
Estimating Confidence Intervals in a Tax Microsimulation Model
Tables
Population and Sample Size of TPC Microsimulation Model, 2019
Expanded Cash Income Level (thousands of 2019 dollars) | Population (Tax Unit) | Sample Size | ||
---|---|---|---|---|
Number (thousands) | Percent of Total | Number (thousands) | Percent of Total | |
Less than 10 | 12,323 | 7.1 | 8 | 3.3 |
10–20 | 21,651 | 12.4 | 16 | 6.3 |
20–30 | 19,523 | 11.2 | 16 | 6.3 |
30–40 | 15,976 | 9.2 | 14 | 5.5 |
40–50 | 13,399 | 7.7 | 12 | 4.8 |
50–75 | 25,288 | 14.5 | 27 | 10.4 |
75–100 | 16,983 | 9.7 | 20 | 7.8 |
100–200 | 31,667 | 18.1 | 43 | 16.8 |
200–500 | 14,026 | 8.0 | 35 | 13.8 |
500–1,000 | 1,826 | 1.1 | 16 | 6.3 |
More than 1,000 | 837 | 0.5 | 40 | 15.7 |
All | 174,690 | 100.0 | 256 | 100.0 |
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Source: Urban-Brookings Tax Policy Center Microsimulation Model (version 0319-1).
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Note: The sample exclude tax units with negative AGI or ECI.
Partially Restore the Personal Exemption to $4,000, Selected Income Groups, 2019
Expanded Cash Income Level (thousands of 2019 dollars) | Tax Units with Tax Cut | Percent Change in After-Tax Income | Average Federal Tax Change ($) | ||
---|---|---|---|---|---|
Percent of Tax Units | Average Tax Change ($) | ||||
75–100 | 94.239 (0.314) | −1,085.1 (4.5) | 1.370 (0.008) | −1,022.6 (5.7) | |
[93.599, 94.843] | [−1,094.0, −1,076.8] | [1.351, 1.383] | [−1,032.4, −1,009.9] | ||
200–500 | 98.470 (0.080) | −2,496.9 (10.7) | 1.077 (0.006) | −2,458.6 (10.9) | |
[98.296, 98.615] | [−2,515.1, −2,475.3] | [1.065, 1.088] | [−2,479.3, −2,435.9] | ||
More than 1,000 | 0.620 (0.176) | −1,214.3 (242.8) | 0.000 (0.000) | −7.5 (2.6) | |
[0.334, 1.054] | [−1,680.9, −789.1] | [0.000, 0.001] | [−13.2, −2.9] | ||
All | 62.332 (0.131) | −1,216.4 (2.8) | 0.933 (0.004) | −758.2 (1.7) | |
[62.033, 62.542] | [−1,220.9, −1,210.7] | [0.927, 0.943] | [−761.6, −754.6] | ||
Addendum: Confidence Intervals Calculated Using Bootstrap and Using Normal Approximation of BSE | |||||
75–100 | Bootstrap | [93.599, 94.843] | [−1,094.0, −1,076.8] | [1.351, 1.383] | [−1,032.4, −1,009.9] |
Normal with BSE | [93.624, 94.854] | [−1,093.9, −1,076.2] | [1.354, 1.386] | [−1,033.7, −1,011.4] | |
200–500 | Bootstrap | [98.296, 98.615] | [−2,515.1, −2,475.3] | [1.065, 1.088] | [−2,479.3, −2,435.9] |
Normal with BSE | [98.313, 98.628] | [−2,517.9, −2,475.9] | [1.065, 1.089] | [−2,479.9, −2,437.4] | |
More than 1,000 | Bootstrap | [0.334, 1.054] | [−1,680.9, −789.1] | [0.000, 0.001] | [−13.2, −2.9] |
Normal with BSE | [0.275, 0.966] | [−1,690.2, −738.4] | [0.000, 0.001] | [−12.6, −2.4] | |
All | Bootstrap | [62.033, 62.542] | [−1,220.9, −1,210.7] | [0.927, 0.943] | [−761.6, −754.6] |
Normal with BSE | [62.075, 62.589] | [−1,221.8, −1,210.9] | [0.926, 0.941] | [−761.6, −754.8] |
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Source: Urban-Brookings Tax Policy Center Microsimulation Model (version 0319-1).
