{
  "alt": "Line chart of three fitted age profiles for the CES with confidence bands. The age effect on the Democratic vote falls steeply from the youngest to the oldest band under the constraint of no trend across birth years and under the constraint of no trend across elections, by {fact:apc_ces_span_cohort} and {fact:apc_ces_span_period} points. Under the constraint of no trend across ages the profile is nearly flat, with a span of {fact:apc_ces_span_age} points. The ANES view shows the same pattern with smaller spans.",
  "caption": "The three profiles fit the vote shares of every age band in every election identically, and they differ by a straight tilt: each constraint sets the straight-line trend of one of the three effects to zero. The curvature is the same in all three, so where a profile bends is identified, and its overall slope is not. Each line is centred on its mean, and bands are 95% intervals from {fact:apc_reps} bootstrap replicates.",
  "data": [
    {
      "age": 19.5,
      "conf_high": 14.1515,
      "conf_low": 9.54418,
      "estimate": 11.9338,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across birth years"
    },
    {
      "age": 23.5,
      "conf_high": 13.3754,
      "conf_low": 9.51701,
      "estimate": 11.4595,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across birth years"
    },
    {
      "age": 27.5,
      "conf_high": 9.8129,
      "conf_low": 6.33991,
      "estimate": 8.06467,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across birth years"
    },
    {
      "age": 31.5,
      "conf_high": 8.47755,
      "conf_low": 5.126,
      "estimate": 6.77716,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across birth years"
    },
    {
      "age": 35.5,
      "conf_high": 5.58308,
      "conf_low": 2.33959,
      "estimate": 3.90379,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across birth years"
    },
    {
      "age": 39.5,
      "conf_high": 3.51996,
      "conf_low": 0.600573,
      "estimate": 2.09826,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across birth years"
    },
    {
      "age": 43.5,
      "conf_high": 2.16387,
      "conf_low": -0.576285,
      "estimate": 0.809937,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across birth years"
    },
    {
      "age": 47.5,
      "conf_high": -0.225375,
      "conf_low": -2.76293,
      "estimate": -1.48908,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across birth years"
    },
    {
      "age": 51.5,
      "conf_high": -3.30614,
      "conf_low": -5.84449,
      "estimate": -4.58648,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across birth years"
    },
    {
      "age": 55.5,
      "conf_high": -4.73506,
      "conf_low": -7.19908,
      "estimate": -5.98204,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across birth years"
    },
    {
      "age": 59.5,
      "conf_high": -5.78361,
      "conf_low": -8.2548,
      "estimate": -7.00513,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across birth years"
    },
    {
      "age": 63.5,
      "conf_high": -6.35076,
      "conf_low": -8.97949,
      "estimate": -7.69019,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across birth years"
    },
    {
      "age": 67.5,
      "conf_high": -6.62858,
      "conf_low": -9.69079,
      "estimate": -8.02217,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across birth years"
    },
    {
      "age": 71.5,
      "conf_high": -8.56803,
      "conf_low": -11.8435,
      "estimate": -10.272,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across birth years"
    },
    {
      "age": 19.5,
      "conf_high": 17.2728,
      "conf_low": 11.6472,
      "estimate": 14.456,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across elections"
    },
    {
      "age": 23.5,
      "conf_high": 15.8035,
      "conf_low": 11.4859,
      "estimate": 13.5937,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across elections"
    },
    {
      "age": 27.5,
      "conf_high": 11.7855,
      "conf_low": 7.93408,
      "estimate": 9.81085,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across elections"
    },
    {
      "age": 31.5,
      "conf_high": 10.0461,
      "conf_low": 6.41926,
      "estimate": 8.13531,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across elections"
    },
    {
      "age": 35.5,
      "conf_high": 6.58862,
      "conf_low": 3.32524,
      "estimate": 4.8739,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across elections"
    },
    {
      "age": 39.5,
      "conf_high": 4.05935,
      "conf_low": 1.09912,
      "estimate": 2.68032,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across elections"
    },
    {
      "age": 43.5,
      "conf_high": 2.34757,
      "conf_low": -0.401705,
      "estimate": 1.00396,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across elections"
    },
    {
      "age": 47.5,
      "conf_high": -0.416009,
      "conf_low": -2.97848,
      "estimate": -1.6831,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across elections"
    },
    {
      "age": 51.5,
      "conf_high": -3.76219,
      "conf_low": -6.56976,
