RMW nor to be identical across industries. This flexibility is purchased at the cost of estimating large numbers of parameters, a considerable computational burden. We use the first and last panels, 1947 and 1982, to test two obvious constraints: symmetry for increases and decreases in the RMW within each industry, and identical wage and employment responses across industries. In both, a LR statistic that tests the symmetry constraint has a probability value smaller than .00001, and imposition of symmetry results in a substantial decline in the magnitude of the point estimates of the employment effect, but not those of the wage effect. The cross-industry constraint is rejected at a size less than .01 in the 1947 panel and less than .00001 in the 1982 panel. Furthermore, in the 1947 panel, if either of these constrained models was the base model, we would not reject the null of no employment response at the. 1 level nor that the wage effect is zero in the model with identical wage and employment response across industries. The industry results are consistent with prior work that found substantial interindustry differences in the employment response. 4.2 Industry-Specific Estimates of Wage and Employment Elasticities Turning to the industry-specific results, we are confronted with a large number of estimated wage and employment elasticities. In the 1947 panel, there are 11 estimates of wage elasticities with respect to the minimum wage and their associated p values, another 11 estimates and 11 p values for employment when the relative minimum wage rises, and a final 11 estimates and p's for employment when the relative minimum wage declines--a total of 66 estimated parameters. For other panels with more industries, the number of parameters is proportionately greater. This wealth of material is not readily absorbed from a table. Instead, we adopt a graphical format that compactly summarizes this information and better delineates the relationships between elasticities and p values. To ease the readers initial exposure to the diagrams, Figure 1 shows an enlargement of the first column of Figure 2, the 1947 panel. Figure 2 depicts estimates of the wage and employment elasticities and their p values and Figure 3 shows the paired wage and employment elasticities. [FIGURES 1-3 OMITTED] Figure 2 is organized by panel and type of elasticity. The five panels used for estimation form the columns of diagrams from longest (1947) to shortest (1982). The three rows of diagrams are, from top to bottom, the estimate of the elasticity of average wages, the elasticity of employment when the RMW increases, and the elasticity of employment when the RMW wage falls. To understand these graphs, consider first the estimates of wage elasticities for the 1947 panel, the upper diagram in Figure 1 (and the extreme upper left diagram in Fig. 2). The elasticity and p value pairs are shown as circles for elasticities that satisfy a two-sided, 5% asymptotic significance criterion and as smaller x's for those that do not. Elasticities are measured along the vertical axis; the horizontal dotted line indicates an elasticity of zero. As indicated on the vertical axis, wage elasticities range between -.03 and .65. The boxplot to the left shows the distribution of the estimated elasticities (a legend for the boxplots can be found in the upper right side of Fig. 1). The median elasticity, .05, is denoted by the center line of the box. The lower end of the box locates the first quartile; the upper end locates the third quartile. Consistent with expectations about the effect of the minimum wage, all but two values are positive (above the horizontal line), but many are close to zero. The statistical significance of the estimates, the asymptotic p values (derived from a LR test of the unconstrained model nesting a model in which the industry parameters are constrained to sum to zero), are measured along the horizontal axis, and range from virtually 0 to .5. The significant estimates and associated p values are presented in a small table at the top of the diagram, all identified by three-digit SIC designations. To lengthen the interval of greatest interest, [0, .05], the horizontal (p value) axis is presented on a logarithmic scale, although the tick marks are labeled by the actual p value. Below the scatterplot is a boxplot that depicts the distribution of p values, and its center line indicates that the median p value is .12. The vertical dotted line is drawn at a p value of .05, the critical point for a 5% test of the null hypothesis. The five elasticity estimates to the left of the line pass the 5% criterion and are larger than the six to the right, which do not. Elasticities for significant estimates range from .1 to .65 with a median of .14; a 10% increase in the minimum boosts the average wage by between 1% and 6.5%. The next graph in Figure 1 displays the estimated employment response to increases in the relative minimum wage, and is constructed along the same principles. The elasticity estimates are the sum of the three RM[W.sup.+] coefficients in (2), [[summation of].sup.2.sub.i=0] [u.sub.i]. The estimates of the elasticity are close to 0, ranging from -.01 to .03, with a median of -.006. The p values range between .04 and .83, with a median of .27. Only one of the estimates is statistically significant (SIC 394), and it is small and positive (.03) rather than negative as anticipated, suggesting that a 10% increase in the relative minimum wage boosts employment by about 3%. The last graph in Figure 1 displays the employment elasticities when the relative minimum wage decreases, [[summation of].sup.2.sub.t=0] [v.sub.t] in (2). Because of the use of the absolute value of RMW, the anticipated sign of this elasticity is positive, the reverse of that anticipated for an increase in the relative minimum wage. The elasticity estimates range between -.07 and. 15, with a median of .00. The p values range between .016 and .90, with a median of .23. Four of the estimates are statistically significant (for SICs 228, 233, 314, and 394), but one of these is negative (-.07 for SIC 233): that is, employment declines when the relative minimum wage falls. Of the other three, the largest elasticity is .15 in SIC 394. For ease of comparison within panels, the horizontal axes in the graph are drawn to the same scale. We can quickly see that 5 of the 11 industries display a detectable wage response to increases in the minimum wage (the 5 to the left of the vertical dotted line in the top graph). Only one industry displays a detectable employment response to an increase in the minimum wage (the one to the left of the vertical dotted line in the middle graph) and four display a detectable employment response to declines in the minimum