Disentangling misreporting from genuine adaptation in strategic settings: a causal approach
Authors: Dylan Zapzalka
Trenton Chang
Lindsay Warrenburg
Sae-Hwan Park
Daniel K Shenfeld
Ravi B Parikh
Jenna Wiens
Maggie Makar
Venue: NeurIPS 2025 poster ()
Keywords: Causal Inference
Machine Learning
Strategic Adaptation
Misreporting
Primary area: probabilistic_methods
TL;DR: We propose a causally motivated estimator to quantify the extent to which strategic agents misreport their features.

Abstract: In settings where ML models are used to inform the allocation of resources, agents affected by the allocation decisions might have an incentive to strategically change their features to secure better outcomes. While prior work has studied strategic responses broadly, disentangling misreporting from genuine adaptation remains a fundamental challenge. In this paper, we propose a causally-motivated approach to identify and quantify how much an agent misreports on average by distinguishing deceptive changes in their features from genuine adaptation. Our key insight is that, unlike genuine adaptation, misreported features do not causally affect downstream variables (i.e., causal descendants). We exploit this asymmetry by comparing the causal effect of misreported features on their causal descendants as derived from manipulated datasets against those from unmanipulated datasets. We formally prove identifiability of the misreporting rate and characterize the variance of our estimator. We empirically validate our theoretical results using a semi-synthetic and real Medicare dataset with misreported data, demonstrating that our approach can be employed to identify misreporting in real-world scenarios.

Disentangling Misreporting from Genuine Adaptation in Strategic Settings: A Causal Approach
Dylan Zapzalka' Trenton Chang' Lindsay Warrenburg?
Sae-Hwan Park2
Daniel K. Shenfeld Ravi B. Parikh Jenna Wiens*
Maggie Makar! Emory University
University of Michigan University of Pennsylvania fdylanz, mmakar) (makar)@umicao @umi sumichh.. edu
Abstract
In settings where ML models are used to inform the allocation of resources, agents affected by the allocation decisions might have incentive strategically change their features to secure better outcomes. While prior work has studied strategic responses broadly, disentangling misreporting from genuine adaptation remains fundamental challenge. In this paper, we propose a causally-mote motivated approach to identify and quantify how much agent misreports average by distinguishing deceptive changes in their features from genuine adaptation. Our key insight is that, unlike genuine adaptation, misreported features do causally affect downstream variables (i.e., causal descendants). We exploit this asymmetry by comparing the causal effect of misreported features on their causal descendants as derived from manipulated datasets against those from unmanipulated datasets. We formally prove identifiability of the misreporting rate and characterize the variance of our estimator. We empirically validate our theoretical results using a semi-synthetic and real Medicare dataset with misreported data, demonstrating that our approach can be employed to identify misreporting in real-world scenarios.
Introduction
Machine learning models are increasingly used by decision-maken to guide decisions about the allocation critical resources, such as in loan applications, or determining government payouts to private insurers [2] 47 [4]. In these contexts, organizations-nnn refeered to aggens-min have an incentive to strategically change their features to secure better outcomes
32 They can do so through genuine adaptation misreporting. Genuine adaptation refers agents genuinely changing their behavior, causing the actual values their features to change. This leads to real improvements and authentic changes. Misreporting refers to agents not changing their behavior but instead reporting incorrect feature values to manipulate the allocation process, creating an illusion of improvement without any real change. Incentivizing genuine adaptation often desirable the decision-maker, as it can lead to improvements in the target outcome [7]. Misreporting, however, is never desirable the decision- as leads to incorrect predictions and inefficient resource allocation.
As a running example, we consider the U.S. Medicare Advantage (MA) program, where the govern- ment uses public risk adjustment model allocate payments privately-owned insurers based on enrollee health 37 B1. This risk adjustment model designed to recommend higher payments to insurers for higher-risk, sicker enrollees (3] In response, private insurers may genuinely change their enrollees' health by providing targeted interventions to high-risk enrollees, reducing their costs and increasing their profit margins. Alternatively, they may resort to misreporting, or "upcoding," by inflating diagnosis codes to make enrollees appear sicker, which in turn increases payments without additional treatment expenses [23]. Upcoding has led to estimated $50 billion in overpayments (29 and over $ $100 million in auditing efforts in 2024 alone [3]. Estimating the extent of misreporting is therefore critical for prioritizing oversight and promoting resource efficiency.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

In this work, we develop a causal framework for detecting and quantifying misreporting in the presence of genuine adaptation. Our key insight is that misreporting, unlike genuine adaptation. does not causally affect the descendants of a given feature. Consequently, misreporting leads to biased causal effect estimates between the feature and its descendants. We exploit this asymmetry by comparing the estimated causal effect of a feature on its descendants in both manipulated and unmanipulated datasets to infer a misreporting rate, We assume access to both types of data, where the unmanipulated dataset is collected in setting where there are no incentives to misreport, such as a setting prior to model deployment.
Our contributions are summarized as follows. (I) We recast the problem of quantifying the misreporting rate as causal problem, showing that causal descendants of features can be used to distinguish changes due to genuine adaptation and misreporting. (2) We propose a novel estimator for the misreporting rate that leverages discrepancies in causal effect estimates computed from manipulated data and unmanipulated data where incentives to misreport are absent. (3) We provide theoretical guarantees, including conditions under which the misre- porting rate is identifiable, and variance analysis of our estimator. (4) We empirically vali- date the performance of our estimator, showing that outperforms baseline approaches on a semi-synthetic and real Medicare dataset. Code for our experiments is publicly available at https://gi //gt:/bb..t.t....///gg htwp:/yaaiiinnssaaaaaaaaaaaaatto htt.://rperrttiinneeeitttti.....
2
Related Work
Strategic Classification and Regression. Our work is related to work on strategic classification and
regression, where agents may change their features at some cost [T5] I0 28. However, it differs in two key aspects. (1) The primary goal is to find model that is robust to the distribution shifts caused by gaming, often relying on known agents' cost functions and iterative model retraining [36]. In contrast, we seek to estimate how much agents misreport.
(2) Our method doesn't 't require the unrealistic assumptions of a known agent's cost function or iterative model training.
Causal Strategic Classification. Recent work views strategic classification/rcgrrssioo through a causal lens 332 17 [9] where agents can only genuinely adapt their features. They distinguish between two types of genuine adaptations: improvement and gaming, which correspond to modifi- cations to features that are and are not causally related to the target label, respectively [32]. Unlike us, their focus is on creating models robust to both forms of genuine adaptation [99 and finding
models that incentivize improvement over gaming 17). Closest to our work is Chang et al. [6], who propose an algorithm that can rank agents by their propensity to misreport their features. Unlike our work, their approach can only partially identify how much agents misreport, and they do not make a distinction between misreporting and genuine adaptation. Moreover, their approach works by estimating the causal effect of the agent on the observed feature, whereas our method leverages causal effect estimates the causal descendants of the feature, which allows us to distinguish misreporting from genuine adaptation.
Auditing Policies. Other work seeks to disincentivize agents from misreporting their features through auditing [T] 12]. They define a setting where the decision-makes deploys transparent auditing policy that allows them to reveal the true features of limited number of agents selected by the policy. If the agent's true features differ from their reported features, they endure a penalty, which incentivizes them to report their true features. Instead of performing costly audits, our work estimates misreporting by relying on additional unmanipulated data from settings where agents have no incentive to misreport, c.g., data collected before any model was deployed.
Anomaly/Fraud Detection. Our work is closely related anomaly detection methods aimed at identifying fraudulent instances within a dataset, such as those arising in credit card transactions or insurance claims 18 [5]. Most relevant are one-class classification algorithms 40 30 39) which are trained on an unmanipulated dataset to detect anomalies in manipulated dataset. Unlike our work, these methods focus on identifying specific instances that are anomalous or misreported, whereas our method estimates a rate of misreporting in a dataset. These methods also rely on the assumption that misreported data points differ significantly from normal data points. Our method instead relies on causal assumptions, specifically, that misreporting does not affect the causal descendants of features.

---

(a)
(b)
(c)
(d)
Figure 1: Causal DAGs that describe the setting of this paper. White nodes are unobserved whereas grey nodes are observed. Double-line arrows represent misreporting while dashed arrows represent genuine adaptation. DAGs (a)-(c) represent manipulated data- Sata-generating processes while DAG (d) represents unmanipulated data. The DAG in (a) represents our simplified main setting, (b) represents setting with selection bias, (c) depicts setting with unobserved confounding between A and Y, and (d) represents unmanipulated data with potential genuine adaptation but no misreporting.
3 Preliminaries
Setup. We study a setting where some agents may either genuinely adapt and/or misreport their features. Let denote the agent identity, X the true features, X the (potentially misreported) agent- reported features, Y downstream variable causally influenced by X", and C observed features that may act as confounders or effect modifiers for the relationship between X and Y. We use uppercase letters to denote variables and lowercase letters for their realizations.
We assume that we have access two datasets: (I) A possibly manipulated dataset D= [(x Vi. Ct I P. where P follows any of the DAGs in (a)(c). (). (2) An ummanipllated dataset D = {xx yi, G)) ~ P* generated according to DAG I(d) D* may be pre-deployment data used train the decision-making model, as agents have incentive to manipulate their features before the model is deployed. We do not require access to agent identities in D=, nor do we assume that the same agents appear in both datasets.
In Figure ! we use dashed arrows to indicate genuine adaptation and double-line arrows to indicate misreporting. In D(G] which represents the unmanipulated distribution, only genuine adaptations are allowed. For clarity, we present our main analysis assuming D is sampled according to the DAG results apply without modification to the more complicated DAGs in Figure [b) which include selection bias via an unobserved variable inftuencing both A and X" or unobserved confounder U between A and Y. Additional allowable DAGs are included in Appendix
in Figure ((a] However,
Running example. In Medicare claims, DD* can be insurance claims covered directly by the govern- ment (i.c., Traditional Medicare (TM)), where there is no incentive to misreport. can be claims covered by private insurers. Selection bias could happen, for example, when price-sensitive enrollees (S) who are less likely to have chronic conditions (X*) prefer private insurance (A). Confounding between A and Y could occur if enrollees who prefer private insurance (A) tend to be sicker (Y),
Assumptions. We assume that X" and X are binary whereas all other variables may be continuous. Without loss of generality, we assume that X which means that agents are not incentivized to misreport features where X 1, as formally stated in Assumption]] We adopt the notation of the Neyman-Rule potential outcomes framework (38). where X x(X* = x*) defined as the counterfactual outcome that we would get X* set to x².
is associated with a higher payout than X 0
[
Assumption (Optimal Misreporting). Vi, [2 1)
We assume that agents are incentivized to misreport only X* and genuinely adapt it as follows.
Assumption 2 (Useful Modifications). Agents may only misreport X*, or genuinely adapt it by intervening on X its ancestors.
Under this setting, our goal is to determine how much an agent misreported their features, without access the true features X*. Letting Pa(V) = P(V) A a) for an arbitrary variable V, we define estimand of interest as follows:
3

---

Definition (Misreporting Rate). MR = Po = 0
This definition of the MR quantifies the conditional probability that a reported feature is false. We also show in Appendix that our analysis can be trivially extended to other variants such as the false positive rate, (X I[X* 0). and the marginal difference (X 1) Pa 1).
Key to our suggested approach will be our ability to estimate the causal effect X on Y. We also require the typical assumptions used in causal inference, defined below.
Assumption& 3. The features X", C, and the potential outcomes Y(x* = YX = 0) satisfy the following properties:
1. No unmeasured confounding: Y(0), ((1) 1
2. Overlap: Pa(X* = x² 1 Pa
00 Va",
3. Consistency: (i(x))= X;
Finally, we assume that the conditional average treatment effects are invariant across Pa and P for all values of a.
Assumption 4. Ep, YO)CC = d Ep. (1 Y( = Vc,
This assumption allows to leverage unmanipulated data D recover causal effects needed for estimating misreporting in D.
4
Estimating Misreporting Rates
Recall that our goal to estimate the misreporting rate for given agent, defined in Definition T The core challenge lies in the fact that we only observe the reported features X, but not the true features X This means that the estimand not identifiable from DD alone. A naive approach would be to combine 'D and "D" to estimate the causal effect of A on the observed feature values. However, this would yield a biased estimate of the misreporting rate because it gives an estimate of both the effect of genuine adaptation and misreporting, i.e., biased estimate of misreporting, establish in Appendix E Instead, we estimate the misreporting rate by leveraging the distinct causal consequences that agent interventions corresponding to genuine adaptation and misreporting have on the downstream variables Y.
In Section we present our main estimator for the misreporting rate. In Section 4.2 we analyze the variance of our estimator and give guidance on how to generate low-variance estimator.
4.1 Our causal misreporting estimator (CMRE)
Our key insight that genuine adaptation and misreporting have different effects on the causal descendants of X When an agent genuinely adapts X', this results in a change its causal descendant, Y. In contrast, when agents misreport, they only change the reported feature X, which doesn't causally affect Y. To illustrate, in running Medicare example, if an enrollee truly has cancer (X** = 1). this will cause them to experience cancer-related symptoms (Y). In contrast, if an insurer falsely reports cancer diagnosis for an enrollee (X* 0, X 1), the misreporting itself has no causal effect on the patient's 's symptoms.
This difference allows distinguish between misreporting and genuine adaptation. To make progress, we define the "reported" group as the group for whom X and define the true average feature effect the reported (TAFR) and the nominal average feature effect on the reported (NAFR) as follows:
the causal effect of X on Y and that of X on Y signature to
Th = 1 (E 1)[C c| (Y 0)CC (C 1)de,
and
c|
respectively. These two expressions are similar to the average treatment effect on the treated, commonly studied estimand in causal inference. They define the true and nominal causal effects for