      "estimate": -5.16854,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across elections"
    },
    {
      "age": 55.5,
      "conf_high": -5.57174,
      "conf_low": -8.32809,
      "estimate": -6.95214,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across elections"
    },
    {
      "age": 59.5,
      "conf_high": -6.98529,
      "conf_low": -9.74489,
      "estimate": -8.36327,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across elections"
    },
    {
      "age": 63.5,
      "conf_high": -8.00347,
      "conf_low": -10.8854,
      "estimate": -9.43637,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across elections"
    },
    {
      "age": 67.5,
      "conf_high": -8.61229,
      "conf_low": -12.0666,
      "estimate": -10.1564,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across elections"
    },
    {
      "age": 71.5,
      "conf_high": -10.7706,
      "conf_low": -14.7063,
      "estimate": -12.7943,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across elections"
    },
    {
      "age": 19.5,
      "conf_high": 2.21118,
      "conf_low": -1.62485,
      "estimate": 0.319102,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across ages"
    },
    {
      "age": 23.5,
      "conf_high": 3.18411,
      "conf_low": 0.0414277,
      "estimate": 1.63174,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across ages"
    },
    {
      "age": 27.5,
      "conf_high": 1.38199,
      "conf_low": -1.44721,
      "estimate": 0.0237555,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across ages"
    },
    {
      "age": 31.5,
      "conf_high": 2.03513,
      "conf_low": -0.947379,
      "estimate": 0.52312,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across ages"
    },
    {
      "age": 35.5,
      "conf_high": 0.924645,
      "conf_low": -2.01359,
      "estimate": -0.563379,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across ages"
    },
    {
      "age": 39.5,
      "conf_high": 0.799374,
      "conf_low": -2.04087,
      "estimate": -0.582048,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across ages"
    },
    {
      "age": 43.5,
      "conf_high": 1.29968,
      "conf_low": -1.49335,
      "estimate": -0.0834977,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across ages"
    },
    {
      "age": 47.5,
      "conf_high": 0.694064,
      "conf_low": -1.8884,
      "estimate": -0.595649,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across ages"
    },
    {
      "age": 51.5,
      "conf_high": -0.680469,
      "conf_low": -3.12767,
      "estimate": -1.90618,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across ages"
    },
    {
      "age": 55.5,
      "conf_high": -0.437892,
      "conf_low": -2.54452,
      "estimate": -1.51486,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across ages"
    },
    {
      "age": 59.5,
      "conf_high": 0.199589,
      "conf_low": -1.77185,
      "estimate": -0.751087,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across ages"
    },
    {
      "age": 63.5,
      "conf_high": 1.34982,
      "conf_low": -0.542376,
      "estimate": 0.350723,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across ages"
    },
    {
      "age": 67.5,
      "conf_high": 2.82882,
      "conf_low": 0.609461,
      "estimate": 1.80561,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across ages"
    },
    {
      "age": 71.5,
      "conf_high": 2.74044,
      "conf_low": 0.0852753,
      "estimate": 1.34265,
      "n": 169858,
      "panel": "ces",
      "series": "No trend across ages"
    },
    {
      "age": 19.5,
      "conf_high": 14.2208,
      "conf_low": 6.84901,
      "estimate": 10.387,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across birth years"
    },
    {
      "age": 23.5,
      "conf_high": 7.16105,
      "conf_low": 1.35724,
      "estimate": 4.20693,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across birth years"
    },
    {
      "age": 27.5,
      "conf_high": 5.9359,
      "conf_low": 0.535419,
      "estimate": 3.10451,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across birth years"
    },
    {
      "age": 31.5,
      "conf_high": 3.24838,
      "conf_low": -1.55619,
      "estimate": 0.792901,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across birth years"
    },
    {
      "age": 35.5,
      "conf_high": 2.39552,
      "conf_low": -2.06735,
      "estimate": 0.120741,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across birth years"
    },
    {
      "age": 39.5,
      "conf_high": -0.65758,
      "conf_low": -5.02024,
      "estimate": -2.79217,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across birth years"
    },
    {
      "age": 43.5,
      "conf_high": 1.24216,
      "conf_low": -3.36012,
      "estimate": -1.05084,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across birth years"
    },
    {
      "age": 47.5,
      "conf_high": 2.22571,
      "conf_low": -2.59344,
      "estimate": -0.164326,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across birth years"
    },
    {
      "age": 51.5,
