F Danneville
email: francois.danneville@univ-lille.fr

C Loyez

K Carpentier

I Sourikopoulos

E Mercier

A Cappy

A Sub-35 pW Axon-Hillock artificial neuron circuit

Keywords:

Artificial Intelligence (AI) applications are developing at a high rate, facing soon a tremendous energy challenge. In this context, the original Axon-Hillock (AH) Artificial Neuron (AN) has been optimized to achieve ultra-low power (ULP) consumption. The membrane capacitance was taken out, and in order to drastically reduce its power consumption, the (feedback) capacitance is lowered to 5 fF, the transistors gate width is reduced to 120 nm and the supply voltage is decreased to as low as 200 mV. Designed and fabricated using 65 nm CMOS Technology, the refined AH neuron features a standby power of 11 pW, and when excited, a power consumption that does not exceed 30 pW for a firing frequency of 15.6 kHz. Its energy efficiency per spike is lower than 2 fJ / spike when the DC power is included (around 1 fJ / spike excluding the DC power), for an area of 31 µm². These performance confer to this ULP AH neuron a high potential for future development of highly energy efficient Spiking Neural Networks, required to design future neuroprocessors embedded in various applications (smart visual sensors for autonomous vehicles, robotics).

Introduction

Moore's law is reaching its end, which paradoxically may be viewed as an opportunity [START_REF] Waldrop | The chips are down for Moore's law[END_REF]. This motivates to investigate new paradigms particularly to address the energy dissipation challenge for huge AI applications. In this context, spiking neural networks (SNNs) constitute an interesting alternative to process information, in view of providing cognitive characteristics. Hence, the development of high energy efficient artificial neurons and synapses using standard CMOS technology is important. In a previous work [START_REF] Sourikopoulos | A 4-fJ/Spike Artificial Neuron in 65 nm CMOS Technology[END_REF], we have proposed an AN having an outstanding energy efficiency of few fJ / spike, whose features are very close to the biology, because it constitutes an approximation of biological Morris-Lecar (ML) model. In its simplest version, this ML AN uses only six transistors and two capacitances (Fig. 1). Its performance was basically achieved by applying the following design rules: decreasing as much as possible the supply voltage and the membrane capacitance values. Following this work, we have carefully looked throughout the abundant literature for other CMOS based AN architectures [START_REF] Indiveri | Neuromorphic Silicon Neuron Circuits[END_REF][START_REF] Basu | Nullcline-Based Design of a Silicon Neuron[END_REF][START_REF] Joubert | Hardware spiking neurons design: Analog or digital?[END_REF][START_REF] Cruz-Albrecht | Energy-Efficient Neuron, Synapse and STDP Integrated Circuits[END_REF], to identify which one would possibly be competitive in terms of reducing both the DC power and the energy efficiency against the ML AN. It turned out that the Axon-Hillock (AH) artificial neuron originally proposed by C. Mead [START_REF] Mead | Analog VLSI and Neural Systems[END_REF] was worth to be optimized to address the ultralow power challenge, and this is the main objective of this work. The rest of this article is organized as follows: The original AH AN architecture is recalled and the simplified version that was implemented onto silicon is presented. Then the electrical behavior, power consumption, temperature and supply voltage dependence, process variability robustness, are discussed for the refined AH AN. All simulations were carried out by Spectre simulator, on typical corner PDK models, and performed at 300°K (besides temperature sweeps). Details about the circuit fabrication and measurement setup follow and then experimental AH AN results and performances are presented at 300°K. This article concludes with a benchmarking of state-of-the-art artificial neurons in conclusion.

From the Original Axon-Hillock to its simplified ultra low power version

Original Axon-Hillock

The original Axon-Hillock circuit is presented in Fig. 2 [START_REF] Indiveri | Neuromorphic Silicon Neuron Circuits[END_REF][START_REF] Mead | Analog VLSI and Neural Systems[END_REF]. The circuit is made of a Voltage Amplifier (VA) -usually made using two inverters cascaded in series-and uses two capacitances: the membrane capacitance Cmem and a feedback capacitance Cf. Iex is the excitatory current, which mimics the overall synaptic current flowing out of the dendritic tree. Because the main objective was to achieve extremely low DC power and an outstanding energy efficiency for any spike generation, the following arrangements were applied with respect to the original circuit shown in Fig. 2. The first one was to remove the explicit membrane capacitance Cmem, keeping only the parasitic component, which corresponds to the first inverter input capacitance. The second one was to remove MNW, the nMOS to which the "weight" voltage Vpw, is applied in Fig. 2; the current Ir can be set by adjusting transistor dimensions as explained in the next section. The (nominal) supply voltage VDD was chosen to 200 mV, ensuring that MOSFETs will operate in deep subthreshold regime. The source to drain voltage of any MOSFET conductive channel cannot exceed VDD. Such a supply voltage favors low power consumption. After these arrangements, the refined AH architecture is depicted in Fig. 3.

Basic behavior of the refined Axon-Hillock circuit

The basic behavior of the circuit drawn in Fig. 3 is as follows: without excitatory current (Iex = 0 A), the output and membrane voltages (Vmem and Vout) are 0 V, Cf is not charged and MN3 (nMOS) is OFF. When an excitatory (DC) current Iex is applied, a charge is stored by Cf and Vmem increases. When the magnitude of Iex is sufficient, Vmem reaches the switching voltage of the first inverter, both inverters change states, and Vout rises towards VDD (Fig. 4). Meanwhile, a positive feedback occurs through Cf, pulling up the membrane voltage Vmem to a positive value higher than Vout and MN3 turns ON. Vout magnitude is limited by the voltage, which develops between drain and source of MP2, following the increase of the reset current Ir. Ir is now set by the conductance ratio (and effectively the sizing) of the pull-up (MP2) and pull-down (MN3) transistor. With Vout in a high state, having an Ir much larger than Iex, will cause Vmem to decrease and to reach (again) the switching voltage of inverter 1 (Fig. 4); as a result, the inverters switch again, forcing Vout to 0 V. Vmem changes sign, thus source and drain electrodes for MN3 are interchanged. Through the adding currents (Iex + │Ir│), the membrane potential is rising towards positive values and when the membrane potential crosses 0 V, source and drain for MN3 recover their original location (that is, the source is connected to the ground in Fig. 3) and leading MN3 to be turned OFF again. Cf is charged again through only Iex, and the cycle starts again.

Power consumption of the refined AH circuit

First of all, when the neuron is not excited (Iex = 0 A), the total DC power consumption of inverter 1 (Pinv1) and of inverter 2 (Pinv2) is around 1 pW in simulation (W/L=120nm/65nm for transistors, Cf =5 fF). This low power consumption is explained by the fact that that both the membrane and output voltages are 0 V when the neuron is not excited. Nevertheless, when an excitatory current is applied while not sufficient to trigger a spike, the membrane voltage increases; it turns out that both MP1 and MN1 are in an "on-state", which contributes to increase the DC current. Hence, just before the AH is going to fire, the DC current of inverter1 has increased to around 20 pA, which leads to a dissipated DC power of 4 pW. At the mean time, Pinv2 is negligible.

When the AH is firing, the power delivered to each inverter is plotted in Fig. 5 (note that a power consumption analysis of the Axon-Hillock neuron can be found in [START_REF] Yao | VLSI Extreme Learning Machine: A Design Space Exploration[END_REF]). The power is obtained through the product of VDD times the DC current (that is, the mean value) for each inverter.

In Fig. 5, the dissipated power of inverter 1 (Pinv1) is rather constant while those of inverter 2 (Pinv2) continuously increases. The capacitive load of inverter 1 is limited to a low value, set by the parasitic capacitance of inverter 2, making its "switching power" negligible. Nevertheless, because the membrane voltage slowly varies as a function of time (see Fig. 4), the current IMP1 is also slowly varying with a rising time close to the period of the spike; thus, the inverter 1 dissipates a "short-circuit power" [START_REF] Dokic | Subthreshold Operated CMOS Analytic Model[END_REF], almost independent of the firing frequency (Fig. 5).

The situation is very different for inverter 2. Indeed, as shown in Fig. 4, out of TH duration, Vout is close to 0 V, forcing the current flowing in MP2/MN2 to a low value; indeed, the supply voltage mainly delivers the current IMP2 during the spike duration TH (Fig. 4), which is found almost independent through simulation. Because during TH, IMP2 equals the capacitive current flowing in Cf, Pinv2 is frequency dependent, signature of a "switching power".

From this qualitative analysis, it turns out that Pinv1 is the major neuron dissipated power for the low excitatory currents (or low firing frequencies) while Pinv2 is the major one for the highest excitatory currents (or high firing frequencies). In this context, the elements sizing for the designed AH NA were chosen by following these considerations: (i) in order to decrease as much as possible the DC/short-circuit powers, the gate width (W) for all transistors were chosen as low as possible (for the CMOS technology used), (ii) in order to reduce as much as possible the switching power, the value for feedback capacitance Cf was chosen as low as possible, paying attention that it remains much higher than parasitic capacitance of inverter 1.

Impact of Temperature

The variation of spike frequency is plotted as a function of temperature in Fig. 6, for Iex = 10 pA. When temperature increases from 25°C to 40°C, a 20% spike frequency decrease is observed. Such a drop is directly related to the deep sub-threshold operation of the CMOS transistors [START_REF] Degnan | On the temperature dependence of subthreshold currents in MOS electron inversion layers, revisited[END_REF].

Impact of supply voltage (VDD) variation

The variation of spike frequency is plotted as a function of the supply voltage in Fig. 7. For constant Iex = 10 pA and a supply voltage variation of 0.2 ± 0.05 V the frequency shift is of ± 25% from the nominal firing frequency (that is 12 kHz for VDD = 0.2V). Fig. 7 provides also good information about how the AH AN could behave to potential VDD noise perturbation.

Process variability robustness

As previously mentioned, the transistors are operating in deep-threshold regime, and their current-voltage characteristics are subject to variations. Fig. 8 shows a Monte Carlo simulation with one thousand simulations with the criterion to have the AH AN spiking output peak-to-peak voltage greater than half of VDD. As it is seen in Fig. 8, the yield was 820/1000. In conclusion to this section, we should underline that the extremely low excitation and consumption characteristics of the proposed circuit are indeed accompanied by an important margin of operation to what regards PVT variation. This should be taken into account when designing multineuron networks with information representation schemes utilizing spiking frequency, inter-spike interval, time to first spike etc.