---

the population for whom X = 1. We focus on causal effects for the "reported" group defined by X because the MR as defined Defnition Dis a conditional estimand over X =
Although observing a difference in T. and Ta indicates that an agent misneported, doesn't t give us a rate which agent misreports. To obtain the misreporting rate, we must compare the difference in the NAFR and TAFR relative to the baseline causal effect of X on Y for the group that is misreported. Since only the variable X* influences an agent's decision the misreported group will be a random sample of the group where X = 0 once we condition on the agent. Therefore, the average causal effect of X on Y for the misreported will be the average causal effect on the datapoints where X O. We define this as the true average feature effect on the misreported (TAFM):
misreport a datapoint,
52 : / f
1]CC - -)C =cX' 0)dc.
Next, we show that the MR can in principle be quantified as the rate of the differences between the TAFR and NAFR over the TAFM.
Lemma (Estimator for the misreporting rate). Let Assumptions hold. Then 82 * 0. the MR
can be expressed as:
Ta Ta
Pa 1)
8
The proof for Lemma and all other statements in this subsection presented in Appendix B The lemma states that we can quantify the MR by comparing the true and nominal causal effects of X on Y and X Y respectively. While instructive, Lemma is not very useful as we do not have access to X for agent and hence we cannot directly estimate Ta or 6 from the manipulated data alone.
To resolve this issue, we leverage the unmanipulated dataset D to estimate two other quantities in place Ta and o7. Specifically, we define
/ (E-' c] E.---
To =
O) 0) 0) Pa c| 1)dc
and
8/ = (EP- = =1]C = Ep. [Y 0) = c) = c|. 0)dc.
Both Ty and 64 identifiable because X is observed in the unmanipulated dataset and can be used as valid estimators of T and 6% to estimate the MR, as we show in Theorem [
Theorem (Identifiabilitt) Let Assumptions hold. Then for 8, * 0, Pa(x = 0|x = 1) is identifiable and can be expressed as:
T/d
Pa = - 1)
8
The proof of Theorem relies on (1) the invariance of conditional causal effects of X on Y across P. and pa and (2) our assumptions about agent behavior to show that T'd = and 8 5% We then show that the misreporting rate is identifiable as both 5% and T' are identifiable from D, D and standard causal effect assumptions.
Approach. Guided by Theorem [ we now introduce our primary estimator the causal misreporting
estimator (CMRE)- which estimate the misreporting rate for each agent. CMRE proceeds by estimating the conditional average treatment effect (CATE) over D* and for an agent a over D, which denote 8 (c) and (c) using typical causal estimators such S-learners, T-learners (27), double/debiase ML methods [9] 93 and doubly robust estimators [25). We demonstrate the estimation process using S-learners, which we used for our empirical analysis in Section 5 Specifically, for each agent a in D we estimate the following
fc = arg min
1
Σ HiEDoo,a
e(f(s, 04). and (a(c) = fa(c, 1) fa(c, (1)
JEF Na
5

---

where F is a suitable function class, E is some loss function and Na is the number of data points in D for which A a. Similarly, we can get an estimate of 0 (c))
(c, x") = arg min
Σ WED:
(f(cs 2.). and (c) (
(2)
FEF M
Finally, our estimates for Tar Ta and d' be computed as follows, where Nan is the number of datapoints in 'D where A = and X
F/
Σ
8" (G),
f
Σ
O(c)),
& Noo
Σ (c)).
(3)
Na1
No1
2IE D. ag
IEDD. G2 m
BE 0,
Our full algorithm is summarized in Appendix estimate conditional versions of the misreporting rate by estimating CATE versions of the TAFR, NAFR, and TAFM estimands conditioned on any features of interest. Although this may increase the variance, it may be mitigated by using double MI methods (9) rather than S-learners.
note that our approach can extended to
4.2 Analyzing the variance our estimator
In this section, analyze the asymptotic variance of our estimator give guidance how obtain a low-variance estimator of the MR. We aim to show that if multiple causal descendants of X* are known, the causal descendent with the strongest causal relationship X should be used will result in the lowest asymptotic variance. For simplicity, we limit our analysis to setting where the MR can be estimated from parametric estimators fa. Fg and 8' that are asymptotically normal. We characterize the asymptotic variance of MR estimator under these assumptions in Theorem P
Theorem (Variance). Let far Fo and 8' be asymptotically normal estimators with asymptotic variance of or., o²g- and oz-- Also let OTarl Tro8, and 08,7% denote the covariance between the estimators and = denote convergence in distribution. Suppose that N -M -1, then for 8 + and 8 *
F/ Fa 8'
Tu Ta 4 N(O, 8'
02. 0²
-20T/T
Ta -T +2
(Ta Td)2
(Tr18% - -rr
8.²
8
8' 8%
Theorem 2 shows that the asymptotic variance will increase significantly as 8', + 0 as each term in the variance is divided by either 822 5.3 and 8,4, Thus, the causal descendent with the largest estimate of 8, should be used calculate the MR.
5 Empirical Results
We evaluate the performance of our approach (CMRE) on semi-synthetic and real-world data. We show that CMRE consistently yields reliable estimates of the MR, even when genuine adaptation present, and outperforms relevant baselines.
Baseline Algorithms We compare CMRE against the following baselines. (1) Natural Direct Effect Estimator (NDEE): this estimates the natural direct effect of the agent on the feature X as proxy for MR. We expect it to fail when genuine adaptation non-zero, as it cannot distinguish between the direct causal effect of A (misreporting) and the causal effect mediated through X (genuine adaptation) without access to X*. (2) Naive Misreporting Estimator (NMRE): this similar to our approach but doesn't tt control for confounding between X and Y. It is used to highlight the importance of controlling for confounding when estimating the MR. (3) One-Class SVM (OC-SVM): an anomaly detection approach trained on D where X 1. It then detects which data points in D where where X are outliers. It highlights the limitations using anomaly detection methods for MR estimation. Both CMRE and NDEE use S-learners 277 with an XGBoost [ for causal effect estimation. NMRE relies on a affference-in-meann estimator since it doesn't control for confounding. Additional implementation details are in Appendix D

---

0.8
Estimated MR
0.8
0.5
NMRE
CMRE (Ours)
OC SVM
NDEE
0.4
0.4
0.2
0.2
0.0
0.3
0.2
0.3
0.1
0.2
0.3
0.05
0.10
0.15
0.20
Causal Effect A on X*
Causal Effect of X" on
Misreporting Rate
Figure 2: Results from the loan fraud dataset. The æ-axis is the causal effect of A on X (left), causal effect of X on Y (middle), and the misreporting rate (right). The y-axis is the estimated misreporting rate. Dashed lines represent the true misreporting rate and the eπror bars represent the standard deviation. Our approach (CMRE) accurately estimates the MR for all levels of genuine adaptation, the causal effect X on Y, and misreporting rates. The variance for our estimator depends on the magnitude of the causal effect of X on Y. Baselines that do not adjust for confounding (NMRE) or do not distinguish between genuine adaptation and misreporting (NDEE) give biased estimates in various cases. Anomaly detection methods (OC-SVM) are unable to distinguish misreported data points from unmanipulated data points.
5.1 Semi-synthetic data experiments: Loan fraud
We simulate a scenario where loan applicants may misreport their employment status to improve their chances of loan approval. Here, we focus on simple setting where we'l re interested in the overall MR rather than the MR for a specific agent. We leave the multi-agent analysis to Section 5.2
We simulate setting where D' was collected before a model used to estimate the risk of default was deployed and is the data collected after. We extract the confounders from a real credit card dataset (n = 30, 000) (55 46), with C' = (CA, Cs, CE, CM) denoting age, sex, education, and marital status. We simulate the outcome Y, true employment status X* reported employment status X, and agent identity A follows:
A; 0
+ Cs.) + + Cmi)).
+ X," ~ Bemnoll((..5++00000 O.3 + 3AAd)) O.IC +xx-x;xx,, X; X; + A,(1 X; Bernouli((1)
Y; ~ Bernouli +
where y is picked target desired MR (default = 0.2) and we 3 0.3 and 3x- 0.4 unless otherwise specified. All samples with A; = 1 are assigned to D and the rest to D
Each experiment is repeated 100 times each with different draw of A. X, 80/20 train/test split of 'D where our models are trained on the larger split and the MR is estimated using the smaller split. We do not split D it is only used to train the models. We present the means and standard deviations of the MR estimates across these 100 runs. Additional results and details can be found in Appendix [
X* and Y. We
Varying the amount of genuine adaptation. First, we examine how changes in genuine adaptation affect the MR estimates, highlighting the need to account for genuine adaptation when estimating the MR. To vary the amount of genuine adaptation, we simulate 7 settings with 3 between 0.0 and 0.3.
The results are shown in Figure (left), where the r-axis shows the different values of 9 and the y-axis is the estimated MR. The dashed line shows the value of the MR. The results show that our approach (CMRE) gives unbiased, stable estimates of the MR that are unaffected by the level of genuine adaptation. This signals that CMRE can successfully disentangle misreporting from genuine adaptation. By contrast, genuine adaptation affects the estimates from NMRE and NDEE. Notably, NMRE generally gives biased estimates because it does not control for confounding. As genuine adaptation increases, NMRE gives worse estimates due to shift in the relationship between X* and C' across D and D that NMRE does not control for by not conditioning on C. Despite being rooted in mediation analysis, NDEE is unable to disentangle the direct causal effect of A on X from the
7

---

effect mediated through X without access to X". This means that it gives an unbiased estimate only when genuine adaptation is zero, i... there no path from A to X through X OC-SVM gives biased estimates for all levels of genuine adaptation because the misreported data points are still plausible under D
Varying the causal effect of X on Y. Next, we empirically test our characterization of the variance of our estimator (Theorem 2) by varying the causal effect of X on Y. To vary the causal effect of X on Y, we simulate 5 settings with the causal effect of X on Y, 3x- = [0.1, 0.2, 0.3, 0.4, 0.5).
The results are shown in Figure (middle), where the z-axis shows the causal effect of X" on Y. the y-axis represents the estimated MR, and the dashed line denotes the true MR. The results show that our approach (CMRE) is unbiased, regardless of what the causal effect between the feature and outcome is. However, small causal effects result in high-variance estimates for CMRE consistent with Theorem 2 The NMRE estimates biased but do improve the causal effect of X Y increases, as the unobserved confounders have a diminished contribution towards the full estimate as the causal effect X on Y itself increases. In contrast, the estimates of NDEE do not vary, as the causal effect of X on Y has no impact on the causal effect of A on X. Similarly, the estimates of OC-SVM are biased but invariant because the misreported data points are still plausible under D
Varying the misreporting rate. Finally, we consider how varying the true MR affects our approach and the baselines. To that end, we simulate 5 datasets with MR between 0 and 0.2.
Figure 2 (right) shows the results. The --axis and the dashed line show true MR whereas the y-axis shows the estimated MR. The results show that, unlike the baselines, our approach is always able to accurately estimate the MR. NDEE gives biased estimates since the genuine adaptation is non-zero. OC-SVM is invariant to the MR, indicating that it is completely unable to distinguish between normal and misreporting samples. The inaccuracy in NMRE arises due to uncontrolled confounding whereas by controlling for all confounders, CMRE leads to accurate estimates.
5.2 Real data experiments: Misreporting in Medicare insurance claims
Next, we highlight the utility of our approach in a real data setting. We aim to identify if private insurers misreport enrollees' diagnoses to secure higher government payouts, and which insurers have a higher misreporting rate.
Background. The government calculates payouts using a public risk adjustment model based on enrollee demographics (age, sex, race) and current diagnoses (X"), as measured by Hierarchical Condition Categories (HCCs) at year (t - 1) (37] to predict future healthcare costs. This model is trained on Traditional Medicare (TM) enrollees, who only use government insurance, which provides an unmanipulated dataset, DD" as there's no incentive to misreport. In contrast, data from private insurers, D, may be manipulated. We expect to find evidence of misreporting or "upcoding" of HCCs included in the risk adjustment model by private insurers, consistent with existing literature [1 42 Estimating misreporting rates has been difficult, as private insurers claim diagnosis rate differences result from their improved care (i.e., genuine adaptation). For instance, private insurers may provide greater access to wellness benefits, screening assessments, and nome-based care that result in an improvement of various conditions, while also identifying conditions that would have remained unreported in TM. Our proposed estimator can make progress toward resolving this stag-standing issue by distinguishing between genuine adaptation and misreporting.
Setup. We use mortality during year / as the downstream outcome Y and consider the set of confounders to be enrollee demographics as well as HCCs measured in the previous year, / - 1. To ensure that C' is unmanipulated, we consider only the population of "switchers": enrollees who were covered by the government in year t but switched to private insurer in year t. For these enrollees, their possible confounding HCCs (C) were reported during their government coverage but the HCCs used to calculate risk (X) were reported during their private coverage.
Here, we do not have access to the ground truth MR. Instead, we gauge the quality of our MR estimates for HCCs included in the payment model by comparing them to estimates of non non-payment HCCs: diagnoses that are not included in the government's 's risk adjustment models. Private insurers have no incentive to misreport these HCCs and we expect the true MR for the non-payment HCCs to be zero. To obtain a 95% confidence interval for our estimator, we used bootstrapping with 1000 samples. To ensure small interval, as represented by the error bars, we only considered the
8

---

MR Estimates for HCCs
Estimated MR for Nonpayment HCC
Estimated MR for Payment HCC
0.4
0.2
MR Estimate
02
0.5
0.0
0.2
-0.3
HCG117
HCC50
HECZ1
HCCB
CMRE
NDEE
NMRE
CMRE
NDEE
NMRE
Nonpayment HCCs
Payment HCCs
CMRE
NDEE
NMRE
Insurance
Insurance
Insurance
Insurance
Insurance
Figure 3: For each plot, the y-axis represents the estimated MR for an HCC code and the error bars represent a 95% confidence interval. (Left) The z-axis has two nonpayment HCCs (HCC117 and HCC50) and two payment HCCs (HCC21 and HCC8). Our approach (CMRE) has a MR estimate close to zero for nonpayment HCCs and significantly above zero for the payment HCCs, which aligns with what is expected in current literature. Baselines that fail to distinguish genuine adaptation from strategic adaptation (NDEE) seem to underestimate the MR and baselines that do not control for confounding (NMRE) seem to overestimate the MR. (Middle and Right) The æ-axis represents the baselines. The middle plot represents estimates for HCC50 and the right plot represents MR estimates for HCC8 across different private insurers (agents). Similar to the left plot, NDEE seems to underestimate the MR across most agents and NMRE overestimates.
payment and nonpayment HCCs where at least 1% of switcher enrollees in year had the HCC code, and the causal effect of the HCC on Y. as estimated using D', is greater than 0.1 (consistent with Theorem 2) To further reduce variance, future work can explore alternative causal descendants that exhibit stronger causal relationships with each feature or employ different causal effect estimators (e.g., doubly robust or double ML methods [25 9).
We conduct two sets of analysis: in the first, we present the overall misreporting rate for all insurance companies (i.e., all agents) on the top two payment and non- pa--paymnnt HCCs with the highest causal effect estimates on Y. Second, we look at variations in the MR across multiple agents, i.e., multiple insurance companies. Results for OC-SVM are only in the Appendix, as the method fails to distinguish between normal and misreported samples, consistent with observations in the semi-synthetic results. We include additional results and details in Appendix F and
Results. Figure 3 (left) shows the MR estimates for all insurance companies for two nonpayment HCCs (left of the vertical dashed line) and two payment HCCs (right of the vertical line). Our approach (CMRE) is the only approach that passes the sanity check: it gives MR estimates that are not statistically significantly different from zero for the nonpayment HCCs. This is consistent with our expectation that private insurers have no incentive to misreport nonpayment HCCs. Conversely, CMRE estimates significantly high misreporting rates for both of the payment HCCs. These results are validated in the health policy literature. For instance, HCC21 (Protein Calorie Malnutrition), has long been suspected to be improperly reported as it is reported at much higher rates than TM, leading it to be removed from the risk adjustment model years after our data was collected [4. (6). In contrast, NMRE estimates high misreporting rate for all HCCs, NDEE estimates a negative misreporting rate for all HCCs, which does not align with what is expected. All OC-SVM results are included only in Appendix F since they are consistently incorrect.
For the agent-level analysis. we focus on the top payment and the top nonpayment HCC to simplify our visualizations. Figure (middle and right) show that the main conclusions from the aggregate level analysis hold on the agent-level: our approach is the only approach that reports MR rates not statistically significantly different from zero for nonpayment HCCs across all insurance companies. Our approach estimates that 2 out of the 5 insurance companies have misreporting rates that are statistically significantly different from zero. None of the baselines give consistently reliable estimates for the nonpayment HCCs. NDEE continues to underestimate the MR whereas NMRE overestimates the MR.
Conclusion
In this work, we propose a causal approach to estimating how much strategic agents misreport their features. We show that the misreporting rate is fully identifiable by comparing causal effect estimates

