Augmenting the Human Capital Earnings Equation with Measures of Where People Work

I. Introduction

Standard earnings equations relate log earnings of individuals to their measured human capital or demographic attributes.¹ These equations account for a sizable proportion of the variation in individual earnings but still leave a sufficiently large residual among workers with the same measured characteristics to challenge “the law of one price” in the US labor market. Exemplifying the dispersion of earnings for workers with similar skills, Devroye and Freeman (2001) found that variance of log earnings among US workers within narrow bands of adult literacy test scores exceeded the variance of earnings among all workers in the United Kingdom, the Netherlands, and Sweden. Much of the increased earnings inequality in the United States from the 1970s to the 2000s, moreover, has taken the form of increased inequality among workers with the same measured human capital or demographic attributes.

What underlies the level and change in the residual variance from log earnings equations? One identifiable factor is the firm or establishment that employs the worker. The simplest market-clearing models postulate either a single wage or a narrow band of wages associated with costs of information and mobility among jobs for workers with comparable skills, but the evidence often shows that employers pay sizable differences for workers with the same measured attributes.² Commensurately, the same worker often earns substantially more or less working for different employers in closely aligned periods of time.

II. ANOVA of Establishment Earnings

To see the extent to which earnings of individuals depend on where they work in the United States in recent years, we analyzed the log earnings of individual workers in the Longitudinal Employer-Household Dynamics (LEHD) Employment History Files for the nine states with LEHD data from 1992 through 2007.³ We decomposed the total variance of log earnings into a part attributable to differences in earnings among establishments and a part due to differences in earnings of workers within establishments. To keep as many observations as possible on each individual for panel data analysis, we included all jobs observed in the second quarter of each year in the LEHD. We estimated establishment effects by regressing the log earnings of individuals on establishment dummies separately for each year and then used the variance of the estimated coefficients on establishment dummies to measure the variance of log earnings due to the between-establishment effect. The remaining variance reflects earnings differences within establishments and interactions between individuals and establishments. Since the ANOVA does not adjust earnings for the measured attributes of individuals within establishments or for establishment differences in average worker attributes or observable establishment attributes, the calculations are a descriptive representation of the raw earnings data.

Table 1 displays the results of the ANOVA for 1992–2007 for the whole US economy and for eight large one-digit sectors. The columns give the total variance of individual earnings in 1992 and 2007, the share of the variance attributable to variance among establishments, the change in variance over time, and the share of the change attributable to increased variance of earnings among establishments. The first line shows that in the economy as a whole 48% of the variance of log earnings among workers comes from variation among establishments and that 66% of the 0.091 increased variance of earnings is due to the increase in variance among establishments.⁴

The remaining lines of Table 1 show differences in the level and change in the variance of log earnings among sectors. Variance is highest in business services and in finance, insurance, and real estate and is lowest in manufacturing; in mining, utilities, and transportation; and in private services. The share of the total variance associated with establishments is largest in business services and private services and is lowest in health, education, and social services. Manufacturing, on which this paper focuses, has lower variance of earnings than the economy as a whole, is close to the economy-wide share of variance associated with earnings differences among establishments, and has a lower establishment share of the 1992–2007 increase in variance.

What employer attributes determine whether an employer pays above- or below-average market wages? How much do the individual attributes in standard log earnings equations and unobserved individual attributes associated with earnings affect the contribution of the employer effects on the variances shown in Table 1? What economic forces compress earnings across employers? What forces increase divergence? Do earnings differentials associated with worker characteristics differ by employer enough to contribute to the overall dispersion of earnings?

