Data streams converging into clear decision points with a marginal treatment effects graph.

Marginal Treatment Effects: How to Make Better Decisions When the Data Isn't Perfect

Theo Raines in Business & Economy August 2025 • 5 min read.

"A Deep Dive into Monotonicity and Its Impact on Analyzing Treatment Outcomes"

In the world of data analysis, we often seek to understand the impact of a particular treatment or intervention. Whether it's a new drug, a job training program, or a policy change, we want to know if it's making a difference and, if so, how much. Marginal treatment effects (MTE) provide a powerful framework for answering these questions. MTE, introduced by Björklund & Moffitt (1987) and generalized by Heckman & Vytlacil (1999, 2005), offer a way to estimate the effects of treatments, especially when those treatments are influenced by continuous factors.

Imagine you're evaluating a program designed to help people find jobs. Some people are highly motivated and would likely find work regardless. Others are less motivated and need a stronger push. An MTE analysis can help you understand how the program affects people with different levels of motivation, providing a much richer picture than a simple average.

However, MTE analysis isn't without its challenges. One key assumption is monotonicity. Monotonicity, in simple terms, means that the factor influencing treatment (like a judge's strictness in sentencing) consistently pushes people in one direction. But what happens when this assumption is violated? This article explores the robustness of MTE analysis when monotonicity is not perfectly met, drawing insights from recent research by Sigstad (2024).

What Happens When Things Aren't So Straightforward? The Monotonicity Challenge

Data streams converging into clear decision points with a marginal treatment effects graph.

The core of the issue lies in something called "monotonicity." Think of it like this: Imagine you're studying the impact of different judges on sentencing. Monotonicity would mean that a stricter judge is always stricter than a more lenient judge. But what if a judge is stricter in some cases but more lenient in others? That's a violation of monotonicity, and it can throw a wrench into your MTE analysis.

Imbens & Angrist (1994) monotonicity requires that each judge is weakly stricter than more lenient judges in each case. Thus, if Judge A is stricter than Judge B in one case, Judge A cannot be more lenient than Judge B in another case. As shown in Sigstad (2024), this assumption is frequently violated among judges.

It's important to understand how MTE-based treatment effect estimates are affected by monotonicity violations. In this note, I derive necessary and sufficient monotonicity conditions for MTE-based estimates of popular treatment effects to identify the parameters of interest. Fortunately, it turns out that even when Imbens-Angrist monotonicity is violated, MTE-based estimates of these parameters might still be consistent. I first consider MTE-based estimates of LATE—the average treatment effect for agents affected by the instrument. The necessary and sufficient condition for MTE analysis to identify LATE is that monotonicity holds between the two most extreme instrument values. For instance, in the random-judge design, this condition requires that the strictest judge is always stricter than the most lenient judge. As shown in Sigstad (2024), this condition is much more plausible in random-judge designs than Imbens & Angrist (1994) monotonicity. Thus, even though conventional MTE analysis assumes Imbens-Angrist monotonicity, MTE-based LATE estimates can be highly robust to plausible levels of monotonicity violations.

The good news is that recent research suggests MTE analysis can be more robust than previously thought. Even when the strict assumption of monotonicity is violated, MTE-based estimates can still provide valuable insights. This is particularly true when focusing on the average treatment effect for those most affected by the instrument (LATE – Local Average Treatment Effect).

What’s the Bottom Line? MTE is Still a Powerful Tool

Marginal treatment effects offer a sophisticated way to analyze treatment outcomes, providing nuanced insights beyond simple averages. While the assumption of monotonicity is important, recent research shows that MTE analysis can be surprisingly robust even when this assumption is not perfectly met. By understanding the limitations and potential pitfalls, you can leverage MTE to make better, more informed decisions.

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This article is based on research published under:

DOI-LINK: https://doi.org/10.48550/arXiv.2404.03235,

Title: Marginal Treatment Effects And Monotonicity

Subject: econ.em

Authors: Henrik Sigstad

Published: 04-04-2024

Everything You Need To Know

What are Marginal Treatment Effects (MTE) and why are they useful?

Marginal Treatment Effects (MTE) are a framework for understanding the impact of a treatment or intervention, such as a new drug, job training program, or policy change. They provide a way to estimate treatment effects, especially when the treatment is influenced by continuous factors. Unlike simple averages, MTE analysis allows for a more nuanced understanding of how a treatment affects individuals with varying characteristics, for instance, different levels of motivation in a job training program. This richer picture enables better decision-making by identifying which groups benefit most from an intervention.

What is Monotonicity and why does it matter in MTE analysis?

Monotonicity is a key assumption in MTE analysis. It implies that the factor influencing treatment, like a judge's strictness in sentencing, consistently pushes individuals in one direction. In simpler terms, if a stricter judge is always stricter than a more lenient judge, monotonicity holds. Violations of monotonicity can undermine the accuracy of MTE estimates. Recent research, however, suggests that MTE analysis can be robust even when monotonicity is not perfectly met, particularly when focusing on the Local Average Treatment Effect (LATE).

How can monotonicity be violated in the real world, and what are the implications?

Monotonicity can be violated when the factor influencing the treatment does not consistently push individuals in the same direction. For example, imagine judges with varying sentencing tendencies. If a judge is stricter in some cases but more lenient in others compared to another judge, then the monotonicity assumption is violated. This can introduce biases into MTE analysis, potentially leading to inaccurate estimates of treatment effects. The research by Sigstad (2024) highlights that this is a common occurrence, such as among judges. The implications are that the conventional MTE analysis assumptions may not always hold true, and researchers need to understand the limitations and potential pitfalls of MTE when monotonicity is violated.

How robust are MTE-based estimates to violations of the Imbens-Angrist monotonicity assumption, and what conditions must be met?

Even when the strict Imbens-Angrist monotonicity assumption is violated, MTE-based estimates can still be consistent. The necessary and sufficient condition for MTE analysis to identify the LATE, is that monotonicity holds between the two most extreme values of the instrument. In a random-judge design, this means the strictest judge is always stricter than the most lenient judge. Sigstad (2024) shows that this condition is more plausible than Imbens & Angrist (1994) monotonicity. This suggests that MTE-based LATE estimates can be highly robust to plausible levels of monotonicity violations.

What is the Local Average Treatment Effect (LATE) and how does it relate to the robustness of MTE analysis?

The Local Average Treatment Effect (LATE) is the average treatment effect for those most affected by the instrument. MTE analysis, when focusing on LATE, can be surprisingly robust to violations of the monotonicity assumption. The research suggests that even when the overall assumption of monotonicity is not perfectly met, the MTE-based estimates of LATE can still provide valuable insights. This makes MTE a powerful tool for analyzing treatment outcomes, as it allows for nuanced insights even when the data doesn't perfectly align with the assumptions.