---

between a possibly manipulated and unmanipulated dataset. We also analyze the variance of our estimator, showing that decision maker can accurately estimate the misreporting rate of a feature given a causal descendent with strong causal relationship. We highlight the utility of our approach across empirical experiments over a semi-synthetic and a real Medicare dataset.
Limitations, Broader Impacts, and Future Work. Our work introduces a novel framework for disentangling genuine adaptation from misreporting, opening several promising directions for future research. First, our method assumes the absence of unobserved confounding, a standard but untestable assumption in causal inference. Future extensions could incorporate sensitivity analysis techniques to assess robustness under potential violations of this assumption [44] 24 22). Second, the current framework focuses on binary misreported features; extending to categorical and continuous variables remains an important next step toward broader applicability. Finally, in many real-world settings, downstream causal variables may be unobserved or only observed after long delay. Addressing this limitation through the use of surrogate or proxy outcomes [] offers another valuable direction for future work.
We also acknowledge that this method could be used to disproportionately target certain organizations that may not have the resources to adequately respond to claims of misreporting. To mitigate this issue, we recommend the integration of impact assessments to be used alongside our method to mitigate such disparities.
Acknowledgments and Disclosure of F Funding
We thank the reviewers for their insightful comments. Special thanks Ezekiel Emanual, Claudia Shi, Cecilia Fhrlichman, and Rohan Singh for their valuable feedhack. We also thank Michael Shafir and the Advanced Research Computing team at the University of Michigan for assistance with data access and usage, as well as Will Ferrel for coordinating our meetings. This research was supported in part through computational resources and services provided by Advanced Research Computing at the University of Michigan, Ann Arbor. The authors are supported by grant from Schmidt Futures (Award No. 70960). The funders had no role in the study design, analysis of results, decision to publish, or preparation of the manuscript. This study deemed exempt and not regulated by the University of Michigan institutional review board (IRBMED; HUM00230364), This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-2241 144. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
References
[1] Susan Athey, Raj Chetty, Guido W Imbens, and Hyunseung Kang. The surrogate index: Combining short-term proxies to estimate long-term treatment effects more rapidly and precisely. Technical report, National Bureau of Economic Research, 2019.
[2] Eric P Baumer, JW Andrew Ranson, Ashley N Arnio, Ann Fulmer, and Shane De Zilwa. Illuminating dark side of the american dream: assessing the prevalence and predictors of mortgage fraud across us counties. American Journal of Sociology, 123(2):549 (00)))33966633,.0000 2017.
[3] Jason Brown, Mark Duggan, Ilyana Kuziemko, and William Woolston. How does risk selection respond to risk adjustment? new evidence from the medicare advantage program. American Economic Review, (03(10)3335-3334, 2014.
[4] Caroline S Carlin, Roger Feldman, and Jeah Jung. The mechanics of risk adjustment and incentives for coding intensity in medicare. Health services research. 59(3)=e14272, 2024.
[5] Varun Chandola, Arindam Banerjee, and Vipin Kumar. Anomaly detection: A survey, ACM computing surveys (CSUR), 41(3):1-58. 2009.
[6] Trenton Chang, Lindsay Warrenburg, Sae-Hwan Park, Ravi Parikh, Maggie Makar, and Jenna Wiens. Who's gaming the system? a mausally-motivated approach for detecting strategic adaptation. Advances in Neural Information Processing Systems, 37:42311 1-44448, 2024.
10

---

[7] Tianqi Chen and Carlos Guestrin. XGBoost: A scalable tree boosting system. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. KDD '16, pages 785-794, New York, NY, USA, 2016. ACM. ISBN 978- 1-4503-42322-2 doi:
10.1 141114//93962..0 293.9997772229997898 URL http://doi acm. org/ 10. 1145/ 101111112299999 2939672 2939785
[8] Tianqi Chen and Carlos Guestrin. Xgboost: A scalable tree boosting system. In Proceedings of the 22nd acm sigkdd international conference knowledge discovery and data mining, pages 785-794, 2016.
[9] Victor Chernozhukov, Denis Chetverikov, Mert Demirer, Esther Duflo, Christian Hansen, Whitney Newey, and James Robins. Double/debiased machine learning for treatment and structural parameters, 2018.
[10] Jinshuo Dong, Aaron Roth, Zachary Schutzman, Bo Waggoner, and Zhiwei Steven Wu. Strategic classification from revealed preferences. In Proceedings of the 2018 ACM Conference on Economics and Computation, pages 55-70, 2018.
[11] Andrew Estornell, Sanmay Das, and Yevgeniy Vorobeychik, Incentivizing truthfulness through audits in strategic classification. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 35, pages 5347-5354, 2021.
[12] Andrew Estornell, Yatong Chen, Sanmay Das, Yang Liu, and Yevgeniy Vorobeychik. Incen- tivizing recourse through auditing in strategic classification. In I/CAI, 2023.
[13] Centers for Medicare and Medicaid Services, Centers for medicare and medicaid services 2024, con.reoncicnnogesiiiinnnaaal pdf
2024. httttp:///ettt cms wttp://///.ee////ooo///////////.
ustifications eeteiiaattnneeetttttesss-s--ssee -tp. wtt.eeaiiinn..spppppprraaaaaaana
[14] Michael Geruso and Timothy Layton. Upcoding: evidence from medicare on squishy risk adjustment. Journal of Political Economy, 128(3):984-0066, 2020.
[15] Moritz Hardt, Nimrod Megiddo, Christos Papadimitriou, and Mary Wootters. Strategic classi- fication. In Proceedings of the 2016 ACM conference innovations in theoretical computer science, pages 111-122, 2016.
[16] Charles R. Harris, K. Jarrod Millman, Stéfan J. van der Walt, Ralf Gommers. Pauli Vir- tanen, David Cournapeau, Eric Wieser, Julian Taylor, Sebastian Berg, Nathaniel J. Smith, Robert Kern, Matti Picus, Stephan Hoyer, Marten H. van Kerkwijk, Matthew Brett, Allan Hal- dane, Jaime Fernández del Río, Mark Wiebe, Pearu Peterson, Pierre Sheppard, Tyler Reddy, Warren Weckesser, Hameer Abbasi, Christoph Gohlke, and Travis E. Oliphant. Arra programming with NumPy. Nature, 585(7825):357 362, September 2020. doi: 10. 111008//4158--20-22222 2649-22 httpp://///
Kevin
10 1038 00000///4188 020---022226499--
[17] Keegan Harris, Dung Daniel T Ngo, Logan Stapleton, Hoda Heidari, and Steven Wu. Strategic instrumental variable regression: Recovering causal relationships from strategic responses, In International Conference on Machine Learning, pages 8502-8522. PMLR, 2022.
[18] Waleed Hilal, Andrew Gadsden, and John Yawney. Financial fraud: a review of anomaly detection techniques and recent advances. Expert systems With applications, 193:1 113:1,6429, 2022.
[19] Guy Horowitz and Nir Rosenfeld. Causal strategic classification: A tale of two shifts. In International Conference on Machine Learning, pages 13233-13253. PMLR, 2023.
[20] J. D. Hunter. Matplotlib: A 2d graphics environment. Computing in Science & Engineering, 9 (3):90-95, 9500995,22 2007. doi: 10. 109/MCSE.2007.55
[21] Devansh Jalota, Matthew Tsao, and Marco Pavone. Catch me if you can: Combatting fraud in artificial currency based government benefits programs. arXiv preprint 16X1v:2402.16162. 2024.
[22] Andrew Jesson, Sören Mindermann, Yarin Gal, and Uri Shalit. Quantifying ignorance in individual-leved causal-effect estimates under hidden confounding. In International Conference on Machine Learning, pages 1829-4833 PMLR, 2021.

---

[23] Keith A Joiner, Jianjing Lin, and Juan Pantano. Upcoding in medicare: where does it matter most? Health Economics Review, 14(1):1, 2024.
[24] Nathan Kallus, Xiaojie Mao, and Angela Zhou. Interval estimation of individual-level causal effects under unobserved confounding. In The 22nd international conference artificial intelligence and statistics, pages 2281 1281-2 PMLR, 2019.
[25] Edward H Kennedy. Towards optimal doubly robust estimation of heterogeneous causal effects. Electronic Journal of Statistics, 1702)3008-3049, 2023.
[26] Richard Kronick and Pete Welch. Measuring coding intensity in the medicare advantage program. Medicare & Medicaid Research Review, ((2:=mmm201140000 2014.
[27] Sören R Künzel, Jasjeet S Sekhon, Peter J Bickel, and Bin Yu. Metalearners for estimating heterogeneous treatment effects using machine learning. Proceedings of the national academy of sciences, 1 16(10):156-4165 2019.
[28] Sagi Levanon and Nir Rosenfeld. Strategic classification made practical. In International Conference on Machine Learning, pages 6243-6253. PMLR, 2021.
[29] Steven M Lieberman and Paul B Ginsburg. Improving medicare advantage by accounting for large differences in upcoding across plans. Health Affairs Forefront, 2025.
[30] Larry M Manevitz and Malik Yousef. One-class syms for document classification. Journal of machine Learning research, 2(Dec): 13--144, 2001.
[31] J Michael McWilliams, John Hsu, and Joseph Newhouse. New risk-adjustment system was associated with reduced favorable selection in medicare advantage. Health Affairs, 31(2)): 2630-2640, 2012.
[32] John Miller, Smitha Milli, and Moritz Hardt. Strategic classification is causal modeling in disguise. In International Conference Machine Learning, pages 6917-6926. PMLR, 2020.
[33] Xinkun Nie and Stefan Wager. Quasi-oracle estimation of heterogeneous treatment effects. Biometrika, 108(2):299-319, 2021.
[34] The pandas development team. //doi. org/10. 5281/zenodo. 3509134
Pandas, February 2020. URL https
[35] F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay. Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12:2825-2830. 2011.
[36] Juan Perdomo, Tijana Zmni, Celestine Mendler-Dünnerr, and Moritz Hardt. Performative prediction. In International Conference on Machine Learning, pages 7599-7609. PMLR, 2020.
[37] Gregory C Pope, John Kautter, Randall P Ellis, Arlene S Ash, John Z Ayanian, Lisa I lezzoni, Melvin Ingber. Jesse M Levy, and John Robst. Risk adjustment of medicare capitation payments using the ems-hee model. Health care financing review, 25(4): 19, 2004.
[38] Donald Rubin. Causal inference using potential outcomes. Journal of the American Statistical Association, 100(469):322-33) 2005.
[39] Lukas Ruff, Robert Vandermeulen, Nico Goernitz, Lucas Deecke, Shoaib Ahmed Siddiqui, Alexander Binder, Emmanuel Müller, and Marius Kloft. Deep one-class classification. In International conference machine learning, pages 4393 4402. PMLR, 2018.
[40] Nacem Seliya, Azadeh Abdollah Zadeh, and Taghi M Khoshgoftaar. literature review on one-class classification and its potential applications in big data. Journal of Big Data, 8:1-31, 2021.
[41] Yonadav Shavit, Benjamin Edelman, and Brian Axelrod. Causal strategic linear regression, In International Conference Machine Learning, pages 8676-8686 PMLR, 2020.
12

---

[42] Elaine Silverman and Jonathan Skinner. Medicare upcoding and hospital ownership. Journal of health economics, 23 2004.
[43] Larry Wasserman. All of statistics: a concise course statistical inference. Springer Science Business Media, 2013.
[44] Steve Yadlowsky, Hongseok Namkoong, Sanjay Basu, John Duchi, and Lu Tian. Bounds on the conditional and average treatment effect with unobserved confounding factors. Annals of statistics, 50(5):2587, 2022.
[45] I-Cheng Yeh. Default of Credit Card Clients. UCI Machine Learning Repository, 2009. DOI: htpps://bbi.rr/1102444//////
[46] I-Cheng Yeh and Che-hui Lien, The comparisons data mining techniques for the predictive accuracy of probability of default of credit card clients. Expert systems with applications, 36(2): 2473 -480, 2009.
[47] Qing Zhan and Hang Yin. A loan application fraud detection method based on knowledge graph and neural network. In Proceedings of the 2nd international conference innovation in artificial intelligence, pages 111-115, 2018.
A Additional DAGs
(a)
(b)
(c)
(d)
M
M
(e)
(I
(g)
(h)
Figure 4: Causal DAGs that describe the setting of this paper. White nodes are unobserved, whereas grey nodes are observed. Double-line arrows represent misreporting, while dashed arrows represent genuine adaptation. DAGs (a)-(g) represent manipulated generatenn processes, while DAG (h) represents unmanipulated data.
Figures 4(a) 4(g)
represent settings in which agents may either genuinely adapt or misreport their
features. In contrast, adapt their features. all cases shown in Figures ((() 4(g) the decision maker lacks access to X"
scenario involving trustworthy agents that only genuinely
but observes X, A. C, and Y. While the main focus of the paper was the DAG in Figure 4(a) our
findings extend naturally to the more complex settings depicted in Figures 4(b) 4g))
Specifically, the DAGs in Figures (bb) and 4(1) represent scenarios where some unknown confounding bias may exist between and X e.g.g S. the context the Medicare example discussed the
main text, this could arise if enrollees with more chronic conditions (X*) are more likely to enroll in a private health insurance plan (A). Notably, our approach doesn's 't require controlling for S, as it's not a confounder between X* and Y.
13