We examine these questions for manufacturing. We focus on manufacturing because of the quality of data on that sector: the Annual Survey of Manufacturers (ASM) provides information on manufacturing establishments annually that is unavailable for other sectors and detailed evidence on investment in capital and other inputs that are likely to affect labor productivity across establishments, potentially leading to heterogeneity of pay through some kind of rent-sharing mechanism.⁵ For our analysis, we combined individual earnings from the LEHD with data on worker attributes from the decennial census and the Current Population Survey (CPS), data on establishment attributes from the Census of Manufacturing, and data on firm attributes from the Longitudinal Business Database (LBD) and the Survey of Industrial Research and Development (SIRD).⁶

III. Methodology

The traditional human capital earnings equation (Mincer 1974) relates earnings w_it of individual i in period t to observable measures/indicators of personal skill and other individual characteristics that ideally reflect productivity but that may also reflect employer attitudes or perceptions resulting from prejudicial or statistical discrimination:

Our augmented earnings equation adds the measured and unmeasured characteristics of an individual’s establishment/firm to equation (1):

Having multiple observations on a person along with employer identifiers in longitudinal data allows us to decompose the job effect into an individual fixed effect via a dummy variable for each worker, an establishment fixed effect via a dummy variable for each employer, and a match component orthogonal to the individual and establishment fixed effects per the Abowd-Kramarz-Margolis (AKM) decomposition (Abowd et al. 1999): ${\psi }_{\mathit{ij}}={\alpha }_i+{ɸ}_j+{\xi }_{\mathit{ij}}$. Defining ${\alpha }_i=X_{i}B+a_i$ and ${ɸ}_j=Z_{j}D+{\phi }_j$, where X and Z are covariates for each individual and establishment, we identify the B and D parameter vectors by assuming that the residual of the individual fixed effect is orthogonal to individual fixed characteristics and that the residual of the establishment fixed effect is orthogonal to establishment fixed characteristics. However, the components of both fixed effects can correlate with time-varying characteristics and each other. Our final augmented equation is

Comparing equations (1) and (3), if personal skills and attributes are the sole factors included in the estimation, the coefficients of equation (1) estimate the gross return to those skills/attributes inclusive of possible gains from access to different employers, whereas the coefficients of equation (3) measure the net return exclusive of the earnings characteristics of employers. Alternatively, to the extent that the covariates in equation (1) are correlated with the equation (2) variables, the estimated coefficients of (1) can be viewed as biased estimates of the net effects of skills/attributes in equation (2).

IV. Variance Decomposition in Manufacturing

Table 2 gives a variance decomposition for the subset of manufacturing workers for whom we match observations in the LEHD and CoM to decennial census or CPS files. This is the sample on which the rest of our analysis focuses. The increase in variance in the subsample falls short of the increase in the full LEHD—a variance of 0.272 compared with the Table 1 figure of 0.398 in 1992 and a variance of 0.330 compared with 0.490 in 2007, producing a smaller increase in variance over time. A major reason is that the matched sample loses many small establishments where earnings are relatively low. The proportion of the variance in log earnings attributable to between-establishment differences is as a result lower as well. The 43% contribution of increased earnings between establishments in the matched sample is smaller than the 57% in the full LEHD. The matched sample understates the contribution of establishments to the variation in earnings.

As establishments belong to firms that include other establishments, all of which may be covered by firm-wide human resource and compensation policies, we decomposed the between-establishment contribution to the variance of earnings into an effect associated with firms and an effect associated with establishments within firms. We did this in two stages: first by regressing log of earnings on dummy variables for establishments and then by regressing estimated establishment fixed effects on dummy variables for firms. The proportion of the variance attributed to firms reflects the overall pay practices of firms, while the remaining proportion reflects pay differences among establishments in the same firm.

The Table 2 calculations show that consistent with the emphasis of Song et al. (2015) on the importance of the firm in accounting for the increased dispersion in worker earnings over time, the firm component dominates the variation in log earnings among establishments. In our manufacturing data, 90.4% (=0.113/0.125) of the variance in earnings between establishments in 1992 is assigned to firm fixed effects and 93.3% (=0.140/0.150) of the establishment variance in 2007 is similarly assigned to firm fixed effects. Over time, moreover, the variance in establishment earnings for establishments within firms fell, so that 110% (=0.47/0.43) of the increased earnings dispersion associated with establishment was due to increased earnings variance among firms.¹⁰