wage (again to the left of the vertical dotted line in the lower graph). Only 5 of 22 employment responses are statistically significant and of these, two have signs opposite the predicted effect. Only two of the five industries in which the average wage responds to minimum-wage increases display detectable employment effects and one of these is incorrectly signed. Examination of the nonsignificant employment effects, the x's to the right of the dotted vertical line in the middle and lower graph, indicates that the point estimates are typically close to zero. Their lack of statistical significance is due not to imprecision in the estimates, large standard errors, but to small estimated elasticities. Figure 2 displays the same general pattern repeating itself in the other panels. There is a statistically significant positive response in the average wage in about half of the industries in each panel, most of considerable magnitude. (Notice that within each row, the vertical axes are drawn to the same scale.) Because the maximum elasticity declines over time, from .65 in the 1947 panel to .07 in the 1982 panel, the range shrinks, but the minimum, fluctuating between -.03 and -.01, and the median, varying between .02 and .05, are fairly stable from panel to panel. Of the 64 statistically significant wage elasticity estimates in the five panels (covering 33 distinct two- and three-digit SIC industries), only 1 is negative, SIC 228 in the 1982 panel. The second and third rows tell a different story about the employment response. Over the five panels, only 18 of the employment responses to increases in the relative minimum wage (spread over 13 three-digit SIC industries) are statistically significant, and 4 of these are positive rather than negative. Twenty-one of the employment responses to declines in the relative minimum wage (spread over 19 industries) are statistically significant, and 10 of these, nearly half, are negative. In all, only 39 of 256 possible employment responses, 15%, are statistically significant, and 7 have the wrong sign--positive when the relative minimum wage rises (e.g., SIC 526 in the second row of the 1982 panel) or negative when the relative minimum wage falls. Consider the 1964 panel more closely. It has a broad mix of industries, about two-thirds in manufacturing and one-third in retail trade and services, and it is the longest panel that contains SIC 58, eating and drinking establishments. The p values of the wage response to increases in the minimum wage range from 0 to .97, with a median value of .01 and a first quartile of .000. The range of elasticity estimates is [-.02, .33], with a median of .04. For the 19 statistically significant estimates (56% of the total), the range is [.03, .33] and the median is .09. The p values for the employment response to increases lie in the range [.008, .78] with a median value of .31 and a first quartile of .24. The elasticity estimates lie in a narrow range around zero [-.04, .03], with a median of .002 and a first quartile of -.003, and are statistically significant in three industries (9%), only 2 of which are among the 19 with a statistically significant wage response. For responses to relative minimum-wage declines, the p values lie in the interval [.02, .76], and have a median value of .30 and a first quartile of. 11. The employment elasticities themselves range from -. 10 to. 16, with a median value of .01, and first quartile of -.01. Five industries, 26% of those displaying a significant wage response, also display a significant employment response. In two of the five, employment declines when the relative minimum wage falls. There are relatively few significant estimates and they tend to be small in magnitude. The estimates are characterized by several strong patterns that together indicate a stronger relationship between the minimum wage and average wages than between the minimum wage and employment. The effect of the minimum wage on the average wage is typically larger in magnitude than the employment effect. This results in many more significant wage elasticities than employment elasticities. Although 49% of the wage elasticities pass a 5% test of significance, only 13% of the employment elasticities are significant when the relative minimum wage rises and only 16% are significant when the relative minimum wage declines. The smaller proportion of significant employment effects does not result from a lack of precision in estimation. While prior industry research has suffered from imprecision in estimates that originate in small sample sizes (see the discussion in Brown et al. 1982, pp. 514-522, p. 520, in particular), the current estimates are more powerful. Many of the statistically significant estimates are close to 0, falling in a range of -.01 to -.04, but, as can be seen from the figures, the nonsignificant estimates are typically even smaller and this underlies their low statistical significance. The wage elasticities are also more consistent with our priors than are the employment elasticities. Although all but one of the significant wage elasticities are correctly signed (positive), many of the significant employment elasticities' signs are inconsistent with our priors. The difference between the wage and employment elasticities is marked, but is not entirely unexpected. The minimum-wage effect on wages is direct, whereas its effect on employment is indirect, operating through the labor demand curve. Nevertheless the industries under consideration are those in which employment should be responsive to minimum-wage increases, so the modest employment elasticities in the presence of substantial wage elasticities does not support the standard hypothesis. It would, however, be premature to conclude that the minimum wage does not affect employment. The findings for employment may result from inclusion of industries in which minimum wage increases were not binding. For industries in which few, if any, workers are earning less than the new minimum wage, increases in the minimum can have only a slight effect on employment. The use of panels that consist largely of such industries would result in estimates of employment elasticities which are, as observed in our work, small in magnitude, varied in sign, and often nonsignificant. Although the data in Table 2 provide some assurance that this is not an issue for the industries under study, further evidence would strengthen the current results. 