indicator and lagged participation, and indicators for whether he/she would remain in the city permanently if policy permitted and whether he/she is working or not. **W** 0 _ij_ is a set of pre-treatment firm size and ownership indicator variables for the employer of individual _i_ ; and _δj_ are city fixed effects, which control for both time invariant city-level factors and within city changes between years 0 (2015) and 1 (2016), including systematic changes in the costs and benefits of the health insurance and pension schemes.<sup>15</sup> The coefficient of interest in equation (1) is _β_ , the average treatment effect of exposure to the information intervention.

Existence, or lack, of a written employment contract introduces one potential source of heterogeneous impacts. In design of the intervention and at the pre-analysis stage, the team anticipated that the effect of providing information about social insurance will differ considerably depending on whether a respondent has an employment contract. As shown in Figure 1, health insurance and pension participation rates for those with employment contracts in 2015 were 72%, while participation was only 13% for those without a written contract. As it is likely that those without a written contract will be most affected by the information intervention, we estimate equation (1) including an indicator for “no written contract” in 2015, _NC_ 0 _ij_ , and the interaction of _NC_ 0 _ij_ and the treatment indicator, _Tij_ : In this specification, the coefficients of interest are _β_ , which indicates the treatment effect for individuals with a written contract in 2015, and _β_ + _φ_ , treatment effect for individuals without a written contract in 2015. _φ_ indicates whether or not the treatment effects for the two groups differ.

Subsequent to the intervention, recognition of the variation in premiums across cities and apparent heterogeneity in responses to treatment, led the team to examine whether the effects of providing information varied with relative premia.<sup>16</sup> Another plausible factor influencing participation decisions are the magnitudes of premiums relative to earnings for health insurance and pension programs. As will become apparent in our discussion of results below, premiums vary considerably by city, and information may interact with price in influencing the decision to participate. To this end, we next estimate models in which the treatment indicator, _Tij_ , is interacted with a city relative price (premium) variable:

> 15As the randomization was implemented separately in each of the 13 cities in the sample and city level costs and benefits vary significantly, the baseline model includes the set of city fixed effects, _δj_ , along with the treatment indicator and lagged participation. Further, as randomization into treatment was implemented at the household level, we equally weight each household in the following analysis to provide efficient estimates (Athey and Imbens, 2017). Household members may also share cost and benefits of social insurance in China, and social insurance participation is a joint decision of household members, especially for poor migrant households.

> 16While examining this dimension of heterogeneity was not part of a pre-analysis plan, the cities (and all the differences across them) were chosen as part of the pre-analysis as they were part of the baseline survey.

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