2.1. Theoretical and empirical literature

The link between the level of collective bargaining and within-firm wage inequalities can be framed by several approaches, with contrasting predictions about whether firm-level bargaining should result in higher or lower within-firm inequality, compared to centralized bargaining.

Economic theories primarily stress firm-specific incentives as drivers of the adoption of firm-level agreements. On the one hand, decentralized bargaining should increase within-firm inequality in models where firm-level agreements are designed to elicit or selectively compensate the contribution of different employees to the firms’ performance and objectives (Bayo-Moriones, Galdón-Sánchez and Martínez-de-Morentin 2013). This may happen under performance-related pay or other compensating differential schemes consistent with tournament theory (Lazear and Rosen 1981). The same may occur when firm-level schemes are used to remunerate human capital or particularly valuable firm-specific resources selectively, taking a resource-based view of the firm, or to solve transaction costs and agency problems arising for different occupational groups (Eisenhardt 1989; O’Shaughnessy 1998). On the other hand, local bargaining may also reduce within-firm inequality compared to centralized bargaining if firm-level agreements respond to workers’ pursuit of re-distribution, fairness or equity. This may stem from the preference of workers or unions to equalize wages (across but also within firms), as described in “insider–outsider models with unions” (Lindbeck and Snower 1986 and 2001) or “fair wage” theories (Akerlof 1984).

Other mechanisms linking within-firm wage inequalities to centralized or decentralized bargaining are suggested by wage-setting models that explain the wage gap between the market-clearing wage and the wage actually paid to workers, on the basis of efficiency-wage, rent-sharing or differential compensation for unmeasured worker ability. Although these practices are more directly related to between-firm wage inequalities, they may also affect inequalities within a firm if they are used by employers to selectively reshape the overall pay scale in order to adjust the wages of specific groups of workers and not of others. It is, however, difficult to formulate predictions on whether these practices would result in increased or decreased within-firm pay inequality. Their effect depends on their actual implementation and on the willingness of workers and unions to pursue egalitarian objectives of standardizing wages in firm-level negotiations.

Beyond the incentive motives analysed by economists, other literatures highlight the role of different firm-specific characteristics on the internal wage structure of firms. Sociological and socio-economic research stresses the role of organizational inertia and the relative balance of power among groups within organizations, particularly in organizational approaches to stratification that discuss the firm as the central locus of wage inequality creation (Stainback, Tomaskovic-Devey and Skaggs 2010; Cobb 2016). Resistance to change favours the continuation of individuals’ positions and the wage structure within a firm, whereas the resolution of conflicts among groups with different goals and power in the hierarchical, organizational and occupational structure may result in either reducing or increasing inequalities within firms, both statically and over time (Blau and Duncan 1967; Goldthorpe and Hope 1972; Wright 1980; Erikson and Goldthorpe 2002).

Overall, the implementation of firm-level bargaining can vary considerably across firms, with uncertain outcomes on within-firm wage inequality depending on the relative strength of the factors mentioned above. The relationship of firm-level bargaining with within-firm wage inequality remains ultimately an empirical question.

Mirroring the contrasting predictions in the theoretical literature, the few existing empirical studies on the matter (all relating to the 1990s and early 2000s) find mixed results. Dell’Aringa and Lucifora (1994) examine data for Italy for the year 1990 (using a sort of national precursor to the SES) and find that within-firm wage dispersion does not differ between firms that only apply centralized bargaining and those that also apply firm-level agreements. This result is confirmed for Belgium, Ireland, Italy and Spain for the year 1995 by Dell’Aringa et al. (2004), highlighting the need to include residual wages and control variables in estimation models. Indeed, they show that wider unconditional within-establishment wage inequality, observed for enterprises covered by a single-employer agreement, disappears when a large set of controls is included. Conversely, using data for 1995, Canal Domínguez and Rodríguez Gutiérrez (2004) find that firm-level bargaining reduces within-firm wage dispersion in Spain. Lastly, Addison, Kölling and Teixeira (2014) find a modest widening of within-establishment wage dispersion for establishments that exit sectoral agreements, using a panel of German establishments over the period 1996–2008.

