Reallocation and the Role of Firm Composition Effects on Aggregate Wage Dynamics

During downturns, aggregate wages appear to respond very little to business cycle fluctuations. This holds true even for the recent recessionary period, despite the duration and the severity of the crisis. Common explanations include wage rigidities resulting from various market frictions – see Adamopoulou et al. (2016); Verdugo (2016); Devicienti, Maida and Sestito (2007) and Dickens et al. (2007). However, the existing literature has also provided evidence that low-paid workers were more severely affected during the recent downturn and therefore composition effects might have played a particularly important role in shaping aggregate wage dynamics – see, for instance, Daly and Hobijn (2016) for the US and Verdugo (2016) for the Eurozone countries.

In this paper, we contribute to this literature by documenting the relevance of firm composition effects – as opposed to worker composition effects – for aggregate wages. We conduct our analysis on a newly available set of social security data covering the universe of employers between 1990 and 2015 in Italy and comprising a random sample of employees for the same period. We proceed by first implementing a standard Blinder–Oaxaca (BO) decomposition exercise (Blinder, 1973 and Oaxaca, 1973), augmented with employer-level characteristics. This exercise allows us to quantify separately the parts of average wage changes that are due to changes in employers’ and those due to changes in workers’ average characteristics in the economy. Since matched employer–employee datasets were previously not easily available, the firm side of the adjustment has often been neglected in the earlier literature. Recently, some papers have investigated and stressed the relevant role of firm heterogeneity and job characteristics for the cyclical behavior of wages of new hires and job movers (Gertler et al., 2016, Carneiro et al., 2012 and Kauhanen and Maliranta, 2017), as well as for the increasing inequality of wages (Card et al., 2013 and Song et al., 2018). Little is known about their role in explaining the evolution over time of aggregate wages.

By applying the simple BO exercise in Italy, we find that composition effects matter substantially for aggregate wage dynamics and increasingly so after the recent crisis. When we distinguish between employers’ and workers’ characteristics, we find that employers’ characteristics, which used to matter a little, account for an increasingly large share of these effects in the recent years, and even surpassed that of workers’ characteristics.

Changes in employers’ characteristics may reflect changes in the characteristics of the firms populating the economy – the type of firms entering or exiting the market, the wage premia of incumbents, and other firms’ characteristics,

For instance, Litan and Hathaway (2014) show that firms are aging in the US.

Through the OP decomposition, we decompose aggregate wages into the simple unweighted average of the wage across firms (within component) and a correlation term between wage and employment across firms (the OP component). The first term captures changes in aggregate wages that are due to changes in firms’ average wages common to all firms – due to inflation, aggregate shocks, changes in firms’ average characteristics, etc.; the second term captures changes in aggregate wages that are due to workers’ changing jobs and shifting between low-and high-paying firms.

When workers are randomly allocated across firms, the correlation between the wage and employment is zero; when workers are reallocated to high-paying firms, the correlation between size and wages across firms becomes positive – the OP term increases – and the aggregate wage increases above the within term, purely as a result of a composition effect.

To conclude, we suggest a possible interpretation of this employment shift from low- to high-wage firms and its contribution to aggregate wage dynamics, in terms of changes in allocative efficiency and aggregate productivity. This interpretation takes the stand from the well-documented fact that wages and labor productivity are correlated across firms. We show that this correlation holds in our data and that changes in the OP contribution to the aggregate wage are positively associated with changes in productivity at the two-digit sector level and with a measure of competition (Herfindahl index). This evidence is indirect and only suggestive, and we leave to future research a full test of our hypothesis and an exploration of its implications.

The paper proceeds as follows. After describing the data in section 2, we replicate composition studies by employing a standard tool in labor economics to assess differences among groups of workers, the BO decomposition, which we augment with employers’ characteristics – section 3. We proceed by applying on wage data a standard measure of reallocation, the OP decomposition (Olley and Pakes, 1996) – section 4. Section 5 proposes an interpretation in terms of allocative efficiency of the analysis conducted on wage data. Finally, section 6 concludes and proposes avenues for future research.