---

Finally, the DAGs in Figures 4()) 4 capture settings where an agent may genuinely adapt their features by intervening on a mediator M that lies between A and X For example, this could occur private health insurers (A) are more likely to offer free gym memberships (M), which influence the true health status of their enrollees (X*). ). As before, our approach does not require any knowledge of the mediators an agent intervenes on in order estimate the misreporting rate, as M is not confounder of X and Y. The DAGs in Figures 4(c) 4(e) and 4(g) illustrate settings where an unobserved confounder may influence both and Y. example, this could occur if enrollees who prefer private insurance plans (A) also happen to have worse health outcomes (Y). Again, our approach does not require controlling for U. Although U is a confounder of X* and Y, the backdoor path can be blocked by conditioning on A, which means that an adjustment for U is unnecessary.
B
Main Proofs
Each of the proofs within this Section assume that the dataset D Pa is generated according to any one of the DAGs in Figures 4()
B.1 Proof for Lemma
Lemma i important to build up to Theorem I It shows that the MR can be estimated by comparing the true and nominal causal effects of X on Y and X on Y.
Lemma A1 (Estimator for the misreporting rate; Lemma D in the main text). Let Assumptions 7 hold. Then for 8 # O, the MR can expressed as:
T/ To
Pa = 0|8 = 1)
8
Proof. Our proof proceeds three main steps. First, we decompose тa into two terms: T and an additional bias term. Second, we show that this additional term can be written as function of our
target estimand, P(X 0|X = 1). Third and finally, we show that using simple algebra, we can express our target estimand as function of T Fa and 8
14

---

Step 1: Decomposing into -. and an additional term
(B -|t.://awaaa..a.aa1aa11.1....... = 1)dc
Ta
|Ba.KK_-.Cccc----R-------------0 c|x X 1)dc
+
c| = 1)dcc
0, = 0,
CP - 1)de
EP. = C, - c|( - P,(x = x = 1, c| = 1)dc
C
+
1 0,C PPPa =0,
=
= 1)de
Ep. C,C c/P.(C c/X = 1)dc
X = 1, -PPccPPPCCC c = 1)dc
C
EP. 1,C cPP X|X -,C= c|X 1)de
J
+
EP, = C. - PX - -, c|X = 1)de
LY = =0C = c = c/x 1)de
Th (ER 1, - Ep, Y|X 0,C1) = LL, 1)dc.
The third equality holds as Y x|X*, for the DAGs in Figure ((a) 4(g) and the fourth equality holds due to Assumption [
Step 2:
Expressing the additional term as a function of P(X* = 0| Next, to explicitly show that this additional term is direct consequence of misreporting, we can rewrite it in terms of the misrepoting rate:
=
Ep Y 1, 1, E = 0, 0,C1) = = -X =)de
EEP 1|X' 1, Ep, -x''' = Pa(x Pa(X* -,
Pa = Pa = 1)de
IY = 1, - -
=0,T)/= 0|X 1)P 0, 1)de
= Pa(X = -| = 1) / (E 10= =1,] - E,, = ( = 0, X = 1)de
PP(X* X|X 1)
|Y - O,C = 0)de
Pa(X = 0|X =) 1)
EP,Y((X* = =1]C - Ex, = O) - = 0)de
C
PA(X" = X|X = 1)6".
The fourth equality comes directly from the fact that C 1. X|X*, A for the DAGs in Figures 4(a) 4(g) The fifth equality comes from Assumption 3, as all confounders are controlled for. Notably, both M and S are not confounders of X" and Y. The variable U is confounder of X and Y. however, the
15

---

backdoor path is blocked by A. so it doesn' 't need to be directly controlled for. Overall, this shows that any difference between Ta and T. is directly related the misreporting rate.
Getting the expression for the final target estimand Finally, we can obtain way to estimate the misreporting rate by rearanging the terms:
Step 3:
T Pa(x = 0|.X 1)d2 = Pa(X" 0|X 1) 7a Ta
8
for 8% + 0. Therefore, by comparing the difference in causal effects, we can identify the misreporting rate.
B.2 Proof for Theorem
We now build upon the result from Lemma [ as we work toward our main theorem. Before presenting the proof of Theorem 1. we first introduce additional Lemma which shows that Tax To and 8 identifiable using D and DD along with standard causal estimation assumptions. Then, in Theorem [ we demonstrate that the misreporting rate identifiable by showing that T/2 = Ta and 8g 6g. This proof follows from Assumption 4 which states that the conditional causal effect of X on Y will remain invariant across both strategic and non-strategic populations.
Lemma A2 (Identifiability of Tas Ta and 8%). Let Assumption hold. Then Ta To and 8 are identifiable using D and D''
Proof. First, recall that
- -B 0, cC) = c/X = 1)dc.
We know that Ta identifiable using only as X, and all known in D. Next, recall that
T'a = / (B- D)CC c Ep- = c|X 1)dc
and
8.2 = = ((= E = c|X 0)de.
Again, we know that (C c|X 1) and Pa c|X 0) are identifiable using only D. Therefore, to show that T- and 6, are identifiable, we must show that
Ep- Y(X* 1) = c] Ep- ( 0] c cl
identifiable. This follows immediately from Assumptions 3
(XX* 1) = E 0)[C
= Epp [Y(X" [XX'' = = -
-0 = 0
-,, 0,
Therefore, Tos The and 8 are identifiable using D and D'.
Theorem A1 (Identifiability; Theorem T in the main text). Let Assumptions 4 hold. Then for 8. + 0, (x 0,x = 1) is identifiable and can be expressed as:
Pa(x 0 1) T/ Ta
8%
Proof. We know that Tos T/ and & are identifiable using and D* by Lemma A2 Therefore, to complete this proof, we only need to show that T/d 7/ and 6%, 8% implied by Lemma
16

---

First, we show that T- = T. Recall that
To = / - 00
= 1)dc
and
Ta -= - (Br, (F,, 1|CC= Er
( =)) 1)dc.
Since
Ep. - (()))
for all by Assumption it follows immediately that T/2 T
Next, recall that
8. = I 1VC - = -) cc) = c| = 0)dc
and
87 = (BB = -
Ep.
cc) c|x 0)dc.
We already know that the conditional causal effects of X* on Y are the same across p and Pa- remains to show that PC c|X* 0) PC c| 0) for all values of show that 8 = 8 We establish this equality next.
To show this, simply apply the law of total probability follows:
Pa(C c| = 0) = Pa(C = c|X = 0, X = 1)P(X" =1 = 0)
+ Pa(C c|X = 0, X* P) = 0)
= PP((C = c|X = 0, = 0)
PCCCC c 0).
The second equality follows because P.(X 1|X 0) and
by
Assumption I The third equality follows as C T X|A,, X for all DAGs in Figures 4(a) 4(g) Note that this finding is intuitive: it can be traced back to the assumption that the agents pick who to misreport at random, which is implied by the DAGs.
Thus, the MR is identifiable.
B.3 Proof for Theorem
Theorem A2 (Variance; Theorem 2 in the main text). Let Pa. H/v and 8 be asymptotically normal estimators with asymptotic variance of o², dzy. and oz.- Also let drath Trg6,, and 08,+% denote
the covariance between the estimators and & denote convergence in distribution. Suppose that N = M- n, then for 8, # 0 and 8% #0,
T/ Ta 8/
2² o2 - 20
Fa T/ (orr55 - -r.65] (Ta (Ta- Tg)
71
81
N(O,
8.2
+2
8/33
8'
08
Proof. By the definition of asymptotic normality, each estimator has the following asymptotic distributions, where o² is asymptotic variance of f o² is asymptotic variance of fo. and of is asymptotic variance of 8:
Vnit' - rdl 4 NNO, o3)) Vnlfa - Tal $ NO0 o2.), and
Vnl8's 511 4 N( oz

---

To proceed, we define the function of Fa. (,) as an estimator for the misreporting rate:
g(fa. Fa. 51)
8
Since F/ Fa. 8 are asymptotically normal, can apply the delta method variance of g( fas &.), which states that
43 to find the asymptotic
Vnlg(Fa: Fa. 5,) g( 8.11 4 NoO. Vo(Ta: Ta, 8.) Ta. 8,)
where
Vg(TT: Tas 5a) =
6/
and
o
Tat
T6
E
T
o
T Te
0
0%
Therefore, calculate the asymptotic variance follows:
a2
T
Vi((T, Tax Ta. 82) EVg(Ta Tax Ta. 8,)
0%
Tr
o
TagTa
0rg8
T 8,
0
0 &
0g To 67
+
To
8
87
T 8
1
0
To
8
1
T 5g
08, 8%
08 Tu
+ o
To
0 Ta
+
0
82
3
1
Ta
Tr 8
0 Ta
822
0
8
8 3
Ta 72)
Ta
+ 08 T
8
08, Ta
8
%
8
8 2
+
0 Ta
8
20 r Tu 8
Ta To
+ 20 20
8
8
8
20 -.88
8
6
(Ta
T2)2
+ 0
8/ 4
1
00
-20
8/2
Ta 7/l
+
( -oT,8%)
8
(Ta +/
+
82
Therefore, vT(
--
-'- %/
asymptotically converges to the following normal distribution:
8%
71
T'4
Ta
4 No.
02.
o2
20
+2
Ta
To (ar28
-rr
(Ta
70)²
8'
8'
8 2
8'3
8'
8
18

---

C
Additional Estimands
In this section, we show that we can identify the main estimand of interest, Pa(x = 1 = 0), can also identify other useful estimands, which are defined below.
Definition (Difference in Marginals). DIM (X
Pa(X=
Definition (False Positive Rate). FPR Pa Pa 1|X 0).
The estimand in definition can simply be interepreted as the false positive rate whereas the estimand definition 2 can be thought as the probability that a feature was misreported.
To establish that the estimand in definition 2 is identifiable, we first establish that our estimand of interest, (X =) Pa (X* = 0), can expressed as the joint distribution Pa = X = 0)
in Lemma A3 Identifiability follows from Theorem and simple application of Bayes rule both Pa = x 1) and (a = 1) are identifiable.
Additionally, since Lemma A3 implies that both P. = 1,X* = 0) and Pa(X = 0) are identifiable, we can show that the estimand in definition 3 is also identifiable.
Lemma A3. Let Assumption 7 hold. Then Pa(X 1) Pa 1) Pa(x 1,X*
Proof.
= Pa(X = 1, - Pa(x
-P(( 1,X" =0)+P((X = 1|X (X" -10 -1)-P =)
= =Pa( = =0) -,,- P
P = P-(X"== =1);
where the second equality follows because -IX=|XX* = by Assumption 1
Corollary A1 (Identifiability of difference in marginals). Let Assumptions hold. Then 8¹ # 0, Pa(X 1) Px(X* = 1) is identifiale and can be expressed as:
T'd
Pa(x 1) Pa(x =
x Pa(x=1),
8'
Proof. The proof relys a simple application of Bayes rule, and results from Lemma A3 and Theorem 1. Specifically, we have that:
Pa(X = 1) - Pa =1) - 1,, =
PX 0|X - 1) =
where the first equality follows by Lemma A3 and the second equality follows by Bayes rule. By
theorem 1, the first term (P, (X* 0|x 1)) identifiable, and Pa(X 1) is identifiable because
all variables required for estimation are observed.
Corollary A2 (Identifiability of false positive rate). Let Assumptions hold. Then for 8, + 0, Pa 1|x* = 0) identifialle and can be expressed as:
T To
Pa(X = 1|X =
x Pa 1).
8'
Proof. From Lemma
A3
we can derive P(X* = 0) as follows:
Pa(X = Pa = =1) Pa(x 1, =
1 -1 -=)) Pa(X" =1) =
=0)] PIXp =1) =
Pa(X 0)
-0) = PX(X' =0)
19

---

By Bayes' theorem, we can write the estimand as
Pa(x = 1|X* 0) Pa(x =
= 1)Pa(X =)
Pa(X*= Pa(X* = 0|X = -X) 1I
Pa(x Pa -,,
Thus, since Px(X* = - 1 1,
0), Pa(X =), and Pa 0) are identifiable,
Pa(X 11 | 0) must be identifiable.
D Datasets
D.I Medicare Dataset
The medicare dataset used in our experiments consists of insurance claims data from real U.S. Medicare enrollees enrolled in either Traditional Medicare or private medicare insurance plan. The data was provided to the authors under a data usage agreement with the Centers for Medicare and Medicaid Services (CMS). For our experiments, we only use enrollees that had Medicare coverage in both 2019 (f) and 2018 (t - 1). We exclude enrollees who were dual-eligible (i.e., are eligible for both U.S. Medicaid and Medicare), had end-stage renal disease, or were below the age of 65 for the year t 1. In addition, we exclude all enrollees who resided outside of the 50 U.S. states, the District of Columbia, Puerto Rico, the U.S. Virgin Islands.
Each of the private medicare insurers treated as strategic agent that may misreport enrollee features. We used five agents in total for our experiments. Four agents correspond to the largest private insurers based on the total number of enrollees in year t. The fifth agent is created by aggregating the enrollees from all other smaller insurers. In contrast, Traditional Medicare was treated as a trustworthy agent that doesn't manipulate enrollee data, as there is no incentive to misreport.
The goal our analysis assess how much private medicare insurers misreport HCC codes, which are binary variables that indicate if an enrollee has been diagnosed with specific medical condition. We use V23 HCC codes, as defined by CMS, which are derived by mapping ICD-10 diagnosis codes reported in the claims data. There are two types of HCC codes: payment HCCs, which are used by risk-adjustment model to predict future healthcare costs, and nonpayment HCCs, which are not used to determine costs. We expect the misreporting rate for each nonpayment HCC to be zero as there is no incentive for private insurers to misreport them.
For our analysis, we partition the enrollees into two different cohorts: stayers and switchers. To derive the stayers cohort, we sampled enrollees enrolled in Traditional Medicare for all 12 months in year ( - 1 and were not enrolled in private insurance plan in year 1. For the switchers cohort, we used enrollees that were enrolled Traditional Medicare for all months year 1 and were enrolled in private insurance plan for at least one month in year t. We only used a 20% random sample of the eligible stayers cohort (868255 samples) and 100% of the eligible switchers cohort (166539 samples). For the outcome (Y), we use the enrollee's 's death status in year t.
For the features (X), used both payment and nonpayment HCC codes, consisting of 83 and 99 codes, respectively, As covariates, we used the enrollee's 's age, race, sex, and the payment HCCs from year
ensure they were not misreported. To obtain low variance estimates, we restricted our analysis to payment and nonpayment HCCs with the largest causal effects on death and where at least 1 1% of the switchers enrollees in year had the HCC code.
D.2 Loan Datasets
In our loan dataset simulations, we model a setting where loan applicants may either genuinely adapt or misreport their employment status to improve their chances of getting approved for a loan. For each of our simulations, we simulate a single strategic agent (A = 1) and single nonstrategic agent (A = 0). In addition to the semi-synthetic dataset used for the experiments in Section 5, we generate
20