      "conf_high": 1.49985,
      "conf_low": -3.17336,
      "estimate": -0.67718,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across birth years"
    },
    {
      "age": 55.5,
      "conf_high": -1.07486,
      "conf_low": -5.6548,
      "estimate": -3.32038,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across birth years"
    },
    {
      "age": 59.5,
      "conf_high": -0.191652,
      "conf_low": -4.96848,
      "estimate": -2.5022,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across birth years"
    },
    {
      "age": 63.5,
      "conf_high": -0.865794,
      "conf_low": -5.72761,
      "estimate": -3.28769,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across birth years"
    },
    {
      "age": 67.5,
      "conf_high": 0.617692,
      "conf_low": -4.62212,
      "estimate": -1.92899,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across birth years"
    },
    {
      "age": 71.5,
      "conf_high": -0.117545,
      "conf_low": -5.59865,
      "estimate": -2.8883,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across birth years"
    },
    {
      "age": 19.5,
      "conf_high": 10.2653,
      "conf_low": 2.38952,
      "estimate": 6.16734,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across elections"
    },
    {
      "age": 23.5,
      "conf_high": 3.6379,
      "conf_low": -2.23647,
      "estimate": 0.636458,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across elections"
    },
    {
      "age": 27.5,
      "conf_high": 2.90217,
      "conf_low": -2.29373,
      "estimate": 0.183208,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across elections"
    },
    {
      "age": 31.5,
      "conf_high": 0.995369,
      "conf_low": -3.88071,
      "estimate": -1.47922,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across elections"
    },
    {
      "age": 35.5,
      "conf_high": 0.698293,
      "conf_low": -3.70109,
      "estimate": -1.5022,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across elections"
    },
    {
      "age": 39.5,
      "conf_high": -1.59523,
      "conf_low": -5.94518,
      "estimate": -3.76593,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across elections"
    },
    {
      "age": 43.5,
      "conf_high": 0.864318,
      "conf_low": -3.68701,
      "estimate": -1.37543,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across elections"
    },
    {
      "age": 47.5,
      "conf_high": 2.56458,
      "conf_low": -2.3166,
      "estimate": 0.160263,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across elections"
    },
    {
      "age": 51.5,
      "conf_high": 2.48607,
      "conf_low": -2.17346,
      "estimate": 0.296586,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across elections"
    },
    {
      "age": 55.5,
      "conf_high": 0.593292,
      "conf_low": -4.13961,
      "estimate": -1.69744,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across elections"
    },
    {
      "age": 59.5,
      "conf_high": 2.03636,
      "conf_low": -2.54325,
      "estimate": -0.230077,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across elections"
    },
    {
      "age": 63.5,
      "conf_high": 2.10391,
      "conf_low": -2.73236,
      "estimate": -0.36639,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across elections"
    },
    {
      "age": 67.5,
      "conf_high": 4.24743,
      "conf_low": -1.08523,
      "estimate": 1.64148,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across elections"
    },
    {
      "age": 71.5,
      "conf_high": 4.08603,
      "conf_low": -1.57697,
      "estimate": 1.33135,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across elections"
    },
    {
      "age": 19.5,
      "conf_high": 8.96611,
      "conf_low": 2.51242,
      "estimate": 5.66352,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across ages"
    },
    {
      "age": 23.5,
      "conf_high": 2.83019,
      "conf_low": -2.30036,
      "estimate": 0.210143,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across ages"
    },
    {
      "age": 27.5,
      "conf_high": 2.50867,
      "conf_low": -2.53631,
      "estimate": -0.165596,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across ages"
    },
    {
      "age": 31.5,
      "conf_high": 0.591109,
      "conf_low": -4.20665,
      "estimate": -1.75051,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across ages"
    },
    {
      "age": 35.5,
      "conf_high": 0.524534,
      "conf_low": -3.84381,
      "estimate": -1.69598,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across ages"
    },
    {
      "age": 39.5,
      "conf_high": -1.72406,
      "conf_low": -6.10778,
      "estimate": -3.8822,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across ages"
    },
    {
      "age": 43.5,
      "conf_high": 0.812235,
      "conf_low": -3.7074,
      "estimate": -1.41419,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across ages"
    },
    {
      "age": 47.5,
      "conf_high": 2.59512,
      "conf_low": -2.21977,
      "estimate": 0.199019,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across ages"
    },
