This paper provides new identification results for causal effects of ordered, nonbinary treatments using multiple binary instruments. The key contribution is the identification of a new causal parameter that simplifies the interpretation of causal effects and is applicable in many settings due to a mild monotonicity assumption. This paper further leverages recent advancements in causal machine learning for both estimation and the detection of local violations of the underlying monotonicity assumption. The methodology is applied to estimate the returns to education and assess the impact of having an additional child on female labor market outcomes.

We consider endogenous binary treatment with multiple binary instruments. We propose a novel limited monotonicity (LiM) assumption that is generally weaker than alternative monotonicity assumptions in the literature. We define and identify (under LiM) the combined compliers local average treatment effect (CC-LATE), which is arguably a more policy-relevant parameter than the weighted average of LATEs identified by two-stage least squares (TSLS), and is valid under more general conditions. Estimating the CC-LATE is trivial, equivalent to running TSLS with one constructed instrument on a subsample. We use our CC-LATE to empirically assess how knowledge of HIV status influences protective behaviors.

In October 2011, Denmark introduced the world’s first and, to date, only tax targeting saturated fat. However, this tax was subsequently abolished in January 2013. Leveraging exogenous variation from untaxed Northern-German consumers, we employ a difference-in-differences approach to estimate the causal effects of both the implementation and repeal of the tax on consumption and expenditure behavior across eight product categories targeted by the tax. Our findings reveal significant heterogeneity in the tax’s impact across these products. During the taxed period, there was a notable decline in consumption of bacon, liver sausage, salami, and cheese, particularly among low-income households. In contrast, expenditure on butter, cream, margarine, and sour cream increased as prices rose. Interestingly, we do not observe any difference in expenditure increases between high and low-income households, suggesting that the latter were disproportionately affected by the tax. After the repeal of the tax, we do not observe any significant decline in consumption. On the contrary, there was an overall increase in consumption for certain products, prompting concerns about unintended consequences resulting from the brief implementation of the tax.

This paper is the first to causally quantify gender differences in healthcare utilization to better understand the male-female health-survival paradox, where women live longer but experience worse health outcomes. Using rich Danish administrative healthcare data, we apply a staggered difference-in-differences approach that exploits the randomness in treatment timing to estimate the causal impact of adverse health shocks, such as non-fatal heart attacks or strokes, on healthcare use. Our findings suggest that men consistently use more healthcare than women, shedding light on the underlying factors driving gender disparities in health outcomes. These insights contribute to the broader discourse on healthcare equity and inform policy interventions aimed at addressing these imbalances.