---

additional datasets based on different DAGs in Figure 4 The data generation process for the other datasets explained in Appendix
All the simulations use the covariates extracted from a real credit card dataset [5 These include three binary variables: marriage status (CM), (Cs), and education (Cæ), well as another variable representing a person's 's age (C'A). We use min-max normalization so that CA is between and 1. The agent variable (A), the variable for employment status (X*), and the variable indicating a loan applicant defaulted (Y), are all generated using the covariates. Misreporting is done in accordance with the following equation:
X, X A,(1 X; Bernoulli(s)
where μ picked to target desired MR (default = 0.2). Each experiment repeated 100 times, with new draws of X, and Y. Across all experiments, we use an 80/20 train/test split of D.
E Estimators
In this section, we present additional details about our primary method (CMRE) as well as the baseline approaches (NMRE, NDEE, and OC-SVM). We also specify the hyperparameters and libraries used to implement each method in our experiments.
E.1 CMRE
Recall that for a suitable function class F, a loss function l, and Na the number of data points in 'D for which A we define
fa(c,x) = arg min JEF Na
Σ
((f(c, and Oa(c) = falc,, (4)
and
f"(cxx") arg min feF M
Σ ((((,,))) and ((c)
(5)
Recall that Nar denotes the number of data points in for which A a and X r. Using this, we compute the estimates for Ty Ta and 6', as follows:
#/
Σ (G)), =1, a:=0
i
Σ ((c),, =1
&
Σ (c)) (6)
Na1
NA1
Noo
isE =,
To estimate (c) and 8 (c), we employ an S-learner, where the models fa and f are implemented using XGBoost. We the default hyperparameters provided by the XGBoost library in Python to train each model 77.. including a learning rate 0.3, a maximume tree depth of 6, and L2 regularization with coefficient of 1.
The complete algorithm for CMRE is summarized in [ We note that for our experiments, we split D such that the data used to train fo (c, r)) in equation 4is is different than the data used to estimate the MR equation 6 Specifically, 80% of the data D is used to train fa(c, x) in equation and the
other 20% used to estimate //, 4. and 8 0-
E.2 NMRE
NMRE adopts similar strategy to CMRE for estimating the misreporting rate. Specifically, leverages the differences in causal effect estimates. However, the key distinction between NMRE and CMRE that NMRE doesn't account for potential confounders or treatment effect modifiers between X and Y. As result, NMRE employs simple difference- ieeeeeii--meee in-means estimator to estimate
21

---

Algorithm CMRE algorithm
Input: D (z Mis Cs a;) and D { Ui, 1:
Output: MR, an estimate of the MR for each agent for each agent do
Estimate fg (c) using equation
Estimate 0" using equation
Estimate F/2 Fa. and & using equation
return PA
end for 8'a
the average effect of the feature on Y over both DD and D. Therefore, to estimate the MR for a given agent a, we define
Σ
Σ
M1
y1
Mu
yi
iHED"
=;=1
and
Σ Y:
Σ
yk
(8)
No1 IED,,,=),
No0
iiED
where M2 the number of datapoints in D* where X E. The misreporting rate is the estimated as:
7' fo
MR
The complete algorithm for NMRE is summarized Algorithm
Algorithm NMRE algorithm
Input: D (J Mis C2 a.) and D {(=), Mis c:))
Output: MR, an estimate the MR for each agent for each agent do
Estimate z' using equation
Estimate fa using equation
return end for
E.3 NDEE
The NDEE baseline estimates the misreporting rate by computing quanitity similar the natural direct effect of A on X, divided by the probability Px = 1). Specifically, we estimate
Pa - / ( XX|C =c) = c)dC.
1
Assuming that all datapoints in Pa are generated a single trustworthy agent a", the integral term,
[( E
can be interpreted as the natural direct effect of A X within the treated population (i.e., data points where A = are the treated whereas a" refers to the untreated), when C controls for all mediators and confounders between and X. We next show how estimate the NDEE in practice, which is as follows.
22

---

Dataset Preparation. We modify the original dataset D such that D where a, a² for all a, Next, we combine both D and D to create unified dataset:
f 3e, Ci, a;)
D' D'=DUPD
Causal Effect Estimation Let F denote suitable function class and é loss function. We then learn function
f(e,a) = arg min f'E
Σ a))
(10)
N M
RED
Next, we estimate the natural direct effect of A over the treated population as follows:
1 Σ
NDE
f(c,a) - f(c,
(1I)
Na
iED,
Probability Estimation
The probability Pa(X = 1) can be estimated simply as
To N
1
Σ
3;
(12)
The full algorithm summarized in The model [[c, a) is implemented using XGBoost, where we the default hyperparameters provided by the XGBoost library in Python [7] learning rate of 0.3, maximume tree depth of 6, and L2 regularization with coefficient of 1).
Algorithm 3 NDEE algorithm
Input: D (2,, yi, Cs a.) D = {(x], yr, M. and {(1,, Uss Cr a.)
Output: MR, an estimate of the MR for each agent
for each agent do
Estimate (c, a)) using equation 10
Estimate ÂNDE using equation
Estimate na using equation 12
return 1 fNDE
end for
When the NDEE accurately estimate the MR? We show that if A does not directly causally effect X*, is possible to obtain an accurate estimate of the misreporting rate using the NDEE. To show this, we can rewrite the misreporting rate follows:
MR Pa(X* = - 1)
Pa(x -X' Pa(X'=11
11(x=1)
1
(Ep,(A) -Xp
Pa(X 1)
1
P.(X = 1) (Ep. =
= c)dC.
Thus, unless Ep [X* c) Ep-IX*IC - = c). the NDEE will give a biased estimate of
misreporting rate. This equality will hold if X* A A'C, which can only be true if A does not directly affect X Therefore, we should expect the NDEE to only work in settings where agents not directly genuinely adapt their features.
23

---

E.4 OC-SVM
Under our assumptions, no data points where X = 0 are misreported. Therefore, we restrict the OC-SVM approach to a subset of the data from DD and DD where X = which we denote as Di and Di, respectively. To train One-Class SVM model, we use data from D7, which is assumed to contain no misreported instances. The One-Class SVM model, denoted as gV,, c), is trained to identify outliers/misreporteed instances using only the variables Y and C. The model outputs if datapoint is classified an outlier, and 0 otherwise.
For given agent a, we estimate the misreporting rate using the OC-SVM as:
MR
E HEDLLa
glu. c.).
No1
We use the One-Class SVM implementation from the scikit-learn library [35. Given our assumption that all data points in Dj are correctly reported, we used a small v parameter (0.01). Additionally, we use an RBF kernel with bandwidth parameter 7 = 0.1.
F
Additional Experiments
F.1
Medicare Experiments
presents our Medicare experiments including the results from the OC-SVM estimator. The estimated misreporting rate for the OC-SVM consistent across all HCC codes and agents, reflecting the results from our semi-synthetic loan dataset experiments. This suggests that the OC-SVM is unable to distinguish misreported data points from normal data points.
Figure 5
Tables 1 and 2 provide information about each of the nonpayment and payment HCCs that had & and were present in at least 1% of the switcher enrollees. For each HCC code, the tables report the estimated MR using CMRE, the number of stayer and switcher enrollees in year t, 6%, and the lower and upper bounds for the 95% confidence interval. We exclude HCCs that were nonpayment in year t but were used as payment HCCs for the risk adjustment model in year + 1, due to the potential incentive for agents to misreport them.
MR Estimates for HCCs
Estimated MR for Nonpayment HCC
Estimated MR for Payment HCC
0.4
0.2
MR Extimtte
0.5
0.0
-0.2
00.2
-0.5
CMRE
NDEE
OC-SVM
Nonpaymen
HCC+
Payment HCCs
Figure 5: For each plot, the y-axis represents the estimated MR for HCC code and the error bars represent a 95% confidence interval. (Left) The x-axis has two nonpayment HCCs (HCC117 and HCC50) and two payment HCCs (HCC21 and HCC8). Our approach (CMRE) has a MR estimate close to zero for nonpayment HCCs and significantly above zero for the payment HCCs, which aligns with what is expected in current literature. Baselines that fail to distinguish genuine adaptation from strategic adaptation (NDEE) seem to underestimate the MR and baselines that do not control for confounding (NMRE) seem to overestimate the MR. OC-SVM has similar estimate for each HCC, making it ineffective at identifying misreported data points. (Middle and Right) The rr-axis represents the baselines. The middle plot represents estimates for HCC50 and the right plot represents MR estimates for HCC8 across different private insurers (agents). Similar to the left plot, NDEE seems to underestimate the MR across most agents, and NMRE overestimates, and the MR estimates for OC-SVM are consistent across all agents and HCC codes.
24

---

Table 1: menpayment HCCs with & > 0.1 and present in at least 1% of switcher enrollees.
HCC
Full Name
MR
Stayers
# Switcceess
8
LCB
UCB
Delirium and
50
.015
32294
4535
.175
-.138
.091
Encephalopathy
Pleural
117
.019
39037
5601
.153
-.103
.120
Effusion/ Pneumothorax
Table 2: Payment HCCs with 8
0.1 and present in at least 1% of switcher enrollees.
HCC
Full Name
MR
Stayers # Switchers
8
LCB
UCB
Metastatic Cancer and
8
.130
18762
2646
.276
.037
.238
Acute Leukemia
Protein-Call Calorie
21
.277
21460
3338
.270
.109
.285
Malnutrition
Bardio-Respiratoyy
84
.046
40308
6292
.247
-030
.103
Failure and Shock
Artificial Openings for Feeding or Elimination Septicemia, Sepsis, SIRS, and Shock
188
.004
10528
1684
.194
-,110
.210
2
.112
28297
4309
.190
.040
.288
135
Acute Renal Failure
-004
49021
7868
.130
-007
.116
103
Soniplegia/Hemiparees
.241
12589
2395
.129
.066
.439
Acute Myocardial Infarction
86
.033
20555
3230
.117
1.121
.217
F22
Loan Dataset Experiments
We conduct additional experiments using alternative versions the loan fraud dataset to show how well method and the baselines work under the DAGs defined in Figure 4 We also include two additional baselines that were not in the main paper: NDEE (no C) and NDEE (no S). Unlike the standard NDEE model, which controls for all covariates, NDEE (no C) doesn't control for confounders between X and Y, and NDEE (no S) doesn't 't control for common causes of A and X*, e.g., S. These variants are used highlight the importance of controlling for S for NDEE.
F.2.1 Simulation
The first simulation replicates the setup used to generate the results in Section 5. It includes four confounders of X* and Y: education (Cæ), sex (Cs), marriage (CM), and age (Ca). Among these variables, sex and marriage also causally effect A, reflecting a similar scenario represented by the DAG in Figure (g) The simulation details are provided below:
A; ~ Bermouli + 0.3(1 Cs:) + 0.3(1 CM.)),
X Bemoulli(0.05. 0.050 + 0.3Cs, + +3AAi);
Y Bernulli 0.05C 0.3C', CM, +xx
X₃ X + A, XX" Bernoull(μu).
In this simulation, NDEE (no S) doesn't 't control for either C's or Cм. Our main method, CMRE. controls for all covariates as they are all confounders between X* and Y. 8A = 0.3 and 8x. = 0.4 unless specified otherwise. The results for this simulation are shown in Figure
F.2.2 Simulation
The second simulation includes three confounders of X* and Y: education (CF). sex (Cs), and age (CA). Marriage (Om) common cause of A and X* and an agent genuinely adapts eduction, reflecting similar scenarios represented by the DAGs in Figure 4(a) and 4(b) In addition, eduction is
25

---

0.8
Estimated MR
0.5
0.6
0.6
0.0
0.4
0.4
0.2
0.2
0.0
0.0
0.0
0.1
0.2
0.3
0.2
0.4
0.0
0.1
0.2
Causal Effect of on X"
Causal Effect X on Y
Misreporting Rate
f CMRE (Ours]
NMRE
4
NDEE (All)
NDEE (no S)
OCSVM
Figure 6: The z-axis is the causal effect of A on X (left), causal effect X on Y (middle), and the misreporting rate (right). The y-axis is the estimated misreporting rate. Dashed lines represent the true misreporting rate and the error bars represent the standard deviation. Our approach (CMRE) accurately estimates the MR for all levels of genuine adaptation, the causal effect of X on Y. and misreporting rates. The variance for our estimator depends on the magnitude of the causal effect of X on Y. Baselines that do not adjust for confounding (NMRE) or do not distinguish between genuine adaptation and misreporting (NDEE) give biased estimates in various cases. NDEE is accurate when there is no genuine adaptation whereas NDEE S) is not, highlighting the need for controlling for common causes of A and X Anomaly detection methods (OC-SVM) are unable to distinguish misreported data points from unmanipulated data points.
also treatment effect modifier. The simulation details provided below:
A₁ Bemnolli(0.05 0.4(1 -ar))),
Cg CE: + (1 CF.) A
X (emmoull((0055.. 0.25C 0.10 0.1C +,A,))
Y; ~ Bemoulli (0.05 + 0.2C%, + 0.1CA + (8x- )x;1),
X₃ X A2 - X, Bernoull((u);
In this simulation, NDEE (no doesn't it control for Cм and NDEE (no C) only controls for CM- Our main method, CMRE, only controls for Cg. Cs, and CA. 3^ = 0.1, 8M = 0.2, and [xx = 0.4 unless specified otherwise. The results for this simulation are shown in Figure
F.2.3 Simulation
The third simulation includes three confounders of X* and Y: education (CE), sex (Cs), and age (CA). Marriage (CM) is common cause of A and Y and an agent genuinely adapts education. reflecting the scenario represented by the DAG in Figure 4(c) In addition, education is also a treatment effeett modifier. A 0.1, 8M 0.2, and Bx- 0.4 unless specified otherwise. The simulation details are provided below:
A ~ Bemoulli(0.05 + 0.4(1 Om.)),
C Ce; + (1 (r.Cr, A, Bernoulll(())
X Bemoulli + 0.10 0,10 + 0.10 Ai)
Y (000ouli(0.05 0.20 +. 0.05C + (3x- +0,1C))
X, ~ X + A, - X; Bernoulli(p).
In this simulation, NDEE (no C) only controls for Cm. Our main method, CMRE, only controls for Cg, Cs, and CA. The results for this simulation are shown in Figure
F.2.4 Simulation
The fourth simulation includes two confounders of X and Y: sex (Cs), and age (CA). Marriage (CM) ) is common cause of A and Y and agent genuinely adapts education, which is mediator
26