Our study complements this limited literature by providing a framework to compare within-firm inequality under centralized and firm-level bargaining across European countries with different institutional traditions and analyse how the relationship changed over time.

2.2. Wage-setting frameworks in selected countries and working hypotheses

The main features of the national bargaining systems of the countries included in our study, over the period covered by the data, are summarized in table SA1 in the supplementary online appendices.

On the one hand, despite a general trend towards devolution of bargaining levels in the period under analysis, countries arguably show significant differences in terms of the scope, coverage and extent of derogation of firm-level bargaining from centralized bargaining. Although the sign of the relationship between firm-level bargaining and within-firm wage inequality is theoretically uncertain overall, the institutional setting in some countries may favour the inequality-enhancing effects of firm-level agreements. In particular, the national systems of Czechia and the United Kingdom are more likely to result in firms that bargain locally having more unequal wage structures, compared to firms that only bargain at more centralized levels. More egalitarian outcomes seem likely to be associated with firm-level contracts in Germany and Spain, whereas no effect is predicted to emerge in Belgium and outcomes are uncertain in France. Our choice to perform separate analyses by country is precisely intended to verify such potentially heterogeneous effects.

On the other hand, we also observe some broad similarities across some countries, especially as regards the prevailing locus of collective bargaining. In line with Fulton (2013), the countries can be assigned to different “bargaining regimes”: Belgium is an emblematic example of an “inter-industry/national regime”; in contrast, Czechia and the United Kingdom represent instances of an “individual-employer regime”; Germany and Spain fall into an intermediate “sectoral regime”; and France is an outlier, owing to the particularly complex interaction across all bargaining levels. Accordingly, one might expect that firm-level agreements in countries assigned to one same regime would affect inequality in a similar way, and that this effect would possibly be more similar than country-specific institutional features alone would predict. Nevertheless, it is difficult to predict whether egalitarian or inequality-enhancing pressures would prevail in economies where firm-level bargaining has always been commonplace (such as Czechia and the United Kingdom), or in countries that traditionally favour more centralized forms of bargaining (such as Belgium, France, Germany and Spain). In this last category, the law or workers’ action may prevent firm-level contracts from introducing inequalities in firms’ internal wage structures. This would reduce the likelihood that, in these countries, firms bargaining locally present more unequal wage structures – if at all – than firms bargaining at higher levels, compared to Czechia and the United Kingdom. However, firm-level bargaining may also be used by firms to differentiate internal wages, precisely to escape the rigidity and complexity of negotiations typical of more corporatist regimes. If this second tendency prevails, we may find higher within-firm inequality under firm-level bargaining in Belgium, France, Germany and Spain, compared to the United Kingdom or Czechia.

An additional – to some extent extreme – hypothesis is that, as wage-setting institutions progressively converge, blurring the institutional differences across countries or the borders across regimes (see Baccaro and Howell 2017), any predicted difference in the relationship between firm-level bargaining and within-firm wage inequality may eventually lose significance. If this were the case, our empirical analysis should reveal the same or comparable effects across all countries.

Regarding time effects, the evolution of national wage bargaining systems (see table SA1 in supplementary online appendix A) suggests two main hypotheses. On the one hand, as the legal provision stipulating firm-level collective agreements was introduced in all countries before the period under study – around the end of the 1990s and the early 2000s – the years spanned by our data correspond to a relatively stable phase for national bargaining frameworks. There are signals that firm-level bargaining was spreading and gaining ground over the period, but no major reforms were implemented (except in France in 2016). We can thus expect a steady increase in the use of firm-level bargaining and a steady increase in the associated extent of within-firm inequality without major time breaks. On the other hand, we might expect significant change in the second part of the sample period, because of the Great Recession of 2008–09 and the ensuing deep financial and debt crises in Europe from 2012 to 2013. As wages were under pressure, firms may have increased their use of flexibility to adjust wages locally through firm-level agreements in the years 2014–18. The effect of firm-level bargaining may thus be greater in later years.