5. THE WAGE FILTER One remedy to this problem is to refine our focus to industries in which increases in the minimum wage are binding, that is, to "wage-filter" the data. The CES data do not include information on the proportion of employees bound by increases in the minimum wage, but our wage estimates indicate industries in which the minimum wage affects the mean wage. A statistically significant, positive wage elasticity suggests an industry has adjusted to the increase in the minimum wage through layoffs, wage increases for lesser paid employees, and/or other adjustments of their labor force, which, in turn, trigger a detectable employment effect. Although differences in the ability of industries to substitute toward higher productivity/high-wage labor may attenuate this relationship, the industries under consideration, including gas stations, dairy stores, and restaurants, seem unlikely to have sufficient opportunities of this nature for labor substitution to have a substantial independent effect on the average wage. The expected negative minimum wage/employment relationship should then be more common among the wage-filtered results than among the full set of low-wage and youth industries. We use statistically significant wage effects as a threshold test for detectable employment effects. We apply the wage filter by focusing the analysis on pairs of wage and employment estimates in which the wage elasticity is positive and passes a two-sided 5% asymptotic test of significance (see Table 6). Figure 3 depicts the wage-filtered data. The figure is organized somewhat differently than Figure 2. The panels are arranged in rows. The top row is the 1947 panel; other panels follow chronologically with the 1982 panel in the bottom row. Wage elasticity/employment elasticity pairs are divided between estimates when the relative minimum wage increases (left column) and when the relative minimum wage declines (right column). A preliminary issue in using the wage filter is to assess whether the results from the wage equations are consistent with the anticipated relationship between the minimum wage and industry average wages. We expect that industries with a high relative minimum wage have more low-wage employees; therefore, the average wage in those industries will respond more strongly to increases in the minimum wage. We plot our estimated wage elasticities against the average relative minimum wage over the life of the panel for each industry (center column of Fig. 3). The scatter of statistically significant estimates in this column should slope up and to the right, whereas the statistically insignificant estimates should cluster in the lower left. This is, in fact, what we see in all five panels, especially in the three longest panels. (The statistically significant elasticity represented by the circle all the way to the left in the 1964, 1972, and 1982 panels is for SIC 58, eating and drinking establishments, with its lower minimum wage.) The drift to the left of the maximum relative minimum wage that is apparent in scanning down this column is indicative of the general decline in the value of the relative minimum wage since the late 1950s or 1960s. What about the distribution of estimated employment elasticities? First consider increases in the minimum wage and their estimated effect in the 1958 panel (second row, first column). Wage elasticities are on the y axis and the boxplot depicts the distribution of the significant elasticities. Employment elasticities are on the x axis, where the vertical dotted line indicates a zero elasticity, and the horizontal boxplot beneath the graph depicts the distribution of wage-filtered employment elasticities. Small x's indicate industries that do not pass the wage filter; squares indicate those that do, with solid squares used for employment elasticities that are statistically significant in a 5% test. Sixteen industries passed the wage filter in the 1958 panel (left graph). Point estimates of the elasticity of industry average wages with respect to the minimum wage range from .03 to .36, with a median value of. 10. Turning to the employment elasticities, point estimates range from -.02 to .02, with a median of .00. One would expect that larger negative employment effects would be associated with larger wage elasticities, but there is no evidence for this. Evidence for a negative employment effect is found in both of the significant elasticities, but these are small in magnitude (no more than -.02). The pattern is similar in the other panels. In the 1947 panel, five industries pass the wage filter. All five employment elasticities are negative but close to zero (the range is [-.01, .00]) and not statistically significant. Given their similar composition, it should be no surprise that the graph for the 1964 panel resembles the 1958 panel; its slightly greater range of elasticity estimates in both directions reflects the larger number of industries both in the panel and that pass the wage filter (34 versus 28 in the 1964 and 1958 panels, respectively, and 19 versus 16 for the wage filter). The 1972 panel accords better with expectations. Twelve of the 16 wage-filtered employment elasticities are negative, of which 4 are significant in a 5% test. Again, the estimated values are small; three are -.01, and one is -.02. In the 1982 panel, five of the seven wage-filtered elasticities are negative, and the one that is statistically significant (SIC 526) has the largest impact on employment of any wage-filtered estimates to be found in any panel, -.08. In summary, wage-filtering the employment elasticities for increases in the relative minimum wage still suggests that employment effects are not consistently significant or negative and that they are substantially smaller in magnitude than the consensus range of -.1 to -.3. The right column depicts the wage/employment elasticity pairs for declines in the relative minimum wage. The construction of the diagrams follows that used for increases in the relative minimum wage. In this graph, employment elasticities consistent with the hypothesis of a negative employment effect will be positive, to the right of the vertical dashed line. (Recall that signs have been switched to match the direction of the employment response to a decline in the relative minimum wage.) The range of employment elasticities for the 16 industries that pass the wage filter in the 1958 panel is [-.08,.14]. Of these 16, only 6 have positive employment responses to declines in the relative minimum wage; 10 are negative or zero (to two decimal places). Both of the significant estimates are among these latter 10. In the 1947 panel, the two statistically significant employment elasticities that pass the wage filter are roughly equal in magnitude and opposite in sign. In the 1964 panel, where the range of wage-filtered employment elasticities is [-.10,. 