The name is absent

lt = Y 0 + Y1 lt -1 + Y 2Уи ⁺ Y 3 rt - Y 4 wt ⁺ Y 5 T ⁺ ɛ it,

where l_it is (log) employment in firm i at time t , y_it is real output, r_t the (real) rental cost of capital,
w_t real wages and T a time trend to control for (Hicks-neutral) technical progress.¹² How variables are
measured and constructed is described in Appendix 2. The speed of adjustment is negatively related to
the persistency in time of labour demand ( 71 ), and equal to (1 -Yι ). The extent of the adjustment is
measured by the elasticity with respect to output ( Y 2 ) and factor prices ( Y 3 and 7₄ ). The effect of
technical progress is captured by the coefficient Y5. To account for unobservable components at the
firm level we estimate equation (1) in first differences.¹³

To test whether labour demand parameters are significantly different between MNEs and NEs,
we introduce a dummy variable mne , which is 1 when the firm is owned by a foreign MNE and 0
otherwise. This dummy is interacted with the explanatory variables so as to derive different sets of
coefficients for the two types of firms:¹⁴ After re-expressing equation (1) in first differences we obtain:

ʌ l_it = 7⅛_it-1 + 72 ʌУ и + 73 ʌrlt - 7,ʌw_u + 75 + 7m mneʌl,-1

⁺77mneʌy_it ⁺ 7mmneʌr_it ^- 7,mne^w_lt ⁺ γ_wmne_l ⁺ д₇

Note that the MNE status of firms (the mne dummy) may be capturing also the effect of other factors
(mainly industry or size). For this reason, we have introduced size and sector controls by interacting j,
j'=1,2,...,J, size classes and k, k = 1,2,...,K, sector dummies with the trend term as follows: ¹⁵

JK

ʌl_it = 7ʌl_it-1 ⁺ 72ʌy_it ⁺ 7arιt^- 7,ʌwu ⁺ 75 ⁺ ∑ 75DD^{lm +} ∑ 7k5^ect_k

j=i                   k=1                    .             ⁽³⁾

+ 7mneʌl_{it 1} + 7∏mne,Ay,_t + 7,mne,.ʌ.r,_t -7₀mne,Aw,_t + 7mine, + v,_t

6θ l lt-1 Il l S lt Io l lt Iy l lt /10 l lt

¹² Note that in equation (1) labour and capital earnings are expressed in real terms, by using industry-level producer price
indexes as deflators (see Appendix 2). We do not include in the equation the (real) prices for other inputs (intermediates,
materials, energy...) assuming they are closely correlated with industry-level producer price indexes.

¹³ It is known that that using differenced variables aggravates measurement errors. The use of long time differences (5 years
or more) attenuates the problem (Griliches and Hausman (1986)). In our case, however, this strategy would have implied a
very severe reduction in the number of observations.

¹⁴A similar methodology can also be found in Bruno, Falzoni and Helg (2002), a paper examining the effects of trade
integration and MNEs on sectoral labour demands.

¹⁵ As for size, a fivefold partition is used: up to 100, 100-250, 250-500, 500-1000 and above 1000 employees. As for sectors,
the following partition is used, based on Pavitt’s classification: two supplier dominated sectors, two scale-intensive sectors,
one specialised supplier sector and one science-based sector.

Controls have also been carried out by interacting all variables with size and sectoral dummies. Results are in general robust,
particularly to the inclusion of size dummies. However, when all potential interactions are introduced, the number of
coefficients increases remarkably and the interpretation becomes harder. For this reason, these results are not reported.

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