3.1. Data source and sample

The SES data set collected by Eurostat is an established source of data on labour dynamics in Europe. It encompasses a rich set of earnings-related, personal and jobs-related variables for many workers in the EU, matched with data on some characteristics of the employing firms. It has been used in other empirical studies, particularly within the vast literature on between-firm inequality and its determinants. Early national editions of the survey, covering the 1990s, were used in the few existing studies that examined our research question, as discussed in section 2.

The SES data collection strategy selects a random sample of firms (stratified by size, sector of activity and geographical location) for each country and survey year to be representative of the national industrial relations system. Within each selected firm, it draws a representative sample of employees and, for those employees, provides a large set of personal and job-related characteristics, including wages, age, sex, education, type of contract, tenure, occupation type and others. As such, the available data set can be seen as a matched employer–employee data set, providing a unique source for consistent comparisons across economies.

Of course, the SES data have their own limitations. First, the sample of business units considered in the SES generally includes those with at least ten employees, which limits the analysis as far as micro firms are concerned. Second, although the surveying procedure provides information on an impressive number of workers across Europe (about 10 million per survey year), the sampling rate of employees varies by firm size and by country. Third, the data concerning employees’ personal and work-related characteristics are very rich, but the information on firms is limited to five variables: size class, geographical location, sector of activity, public or private control and – crucial for our purposes – the level of wage bargaining adopted in the firm. Fourth, the survey does not allow the same workers to be identified across waves. This implies that a panel data set cannot be identified, following the surveyed employees or firms over time. Thus, although the rich set of individual characteristics should cure a great deal of omitted variable bias in estimating residual wages (see section 4 below for details), it is not possible to control fully for time-invariant unobserved worker characteristics.

For this study, we used the 2006, 2010, 2014 and 2018 waves of the SES. The countries included in the analysis – Belgium, Czechia, France, Germany, Spain and the United Kingdom – were selected based on two criteria: first and foremost, the availability of information about the type of bargaining in place in the sampled firms, which forced us to exclude countries where none or only a handful of firms responded to the specific SES question on the issue; and second, as discussed in the previous section, we wanted to ensure a reasonable representation of different institutional contexts and industrial relations traditions in Europe. We kept the United Kingdom in the sample, even though it does not provide figures for the 2018 wave, as the paramount example of the Anglo-Saxon individual-centred bargaining system.²

Given that, by definition, measuring within-firm wage inequality requires observing wages for at least two employees in one single firm, we define our working sample as including only firms with at least three sampled employees. It is also worth noting that, even though we pool firms across pairs of survey waves in the empirical analysis, this provides repeated cross-sectional data, since the SES does not report any identification code that can be used to match the same firm over time.

3.2. Types of collective bargaining agreements

For our purposes, the key information provided by the SES relates to a question about the type of wage bargaining practised at each firm. This allows us to distinguish three broad cases of collective bargaining coverage. The first case includes centralized bargaining agreements, or what the SES calls “Type-A: National level or inter-confederal agreements”, “Type-B: Industry agreements” or “Type-C: Agreements for individual industries in individual regions”. The second case includes firm-level bargaining, where firms depart from centralized agreements. The SES categorizes such cases as “Type-D: Enterprise or single employer agreements”, “Type-E: Agreements applying only to workers in the local unit” or “Type-F: Other types of firm agreements”. The third case is the lack of collective bargaining agreement (“Type-N: No collective bargaining exists”).³

