Surveys that measure subjective states like happiness or preferences often generate discrete ordinal data. Ordered response models, which are commonly used to analyze such data, suffer from a fundamental identification problem. Their conclusions depend on unjustified assumptions about the distribution of a latent variable. In this paper, we propose using survey response times to solve that problem. Response times contain information about the distribution of the latent variable even among subjects who give the same survey response, through a chronometric effect. Using an online survey, we test and verify the existence of the chronometric effect. We then provide theoretical conditions under which group differences in happiness or other variables are detectable based on response time data without making distributional assumptions. In our survey, we find evidence supporting the assumptions of traditional ordered response models for some common survey questions but not for others.