Circuit fabrication and measurement setup

The AH neuron implemented onto silicon was designed using W/L=120nm/65nm transistors (all transistors have the same dimensions, with all nMOS body contacts connected to ground and all pMOS body contacts connected to VDD) and a MOM feedback capacitance Cf=5fF. It was fabricated using TSMC 65 nm process in the LP option. It used external biasing, as shown in Fig. 6 ("VDD", "VSS" and VEX pads). The excitation current was tuned through on-chip externally biased transconductance MPex (Fig. 9) modeling the synaptic pre-neuronal excitation. The electrical measurements were performed on a probe station and voltage supplies resolution in the order of 100 fA.

In order to save area on the chip (this one comprised other circuits and the available area was constrained), a common VDD -set to 200 mV-was connected to both the AH neuron and the excitation transconductance. The AH neuron output was monitored through an on-chip unity gain buffer ("VOUT-buffer" pad in Fig. 9) that was designed ensuring that the frequency response of the neuron circuit would not be affected. More precisely, the buffer featured a high input impedance (corresponding to a capacitance equal to 3 fF, the impact of parasitic DC current is negligible). The output buffer also featured independent DC supply (connected to the pads "VDDANA" and "VSSANA" in Fig. 9) to enable accurate power consumption measurements. The AH neuron core area is 31 µm 2 .

Experimental results

Measurements, using the protocol described in the previous section, were performed on the chip. A step response is reported in Fig. 10. A voltage VEX close to VDD, so that the neuron doesn't spike, is initially applied to the gate of MPex, thus corresponding to an off-state. After 400µs, a VEX step is applied and the AH neuron generates spikes for as long as VEX is sustained. When VEX returns to its initial value (≈ VDD), the neuron is not excited anymore. Because it was not possible to check the exact buffer gain value (theoretically equal to unity), the DC bias current source connected to the buffer was tuned so that the maximum voltage for VOUT-buffer reaches 200 mV (VDD). As it is shown, the shape of the output waveform (Fig. 10) agrees well with the simulated waveform in Fig. 4. After verifying the correct behavior of the simplified AH neuron, its performance was measured in terms of frequency, power consumption and spike energy efficiency. Because the excitation current is tuned by adjusting the gate voltage applied on pad "VEX" of the transconductance (Fig. 9), the measured (DC) current Idd delivered by the supply voltage -the only one accessible-varies. As shown in Fig. 9, Idd corresponds to the summation of both the excitatory current Iex (flowing out the transconductance) and the current consumed by the neuron Ineuron (transconductance and neuron supply voltages are physically connected to the same supply pad). Thus, the actual power consumption and energy efficiency for the designed AH neuron are likely slightly better.

In Fig. 11, the AH neuron starts firing with a frequency equal to 290 Hz (Idd = 57 pA), then the firing frequency continuously increases up to 15.6 kHz (Idd = 150 pA), covering more than a decade of frequency. The power consumption, which is reported in Fig. 11, corresponds to the product of the supply voltage times the supply current VDD x Idd (VDD=200mV). On one hand, it corresponds to the "DC power" when the AH neuron is not excited. On the other hand, it includes both the DC and dynamic powers when the AH neuron is excited. As shown in Fig. 11, the DC power is around 11 pW, while when the AH neuron reaches its highest frequency, the power consumption goes up to 30 pW; the excess of power -19 pW-corresponds to the dynamic power. Knowing the power consumption and firing frequency, the energy efficiency per spike of the AH neuron, including or excluding the DC power, was calculated (Fig. 12). In this plot, when the DC power is included, the energy efficiency is equal to 10.2 fJ / spike for a spike frequency of 1.2 kHz and drops afterwards to attain its lowest value of 1.9 fJ / spike for the highest spike frequency. As discussed in Section 2 related to the power dissipation discussion, when the AH neuron is spiking at low frequencies, the dissipated power of inverter 1 (almost frequency independent) is the most important, which explains the decrease of energy efficiency in Fig. 12. On the other hand, for the highest firing frequencies, the inverter 2 dissipated switching power explains why the energy efficiency becomes independent.

It is to be noted that when the DC power (namely, the power when Iex = 0 A) is deducted, the energy efficiency stands around 1 fJ/spike, whatever the firing frequency.

Conclusion

The performance of recent state of the art neuron implementations is reported in Table 1. Let us describe the performance reported in Table I. In [START_REF] Basu | Nullcline-Based Design of a Silicon Neuron[END_REF] the capacitances are in the order of few hundred fF and voltages are higher than 1V. In [START_REF] Joubert | Hardware spiking neurons design: Analog or digital?[END_REF], the architecture corresponds to a leaky integrate and fire AN, which adds up an extra circuit (comparator) to set the firing threshold AN, the latter contributing to extra power consumption. Moreover, the membrane capacitance is equal to 500 fF and the AN operates at supply voltage VDD around 1 V. In [START_REF] Cruz-Albrecht | Energy-Efficient Neuron, Synapse and STDP Integrated Circuits[END_REF], the architecture of the AN is based on a transconductance amplifier designed with more than 10 transistors, and operates under VDD equal to 0.6 V. It is obvious that for these AN, a down-scaling on the membrane capacitance nor on the supply voltage VDD was not carried out, leading to a non-optimized energy efficiency. In light of the comparison between the ML [START_REF] Sourikopoulos | A 4-fJ/Spike Artificial Neuron in 65 nm CMOS Technology[END_REF] and the AH neurons, the following comments can be addressed: (i) the DC power is three times lower for the AH. As already stated, the main reason lies in the fact that both the membrane and output voltages are 0 V when the neuron is not excited. When not excited, the membrane voltage is of few tens of mV for the ML, making the sodium (MPNa) and potassium (MNK) transistors (Fig. 1) dissipating a DC power, (ii) the energy efficiency per spike (including the DC power) is better for the AH: the benefit comes from the lower DC power and also the use of only one capacitance.

It is to be noted that the emulation of bursting mode (of interest in a robotic context) or the highlight of stochastic resonance, which has been shown for the ML [START_REF] Danneville | Ultra low power analog design and technology for artificial neurons[END_REF], could also be obtained with the AH.

In conclusion, we believe that the ULP AH neuron presented in this work constitutes a serious candidate for SNNs design, if combined with synapses such the one described in [START_REF] Bartolozzi | Synaptic dynamics in analog VLSI[END_REF], to address the energy dissipation challenge to come due to the growing AI applications. Further works need to address the temperature sensitivity of such a subthreshold circuit.

Fig. 1 .

 1 Fig. 1. Simplified Morris-Lecar Neuron Circuit.

Fig. 2 .

 2 Fig. 2. Original Axon-Hillock artificial neuron (as drawn in [3]).

Fig. 3 .

 3 Fig. 3. Refined AH artificial neuron.

Fig. 4 .

 4 Fig. 4. Membrane and output voltages (Cadence simulation), for Iex = 10 pA (W/L=120nm/65nm for transistors, Cf =5 fF).

Fig. 5 .

 5 Fig. 5. Power dissipated (Cadence simulation) in each inverter of the AH refined neuron when excited (W/L=120nm/65nm for transistors, Cf =5 fF).

Fig. 6 .

 6 Fig. 6. Firing frequency (Cadence simulation) as function of temperature, for Iex = 10 pA (W/L=120nm/65nm for transistors, Cf =5 fF).

Fig. 7 .

 7 Fig. 7. Firing frequency (Cadence simulation) as function of VDD, for Iex = 10 pA (W/L=120nm/65nm for transistors, Cf =5 fF).

Fig. 8 .

 8 Fig. 8. Monte Carlo (Cadence) simulation: the criterion is to have the AH AN output voltage magnitude exceeding 50% VDD (half VDD).

Fig. 9 .

 9 Fig. 9. Chip photograph (left) and block diagram (right).

Fig. 10 .

 10 Fig. 10. Waveform of the AH AN output voltage.

Fig. 11 .

 11 Fig. 11. Firing frequency and power consumption as a function of the DC current (Idd) delivered by the supply voltage VDD.

Fig. 12 .

 12 Fig. 12. Energy efficiency as a function of the spiking frequency

Table 1

 1 Comparison of recent silicon artificial neuron implementations

	Ref.	Node (nm)	Area (μm 2 )	Spiking frequency (Hz)	Power (W)	Energy Efficiency (pJ/ spike)
	[5]	350	1887	100	1.74n	17.4
	[6]	65	120	1.9 10 6	78µ	41
	[7]	90	442	100	40p	0.4
	[2]	65	35	26 x 10 3	105p	0.004
	This	65	31	15.7 x 10 3	30p	0.002
	work

Acknowledgements

The authors acknowledge IRCICA and SATT NORD for the financial support. The personnel of the "Centrale de Caractérisation" of IEMN for its contribution to the electrical measurements of the chips. The authors also acknowledge the contribution of CEA Leti staff for its permanent support to this work.


Clément Malgouyres
email: malgouyres-cmalgouyres@gmail.com

Thierry Mayer
email: thierry.mayer@sciences-po.fr

Clément

EXPORTS AND LABOR COSTS: EVIDENCE FROM A FRENCH POLICY

Keywords: JEL Classification: H32, F14, F16, D04 labor costs, firm-level exports, competitiveness labor costs, firm-level exports, competitiveness JEL: H32, F14, F16, D04

We investigate the role that labor costs hold in exporters' performance. To do so, we exploit a large-scale French reform that granted most firms a tax credit proportional to the wagebill of their employees paid below a given threshold. This policy effectively translated into a cut in labor cost whose magnitude varies depending on firm-specific wage structures. We use the predicted treatment intensity based on pre-reform composition of the labor force as an instrument for the actual policy-induced firm-level change in labor costs. Although our point estimates are consistent with commonly estimated firm-level trade elasticities combined with reasonable labor shares in total costs, coefficients are found to be very noisy, suggesting lack of robust evidence of a causal effect of the policy. We discuss several potential explanations for our results as well as their implications.

