kmr: A Command to Correct Survey Weights for Unit Nonresponse using - PowerPoint PPT Presentation

kmr: A Command to Correct Survey Weights for Unit Nonresponse using Group’s Response Rates Ercio Munoz CUNY Graduate Center and Stone Center on Socio-Economic Inequality Stata Conference Chicago 2019 July 12, 2019 1 / 21

Motivation 2 / 21

Bias in inequality measures due to unit nonresponse Bollinger et al. (2019, JPE) links internal CPS data to Social Security admin. data to show that nonresponse across the earnings distribution is U-shaped. - Korinek et al. (2007, J. Econometrics) proposed a method to correct for unit nonresponse bias using response rates by region. Advantages: 1) It does not assume ignorability within the smallest unit and 2) relies solely on data from the survey. - The method has been recently used with data from Egypt and EU (see Hlasny & Verne 2018a, 2018b). 3 / 21 - There is evidence that income systematically afgects survey response. For example,

Bias in inequality measures due to unit nonresponse Bollinger et al. (2019, JPE) links internal CPS data to Social Security admin. data to show that nonresponse across the earnings distribution is U-shaped. - Korinek et al. (2007, J. Econometrics) proposed a method to correct for unit nonresponse bias using response rates by region. Advantages: 1) It does not assume ignorability within the smallest unit and 2) relies solely on data from the survey. - The method has been recently used with data from Egypt and EU (see Hlasny & Verne 2018a, 2018b). 3 / 21 - There is evidence that income systematically afgects survey response. For example,

Bias in inequality measures due to unit nonresponse Bollinger et al. (2019, JPE) links internal CPS data to Social Security admin. data to show that nonresponse across the earnings distribution is U-shaped. - Korinek et al. (2007, J. Econometrics) proposed a method to correct for unit nonresponse bias using response rates by region. Advantages: 1) It does not assume ignorability within the smallest unit and 2) relies solely on data from the survey. - The method has been recently used with data from Egypt and EU (see Hlasny & Verne 2018a, 2018b). 3 / 21 - There is evidence that income systematically afgects survey response. For example,

This presentation suggested by Korinek et al. (2007), which estimates a micro compliance function that can be used to re-weight the survey. - Introduce a Stata command (kmr) to implement this method (Morelli and Munoz, 2019a). - Show the command in use with an empirical example: Inequality, total income, and poverty rate in the US estimated with the CPS correcting for unit non-response (Morelli and Munoz, 2019b). 4 / 21 - Briefmy describe the econometric method to correct for unit non-response bias

This presentation suggested by Korinek et al. (2007), which estimates a micro compliance function that can be used to re-weight the survey. - Introduce a Stata command (kmr) to implement this method (Morelli and Munoz, 2019a). - Show the command in use with an empirical example: Inequality, total income, and poverty rate in the US estimated with the CPS correcting for unit non-response (Morelli and Munoz, 2019b). 4 / 21 - Briefmy describe the econometric method to correct for unit non-response bias

This presentation suggested by Korinek et al. (2007), which estimates a micro compliance function that can be used to re-weight the survey. - Introduce a Stata command (kmr) to implement this method (Morelli and Munoz, 2019a). - Show the command in use with an empirical example: Inequality, total income, and poverty rate in the US estimated with the CPS correcting for unit non-response (Morelli and Munoz, 2019b). 4 / 21 - Briefmy describe the econometric method to correct for unit non-response bias

Methodology 5 / 21

Intuition: 3x3 model of selective compliance 30 2 30K 30 15 1/2 2 100K 3 30 1/10 3 20K 30 30 1 However, we do not know the total number of households sampled and the probability of response by income. 1 30 Assumption: Response does not change across regions and depends on income. 20K By household income, the number of answers should equal the total number of households sampled multiplied by the probability of response: Region Income Sampled Answers Probability 1 30 20K 30 1 1 30K 30 15 1/2 2 6 / 21

Intuition 30 P 30K 2 100K 3 90 P 100K 3 20K 30 P 20K What we do know is the total number of household sampled by region, and we can use it Region Answers Sampled by region 1 60 2 90 3 30/P 20K 30 90 15 30K 2 to solve for P i : Region Income Answers Sampled by region Probability 1 20K 30 60 P 20K 1 30K 15 60 P 30K 2 20K 30 90 P 20K 7 / 21 30/P 20K + 15 / P 30K 30/P 20K + 15 / P 30K + 3 / P 100K