V. Cross-Section Earnings Equations

Column 1 of Table 3 records estimated coefficients and standard errors for ordinary least squares regressions of the benchmark cross-section log earnings equation with years of schooling, age, gender, and some interactions to allow for differences in effects among those attributes. In addition, the regression includes 171 geographic area dummies and 16 year dummies so that the coefficients are estimated within year and area. The estimated coefficients are similar to those typically found in the human capital earnings literature: an estimated average return to years of schooling of about 9.4% per year and a concave age profile captured by the negative squared term and gender and race earnings gaps at 30% and 17%, respectively. The R² of the equation of 0.45 is larger than the R² in earnings functions fit on CPS data,¹¹ presumably because variation in earnings in the entire economy exceeds that in manufacturing and/or because the administrative LEHD earnings has less measurement error than self-reported earnings in the CPS.

Column 2 adds a set of workplace variables to reflect place of employment: four-digit NAICS industry dummies, the log number of employees of the firm, the log number of employees in the establishment, and establishment age and its square.¹² The estimates show significant firm and establishment effects and a concave earning-establishment age profile. Adding the firm and establishment characteristics raises the R² to 0.505 and thus explains 10% of the residual variance of earnings for demographically similar persons. The firm and establishment variables shrink the positive coefficients on years of schooling and age and the negative coefficients on gender and being nonwhite, indicating that some of the impact of those factors comes through sorting of workers among establishments and industries within manufacturing.

Column 3 adds variables relating to the attributes of the establishment’s workforce: mean years of schooling, mean age, share female, and share nonwhite; capital structures per worker and capital equipment per worker; the export share of establishment revenues; and the R&D investment of the firm to which the establishment belongs. The most striking result is the high estimated coefficient on the years of schooling of all workers. The estimated 0.069 coefficient on the mean years of schooling in the workers’ establishment compared with the 0.074 coefficient on the workers’ own education suggests that it is almost as good to work in an establishment with more educated workers as it is to have more education. The estimates also show that workers earn more in establishments with older workers and less in establishments with a larger proportion of female or nonwhite workers. More capital equipment per worker raises earnings more than more capital structures per worker (a coefficient difference of 0.046 vs. 0.007), and earnings are higher in establishments with a high export share. Finally, earnings rise with R&D intensity of a firm: workers in firms with 1 standard deviation higher R&D intensity average 2% more earnings.

Column 4 gives the regression results with dummy variables for firms added to the equation, while column 5 gives results with dummy variables for establishments replacing those for firms. With establishment fixed effects in the model, it is no longer possible to identify separately the linear effect of establishment age and the time dummies, so we have removed the linear term for establishment age. Since the effect of linear age is now absorbed by the time dummies, none of the remaining estimators are affected. Addition of the firm fixed effects substantially reduces the estimated impact of the number of employees at the firm, indicating that short-run changes in firm employment have little effect on earnings but only reduce the coefficient on number of employees at the establishment modestly. The column 5 estimates with dummy variables for establishment also markedly reduce the coefficient for firm employment but leave a substantial effect of establishment employment on earnings. With establishment fixed effects in the equation, the positive effect of establishment employment suggests that an establishment operates along a rising supply curve of labor for short-term increases in employment, which suggests some monopsony power in the labor market (Manning 2005).

Addition of the firm and establishment dummies naturally shrinks the estimated effect of firm and establishment variables on earnings. The column 4 firm fixed effects regression eliminates the negative relationship between the share of nonwhite employees. Working in an establishment with a large nonwhite share is associated with low earnings, but short-run changes in the nonwhite share do not affect establishment earnings much. The column 4 fixed effects regression also greatly weakens the relationship between R&D and earnings, reducing the estimated coefficient by more than 80%. While R&D firms pay more than firms that do less R&D, changes in R&D activity within a firm have little effect on earnings.