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Notes: Proposal would partially restore the personal exemption of $4,000 in 2019.
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Numbers in parentheses are bootstrapped standard errors (BSE). Numbers in brackets are confidence intervals.
Comparison of Population and Sample Size Affected by Partially Restoring the Personal Exemption to $4,000, Selected Income Groups, 2019
Expanded Cash Income Level (thousands of 2019 dollars) | All Tax Units | Tax Units with Tax Change | Tax Change ($) | |||||
---|---|---|---|---|---|---|---|---|
Population Number | Sample Number | Population | Sample | Minimum | Maximum | |||
Number | Share within Income Group | Number | Share within Income Group | |||||
200–500 | 14,026,200 | 35,400 | 13,815,800 | 98.50% | 32,220 | 91.00% | 14 | 11,000 |
More than 1,000 | 836,500 | 40,100 | 5,190 | 0.62% | 71 | 0.18% | 15 | 3,840 |
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Source: Urban-Brookings Tax Policy Center Microsimulation Model (version 0319-1).
Increase the Standard Deduction to $4,000, Selected Income Groups, 2019
Expanded Cash Income Level (thousands of 2019 dollars) | Tax Units with Tax Cut | Percent Change in After-Tax Income | Average Federal Tax Change ($) | ||
---|---|---|---|---|---|
Percent of Tax Units | Average Tax Change ($) | ||||
50–75 | 79.993 (0.399) | −625.8 (2.4) | 0.921 (0.006) | −500.6 (2.9) | |
[79.140, 80.676] | [−629.7, −620.9] | [0.909, 0.931] | [−505.9, −494.4] | ||
200–500 | 79.289 (0.329) | −1,621.6 (5.3) | 0.563 (0.003) | −1,285.7 (7.0) | |
[78.622, 79.919] | [−1,631.7, −1,612.3] | [0.556, 0.569] | [−1,296.7, −1,268.5] | ||
More than 1,000 | 23.048 (0.548) | −2,130.7 (26.4) | 0.023 (0.001) | −491.1 (13.4) | |
[22.019, 24.250] | [−2,180.3, −2,077.4] | [0.021, 0.025] | [−521.0, −466.6] | ||
All | 58.636 (0.141) | −889.3 (1.8) | 0.642 (0.003) | −521.4 (1.2) | |
[58.391, 58.910] | [−893.3, −886.0] | [0.638, 0.648] | [−523.8, −519.0] | ||
Addendum: Confidence Intervals Calculated Using Bootstrap and Using Normal Approximation of BSE | |||||
50–75 | Bootstrap | [79.140, 80.676] | [−629.7, −620.9] | [0.909, 0.931] | [−505.9, −494.4] |
Normal with BSE | [79.211, 80.775] | [−630.4, −621.2] | [0.910, 0.932] | [−506.3, −494.9] | |
200–500 | Bootstrap | [78.622, 79.919] | [−1,631.7, −1,612.3] | [0.556, 0.569] | [−1,296.7, −1,268.5] |
Normal with BSE | [78.645, 79.934] | [−1,632.0, −1,611.1] | [0.556, 0.570] | [−1,299.5, −1,271.9] | |
More than 1,000 | Bootstrap | [22.019, 24.250] | [−2,180.3, −2,077.4] | [0.021, 0.025] | [−521.0, −466.6] |
Normal with BSE | [21.974, 24.122] | [−2,182.5, −2,079.0] | [0.021, 0.024] | [−517.3, −464.9] | |
All | Bootstrap | [58.391, 58.910] | [−893.3, −886.0] | [0.638, 0.648] | [−523.8, −519.0] |
Normal with BSE | [58.361, 58.912] | [−892.7, −885.8] | [0.637, 0.647] | [−523.8, −519.1] |
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Source: Urban-Brookings Tax Policy Center Microsimulation Model (version 0319-1).
