Monetary and Non-monetary Barriers to Accessing Environmental Public Benefit Programs: Experimental Evidence from California

This study will distribute a small number of portable residential air purifiers to residents in California. We sample a subset of California addresses and send an offer letter to purchase air purifiers at a discount. In the offer letter, we randomize the subsidy rate, the ordeal cost of application, and the amount of information pertaining to air quality and mitigation strategies. We will observe whether each letter recipient applies to the program through our online application portal. The following list summarizes the features of the treatment arms.

• T0: “Control” arm. The letter will encourage recipients to apply for an air purifier through our website. They will not be offered a subsidy, except for free shipping.
• T1: 50% subsidy treatment. The letter will encourage recipients to apply through our website for a 50% discount on an air purifier, plus free shipping.
• T2: 75% subsidy treatment. The letter will encourage recipients to apply through our website for a 75% discount on an air purifier, plus free shipping.
• T3: 95% subsidy treatment. The letter will encourage recipients to apply through our website for a 95% discount on an air purifier, plus free shipping.
• T4: 100% subsidy treatment. The letter will encourage recip- ients to apply through our website for a free (100% discount) air purifier, plus free shipping.
• T5: 100% subsidy treatment with time costs. The letter will encourage recipients to apply through our website for a free air purifier. Applicants will be asked to fill out a longer form on the application portal that we expect to take approximately 15 minutes, as opposed to 5 minutes in other treatment arms.
• T6: 100% subsidy treatment with proof of residence. The letter will encourage recipients to apply through our website for a free air purifier. Applicants will be asked to upload proof of residence, such as a bill delivered to them with their name and address on it. The treatment is otherwise identical to T3.
• T7: 100% subsidy treatment with proof of residence and information about the application process. The information is identical to T5, except for the following. First, the letter includes additional details about the types of forms that are required as proof of residence. Second, the letter also contains a link to our website that gives additional information about the application process.
• T8: 100% subsidy treatment with information about air quality. The letter will encourage recipients to apply through our website for a free air purifier. They also receive additional information about the health impact of air pollution, summary statistics on poor air quality days in California overall and for their county based on the U.S. EPA AQI Report, and a link on our website for additional information about the health impact of air pollution and mitigation strategies.

2026-01-15

2027-01-15

• 1 if a letter recipient provides all required information and clicks “submit” on the application form and zero otherwise.
• Natural log of self-reported annual household income of the applicant from 2025. The measure is collected as part of the application questionnaire.

N/A

• average PM2.5 concentration between 2021-2023 for the address’ Census Tract, based on CARB’s estimates
• 1 if White non-Hispanic, zero otherwise, based on the race and ethnicity estimates in the mailer data
• 1 if language at home is English, zero otherwise, based on the language estimates in the mailer data
• 1 if the household’s estimated income is at or below $75,000, and 0 otherwise and non-missing, based on the binned income estimates from the mailer data
• Several thresholds (below 100%, 138%, 200%, 300%, and 400%) against the federal poverty line (FPL), based on the binned income and household size estimates from the mailer data

See PAP for more details.

The sampling frame is based on a mailing list purchased from a direct mailing company, containing approximately 12 million individuals from the State of California. We stratify the restricted mailing list based on the estimated income, household size, and county-level PM2.5 concentration. We use the mailing list's binned measure for estimated income. We group the household size into 1, 2, 3, and 4 or larger. We aggregate the PM2.5 measures into quartiles at the county level. The strata are interactions of the income, household, and PM2.5 bins. We sample approximately 90,000 addresses from the stratified list, with twice as large a sampling probability for strata with household income less than $75,000. We employ differential weights so that the program targets lower-income households, as per the policy objective of our subsidized air purifier program.

We assign each of the 90,179 sampled addresses to eight groups via stratified randomization. We use the same stratifying variables as in sampling. To identify the optimal sample split across treatment arms, we specify 6 broad hypotheses that we test based on which of the 9 treatment groups, as follows:
• price variations in the positive price range (T0, T1, T2, and T3)
• non-zero prices v.s. zero price (T3 and T4)
• additional time costs (T4 and T5)
• proof of residency (T4 and T6)
• additional information pertaining to proof of residency (T6 and T7)
• additional information about air pollution and its health impact (T4 and T8)
We then count the “uses” per treatment group, as shown in Table 1 of the PAP. The resulting sample sizes by treatment group are shown in Table 2 of the PAP. We then follow the square-root allocation rule to convert the uses to the sample allocation ratio.

Not available

Randomization done in office by a computer (Stata)

Individual

No

N/A

90,179 addresses

Number of addresses per treatment group:
T0: 6,575
T1: 6,590
T2: 6,579
T3: 11,293
T4: 18,483
T5: 9,194
T6: 13,067
T7: 9,203
T8: 9,195

We calculate the minimum detectable treatment effect sizes for the two primary outcome variables based on the prespecified empirical strategy. We calculate minimum detectable effects (MDEs) on a range of baseline response rates between 0.25% and 5%. When necessary, we pick 0.34% and 2% for low and high response-rate scenarios, based on baseline results. For the log income outcome variable, we assume the baseline mean of 11.07 with the standard deviation of 1.01, based on summary statistics from the pilot data. We calculate these MDEs for a given pair of treatment arms, which could be as small as approximately 6,600 recipients each, or as large as approximately 11,000 and 18,000 recipients. We assume a 0% attrition rate because the outcome of interest is whether a recipient applies and is, by definition, fully captured in the data. For the pairwise comparison of 6,600 v.s. 6,600 recipients, we expect the baseline response rate to be around the lower end of the chosen range (i.e., closer to 0.25%). At the baseline response rate of 0.25%, the MDE is .27% with Bonferroni correction. We expect the baseline response rate for the pairwise comparison of 11,000 v.s. 18,000 recipients to be relatively large, at around 2%. In that scenario, the MDE is 0.52% with Bonferroni correction. As such, we are well-powered to detect economically meaningful differences in application rates. For the applicants’ log income outcome variable, the MDE is 164% of the mean for the pairwise comparison of treatment groups with the smallest numbers of applicants, and 38% for those with the largest numbers. We take these MDE estimates as speculative, as they rest on additional assumptions about application rates. We plan to test the robustness of the effects of treatment conditions on applicant characteristics through a series of heterogeneous treatment effect estimates.