The column 5 regression, which includes establishment fixed effects, further shrinks the coefficients of most of the establishment workforce characteristics compared with those in column 3. The estimated 0.0690 effect of the mean years of schooling on earnings in column 3 drops to 0.0249 in column 5, while the estimated −0.3176 for being female in column 3 drops to −0.1084 in column 5. While measurement error usually accounts for some of the lower coefficient on variables in longitudinal analysis compared with cross-section analysis (Freeman 1984), the pooling of observations to create average characteristics is likely to diminish measurement error so that huge drops in the effects of these characteristics are likely to at least in part reflect economic behavior as firms adjust earnings to changing characteristics gradually over time.

VI. Panel Earnings Equations

The longitudinal structure of the LEHD allows us to estimate the effects of employer characteristics on earnings for the same individual in two ways: (1) by comparing workers who remain in the same job while management changes characteristics of the establishment or does nothing to offset changes due to factors outside management control, such as workers retiring or quitting for another job without replacing the leaver with someone similar, and (2) by comparing workers who quit an employer with one set of characteristics to join an employer with other characteristics. Outside of recession years, the bulk of the labor mobility comes from worker decisions to move to a new employer willing to hire them. In recessions, mobility depends more on the layoff decisions of firms, with the number of layoffs increasing to approach or exceed the number of quits.¹³ While our data lack information on whether a worker left a job by quitting or by layoff, recession years are less frequent than nonrecession years in our data, which suggests that the bulk of the worker changes reflect quits rather than layoffs.¹⁴

Table 4 presents estimates of the effect of employer attributes on the earnings of the same worker when those attributes change. Column 1 shows the results of adding individual fixed effects to the basic log earnings regression from column 3 in Table 3 for all workers in the matched sample. The coefficients on some employer variables decline with the addition of the worker fixed effects: the estimated coefficient for average years of schooling of workers in an establishment falls by 59% (from 0.0737 to 0.0299), suggesting that much of the large coworker schooling effect is due to positive sorting of workers by unmeasured individual characteristics into establishments with more educated workers. The coefficient on the equipment stock of capital per employee drops more massively by 70% (from 0.0462 to 0.0140), suggesting positive sorting of unmeasured individual characteristics into establishments with more equipment capital. And the coefficient on R&D drops by 83% (from 0.762 to 0.1290), suggesting that most of the cross-section R&D effect is due to a positive matching between R&D firms and unmeasured individual characteristics.

The next two columns unpack the fixed effects model into its two parts. Column 2 estimates the effect of employer characteristics on the earnings of workers who stay in the same establishment. This specification controls for what we call “job-individual fixed effects”—the unique combination of an individual and the establishment, which encompasses both the establishment fixed effects and the individual fixed effect from the AKM decomposition, in addition to a potential match-specific fixed effect. As in Table 3, the linear effect of establishment age is no longer separately identified from the time effects and is thus omitted from the model. Column 3 estimates the impact of employer factors on the earnings of workers who changed employers, which identifies the effects of establishment characteristics through changes in the employer and thus does not control for establishment fixed effects or match-specific effects.¹⁵

For most establishment characteristics, the column 3 estimated effects of worker-initiated changes have a much greater impact on earnings than do the column 2 estimated effects of employer-initiated changes. Moving to a firm that has greater employment gives an earnings increase of 0.0162, while working in a firm that increases employment changes gives a 0.0056 boost to earnings—about one-third as large. Moving from an establishment with more years of schooling increases earnings by 0.0322, compared with an increase in earnings of 0.0048 when a worker’s current establishment increases its years of schooling. Moving to an establishment with older workers raises the earnings of the mover, while staying in an establishment with a rising age of the workforce reduces the worker’s earnings. The effect of R&D on earnings is more than twice as large for movers than for stayers (0.2075 vs. 0.0860). But not all characteristics have a larger effect for movers than for stayers. An increase in establishment employment has a modestly larger effect for persons who stay with an establishment than for those who move, and similarly for the share of nonwhites.