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Notes: Proposal would increase the standard deduction by $4,000 for single filers and married couples filing separately, $8,000 for married couples filing jointly, and $6,000 for heads of household in 2019.
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Numbers in parentheses are bootstrapped standard errors (BSE). Numbers in brackets are confidence intervals.
Increase the Top Income Tax Rate to 41 Percent, Selected Income Groups, 2019
Expanded Cash Income Level (thousands of 2019 dollars) | Tax Units with Tax Increase | Percent Change in After-Tax Income | Average Federal Tax Change ($) | ||
---|---|---|---|---|---|
Percent of Tax Units | Average Tax Change ($) | ||||
200–500 | 0.062 (0.014) | 2,044.6 (444.8) | −0.001 (0.000) | 1.3 (0.3) | |
[0.038, 0.091] | [1,349.4, 2,956.2] | [−0.001, 0.000] | [0.8, 1.9] | ||
500–1,000 | 18.225 (0.530) | 4,127.8 (111.2) | −0.147 (0.006) | 752.3 (29.8) | |
[17.236, 19.150] | [3,909.4, 4,363.9] | [−0.156, −0.135] | [691.6, 800.8] | ||
More than 1,000 | 77.965 (0.571) | 52,878.8 (1,006.8) | −1.917 (0.049) | 41,226.8 (808.0) | |
[76.552, 78.925] | [51,126.9, 54,963.1] | [−1.996, −1.827] | [39,944.2, 43,177.1] | ||
All | 0.569 (0.006) | 36,127.7 (759.5) | −0.253 (0.005) | 205.7 (3.9) | |
[0.555, 0.581] | [34,865.4, 37,852.8] | [−0.264, −0.246] | [199.5, 214.6] | ||
Addendum: Confidence Intervals Calculated Using Bootstrap and Using Normal Approximation of BSE | |||||
200–500 | Bootstrap | [0.038, 0.091] | [1,349.4, 2,956.2] | [−0.001, 0.000] | [0.8, 1.9] |
Normal with BSE | [0.034, 0.089] | [1,172.8, 2,916.3] | [−0.001, 0.000] | [0.7, 1.9] | |
500–1,000 | Bootstrap | [17.236, 19.150] | [3,909.4, 4,363.9] | [−0.156, −0.135] | [691.6, 800.8] |
Normal with BSE | [17.186, 19.264] | [3,909.9, 4,345.6] | [−0.158, −0.135] | [693.9, 810.6] | |
More than 1,000 | Bootstrap | [76.552, 78.925] | [51,126.9, 54,963.1] | [−1.996, −1.827] | [39,944.2, 43,177.1] |
Normal with BSE | [76.846, 79.084] | [50,905.5, 54,852.0] | [−2.013, −1.822] | [39,643.2, 42,810.5] | |
All | Bootstrap | [0.555, 0.581] | [34,865.4, 37,852.8] | [−0.264, −0.246] | [199.5, 214.6] |
Normal with BSE | [0.557, 0.582] | [34,639.1, 37,616.4] | [−0.262, −0.244] | [198.1, 213.2] |
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Source: Urban-Brookings Tax Policy Center Microsimulation Model (version 0319-1).
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Notes: Proposal would increase the top income tax rate to 41 percent in 2019.
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Numbers in parentheses are bootstrapped standard errors (BSE). Numbers in brackets are confidence intervals.
