Ceci N'est Pas un Proxy
Chaturvedi, Das, and Mahajan (2024) argue that female reservation in the 2015 Gram Panchayat elections raised household toilet provision more in villages with a higher Muslim share. At low Muslim share the estimated reservation effect is essentially zero. In villages where Muslims make up about a quarter of the population, reservation raises the probability of toilet allocation by roughly 10 percentage points on a baseline of 10 percent, nearly doubling it. The paper reads this gradient as evidence that descriptive representation produces larger policy shifts where the female-male preference gap is larger.
The theoretical framework comes from Chattopadhyay and Duflo (2004). Female and male leaders allocate resources as a weighted function of constituent preferences, with female leaders placing more weight on women's preferences, and the treatment effect of reservation on any good is proportional to the female-male preference gap on that good. If women and men want the same thing, the leader's gender does not matter for policy. CDM extend this. They argue that in their UP setting the supply-side channel — female-male differences in leader ideal points — is small, based on close-election tests between Muslim and Hindu Sarpanches that find no differential effect. The treatment effect instead comes from a demand channel: women express their preferences more strongly under female leadership, and that expressed demand shifts allocation. Both channels produce the same functional form, but the demand channel is the specific mechanism the paper defends. Muslim share enters as a proxy for the size of the gap on toilets, and the proxy rests on two claims stated separately in Sections 3.1 and 3.2. The first is that women prefer toilets more than men, motivated by Coffey et al. (2014) and related work. The second is that this gap is larger among Muslims than Hindus, because Hindu norms around purity and pollution make in-home toilets culturally problematic while mobility restrictions on Muslim women raise their demand.
For that chain to support the headline interpretation, three things have to hold. First, Muslim share must actually proxy the female-male gap in preference for toilets, not some other kind of gradient. Second, that preference gap must be present in Uttar Pradesh alone, the setting where the policy effect is estimated. Third, the magnitude of the policy response must be commensurate with what the preference evidence predicts, not several times larger and not identically sized for reasons that would require an unusual model of how leaders respond to constituents. The evidence runs into trouble on all three counts.
Alignment problems
The paper's case has three moving parts: a preference gap in Table 2, a policy result in Table 3, and a demand mechanism in Tables 4 and 5 that is supposed to connect them. Evidence for each part comes from a different sample, and the samples do not line up in the way the argument requires. The preference gradient in Table 2 is not present in UP, where Table 3 is estimated. It is not driven by Muslim women, the group the proxy is supposed to represent. The demand mechanism is precisely estimated only for Muslim female-headed households, who are a small slice of Table 3's sample.
The preference gradient is not present in UP. The SQUAT survey that supports Table 2 is pooled across five north Indian states: Bihar, Uttar Pradesh, Haryana, Madhya Pradesh, and Rajasthan. The policy result in Table 3 is from UP alone. Running Table 2's stated-preference specification by state shows that the Female × Muslim share interaction in UP is −0.404 (SE 0.252) on top-priority preference and −0.224 (SE 0.260) on top-two priority. Both are negative and neither is distinguishable from zero. The pooled positive coefficient is driven by Bihar and Madhya Pradesh. The preference gradient that is supposed to explain the policy result does not exist in the setting where the policy result is estimated. The paper does not report or discuss state-level heterogeneity in Table 2.
The pooled gradient is not driven by Muslim women. Table 2 includes village fixed effects but does not separate Hindu and Muslim women. The Female × Muslim share interaction captures the behavior of all women in higher-Muslim-share villages, Hindu women included. Table C7 adds a triple interaction Muslim × Female × Muslim share to decompose the coefficient. In the household-fixed-effects specification, the Female × Muslim share coefficient, which now represents the Hindu women's gradient, is 0.170 and significant. The additional Muslim premium is −0.109 and insignificant. The preference gradient that the paper offers as a proxy for Muslim women's stronger demand is not coming from Muslim women specifically. It is coming from Hindu women in villages with a higher Muslim share. Whatever produces their higher expressed preference for toilets, whether it involves neighborhood safety, dress norms, or something about selection into these villages, is not the within-Muslim-household channel the theoretical argument requires.
Mechanism evidence concentrates in a small subgroup. Table 4 (complaints to the sarpanch) reports a Muslim FHH × Female reservation coefficient of 0.242 that is statistically significant; the Hindu FHH coefficient is smaller and imprecisely estimated. Table 5 (toilet allocation to female-headed households) shows the same asymmetry. Under Hindu sarpanches, the coefficient for Muslim FHHs is 0.346 and significant while the coefficient for Hindu FHHs is 0.050 and imprecise; the paper reports that the difference between the two is significant at p = 0.02. Under Muslim sarpanches, both the Hindu FHH (0.360) and Muslim FHH (0.489) coefficients are large in magnitude, but only the latter is precisely estimated. Whether Hindu FHHs respond substantially is a live possibility the data do not rule out, and the 0.36 point estimate under Muslim sarpanches is consistent with a non-trivial effect — but the clear statistical signal for the mechanism is confined to Muslim female-headed households. Female-headed households are about 4 percent of Table 3's sample, and the precisely-estimated mechanism evidence runs through a subset of that 4 percent.
