Product and labour market imperfections in the Italian manufacturing sector: a firm-level analysis

Abstract

Despite the extensive literature on product market power, evidence on markups at the firm level and which also accounts for labour market power is still limited. In this paper, we investigate the trends in both these market frictions in a large sample of Italian manufacturing firms over the period 2010–2018. In doing so, we devote particular attention to the factors underlying product market power, and especially to the way the markup is related to labour market power and the labour share of income. Our analysis reveals that, during the selected years, the manufacturing sector has experienced a limited rise in markups and a shift in labour market power away from firms and towards workers. These dynamics are mostly driven by within-firm changes. Additionally, the overall growth in bargaining power, which explains the muted positive trend in the labour share, is mainly ascribable to the rise in the average firm-level wages. However, the latter are likely to hide relevant inter-individual heterogeneity, as national data on wage inequality suggest, and monopsony power is still a widespread phenomenon, especially in the Mezzogiorno.

Appendix

1.1 Estimation of the production function

In Sect. 2, following De Loecker and Warzynski (2012), we defined the firm-level markup as the ratio between of the output elasticity of materials and its revenue share:

$$ \mu_{it} = \frac{{\theta_{it}^{M} }}{{\alpha_{it}^{M} }} $$

(9)

where ${\mu }_{it}$ is the markup of firm $i$ at time $t$, ${\theta }_{it}^{M}$ is the output elasticity of materials and ${\alpha }_{it}^{M}$ is the revenue share of materials, also known as cost share or expenditure share of materials. While the expenditure share of materials can be easily computed using firm-level data that are generally available, the related output elasticity needs to be estimated.

In order to get unbiased estimates of ${\theta }_{it}^{M}$ at the firm-year level, we consider the following general production function Q for firm i at time t:

$$ Q_{it} = Q_{it} \left( {L_{it} , M_{it} , K_{it, } w_{it} } \right), $$

(10)

where ${L}_{it}$, ${M}_{it}$ and ${K}_{it}$ are the firms’ inputs (i.e., labour, materials and capital, respectively) and ${w}_{it}$ is firm’s productivity. Unobserved productivity shocks are potentially correlated with input choices, and if not controlled for, can lead to inconsistent estimates of the production function. Accordingly, we employ the Wooldridge-Levinsohn-Petrin (WLP) estimator, as derived from Wooldridge (2009) and implemented in Petrin and Levinsohn (2012). The WLP estimator does not assume constant returns to scale, is robust to the Ackerberg et al. (2015) criticism of Levinsohn and Petrin’s (2003) estimator and is programmed as a simple instrumental variable estimator. The potential endogeneity issues related to the simultaneous determination of inputs and unobserved productivity are addressed by introducing lagged values of specific inputs as proxies for productivity.

Specifically, the estimation strategy used in this paper consists in two steps.

First, we run:

$$ q_{it} = g\left( { l_{it} , k_{it} , m_{it } } \right) + \in_{it} , $$

(11)

where we use a third-order polynomial on all inputs to remove the random-error term ${\in }_{it}$ from the output and hence to obtain estimates of the expected output $\widehat{{q}_{it}}$. Then, we use a general production function of the following type:

$$ \widehat{{q_{it} }} = f_{s} \left( { l_{it} , k_{it} , m_{it} , {\text{B}}} \right) + \omega_{it} + \varepsilon_{it } $$

(12)

where $\widehat{{q}_{it}}$ is the natural log of real sales of firm $i$ at time $t$, ${l}_{it}$, ${k}_{it}$ and ${m}_{it}$ are, respectively, the natural logarithms of the quantities of labour, capital and materials used by the firm and that get transformed into the output according to the production function ${f}_{s}$, $\mathrm{B}$ is the parameter vector to be estimated in order to calculate the output elasticities, ${\omega }_{it}$ is the firm-level productivity term that is observable by the firm but not by the econometrician, and ${\varepsilon }_{it}$ is an error term that is unobservable to both the firm and the econometrician. Productivity is, thus, assumed to be Hicks neutral and specific to the firm, as in the approach using inputs to control for unobservables in production function estimations (Ackerberg et al., 2015; Levinsohn & Petrin, 2003; Olley & Pakes, 1996). We assume that labour is a variable input, and instrument current labour and materials and their interactions with the first and second lags of labour as well as the second lags of capital and materials. To control for time-variant shocks common to all plants, we add year fixed effects.

We adopt a translog specification, which, unlike the Cobb–Douglas, permits us to recover firm-level time-variant output elasticities. The production function is a revenue function, since data on firms’ output prices are not available, and is allowed to change across different sectors, as implied by the subscript s. Leaving subscripts $i$ and $t$ aside for simplicity, the translog function ${f}_{s}$ can be written as:

$$ f_{s} = \alpha + \beta_{L} l + \beta_{K} k + \beta_{M} m + \beta_{{L^{2} }} l^{2} + \beta_{{M^{2} }} m^{2} + \beta_{{K^{2} }} k^{2} + \beta_{KL} kl + \beta_{KM} km + \beta_{LM} lm $$

(13)

Thus, the parameter vector is made up of nine parameters for each sector.

The estimated parameters of the translog production function allow us to compute the output elasticity of materials. Using the estimates of the output elasticity and the calculated revenue shares of materials, we can now compute markups at the firm-year level based on Eq. (1).