Introduction

Competitiveness is one of the most important concerns that is used by policy makers to justify policy reforms aimed at improving/restoring the ability of domestic firms to exhibit high performance on international markets. While the objective is usually macroeconomic in nature, with a goal to ensure a sustainable path of trade balance, the policies involved are often micro-economic. This is especially true in currency unions such as the eurozone, where changes in the nominal exchange rate intended to reduce the consumerrelevant price abroad are not an option. Some of the remaining policy tools available are directed at non-price competitiveness (R&D tax breaks being one example, see e.g. [START_REF] Hombert | Can innovation help us manufacturing firms escape import competition from china?[END_REF]. It is however likely that the impact of this type of measures only manifests itself in the long-run. Shorter-run policies are aimed at reducing the costs of domestic firms with respect to foreign competitors so as to strengthen price competitiveness. Numerous channels of action are possible. The basic idea is that export performance of firms is driven by the export price set by the firm, and that the passthrough of the cut in unit costs to lower export price is high enough to ensure that the market share captured by domestic firms on international markets increases. Any policy reducing the explicit or implicit cost of exports will work under those assumptions. Reducing the price of energy (or the regulations related to how clean the production process is) is an option that has been invoked by the recently elected US administration.1 Cutting the costs of using domestic labor is another obvious candidate that can take di↵erent forms: wage moderation, flexibility in labor market regulations, or transferring the tax burden of social contributions (payroll tax) to other tax sources for instance.

Our paper focuses on the last of those policies. Since 2013, the French government implemented a tax credit aimed at boosting competitiveness and employment, named the CICE in French (standing for Competitiveness and Employment Tax Credit or Crédit d'impôt pour la compétitivité et l'emploi in French). The policy is intended to act as a cut in unit labor costs (see section 3 for all details on the policy change). The tax credit is set proportional to the share of the wagebill paid to workers under a certain threshold (2.5 times the national minimum wage). Each firm receives a transfer of 4% (raised to 6% since 2014) of the total wagebill that is under the threshold. This policy design gives us a natural experiment where we can match for each firm the intensity of labor cost reduction (that varies according to its original labor force composition), and its export performances (intensive and extensive margins) before and after treatment. Our results cast doubts on the e↵ects to be expected from reductions in labor costs regarding export performance. While the magnitude of our point estimates are consistent with expectations, i.e. commonly estimated firm-level trade elasticities multiplied by reasonable values of the share of labor in total costs, coe cients are found to be very noisy, suggesting lack of robust evidence of a causal e↵ect of the policy.

A recent paper with similar motivation to ours is [START_REF] Decramer | How do exporters react to changes in cost competitiveness?[END_REF], which looks at how unit labor costs a↵ect export performance using Belgian firm-level data. This paper finds quite large and significant elasticities, when regressing the change in (log of) exports on the change in (log of) unit labor costs. When adopting the same specification, we also find that a 10% increase in unit labor costs is associated with around 2% lower exports. Another related paper is [START_REF] Gan | The higher costs of doing business in china: Minimum wages and firms' export behavior[END_REF], who evaluate how regionally-driven changes in the minimum wage faced by Chinese exporters a↵ect their competitiveness. In contrast to [START_REF] Decramer | How do exporters react to changes in cost competitiveness?[END_REF], we evaluate a policy that specifically reduced labor costs in a heterogeneous manner depending on the initial wage structure of the firm. This o↵ers a natural instrumentation strategy based on the administrative threshold that determines which employees are eligible to the policy. Compared to [START_REF] Gan | The higher costs of doing business in china: Minimum wages and firms' export behavior[END_REF], our work does not rely on the exogeneity of changes in the minimum wage decided by local authorities. The policy change is national, and heterogeneity in the treatment only comes through pre-treatment composition of the labor force across firms. The French government had an aim to bolster national competitiveness, not export performance of the subset of firms that had a specially high share of workers below a certain threshold. The choice of the precise threshold was itself not anticipated, and driven by a mix of considerations related to the impact on unemployment and to budgetary constraints rather than pre-trends of di↵erent groups of firms. 2In addition to evaluating the impact of a change in labor costs on the competitiveness of firms on export markets, our paper contributes to the literature on price elasticities in trade. The largest set of papers in this vein uses variation in tari↵s and / or exchange rates as price shifters. [START_REF] Berman | How do di↵erent exporters react to exchange rate changes?[END_REF], [START_REF] Fitzgerald | Exporters and Shocks[END_REF], Bas et al. (2017), [START_REF] Berthou | Variable trade costs, composition e↵ects and the intensive margin of trade[END_REF] are recent contributions that all use firm-level response to ad valorem tari↵s and exchange rate variation in export markets. [START_REF] Amiti | Importers, exporters, and exchange rate disconnect[END_REF] and [START_REF] Piveteau | Estimating firm product quality using trade data[END_REF] use a related approach, where they calculate the change in marginal cost implied by the initial composition or inputs imported by each firm, interacted with exchange rate changes in its sourcing country, which they use to predict changes in export prices and therefore export values. One of the most important finding of that literature is the so-called international elasticity puzzle: the response of demand to changes in tari↵s is much larger than the impact of changes in exchange rates, with elasticities typically being estimated (in absolute value) between 3 and 5 for tari↵s, and often lower than 1 for exchange rates. This is a puzzle since most of our theoretical framework would predict those two (delivered) price shifters to have the same e↵ect on trade flows. [START_REF] Fontagné | The International Elasticity Puzzle Is Worse Than You Think[END_REF] also use the reaction of firm-level exports to tari↵s and exchange rates, but add the impact of changes in f.o.b prices at the firm level instrumented by a cost shifter based on how firms di↵er in their electricity bill. The idea is that changes in electricity prices are mostly driven by regulatory changes interacted with di↵erences in contract dates and length, that are exogenous to the firm, and do not a↵ect exports directly. This is one of the most proximate investigation to ours since the dimension of the estimating variable is firm-level, with a credible claim for exogeneity and therefore causality in the estimation of the price elasticity. Their results start by reproducing the international elasticity puzzle: the response of exports to changes in tari↵s is much larger than the response to changes in exchange rates. They also show that the changes in f.o.b prices by the exporter have a large impact on demand, with an elasticity estimated around -5. Compared to this literature, we base our estimates of the trade elasticity on a policy change, that a↵ected unit costs of di↵erent firms in a heterogeneous manner.

The remainder of the paper is as follows: Section 2 structures our analysis in terms of the underlying theoretical motivation. Section 3 describes the data used, in particular how we merge the di↵erent elements of firm-level data sources to calculate the intensity of treatment of di↵erent firms in terms of their labor costs. Section 4 proceeds with results for di↵erent margins of adjustment to changes in labor costs, before concluding with section 5.

Theoretical motivation

Our theoretical motivation is based on [START_REF] Crozet | Quality Sorting and Trade: Firm-level Evidence for French Wine[END_REF], who develop the firm-level export predictions of the [START_REF] Melitz | The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity[END_REF] model and in particular its implications in terms of empirical implementation. Firms, indexed i and characterized by their unitary cost

↵

i (the inverse of their TFP), operate under monopolistic competition to serve CES consumers in di↵erent markets n with their unique variety. Note that we work with exporters from a single origin country, France, and therefore have no origin country subscript. The representative consumer in n has utility

U n = ✓Z ⌦n (q n (↵ i )/b n (↵ i )) 1 d↵ i ◆ 1
, where q n (↵ i ) is the quantity consumed of variety i. The b n (↵ i ) term is an idiosyncratic demand shock which lowers utility of individuals in n when consuming this precise variety. The pricing part is the usual constant markup over marginal cost (C

i ): p(↵ i ) = 1 C i . The delivered price incorporates an iceberg trade costs (⌧ n ), such that p n (↵ i ) = p(↵ i )⌧ n .
With all those elements at hand, the equilibrium sales of firm i in n write:

x n (↵ i ) = ✓ 1 ◆ 1 [C i ⌧ n b n (↵ i )] 1 X n P 1 n , (1)
where X n and P n respectively represent total expenditure and the ideal CES price index in n. Taking logs, we have an estimable equation where the log exports should react to any change in marginal costs with an elasticity reflecting the price elasticity of consumers ( 1):

ln x n (↵ i ) = (1 ) ln ✓ 1 ◆ +(1 ) ln C i +(1 ) ln ⌧ n +ln ✓ X n P 1 n ◆ +(1 ) ln b n (↵ i ).
(2) Let us now enter into the details of this cost function. We assume functional form to be a Cobb-Douglas aggregator of several factors, one of which is labor. Among workers, we distinguish between low/medium skill workers who are eligible to CICE and high-skill workers who are not:

x i = l µ i i J Y k=1 v ik ik ! 1 µ i 1 ↵ i
where l i represents labor employed, itself a Cobb-Douglas aggregation of eligible (l e ) and non-eligible (l n ) parts such that l

i = (l e i ) ⌘ i (l n i ) 1 ⌘ i . Other factors k are used in quantities v
ik by firm i and we assume constant returns such that:

µ i + (1 µ i ) P k ik = 1 , P k ik = 1.
A set of additional assumptions will greatly ease interpretation of results. Inside a sector s, we assume that (i) unit input requirements ik and factor prices r ik faced by firms are the same, (iii) the share of labor µ s is constant inside an industry. Unit costs then take the following form:

C i = ↵ i w µs i Y k r k sk ! 1 µs B s | {z } =c i = ↵ i c i (3)
where

B s = µ µs s Q k sk sk (1 µs) and w i = (w e i ) ⌘ i (w n i ) 1 ⌘ i ⇥ (⌘ i ) ⌘ i (1 ⌘ i ) (1 ⌘ i )
. It is critical here that (even though we do not model explicitly labor markets for di↵erent skills) we let firms have di↵erent labor costs. Particularly important will be the fact that di↵erent firms have di↵erent shares of their labor force eligible to the policy change (⌘ i ), which we consider to be a constant technological parameter.

