Thanks for your comments.
1. This is a fair point. In the Supplemental Material, we explore cross-country differences in email usage. When we statistically adjust for country-level differences in email usage (using World Bank data), the country ranking remains essentially the same (adjusted rankings correlate over 0.90 with non-adjusted rankings). Also, when you restrict the data only to drop-offs performed at hotels -- which tend to rely on email more than other settings -- you see the same pattern of results.
2. Also a good point. However, there are mechanical problems with using the marginal differences between conditions -- for example, countries with high reporting rates in the NoMoney condition will be naturally capped in the possible size of the treatment treatment effect, compared to those with low reporting rates. Because the scale is bounded at 0 and 100% you're also fighting against reversion to the mean at the low and high ends of the distribution. FWIW we find that absolute levels of reporting rates correlate very highly with other known proxies of honesty both within and between countries (measures like tax evasion, corruption, etc), whereas relative differences between conditions do not.
3. We explicitly test this by randomly varying whether the wallets contained a key or not (valuable to the owner but not the recipient), while holding the rest of the contents in the wallet constant.