Mechanically, the differences between the column 2 stayers-based estimates and the column 3 movers-based estimates reflect the fact that the stayers analysis controls for unobserved establishment fixed effects and thus removes correlations between those effects and the earnings, while the movers model does not do this. But the differences also reflect economic behavior. A worker who chooses to change employers will likely require a larger increase in pay to cover the costs of mobility than one who stays at a job. An establishment that changes characteristics will likely adjust operations slowly and alter pay less in the short run compared with employers whose characteristics differ over longer periods and whose pay structures reflect long-term differences in the mode of operating.¹⁶

Earnings equations with individual fixed effects cannot identify the relation between stable individual characteristics and earnings: those effects are absorbed in the individual dummy variables. But it is possible to learn something about how years of schooling and demographic factors such as gender, race, or age affect the individual fixed effects by regressing the estimated fixed effect for individuals on those characteristics. Say we have 10 workers with two defining characteristics, years of schooling and gender. The fixed effects earnings equation would produce estimated coefficients for each of the 10 workers that could be regressed on the workers’ schooling and gender to capture their relation to the fixed effects. Columns 1–3 of Table 5 give the results of such an analysis in three regression models. Model 1 uses estimated individual fixed effects from a regression without employer characteristics.¹⁷ Model 2 uses estimated individual fixed effects from a regression with observable employer characteristics. Model 3 uses estimated individual fixed effects from a stayers’ regression that includes establishment and match-specific fixed effects (eq. [3]). The estimated relations between the individual effects that are positively related to the characteristics of employers decline across the columns as we add increasing information on where the employee works. The returns to years of schooling drops from 0.1076 for the model 1 specification that has no controls for employee characteristics to 0.0841 for the model 3 specification that controls for observed and unobserved establishment effects. The coefficient on female falls by 12%, and the coefficient on age falls by 18%.

The bottom line in Table 5 (“Variance of the estimated unobserved individual effects”) shows how the addition of establishment characteristics reduces the contribution of the fixed effects for individuals to the variation of earnings among workers. In model 1, the individual fixed effect variance is 0.149, or 51% of the total variance. In model 2, which includes measured establishment characteristics, the individual fixed effect variance falls to 0.127, or 43% of the total variance. In model 3 with observed and unobserved establishment characteristics, the variance of the individual effect is 0.112, or about 38% of the total variance in earnings. Put differently, establishment factors account for 25% ($\left(0.149-0.112\right)/0.149$) of the variance of estimated individual effects.

VII. A Full Decomposition

Table 6 summarizes our findings with a full decomposition of log earnings in the augmented earnings equation. The standard individual characteristics of years of schooling, age, gender, and race account for 26% of the total variation in earnings; unobserved individual effects account for 37% of the variation; observed establishment characteristics account for 8% of the variance; unobserved establishment effects account for 7% of the variance; and the match component accounts for 3% of the variance. The covariance between the individual and establishment components of the earnings equation adds 13% of the variance. The remaining variation arises from the transitory within-match residual comprising 7% of the total variation and to small negative covariance terms between the observed and unobserved parts of the individual and establishment components, respectively.¹⁸ The most important factors relate to individuals, but employer factors and their relation to individual factors are significant and substantive.

VIII. The Sorting of Workers between Establishments

The interaction between individual characteristics and establishment characteristics suggests that sorting of workers with given characteristics among workplaces with different characteristics affects inequality at large. Positive assortative matching of workers high in measured or unmeasured skills/wages to high-wage establishments raises the inequality of earnings. By contrast, assortative matching of workers with workers of similar measured skill does not create “extra inequality” but points to the complementarity of skills of similar workers in the production process and allocation of labor.

Assortative matching also affects the interpretation of estimated coefficients on particular variables. When workers positively sort by education into higher-paying establishments, the traditional log earnings equation that excludes establishment factors captures two effects in its estimated coefficient on years of schooling: the return of higher skills to earnings within an establishment and the differential access that schooling gives workers to obtaining jobs in higher-paying establishments. Addition of dummy variables for establishments limits the effect of years of schooling to its effect within an establishment. Given that sorting of workers between establishments affects the dispersion of pay and the returns to individual characteristics, we analyze next the ways in which workers and firms match up.

