̃ ̃ ̃ _β_ 1 = 0 and _β_ 1 + _β_ 3 = 0. The disadvantage of this more flexible form is statistical power, especially with three treatment arms.<sup>55</sup> We are also interested in correcting for the average bias in survey-based treatment effects, which we get from _β_ 1 from equation 2. But the more flexible form provides insight into the patterns of measurement error. For instance, if there is a general desirability bias in the survey, then _β_<sup> ̃</sup> 0 + _β_<sup> ̃</sup> 2 _<_ 1, whereas if underreporting is concentrated among men who commit crimes and were treated, then _β_<sup> ̃</sup> 1 + _β_<sup> ̃</sup> 3 _<_ 0.<sup>56</sup>

**Results for sensitive behaviors** We estimate equations 2 and 3 in Table 10. For sensitive behaviors, almost none of the coefficients on treatment indicators or interactions are statistically significant. We see little evidence of the therapy inducing a desirability bias, and indeed the effects run in the opposite direction.

Indeed, looking at the index of four sensitive measures (Panel (a), Column 5), _β_ 1 is actually greater than zero for therapy and therapy plus cash, implying that the impacts of therapy are, if anything, larger than the survey data imply. Appendix F displays these updated treatment effects. For example, using survey data alone, the treatment effect (standard error) of therapy and cash on the sensitive behaviors index is -0.4 (0.09), a 36% decrease. The results from Panel (a), Column 5 suggest that the adjusted treatment effect should be -0.516 (.194), significant at the 1% level.

The results of the more flexible regression in Panel (b), Column 5 shows that these averages conceal important heterogeneity. Treated men who we think did not engage in the sensitive behaviors tend to over-report them ( _β_<sup> ̃</sup> 1<sup>_Both_</sup> _>_ 0), and treated men engaged in the sensitive behaviors seem to under-report them ( _β_<sup> ̃</sup> 1<sup>_Both_</sup> + _β_<sup> ̃</sup> 3<sup>_Both_</sup> _<_ 0).<sup>57</sup>

**Results for expenditures** All treatment arms associated with a roughly 0.3 increase in our proxy for measurement error (Panel (a), Column 8). There is underreporting across all arms, but it is greatest in the control group. This could have implications for one of our main findings, on income. Using survey data, the treatment effect of cash only on the 2-item expenditure index is 0.08 (0.052), which is consistent with the short run increase in consumption we observed among cash recipients. But adjusting for observed measurement error, the adjusted treatment effect is -0.205 (0.143).

> 55With 240 observations in total, each parameter is estimated off of roughly 30 observations, putting us on a steep part of the power curve.

> 56Moreover, if men honestly report crime in the survey then _β_  ̃0 should be close to zero and _β_  ̃2 should be close to 1. Appendix F derives and interprets these regressions in more detail.

> 57Also, note that, on average, _β_  ̃0 _>_ 0, _β_  ̃2 _<_ 1, and _β_  ̃0 + _β_  ̃2 _<_ 1 for sensitive measures (Column 5). This is consistent with what we observe in Table 9: slight survey underreporting of sensitive behaviors, and 20–30% non-correspondence between survey and validated measures.

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