    {
      "age": 51.5,
      "conf_high": 2.51173,
      "conf_low": -2.01082,
      "estimate": 0.412854,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across ages"
    },
    {
      "age": 55.5,
      "conf_high": 0.661785,
      "conf_low": -3.72383,
      "estimate": -1.50366,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across ages"
    },
    {
      "age": 59.5,
      "conf_high": 2.27311,
      "conf_low": -2.24115,
      "estimate": 0.0412147,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across ages"
    },
    {
      "age": 63.5,
      "conf_high": 2.33148,
      "conf_low": -2.39301,
      "estimate": -0.0175868,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across ages"
    },
    {
      "age": 67.5,
      "conf_high": 4.36208,
      "conf_low": -0.194555,
      "estimate": 2.0678,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across ages"
    },
    {
      "age": 71.5,
      "conf_high": 4.07293,
      "conf_low": -0.531301,
      "estimate": 1.83518,
      "n": 30571,
      "panel": "anes",
      "series": "No trend across ages"
    }
  ],
  "id": "apc_profiles",
  "notes": [
    "The model gives each 4-year age band from 18 to 73, each presidential election and each 4-year birth cohort an effect on the Democratic share, and is fitted by weighted least squares to the cell means (the linear probability model). Because birth year equals election year minus age, the three sets of effects are not identified: adding a straight line to the age effects and the cohort effects and subtracting one from the election effects leaves every fitted cell unchanged. The profile shown is the minimum-norm fit shifted by the straight line that gives the stated constraint.",
    "The fitted shares in every cell are identical under the three constraints, to within floating-point rounding. Voters aged 74 and over fall outside the 4-year grid. The CES is an opt-in online panel, so its intervals describe sampling variation among panel members and leave out how respondents joined the panel."
  ],
  "source": "CES Cumulative File, presidential elections 2008-2024; weighted (weight_cumulative); two-party presidential voters; weighted least squares on the age-by-election grid, seeded respondent bootstrap",
  "spec": {
    "annotations": [
      {
        "label": "Average age effect",
        "type": "y-rule",
        "y": 0
      }
    ],
    "colors": {
      "No trend across ages": "cat3",
      "No trend across birth years": "cat1",
      "No trend across elections": "cat2"
    },
    "hi": "conf_high",
    "lo": "conf_low",
    "n": "n",
    "series": "series",
    "x": "age",
    "xDomain": [
      18,
      74
    ],
    "xLabel": "Age band midpoint (years)",
    "y": "estimate",
    "yDomain": [
      -20,
      25
    ],
    "yFormat": {
      "digits": 1
    },
    "yLabel": "Age effect on the Democratic share (points)"
  },
  "subtitle": "Age effect on the Democratic share of the two-party vote, points, 4-year age bands from 18 to 73, from a model with an effect for every age band, election and birth cohort, under three constraints; 95% bootstrap intervals",
  "table": {
    "columns": [
      {
        "key": "panel",
        "label": "Survey"
      },
      {
        "key": "series",
        "label": "Constraint"
      },
      {
        "format": {
          "digits": 1
        },
        "key": "age",
        "label": "Age band midpoint (years)"
      },
      {
        "format": {
          "digits": 1,
          "signed": true
        },
        "key": "estimate",
        "label": "Age effect (points)"
      },
      {
        "format": {
          "digits": 1,
          "signed": true
        },
        "key": "conf_low",
        "label": "95% bootstrap interval low"
      },
      {
        "format": {
          "digits": 1,
          "signed": true
        },
        "key": "conf_high",
        "label": "95% bootstrap interval high"
      }
    ]
  },
  "title": "In the CES the age effect from the youngest to the oldest band is {fact:apc_ces_span_cohort} points if birth years carry no trend, {fact:apc_ces_span_period} if elections carry none and {fact:apc_ces_span_age} if ages carry none",
  "type": "line",
  "views": [
    {
      "filter": {
        "panel": "ces"
      },
      "id": "ces",
      "label": "CES 2008 to 2024"
    },
    {
      "caption": "The three profiles fit the ANES vote shares equally well and differ by a straight tilt, as in the CES, and the curvature, including the high estimate for the youngest band, is the same in all three. The span is the oldest band's effect minus the youngest band's, in points of Democratic vote share, with a 95% interval from a bootstrap.",
      "filter": {
        "panel": "anes"
      },
      "id": "anes",
      "label": "ANES 1952 to 2024",
      "spec": {
        "yDomain": [
          -12,
          14
        ]
      },
      "title": "In the ANES the same three constraints give age effects from the youngest to the oldest band of {fact:apc_anes_span_cohort}, {fact:apc_anes_span_period} and {fact:apc_anes_span_age} points"
    }
  ],
  "width": "wide"
}