Skill upgrading and wage gap: a decomposition analysis for Italian manufacturing firms

Abstract

The paper investigates the evolution of the employment and wage structure of Italian manufacturing firms in the early 2000s. It implements a decomposition analysis that breaks the variation in the skilled-wage bill ratio down into employment and wage movements and further disentangles these movements into shifts between or within sectors, and within sectors, between, or within firms. The study provides a methodological framework which consistently combines the industry-level analysis with the firm-level one, and which simultaneously takes account of changes in skill intensity and the wage gap. The results suggest that most of the changes are reported within firms, where one observes a skill-upgrading effect not followed by a price adjustment. The increase in the relative employment of skilled workers and the decrease in the wage gap between high- skilled and low-skilled workers can be substantially attributed to changes in exporters and importers and in more productive firms. Finally, the paper further accounts for changes in the hourly wage premium and skill intensity, and it shows that the annual wage gap is induced by a substantial fall in the hourly wage premium and by an increase in the numbers of hours worked by the skilled factor.

Appendix

1.1 Checking the consistency of the database

In this appendix, we check the representativeness of our data set with respect to the universe of Italian manufacturing firms. In particular, we check whether the sectoral distribution of Micro.3 is representative of the overall population using ASIA (Archivio Statistico Imprese Attive) which is the registry of active firms in Italy. In ASIA, firms are classified according to their main activity, as identified by ISTAT’s standard codes for sectoral classification of business (5-digit ATECO).

Table 7 Coverage of the data set: number of firms and percentage by sector (2003)

We compute a Wilcoxon–Mann–Whitney test for independence, which is a non-parametric analog to the independent samples t test and can be used when you do not assume that the dependent variable is a normally distributed interval variable (one has only to assume that the variable is at least ordinal). A large value of the test statistic for the Wilcoxon–Mann–Whitney indicates that the frequencies observed in the sample is very different from the one observed in the population. Indeed, the distributions of both groups are equal under the null hypothesis. In Table 7, we report the share of each manufacturing sector in terms of number of firms for the universe of Italian manufacturing firms (ASIA) and the population contained in Micro.3 for 2003. According to the values reported in the table, we accept the null hypothesis, that is the distribution of the number of firms in each sector in the sample does not differ from that of the entire population. Indeed, the small values for the Wilcoxon–Mann–Whitney tests confirm that there is a correspondence between the frequencies of the Micro.3 database and the one of the entire population of firms.

1.2 Checking the consistency of the balanced database

In this appendix, we check whether we introduce any sample-selection bias when considering the balanced data set. Table 2 shows the number of firms which are sampled each year and those that are active over two consecutive years. On using a balance panel, the number of firms in the sample diminishes from 66,387 to 29,173. In Table 8, we investigate whether the smaller sample, consisting of firms present in both 2003 and 2004, is representative of the whole number of firms operating in 2003.³¹ One expects those firms active on a continuous basis to be on average larger: this is because the probability of being sampled for a firm with fewer than 100 employees is lower, and also because larger firms are more likely to survive (Geroski 1995; Sutton 1997). Indeed, the average value of sales, exports, and imports is marginally higher in firms that produce in both 2003 and 2004. However, the shares of skilled workers in employment as well as the ratios of the wage rate of skilled workers to the average wage are similar between the two samples. Thus, since our analysis will focus on the wage and skill structure of firms, we should not incur any large selection bias.

Table 8 Variables statistics for active and continuous firms

1.3 Alternative approaches to the decomposition analysis

This section presents the formula for the decompositions provided by Bernard and Jensen (1997), Biscourp and Kramarz (2007), and Manasse and Stanca (2006). Equations 12 and 13 show the decompositions proposed by Bernard and Jensen (1997), respectively, for the skill intensity and the wage bill ratio variations.

$$\begin{aligned} \Delta \frac{L_{\rm sk}}{L}=\underbrace{\sum _{j}\Delta \frac{L_{{\rm sk}_{j}}}{L_{j}}\overline{\left( \frac{L_{j}}{L}\right) }}_{\rm within}+\underbrace{\sum _{j}\Delta \frac{L_{j}}{L}\overline{\left( \frac{L_{{\rm sk}_{j}}}{L_{j}}\right) }}_{between} \end{aligned}$$

(12)

$$\begin{aligned} \Delta \frac{{\rm WB}_{\rm sk}}{{\rm WB}}=\underbrace{\sum _{j}\Delta \frac{{\rm WB}_{{\rm sk}_{j}}}{{\rm WB}_{j}}\overline{\left( \frac{{\rm WB}_{j}}{{\rm WB}}\right) }}_{{\rm within}}+\underbrace{\sum _{j}\Delta \frac{{\rm WB}_{j}}{{\rm WB}}\overline{\left( \frac{{\rm WB}_{{\rm sk}_{j}}}{{\rm WB}_{j}}\right) }}_{between} \end{aligned}$$

(13)

where j stays for sector or firm.