Substituting (3) in (2), and introducing a time dimension t, the export equation becomes:

ln x int (↵ it ) = cst. + (1 )µ s ln w it + (1 ) " ln B s + (1 µ s ) X k ks ln r kst # | {z } =FEst + (1 ) ln(⌧ nt ) + ln X nt (1 ) ln P nt | {z } =FEnt + (1 ) ln ↵ it + (1 ) ln b int | {z } =" int = (1 )µ s ln w it + FE nt + FE st + " int (4)
Firm-level exports are therefore explained by a set of destination-time and sector-time fixed e↵ects, and our variable of interest, i.e. the relevant wage at the firm-level, w it . Setting aside for a moment measurement issues on w it , the presence of ↵ it in the error term raises an obvious concern in the estimation of equation ( 4). It is quite likely that there exists a cross-sectional correlation between the TFP of firm i and the wages which it faces (for instance because of the average wage level in the area in which it is located). We solve this correlation by separating ↵ it between a time-invariant unobserved component and measured covariates that are allowed to vary over time: ln

↵ it = ln ↵ i + W 0 ↵ it + u it
where W ↵ it is a set of exogenous time-variant TFP determinants, and is a vector of associated parameters. First-di↵erencing equation (4), we obtain:

ln x int (↵ it ) = (1 )µ s ln w it + (1 ) W 0 ↵ it + FE nt + FE st + (1 )( u int + b int ) (5)
We model the CICE as a policy providing a subsidy on the eligible part of the labor force at a rate ⌫. The e↵ective labor cost in logs writes:

ln w it [⌫] = ⌘ i ln(w e it [⌫](1 ⌫)) + (1 ⌘ i ) ln w n it [⌫] ( 6 )
Notation w e it [⌫], and w n it [⌫]) makes it explicit that the pre-subsidy wages can be a↵ected by the policy. Equation (6) makes it clear that the direct negative e↵ect of a rise in rate ⌫ on the e↵ective labor cost can be partly attenuated by a rise in equilibrium pre-subsidy wage. An advantage of our ex-post approach is to capture both direct and indirect e↵ects through which the CICE policy is likely to impact e↵ective labor costs. 3 One can decompose the change in e↵ective labor costs between the part linked to the CICE policy, and the part that would have happened without the policy:

ln w it+1 = ln w it+1 [⌫ t+1 ] ln w it [⌫ t ] = ln w it+1 [⌫ t+1 ] ln w it+1 [⌫ t ] + ln w it+1 [⌫ t ] ln w it [⌫ t ] = ⌘ i ln ✓ 1 ⌫ t+1 1 ⌫ t ◆ + ⌘ i ln ✓ w e it [⌫ t+1 ] w e it [⌫ t ] ◆ + (1 ⌘ i ) ln ✓ w n it [⌫ t+1 ] w n it [⌫ t ] ◆ + l n w it+1 [⌫ t ] ln w it [⌫ t ] | {z }
Change in labor costs that would have occurred without the policy (7)

We assume that the change in labor costs that would have taken place without CICE can be captured by a combination of sector-time fixed e↵ects and a set of observables. Formally, we model ln w

it+1 [⌫ t ] ln w it [⌫ t ] such that : ln w it+1 [⌫ t ] ln w it [⌫ t ] = W 0 ↵ it + FE st + v it , (8)
where we assume that the sets of observables that drive the firm-level TFP and wages over time are the same. The direct e↵ect of the CICE policy on labor costs is

[⌘ i ln(1 ⌫ t )] = ⌘ i ln ⇣ 1 ⌫ t+1 1 ⌫t
⌘ , which will be our variable of interest in the regression analysis. Let us denote e w e 1 ⌫ and e w n 1 ⌫ the elasticities of eligible and non-eligible wages with respect to 1 ⌫. Inserting equation ( 7) and (8) in equation ( 5) yields, after a few manipulations, 4

3 The indirect e↵ects are potentially important. The total elasticity of e↵ective labor costs with respect to the subsidy rate ⌫ writes:

d ln w it d ln ⌫ = ⌘ i ⌫ 1 ⌫ + ⌘ i @ ln w e it @ ln ⌫ + (1 ⌘ i )
@ ln w n it @ ln ⌫ Without the indirect e↵ect, a 50 % increase in ⌫ (which happened between 2013 and 2014, when the rate went from 4 to 6%) has a direct e↵ect of -1.46% on labor costs if 70 % of the firm's wagebill is eligible (⌘ = 0, 7). However, this fall will be largely dampened even for very low values of wage elasticities with respect to ⌫. For instance, for a 1% elasticity of eligible wages, the overall fall in labor costs is reduced to -1.1% (-0.96% if non-eligible wages also react with a 1% elasticity).

4 Substituting ( 7) and ( 8) in (5), we obtain

ln x int (↵ it ) =(1 )µ s [⌘ i ln(1 ⌫ t )] + (1 )µ s ⌘ i ln ✓ w e it+1 [⌫ t+1 ] w e it+1 [⌫ t ] ◆ + (1 )µ s (1 ⌘ i ) ln ✓ w n it+1 [⌫ t+1 ] w n it+1 [⌫ t ] ◆ + (1 ) W 0 ↵it ⇢ + FE nt + FE st + (1 )( u int + b int + v it ),
where ⇢ ⌘ + combines the e↵ects of the set of observables W on unit input coe cients and wages.

the final equation:

ln x int (↵ it ) =(1 )µ s (1 + e w e 1 ⌫ e w n 1 ⌫ ) [⌘ i ln(1 ⌫ t )] + (1 ) W 0 ↵ it ⇢ + FE st + FE nt + (1 )( u int + b int + v it ). (9)
If the policy has no impact on wages (e w e 1 ⌫ = 0 and e w n 1 ⌫ = 0), the coe cient estimated on our treatment variable identifies the product of two structural parameters: labor intensity in sector s multiplied by the price elasticity of demand: ( 1)µ s . Considering a labor intensity such that µ s is in a 20 to 25% range, and a value for around 5 or 6,5 we expect a coe cient around -1 of the CICE policy on exported values in the absence of wage response.

Potential e↵ects on wages complexify the interpretation of the coe cient on the treatment variable since it is then ( 1)µ s (1 + e w e

1 ⌫ e w n 1 ⌫ ). The heterogeneity in the e↵ect then comes not only from the factor intensity of this sector, but also from the reaction of eligible vs non-eligible labor. The structural interpretation of coe cients is more difficult, although it does not a↵ect the validity of the reduced form identification of the treatment e↵ect.

A final issue in estimation of the CICE policy on exports is a selection bias. The flow, ln x int (↵ i ), is only observed for the combinations of firm-destinations that are profitable, i.e. when the following condition is met:

⇡ int (↵ it ) = x int (↵ it )/ f n > 0 ( 1 0 )
This introduces a selection in the sample likely to create a correlation between the error term and RHS variables. For instance, among the firms with high labor costs, only the ones having had a particularly strong draw on the idiosyncratic demand shock 1/b n will be exporting to n. This will create an attenuation bias in estimated coe cients. A way to minimize the issue is to proceed to robustness checks using a subsample of firms large and productive enough to be considered su ciently distant from the cost cuto↵

Noting that ln ⇣ w e it+1 [⌫t+1] w e it+1 [⌫t] ⌘ = e w e 1 ⌫ ln 1 ⌫t+1 1 ⌫t = e w e 1 ⌫
ln(1 ⌫ t ), we can regroup terms such that:

ln x int (↵ it ) =(1 )µ s (1 + e w e 1 ⌫ e w n 1 ⌫ ) [⌘ i ln(1 ⌫ t )] + (1 )µ s e w n 1 ⌫ ln(1 ⌫ t ) + FE st | {z } =FEst + (1 ) W 0 ↵it ⇢ + FE nt + (1 )( u int + b int + v it ).
for profitable exports so that the error term is unlikely to matter much for their entry decision. We follow this approach by focusing some of our analysis on a subsample of firms that serve continuously their markets (destination) during the entire sample period (2010)(2011)(2012)(2013)(2014)(2015) and that belong to the top quartile in terms of number of markets served.6

3 Data

The genesis of the CICE reform

In this section, we describe the policy we are using in order to gauge to what extent labor costs matter for exporting firms. This policy, labeled CICE by the French authorities, was decided in 2012, in a period of challenging economic situation for the newly elected government. Corporate profits were considered to be at a historically low level7 and French firms had been rapidly losing market share in foreign markets for several years [START_REF] Bas | In search of lost market shares[END_REF]. In that context, the government ordered a report on the state of the manufacturing sector in France [START_REF] Gallois | Pacte pour la compétitivité de l'industrie française[END_REF]. The report, often referred to as Rapport Gallois, named after its main author, advocated in favor of large cuts in payroll taxes for employees earning up to 3.5 times the amount of the current minimum wage. While there had been large cuts in payroll taxes since the early nineties, those were concentrated on low wages. At the time of CICE implementation, those pre-existing tax cuts were indeed concentrated on the bottom of the wage distribution (up to 1.6 times the minimum wage, see Figure 1). Extending the payroll tax cuts to workers higher up in the wage distribution was presented as a way to target manufacturing and exporting firms who tend to pay higher wages and therefore did not benefit from the pre-existing tax cut programs.

A debate engaged after the initial proposal of the Rapport Gallois, which was considered by many to be too costly and was criticized by labor economists who contended that the employment e↵ects of cuts in payroll taxes are stronger when targeted on low wages where demand is more price elastic and unemployment is high (see [START_REF] Cahuc | Alléger le coût du travail pour augmenter l'emploi: les clés de la réussite[END_REF] for an example of that view). As a compromise, a threshold of 2.5 times the minimum wage was chosen and passed into law. Finally, in order to ease the short-term fiscal impact in a time of tight budgetary constraints, the government chose to opt for a tax credit system rather than a (direct) payroll tax cuts. Firms could claim a corporate tax credit at a rate proportional to the wagebill accrued to workers earning less than 2.5 minimum wages. The rationale for this choice was to change firms' incentives immediately while delaying the budgetary burden of the policy by a year. The policy was put in place in January 2013, with a tax credit rate of 4% (of the wagebill of all workers under 2.5 minimum wages). In January 2014, the rate was raised to 6%. Concretely, in the case of a financial year ending 31 December 2014, the CICE relating to remuneration paid in 2014 is deducted from the tax due for the financial year ending 31 December 2014. In case the CICE amount exceeds the tax that is owed by the firm, the tax credit can be used against taxes due for the next three financial years (e.g. 2015, 2016 and 2017). After three years, the tax credit is refunded to the firm. Interestingly for our purpose, we note that no other regulatory thresholds existed at 2.5 times the minimum wage prior to this reform.

