Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
We will test each of our three main hypotheses by means of a two-prong approach. The first approach is more conservative, and it is based on non-parametric two-tailed Wilcoxon Mann-Whitney tests on the difference of the distribution of the outcomes of interest, between treatments. The unit of observation here is the average outcome per matching group, across all rounds, thus we have 48 observations in total. This allows us to detect an effect of 0.85 of a s.d. with α=0.05 and (1-β)=0.8. Based on the data collected by Bigoni et al. (2017), this corresponds to a difference of 3 p.p. in the share of pairs who enter renegotiation when an exogenous shock takes place (HP1), a difference of 5 p.p. in the rate of success of renegotiation (HP2), and a difference of 0.9 units (out of 20) in the surplus allocated to the Seller in the renegotiation stage, when renegotiation is successful
The second approach relies on the panel structure of our dataset and allows us to control for the learning dynamics across periods. Based on the simulations obtained via the Stata pc_simulate package (Burlig et al., 2020), this allows us to detect a variation of 4 p.p. in the share of pairs who enter renegotiation when an exogenous shock takes place (HP1), a difference of 6 p.p. in the rate of success of renegotiation (HP2), and a difference of 0.9 units (out of 20) in the surplus allocated to the Seller in the renegotiation stage, when renegotiation is successful, with α=0.05 and (1-β)=0.8.