Centralized wage bargaining is the dominant form of wage-setting among the firms in our sample in Belgium, France and Spain, covering around 70–90 per cent of firms and 65–85 per cent of employees (see table SB1 in supplementary online appendix B). Firm-level agreements in these countries cover only about 6–20 per cent of firms and 15–25 per cent of employees, while a smaller share of firms and employees are not covered by any collective agreement. In Germany, although most companies (67–74 per cent) are not covered by collective agreements, these are mostly small in size and thus represent less than half of the employees sampled. A larger share of employees are covered by centralized agreements, while firm-level agreements are comparatively rare, covering around 3–6 per cent of firms, and around 3–7 per cent of employees. In Czechia and the United Kingdom, the share of firms and employees not covered by collective bargaining is comparable to Germany’s, but among those covered by some form of collective bargaining, firm-level agreements are more frequent, consistent with our description of market-oriented regimes in the previous section. Over time, the share of firms and employees covered by firm-level agreements fluctuates but remains essentially stable in all countries except Czechia. This is consistent with the intuition that the devolution of bargaining levels continued but did not become stronger over the sample period, as the major institutional changes occurred beforehand.

The focus of this article is on bargaining decentralization, which involves a shift from coordinated central bargaining to decentralized firm-level bargaining and is a separate phenomenon from the complete lack of collective wage agreements. Therefore, in our empirical analysis we only consider firms that do apply some form of collective bargaining. We define a variable FLB, which compares the firms that apply firm-level bargaining (FLB = 1) and those that only apply centralized bargaining (FLB = 0).⁴

3.3. Measuring wage inequality within firms

Within-firm wage inequality is measured on the basis of the hourly compensation of employees reported in the SES. To account for differences in workforce composition and corporate characteristics across firms, and in line with an established practice in the literature on wage inequalities – dating back to at least Winter-Ebmer and Zweimüller (1999) – a meaningful comparison of wages across individuals requires isolating the component of individual wage that is not directly related to the average market compensation of job, personal and other characteristics of otherwise similar individuals.

As our measure of within-firm inequality for each firm j, we take the interdecile range of residual log-wages, that is, the gap between the 90th and 10th percentile log-wage premiums:

$\Delta w_j^{90/10}={\widehat{w}}_j^{90}-{\widehat{w}}_j^{10}$       (1)

where ${\widehat{w}}_j^p$ is the pth percentile of the distribution of the residual wage ${\widehat{w}}_{ij}$ obtained for each employee i of firm j from the following Mincer-type regression estimated separately by country and by survey year:

$\begin{array}{rr}\hfill log\left(W_{ij}\right)& \hfill =b_0+b_2\hspace{0.17em}{\text{experience}}_{ij}+b_3\hspace{0.17em}{\text{experience}}_{ij}^2+b_1\hspace{0.17em}{age}_{ij}+\hspace{0.17em}{b}_4\hspace{0.17em}{sex}_{ij}+\hspace{0.17em}{b}_5\hspace{0.17em}{education}_{ij}\\ \hfill & \hfill +\hspace{0.17em}{b}_6\hspace{0.17em}{contract}_{ij}+\hspace{0.17em}{b}_7\hspace{0.17em}{part\_time}_{ij}+\hspace{0.17em}{b}_8\hspace{0.17em}{occup}_{ij}+\hspace{0.17em}{b}_9\hspace{0.17em}{share\_ft}_{ij}+\varphi \hspace{0.17em}F{E}_j+w_{ij}\end{array}$       (2)

In this Mincer equation, log(W_ij) is the logarithm of the hourly wage as reported in the SES, which is regressed against a standard set of employee individual and job characteristics: years of tenure, age, sex, education level (International Standard Classification of Education – ISCED), type of contract (permanent, temporary or apprenticeship), a dummy for part-time contract, occupation (International Standard Classification of Occupations – ISCO) and the share of full-time working hours. Lastly, we include a firm fixed effect FE_j.

