{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "MRCBJ0WDR0"
    }
  ],
  "body": "\n## Summary\n\nThe generalized method of moments (GMM) estimates parameters from moment conditions $E[g(X, \\theta_0)] = 0$, possibly more conditions than parameters.\nIt chooses $\\theta$ to make the sample averages of the moment functions as close to zero as possible in a weighted quadratic norm.\nIt contains the method of moments, least squares and instrumental variables estimation as special cases.\nIt was introduced in econometrics by Lars Peter Hansen.\nIt is a standard tool there because it does not need a full model of the data.\n\n## Explanations\n\n### L1 human\n\nSuppose the theory gives you more facts about averages than you have unknown numbers.\nWith noisy data you usually cannot make all the sample averages match exactly.\nGMM picks the parameter that makes the mismatches as small as possible, giving more weight to the averages that are measured more precisely.\nFor Poisson counts, both the mean and the variance equal the parameter $\\lambda$, and GMM combines the two facts into one estimate.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "62F10",
      "62P20"
    ],
    "name": "Generalized method of moments",
    "same_as": {
      "wikidata": "Q683131",
      "wikipedia": "Generalized method of moments"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Generalized_method_of_moments"
      }
    ],
    "tag": "ZPVMCCDYZ5"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/ZPVMCCDYZ5/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/ZPVMCCDYZ5.md",
  "msc": [
    "62F10",
    "62P20"
  ],
  "name": "Generalized method of moments",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/ZPV/ZPVMCCDYZ5.md",
  "status": null,
  "tag": "ZPVMCCDYZ5",
  "uri": "m2://ZPVMCCDYZ5",
  "url": "https://tamnd.github.io/math2/wiki/generalized-method-of-moments/",
  "writing": {
    "tag": "ZPVMCCDYZ5",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}