Moreover the reform is unlikely to have been anticipated by firms. Indeed, as mentioned above, the government's decision to implement the CICE was taken in reaction to the Gallois report about the state of manufacturing in France which was released on November 5, 2012. The original proposal contained in the report was deemed excessively costly and the actual CICE ended up di↵ering substantially from the proposal: it was implemented as a corporate income tax credit instead of a direct cut in social contribution and, most importantly, its threshold was set up to 2.5 instead of 3.5 times the minimum wage. Little time elapsed between the release of the report -November 5 th 2012 -and the implementation of the modified version of the CICE beginning January 1 st 2013 (from Finance Act of December 29 th 2012). This reduces the chances that firms could anticipate and adapt their wage policy in 2012 to maximize the amount of the tax credit to be received based on the 2013 wage structure.

The parameters of the policy

The schedule for the CICE in 2014 is presented in Figure 1. The x-axis features the ratio of the worker's wage over minimum wage, while the y-axis represents the reduction in labor cost due to the policy change. Panel (a) shows the reduction in terms of percentage of the total wage paid, while panel (b) expresses it in annual euros saved on each worker. There are two curves on each panel. The first one shows the schedule of payroll tax cut that existed before 2014, and which was maintained as is. The second one shows the tax cut schedule of the CICE: flat at 6% before the 2.5 threshold, 0 afterwards. Marginally, the firm receives a tax credit that is equal in 2014 to 6% (4% in 2013) of the total labor Note: Prexisting payroll tax cuts refer to the general payroll tax cuts applicable prior to the CICE -so-called "exonérations générales de cotisations sociales" (see [START_REF] Bunel | The e↵ects of reduced social security contributions on employment: An evaluation of the 2003 french reform*[END_REF][START_REF] Cahuc | Alléger le coût du travail pour augmenter l'emploi: les clés de la réussite[END_REF].

cost on each worker that is paid less than 2.5 times the minimum wage. At the threshold of 2.5 times the minimum wage, the firm gets a tax credit that amounts to about 2,500 euros per worker-year.

It is important to note that the discontinuity occurs at the worker level, while our variables of interest (export performance, labor cost) are intrinsically defined at the firmlevel. We could exploit a discontinuity at the firm-level if we focused on those firms whose entire workforce is located slightly below the 2.5 minimum wage threshold (fully treated) versus firms paying all of its employees just above the threshold (untreated). However, all firms in our sample exhibit su cient wage variation to make it impossible to implement a firm-level regression discontinuity design. Against this di culty, we choose to rely on continuous variation in treatment -which is the sum of worker-level binary eligibility variables -within a di↵erence-in-di↵erence setting.

How much does each firm receive in terms of tax cuts therefore depends on the composition of its labor force. A firm that has all of its employees paid at the minimum wage sees its labor costs reduced by 4% between 2012 and 2013. At the other extreme, a firm where every employee earns more than the 2.5 threshold is not treated and has unchanged labor costs. Figure 2 shows the distribution of the treatment intensity in our sample of continuing exporters between 2010 and 2015. Panel (a) spans over firms, and shows a histogram of the CICE-implied labor cost reduction in the first two years of treatment, based on the amount truly received. While a substantial share of exporters have all of their employees under the threshold,8 and therefore have an overall treatment of 4% in 2013 and 6% in 2014, there is substantial variation of the intensity of treatment in the population of French exporters. Panel (b) shows the most a↵ected industries in our sample, calculating the average intensity of treatment across the 2-digit manufacturing industries to which our exporters belong. Wood, Furniture, Food and Textile are among the industries where continuing exporters are the most heavily treated. Chemicals, Pharmaceuticals, Beverages, are representative examples of the other side of the spectrum, where wages are high enough for a large portion of the employees to be untreated.

Firm-level trade and workers

Firm-level data come from a combination of four sources. The first one is produced by the customs o ce, and compiles the exported values and quantities for each firmdestination-product combination. The second one, produced by the French statistical institute (INSEE), contains balance-sheet data for firms. It uses the same identifier for the firm, and is mostly used in our sample to obtain control variables, such as valueadded or the capital stock. The third source is the employer-employee data also created by INSEE, and named DADS. All workers of a given firm (identified with same number as the two other sources) are recorded in DADS, which we use to obtain hourly wages. This very rich source is critical for calculating the predicted intensity of treatment at the firm level. The fourth source is an administrative file, named MVC, that contains the actual amount of tax credit claimed by each firm. We use it to compute the treatment intensity which we will then instrument with the predicted treatment intensity as computed using the DADS dataset.

We keep firms that are present in all four datasets and for which the main activity reported belongs to manufacturing. Furthermore, we exclude firms that are in the top percentile in terms of CICE intensity (those do report considerably more than that the maximum rate that should be possible to claim) in any given year. We finally focus on a balanced sample of firms present in the dataset over the 2010-2015 period. The sample we use for the extensive margin analysis is the set of firms that are continuously present in the balance-sheet and employer-employee datasets over the 2010-2015 period. The one we use for the intensive margin analysis is the set of continuous exporters over the same period. We refer to the first and second samples with ME and MI respectively. The MI sample (described in Table 1) exhibits a ratio of tax credit over wagebill that is smaller than the ME one (described in Table 2). This reflects the usually found overall exporter premium on variables such as value-added, size and wages also found here. Even though the MI firms constitute a sample of manufacturing firms that are productive enough to remain exporters over the whole sample, the ratio of exported value over total sales is still at a low 12.4% for the median firm, which typically serves 7 markets. The average ratio of exports to total sales is at 25%. Table 2) also shows that the proportion of exporters is 37%. Both numbers are higher than the usual figures for the US (18% for average exporter shares, 14% for ratio of export value over total sales) reported in [START_REF] Bernard | Firms in international trade[END_REF]. Note however that the sample here is manufacturing only, and constrained to continued presence in several firm-level datasets over 5 years, which probably selects larger firms. [START_REF] Mayer | The Happy Few: The internationalisation of European firms. New facts based on firm-level evidence[END_REF] report export participation rates and share of exports in total sales that are very comparable to ours for several European countries with samples constrained to have firms above a certain size.

Results

Descriptive evidence

One important characteristic of the CICE policy is that it mostly a↵ects firms that were initially less export-oriented. Firms that do export in positive amounts, and those that have the highest share of exports in their total sales tend to pay higher wages, and are therefore the ones where the treatment is less intense. Panels (a) and (b) of Figure 3 show those two negative relationships: export intensity and export probability both decline with the lagged amount of subsidy received in 2014.9

The top 5% CICE recipients (as a share of wagebill) in 2013 had an average ratio of exports over turnover of 17 % in 2012. The same ratio for the bottom 5% of recipients was 40 %. The extensive margin evidence is more complex, and clearly non-monotonous in the top part of the treatment intensity.

b: Extensive margin: probability of export

Note: Each dot corresponds to a quantile (20) of the treatment intensity in 2014. The x-axis reports treatment intensity, while the y-axis plots the average export intensity / share of exporters in the corresponding quantile.

We also present graphical evidence regarding the first-stage of our instrumentation strategy in Figure 4 among the sample of continuing exporters (left panel) and all firms (right panel). For both sample, we see a clear positive relationship between the instrumental and the endogenous variables that is approximately linear, when aggregating over 20 bins of the instrument.

The impact of CICE on exports Empirical approach

We implement the estimation of equation ( 9) at the destination ⇥ firm-level. We choose to retain the destination dimension despite the fact that our variable of interest only varies at the firm-level because destination-specific shocks that are potentially correlated with exposure to the labor cost reduction induced by the policy could cause bias in our estimates. The estimating equation writes as follows:

ln x int = D it + W 0 ↵ it ⇢ + FE nt + FE st + " int (11) with D it ⌘ ln ⇣ 1 C it W it ⌘ the empirical counterpart of the treatment variable [⌘ it ln(1 ⌫ t )].
We denote with C it the amount of CICE subsidy received and W it as total (gross) wagebill. 10 W 0 ↵ it includes a list of controls likely to drive the evolution of firm-level unit 10 We could have built the variable ⌘ it ln(1 ⌫ t ) using solely the DADS matched employer-employee, computing the wage share of eligible labor (⌘ it ) and applying the rate of subsidy ln(1 ⌫ t ). The resulting variable should be equal to our measure C it /W it -where the denominator is computed using the DADS dataset and the numerator comes from a special administrative files on claimed tax credits. Nevertheless it is only approximately true due to the fact that minor components of labor earning to which the tax credit do not apply are included in the DADS measure of wages -e.g. work-related expenses. We therefore prefer to use the C it /W it ratio. The variable ln(1 C it /W it ) is a very close counterpart to the variable relevant in the theoretical framework as both variables are equal up to a first-order approximation. Indeed we can see that ⌘ it ln(1 ⌫ t ) ⇡ ⌘ it ⌫ t where the first order approximation is costs, beyond the global evolution of the sector in France captured by FE st -which is a 3-digit sector ⇥ year fixed-e↵ect.

In order to causally assess the impact of the cut in payroll taxes, we use an instrumental variable Z it corresponding to lagged predicted amount received ⌘ i,t 1 ln(1 ⌫ it ), used either directly or as an instrument for D it , and constructed as

Z it = eligible wagebill i,t 1 wagebill i,t 1 ⇥ ln (1 ⌫ t ) , ( 12
)
where ⌫ t is the rate of payroll tax cut implied by the CICE policy, 4% in 2013, 6% since 2014.

OLS and IV results

Putting aside causality issues as a start, we first present regressions between the amount of subsidy received and export performance, that should be interpreted as correlations without taking a stance on the direction of causality. Results for several specifications are presented in Table 3.

The first three columns include all firms, while the last three limit attention to the set of firms considered far enough from the truncation point of profitable exports so that selection issues should be minimized. Those are the ones that serve continuously their markets over the entire sample period (2010)(2011)(2012)(2013)(2014)(2015) and belong to the top quartile of exporters in terms of number of destination. We experiment with di↵erent sets of fixed e↵ects and controls over columns. Columns (1), ( 2), ( 4) and ( 5) simply have sectoryear e↵ects, while columns (3) and ( 6) introduce destination-year e↵ects. The treatment intensity variable has the expected negative sign but is too noisy to be significant in all columns. The magnitude of the coe cient is also smaller than expected, given reasonable estimates of consumers' price elasticity and the share of labor in production costs.