16] and the median is .00, two of the five statistically significant estimates are negative, including the one in the industry with the largest wage elasticity. In the 1972 panel, the range is much narrower, [-.05, .06], the median remains zero, and the one statistically significant employment response is negative, not positive. Only in the 1982 panel is the pattern more along the expected line: all of the wage-filtered employment elasticities are positive, with a range of .01 to .12 and a median of .02. However, only two of the employment elasticities are significant. Overall, 12 of 63 wage-filtered employment elasticities (19%) are statistically significant, and only half of these (with a range of [.04, .16] and a median of .10) display the anticipated positive employment response. 6. INTERPRETATION The magnitudes of the employment effects obtained in this research may be more readily understood if presented as the estimated number of jobs lost due to minimum-wage increases. We calculate the short run disemployment effect as the product of the change in the relative minimum wage, the estimated elasticity of employment with respect to increases in the minimum wage, and the industry employment in the month preceding the increase for each minimum-wage increase and industry in a panel. The long run effect is the ratio of the short run effect to the quantity 1 minus the elasticity of current employment with respect to lagged employment. Rather than present another large set of estimates, we sum both the short and the long run estimates across industries and minimum-wage increases for our panels. The point estimates for the 1947 panel indicate that since 1950, industries in that panel have lost about 8,600 jobs immediately following increases in federal minimum wage, and slightly less than twice that, 15,500, in the longer term. Roughly 40% of each of these numbers is due to the 1950 increase when the minimum wage rose nearly 90%. Over this same period, aggregate employment in this panel has, until recently, been at least 2 million. The cumulative losses are larger for the 1972 panel--more than 90,000 immediately and nearly 120,000 over the long run since 1974--but employment in this panel has grown from 15 million at its beginning to 25 million at the end. The disemployment effects in the balance of the panels are smaller both in absolute size and relative to total industry employment. These estimates indicate that the minimum wage has modest effects on total employment, although increases may disproportionately impact the lower wage workers within these industries. Why are the employment elasticities so small and so rarely statistically significant? Perhaps historical increases in the minimum wage have been rather modest, particularly relative to industry average wages. Although the 1950 increase raised the relative minimum wage by more than 60% in the industries of the 1947 panel and the 1974 increase raised it by between 15% and 25%, these were exceptional. Many of the increases raised the relative minimum wage by less than 10% on average (for industries in these panels); for a number of others, the maximum increase in the relative minimum wage was less than 10%, and for several more, the maximum increase was only slightly larger than 10%. In a world in which firms are continually buffeted by many forces, increases of these magnitudes may be too small to elicit substantial changes in employment practices. Another possibility is that although the increases in the minimum wage are relatively large, the minimum wage itself is so low as to be of nt concern, lf it is low enough, few employees will be affected by increases. The numbers in Table 2 do not bear this out. For many of the industries under study, at least 15-20% of employees earn a small enough amount to be directly affected by increases in the minimum wage since 1974. The fraction is often substantially larger. The wage-filter results also suggest that the modest number of statistically significant employment effects is not due to the inclusion of large numbers of industries in which the minimum wage is ineffective. These smaller employment effects relative to those found in studies of teenagers may also reflect a difference in perspective between industry and demographic studies, the difference between net versus gross. If firms take advantage of minimum-wage increases to replace teenagers with more dependable older workers, a study of the impact of the minimum wage on teenagers would capture only the disemployment effect. However, in industry studies this disemployment effect would be at least partially offset by the substitution of workers from groups that tend to be more productive, with consequently smaller net employment elasticities. Burdett and Mortensen's (1998) model of equilibrium search provides an additional explanation. In this model, employers recognize that workers' optimal strategy involves a reservation wage and that this varies across workers. For example, the reservation wage of those who are currently employed is greater than that of the unemployed. This strategic element gives employers some monopsony power. With homogeneous labor and reservation wages that are less than labor's marginal product, the minimum wage can rise, up to a point, without decreasing employment and perhaps even increasing it as the effect of the monopsony is reduced. Van den Berg and Ridder (1998) revised this model to allow for productivity differences among workers. In their version, which leads to a segmented labor market, increases in the minimum wage can reduce employment in less productive segments without having the same effect on more productive ones. Theories of temporal labor monopsony also suggest that increases in the minimum wage may not be associated with disemployment and may, under certain conditions, be associated with increased employment (Dickens, Machin, and Manning 1999). The weak disemployment effects found in this research are then compatible with some more recent models of labor market behavior. Is the relatively small number of results that are both significant and correctly signed (32 out of 256) consistent with a general equilibrium framework? There, increases in the minimum wage that result in a global employment decline may well involve employment declines in some but not all industries as patterns of demand shift in response to income and substitution effects. However, as the quote in the Introduction from Brown et al. (1982) indicates, the industries under study are those in which detectable employment effects would be expected. Absent pronounced effects in these industries, it is uncertain where such effects would be found. As explanations for the small employment effects detected in this study, we are left with a history of minimum-wage increases that are generally modest in comparison with the other factors that firms encounter, an analytic focus on net rather than gross disemployment effects, and strategic behavior due to asymmetric information. 