A firm level perspective on migration: the role of extra-EU workers in Italian manufacturing

Abstract

A production-theory approach to migration is adopted in this paper to address the role of migrant workers from extra-EU countries in Italian manufacturing firms. The adoption of flexible functional forms to model firm-level technology lets us directly derive different measures of elasticity from the coefficients of the estimated production and cost functions. The use of foreign labour is shown to affect the industry composition in favour of low skill intensive sectors and the estimated cross demand elasticities confirm the complementarity between migrant and native workers found in previous studies. However, the two labour inputs prove to be substitutes in terms of the Morishima elasticity of substitution: in general, firms tend to increase the foreign labour intensity of production in response to a decline in migrants’ wage, while the migrant to domestic labour ratio responds to changes in the domestic workers’ wage only for firms in low skill intensive sectors.

Appendices

Appendix 1: Wage bill—comparison WHIP balance sheet

In order to check the consistency of information on wages at region-sector level sourced from WHIP with firm level evidence on total expenditure on wages and salaries (wage bill) from balance sheet data, for each firm we re-compute the total wage bill on the basis of region-sector level average wages for domestic and extra-EU workers. Thus for each firm we compute:

$$\begin{aligned} Wage Bill\_WHIP_{iRSt}= wage^{Natives\ WHIP}_{RSt}*L_{D\ it}+ wage^{Extra\text {-}EU\ WHIP}_{RSt}*L_{M\ it} \end{aligned}$$

(7)

We thus compare the wage bill in Eq. 7 to the total wage bill from balance sheet directly retrieved from balance sheet data available in Capitalia for each firm $i$ located in region $R$ and operating in sector $S$ at time $t$ . First, we compute the correlation coefficient which is extremely high, 96 %. Second, for each year of our sample and for the sub-sample of firms employing migrants in 2003, we compare the whole distribution of the two variables in logs. Quantile–quantile plots in Figure A, thus, confirm that when combining the region-sector level information on wages by worker nationality from WHIP with firm level information on domestic and extra-EU labour units we get a firm level total wage bill that is highly consistent with the one firms declare in their balance sheet.

Appendix 2: Regularity conditions—monotonicity

Share	Production function				Cost function
	$Y=F(L_D,L_M,K,IM,IS)$		$Y=F(L_{DW},L_{DB},L_M,K,IM,IS)$		$Y=F(L_D,L_M,K,IM,IS)$		$Y=F(L_{DW},L_{DB},L_M,K,IM,IS)$
	Mean	%Viol.	Mean	%Viol.	Mean	%Viol.	Mean	%Viol.
$S_{L}$	0.198		0.19		0.216		0.210
$\hat{S}_{L}$	0.186		0.19		0.218		0.212
$S_{L_{D}}$	0.131				0.165
$\hat{S}_{L_{D}}$	0.144	1.4			0.204	4.16
$S_{L_{DW}}$			0.05				0.052
$\hat{S}_{L_{DW}}$			0.06	2.10			0.029	0.00
$S_{L_{DB}}$			0.08				0.087
$\hat{S}_{L_{DB}}$			0.08	1.00			0.076	1.20
$S_{L_{M}}$	0.010		0.01		0.013		0.012
$\hat{S}_{L_{M}}$	0.014	2.7	0.02	3.41	0.013	25.75	0.012	12.55
$S_{IM}$	0.468		0.47		0.496		0.509
$\hat{S}_{IM}$	0.520	0.5	0.51	0.00	0.496	0.00	0.507	0.00
$S_{IS}$	0.249		0.25		0.288		0.281
$\hat{S}_{IS}$	0.282	0.7	0.28	1.00	0.286	0.00	0.281	0.00
$S_{K}$	0.033		0.03
$\hat{S}_{K}$	0.039	1.6	0.04	1.00

1. The columns “Mean” contain the computed ($S$) and estimated ($\hat{S}$) revenue share of inputs. The columns “%Viol.” contain the percentage of observations violating the monotonicity condition

Monotonicity entails non-negative estimated revenue/cost shares. The Table above shows the shares computed from balance sheet data, $S_{i}$, and their predicted values, $\hat{S}_{i}$, as obtained from the estimation of the production function and cost function, respectively with five and six inputs. The two sets are pretty similar thus confirming the goodness of the estimation. To verify the reliability of our predicted shares, we make use of the average wages from WHIP, calculate the shares of migrant and domestic workers in total output and total cost and compare them to the average of their prediction from the estimates of the empirical model. The total % of violation of monotonicity, i.e. the number of negative predictions, is fairly low in general and slightly higher for the predicted share of migrants from the cost function. However, comparing the predicted and “actual” shares of foreign and domestic workers in total output and in total cost we find that, although not exactly equal, the prediction reflects our calculations (a slightly worse performance is shown for domestic labour shares, especially white collar, from the cost function). Sample averages and the average predictions for material, services and capital are very similar too. The estimations reported in the test have been obtained by dropping from the sample the observations that violate monotonicity.