Table 7 gives the correlation coefficients for sorting by key earnings determinants. The largest correlations show considerable sorting of workers with workers like themselves: correlations of educated workers with educated workers (0.477), of older workers with older workers (0.333), of females with females (0.349), and of nonwhites with nonwhites (0.471). But other characteristics of employers are sufficiently correlated with worker characteristics to suggest sorting of workers among establishments beyond homophily. Educated workers work in large firms and in R&D-intensive firms, in establishments with high capital per worker and high export shares. These patterns make it likely that some of the education earnings premium comes through the greater likelihood that educated workers find jobs in employers with other earning-enhancing characteristics. Older workers are also associated with establishments with high-earning characteristics, although the correlations are much smaller. By contrast, women work in establishments with lower capital intensity, and nonwhite workers are largely employed in establishments with low-earning characteristics.

The bottom two lines of the table shows the correlation between a composite measure of the establishment contribution to earnings through observed variables plus industry and region, weighted by their estimated effect on earnings, and through establishment fixed effects. Both the establishment observables and the fixed effects are highly correlated with years of schooling, making schooling potentially the most important dimension of worker sorting among establishments.

Figure 1 summarizes the relations between the characteristics of workers and those of the establishments where they work via the correlations between indices of the observed characteristics as a group, weighted by their respective coefficients in the earnings equation, and the fixed effects associated for workers as well as for establishments. The largest correlation is between the individual observables weighted by their contribution to earnings and establishment observables weighted by their contribution to earnings (0.253), followed by the correlation between the individual observables and the establishment unobserved fixed effect. By contrast, the fixed effect of individuals is weakly positively correlated with the establishment observables, while the individual unobservables and unobserved establishment fixed effects are negatively correlated—a result consistent with Abowd et al. (2014). As Andrews et al. (2008) notes, a negative correlation between two unobserved components of earnings could result from sampling and measurement errors,¹⁹ so the safest conclusion from these correlations is that sorting of workers occurs largely on observable characteristics.

IX. Mobility across Employers

The impact of employer characteristics on the earnings of workers with similar measured characteristics and fixed effects and the Table 7 and figure 1 correlations direct attention to the potential role of worker mobility among employers in determining pay. To what extent does mobility from job to job raise pay? How often do workers who start their careers in establishments with low-earning characteristics move to firms with better observable and unobservable characteristics over time? And conversely, how much downward firm mobility is there among workers who begin their careers at firms with high-earning characteristics?

To examine the transitions of workers among establishments with different establishment components of earnings, we formed a transition matrix for workers in our data in both 1992 and 2007. We attached to every worker the total establishment contribution to earnings, defined as the sum of the contribution to earnings of the time-varying establishment characteristics, such as firm size and R&D spending; the fixed observables, such as industry and region; and the unobserved establishment effects. With an establishment contribution for each worker in 1992 and 2007, the natural measure of each worker’s mobility is the change in the establishment component of earnings of their employer in those years.

Table 8 summarizes the transition pattern by quintiles of the distributions, ordered from low-paying firms in quintile 1 to high-paying firms in quintile 5. The rows in the table show the distribution of workers by the 1992 quintile distribution of their employer into the 2007 quintile distribution of their employer. While the largest probabilities are for workers to remain in the same quintile over time, there is evidence of upward movement among establishments. Workers in the low quintiles have larger shares going up in the distribution than workers in the top quintiles have shares falling in the distribution. Among workers in the third quintile, 38% move to a higher quintile, whereas only 21% move down and 40% remain in the same quintile. New workers come into the distribution of firms at the lower end and change jobs over time to produce a lifetime move up the distribution. Measured by productivity of establishments rather than earnings, Haltiwanger, Hyatt, and McEntarfer (2018, in this issue) find a similar pattern in productivity, with younger workers in particular moving from less productive to more productive firms over time.