7. CONCLUSION The last decade has seen a remarkable diversification of approaches to measuring the consequences of the minimum wage. This research returns to an older approach, updating it with contemporary techniques and a focus on industries that are most likely, a priori, to be affected by the minimum wage. Although we find substantial evidence that increases in the minimum wage raise the mean wage, the evidence for a consistent or pronounced negative effect on industry employment is weaker. Approximately half of the wage elasticities are statistically significant and all but one of these are correctly signed, but fewer than one in five of the employment elasticities are statistically significant and one-quarter of these are of the wrong sign. The significant employment elasticities are relatively small in magnitude, with only 9 of the 39 significant results as large as .1 in absolute value. The small size of the statistically significant elasticities is encouraging; the union of long time series with a panel structure allows for reliable detection of employment elasticities that are close to zero and so improves on prior industry research. These estimates also suggest a smaller employment effect than found in previous studies of services and manufacturing. Applying a wage filter to limit the analysis to industries where we are reasonably confident that increases in the minimum wage affect a substantial number of employees does not alter the character of the findings. The use of modern time series techniques to measure the wage and employment effects of the minimum wage in low-wage industries indicates that minimum-wage increases often raise wages, but much more rarely reduce employment. These findings reinforce other research that suggests that the negative employment effects are less consequential than generally believed. APPENDIX: DETAILS OF TELSER'S SUR ESTIMATION Following OLS estimation of the equations in the system, residuals from the all other equations are placed into each equation to obtain consistent SUR estimates of coefficients. Consider the following three-equation example, where [X.sub.1], [X.sub.2], and [X.sub.3] are matrices of variables with some variables in common: [Y.sub.1] = [X.sub.1][[beta].sub.1] + [[epsilon].sub.1], [Y.sub.2] = [X.sub.2][[beta].sub.2] + [[epsilon].sub.2], [Y.sub.3] = [X.sub.3][[beta].sub.3] + [[epsilon].sub.3]. We first obtain OLS estimates of [[beta].sub.1], [b.sub.1], and of the residuals [u.sub.1]. We then estimate the equation [Y.sub.2] = [X.sub.2][b.sub.2] + [u.sub.1][[alpha].sub.21] + [[epsilon].sub.2], again through OLS, to get estimates of [[beta].sub.2], [b.sub.2]. The residuals to be plugged into the third equation are calculated as [u.sub.2] = [Y.sub.2] - [X.sub.2][b.sub.2]. We then use OLS to estimate the equation [Y.sub.3] = [X.sub.3][b.sub.3] + [u.sub.1][[alpha].sub.31] + [u.sub.2][[alpha].sub.32] + [[epsilon].sub.3], This completes the first round. Hereafter, we estimate equations of the form [Y.sub.i] = [X.sub.i][[beta].sub.i] + [summation over (j [not equal to] i)] [u.sub.j][[alpha].sub.ij] + [[epsilon].sub.i] = [X.sub.i][[beta].sub.i] + [summation over (j [not equal to] i)] ([Y.sub.j]- [X.sub.j][b.sub.j])[[alpha].sub.ij] + [[epsilon].sub.i] from the most recent estimation of equation i. The system is iterated to convergence. Once the Telser technique converges, the resulting estimates are used as starting values for iterative maximum likelihood. The dimensionality of the system remains problematic. Instead of maximizing simultaneously over all parameters in all equations, we maximize only over those parameters in the two equations for a single industry, holding all parameters in the equations for all other industries fixed. Once convergence over these parameters is attained, they are fixed and we estimate the two equations of the next industry. This process is repeated until the entire system converges. Although time consuming, this approach reduces the dimensionality of the system to a manageable magnitude and provides a feasible GLS estimator for a complex system. [Received July 2000. Revised August 2003.] | |
Table 1. Average Value of the Relative Minimum Wage
by Industry in Each Panel
Starting year of panel
SIC Description 47 58 64 72 82
22x Textile mill products, excluding
misc. (229) .54
221 Broadwoven fabric mills, cotton .57 .55
222 Broadwoven fabric mills,
synthetics .55 .54
223 Broadwoven fabric mills, wool .55 .54
224 Narrow fabric mills .60 .59 .52
225 Knitting mills .61 .60 .53
226 Textile finishing, except wool .53 .54 .53
227 Carpets & rugs .56 .55
228 Yarn & thread mills .61 .62 .60 .51
229 Miscellaneous textile goods .51 .50
23 Apparel & other textile products .61 .58
231 Men's & boys' suits & coats .53 .55 .54
232 Men's & boys' furnishings .69 .71 .70
233 Women's & misses' outerwear .58 .62 .62
234 Women's & children's undergarments .67 .69 .68
236 Girls' & children's outerwear .67 .70 .69
239 Miscellaneous fabricated textile
products .57 .56
244 Wood containers .59 .57
302 Rubber & plastics footwear .60 .56
31 Leather & leather products .56
31x Leather & leather products,
excluding tanning &
finishing (311) .62
314 Footwear, except rubber .62 .64 .64
316 Luggage .59
317 Handbags & personal leather goods .66 .65
385 Ophthalmic goods .53 .53 .51
387 Watches, clocks, watchcases, &
parts .52 .54 .54 .52
393 Musical instruments .51 .51
394 Toys & sporting goods .55 .56 .56 .53
395 Pens, pencils, office, & art
supplies .51 .50
515 Farm-product raw materials stores .52
525 Hardware stores .61 .58
526 Retail nurseries & garden stores .60 .57
53 General merchandise stores .60 .57
531 Department stores .61 .60
533 Variety stores .79 .76
54 Food stores * .49
541 Grocery stores .63 .61
546 Retail bakeries .54 .51
553 Auto & home supply stores .64 .63
554 Gasoline service stations .54 .53
56 Apparel & accessory stores .65 .64 .61
561 Men's & boys' clothing stores .58 .57
562 Women's clothing stores .72 .71
565 Family clothing stores .70 .69
566 Shoe stores .65 .64
571 Furniture & home furnishings
stores .52 .50
58 Eating & drinking places .36 .40 .39
59x Misc. retail est., excluding fuel
dealers (598) .58
591 Drug stores & proprietary stores .64 .62 .56
594 Miscellaneous shopping goods
stores .58
599 Retail stores, nec .53
602 Commercial banks .54
701 Hotels & motels .58 .62 .57
721 Laundry, cleaning, & garment
services .62 .58
723 Beauty shops .59 .55
734 Services to buildings .57 .55
752 Automobile parking .63 .59
753 Automotive repair shops * .41
754 Automotive services, except repair .66 .61
805 Nursing & personal care facilities .62 .55
83 Social services .56
835 Child day care services .66
* Included under youth industry criterion.