Appendix 3: Regularity conditions on own partial price and demand elasticities—quasi-concavity

	Production function						Cost function
	$\varepsilon _{p_{i}x_{j}}$ based on:						$\eta _{x_{i}p_{j}}$ based on:
	Mean $\varepsilon _{ij}$ across $i$	Median$\varepsilon _{ij}$ across $i$	Estimated shares	Calculated shares	Violations (%)		Mean $\eta _{ij}$ across $i$	Median $\eta _{ij}$ across $i$	Estimated shares	Calculated shares	Violations (%)
	$Y=F(L_D,L_M,K,IM,IS)$						$Y=F(L_D,L_M,K,IM,IS)$
$\varepsilon _{p_{L_{D}}x_{L_{D}}}$	−0.01	−0.30	−0.23	−0.18	14.39	$\eta _{x_{L_{D}}p_{L_{D}}}$	−0.70	−0.73	−0.74	−0.77	0.00
$\varepsilon _{p_{L_{M}}x_{L_{M}}}$	−0.74	−0.83	−0.90	−0.87	0.06	$\eta _{x_{L_{M}}p_{L_{M}}}$	−2.49	−1.31	−1.28	−1.46	0.00
$\varepsilon _{p_{IM}x_{IM}}$	−0.04	−0.10	−0.09	−0.10	9.17	$\eta _{x_{IM}p_{IM}}$	−2.58	−2.54	−2.51	−2.52	0.00
$\varepsilon _{p_{IS}x_{IS}}$	0.10	−0.15	−0.12	−0.07	17.19	$\eta _{x_{IS}p_{IS}}$	−3.96	−3.87	−3.89	−3.82	0.00
$\varepsilon _{p_{K}x_{K}}$	−0.53	−0.65	−0.62	−0.57	2.39
	$Y=F(L_{DW},L_{DB},L_M,K,IM,IS)$						$Y=F(L_{DW},L_{DB},L_M,K,IM,IS)$
$\varepsilon _{p_{L_{DW}}x_{L_{DW}}}$	−0.41	−0.59	−0.59	−0.49	3.55	$\eta _{x_{L_{DW}}p_{L_{DW}}}$	−0.44	−0.82	−0.83	−0.87	0.00
$\varepsilon _{p_{L_{DB}}x_{L_{DB}}}$	−0.62	−0.67	−0.54	−0.52	0.50	$\eta _{x_{L_{DB}}p_{L_{DB}}}$	−0.23	−0.81	−0.84	−0.84	1.21
$\varepsilon _{p_{L_{M}}x_{L_{M}}}$	−0.83	−0.89	−0.92	−0.86	0.00	$\eta _{x_{L_{M}}p_{L_{M}}}$	−1.71	−1.27	−1.26	−1.26	0.00
$\varepsilon _{p_{IM}x_{IM}}$	−0.01	−0.1	−0.09	−0.09	9.65	$\eta _{x_{IM}p_{IM}}$	−2.61	−2.56	−2.53	−2.51	0.00
$\varepsilon _{p_{IS}x_{IS}}$	0.4	−0.15	−0.11	−0.07	17.56	$\eta _{x_{IS}p_{IS}}$	−4.16	−4.05	−4.07	−4.07	0.00
$\varepsilon _{p_{K}x_{K}}$	−0.68	−0.73	−0.73	−0.67	0.56

1. $\varepsilon$ is the partial price elasticity computed according to the following formula: $\varepsilon _{p_{i}x_{j}}=c_{ij}*S_{j}=\frac{\alpha _{ij}+S_{i}*S_{j}}{S_{i}}$

Sufficient condition for quasi-concavity is that the bordered Hessian is negative semi-definite and this is validated both at the mean and the median of the sample. The elements on the main diagonal of the matrix, i.e. the own partial price and demand elasticities $f_{ii}$, need therefore to be non positive and the table above shows that this is the case for our sample. The columns respectively report the sample mean and median elasticities computed according to formulas $\varepsilon _{p_{i}x_{j}}=c_{ij}*S_{j}=\frac{\alpha _{ij}+S_{i}*S_{j}}{S_{i}}$ and $\eta _{x_{i}p_{j}}=\sigma _{ij}*S_{j}=\frac{\beta _{ij}+S_{i}*S_{j}}{S_{i}}$, and the elasticities evaluated at the mean of the prediction of the (revenue/cost) shares and at the mean of the shares calculated using WHIP wages. In the former case, we calculate the elasticity for each observation in the sample and then take respectively the average and the median together with the average and the median significance level. The four sets of elasticities are negative and bear consistent insights, in particular the own price and demand elasticities are often very similar to the shares computed on the sample data.

The average of the predicted own price elasticity is surprisingly positive for services, but since we are going to work with elasticities calculated at the mean of the predicted shares this will not represent a problem in the analysis. Finally, the last column displays the share of observations with positive estimated elasticities: a few violations occur for some observations, especially in the case of the production function, however they do not affect the results shown in the text (Wales 1977).