Now I have a data from an African country concerning (i) levels of corruption across public sectors and (ii) perceptions of service quality from households (bad, medium and high). The data consist two types of household: those who have used the public services and those who have NOT.
I have read several papers from some respected journals (World Development, Journal of Development Economics) that address the problem of selectivity bias: those who have not engaged in public services might do so because they knew they would have to bribe (corruption) or they had bad experience from the past, and they would end up feeling bad.
Authors from the papers, however, do not use Heckit models, that I have learned from my degree. Instead, they argue that by running two regressions: (i) using data on those who actually used the services and (ii) all households in the sample, regardless of the service usage. I feel this approach is not correct.
I wish to understand further how selection bias, particularly in this example, should be handled. Some problems with the data are that the data might be subjective, quite small (around 500 households), and prone to measurement errors. Do you have any suggestions on dealing with the problems?