The group producing the Table 2 preference gradient is all women, primarily Hindu. The group with the clearest statistical evidence for the mechanism in Tables 4 and 5 is Muslim female-headed households. The group in Table 3 is all eligible households, overwhelmingly Hindu and not female-headed. The precise evidence at each step runs through a different population.
The preference evidence is fragile on its own terms
Three further properties of the stated-preference columns in Table 2 weaken them as evidence. The first concerns the baseline claim from Section 3.1. In the specification that supports the differential claim (Table 2's columns (3) through (5), which include the Female × Muslim share interaction), the Female main effect is 0.033, −0.012, and 0.001, none of them distinguishable from zero. The Hindu gender gap in stated preference is essentially zero. This is formally consistent with the paper's theoretical prediction that the gap is larger among Muslims, but it also means that in the population most relevant to the Table 3 result, which is overwhelmingly Hindu, the paper's premise that women prefer toilets more than men does not hold on average. The gender difference in stated preference comes through the Muslim-share interaction and effectively through Muslim women alone.
The second is that the outcome means are high: 46 percent for top priority, 65 percent for top-two, 78 percent for top-three. Nearly everyone in the sample, male and female, already ranks toilets as a priority, and a linear probability model pushes predicted values toward or past one at higher Muslim shares. The third is that the UP sample size is small: 392 respondents for columns (3) through (5), compared to 1,825 individuals in the usage columns.
Calibration
The cleanest way to connect Table 2 to Table 3 is through columns (3) through (5), which measure stated preference among non-owners. That sample matches Table 3's sample of eligible households without toilets. The Female × Muslim share coefficients in those columns are 0.336, 0.434, and 0.378, with the last two significant. A 10 percentage point increase in Muslim share raises the stated-preference gender gap by roughly 3.4 to 4.3 percentage points. Table 3's interaction implies a 10 percentage point increase in Muslim share changes the reservation effect by roughly 3 to 5 percentage points, using the middle column's estimate of −0.0272 + 0.403s. The two gradients sit in essentially the same range.
Matching gradients mean the channel — supply, demand, or combined — maps preferences into policy at unit rate. Under the supply reading, α_F ≈ 1 and α_M ≈ 0: female leaders respond almost exclusively to women, male leaders to men, with minimal cross-gender responsiveness. Under the demand reading, every unit of expressed preference gap translates to a unit of policy gap with no attenuation anywhere along the chain.
The demand reading is the one CDM defend, which makes the representation-elasticity literature a direct benchmark. A pass-through of one from a group-specific preference gap to a policy allocation gap would be extraordinary. Across four decades of empirical work, pass-through coefficients typically fall in the 0.1 to 0.4 range, with an upper bound of roughly 0.5 to 0.6 on highly salient single-issue questions. Gilens (2005) reports logit coefficients of 1.22 at the 10th income percentile and 2.25 at the 90th, but when the rich and poor actually disagree, the 10th-percentile coefficient collapses to 0.04 and is statistically indistinguishable from zero. Gilens and Page (2014) find average-citizen influence statistically indistinguishable from zero after purging the correlated component of preferences. Branham, Soroka, and Wlezien (2017) show that when the rich and middle disagree, the rich win 53 percent of the time versus 47 percent for the middle, a pass-through of roughly 0.9 on the selected disagreement cases but an order of magnitude smaller across the full sample. Audit studies on race find differential treatment effects of 5 to 18 percentage points on response rates that translate to far smaller pass-through once scaled by the preference gap. Lowande, Ritchie, and Lauterbach (2019), the closest analogue to the question here, find that female legislators are about 8 percentage points more likely to contact agencies on behalf of women, a relative effect of about 40 percent on a baseline of 20 percent, still well below unity on the absolute scale. Miller and Stokes (1963) dyadic correlations between district opinion and roll-call voting sit around 0.3 for social welfare and 0.6 for civil rights.
The literature on India produces similarly bounded estimates. Chattopadhyay and Duflo themselves, in the paper that originated this framework, explicitly note that α cannot be separately identified from their other structural parameters, and the coefficient on reservation interacted with village-specific female complaints (R·D_ij in their equation 3) is insignificant: female pradhans in their West Bengal and Rajasthan data do not respond more to local female preference gaps than to their own ideal points. Pande (2003) finds that SC reservation does not raise SC welfare spending and that ST reservation does not affect job quotas, implying partial and uneven pass-through. Bhalotra, Clots-Figueras, Cassan, and Iyer (2014) find that Muslim political representation improves outcomes broadly without differential Muslim-favoring effects, a non-delegate pattern.
A unit elasticity in rural UP gram panchayats, with newly elected, often first-time, sometimes proxy woman pradhans, would be the tightest delegate-style pass-through documented anywhere. The more natural reading is that the numerator and the denominator of the implied elasticity are both being scaled by the same Muslim-share slope, and their ratio is mechanically close to one without corresponding to a real structural pass-through.