Second, in the case where a shock affects one means of payment, I expect no significant difference between merchants with similar characteristics (i.e., ∆ _i, jSt_ +2 = 0) but a strong substitution between payment methods for the merchants with this method (i.e., ∆ _i, jSt_<sup>_card_</sup> +2<sup>=</sup><sup>_−_∆</sup><sup>_i,jS_</sup> _t_<sup>_cash_</sup> +2<sup>_>_0).The</sup> increase in the contactless payment limit should therefore replace the sales from the other payment methods towards this payment method. However, if ∆ _i, jSt_<sup>_card_</sup> +2<sup>_>_0 and ∆</sup><sup>_i,jS_</sup> _t_<sup>_card_</sup> +1<sup>_>_0, in addition to the</sup> first shock that shows the resilience of merchants with contactless technology to the global shock, the increase of the contactless payment limit allows these merchants to make more new sales and significantly increases substitution between card and cash sales. To estimate the impact that can be exclusively attributed to the second shock, we have to substrate the impact of the previous shock due to the fact that the latter may also influence the next one. Hence, if (∆ _i, jSt_<sup>_card_</sup> +2<sup>_−_∆</sup><sup>_S_</sup> _t_<sup>_NewClient card_</sup> +2 ) - (∆ _i, jSt_<sup>_card_</sup> +1<sup>_−_∆</sup><sup>_i,jS_</sup> _t_<sup>_NewClient card_</sup> +1 ) _>_ 0 there is a sharp substitution between card and cash technologies that can be exclusively attributed the the second shock. The increase of the contactless payment limit may substitute contact payment to contactless payment. Moreover, it is possible to estimate the substitution between card payment methods. If for instance _Si_<sup>_contact_</sup> _,t_ +2<sup>_−Scontact_</sup> _j,t_ +2<sup>_<_0 and</sup><sup>_S_</sup> _i_<sup>_card_</sup> _,t_ +2<sup>_−Scard_</sup> _j,t_ +2<sup>_>_0,</sup> then a negative externality occurs, and the merchants gain lower sales from contact card payments while still gaining from the shock via a cannibalization between contact and contactless payments. Finally, note that if ∆ _i, jSt_<sup>_card_</sup> +3<sup>_−_∆</sup><sup>_i,jS_</sup> _t_<sup>_card_</sup> +2<sup>_>_0, after removing the effects of previous shocks that affect</sup> the whole market and one of means of payment, the second shock as a whole increases the sales of merchants contactless payment relative to those without. This highlights the ability of merchants with the latest technology to mitigate the effect of a second shock that impacts the whole economy.

Using card-sales transactions data, score matching and difference-in-differences methods, I propose in the next section to study the resilience of merchant with contactless payment to three shocks that happened in 2020 in France and then to estimate the substitution between payment methods. I intend to compare merchants who do contactless transactions to those who do only contact payment, with similar observable characteristics.

# **2.3 Raw Data and Sample Design**

Thanks to a partnership with Cartes Bancaires CB, I have access to a unique data set on card-sales transactions for all merchants in France from 2019:01 to 2020:12. Created 1984 by the French banks, Cartes Bancaires CB is one of the leading schemes in France with 73 million CB cards and 2 million CB-affiliated merchants. It collects the CB card transactions for all CB merchants including 9