Biscourp and Kramarz (2007) present the decomposition as in Eq. 14, where the between and within firms movements are run over each single industry s

$$\begin{aligned} \Delta \frac{L_{{\rm sk}_{s}}}{L_{s}}=\underbrace{\sum _{i\in {s}}\Delta \frac{L_{{\rm sk}_{i}}}{L_{i}}\overline{\left( \frac{L_{i}}{L_{s}}\right) }}_{\rm within}+\underbrace{\sum _{i\in {s}}\Delta \frac{L_{i}}{L_{s}}\overline{\left( \frac{L_{{\rm sk}_{i}}}{L_{i}}\right) }}_{\rm between}. \end{aligned}$$

(14)

The contributions from each industry are then aggregated together to obtain an aggregate weighted within component

$$\begin{aligned} {\left( \Delta \frac{L_{\rm sk}}{L}\right) }^{\rm wit}={\sum _{s}\overline{\left( \frac{L_{s}}{L}\right) }\sum _{i\in {s}}\Delta \frac{L_{i}}{L_{s}}\overline{\left( \frac{L_{{\rm sk}_{i}}}{L_{i}}\right) }}+{\sum _{s}\overline{\left( \frac{L_{s}}{L}\right) }\sum _{i\in {s}}\Delta \frac{L_{{\rm sk}_{i}}}{L_{i}}\overline{\left( \frac{L_{i}}{L_{s}}\right) }} \end{aligned}$$

(15)

where each industry contribution is weighted according to the industry share in total workforce.

Finally, Manasse and Stanca (2006) run their decomposition analysis only at the firm level, but they nest together the wage bill with employment and wage decompositions as follows:

$$\begin{aligned} \Delta \frac{{\rm WB}_{\rm sk}}{{\rm WB}}=\Delta \sum _{i}\frac{W_{{\rm sk}_{i}}}{W}\frac{L_{{\rm sk}_{i}}}{L}=\sum _{i}\underbrace{\Delta \frac{W_{{\rm sk}_{i}}}{W}\overline{\left( \frac{L_{{\rm sk}_{i}}}{L}\right) }}_{\rm Wtot}+\sum _{i}\underbrace{\Delta \frac{L_{{\rm sk}_{i}}}{L}\overline{\left( \frac{W_{{\rm sk}_{i}}}{W}\right) }}_{\rm Ltot} \end{aligned}$$

(16)

where the subscript $i=1,\ldots ,I$ identifies only the firms sampled. They further decompose Eq. 16 into the corresponding within and between components as follows:

$$\begin{aligned} {\rm Wtot}= & {} \sum _{i}\Delta \frac{W_{{\rm sk}_{i}}}{W}\overline{\left( \frac{L_{{\rm sk}_{i}}}{L}\right) } \nonumber \\= & {} \left[ \underbrace{\sum _{i}\Delta \frac{W_{{\rm sk}_{i}}}{W_{i}}\overline{\left( \frac{W_{i}}{W}\right) }}_{\rm Wwit}+ \underbrace{\sum _{i}\Delta \frac{W_{i}}{W}\overline{\left( \frac{W_{{\rm sk}_{i}}}{W_{i}}\right) }}_{\rm Wbet}\right] \overline{\left( \frac{L_{{\rm sk}_{i}}}{L{}}\right) } \end{aligned}$$

(17)

$$\begin{aligned} {\rm Ltot}= & {} \sum _{i}\Delta \frac{L_{{\rm sk}_{i}}}{L}\overline{\left( \frac{W_{{\rm sk}_{i}}}{W}\right) } \nonumber \\= & {} \left[ \underbrace{\sum _{i}\Delta \frac{L_{{\rm sk}_{i}}}{L_{i}}\overline{\left( \frac{L_{i}}{L}\right) }}_{\rm Lwit}+\underbrace{\sum _{i}\Delta \frac{L_{i}}{L}\overline{\left( \frac{L_{{\rm sk}_{i}}}{L_{i}}\right) }}_{\rm Lbet}\right] \overline{\left( \frac{W_{{\rm sk}_{i}}}{W}\right) } \end{aligned}$$

(18)

1.4 Hourly decomposition by different categories

This section presents the hourly decomposition by categories. Results are in line with what emerges from the annual decomposition. Table 9 shows that intensive exporters, importers, and more productive firms, while rising fast their skill intensity, experience a drop in the hourly wage premium. This fall is even larger than the annual one; as in these firms, the relative number of hours worked by the skilled factor rise.

Table 9 Hourly decomposition: sub-samples averages by trade activities and productivity