Accordingly, the residual w_ij is a wage premium capturing the deviation of individual-specific wage from the average wage that could be expected for an employee of firm j based on their characteristics, while also controlling for firm-specific average wage premium paid in firm j, captured by firm fixed-effect FE_j. For example, if a firm had a policy of paying exactly a 10 per cent premium on average market wages to its employees, this firm-level premium would be accounted for by the coefficient φ and this firm’s wage policy would have no net effect on within-firm wage inequality in equation (1), allowing for meaningful comparison across individuals and firms.⁵

Taking the interdecile range of within-firm distribution of wage premiums allows us to examine if firm-level bargaining is used by firms to adjust wages of low-paid or high-paid employees. In fact, as we detail in the next section, we can split the effect of firm-level bargaining on the two percentiles. Other measures of inequality usually employed in the literature, such as the variance (or the standard deviation), do not allow us to identify the source of increased or reduced inequality.

4.1. Firm-level bargaining and within-firm inequality

Our empirical setup is intended to estimate whether there is a significant difference in within-firm inequality between firms under firm-level bargaining and those under centralized bargaining, and whether this gap varies (i) by country and (ii) over time, across the initial two (2006 and 2010) or the subsequent two (2014 and 2018) survey waves available in the SES data.

We estimate the following two regression models for each country, one pooling the data for the 2006 and 2010 SES waves:

$\begin{array}{rr}\hfill \Delta w_j^{90/10}& \hfill \begin{array}{l}={\alpha }_0+{\alpha }_1\hspace{0.17em}FL{B}_j+{\alpha }_2\hspace{0.17em}{Y}_j^{2010}+{\alpha }_3\hspace{0.17em}{Y}_j^{2010}\times FL{B}_j+\gamma \hspace{0.17em}{\widehat{FLB}}_j\\ +\hspace{0.17em}\zeta X_j+\hspace{0.17em}\eta \hspace{0.17em}{sector}_j+\hspace{0.17em}\theta \hspace{0.17em}{region}_j+{ϵ}_j\hspace{0.33em}\end{array}\\ \hfill & \hfill \end{array}$    (3)

and the other pooling the data for the 2014 and 2018 waves:

$\begin{array}{rr}\hfill \Delta w_j^{90/10}& \hfill \begin{array}{l}={\beta }_0+{\beta }_1\hspace{0.17em}FL{B}_j+{\beta }_2\hspace{0.17em}{Y}_j^{2018}+{\beta }_3\hspace{0.17em}{Y}_j^{2018}\times FL{B}_j+\gamma \hspace{0.17em}{\widehat{FLB}}_j\\ +\hspace{0.17em}\zeta X_j+\hspace{0.17em}\eta \hspace{0.17em}{sector}_j+\hspace{0.17em}\theta \hspace{0.17em}{region}_j+\hspace{0.17em}{ϵ}_j\end{array}\\ \hfill & \hfill \hspace{0.33em}\end{array}$       (4)

In both models, $\Delta w_j^{90/10}$ is the measure of within-firm wage inequality defined in equation (1), computed for each firm j; FLB_j indicates whether firm j applies centralized bargaining (FLB_j = 0) or firm-level bargaining (FLB_j = 1); $Y_j^{2010}$ and $Y_j^{2018}$ are dummy variables indicating whether firm j is sampled in the final year of the two wave pairs, that is, in 2010 or 2018, respectively; X_j is a set of firm characteristics and workforce composition variables (discussed below); sector_j and region_j are fixed effects for the economic sector (reported in the SES at 1-digit NACE⁶) and geographical location (reported in SES at NUTS 1 level⁷) of the firm, respectively; ${\widehat{FLB}}_j$ is a propensity score representing the probability that firm j adopts firm-level bargaining, included to correct for potential endogenous selection effects (discussed below); ϵ_j is an idiosyncratic error term.⁸