The source for our data consists of social security payments to the Italian National Social Security Institute (INPS) made by reporting units (“establishments”) for their employees (with an open-ended or fixed-term contract) between 1990 and 2016. From this master data, INPS extracts two datasets. The first dataset consists of the universe of firms with at least one employee at some point during a given calendar year – this extraction covers the years only until 2015, and it provides data at the firm level.

There is a provisory version of firm-level data for 2016 that we only use in the BO decomposition exercise combined with the consolidated data for workers.

In the data appendix, we assess the quality of our data against the Eurostat National Accounts (ENA; ESA, 2010) and the Eurostat Structural Business Statistics (ESBS) and conclude that INPS data provide a reasonably good approximation of national aggregates from official statistics regarding employer business demographics, employment, and gross wages. INPS data do not contain balance sheet information, implying that there is no direct information on labor productivity. However, this information can be retrieved for the subset of firms that are limited companies using Cerved, the business register containing balance sheet data for the universe of firms with this legal form of incorporation. In the data appendix, we conclude that, when combined with Cerved, the INPS data also return a reasonably good picture of balance sheets, but only for firms with at least 20 employees.

Tables A1 and A2 in Appendix report a broad set of descriptive statistics on firms with at least one employee in the private nonagricultural sector and their workers, respectively. Over the 25 years considered, the share of industrial firms over the total number of firms declines from 49% to 35%, average firm size declines from 8 in 1990 to 7.4 employees in 2012 and then rises again to about 7.6 in the last 3 years, the pool of employers increases from 1.1 to about 1.4 million, and the nominal monthly gross average wage at the firm level almost doubles from 1,102 in 1990 to 2,156 euros in 2015. Regarding workers, we observe that the average age of employees in Italy increases from about 36 years in 1990 to 41 years in 2016; the share of women increases as well, from 30% to 36%, while, also due to the rising importance of the service sector, the share of blue collars declines from 64% to 59%.

We use the employer–employee data from INPS to replicate and extend previous work on the rising importance of worker composition effects in explaining aggregate wage dynamics over time and particularly during and after the recent crisis (Daly and Hobijn, 2016; Verdugo, 2016). Compared to the data used in these studies, the INPS data have the advantage of covering a longer time span, thus allowing us to study the evolution of composition effects with a very long time perspective. More importantly, the availability of information on the employer side allows us to build and expand on this literature by quantifying firm composition effects, due to changing employer characteristics, along with worker composition effects, due to changes in workers’ characteristics. To our knowledge, most of the existing literature has overlooked the importance of changes in employers’ characteristics in explaining aggregate wage dynamics. Some recent papers have stressed the increasing relevance of firm-level characteristics in explaining wage premia from job-to-job movements (Gertler et al., 2016; Carneiro et al., 2012) or wage losses from being displaced (Lachowska et al., 2018; Heining et al., 2018), as well as in determining earnings inequality in many different countries (see, for instance, Card et al., 2013; Song et al., 2018). What we seek to quantify is how much employers’ characteristics matter in explaining aggregate wage growth. For this purpose, we use a standard BO decomposition (Blinder, 1973; Oaxaca, 1973) that provides us with a synthetic measure to analyze average wage changes between two consecutive years and to determine the part due to compositional effects. The BO decomposition is usually implemented to disentangle the sources of wage differences between two subgroups of the population in the same year (i.e. men and women). We use it instead to evaluate how average wages differ between pairs of consecutive years for the entire population of employees in the private sector excluding agriculture. We first run a Mincerian wage equation (Mincer, 1974) for every year, therefore allowing coefficients to change over time. Then, for every couple of consecutive years, we decompose the change in log wages in the part due to changes of the coefficients between the two years (the coefficient effect) and the part due to changes over time in average characteristics of workers of the firms they are employed at (the composition effect). More specifically, we use the micro data at the worker level,

The data are collapsed at the worker-year level by considering the job of the longest duration, so as not to oversample workers with multiple employment spells within the same year.

where w_ijt refers to the daily wage of worker i employed in firm j in year t,

The wages of part-time workers are in full-time equivalent units.