Table 2. Fraction of Employees Who Earned Below the New Minimum Wage
SIC Industry 97 96 91 90
Low-Wage Industries
533 Variety stores 44.1 24.6 9.1 27
562 Women's clothing m m m m
835 Child day care 25.2 17.3 8.7 20.6
566 Shoe stores 23.2 14.5 5.5 13.4
565 Family clothing m m m m
554 Gas service stn 27.2 12.3 10.2 15.7
546 Retail bakery 20.1 14.3 7.5 20
238 Misc apparel str 27.6 11.5 8.9 15
525 Hardware str 19.1 9.1 4 11.7
591 Drug stores 18.7 10.3 4.8 12.4
721 Laundries 25.7 11 6 12.5
723 Beauty shops 32.6 19.1 13.9 19.7
701 Hotels & motels 19.6 11.7 8.5 14.2
734 Building services 21.7 10.1 6.7 11.9
805 Nursing facility 11.9 5.9 4.2 9.3
531 Department stores 10.5 7.9 4.2 9.7
225 Knitting mills 6 3.5 3.7 9.2
599 Retail stores m 14.6 6 12
239 Misc fabr textile 13.3 7.4 2.3 3.9
561 Mens clothing m m m m
553 Auto/home supply 12.1 4.5 1.5 4.7
Youth Industries
58 Eating/drinking places (#) 9.6 7.3 6.8 .7
58 Eating/drinking places 48.6 33.7 25.4 35.2
541 Grocery stores 27.4 14.7 6.4 13.2
311 Leather tanning s 11.2 -- 7.4
545 Dairy prod stores 51.3 19 14.6 29.1
753 Auto rental 9.9 2.3 3.7 5.2
High-Wage Industries
731 Advertising .4 2.6 1.2 .9
371 Auto vehicle 2.4 .6 .4 .4
331 Blast furnaces 2.5 .6 0 .9
871 Eng/arch services 2.1 1 .5 .5
483 Radio/TV brdcst 1.7 4.1 1.7 3.1
SIC Industry 81 80 79 78
Low-Wage Industries
533 Variety stores 16.2 16.2 54.5 59.8
562 Women's clothing 27.2 27.1 40.2 46.8
835 Child day care na na na na
566 Shoe stores 11 9.9 47.6 25.8
565 Family clothing 27.2 27.1 40.2 46.8
554 Gas service stn 21 21.3 49.9 46.6
546 Retail bakery 12.4 11.6 s 61
238 Misc apparel str 32.1 32.2 38.9 42.3
525 Hardware str 12.4 11.7 19.4 28.2
591 Drug stores 21.8 20.5 38 45
721 Laundries 18.6 18.8 43.2 42.2
723 Beauty shops 22 19.3 38.9 42.6
701 Hotels & motels 45.6 35.4 49.1 45.9
734 Building services 14.4 14.4 32.4 31.5
805 Nursing facility 37.9 33 50.3 48.4
531 Department stores 39.3 37.5 33.5 33.3
225 Knitting mills 9.1 7.4 26.9 25.4
599 Retail stores 27.1 23.5 37.7 34.6
239 Misc fabr textile 8.1 9.8 29.7 28
561 Mens clothing 27.2 27.1 40.2 46.8
553 Auto/home supply 10.8 * 12.7 * 25.2 21
Youth Industries
58 Eating/drinking places (#) 3.9 3.4 2
58 Eating/drinking places 78.4 74.2 61.7 3.9
541 Grocery stores 34.1 29.2 23.3 21.4
311 Leather tanning s s s s
545 Dairy prod stores 9.8 s s s
753 Auto rental 9.9 11 14.1 15
High-Wage Industries
731 Advertising 4 5.4 10.9 2.3
371 Auto vehicle 6.1 5.7 .6 .7
331 Blast furnaces 3.6 3.9 0 0
871 Eng/arch services 5.6 4 2.6 4.4
483 Radio/TV brdcst 7.4 7.4 9.8 4.9
SIC Industry 76 75 74
Low-Wage Industries
533 Variety stores 21.6 14.6 50.1
562 Women's clothing 26.5 22.8 33.5
835 Child day care na na na
566 Shoe stores 10.3 9.2 32.6
565 Family clothing 26.5 22.8 33.5
554 Gas service stn 23 19.1 42.1
546 Retail bakery s s s
238 Misc apparel str 33.6 31.7 33.1