The α and β parameters are the main coefficients of interest. The intercepts α₀ and β₀ measure the average level of within-firm inequality in the baseline group of firms under centralized bargaining in the initial years (2006 and 2014, respectively). The coefficients α₁ and β₁ capture the difference in within-firm inequality between firm-level bargaining firms and the baseline of fully centralized bargaining firms in the initial years (2006 and 2014, respectively). Then, α₂ and β₂ measure the change in inequality occurring over time for firms under centralized bargaining between 2006 and 2010 and between 2014 and 2018, respectively, while α₃ and β₃ capture the additional growth in inequality occurring over time for firms under firm-level bargaining, between 2006 and 2010 and between 2014 and 2018, respectively. Separate estimates of the regression models (and thus of the key parameters) by country allow us to account for differences in bargaining systems across countries. In fact, as we discussed above, the definition of firm-level bargaining firms (FLB = 1) is relatively homogeneous in the SES across all countries, while there is greater variation across countries for the bargaining system prevailing in the control group of firms that do not apply firm-level bargaining (FLB = 0).

The identification of the key parameters proceeds as follows. First, sector and regional fixed effects, together with the firm-level controls in X_j, account for factors that jointly determine inequality and adoption of firm-level bargaining, thus potentially creating an omitted variable bias if not included in the regressions.⁹ The vector X_j encompasses in particular two groups of variables available for each firm j in SES. The first group includes corporate characteristics: a categorical variable for firm size (by number of employees) and a dummy for private or public control over the firm. The expectation is that within-firm wage dispersion is lower in large and publicly owned firms, as unions tend to be more powerful in these contexts (Canal Domínguez and Rodríguez Gutiérrez 2004). The second group encompasses the workforce characteristics of firm j, highlighted in previous studies as determinants of wage inequality. For every firm, we measure the share of women employed in the firm; a set of dummies for the modal age of the workforce; the share of employees with secondary or tertiary education; the mean tenure of workers in the firm; the share of managers and professionals (1-digit ISCO codes 1 and 2); the share of part-time employees; and the share of employees with a permanent contract. Although these controls are relevant in theory, their individual relationship with within-firm inequality is difficult to predict in isolation. Usually, within-firm wage differences are expected to rise with age, tenure and education, because wages tend to increase with all these characteristics and dispersion is usually higher in firms where average wages are higher (Canal Domínguez and Rodríguez Gutiérrez 2004). As for gender, the well-documented existence of female wage gaps would predict wider inequality in firms where the proportion of women is lower. Furthermore, earnings inequalities are expected to be lower in firms with a relatively larger proportion of full-time (vs part-time), permanent (vs fixed-term) and blue-collar (vs white-collar) workers, given that these types of employees are generally more likely to unionize, and their firms are thus more likely to be more affected by unions’ efforts to push for equalization of wages among members (Canal Domínguez and Rodríguez Gutiérrez 2004).¹⁰

In addition to including fixed-effects and firm-level controls, when estimating equations (3) and (4), we also address the potential endogeneity of the FLB dummy that may arise from non-random selection of firms. Indeed, there may still be unobserved determinants of the decision to adopt firm-level collective agreements that correlate with the unobserved determinants of the dependent variable of interest. This may occur despite controlling for employer-specific components of wages and firm-level average wages through the preliminary Mincer regression, and despite the inclusion of an extensive set of firm-level covariates. Following a solution adopted in the empirical literature (Card and De La Rica 2006; Daouli et al. 2013), we address this possible source of bias by augmenting the model with a preliminary probit estimate of the probability (propensity score) that a given firm will adopt firm-level collective bargaining ( $\widehat{FLB}$ ). The overall rationale is that if FLB status is essentially assigned randomly conditional on observed controls, then conditioning also upon propensity scores allows us to clean any further bias due to unobserved firm characteristics (see supplementary online appendix C for details). However, we refrain from interpreting our results as fully causal since, as mentioned, the non-panel structure of the SES data does not allow us to follow employees and firms over time, thus preventing us from fully controlling for firm and employee fixed effects.