The mean outcome difference between years t and t-1 can be expressed as

The first and the second terms of the equation above refer to the part of variation in mean wage between years t and t-1 due to changes in workers’ and employers’ characteristics, respectively.

Figure 1 summarizes the relative importance of composition effects and their components in explaining aggregate wage growth. The dotted line refers to the overall contribution of composition effects over time.

In particular, it plots the ratio between the three-year moving average of the part of aggregate wage growth due to composition effects and the three-year moving average of aggregate wage growth. We use the moving average in order to smooth outliers. In some years, aggregate wage growth is very low. For example, for the overall private sector, it is 0.1% in 2009 and 0.3% in 2012; for private services, it is -0.2% in 1999 and -0.1% in 2002. Thus, when computing the fraction of wage variation due to changes in composition, the unsmoothed series behave erratically in certain years (due to the denominator being small and due to changing signs). These results are available from the authors upon request.

Figure 1

Figure 2 analyzes which characteristics matter more for the compositional effect on wages.

Composition effects refer to the type of workers who are employed in the economy (in a certain type of firms) each year.

Figure 2

to the aggregate wage growth in the economy over time, considering six different subperiods between 1991 and 2016.

It therefore plots the average x¯ijt−x¯ijt−1β^t$\left( {{{\bar{x}}}_{ijt}}-{{{\bar{x}}}_{ijt-1}} \right){{\hat{\beta }}_{t}}$in each four- or five-year period for different worker and firm-level characteristics divided by the aggregate wage change between years t and t^-1.

Figure 3

Figure A1

In the rest of the paper, we dig into this firm component and we try to disentangle what drives this increasing role of employers’ characteristics in aggregate wage dynamics. Several alternative explanations, which the BO decomposition cannot tell apart, could lie behind this finding. First, the type of existing firms may have changed, for instance, lower-paying firms (possibly younger or less productive) may be less likely to enter or more likely to exit the market, especially right after a deep recession. Second, all firms may have increased their wages on average. This can happen, for instance, because of a change in wage-setting policies (Gruetter and Lalive, 2008; Card et al., 2013) in response to the recent recession common to all firms, when they were forced to lower their workers’ wages, by squeezing the variable component of salaries or by lowering entry wages (Adamopoulou et al., 2016). Third, it may indicate changes in the employer identity – due to workers changing jobs and moving to higher-paying firms: workers’ allocation across firms has changed substantially in the last decades (Foster et al., 2016, for the US and Calligaris et al., 2018, and Linarello and Petrella, 2017, for Italy), and this can have implications for aggregate wages. In the next section, we distinguish which mechanism lies behind the results we obtain from the BO decomposition by applying on firm-level wage data a standard tool taken from the reallocation literature, the so-called OP decomposition. This method allows us to distinguish the part of aggregate wage changes that is due to: (i) changes in the type of firms entering/exiting the market; (ii) uniform changes in the average wage of all firms; and (iii) changes in the relative size of firms, i.e. on how workers are allocated across higher/lower paying firms.

The OP decomposition is performed on firm-level data, and it splits the aggregate wage – i.e. the employment weighted average of the wage across firms – into two components: a within component and a between component, the so-called OP term. In the appendix, we illustrate a more general – and more involved – version of this decomposition proposed by Melitz and Polanec (2015) allowing us to disentangle also the contributions of firm exit and entry, which however turn out to be not very important for the results. The within component is the unweighted average of the wage across firms; the OP term is the covariance between wages and employment (relative to average firm size, i.e. standardized size) across firms:

within term: w˜t≡1J∑j∈Jwjt${{\tilde{w}}_{t}}\equiv \frac{1}{\left| J \right|}\sum\limits_{j\in J}{{{w}_{jt}}}$

where J is the set of active firms in the economy, sjt≡ejtEt=ejtJet${{s}_{jt}}\equiv \frac{{{e}_{jt}}}{{{E}_{t}}}=\frac{{{e}_{jt}}}{\left| J \right|{{e}_{t}}}$is the employment share of firm j at time t, E_t is the aggregate employment, e_t is the average firm size, and t denotes time. Using Δ to denote first-order differences Δxt=xt−xt−1,$\left( \Delta {{x}_{t}}={{x}_{t}}-{{x}_{t-1}} \right),$we have:

The OP decomposition has a structural interpretation in terms of the characteristics of the allocation: if labor is allocated randomly across firms, then the covariance between size and wages is zero and the aggregate wage is identical to the within component. In this hypothetical initial scenario, when labor is shifted from low- toward high-wage firms, then the covariance becomes positive (ΔOP_t > 0), while the within component remains constant at the initial level (w̃ _t = 0). This implies that the aggregate wage increases, not because wages at the firm level increased, but purely because of a change in the way workers are allocated across firms, entirely captured by the increase in the OP term.

Similarly to the way we displayed results for the BO decomposition, Figure 4 shows the contribution of the OP term to aggregate wage changes, ΔOPtm/Δw¯tm,${\Delta \text{OP}_{t}^{m}}/{\Delta \bar{w}_{t}^{m}}\;,$in the nonagricultural business sector and for manufacturing and service sectors separately from 1999 to 2015 – where m denotes the three-year moving average centered around t,Δxtm=∑h=−11Δxt+h.$t,\Delta x_{t}^{m}=\sum\nolimits_{h=-1}^{1}{\Delta {{x}_{t+h}}}.$

Again, we use a moving average to avoid outliers due to very small numbers in the denominator in certain years. The unsmoothed results are available from the authors upon request.

Figure 4

Next, we use the OP decomposition to construct a counterfactual exercise and quantify the contribution of the reallocation of workers – from low- to high-wage firms – to the dynamics of the aggregate wage. To construct this counterfactual, we compute the part of wage growth not related to workers reallocation by “fixing their allocation” to a base year, OPb/w¯b,${\text{O}{{\text{P}}_{b}}}/{{{{\bar{w}}}_{b}},}\;$and running the within component forward as in the data. Using the identity 1=w¯b+s/w¯b+sc+OPb/w¯b,$1={{\bar{w}}_{b+s}}/\bar{w}_{b+s}^{c}+\text{O}{{\text{P}}_{b}}/{{\bar{w}}_{b}},$we readily obtain the counterfactual aggregate wage level in year b+sw¯b+sc:$b+s\left( \bar{w}_{b+s}^{c} \right):$

Using this artificial series, we construct the counterfactual growth rate for the aggregate wage and find that approximately one-third of aggregate wage growth is explained by the shift of employment composition from low- to high-wage firms in the period after 2004 (Table 1).

Figure 5 plots the series for the actual aggregate wage against the artificial series obtained by compounding the counterfactual growth rates using as a base the year when the OP term starts increasing – 2002 in the manufacturing sector and 2004 in the service sector and nonagricultural business sector.

An obvious limitation of this approach is that it assumes that the distribution of worker types across firms remained invariant throughout the period of the analysis: otherwise, changes in the OP contribution could reflect changes in workers’ composition as well as changes in workers’ allocation. For example, if high-wage firms are indeed firms employing high-wage workers (e.g. white-collar rather than blue-collar workers), then a rising OP contribution may reflect a shift toward high-wage occupations. A way to mitigate this issue is to control workers’ characteristics and apply the OP decomposition to residualized firms’ average wages. Ideally, we would control for the full vector of workers’ characteristics included in the BO decomposition, but this information is available only for a sample of workers. Thus, the results would be severely biased, due to the unequal treatment of small and large firms: since we would have virtually no small firm with a representative enough sample of workers to adjust that firm’s wage, the remaining sample of firms would be severely skewed toward larger firms.

As we will discuss, the OP decomposition is very sensitive to the omission of small firms, which usually represent a large share of the total number of firms, even more so in Italy.

