country.<sup>17</sup> The operator ∆indicates the change between 2006 and 2009. The remaining variables are controls: **B** _i_ is a vector of covariates specific to bank _i_ , and **C** _k_ a vector of additional controls specific to home country _k_ . _ηj_ represents a host country fixed effect, which can be interpreted as capturing (time-invariant) demand-side conditions in country _j_ . _δ_ is our key coefficient of interest: the extent to which the crisis experience of the bank’s home country conditions its lending activity. Finally, _εijk_ is an idiosyncratic error term, which we cluster at the host country level. Our robustness checks reproduce this basic regression in (1), while modifying the selection of control variables populating **B** and **C** , in order to investigate the sensitivity of _δ_ .

A major concern of estimating (1) is the possibility of endogeneity. In the construction of _crisisXP_ , we consider only crises anterior to 2006, to limit simultaneity bias. Nevertheless, endogeneity problems may also result from omitted variables and, more crucially, selection. For instance, countries historically endowed with high-quality institutions may tend to be more resilient to crises in general, but institutional quality can concurrently influence the development of the finance and banking sector of a country; yet observable measures of institutional quality may fail to fully capture this heterogeneity. Banks in countries with a rich history of crises may also systematically differ from those that are not based in such economies, in a way that is not encompassed by the learning effect.

It is therefore necessary to rely on instrumental variable estimates that correct for such endogeneity concerns. We exploit the time variation that exists between the current and the last year in which a currency, stock market, domestic debt, and banking crisis occurred, and use this vector of elapsed time as instruments for the crisis experience variable. Our first stage IV thus estimates: where _λ_ is a constant, **crisisET** _k_ is the vector of excluded instruments (elapsed time since the last currency, domestic debt, stock market, and banking crisis in country _k_ ), and _Ik_ the vector of included instruments (controls from the second-stage baseline). _μk_ is an idiosyncratic error term � clustered at the host country level. The predicted _crisisXP k_ then substitutes the actual _crisesXPk_ in the second stage, analogous to (1), and this new estimate of _δ_ now measures the (local average) learning effect.<sup>18</sup> As in the baseline, we modify the selection of controls in order to analyze the sensitivity of the IV estimates to alternative instrument sets.

> 17Data constraints imply that our key explanatory variable (crisis experience) is in a distinct ontological unit from our dependent variable (bank lending). We believe, however, that such concerns fall short of an outright ecological fallacy. First, it is useful to recall that the country-level crisis variable was constructed by observing the performance of the banks in any given country. Second, while we are indeed drawing inferences about bank experience on the basis of more aggregate data, our claims regarding the relevance of the learning effect are actually tested, rather than simply asserted. Finally, while we regard the main transmission mechanism for learning as occurring within the institution of the bank, the possibility that changes in lending result from country-level institutional transfer does not negate our hypothesis that learning occurs from greater experience with crises.

> 18Strictly speaking, our crisis experience measure is continuous rather than binary, and so referring to _δ_ as capturing a local average treatment effect (LATE) is somewhat of a misnomer. Nevertheless, we wish to stress the fact that the estimate applies only to economies that have nonzero crisis experience (the local effect), and that we are ultimately capturing only the influence of learning on average (the average effect).

13