4.2. Firm-level bargaining and high- and low-paid employees

To better understand the role of firm-level bargaining on within-firm inequality, we estimate the following variations of equations (3) and (4):

$\begin{array}{rr}\hfill w_j^p& \hfill \begin{array}{l}={\alpha }_0+{\alpha }_1\hspace{0.17em}FL{B}_j+{\alpha }_2\hspace{0.17em}{Y}_j^{2010}+{\alpha }_3\hspace{0.17em}{Y}_j^{2010}\times FL{B}_j+\gamma \hspace{0.17em}{\widehat{FLB}}_j\\ +\zeta X_j+\eta \hspace{0.17em}{sector}_j+\theta \hspace{0.17em}{region}_j+{ϵ}_j\end{array}\\ \hfill & \hfill \hspace{0.33em}\end{array}$       (5)

and

$\begin{array}{rr}\hfill w_j^p& \hfill \begin{array}{l}={\beta }_0+{\beta }_1\hspace{0.17em}FL{B}_j+{\beta }_2\hspace{0.17em}{Y}_j^{2018}+{\beta }_3\hspace{0.17em}{Y}_j^{2018}\times FL{B}_j+\gamma \hspace{0.17em}{\widehat{FLB}}_j\\ +\zeta X_j+\eta \hspace{0.17em}{sector}_j+\theta \hspace{0.17em}{region}_j+{ϵ}_j\hspace{0.33em}\end{array}\\ \hfill & \hfill \end{array}$       (6)

where the dependent variable $w_j^p$ is, alternatively, the 90th or the 10th percentile of the distribution of residual wage premiums in firm j, estimated by the Mincer regression described in equation (3).

Importantly, these specifications help to understand the source of the overall difference in $\Delta w_j^{90/10}$ estimated in equations (3) and (4), by comparing the 90th and 10th percentiles of wages across firms operating under centralized and firm-level bargaining. For instance, suppose we found a positive association between firm-level bargaining Δw^90/10 and in a given country. Does it stem from the (residual) wages of the highest-paid employees (w⁹⁰) being higher under firm-level bargaining than in other firms, or from the wages of the lowest-paid workers (w¹⁰) being lower? Furthermore, should no statistical difference in overall inequality Δw^90/10 emerge between different bargaining regimes, the estimates of equation (5) and (6) could tell us, for instance, whether this was owing to the two components being offset in the same direction under firm-level bargaining.

The estimation of equations (5) and (6) follows the same strategy as the baseline models in equations (3) and (4). We perform separate regressions by country, augmented with the same set of firm-level covariates and fixed effects, and preliminary first-step probit estimates of firm-specific FLB propensity scores. The estimates of α₁ and β₁ on the FLB dummy give the difference in average outcomes between firms bargaining locally and those under centralized bargaining in the initial years (2006 and 2014, respectively). The coefficients on the interaction terms α₃ and β₃ capture possible changes in the FLB coefficient over time.

5.1. Within-firm inequality

Table 1 presents the estimates of equation (3), focusing on the period 2006–10.¹¹ In 2006, there is substantial variation across countries in the level of within-firm inequality of the baseline group of companies under centralized bargaining, as revealed by estimated α₀. The lowest level of inequality is in Spain, where the baseline difference is estimated at 0.299, or approximately 30 percentage points. This level is more than doubled for France, which has the highest baseline inequality of around 62 percentage points, while the level in most other countries is around 45–55 percentage points. At the same time, there is mostly no difference in inequality between firms that adopted firm-level bargaining and those under centralized bargaining in 2006. Indeed, the estimated α₁ coefficients are not statistically different from zero, except for the United Kingdom. In this case, the inequality of wage distribution is significantly lower (by about 1.3 percentage points, or around 2 per cent of baseline inequality) for firm-level bargaining firms compared to other firms.