525 Hardware str 13.1 11.6 16.2
591 Drug stores 21.9 18.9 32.8
721 Laundries 22.2 22.6 36.9
723 Beauty shops 22.2 15.3 32.9
701 Hotels & motels 29.3 32.6 48.7
734 Building services 12 10 13.6
805 Nursing facility 37 34.5 43.9
531 Department stores 36.2 35.6 28.4
225 Knitting mills 10.7 10.3 18.6
599 Retail stores 20.4 18.4 30.5
239 Misc fabr textile 8.8 9.1 22.7
561 Mens clothing 26.5 22.8 33.5
553 Auto/home supply 9.7 * 7.6 * 9.7
Youth Industries
58 Eating/drinking places (#) 5 11.7
58 Eating/drinking places 73.4 68 53.6
541 Grocery stores 26.2 28.8 18.1
311 Leather tanning s s s
545 Dairy prod stores s s s
753 Auto rental 10 7 9.4
High-Wage Industries
731 Advertising 2.8 s 1.9
371 Auto vehicle 2.8 1.7 .4
331 Blast furnaces 0 0 .6
871 Eng/arch services 5.1 4.8 1.1
483 Radio/TV brdcst 5.9 4.3 3.9
NOTE: Symbols and abbreviations used in this table are: (#), calculated
at the legal minimum for tipped employees: *, change in definition;
m, missing; na, not a distinct category in earlier CPS industry
classification; s, very small sample (under 30).
Table 3. High-Wage Industries: Average Value of the Relative
Minimum Wage by Industry in Each Panel
Starting year of panel
Description SIC 47 58 64 72 82
Copper ores 102 .33 .30 .28
Crude petroleum and natural gas 131 .33 .33 .31 .28 .27
Operative builders 153 .33
Painting and paper hanging 172 .31 .30 .29 .28
Carpentry and floor work 175 .28
Petroleum refining 291 .29 .28 .27 .25 .22
Flat glass 321 .31 .30 .28 .25
Primary nonferrous metals 333 .33 .32 .26
Nonferrous rolling and drawing 335 .33 .31
Construction and related machinery 353 .32
Railroad equipment 374 .30 .32 .33
Telephone communications 481 .31 .27
Composite high wage industry
(wtd by employment) .31 .31 .30 .30 .28
Table 4. The Size of Each Model
Panel
Number of 1947 1958 1964 1972 1982
Industries 11 28 34 27 28
Equations 22 56 68 54 56
Parameters 620 1,626 1,708 1,327 1,302
Months in sample
(allowing for lags) 574 454 394 286 188
Observations in sample
(months x equations) 12,628 24,712 27,792 15,444 10,528
Table 5. Hypothesis Tests of Each Model p Values for Likelihood Ratio
Tests
Panel
Hypotheses 1947 1958 1964 1972 1982
[H.sub.0]: All minimum-wage terms
in all equations equal zero
([e.sub.0j] = [u.sub.ij]
= [v.sub.ij] = 0, i =
0, 1, 2 and all j) .000 .000 .000 .000 .000
[H.sub.0]: The minimum-wage term in
all wage equations is equal to
zero
([e.sub.0j] =0, all j) .000 .000 .000 .000 .000
[H.sub.0]: The minimum-wage terms
in all employment equations equal
zero
([u.sub.ij] = [v.sub.ij]
= 0, i = 0, 1, 2 and
all j) .007 .004 .002 .000 .000
[H.sub.0]: The minimum-wage terms
in all employment equations add
to zero
([[summation of].sup.2
.sub.t=0] [u.sub.tj] =
[[summation of].sup.2
.sub.t=0] [v.sub.tj] =
0, all j) .002 .051 .086 .001 .000
NOTE: Subscriptj identifies the SIC industry.