---

Estimated MR
0.5
0.4
0.2
0.0
0.0
0.0
0.5
0.2
0.0
0.1
0.2
0.3
0.2
0.1
0.0
0.1
0.2
Causal Effect of A on X"
Causal Effect of X" on
Misreporting Rate
CMRE (Ours)
NMRE
NDEE (All)
NDEE (no S)
NDEE (no C)
F
OCSVM
Figure 7: The r-axis the direct causal effect of on X (left), causal effect of X on (middle), and the misreporting rate (right). The y-axis is the estimated misreporting rate. Dashed lines represent the true misreporting rate and the error bars represent the standard deviation. Our approach (CMRE) accurately estimates the MR for all levels of genuine adaptation, the causal effect of X Y, and misreporting rates. The variance for our estimator depends on the magnitude of the causal effect of X* Y. Baselines that do adjust for confounding (NMRE) or do not distinguish between genuine adaptation and misreporting (NDEE) give biased estimates in various cases. NDEE accurate when there is no genuine adaptation whereas NDEE (no S) and NDEE (no C) are not, as they either don't t control for common causes of A and X or mediators of A and X Anomaly detection methods (OC-SVM) are unable to distinguish misreported data points from unmanipulated data points.
0.8
0.6
0.6
Estimated
0.4
0.2
0.2
0.2
0.0
0.0
0.0
0.2
0.3
0.4
0.0
0.2
Causal Effect of A X*
Causal Effect of X" Y
Misreporting Rate
CMRE (Ours)
NMRE
NDEE (AII)
NDEE
OCSVM
Figure 8: The x-axis the direct causal effect of on X* (left), causal effect of X Y (middle), and the misreporting rate (right). The y-axis is the estimated misreporting rate. Dashed lines represent the true misreporting rate and the error bars represent the standard deviation. Our approach (CMRE) accurately estimates the MR for all levels of genuine adaptation, the causal effect of X on Y. and misreporting rates. The variance for our estimator depends on the magnitude of the causal effect of X on Y. Baselines that do not adjust for confounding (NMRE) or do not distinguish between genuine adaptation and misreporting (NDEE) give biased estimates various cases. NDEE is accurate when there is no genuine adaptation whereas NDEE (no C) is not, as it doesn't 't account for the mediators of A and X Anomaly detection methods (OC-SVM) are unable to distinguish misreported data points from unmanipulated data points.
of A and X*, reflecting the scenario represented by the DAGs in Figure 4(d) and 4(c) The simulation details are provided below:
A; (0 0.4 OM.l))
CE Cg. + (1 -.e..)))...e
X;
BAAA),
0.05C Bx-X;), X, ~ X; + A, (emooll((())
Y, ~ Bernuulii (0.05 0.20,
27

---

In this simulation. NDEE (no C) only controls for Cм and Cg. Our main method, CMRE, only controls for Cs and CA. A^ 0.1. AM 0.2, and 8x- 0.4 unless specified otherwise. The results for this simulation are shown in Figure 9
0.8
0.6
0.4
0.4
Estimated
0.4
0.2
0.2
0.0
0.1
0.2
0.3
0.4 Causal Effect of X" Y
0.0
0.2
Causal Effect of A X*
Misreporting Rate
CMRE (Ours)
NMRE
NDEE (AI))
NDEE C)
OCSVM
Figure 9: The r-axis is the direct causal effect of A on X* (left), causal effect of X Y (middle), and the misreporting rate (right). The y-axis is the estimated misreporting rate. Dashed lines represent the true misreporting rate and the error bars represent the standard deviation. Our approach (CMRE) accurately estimates the MR for all levels of genuine adaptation, the causal effect of X on Y. and misreporting rates. The variance for our estimator depends on the magnitude of the causal effect of X on Y. Baselines that do not adjust for confounding (NMRE) or do not distinguish between genuine adaptation and misreporting (NDEE) give biased estimates in various cases. Both NDEE and NDEE (no C) are accurate when there is no genuine adaptation, they control for all common causes of and X and mediators of A and X Anomaly detection methods (OC-SVM) are unable to distinguish misreported data points from unmanipulated data points.
F.2.5 Simulation
The fifth simulation includes two confounders of X* and Y: sex (C's), and age (CA). Marriage (OM) a common cause and X* and an agent genuinely modifies education, which mediator of A and X", reflecting similar scenarios represented by the DAGs in Figure 4(d) and 4()) The simulation details are provided below:
A Bermouli 0.4(1 CMr))),
Cb CE. + (1 - 4.mm
X; Bernoulli(0.05 + + 0.30%, 0.1CAA + +BA.),
Y ~ Bernoulli(0.055 + 0.3Cs; +.05C 3x=X;),
X, X; + A, X - Bernulli(())
In this simulation, NDEE (no C) only controls for Cas and CE and NDEE (no S) doesn't control for Cм- Our main method, CMRE, only controls for Css and CA. 33 0.1, BB 0.2, and 3x- 0.4 unless specified otherwise. The results for this simulation are shown Figure 10
G Software and Hardware
G.1 Software
All of the code for the experiments was written in Python 3.10.16 (PSF License). The XGBoost models were implemented using the XGBoost 2.1.4 (Apache License 2.0) 7 The OC-SVM baseline was implemented by using scikit-learn 1.6.1 (BSD License) [35], which used the implementation of the One-Class SVM. generate the semi-synthetic datasets and for data processing tasks, both numpy 2.0.2 (modified BSD license) [16] and pandas 2.2.3 (BSD license) 34 were employed. For
the Medicare dataset, HCCPy 0.1.9 (Apache License 2.0) was employed to extract the HCCs from
raw data. All plots were created using matplotlib 1.1 (PSF License) (20].
28

---

0.6
Estimated MR
0.5
0.4
0.4
0.2
0.0
0.0
0.0
0.0
0.1
0.2
0.3
0.2
0.4
0.0
0.1
0.2
Causal Effect
X
Causal Effect X
Misreporting
CMRE (Ours)
NMRE NDEE (AlI)
NDEE (no S)
NDEE (no C)
i
OCSVM
Figure The z-axis is the direct causal effect of on X (left), causal effect of X on (middle), and the misreporting rate (right). The y-axis is the estimated misreporting rate. Dashed lines represent the true misreporting rate and the error bars represent the standard deviation, Our approach (CMRE) accurately estimates the MR for all levels of genuine adaptation, the causal effect of X on Y. and misreporting rates. The variance for our estimator depends on the magnitude of the causal effect of X on Y. Baselines that do not adjust for confounding (NMRE) or do not distinguish between genuine adaptation and misreporting (NDEE) give biased estimates in various cases. Both NDEE and NDEE (no C) accurate when there is genuine adaptation, they control for all common causes A and X and mediators of A and X In contrast, NDEE does not control for common causes of A and X*, which makes it biased. Anomaly detection methods (OC-SVM) are unable to distinguish misreported data points from unmanipulated data points.
G.2 Hardware
experiments were conducted using 16 CPU cores and 32 GB of memory on computing cluster with 2 x 2.5 GHz Intel Haswell (Xeon E5- processors, which was managed using a Slurm resource manager. The simulations for all of the five semi-synthetic loan experiments took approximately 5 hours to complete, whereas the experiments over the Medicare dataset took approximately hours to complete.
29

---

NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: The abstract and introduction claim that propose causally motivated approach to quantify how much a strategic agent misreports (shown in Sections 3 and 4), and claim that show that how much strategic agent misreports is identifiable (shown in Lemma and Theorem 1). We also claim that we characterize the variance of our estimator, which is shown in Theorem 2. Finally, claim that empirically validate our theoretical results over semi-synthetic and real Medicare dataset, which is shown in Section 5.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made in the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
It is fine to include aspirational goals as motivation as long as it is clear that these goals not attained by the paper.
2. Limitations
Question:
Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
Justification: This paper does discuss the limitations - see the "Limitations and Broader Impacts" section in the Conclusion.
Guidelines:
The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create separate "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model vell-specifiiattin, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, e.g., if the approach was only tested few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect on the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and faimess.
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, worse outcome might be that reviewers discover limitations that aren't acknowledged the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an impor- tant role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
30

---

3. Theory assumptions and proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
Answer: [Yes]
Justification: Yes, all assumptions are listed formally and numbered. Each Theorem and Lemma states the full set of assumptions and proofs provided in the Appendix.
Guidelines:
The answer NA means that the paper does not include theoretical results. All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated referenced in the statement of any theorems.
The proofs can either appear in the main paper or the supplemental material, but they appear in the supplemental material, the authors are encouraged to provide short proof sketch provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by formal proofss provided in appendix supplemental material.
Theorems and Lemmas that the proof relies upon should be properly referenced.
4. Experimental result reproducibility
Does the paper fully disclose all the information needed to reproduce the main ex- perimental results of the paper to the extent that it affects the main claims and/or conclusions the paper (regardless whether the code and data are provided or not)?
Question:
Answer: [Yes]
Justification: We have provided sufficient amount of details in the paper so that the semi- synthetic simulations can be reproduced. All model details and hyperparameters that were used are included in the Appendix. Due to restrictions unable to share this dataset with the public. However, we do provide details on how we generated the cohorts of data used in experiments. Guidelines:
the Medicare dataset, are
The answer NA means that the paper does not include experiments.
If the paper includes experiments, a No answer to this question will not perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is dataset and/or model, the authors should describe the steps taken make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution be necessary to either make it possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
specific model and empirical evaluation, may
While NeurIPS does not require releasing code, the conference does require submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) If the contribution is primarily a new algorithm, the paper should make it clear how reproduce that algorithm. (b) If the contribution is primarily the architecture clearly and fully.
model architecture, the paper should describe
(c) the contribution a new model (e.g., a large language model), then there should either be way to access this model for reproducing the results or way to reproduce the model (e.g., with an open-source dataset instructions for how to construct the dataset).
31

---

(d)
We recognize that reproducibility may be tricky in some cases, in which case authors are welcome describe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results.
5. Open access to data and code
Question: Does the paper provide open access the data and code, with sufficient instruc- tions to faithfully reproduce the main experimental results, as described in supplemental material?
Answer: [No]
Justification: To the extent legally permitted, we provide code and access to the semi- synthetic data used in the paper. Due various restrictions regarding the use of the Medicare data, the authors do not have the power share grant access to the data.
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurlPS code and data submission guidelines (https://nips. cc/pu
blic/ gewddes/Codeeuubnii
ssssonoiiccn)s) for more details.
While we encourage the release of code and data, we understand that this might not be possible, so "No" an acceptable answer. Papers cannot be rejected simply for including code, unless this is central to the contribution (e.g., for new open-source benchmark).
The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurlPS code and data submission guidelines (https
//nips http:///ccppllliigguddee////oeee
for more details.
The authors should provide instructions data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. only subset of experiments are reproducible, they should state which ones are omitted from the script and why.
At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).
Providing as much information as possible supplemental material (appended the paper) is recommended, but including URLs to data and code is permitted.
6. Experimental setting/details
Question: Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Answer: [Yes]
Justification: All details on the datasets, train/test splits, and hyperparameters necessary to understanding the results are provided in the Appendix.
Guidelines:
The answer NA means that the paper does not include experiments.
The experimental setting should be presented in the core of the paper to level of detail that is necessary to appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, as supplemental material.
7. Experiment statistical significance
Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Question:
Answer: [Yes]
32

---

Justification: We report the standard deviation via error bars for the baseline estimates across multiple different simulations. This explicitly stated the Figure 2 caption for our semi-synthetic experiment results. For our Medicare experiments, we provide error bars that represent 95% confidence interval, as is stated in the Figure caption.
Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results are accompanied by error bars, confi- dence intervals, statistical significance tests, least for the experiments that support the main claims of the paper.
The factors of variability that the enror bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall
with given experimental conditions).
The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)
The assumptions made should be given (e.g.. Normally distributed errors).
should be clear whether the error bar is the standard deviation or the standard error of the mean.
OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of errors is not verified.
For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that out of range (e.g. negative error rates).
If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables the text.
8. Experiments compute resources
For each experiment, does the paper provide sufficient information on com- puter resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
Question:
Answer: [Yes]
Justification: We provide details of the computational resources used for all our experi- ments in the Appendix, well as how long it takes to experiments.
Guidelines:
The answer NA means that the paper does not include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.
The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (c.g., preliminary or failed experiments that didn't 't make into the paper).
9. Code of ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurlPS Code of Ethics
Answer: [Yes]
Justification: The authors have reviewed the NeurIPS Code of Ethics and confirm that this research conforms to the code of ethics.
Guidelines:
The answer NA means that the authors have reviewed the NeurIPS Code of Ethics.
If the authors answer No, they should explain the special circumstances that require deviation from the Code of Ethics.
33

---

The authors should make sure to preserve anonymity (e.g., if there is special consid- eration due to laws or regulations their jurisdiction).
10. Broader impacts
Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: [Yes]
Justification: This work discusses potential negative impacts in the "Limitations and Broader Impacts" section. We also discuss the potential positive societal impacts in the introduction.
Guidelines:
The answer NA means that there is no societal impact of the work performed.
If the authors answer NA or No. they should explain why their work has no societal impact or why the paper does not address societal impact.
Examples of negative societal impacts include potential malicious or unintended uses (e.g.. disinformation, generating fake profiles, surveillance), fairness considerations (e.g.. deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
The conference expects that many papers will be foundational research and tied to particular applications, let alone deployments. However, if there is direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional unintentional) misuse of the technology.
If there negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms monitor how system learns from feedback over time, improving the efficiency and accessibility ML).
11. Safeguards
Does the paper describe safeguards that have been put in place for responsible release of data models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Question:
Answer: [NA]
Justification: The simple semi-synthetic dataset that we will release poses no risk for misuse. Since the authors are not permitted to release any the the real Medicare data, risks regarding the release of the data are minimized.
Guidelines:
The answer NA means that the paper poses no such risks.
Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model. for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards is challenging, and many papers do not require this, but encourage authors to take this into account and make best faith effort.
12. Licenses for existing assets
Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
34

---

Answer: [Yes]
Justification: Citations are provided for relevant code and data that was used for our experiments. License information is provided and respected.
Guidelines:
The answer NA means that the paper does not use existing assets.
The authors should cite the original paper that produced the code package dataset.
The authors should state which version of the asset is used and, if possible, include URL.
The name of the license (e.g.. CC-BY 4.0) should be included for each asset. For scraped data from a particular source (e.g., website). the copyright and terms of service of that source should be provided.
assett are released, the license, copyright information, and terms of use the package should be provided. For popular datasets, paperswithcode com/ datasets has curated licenses for some datasets. Their licensing guide can help determine the license of dataset.
For existing datasets that re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.
If this information is not available online, the authors are encouraged to reach out to asset's s creators.
13. New assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [Yes]
Justification: The only asset introduced in this paper is code repository used for
experiments. The repository includes a README file that contains all of the instructions necessary for running our code.
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details of the dataset/code/moddl as part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent was obtained from people whose asset used.
At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
14. Crowdsourcing and research with human subjects
Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and sereenshots, if applicable, as well as details about compensation (if any)?
Answer: [NA]
Justification: No crowdsoureing experiments were performed in this paper. The Medicare data used for the experiments was purchased following data usage agreement by the Center for Medicare Services.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing research with human subjects.
Including this information in the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then as much detail as possible should be included in the main paper.
According to the NeurlPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
35