Generalization for I income groups and J geographic areas (I>J) m 1 (3) P i ij m 1 with expected value: (2) 0 Denote the mass of respondents as: (1) form: household response and 0 otherwise, and that the probability of response has a logistic 8 / 21 For each sampled household ϵ , there is a Bernoulli variable D ij ϵ that equals 1 if the e X i θ P ( D ij ϵ = 1 | X i , θ ) = 1 + e X i θ ∫ m ij ij = D ij ϵ d ϵ E [ m 1 ij ] = m ij P i E [ ] = m ij

Generalization for I income groups and J geographic areas (I>J) P i Where W is a positive defjnite weighting matrix. (5) (4) P i ij m 1 i Then the sum of all the ratios for a given region j: 9 / 21 ij m 1 P i ij m 1 i ψ j ( θ ) = ∑ ] } = ∑ { − E [ − m j Given that E [ ψ j ( θ )] = 0, we can stack J moment conditions ψ j ( θ ) into Ψ ( θ ) , so: θ = argmin θ Ψ ( θ ) ′ W − 1 Ψ ( θ ) ˆ

Syntax of the command 10 / 21

Syntax of the command kmr [varlist] [if] [in], groups(varname) interview(varname) nonresponse(varname) options where the options are: - noconstant - generate(newvarname) - graph(varname) - technique(string) - start(num) - maxiter(num) 11 / 21

Empirical example using the CPS 12 / 21

State-level variation in non-response rate in 2018 13 / 21 20.1 − 24.9 17.9 − 20.1 16.9 − 17.9 15.5 − 16.9 13.5 − 15.5 12.8 − 13.5 12.1 − 12.8 11.2 − 12.1 10.2 − 11.2 7.2 − 10.2

Estimates for 2018 - Gini goes from 46.5 to 50.5 Generated by running: kmr ly, groups(statefjp) i(interview) n(typea) 14 / 21

Compliance function in 2018 15 / 21 1 .8 Probability of response .6 .4 .2 0 0 5 10 15 Log(income per capita)

Estimates for 2018 - Gini goes from 46.5 to 53 Generated by running: kmr ly ly2, groups(statefjp) i(interview) n(typea) 16 / 21

Compliance function in 2018 - Adding squared log of income 17 / 21 1 .8 Probability of response .6 .4 .2 0 0 5 10 15 Log(income per capita)

Source: Own elaboration using NBER CPS supplements. Aggregate non-response rate in the CPS on the rise 18 / 21 14 Nonresponse rate (% of interviews) 12 10 8 6 4 1980 1990 2000 2010 2020 Year

19 / 21 Estimates over time {X i θ = θ 1 + θ 2 log ( y i ) } 0 30 25 -1 20 15 -2 10 5 -3 1980 1990 2000 2010 2020 1980 1990 2000 2010 2020 year year Coef. Confidence interval Coef. Confidence interval

Average correction across years 1977-2018 Table: Correction with respect to uncorrected grossed-up weights by state -13.60% 16.60% 46.8% 11.81% -4.88% 11.40% 52.54% 11.64% -8.66% 8.66% 36.71% 8.09% -8.07% 8.07% 40% 8.47% Best model (7-year windows) Poverty rate Total income Top 1% income share Gini Model 20 / 21 X i θ = θ 1 + θ 2 log ( y i ) + θ 3 log ( y i ) 2 - y/y X i θ = θ 1 + θ 2 log ( y i ) + θ 3 log ( y i ) 2 - pooled X i θ = θ 1 + θ 2 log ( y i ) - pooled

References - Korinek, A., J. Mistiaen, and M. Ravallion (2007), “An Econometric Method of Survey.” mimeo - Morelli and Munoz (2019b), “Unit Nonresponse Bias in the Current Population Nonresponse using Group’s Response Rates.” mimeo - Morelli and Munoz (2019a), “kmr: A Command to Correct Survey Weights for Unit 136:213-235 Correcting for Unit Nonresponse Bias in Surveys.” Journal of Econometrics Egypt.” The World Bank Economic Review 32(2) - Hlasny and Verme (2018b), “Top Incomes and the Measurement of Inequality in Econometrics 6(30) Comparative Analysis of Correction Methods using the EU SILC Data.” - Hlasny and Verme (2018a), “Top Incomes and Inequality Measurement: A Welch”. Forthcoming at Journal of Political Economy. What We Know about Earnings Nonresponse Thirty Years after Lillard, Smith, and 21 / 21 - Bollinger, C., B. Hirsch, C. Hokayem, and J. Ziliak (2019), “Trouble in the Tails?