Objectives We examine whether, on average, plea bargaining encourages guilty pleas among defendants who are factually innocent. Methods We develop a formal theory of plea bargaining in which defendants take into account the possibility of false convictions or acquittals when making plea-bargain decisions. We use an incidentally truncated bivariate probit model to test the theory, which predicts that if innocent defendants plead guilty, the correlation (ρ) between the unobserved heterogeneity regarding selection into trial and regarding conviction at trial should be sufficiently positive. The method does not require knowledge of whether individual defendants are factually guilty or innocent. Since ρ is also predicted to vary directly with the unobserved toughness of prosecutors, we develop a decomposition theorem to distinguish between the effects of defendants and prosecutors in plea bargain decisions. Results Using data on 2012 criminal cases decided in Israeli courts from 2010 to 2011, we find that ρ is large and positive. Hence, defendants who did not plea bargain were positively selected in terms of conviction. This means that defendants who accepted plea bargains had smaller counterfactual conviction probabilities than observationally similar defendants who went to trial. ConclusionsThe results indicate that, on average, factually innocent defendants in Israel during this period took plea bargains instead of going to trial. This contradicts "innocence effect" theory, which predicts that factually innocent defendants, on average, reject plea bargains. Our findings are important for research on shadow trial theory, since they show that selection into plea bargains cannot be ignored when inferring counterfactual trial outcomes for plea bargainers.