---

15. Institutional review board (IRB) approvals or equivalent for research with human subjects
Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or equivalent approval/review based the requirements of your country institution) were obtained?
Answer: [Yes]
The Medicare dataset was obtained from the U.S. Center for Medicare and Medicaid Services under data usage agreement authorizing scope of analyses including misreporting and upcoding in U.S. Medicare. IRB review was not required.
Justification:
Guidelines:
The answer NA means that the paper does not involve crowdsourcing research with human subjects.
Depending on the country in which research is conducted, IRB approval (or equivalent)
may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.
16. Declaration of LLM usage
Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required.
Question:
Answer: [NA]
Justification: At no point were LLMs involved in the core method development of this research.
Guidelines:
The answer NA means that the core method development in this research does not involve LLMs any important, original, non-standard components.
Please refer to our LLM policy http:://naarips.cc//aeteeeeeeeee for what should or should not be described.
36


Reviews:
[{"review_id": "NPXPvLRfQq", "reviewer": "Reviewer_9UrE", "summary": "This paper addresses the problem of detecting and quantifying misreporting by strategic agents in settings where machine learning models are used for resource allocation decisions. The key challenge tackled is distinguishing between two types of strategic behavior: genuine modification and misreporting. The authors' core insight is that misreported features do not causally affect downstream variables, unlike genuinely modified features. Leveraging this asymmetry, they compare causal effects derived from manipulated datasets (where misreporting may occur) and unmanipulated datasets (where misreporting is absent) to quantify the misreporting rate.", "questions": "- How robust is the method to violations of the \"no unobserved confounding\" assumption (Assumption 3)?\n- Can the method be generalized to continuous or categorical features?\n- What are the barriers to deploying CMRE in practice (e.g., data access, model transparency)?", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n- The paper provides formal definitions, assumptions, and proofs for identifiability (Lemma 1, Theorem 1) with a clear mathematical treatment.\n- Addresses a gap in the literature by formally distinguishing misreporting from genuine behavioral change.\n- Using the asymmetric effect on causal descendants to identify misreporting is innovative.\n\nWeaknesses\n- The paper could better explain why misreporting doesn't affect causal descendants before diving into technical details.\n- Identifies average misreporting rates but not individual ones.\n- The no unmeasured confounding assumption (Assumption 3) is untestable and potentially unrealistic in many real-world settings.\n- The reliance on causal descendants means the method may not apply to settings where downstream effects are unobservable or delayed.\n- The approach is most useful in settings where agents have incentives to misreport and unmanipulated data is available, which may not cover all strategic ML scenarios.", "was_revised": true, "final_justification": "I have gone through other reviews and the corresponding responses. Most of my concerns have been addressed. This paper proposes a novel approach for estmating the extent to which strategic agents misreport their features. This setting is useful in practice such as credit. Overall, I recommend to accept this paper.", "rebuttal": "We thank the reviewer for their insightful feedback. We are encouraged that the reviewer values the rigor of our theoretical analysis, the gap our work addresses, and the innovation of our approach.\n\n**1 - No unobserved confounding assumption.** The reviewer is correct in that the no unobserved confounding assumption is untestable. However, it is standard in causal inference literature and even causally-motivated work on strategic adaptation [1]. In addition, our method is compatible with existing sensitivity analysis techniques (e.g., [2]) that can relax Assumption 3 and provide bounds on the misreporting rate. Specifically, one can apply sensitivity analysis to get bounds on the estimated causal effects $\\delta'_a$, $\\tau'_a$, and $\\tau_a$, and then apply those bounds through Theorem 1 to obtain a bound on the misreporting rate. We will highlight sensitivity to confounding as a promising direction for future work in the final version.\n\n\n\n**2 - Can the method be generalized to continuous or categorical features?** We note our method assumes only that $X^\\ast$ and $X$ are binary; other variables ($C$, $A$, $Y$) can be arbitrarily defined. We chose this setup since it allows for a straightforward definition of the misreporting rate. However, our approach could potentially be extended to multi-valued or continuous features with additional parametric and behavioral assumptions (e.g., partially linear models and agents misreporting $X^\\ast$ by applying a fixed additive bias, such that $X = X^\\ast + \\delta$ for some constant $\\delta$). We will add this as a promising direction for future work in the final version.\n\n\n**3 - What are the barriers to deploying CMRE in practice (e.g., data access and transparency)?** CMRE requires access to unmanipulated data -- typically available from pre-deployment training data or audits. Importantly, CMRE does not require access to the internals of the deployed model, making it applicable even with non-transparent, black-box decision models. We view the timeliness of our work as particularly conducive to its practical deployment, as it aligns with the need for operational efficiency and transparent models, increasingly expressed by AI regulators [3, 4].\n\n\n**4 - The paper could better explain why misreporting doesn't effect causal descendants before diving into technical details.** We thank the reviewer for this insightful suggestion. In the final version, we will add the following example based on our Medicare fraud use case: \"If a patient truly has cancer ($X^\\ast = 1$), they may experience cancer-related symptoms ($Y$). However, if an insurer misreports a cancer diagnosis ($X^\\ast = 0$, $X = 1$), this misreporting does not cause the patient to exhibit cancer-related symptoms.\"\n\n**5 - [The work] identifies average misreporting rates but not individual ones.** We thank the reviewer for this comment, and wish to clarify that our method estimates a misreporting rate that is conditional on the agent identity rather than a population average. It can be trivially adapted to identify a misreporting rate that is conditional on features of individual datapoints (e.g., an individual's medical history in the Medicare setting), by estimating the conditional average treatment effect (CATE) versions of the TAFR, NAFR, and TAFM estimands in the paper, conditional on any features of interest. This allows us to identify which datapoints are most likely to be misreported.  We will clarify this in the final version.\n\n\n**6 - The reliance on causal descendants means the method may not apply to settings where downstream effects are unobservable or delayed.** The reviewer is correct that our method requires observing downstream outcomes. In practice, these are often available as the same labels used to train the manipulated model (e.g., enrollee costs in the Medicare risk-adjustment model example).\nWhen outcomes are delayed, surrogate or proxy outcomes can be used, consistent with existing causal literature [5]. We will clarify those two points in the final version. \n\n\n**7 - The approach is most useful in settings where agents have incentives to misreport and unmanipulated data is available, which may not cover all strategic ML scenarios.** We agree that our method is useful for settings where there is an incentive to misreport. Such scenarios are common in practice (e.g., healthcare insurance, hiring, and lending). We also note that unmanipulated data is often available from pre-deployment or from audits.\n\n**Citations**\n\n[1] Chang, Trenton, et al. \"Who’s gaming the system? a causally-motivated approach for detecting strategic adaptation.\" Advances in Neural Information Processing Systems, 2024\n\n[2] Kallus, Nathan, Xiaojie Mao, and Angela Zhou. \"Interval estimation of individual-level causal effects under unobserved confounding.\" The 22nd international conference on artificial intelligence and statistics. PMLR, 2019.\n\n[3] Winning the Race AMERICA’S AI ACTION PLAN, White House\n\n[4] Commission, European, et al. Adopt AI Study – Final Study Report. Publications Office of the European Union, 2024\n\n[5] Athey, Susan, et al. The surrogate index: Combining short-term proxies to estimate long-term treatment effects more rapidly and precisely. No. w26463. National Bureau of Economic Research, 2019."}, {"review_id": "ZNGg0qLCRX", "reviewer": "Reviewer_YpE8", "summary": "This work proposes a causal identification and estimation framework for characterizing settings in which agents may strategically manipulate their characteristics to obtain improved outputs. In particular, the authors disentangle to forms of agent responses: genuine modification, in which an agent alters characteristics in such a way that changes their downstream outcomes, and misreporting, in which agents report incorrect features without a change in their underlying features. The paper establishes the identifying conditions under which the misreporting rate can be identified via a corpus with no misreporting and genuine modification + misreporting. The authors propose an estimator for this estimated and analyze its variance properties, then validate it via synthetic and semi-synthetic experiments.", "questions": "In general I think this work makes a valuable contribution, but have concerns in light of my review above. I will raise my score if the questions below are addressed in a satisfactory manner. \n\n- How robust is the theoretical and experimental results to the the misreporting rate is assumed to only depend on the true feature values $X^{*}$? How easily can the framework be extended to support subgroup-dependent misreporting rates? \n\n- To what extent are values of the $\\beta$ range reported in Figure 2 reasonable? More concretely, what is the estimated $\\beta$ value in the experiments with real data, as a reference point?\n\n\n- How robust are the real-data experimental findings to the exclusion conditions designed to reduce variance, and why are these exclusion conditions reasonable? How robust are the synthetic results to coefficient values?", "limitations": "Yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "## Significance.\n\nThe problem of strategic response to incentives is timely and important. The authors clearly articulate the relevance of this problem via a well-motivated example involving the U.S. Medicare Advantage (MA) program, and show that the proposed approach can be used to address policy-relevant estimation problems in this setting. This is a strong example of use case inspired basic research, that likely generalizes to other similar settings. \n\n## Originality. \n\nThe authors clearly situate the proposed work in the context of other related literature in this space and articulate the technical novelty. \n\nMinor: line 74 claims that prior work by Chang et al. [5] can only partially identify misreporting rates - this is not a limitation of their approach, per se, if this existing framework depends on weaker assumptions. Please clarify this in the next version of the draft. \n\n\n## Clarity.\n\nThe work is generally clear and easy to follow. The use of a running example throughout the work is effective in motivating the technical components. \n\nMinor: \n- The use of observed and true features in potential outcome notation $X(X^*=x^*)$ (line 119) is slightly awkward. I do not see this frequently used throughout the text. Consider revising this notation if possible. \n- In Section 4.1, the build-up to Theorem 1 is somewhat long. Consider shifting Theorem 1 towards the beginning of the section to communicate the key idea then draw connections to Lemma 1 after for intuition. If I am following correctly, Thm 1 does not inherit a direct dependence on Lemma 1 and Lemma 1 is included for pedagogical purposes. \n- Line 206: extra equation number. \n- Lines 144-152. Consider translating this text description of the limitations of status quo estimation approaches into a compelling main figure to clearly convey why the proposed approach is important over a naive baseline. This figure might include an illustrative empirical result from the appendix. \n\n## Quality.\n\nThis work generally meets standards for a causal inference paper with the stated objectives. Assumptions are, for the most part, clearly stated. The identification analysis is clean and interesting. The estimation approach and corresponding experiments are generally well-motivated. That said, I do have several key concerns that affect my scores: \n\n### Restrictive modeling setup. \n\nA key concern I have with the current setup is that the misreporting rate is assumed to only depend on the true feature values $X^\\star$. This assumes that no features confound the relationship between $X^\\star$ and $X$ - which is generally quite strong given the motivating example provided by the authors (e.g., misreporting could be higher for patients with certain medical conditions or coverage). Complicating maters further, this assumption seems to be a core technical requirement of the framework. Eg., the authors assume the misreported group will be a random sample of the group where $X^\\star=0$ (line 172). \n\nAt minimum, this should be clearly acknowledged and explained in the preliminaries and limitations. Ideally, there should be further theoretical/experimental analysis probing robustness to this assumptions' violations. For instance, a few guiding questions are: does the existing analysis carry through if we condition on a confounding variable  $X<-V->X^*$ (where $V$ is the confounder) via a stratification approach? If we took such an approach, how would this affect variance of the estimator in cases where some strata have small treatment effects? Is there a way to test whether this independence assumption is violated in practice?\n\nThe assumption that $X$ and $X^\\star$ are dichotomous is also restrictive, albeit less concerning than the assumption above. \n\nOn the other hand, the generality of the framework across settings Fig 1 (a-c) is a clear strength. \n\n### Variance of the estimator.\n\nAs noted in Section 4.2, the proposed estimator will have high variance in cases where the true treatment effect in the unmanipulated dataset is small. We observe this empirically in Figure 2 (center), where confidence intervals are wide when the effect of $X^\\star$ on Y is small. While some variance in the estimator is tolerable, I have concerns that the extent of the variance in these results may affect the substantive conclusions that can be drawn from the estimation approach. For instance, when $\\beta_{X^\\star}=0.1$, the interval spans roughly 0.03-0.4, which is quite large. To what extent are values of the $\\beta_{X^\\star}$ range reported in Figure 2 reasonable? More concretely, what is the estimated $\\beta_{X^\\star}$ value in the experiments with real data, as a reference point? \n\nFurther, we also observe wide confidence intervals with real data experiments. While the authors note that their approach is the only one that provides MR rates not statistically significantly different from zero (line 342), this is trivially satisfied by wide confidence intervals. For instance, the upper and lower bounds exceed those provided by NDEE and NMRE for Fig. 3 (center).\n\nI have further concerns that the experimental setup may mask further variance issues that would arise under realistic application conditions. In particular, the authors report exclusion conditions (line 318-320) designed to reduce variance in estimates. What percent of records were omitted on the basis of these criteria? How do the results look with these filters omitted? \n\n### Estimators & Experiment Setup. \n\nThe below are more minor points. \n\nFirst, the authors leverage S-learners for estimation. While this is a reasonable starting point, this approach is likely to have larger variance than other DR approaches that apply a first-order bias correction. Expanding to DR estimators may improve the variance properties of the proposed estimator. \n\nSecond, the synthetic experiment with hard-coded coefficients may affect the results. Because this is (understandably) the only experiment with access to true misreporting rates, the setup here is important. The authors should report robustness experiments examining how results change under different D.G.P setups (or with randomly sampled coefficients).", "was_revised": true, "final_justification": "The authors have addressed my concerns regarding the scope of the framework and the experiment design. I remain concerned about the variance of the estimator. I raise my score accordingly.", "rebuttal": "We thank the reviewer for their thoughtful and constructive feedback! The reviewer's comment that our work ``is a strong example of use case inspired basic research'' is truly encouraging. We are also encouraged that they found the problem timely and important, our technical novelty well articulated, and the work clear and easy to follow.\n\n**1 - How robust is the [work to the assumption that] the misreporting rate depends only on the true feature values $X^\\ast$? How easily can the framework be extended to support subgroup-dependent misreporting rates?** We appreciate the reviewer's question and clarify two points: (1) our method already accommodates other variables that affect the misreporting rate, (2) it can be trivially extended to even more fine-grained subgroup-dependent misreporting rates.\n\nFirst, the agent variable $A$ can act as a confounder/effect modifier with $X \\leftarrow A \\rightarrow X^\\ast$ exactly as the reviewer suggests (see figure 1a, b, and c). Our method is able to account for $A$, as reflected in the experiments section, figure 3 (middle and right), where we report misreporting rates conditional on $A=a$ (the insurance company). We acknowledge that lines 172-173 were unclear. Originally, these lines said \"... only the variable $X^\\ast$ influences an agent's decision to misreport...\" A more precise statement is \"Conditional on the agent identity, only $X^{*}$ influences the decision to misreport.\" That is, *conditional* on the agent, the misreported group is a random sample of those with $X^\\ast=0$. We will clarify in the final version.\n\nSecond, our method can be trivially extended to accommodate more granular subgroup analysis by estimating CATE versions of TAFR, NAFR, and TAFM estimands conditioned on any features of interest. While this might increase the variance, as the reviewer noted, it reflects a natural trade-off between granularity and statistical stability that can be navigated based on the application. We will include this discussion in the final version.\n\n\n**2 - Variance of the estimator** The reviewer is correct that our approach gives high variance estimates when the causal effect of $X^\\ast$ on $Y$ is low. However, we view this as a strength -- it appropriately reflects uncertainty rather than projecting false confidence, which is critical in high-stakes settings.\n\nWe also clarify that the non-significant estimated MR rates in Fig. 3 (center) are not simply due to wide intervals. As shown in Fig. 3 (left and right), our method detects significant misreporting when present, indicating that the intervals are informative. The wider intervals in real data reflect honest uncertainty, while NDEE and NMRE yield narrower but biased estimates. Thus, our intervals, though broader, lead to more reliable conclusions.\n\nWe note our analysis gives principled approaches for reducing this variance: by picking downstream variables known to be significantly affected by the potentially misreported variable. For example, in our real data analysis, we used mortality as the downstream outcome for simplicity. However, many diagnoses have weak causal effects on mortality, leading to high variance. Using condition-specific downstream outcomes (e.g., insulin for diabetes-related diagnoses) would likely reduce variance. Further reductions in variance are possible, as the reviewer points out, by using DR estimators rather than S-learners. We used S-learners for simplicity. We will clarify these points in the final version.\n\n**3 - Are the $\\beta$'s chosen for the simulation a good reference point for the real data?** We appreciate the reviewer’s question. The $\\beta$ values were chosen to reflect effect sizes observed in the Medicare dataset. Our simulations used $\\beta \\in [0.1, 0.5]$, consistent with estimated effects shown in Appendix F.1, where each diagnosis’s effect on mortality ($Y$) falls between 0.117 and 0.276. \n\n\n**4 - How robust are the real-data findings to the exclusion [criteria], and why are [they] reasonable? What percent of the records were omitted on the basis of these criteria?** We thank the reviewer for the thoughtful question. No patient records were excluded; the criteria only filtered which of the 182 diagnoses were reported in the appendix table, not which patient records were used in the analysis. In other words, the reported estimates and their variances do not change at all when removing these exclusion criteria. We would just have 182 diagnoses reported rather than the top 10. These thresholds were selected with clinical input to ensure stable estimates when using mortality as the outcome by excluding diagnoses clinically known to have minimal impact on mortality (e.g., cataracts or osteoarthritis of the hip or knee). In our final version, we will consider reporting all diagnoses in the appendix.\n\n\n**5 - How robust are the synthetic results to coefficient values?** We chose coefficients so that the Bernoulli input remained in $[0, 1]$ without requiring transformations (e.g., sigmoid), allowing direct interpretability. Specifically, this allowed us to set the $X^\\ast$ coefficient equal to the causal effect. As the reviewer suggests, an alternative is to draw coefficients randomly and apply a sigmoid to the input of the Bernoulli draw, offering more flexibility but requiring additional steps to recover causal effects. We conducted this analysis and found that our conclusions remain robust.\nThe three tables below shows the results from the reviewer's suggested analysis; it shows the squared error of the estimated misreporting rate. Our approach outperforms the baselines in the majority of settings, and performs comparably (not statistically significantly different from) the best baseline in a few of the settings, as indicated by the bold entries in the tables.\n\n\n\n**6 - The assumption that $X, X^\\ast$ are dichotomous is restrictive.** We chose this setup since it allows for a straightforward definition of the misreporting rate. However, our approach could potentially be extended to multi-valued or continuous features with additional parametric and behavioral assumptions (e.g., partially linear models and agents misreporting $X^\\ast$ by applying a fixed additive bias, such that $X = X^\\ast + \\delta$ for some constant $\\delta$). We will add this as a promising direction for future work in the final version.\n\n\n\n**7 -- Other minor comments**\n- **Prior work by Chang et al.**: We appreciate the reviewer's point and will clarify the differences with Chang et al.\n- **Notation on line 119 is slightly awkward**: We will revise the notation as suggested.\n- **Buildup to Theorem 1 is somewhat long**: We appreciate the reviewer's suggestions and will consider restructuring Section 4.1 to enhance the flow.\n- **Extra equation number**: We will remove.\n- **Convert text description to main figure**: We thank the reviewer for this suggestion! We agree that a visual comparison would clarify the limitations of naive estimators and will add a figure illustrating how our method separates misreporting from genuine modification using causal descendants.\n\n\n### Table 1: MSE of Estimated MR vs Causal Effect of $A$ on $X^\\ast$\n\n| Causal Effect of $A$ on $X^\\ast$ | CMRE (Ours) | NMRE | NDEE | OCSVM |\n|---|---|---|---|---|\n| 0.000 | **0.003 ± 0.004** | 0.157 ± 0.022 | **0.000 ± 0.001** | 0.029 ± 0.002 |\n| 0.050 | **0.003 ± 0.004** | 0.126 ± 0.018 | 0.010 ± 0.003 | 0.028 ± 0.002 |\n| 0.100 | **0.003 ± 0.003** | 0.101 ± 0.016 | 0.031 ± 0.005 | 0.028 ± 0.003 |\n| 0.150 | **0.003 ± 0.003** | 0.084 ± 0.017 | 0.054 ± 0.007 | 0.028 ± 0.003 |\n| 0.200 | **0.003 ± 0.004** | 0.068 ± 0.018 | 0.077 ± 0.007 | 0.029 ± 0.003 |\n| 0.250 | **0.003 ± 0.005** | 0.060 ± 0.016 | 0.099 ± 0.007 | 0.029 ± 0.003 |\n| 0.300 | **0.003 ± 0.006** | 0.052 ± 0.018 | 0.118 ± 0.008 | 0.029 ± 0.003 |\n\n### Table 2: MSE of Estimated MR vs Causal Effect of $X^\\ast$ on $Y$\n\n| Causal Effect of $X^\\ast$ on $Y$ | CMRE (Ours) | NMRE | NDEE | OCSVM |\n|---|---|---|---|---|\n| 0.100 | **0.034 ± 0.073** | 38.053 ± 220.579 | 0.118 ± 0.008 | **0.029 ± 0.003** |\n| 0.200 | **0.009 ± 0.019** | 0.060 ± 0.039 | 0.118 ± 0.008 | **0.029 ± 0.003** |\n| 0.300 | **0.004 ± 0.006** | 0.060 ± 0.024 | 0.118 ± 0.008 | 0.029 ± 0.002 |\n| 0.400 | **0.003 ± 0.006** | 0.052 ± 0.018 | 0.118 ± 0.008 | 0.029 ± 0.003 |\n| 0.500 | **0.002 ± 0.003** | 0.041 ± 0.012 | 0.118 ± 0.008 | 0.028 ± 0.003 |\n\n### Table 3: MSE of Estimated MR vs Misreporting Rate\n\n| Misreporting Rate | CMRE (Ours) | NMRE | NDEE | OCSVM |\n|---|---|---|---|---|\n| 0.000 | **0.003 ± 0.003** | 0.073 ± 0.015 | 0.185 ± 0.012 | **0.001 ± 0.001** |\n| 0.050 | **0.003 ± 0.003** | 0.065 ± 0.015 | 0.167 ± 0.011 | **0.001 ± 0.000** |\n| 0.100 | **0.003 ± 0.003** | 0.058 ± 0.015 | 0.150 ± 0.010 | **0.005 ± 0.001** |\n| 0.150 | **0.003 ± 0.003** | 0.051 ± 0.014 | 0.134 ± 0.009 | 0.014 ± 0.002 |\n| 0.200 | **0.003 ± 0.006** | 0.052 ± 0.018 | 0.118 ± 0.008 | 0.029 ± 0.003 |"}, {"review_id": "Z1hWsaPZcW", "reviewer": "Reviewer_pJAD", "summary": "This paper addresses the challenge of distinguishing between genuine modification and misreporting of features by agents in settings where machine learning models are used for resource allocation, such as in loan applications or government insurance payouts. Agents may either genuinely change their behavior (genuine modification) or simply report false features (misreporting) to obtain better outcomes. The authors propose a causally-motivated approach to identify and quantify the average rate of misreporting by leveraging the fact that misreported features, unlike genuinely modified ones, do not causally affect downstream variables. By comparing the causal effect of features on their descendants in both manipulated (potentially misreported) and unmanipulated datasets, they develop an estimator for the misreporting rate. The paper provides theoretical guarantees for the identifiability and variance of their estimator, and demonstrates its effectiveness with experiments on both semi-synthetic and real Medicare datasets.", "questions": "See Weakness.", "limitations": "NA", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "1. Novel Causal Framework: The paper introduces a new causal approach for disentangling genuine modification from misreporting, providing a theoretically grounded solution to a longstanding problem in strategic behavior and resource allocation settings.\n\n2. Theoretical Guarantees: The authors rigorously prove the identifiability of the misreporting rate and analyze the variance of their estimator, offering strong theoretical justification and transparency for their method.\n\n3. Empirical Validation: The approach is thoroughly validated on both semi-synthtic and real-world datasets, demonstrating its practical utility and superior performance.\n\n\n*Weakness*\n\n1. Strong Assumptions Needed: The method relies on some pretty strong assumptions, like no unobserved confounding, which might not always hold in real-world data. If those assumptions are violated, the results could be off.\n\n2. Requires Special Datasets: You need access to both manipulated (possibly misreported) and unmanipulated datasets. In practice, getting a “clean” dataset where no one has any incentive to misreport isn’t always realistic.\n\n3. Limited Scope for Complex Behavior: The framework mostly handles binary features and assumes misreporting only happens in one direction. It doesn’t really cover more complex or nuanced types of misreporting, so its scope is a bit limited.", "was_revised": true, "final_justification": "I sincerely appreciate the authors’ effort in providing such a detailed and comprehensive response. I will keep the positive rating.", "rebuttal": "We thank the reviewer for their insightful feedback. We are encouraged that the reviewer found our causal framework novel and well-motivated, our theoretical analysis rigorous, and our empirical experiments compelling.\n\n**1 - No unobserved confounding assumption.** The reviewer is correct in that the no unobserved confounding assumption is untestable. However, it is standard in causal inference literature and even causally-motivated work on strategic adaptation [1]. In addition, our method is compatible with existing sensitivity analysis techniques (e.g., [2]) that can relax Assumption 3 and provide bounds on the misreporting rate. Specifically, one can apply sensitivity analysis to get bounds on the estimated causal effects $\\delta'_a$, $\\tau'_a$, and $\\tau_a$, and then apply those bounds through Theorem 1 to obtain a bound on the misreporting rate. We will highlight sensitivity to confounding as a promising direction for future work in the final version.\n\n**2 - Access to a manipulated dataset might be unrealistic.** The reviewer is correct in that our approach requires access to an unmanipulated dataset. We note that such data is often available from pre-deployment (where there may be no incentive to misreport) or from audits.\n\n**3 - The framework mostly handles binary features and assumes misreporting only happens in one direction.**\n\n\nWe note our method assumes only that $X^\\ast$ and $X$ are binary; other variables ($C, A$, $Y$) can be arbitrarily defined. We chose this setup since it allows for a straightforward definition of the misreporting rate. However, our approach could potentially be extended to multi-valued or continuous features with additional parametric and behavioral assumptions (e.g., partially linear models and agents misreporting $X^\\ast$ by applying a fixed additive bias, such that $X = X^\\ast + \\delta$ for some constant $\\delta$). We will add this as a promising direction for future work in the final version.\n\nWe also note that while we assume agents only misreport in one direction (e.g., when $X^\\ast=0$), our framework can be easily adapted to the opposite case (e.g., misreporting only when $X^\\ast=1$). Moreover, one-directional misreporting is a realistic assumption -- e.g., in the Medicare context, private insurers are always incentivised to overreport diagnoses to increase reimbursement and have no incentive to underreport. Similar incentive asymmetries exist in school admissions, loan applications, and health insurance quotes (e.g., GPA, employment, health).\n\n\n**Citations**\n\n[1] Chang, Trenton, et al. \"Who’s gaming the system? a causally-motivated approach for detecting strategic adaptation.\" Advances in Neural Information Processing Systems, 2024\n\n[2] Kallus, Nathan, Xiaojie Mao, and Angela Zhou. \"Interval estimation of individual-level causal effects under unobserved confounding.\" The 22nd international conference on artificial intelligence and statistics. PMLR, 2019."}]