Replace Farm Loss Deduction with a Revenue-Neutral Refundable Tax Credit, Selected Income Groups, 2019
Expanded Cash Income Level (thousands of 2019 dollars) | Tax Units with Tax Cut | Tax Units with Tax Increase | Average Federal Tax Change ($) | |||
---|---|---|---|---|---|---|
Percent of Tax Units | Average Tax Change ($) | Percent of Tax Units | Average Tax Change ($) | |||
40–50 | 0.109 (0.029) | −1,368.9 (537.1) | 0.267 (0.065) | 404.1 (101.8) | −0.4 (0.7) | |
[0.062, 0.180] | [−2,743.8, −685.0] | [0.166, 0.462] | [234.1, 614.2] | [−2.0, 1.0] | ||
500–1,000 | 0.531 (0.109) | −3,465.7 (1,568.9) | 1.338 (0.170) | 2,779.1 (400.8) | 18.8 (9.1) | |
[0.386, 0.812] | [−8,022.0, −1,416.6] | [0.990, 1.652] | [2,082.2, 3,748.6] | [−2.7, 32.6] | ||
More than 1,000 | 0.994 (0.077) | −15,499.8 (4,948.4) | 0.922 (0.078) | 7,473.2 (787.6) | −85.1 (50.9) | |
[0.852, 1.171] | [−26,531.3, −7,571.9] | [0.781, 1.073] | [6,012.7, 9,182.7] | [−176.3, −3.0] | ||
All | 0.207 (0.013) | −1,909.9 (221.3) | 0.485 (0.020) | 770.2 (47.8) | −0.2 (0.5) | |
[0.186, 0.230] | [−2,420.9, −1,566.6] | [0.450, 0.522] | [700.7, 884.2] | [−1.3, 0.8] | ||
Addendum: Confidence Intervals Calculated Using Bootstrap and Using Normal Approximation of BSE | ||||||
40–50 | Bootstrap | [0.062, 0.180] | [−2,743.8, −685.0] | [0.166, 0.462] | [234.1, 614.2] | [−2.0, 1.0] |
Normal with BSE | [0.052, 0.166] | [−2,421.6, −316.2] | [0.140, 0.394] | [204.6, 603.6] | [−1.8, 1.0] | |
500–1,000 | Bootstrap | [0.386, 0.812] | [−8,022.0, −1,416.6] | [0.990, 1.652] | [2,082.2, 3,748.6] | [−2.7, 32.6] |
Normal with BSE | [0.318, 0.744] | [−6,540.8, −390.7] | [1.005, 1.670] | [1,993.5, 3,564.6] | [1.0, 36.5] | |
More than 1,000 | Bootstrap | [0.852, 1.171] | [−26,531.3, −7,571.9] | [0.781, 1.073] | [6,012.7, 9,182.7] | [−176.3, −3.0] |
Normal with BSE | [0.843, 1.145] | [−25,198.5, −5,801.0] | [0.769, 1.076] | [5,929.6, 9,016.9] | [−184.8, 14.6] | |
All | Bootstrap | [0.186, 0.230] | [−2,420.9, −1,566.6] | [0.450, 0.522] | [700.7, 884.2] | [−1.3, 0.8] |
Normal with BSE | [0.182, 0.232] | [−2,343.6, −1,476.2] | [0.445, 0.524] | [676.5, 863.9] | [−1.3, 0.8] |
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Source: Urban-Brookings Tax Policy Center Microsimulation Model (version 0319-1).
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Notes: Proposal would replace current-law farm loss deduction with a refundable tax credit equal to 82.5% of total farm loss times the statutory income tax rate in 2019.
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Numbers in parentheses are bootstrapped standard errors (BSE). Numbers in brackets are confidence intervals.
