**Table 5: Conditional associations between (in)formality and performance with and without controls**

|log pro|ductivity||log sales||log total|no. of worki|ng people|cu|stomers abr|oad|
|---|---|---|---|---|---|---|---|---|---|---|
|No<br>controls|Controls A|No<br>controls|Controls A|Controls B|No<br>controls|Controls A|Controls B|No<br>controls|Controls A|Controls B|
|1.289***|0.500***|1.824***|0.829***|0.362***|0.639***|0.344***|0.375***|0.155***|0.0593**|0.0500*|
|(0.369)<br>[0.144]<br>Normalized<br>*** p<0.01|(0.141)<br>[0.151]<br>beta coeffi<br>, ** p<0.05,|(0.469)<br>[0.151]<br>cients in pa<br>* p<0.1|(0.211)<br>[0.154]<br>rentheses. S|(0.0935)<br>[0.0712]<br>tandard err|(0.430)<br>[0.0593]<br>ors in squa|(0.230)<br>[0.0601]<br>re brackets.|(0.251)<br>[0.0603]|(0.254)<br>[0.0261]|(0.0957)<br>[0.0268]|(0.0814)<br>[0.0270]|

The results show substantial decreases in the regression coefficients when additional controls are included. In the case of log productivity, the case of no controls shows a gap of 1.29 log points between the mean productivity of formal and informal firms; addition of controls A reduces the gap to 0.5 log points.<sup>13</sup> In the case of log sales, a gap of 1.8 log points is reduced to 0.83 log points under controls A and to 0.36 log points under controls B. In the case of total number of working people, the difference is reduced from 0.64 log points to 0.34-0.38 depending on whether log productivity is included among the controls. In the case of customers abroad, the difference in the probability of exporting drops from 16 percent to 5 percent, and in fact the latter is significant only at the level of 10 percent. These results suggest significant selection effects in the case of all performance variables.

A more direct way to improve our understanding of the relative weights of selection effects relative to the existence of a causal effect of informality (i.e., the existence of an informality trap) is to create samples of formal and informal firms that are “similar” and compare the performance variables across these otherwise similar samples. The propensity score inverse probability weighting (IPW) estimator is used to assess the degree to which the performance gaps may be due to informality itself. The procedure first estimates a probit model where covariates are used to predict informality and the predicted probability (the propensity score) is used to weight observations to make them similar.<sup>14</sup> Then, the weighted samples of formal and informal firms are used to calculate the mean difference in the performance variables.

The covariates used in the probit model are similar to the ones used in the discussion of correlates of informality below (see section 4.2). Log productivity is both a key performance variable as well as a key driver of selection into formality, as emphasized by Ulyssea. The use of an outcome variable in constructing a propensity score is clearly problematic in cross section data. Since the purpose here is exploratory, two models are used to predict propensity scores. In the first model, log productivity is not

> deviation of 1, which facilitates comparison across different explanatory variables. As such, they measure how many standard deviations the left-hand side variable changes in response to a standard deviation change in a right-hand side variable. 13 The magnitude of the reduction is assessed in the following way:  The coefficient on the informality variable is equal to the difference in the means of log productivity of formal and informal firms. The exponentiated value of the coefficient in turn is equal to the ratio of the geometric means of productivity in formal and informal firms. This means that without any controls, the (unconditional) ratio of the geometric mean of productivity among formal firms to that of informal firms is 3.63 (exp (1.289)= 3.63). Once controls A are introduced, the (conditional) ratio of geometric means for the two groups is reduced to 1.65 (exp(0.50)= 1.65). Hence the presence of covariates reduces the ratio by almost 55 percent ((3.63-1.65)/3.63= 0.55).  Similar calculations show that for sales, the ratio of geometric means is reduced by 77 percent when controls B are introduced, relative to the case where there are no controls. For the case of total number of working people, the reduction is lower, about 24 percent. The effect of covariates on the share of firms with customers abroad is more straightforward to calculate: the difference in the shares is reduced from 16 percentage points to about 5 percentage points: a reduction of 10 percentage points corresponds to about 68 percent of the level of the gap with no controls ((15.5-5.0)/15.5= 0.68).

> 14 Specifically, if the estimated propensity score for observation i is pi, to calculate the “average treatment effect on the treated (ATET)” observations of formal firms are weighted by pi/(1-pi) and those of the informal firms are weighted by 1.

15