By 2010, within-firm wage inequality in firms under centralized bargaining drops compared to the baseline inequality for 2006 (see α₂ estimations) in most countries except Czechia and Germany. For some countries, the change is quite sizeable: around 11 per cent in Spain and 13 per cent in the United Kingdom. Firms bargaining locally in 2010 follow the same trend (see α₃ estimations, which are mostly not significant), except in Spain and France, where such firm-level bargaining dampens (or reverses) the egalitarian trend. In both countries, whereas there is no significant difference between companies that applied centralized and firm-level bargaining for 2006, the results for 2010 indicate a widening gap (around 2.2 percentage points in Spain, 3.6 in France). On balance, while within-firm inequality decreases appreciably in 2010 for Spanish and French firms under centralized bargaining, it narrows substantially less for companies under firm-level bargaining in Spain (adding α₂ and α₃) and even increases for those in France.

Table 2 presents the estimates of equation (4), focusing on the period 2014–18. They confirm the considerable cross-country heterogeneity that already emerged from the 2006–10 estimates. For 2014, the extent of within-firm inequality characterizing the baseline group of firms that only bargain at centralized levels differs by country (see β₀ estimates) and we also observe clear differences in the additional inequality associated with firm-level bargaining (see β₁ estimates). In fact, the levels of within-firm wage inequality are not significantly different for firm-level bargaining firms, compared with other firms, in Belgium, Czechia and the United Kingdom. In contrast, firm-level bargaining results indicate an increase in the Δw^90/10 gap in Germany, Spain and France. This may reflect some particularly strong use of firm-level agreements to differentiate salaries in these countries, in the aftermath of and in response to the crisis period. However, the increase in within-firm inequality associated with firm-level bargaining in these countries does not continue over time. By 2018, the results indicate an increase in wage inequality under firm-level bargaining (see β₃ estimates) only in Czechia, while differences compared to fully centralized firms are not statistically significant for any of the other countries. Conversely, firms that only bargain at more centralized levels change in different ways over time (see β₂ estimates), becoming even more unequal over time in Belgium and Spain but less unequal in Czechia, France and Germany.

5.2. High- and low-paid employees

We then move to the estimates of equation (5) and equation (6), which allow us to estimate separate coefficients of firm-level bargaining for higher- vs lower-paid employees.

The results for the period 2006–10 are reported in table 3. These are informative in explaining the greater inequality under firm-level bargaining observed above for France, Spain and the United Kingdom (see table 1). The lower inequality in UK firm-level bargaining firms in 2006 stems from significantly higher wage premiums paid at the bottom of internal wage distribution in firm-level bargaining firms compared to centralized bargaining firms (see α₁ estimate for q₁₀). In Spain, the lower overall wage inequality Δw^90/10 in 2010 observed earlier for firms under centralized bargaining results from a relative reduction in the 90th percentile wage premiums and a corresponding increase of those at the 10th percentile, leading to an overall wage inequality reduction as a result of both extremes moving closer. Crucially, this reduction in inequality is dampened for both q₉₀ and q₁₀ under firm-level bargaining (see α₃ coefficients), leading to a total 2.17 percentage point difference between the two regimes in 2010. France seems to have experienced a more extreme version of the same dynamics: the wage premiums at the top increased and those at the bottom decreased under firm-level bargaining, leading to an overall difference of 3.6 percentage points.

Table 4 reports the estimates using the 2014–18 data. They reveal that the difference in inequality observed in table 2 in fact originates from different underlying patterns, with firm-level bargaining used differently by firms to adjust wages of low-paid or high-paid employees. The greater Δw^90/10 inequality under firm-level bargaining estimated in 2014 for Germany stems from two combined differences: compared to firms bargaining at centralized levels, a lower 10th percentile and a larger 90th percentile is estimated for firms bargaining locally. That is, they pay low-paid employees less and high-paid employees more. This is not the case for the greater inequality under firm-level bargaining observed in France and Spain in 2014. In these countries, the overall difference comes solely from firms that practise firm-level bargaining, paying their low-paid employees less compared to firms bargaining at centralized levels. The opposite pattern holds for Czechia in 2018, where increased inequality is explained by employees in the 90th percentile earning more under local bargaining.