We now turn to instrumented results, meant to provide a better assessment of the causal e↵ect of the subsidy. An example of endogeneity issue is the tendency of firms experiencing a boom in their exports to "share the rent" with workers through wage increases (see e.g. [START_REF] Carluccio | Trade, Wages and Collective Bargaining: Evidence from France[END_REF]. These wage increases directly impact the CICE treatment variable, which is a↵ected by the share of the wagebill under a certain threshold. This is only one of the many causes that could induce a correlation between the unobserved determinants of export performance (the error term of equation 11) and the subsidy received. Most of the endogeneity concerns suggest an attenuation bias. For instance, reverse causality could even be at work since a negative draw on export markets' taken around ⌫ t = 0 and that ln(1

C it /W it ) ⇡ C it /W it = ⌘ it ⌫ t
where the first order approximation is taken around C it /W it = 0. performance (losing a large contract for instance) could result in wage cuts, making the firm more eligible to CICE.

We therefore instrument the intensity of treatment by a variable that is using the wage structure of the firm before the policy was put in place. This IV is the level of subsidy that the firm was expected to receive from its historical wage distribution. Table 4 report results of the instrumented version of the regressions.

The coe cients obtained are both larger (in absolute value) and more statistically significant. The coe cients obtained for large firms (last 3 columns) are close to -1. Assuming a share of labor in total costs around 20 % implies a price elasticity of demand around 6, compatible with existing literature estimating this elasticity on firm-level exports [START_REF] Fontagné | The International Elasticity Puzzle Is Worse Than You Think[END_REF] being a recent example, particularly relevant since it estimates the trade elasticity using a cost shifter-electricity prices-on French exporters). Adding controls at the firm level and fixed e↵ects for destinations however reduces the magnitude and significance of the e↵ect. This points to a lack of robustness in the e↵ect of this policy on the intensive margin of exports.

Long-di↵erence regressions

We have failed at this point to detect robust e↵ects of the policy on export revenues. It is possible that the policy took time to be e↵ective if, for instance, firms used the subsidy to invest in quality upgrading or in an improvement of the production process. We estimate a slightly di↵erent specification from Equation (11) in order to allow for both time-varying e↵ects and potentially lagged e↵ects of the policy. We keep one observation per firm and project directly the change in export revenue with respect to 2012 for several di↵erent time horizons onto the average policy-induced labor cost variation between 2012 and 2015. As above, the actual policy-induced labor cost variation received is instrumented using the treatment as predicted by the 2012 wage structure. This method has the advantage of allowing for time-varying e↵ects and does not impose dynamic restrictions on the estimates [START_REF] Jordà | Estimation and inference of impulse responses by local projections[END_REF]Zidar, 2017). Results are presented in Table 5. Results are overall disappointing. In the largest sample, the magnitude of coe cients is comparable to the ones from Table 4, but estimates are noisy and sensitive to the period considered when estimating the e↵ect. In the sample focusing on large firms, which is our preferred one for the selection issues mentioned at the end of the theory section, we again find volatile e↵ects, with one coe cient even exhibiting a perverse positive sign.

To summarize, the policy under investigation has mostly shown no robust e↵ect of the intensive margin of exporting patterns. We cannot completely discard the possibility that this policy aimed at reducing labor costs has a delayed e↵ect being channeled through long-run investment decisions. However, with the data at hand, which is limited to 3 Notes: Each column corresponds to the same specification where only the horizon over which the growth of the dependent variable (average annual export growth) is computed varies (2012-2013 for the column 1 and 3, 2012-2014 for columns 2 and 5, 2012-2015 for columns 3 and 6). years post treatment, our results do not strongly point in that direction.

The variable ln

4.2.1

Were more profitable firms more reactive to the policy?

As explained in section 3.1, the CICE is a corporate income tax credit aiming at "mimicking" the e↵ects of a direct cut in payroll tax. Therefore, firms which do not report any taxable profits do not face the same incentives as the ones that can deduct from their corporate taxation the total amount they are entitled to. To enter the details of the policy: a firm with negative or near zero profits in year t does not benefit from the tax credit accrued based on its wagebill during year t 1 at year t but will instead need to wait until t + 1 in case it generates enough taxable income during that period. Firms that are not profitable at any point past t will have to wait for three years until the tax authorities transfer the amount of the tax credit to the firm.

In order to investigate the heterogeneity of e↵ects based on profitability, we introduce an interaction term between the intensity of treatment and a dummy variable which is set to one if the firm reported positive corporate income tax every year between 2010 and 2012 (T P i ). We expect this interaction term to have a negative sign, since it signals a larger impact of the policy for the firms that are likely to obtain the tax credit with the least lag. Results are somehow supportive of the idea that firms are sensitive to the lag between the payroll tax cut entitlement and its payment: all interaction terms are negative, although not significantly so. This points to the fact that the precise design of this type of policy matters: Blurring the connection between the labor cost determinants of the tax cut and the actual payment of the cut (through a delay in this case) seems to weaken the e↵ects of the policy.

Other Outcomes

The impact of the CICE policy on export prices

The overall absence of statistically significant impact of the policy could come from two main causes. The first is that the fall in labor costs is not (or incompletely) passed by firms into their export prices. In that case, the price competitiveness of firms benefiting from the policy would not be a↵ected. The second is that the price elasticity of demand is too low to enable detection of a statistically significant e↵ect.

Our data enables us to calculate unit values which is the best we can do to measure (f.o.b) export prices, dividing value exported by quantities (measured in tons in the customs files). Some (firm ⇥ destination) couples have no quantity available which explains why there is a slightly lower number of observations compared to regressions from Table 4. We first investigate the statistical association between export prices and the policy without looking for the direction of causality. Results are reported in Table 7, with the same set of specifications as in our benchmark on export values. The expected magnitude of the coe cient is quite intuitive. With constant markups, the pass-through elasticity of changes in costs should be one. Therefore, the expected impact on unit values should reflect the share of labor in total marginal costs of the firms. Results show that the response of prices to the amount of labor cost subsidy received depends upon the size of firms. In the full sample, the coe cients imply labor costs shares between 12 and 35% which is reasonable, but none of those e↵ects is significant. For larger firms, the implied shares are much lower, which is probably intuitive, but again the e↵ect is not statistically di↵erent from 0. In sum, the pass-through into export prices is weak at best. One interpretation is that signs and magnitudes of the volume and price e↵ects are coherent, and reasonably consistent with expectations, despite large amount of noise (perhaps due to the complex design of the policy). The other interpretation, is that firms did not consider this policy to be a "true" reduction in labor costs, that could translate into lower prices and large export volumes, explaining that we find no robust e↵ect at the intensive margin.

Impact on the extensive margin

It is possible (although unlikely and not fully consistent with the benchmark model of heterogeneous firms in trade) that the whole of the e↵ects of the evaluated policy took place at the extensive margin, i.e. boosting the entry rate of French firms on di↵erent export markets. In order to allow for a rich structure of fixed e↵ects that is needed in our context we use the Linear Probability Model (LPM) in order to investigate this extensive margin of adjustment to labor cost changes in first-di↵erence. Our dependent variable in the first two columns is identifying entry (1 if the firm did not export in t 1 and does in t, and 0 if it did not change status and -1 if it ceased to export between t 1 and t). The last two columns re-estimate the model in levels, where the LHS is the export status each year. We find again no statistical evidence of a change in export status that could be attributed to the change in labor costs.

(3) (4) I(X it > 0) I(X it > 0) I(X it > 0) I(X it > 0) ln 1 C W it (2)

Comparing ex-post and ex-ante analysis

As an alternative to the ex-post analysis conducted until now, we consider the following ex-ante approach: 1) estimate the impact of unit labor costs on exports in the period immediately preceding the treatment (2010-2012), 2) combining those estimates with the percent change in the labor costs implied by the CICE policy, one can predict what is the expected change in export values linked to the policy. We proceed with step 1 following closely the approach by [START_REF] Decramer | How do exporters react to changes in cost competitiveness?[END_REF], with the LHS being the change in logged export values, and the RHS being the change in unit labor costs (measured as wagebill over value added of the firm).11

Table 9 reports results and contrary to preceding tables, the overall picture is one of negative significant e↵ect of unit labor costs on export patterns. The elasticities are quite robust in significance and magnitude over di↵erent specifications ranging from 17 to 20%. Column (4), which is the most comparable to the specification of [START_REF] Decramer | How do exporters react to changes in cost competitiveness?[END_REF], finds an elasticity of -0.20. Those coe cients are strikingly close to those obtained by [START_REF] Decramer | How do exporters react to changes in cost competitiveness?[END_REF], who also find -0.2 for manufacturing Belgian exporters between 1999 and 2010. 12 We can calculate the "mechanical" fall in labor costs due to the CICE policy by removing the received subsidy from the total wagebill. This reduction in the unit labor costs was around 1.9 % on average in our intensive margin sample between 2012 and 2013. Using this fall combined with coe cients from Table 9, one can quantify that the policy was ex-ante predicted to have a large e↵ect on exports, raising its average growth rate by 0.34 percentage points between 2012 and 2013.

It is therefore a case where the ex-ante and ex-post analysis of a policy measure di↵er dramatically. In our view, those contrasting results suggest a need for careful interpretation of ex-ante approaches, in particular in terms of identification of the e↵ect that is used in the first step and its relevance for the actual policy carried over.13

Conclusion

Our paper investigates the impact of a change in labor costs on export patterns. Using a large panel of French firms, we use a recent policy experiment where a share of gross wages is reimbursed to firms via a tax credit. Firms are treated according to a threshold applied to each employees' compensation. We use the variation in treatment implied by this rule to assess whether export values and/or the probability of participating in export markets is a↵ected by labor costs.