Rescind the Tax-free Treatment of Interest Accruing from Certain Municipal Bonds, Selected Income Groups, 2019
Expanded Cash Income Level (thousands of 2019 dollars) | Tax Units with Tax Increase | Percent Change in After-Tax Income | Average Federal Tax Change ($) | ||
---|---|---|---|---|---|
Percent of Tax Units | Average Tax Change ($) | ||||
40–50 | 0.598 (0.105) | 382.8 (142.4) | −0.006 (0.002) | 2.3 (0.9) | |
[0.412, 0.830] | [174.3, 815.8] | [−0.011, −0.002] | [1.0, 4.5] | ||
200–500 | 10.871 (0.289) | 2,693.2 (124.2) | −0.128 (0.006) | 292.8 (14.4) | |
[10.348, 11.518] | [2,442.2, 2,965.2] | [−0.141, −0.116] | [263.7, 323.0] | ||
More than 1,000 | 50.162 (0.535) | 27,001.5 (1,425.9) | −0.630 (0.033) | 13,544.6 (729.8) | |
[49.325, 51.238] | [24,610.9, 30,036.2] | [−0.697, −0.576] | [12,302.0, 15,143.7] | ||
All | 2.924 (0.050) | 4,272.1 (140.4) | −0.154 (0.005) | 124.9 (3.9) | |
[2.826, 3.014] | [4,021.8, 4,613.3] | [−0.164, −0.145] | [118.0, 133.8] | ||
Addendum: Confidence Intervals Calculated Using Bootstrap and Using Normal Approximation of BSE | |||||
40–50 | Bootstrap | [0.412, 0.830] | [174.3, 815.8] | [−0.011, −0.002] | [1.0, 4.5] |
Normal with BSE | [0.393, 0.803] | [103.8, 661.9] | [−0.010, −0.001] | [0.6, 4.0] | |
200–500 | Bootstrap | [10.348, 11.518] | [2,442.2, 2,965.2] | [−0.141, −0.116] | [263.7, 323.0] |
Normal with BSE | [10.305, 11.437] | [2,449.8, 2,936.6] | [−0.141, −0.116] | [264.6, 321.1] | |
More than 1,000 | Bootstrap | [49.325, 51.238] | [24,610.9, 30,036.2] | [−0.697, −0.576] | [12,302.0, 15,143.7] |
Normal with BSE | [49.113, 51.212] | [24,206.9, 29,796.1] | [−0.695, −0.565] | [12,114.2, 14,975.1] | |
All | Bootstrap | [2.826, 3.014] | [4,021.8, 4,613.3] | [−0.164, −0.145] | [118.0, 133.8] |
Normal with BSE | [2.825, 3.022] | [3,996.9, 4,547.4] | [−0.163, −0.144] | [117.3, 132.5] |
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Source: Urban-Brookings Tax Policy Center Microsimulation Model (version 0319-1).
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Notes: Proposal would rescind the tax-free treatment of interest accruing from certain municipal bonds in 2019.
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Numbers in parentheses are bootstrapped standard errors (BSE). Numbers in brackets are confidence intervals.
Comparison of Confidence Intervals with Standard Errors Calculated from Bootstrapping and the Gatz and Smith Formula
Proposal | Average Tax Change for All Tax Units ($) | ||||
---|---|---|---|---|---|
Mean | Standard Error | Confidence Interval | |||
BSE | GSSE | Bootstrap | Normal Approximation with GSSE | ||
Restore Personal Exemption | −758.2 | 1.7 | 1.9 | [−761.6, −754.6] | [−761.9, −754.4] |
Increase Standard Deduction | −521.4 | 1.2 | 1.2 | [−523.8, −519.0] | [−523.8, −519.1] |
Increase Tax Rate | 205.7 | 3.9 | 19.3 | [199.5, 214.6] | [167.9, 243.4] |
Rescind Tax-free Treatment of Certain Bonds | 124.9 | 3.9 | 11.2 | [118.0, 133.8] | [102.9, 146.9] |
Farm Loss Deduction Replaced with Credit | −0.2 | 0.5 | 2.2 | [−1.3, 0.8] | [−4.5, 4.1] |
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Source: Urban-Brookings Tax Policy Center Microsimulation Model (version 0319-1).
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Notes: The BSE column shows bootstrapped standard errors. The GSSE columns shows the Gatz and Smith formula for calculating standard errors. The Bootstrap Confidence Interval column shows the bias-corrected bootstrap confidence intervals. Finally, the Normal Approximation with GSSE Confidence Interval column shows confidence intervals derived as the means plus or minus the GSSE multiplied by 1.96. Due to rounding, that interval differs slightly from an interval calculated using the values in the table.
Data and code availability
The data for this paper are based on confidential data purchased from the U.S. Internal Revenue Service. Information about purchasing the data may be found at https://www.irs.gov/statistics/soi-tax-stats-individual-public-use-microdata-files
The Stata code used for this paper is open-source and it is available at https://github.com/UrbanInstitute/confidence-intervals-tax-microsimulation