Finally, we characterize the sorting of workers with workers between establishments by Kremer and Maskin’s (1996) index of segregation, $\rho =\mathrm{cov}\left(\omega \underset{\_}{\omega }\right)/V\left(\omega \right)$, where $\underset{\_}{\omega }$ is the average individual component of the establishment and V(ω) is the variance of the individual components of the standard earnings equation. If workers segregate completely between establishments according to their individual earnings components, $\rho =1$, whereas if they randomly allocate between establishments, $\rho =0$. The index of segregation for observable characteristics in our data is 0.24, while the index for unobservable characteristics is 0.17. This supports the implication of the correlations that sorting of workers according to observed individual characteristics, such as years of schooling, age, gender, and race, is considerably stronger than segregation according to unobserved attributes.

We characterize the sorting of workers with establishments by the equivalent Kremer-Maskin (1996) index, ${\rho }_{\mathrm{\Omega }}=\mathrm{cov}\left(\omega ,\mathrm{\Omega }\right)/V\left(\omega \right)$, where Ω is the earnings components of establishment and divide the decomposition into its within-establishment (V^w) and between-establishment (V^b) parts by the identities

In our data, $\rho =0.247$ and ${\rho }_{\mathrm{\Omega }}=0.100$. The within-establishment component is 59% of the variance in earnings, of which 82% arises from the observed and unobserved individual component, 6% arises from the match component, and 12% arises from the residual. The between component contributes 41% of the variance in earnings, of which 36% is due to worker-worker sorting, 30% is due to worker-establishment sorting, and 34% is due to variance of the establishment effect. That most of the within-establishment variation in earnings is associated with variables related to individuals and most of the between-establishment variation in earnings is associated with variables related to establishments and sorting of workers among establishments suggests that the simple within and between decomposition offers powerful insight into the role of supply and demand factors in earnings determination.

X. Conclusion

Augmenting the earnings equation with measured characteristics of employers and unobserved earnings-related fixed effects for establishment or firm adds substantially to the variance in log earnings explicable by an earnings equation. The regressions identify observable employer-side factors—capital equipment per worker, R&D investments, export performance, the level of schooling of an establishment’s workforce, the number of employees, and, up to a point, the age of the establishment—associated with higher worker earnings. While the sizable cross-section effects of measured employer characteristics diminish in longitudinal data with the inclusion of firm and establishment fixed effects, those fixed effects are another manifestation of the importance of where a person works to what they earn.

The evidence that addition of establishment- or firm-related variables reduces the estimated coefficient on the key human capital variable, years of schooling, by about one-fifth directs attention to the role of schooling in giving workers access to higher-paying workplaces. The near comparability of the estimated effect of average establishment schooling and of the individual’s years of schooling (absent firm or establishment fixed effects) further suggests that some of the gains from human capital investments spill over to other workers,²⁰ while the drop in the estimated coefficient on average years of schooling with the addition of establishment fixed effects reflects the strong positive relation between average years of schooling and establishment fixed effects.

The evidence that the estimated coefficients on gender, race, and age diminish when we introduce individual and establishment fixed effects provides further support for the notion that the sorting of workers among employers is important in earnings differentials. Youth, females, and nonwhites are more likely to be found in low-paying establishments, and the coefficients for the establishment-specific average of the demographic characteristics change signs or turns insignificant once we control for job fixed effects. While the dynamics of worker mobility has workers moving to enterprises with higher observable and fixed effects earnings components over time, assortative matching tends to magnify the effect on inequality beyond what would be the direct impact of earnings differences across establishments.

Taken together, the dual findings that where a person works affects their earnings and that sorting of workers among employers accounts for some of the differentials in earnings associated with years of schooling and demographic characteristics raises new questions for analysis: Why does having more educated coworkers affect individual earnings so much? To what extent do costs of mobility account for the greater impact of employee-instituted than employer-instituted changes in the payoff from working with other inputs? How important are explicit human resource and compensation policies in positioning employers in the distribution of earnings? And do their decisions equilibrate the marginal payoffs to paying above- or below-market average levels of pay? Finally, given manufacturing’s modest and declining share of employment, our analysis suggests the value of estimating augmented earnings functions in other industries to see whether the role of employers and sorting of workers found here generalizes to the labor market writ large.