We first find a negative albeit insignificant correlation between exported values and the intensity of policy treatment. This could be explained by issues of reverse causality, whereby firms experiencing negative demand shocks lower their employees' wage rate and therefore are targeted more generously by the tax credit. However, our instrumentation strategy also points to statistically insignificant e↵ects. Essentially, signs and magnitudes of our estimates are as expected, but very noisy. This lack of precision is not related to a weak first-stage as our instrument is strongly predictive of the actual treatment. There are in our view two interpretations.

First, while our instrument solves the issue of reverse causation between the outcome and the policy treatment, it does not solve entirely the issue of unobserved heterogeneity. Time-varying controls and allowing sectors to be flexibly a↵ected by the business cycle is the best we can do on that front but might still be insu cient. The second interpretation is that the policy itself failed to deliver the expected e↵ect of a cut in labor cost. This could be explained by the complex design of the policy which took the form of a tax credit rather than a direct cut in payroll taxes.

We note that the transformation of the CICE from a tax credit into a payroll tax cut has been quite consensual among both government o cials and employers' representatives. We interpret this convergence in opinions as evidence supporting the second interpretation. The likely transformation of the policy, due to take place in 2019, should o↵er a nice setup for future research to disentangle the respective influence of research

Figure 1 :

 1 Figure 1: The schedule of the 2014 CICE and of pre-existing payroll tax cuts

Figure 2 :

 2 Figure 2: The distribution of CICE-implied variation in labor cost

Figure 3 :

 3 Figure 3: Initially export-oriented firms were less exposed to the policy -2014

Figure 4 :

 4 Figure 4: First stage : among continuing exporters and among all firms

  xt ⌘ xt+1 xt. * : p<0.10, ** : p<0.05, *** : p<0.01. Our explanatory variable of interest (actual or instrumented) measures the change in labor costs implied by the CICE policy. The expected sign is therefore negative: a rise in labor cost should reduce exports. The balanced sample covers the years 2012 to 2014 (two period with first di↵erences). K-P Statistic refers to the Kleibergen-Paap statistic for the first stage.

  decline in labor cost implied by the policy based over the years 2012-2015. It is instrumented by [⌘2012 12 15ln(1 ⌫)] which represents the average decline in labor cost implied by the policy based on 2012 wage structure over the years 2012-2015.

  metal products, except machinery and equipment ; 13 Manufacture of textiles ; 23 Manufacture of other non-metallic mineral products ; 29 Manufacture of motor vehicles, trailers and semi-trailers ; 15 Manufacture of leather and related products ; 22 Manufacture of rubber and plastic products ; 24 Manufacture of basic metals ; 30 Manufacture of other transport equipment ; 14 Manufacture of wearing apparel ; 17 Manufacture of paper and paper products ; 32 Other manufacturing ; 28 Manufacture of machinery and equipment n.e.c. ; 11 Manufacture of beverages ; 27 Manufacture of electrical equipment ; 20 Manufacture of chemicals and chemical products ; 26 Manufacture of computer, electronic and optical products ; 21 Manufacture of basic pharmaceutical products and pharmaceutical preparations ; 12 Manufacture of tobacco products ; 19 Manufacture of coke and refined petroleum products. Source: NACE Rev. 2: Statistical Classification of Economic Activities in the European Community.

Table 1 :

 1 Descriptive statistics: Intensive margin sample Notes: The sample includes all firms eligible for the CICE program which are reporting positive exports every year between 2010 and 2015. All monetary variables (value of exports, value-added, wages) are expressed in current euros.

		mean	sd	p50	p5	p95
	CICE over wagebill = C it W it	0.036	0.017	0.037	0.000	0.060
	Export over sales	0.250	3.102	0.124	0.003	0.788
	ln(Exports per worker)	2.242	1.954	2.480	-1.293	4.915
	ln VA per worker	11.028	0.526	11.000	10.322	11.859
	ln Assets	14.588	1.970	14.431	11.610	18.105
	ln Av. wage	10.481	0.285	10.447	10.118	10.944
	ln Hours	10.873	1.447	10.812	8.629	13.389
	# markets served (per year)	13.578	16.604	7.000	1.000	48.000
	Observations	82998

Table 2 :

 2 Descriptive statistics: Extensive margin sample

			mean	sd	p50	p5	p95
	CICE/Wage bill	0.041	0.019	0.041	0.000	0.066
	I(X	it > 0)	0.372	0.483	0.000	0.000	1.000
	ln VA per worker	10.905	0.521	10.882	10.195	11.728
	ln Assets	13.167	1.829	12.924	10.607	16.570
	ln Av. wage	10.427	0.348	10.393	9.964	11.016
	ln Hours	9.698	1.450	9.567	7.549	12.317
	Observations	280950
	Notes: The sample includes all firms eligible for the CICE program which are observed every year between 2010 and
	2015, irrespectively whether they export or not. All monetary variables (value of exports, value-added, wages) are
	expressed in current euros.

Table 3 :

 3 Received CICE and exports (OLS) : p<0.10, ** : p<0.05, *** : p<0.01. Our explanatory variable of interest (actual or instrumented) measures the change in labor costs implied by the CICE policy. The expected sign is therefore negative: a rise in labor cost should reduce exports. The balanced sample covers the years 2012 to 2014 (two period with first di↵erences).

									All firms			Large firms
							(1)		(2)		(3)		(4)	(5)	(6)
							ln x	int	ln x	int	ln x	int	ln x	int	ln x	int	ln x	int
	ln 1 C				-0.239	-0.193	-0.198	-0.190	-0.146	-0.144
	W	it		(0.172)	(0.173)	(0.172)	(0.200) (0.200) (0.199)
	ln VA per worker	i,t 1			0.0122	0.0118	0.0239* 0.0239*
									(0.00970) (0.00971)	(0.0123) (0.0123)
	ln Assets	i,t 1				0.0792*** 0.0796***	0.0502*** 0.0511***
									(0.0124) (0.0124)	(0.0170) (0.0170)
	ln Av. wage	i,t 1				0.00868	0.00919	-0.0264 -0.0255
									(0.0372) (0.0372)	(0.0606) (0.0601)
	ln Hours	i,t 1				0.0620*** 0.0613***	0.0302	0.0294
									(0.0211) (0.0210)	(0.0290) (0.0287)
	Observations				758142	604573	604544	419503	331990	331950
	R 2 Year ⇥ Sector FE Destination ⇥ Year FEs # firms	0.002 p 13829	0.002 p 13788	0.006 p p 13788	0.005 p 4807	0.003 p 4795	0.010 p p 4795

Notes: Robust standard errors reported in parentheses (clustered at the firm level).

xt ⌘ xt+1 xt. *

Table 4 :

 4 Received CICE and exports (IV)

									All firms			Large firms
							(1)		(2)		(3)		(4)	(5)	(6)
							ln x	int	ln x	int	ln x	int	ln x	int	ln x	int	ln x	int
	ln 1 C				-0.968	-0.701	-0.557	-1.397** -0.902	-0.809
	W	it		(0.680)	(0.684)	(0.693)	(0.698) (0.713) (0.723)
	ln VA per worker	i,t 1			0.0124	0.0119	0.0241* 0.0241*
									(0.00970) (0.00971)	(0.0123) (0.0123)
	ln Assets	i,t 1				0.0787*** 0.0793***	0.0498*** 0.0507***
									(0.0124) (0.0124)	(0.0168) (0.0169)
	ln Av. wage	i,t 1				0.00900	0.00941	-0.0259 -0.0250
									(0.0373) (0.0373)	(0.0609) (0.0603)
	ln Hours	i,t 1				0.0621*** 0.0614***	0.0303	0.0295
									(0.0211) (0.0210)	(0.0291) (0.0287)
	Observations				611449	604573	604544	335603	331990	331950
	R 2 Year ⇥ Sector FE Destination ⇥ Year FEs First Stage Coe↵	0.002 p 0.571*** 0.578*** 0.570*** 0.614*** 0.622*** 0.616*** 0.002 0.006 0.003 0.003 0.010 p p p p p p p
							(0.0177) (0.0175) (0.0177) (0.0242) (0.0241) (0.0242)
	K-P stat						1039	1089	1041	645	667	646
	# firms						13827	13788	13788	4807	4795	4795

Notes: Robust standard errors reported in parentheses (clustered at the firm level).

Table 5 :

 5 Long di↵erences: IV estimates

							All firms		Large firms
						(1)	(2)	(3)	(4)	(5)	(6)
						ln x0 12, 0 13	ln x0 12, 0 14	ln x0 12, 0 15	ln x0 12, 0 13	ln x0 12, 0 14	ln x0 12, 0 15
	ln 1 C W 12,15		-0.816	-1.138*	-0.423	-0.614	-0.708	0.297
						(0.504)	(0.621)	(0.754)	(0.520)	(0.696)	(0.897)
	ln VA per worker	i,t 1	-0.00509	0.00250	-0.00688	0.0216	-0.00119	0.00313
						(0.0189)	(0.0220)	(0.0243)	(0.0191)	(0.0264)	(0.0325)
	ln Assets	i,t 1		0.105***	0.170***	0.178***	0.0528*	0.133***	0.173***
						(0.0269)	(0.0331)	(0.0410)	(0.0282)	(0.0370)	(0.0490)
	ln Av. wage	i,t 1		0.0818**	0.114**	0.130**	0.0290	0.0802	0.0448
						(0.0392)	(0.0451)	(0.0529)	(0.0433)	(0.0507)	(0.0624)
	ln Hours	i,t 1		0.0772**	0.136***	0.170***	0.0449	0.0981**	0.132**
						(0.0390)	(0.0454)	(0.0550)	(0.0357)	(0.0452)	(0.0539)
	Observations			150837	134238	129502	83090	83090	83090
	R 2 Year ⇥ Sector FE Destination ⇥ Year FEs K-P stat	0.005 p p 5436	0.008 p p 5158	0.014 p p 5052	0.006 p p 2805	0.009 p p 2805	0.019 p p 2805
	# firms					13487	13238	13089	4752	4752	4752

Table 6 :

 6 Received CICE and exports (IV), heterogeneity based on profitability Our explanatory variable of interest (actual or instrumented) measures the change in labor costs implied by the CICE policy. The expected sign is therefore negative: a rise in labor cost should reduce exports. The balanced sample covers the years 2012 to 2014 (two period with first di↵erences). K-P Statistic refers to the Kleibergen-Paap statistic for the first stage. T P is a binary variable equal to 1 if the firm reported positive corporate income tax during every year between 2010 and 2012. It does not vary over time and is therefore omitted in columns (4) and (6).