Author rebuttal:

Meta-review: This paper introduces a causal inference framework to estimate the extent of misreporting in strategic settings, distinguishing deceptive reporting from genuine behavioral modifications. The approach leverages differences in causal effects on downstream variables across manipulated and unmanipulated datasets, with theoretical guarantees and empirical validation on synthetic and Medicare data.

The paper is well-regarded for its novelty in separating misreporting from genuine modification, the rigor of its identifiability analysis, and the policy relevance of its motivating applications. Reviewers noted that the framework is conceptually elegant, technically sound, and clearly presented, with the Medicare example demonstrating its practical importance.

Remaining concerns focused on modeling assumptions, estimator variance, and generalizability. Reviewers highlighted the reliance on the no unobserved confounding assumption, the restriction to binary features and one-directional misreporting, and the requirement for unmanipulated datasets. While these assumptions are strong, the rebuttal clarified their prevalence in causality work and offered sensitivity analysis and extensions as possible future work. Concerns about estimator variance were acknowledged, though reviewers agreed the method offers more reliable estimates than biased alternatives.

Given the novelty, theoretical contribution, clear positioning in the literature, and thoughtful empirical validation, the reviewers converged toward acceptance despite some minor remaining concerns such as variance of the estimator.

To further strengthen the work, the authors are encouraged to streamline the exposition of key results (e.g., moving Theorem 1 earlier), improve clarity around assumptions and their limitations, and expand on practical strategies for reducing estimator variance. Discussion of extensions to richer feature types and more complex misreporting patterns would also broaden the applicability of the framework.
Decision: Accept (poster)