We show how bounds around preferences parameters can be estimated under various levels of assumptions concerning the beliefs of senders in the investment game. We contrast these bounds with point estimates of the preference parameters obtained using non-incentivized subjective belief data. Our point estimates suggest that expected responses and social preferences both play a significant role in determining investment in the game. Moreover, these point estimates fall within our most reasonable bounds. This suggests that credible inferences can be obtained using non-incentivized beliefs.

The tetrachoric correlation is a popular measure of association for binary data and estimates the correlation of an underlying normal latent vector. However, when the underlying vector is not normal, the tetrachoric correlation will be different from the underlying correlation. Since assuming underlying normality is often done on pragmatic and not substantial grounds, the estimated tetrachoric correlation may therefore be quite different from the true underlying correlation that is modeled in structural equation modeling. This motivates studying the range of latent correlations that are compatible with given binary data, when the distribution of the latent vector is partly or completely unknown. We show that nothing can be said about the latent correlations unless we know more than what can be derived from the data. We identify an interval constituting all latent correlations compatible with observed data when the marginals of the latent variables are known. Also, we quantify how partial knowledge of the dependence structure of the latent variables affect the range of compatible latent correlations. Implications for tests of underlying normality are briefly discussed.

The polychoric correlation is a popular measure of association for ordinal data. It estimates a latent correlation, i.e., the correlation of a latent vector. This vector is assumed to be bivariate normal, an assumption that cannot always be justified. When bivariate normality does not hold, the polychoric correlation will not necessarily approximate the true latent correlation, even when the observed variables have many categories. We calculate the sets of possible values of the latent correlation when latent bivariate normality is not necessarily true, but at least the latent marginals are known. The resulting sets are called partial identification sets, and are shown to shrink to the true latent correlation as the number of categories increase. Moreover, we investigate partial identification under the additional assumption that the latent copula is symmetric, and calculate the partial identification set when one variable is ordinal and another is continuous. We show that little can be said about latent correlations, unless we have impractically many categories or we know a great deal about the distribution of the latent vector. An open-source R package is available for applying our results.

Studies of political persuasion often use an exogenous encouragement as an instrument for persuasive messaging. However, for some people, such encouragement is insufficient, while for others, it is unnecessary. These individuals are excluded from methods that only estimate a treatment effect among compliers. Using the marginal treatment effect framework, we extend research finding that exposure to West German television increases support for communism. We find that, because of self-selection, for those who watch West German TV regardless of signal quality, i.e. always-takers, cutting off West German television would have increased support for communism. Our extrapolation shows that media choices reinforce, rather than mollify, political preferences.

Many researchers use an ordinal scale to quantitatively measure and analyze concepts. Theoretically valid empirical estimates are robust in sign to any monotonic increasing transformation of the ordinal scale. This presents challenges for the point-identification of important parameters of interest. I develop a partial identification method for testing the robustness of empirical estimates to a range of plausible monotonic increasing transformations of the ordinal scale. This method allows for the calculation of plausible bounds around effect estimates. I illustrate this method by revisiting analysis by Nunn and Wantchekon (2011, American Economic Review, 101, 3221–3252) on the slave trade and trust in sub-Saharan Africa. Supplemental illustrations examine results from (i) Aghion et al. (2016, American Economic Review, 106, 3869–3897) on creative destruction and subjective well-being and (ii) Bond and Lang (2013, The Review of Economics and Statistics, 95, 1468–1479) on the fragility of the black–white test score gap.

Ecological inference (EI) is the process of learning about individual behavior from aggregate data. We relax assumptions by allowing for “linear contextual effects,” which previous works have regarded as plausible but avoided due to nonidentification, a problem we sidestep by deriving bounds instead of point estimates. In this way, we offer a conceptual framework to improve on the Duncan–Davis bound, derived more than 65 years ago. To study the effectiveness of our approach, we collect and analyze 8,430 $2\times 2$ EI datasets with known ground truth from several sources—thus bringing considerably more data to bear on the problem than the existing dozen or so datasets available in the literature for evaluating EI estimators. For the 88% of real data sets in our collection that fit a proposed rule, our approach reduces the width of the Duncan–Davis bound, on average, by about 44%, while still capturing the true district-level parameter about 99% of the time. The remaining 12% revert to the Duncan–Davis bound.

The analysis of list experiments depends on two assumptions, known as “no design effect” and “no liars”. The no liars assumption is strong and may fail in many list experiments. I relax the no liars assumption in this paper, and develop a method to provide bounds for the prevalence of sensitive behaviors or attitudes under a weaker behavioral assumption about respondents’ truthfulness toward the sensitive item. I apply the method to a list experiment on the anti-immigration attitudes of California residents and on a broad set of existing list experiment datasets. The prevalence of different items and the correlation structure among items on the list jointly determine the width of the bound estimates. In particular, the bounds tend to be narrower when the list consists of items of the same category, such as multiple groups or organizations, different corporate activities, and various considerations for politician decision-making. My paper illustrates when the full power of the no liars assumption is most needed to pin down the prevalence of the sensitive behavior or attitude, and facilitates estimation of the prevalence robust to violations of the no liars assumption for many list experiment applications.

Forthright characterization of scientific uncertainty is important in principle and in practice. Nevertheless, economists and other researchers commonly report findings with incredible certitude, reporting point predictions and estimates. To motivate expression of incredible certitude, economists suggest that researchers respond to incentives that make the practice tempting. This temptation is the ‘lure’ of incredible certitude. I appraise some of the rationales that observers may have in mind when they state that incredible certitude responds to incentives. I conclude that scientific expression of incredible certitude at most has appeal in limited contexts. It should not be a general practice.