Figure 5

We conclude our analysis by suggesting a possible interpretation of our results, placing the paper in the context of the recent literature on the importance of resource reallocation for aggregate productivity.

Restuccia and Rogerson (2008), Hsieh and Klenow (2009), Guner, Ventura and Xu (2008), and Bartelsman, Haltiwanger and Scarpetta (2013).

Here, we provide some indirect evidence indicating that there may be room for this interpretation, although we are unable to sufficiently corroborate our claim due to data limitations, and we leave a more thorough exploration to future work. The data limitation is that, as it is usually the case, productivity data are available only for limited companies, which are legally compelled to publish their balance sheets. While for large firms this legal form is common, small firms incorporating as limited companies are a strongly selected sample. Figure 6 displays the average labour productivity (for the sample of limited companies in Cerved that can be merged to firms in INPS) and the average wage (for the firms in INPS, i.e. for the entire population of employer businesses) conditional on (log) class size. In the figure, we also report the fraction of firms in INPS that are incorporated businesses and the fraction of firms in INPS that can be merged with Cerved and, therefore, for which we have labor productivity data (right scale). The average wage rises monotonically with the firm size. Instead, firm labor productivity, for our limited sample, is U-shaped: it is extremely high for very small firms and declines with size for firms up to 10–20 employees large and increases monotonically thereafter. The fraction of firms with balance sheet data steeply increases from 10% for firms with one employee to 70% for firms with 20 employees. Table 2 displays the correlation between log size, log firm wage and log labor productivity in 2007

Results are fundamentally the same when considering different years or when averaging the correlation matrix across years. We pick 2007 as it is the year before the onset of the financial crisis.

Figure 6

The OP share of the average wage is extremely sensitive to the censoring of small firms; thus, we are unable to check our interpretation by directly performing our OP analysis on wage and productivity data at the same time.

This is perhaps not surprising: the OP term is the difference between the employment-weighted and the -unweighted average of the wage across firms; excluding small firms affects the second term much more strongly than the first, because the firm size distribution is highly skewed. Linarello and Petrella (2017), using representative balance sheet data for the universe of Italian firms, show that the OP contribution to aggregate labour productivity has been increasing in Italy since the mid-2000s. They also show that this contribution becomes nil when restricting the data to firms with 20 employees or more, explaining the difference with the findings in Calligaris et al. (2018).

We think that these results, though indirect and inconclusive, are worth reporting along with the interpretation of the rising importance of firm composition effects on aggregate wages in terms of reallocation from low- to high-productivity firms. This interpretation is suggestive but could be fruitfully explored in future research with more exhaustive data. If our interpretation turns out to be realistic, it would imply that researchers can use wage data, more easily available, rather than productivity data, usually difficult to obtain for non-listed companies, for the analysis of allocative efficiency.

Composition effects have played an important role in determining the dynamics of aggregate wages during the last decade. In this paper, we focus on the role of firm heterogeneity for aggregate wage dynamics, with reference to the Italian case. By performing a standard BO decomposition exercise, augmented with employer-level characteristics, we distinguish between employers’ and workers’ characteristics. We show that the contribution of composition effects has risen during the last years and that the role of employers’ average characteristics has increased quite dramatically, to even surpass that of workers’ characteristics. As opposed to worker composition effects, which have been extensively investigated by the previous literature, the firm side of the adjustment is usually overlooked.

By applying to wage data a standard measure of reallocation, we document that this increased role of employers’ composition effects can be ascribed to employment shifts from low-paying to high-paying firms. According to our estimates, this reallocation of workers across firms has accounted for approximately one-fourth of aggregate wage growth during the recent recessionary period. Finally, we suggest an interpretation, i.e. this employment shifts from low- to high-wage firms may reflect workers’ movements from low- to high-productivity firms. Owing to the limitations of our productivity data, we could only provide some indirect and temptative evidence of this interpretation, namely, that the contribution of these employment shifts to wage dynamics appears to be positively associated with sectoral changes in productivity and negatively associated with market concentration. We leave a more thorough analysis of this interpretation to future research.