										All firms		Large firms
								(1)		(2)		(3)	(4)	(5)	(6)
								ln x	int	ln x	int	ln x	int	ln x	int	ln x	int	ln x	int
	T P	i ⇥ ln 1 C W	it	-0.0689 (0.330)	-0.0793 (0.331)	-0.0548 (0.331)	-0.165 (0.389)	-0.242 (0.389)	-0.239 (0.390)
	ln 1 C				-1.079	-0.801	-0.669	-1.486** -0.962	-0.865
		W	it		(0.688)	(0.693)	(0.701)	(0.713)	(0.729)	(0.739)
	T P	i						0.0219*** 0.0192*** 0.0203*** 0.0261*** 0.0230*** 0.0233***
								(0.00537) (0.00532) (0.00532) (0.00583) (0.00577) (0.00578)
	ln VA per worker	i,t 1			0.0133	0.0129	0.0250** 0.0250**
										(0.00967) (0.00968)	(0.0123) (0.0123)
	ln Assets	i,t 1				0.0772*** 0.0777***	0.0473*** 0.0482***
										(0.0123) (0.0123)	(0.0165) (0.0166)
	ln Av. wage	i,t 1				0.00704	0.00735	-0.0284	-0.0275
										(0.0373) (0.0373)	(0.0608) (0.0603)
	ln Hours	i,t 1				0.0603*** 0.0594***	0.0279	0.0271
										(0.0209) (0.0207)	(0.0287) (0.0284)
	Observations				611449	604573	604544	335603	331990	331950
	R 2 Year ⇥ Sector FE Destination ⇥ Year FEs K-P stat	0.002 p 513	0.002 p 536	0.006 p p 513	0.003 p 318	0.003 p 327	0.010 p p 318
	# firms						13827	13788	13788	4807	4795	4795
	Notes: Robust standard errors reported in parentheses (clustered at the firm level). xt ⌘ xt+1 xt. * : p<0.10, ** : p<0.05, ***
	: p<0.01.

Table 7 :

 7 Received CICE and unit values (IV)

									All firms			Large firms
							(1)		(2)		(3)		(4)	(5)	(6)
							ln UV	int	ln UV	int	ln UV	int	ln UV	int	ln UV	int	ln UV	int
	ln 1 C				0.123		0.352		0.341		-0.141	0.0741	0.0637
	W	it		(0.423)	(0.421)	(0.427)	(0.431)	(0.439)	(0.444)
	ln VA per worker	it			-0.00820	-0.00813	-0.00354	-0.00374
									(0.00631) (0.00632)	(0.00678) (0.00679)
	ln Assets	it						0.00222	0.00220	-0.00298	-0.00269
									(0.00741) (0.00741)	(0.00812) (0.00810)
	ln Av. wage	it				-0.0168	-0.0173	-0.0313	-0.0311
									(0.0152)	(0.0153)	(0.0202)	(0.0205)
	ln Hours	it						-0.00798	-0.00828	-0.0148	-0.0153
									(0.00767) (0.00772)	(0.00962) (0.00974)
	Observations				535759	529942	529914	344718	341250	341208
	R 2 Year ⇥ Sector FE Destination ⇥ Year FEs # firms	0.002 p 11356	0.002 p 11323	0.004 p p 11323	0.003 p 5904	0.003 p 5889	0.005 p p 5889
	K-P stat						858		910		884		705	732	716

Notes: Robust standard errors reported in parentheses (clustered at the firm level). xt ⌘ xt+1 xt. * : p<0.10, ** : p<0.05, *** : p<0.01. Our explanatory variable of interest (actual or instrumented) measures the change in labor costs implied by the CICE policy. The expected sign is therefore negative: a rise in labor cost should reduce exports. The balanced sample covers the years 2012 to 2014 (two period with first di↵erences).

Table 8 :

 8 Received CICE and export probability (IV)

	First Di↵. model	Fixed e↵ect model
	(1)

  : p<0.10, ** : p<0.05, *** : p<0.01. Our explanatory variable of interest (actual or instrumented) measures the change in labor costs implied by the CICE policy. The expected sign is therefore negative: a rise in labor cost should reduce exports. Controls include VA per worker, value of assets, average wage and total hours workers in the firm (lagged and log).

		.133	0.0496	0.247	0.195
		(0.285)	(0.282)	(0.153)	(0.152)
	Observations	187300	183314	234125	230477
	R 2 Year ⇥ Sector FEs Controls Firm FEs	0.002 p	0.002 p p	0.876 p p	0.877 p p p
	K-P stat	2583	2679	12678	13071
	# firms	46825	46544	46825	46584

Notes: Robust standard errors reported in parentheses (clustered at the firm level). xt ⌘ x t+1 xt. *

Table 9 :

 9 Unit labor cost and exports (2010-2012) Notes: Robust standard errors reported in parentheses (clustered at the firm level). xt ⌘ x t+1 xt. * : p<0.10, ** : p<0.05, *** : p<0.01. Our explanatory variable is defined as the log of labor compensation over valued-added. The expected sign is therefore negative: a rise in labor cost should reduce exports. The balanced sample covers the years 2010 to 2012. Exports are aggregated at the firm-year level in level before computing the logarithm.

		(1)		(2)		(3)		(5)
		ln x	it	ln x	it	ln x	it	ln x	it
	ln(unit labor cost)	-0.171***	-0.170***	-0.168***	-0.200***
	Year FEs Sector FEs Year ⇥ Sector FEs Controls	(0.0152) p	(0.0152) p p	(0.0152) p	(0.0196) p p

The current US administration has mostly motivated its repeal of pre-existing environmental regulations on the ground of their supposed direct negative employment impact on the energy sector (Volcovici and Mason

, 2017). There is a substantial evidence suggesting that environmental regulations, while possibly socially desirable, can reduce manufacturing industry's competitiveness (see e.g.[START_REF] Greenstone | The E↵ects of Environmental Regulation on the Competitiveness of U.S. Manufacturing[END_REF] and trigger substantial displacement and reallocation of jobs across sectors(Walker, 2013).

It is telling that the initial recommendations of the report inspiring the policy were quite di↵erent, and in particular wanted to set a much higher wage threshold and target manufacturing, so as to maximize the benefits expected by the already large exporters (seeFabre, 2012, as well section

3.1 for an overview of the state of the debate as the legislative process was ongoing).

This corresponds to a central value inBas et al. (2017) estimates on French exporters.[START_REF] Head | Gravity equations: Workhorse, toolkit, and cookbook[END_REF] report 5.03 as a median value of such elasticities in the gravity literature.

This approach was adopted in[START_REF] Mulligan | Selection, investment, and women's relative wages over time[END_REF] when studying gender bias in the labor market.[START_REF] Fitzgerald | Exporters and Shocks[END_REF] and[START_REF] Paravisini | Dissecting the e↵ect of credit supply on trade: Evidence from matched credit-export data[END_REF] apply this method in the context of firm-level trade. The generalized Tobit approach proposed by[START_REF] Eaton | Trade in capital goods[END_REF] and applied by[START_REF] Crozet | Quality Sorting and Trade: Firm-level Evidence for French Wine[END_REF] to French exporters could be envisioned. However, the current state of this technique does not easily allow for panel data, which is central in our paper.

The profit rate (defined as ratio of gross operating surplus to value added) was at 30.25% in 2012, a figure lower than in previous years (31.7% over the years 2008-2011 and 32.63% for the years 2000-2010. Source: INSEE, Comptes nationaux).

A small share of firms seem to have received more tax credit than the maximum possible, which reflects some noise in the reporting of either the gross wagebill or of the amount of CICE received.

A very similar relationship holds for 2013 as is displayed in FigureA1in the appendix.

Note that we aggregate exports across destinations at the firm and year level in order to make our specification as comparable as possible to[START_REF] Decramer | How do exporters react to changes in cost competitiveness?[END_REF]. We refer precisely to their Table6, panel a, where the dependent variable is the same as ours.

We also ran this type of regressions for the years 1995 to 2010 on French data and found very comparable estimates.

In preceding versions of our paper, we conducted the ex-post analysis aggregating exports across destinations at the firm-year level. This does not improve the match between ex-post and ex-ante analysis in any discernible way.

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Acknowledgements

This work is supported by a public grant overseen by the French National Research Agency (ANR) as part of the ``Investissements d'Avenir'' program within the framework of the LIEPP center of excellence (ANR11LABX0091, ANR 11 IDEX000502). This work is supported by a public grant overseen by the French National Research Agency (ANR) as part of the ``Investissements d'avenir'' program (reference : ANR10EQPX17, Centre d'accès sécurisé aux données CASD). This research has received funding from the European Research Council (ERC) under the Grant Agreement No. 313522. The views expressed here are those of the authors only and do not necessarily reflect the views of the Banque de France or the Eurosystem. We thank two anonymous referees as well as the editor for very helpful comments.

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This Discussion Paper is issued under the auspices of the Centre's research programme in INTERNATIONAL TRADE AND REGIONAL ECONOMICS. Any opinions expressed here are those of the author(s) and not those of the Centre for Economic Policy Research. Research disseminated by CEPR may include views on policy, but the Centre itself takes no institutional policy positions.

The Centre for Economic Policy Research was established in 1983 as an educational charity, to promote independent analysis and public discussion of open ⇤ This work is supported by a public grant overseen by the French National Research Agency (ANR) as part of the "Investissements d'Avenir" program within the framework of the LIEPP center of excellence (ANR11LABX0091, ANR 11 IDEX000502). This work is supported by a public grant overseen by the French National Research Agency (ANR) as part of the "Investissements d'avenir" program (reference : ANR10EQPX17, Centre d'accès sécurisé aux données CASD). This research has received funding from the European Research Council (ERC) under the Grant Agreement No. 313522. The views expressed here are those of the authors only and do not necessarily reflect the views of the Banque de France or the Eurosystem. We thank two anonymous referees as well as the editor for very helpful comments.

Exports and labor costs: Evidence from a French Policy. ⇤ versus policy design on the disappointing estimated results of the policy.