Table 6. The Wage Filter and the 1990 Minimum Wage Increase
Average wage ($)
in the 2 months before
the minimum-wage increase
Bound All Unbound
SIC workers (%) workers workers
225 9.2 7.25 7.62
239 3.9 7.68 7.85
525 11.7 6.65 7.06
531 9.7 7.05 7.42
533 27.0 5.45 6.14
541 13.2 7.38 7.96
546 20.0 6.21 6.87
553 4.7 7.71 7.91
554 15.7 6.14 6.62
565 27.1 6.09 7.02
566 13.4 6.01 6.39
591 12.4 6.68 7.12
599 12.0 7.23 7.73
701 14.2 6.92 7.47
721 12.5 6.73 7.18
723 19.7 6.85 7.65
734 11.9 6.98 7.44
805 9.3 7.08 7.44
835 20.6 5.95 6.57
Mean 14.1 6.74 7.24
Average wage
if all bound workers
lose jobs after
the minimum-wage increase
Elasticity w/respect
SIC Increase (%) to employment
225 5 .56
239 2 .56
525 6 .52
531 5 .55
533 13 .47
541 8 .59
546 11 .53
553 3 .56
554 8 .50
565 15 .57
566 6 .47
591 7 .53
599 7 .57
701 8 .56
721 7 .54
723 12 .60
734 7 .55
805 5 .55
835 10 .50
Mean 7.6 .54
Wage if no job loss
after the
minimum-wage increase
Average Increase in average
SIC wage ($) wage (%)
225 7.27 .3
239 7.69 .1
525 6.68 .4
531 7.07 .3
533 5.51 1.1
541 7.41 .4
546 6.26 .7
553 7.72 .1
554 6.18 .6
565 6.15 1.0
566 6.04 .5
591 6.71 .4
599 7.26 .4
701 6.95 .5
721 6.76 .4
723 6.89 .6
734 7.01 .4
805 7.10 .3
835 6.00 .8
Mean 6.77 .5
| | ACKNOWLEDGMENTS We wish to thank Mark Watson, an anonymous referee and the editor for comments that led to substantial improvements in the research presented in this article. REFERENCES Baker, M., Benjamin, D., and Stanger, S. (1999), "The Highs and Lows of the Minimum Wage Effect: A Time Series Cross-Section Study of the Canadian Law," Journal of Labor Economics, 17, 299-318. Belman, D., and Wolfson, P. (1999), "Its Bark Is Worse Than Its Bite: The Wage and Employment Effects of the Minimum Wage in the United States," Australian Economic Papers, 38, 143-162. Brown, C., Gilroy, C., and Kohen, A. (1982), "The Effect of the Minimum Wage on Employment and Unemployment," Journal of Economic Literature, 20, 487-528. Burdett, K., and Mortensen, D. (1998), "Wage Differentials, Employer Size and Unemployment," International Economic Review, 39, 257-274. Card, D. (1992a), "Using Regional Variation in Wages to Measure the Effects of the Federal Minimum Wage," Industrial and Labor Relations Review, 46, 22-37. -- (1992b), "Do Minimum Wages Reduce Employment? A Case Study of California, 1987-1989," Industrial and Labor Relations Review, 46, 38-54. Card, D., and Krueger, A. (1994), "Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania," American Economic Review, 84, 772-793. -- (1995), Myth and Measurement: The New Economics of the Minimum Wage, Princeton, NJ: Princeton University Press. -- (1997), "A Re-Analysis of the Effect of the New Jersey Minimum Wage Increase on the Fast-Food Industry With Representative Payroll Data," Working Paper 393, Princeton University, Industrial Relations Section. Currie, J., and Fallick, B. (1996), "A Note on the New Minimum Wage Research," Journal of Human Resources, 31, 404-428. Deere, D., Murphy, K. M., and Welch, F. (1995), "Employment Effects of the 1990-1991 Minimum Wage Hike," American Economic Review, 85, 232-237. Dickens, R., Machin, S., and Manning, A. (1999), "The Effects of Minimum Wages on Employment: Theory and Evidence From Britain," Journal of Labor Economics, 17, 1-22. Greene, G. (1969), "Comparing Employment Estimates From Household and Payroll Surveys," in Monthly Labor Review, Washington, DC: Bureau of Labor Statistics, pp. 9-20. Hungerford, T. (1997), "Does Increasing the Minimum Wage Increase the Incidence of Involuntary Part-Time Work?" mimeo, U.S. General Accounting Office and American University. Katz, L., and Krueger, A. (1992), "The Effect of the Minimum Wage on the Fast Food Industry," Industrial and Labor Relations Review, 46, 6-21. Kaufman, B. (1997), The Economics of Labor Markets, Chicago: Dryden Press. Kim, T., and Taylor, L. (1995), "The Employment Effect in Retail Trade of California's 1988 Minimum Wage Increase," Journal of Business & Economic Statistics, 13, 175-182. Leybourne, S. J., and McCabe, B. P. M. (1994), "A Consistent Test for a Unit Root," Journal of Business & Economic Statistics, 12, 157-166. Mishel, L., Bernstein, J., and Schmitt, J. (2001), The State of Working America 2000-2001, Ithaca, NY: ILR Press (an imprint of the Cornell University Press). Neumark, D., Schweitzer, M., and Wascher, W. (1998), "The Effects of Minimum Wages on the Distribution of Family Incomes: A Non-Parametric Analysis," Working Paper 6536, National Bureau of Economic Research. Neumark, D., and Wascher, W. (1992), "Employment Effects of Minimum and Subminimum Wages: Panel Data on State Minimum Wage Laws," Industrial and Labor Relations Review, 46, 55-88. Telser, L. (1964), "'Iterative Estimation of a Set of Linear Regression Equations," Journal of the American Statistical Association, 59, 845-862. Van den Berg, G., and Ridder, G. (1998), "An Empirical Equilibrium Search Model of the Labor Market," Econometrica, 66, 1183-1221. Paul WOLFSON Amos Tuck School of Business Administration, Dartmouth College, Hanover, NH 03755-9023 (Paul J.
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