Correlation, Causation, Nate Silver’s Calculations

Nate Silver:

Over the past decade or so, divorce has gradually become more uncommon in the United States. Since 2003, however, the decline in divorce rates has been largely confined to states which have not passed a state constitutional ban on gay marriage. These states saw their divorce rates decrease by an average of 8 percent between 2003 and 2008. States which had passed a same-sex marriage ban as of January 1, 2008, however, saw their divorce rates rise by about 1 percent over the same period.

The table below details the divorce rates for the 43 states that reported their divorce statistics to the CDC in both 2003 and 2008. It is calculated by taking the total number of divorces in the state that year, and dividing it by the number of married persons, as reported by the Census Bureau. The result is then multiplied by two, since each divorce involves two people. This is different than how the divorce rate is sometimes calculated, which may be as a share of the overall population rather than the number of married persons; I prefer my approach because it will not penalize a state for having a lot of marriages (and therefore more opportunities for divorce). However, there are also more complicated versions of the divorce rate calculation that account for the age of the married couples, and so forth; these are probably superior, but mine is intended to be a simple approach. The table also lists the percentage change in the divorce rate between 2003 and 2008, and the current status of gay marriage and domestic partnerships within each state.

As is somewhat visually apparent, those states which have tended to take more liberal policies toward gay marriage have tended also to have larger declines in their divorce rates. In Massachusetts, which legalized gay marriage in 2004, the divorce rate has declined by 21 percent and is the lowest in the country by some margin. It is joined at the top of the list by Rhode Island and New Mexico, which do not perform same-sex marriages but idiosyncratically also have no statute or constitutional provision expressly forbidding them, as well as Maine, whose legislature approved same-sex marriage only to have it overturned (although not banned constitutionally) by its voters.

On the other hand, the seven states at the bottom of the chart all had constitutional prohibitions on same-sex marriage in place throughout 2008. The state which experienced the highest increase in its divorce rate over the period (Alaska, at 17.2 percent) also happens to be the first one to have altered its constitution to prohibit same-sex marriage, in 1998.

Tom Maguire:

Let me suggest a factor for which a statistical control wold be appropriate – military families and military divorces.  Per this article, the military divorce rate for was 3.6 percent for the year ending Sept 30 2009, compared to 2.6 percent in Sept 2001, prior to the deployments in Afghanistan and Iraq.

Those figures do not seem to include veterans and National Guardsmen.  I am just guessing that the New England states whose courts led the charge on gay marriage are also under-represented in the population of military families.

As to whether a 1% increase in the military divorce rate could drive a state’s divorce rate from 1.90% to 2.04% (as was the case with Arizona), well, maybe – that is an increase of 0.14%, or 1/7 of the military rate.  Could 1/7 of the Arizona married population have a military connection affected by the Iraq and Afghanistan deployments?  That strikes me as high but not absurdly so.

Scott H. Payne at The League
Ezra Klein:

Does this prove causation? No. Does it prove that opponents of gay marriage rely on some ridiculous arguments? Yes.

Matt Zeitlin

James Joyner:

Beyond all that, Nate’s a much more adept statistician than I am.  But even I know that doing correlation analysis to analyze sophisticated social phenomena is absurd.  Unless we’re factoring in the variables known to impact marriage success rate (age at time of marriage, presence of children from prior marriages, different religious backgrounds, financial circumstances, race, prior cohabitation, etc.) so that we’re comparing apples to apples, we have no way of knowing what impact, if any, the legal status of gay marriage has on the overall divorce rate.

Indeed, Nate admits this:

The differences are highly statistically significant. Nevertheless, they do not necessarily imply causation. The decision to ban same-sex marriage does not occur randomly throughout the states, but instead is strongly correlated with other factors, such as religiosity and political ideology, which we have made no attempt to account for. Nor do we know in which way the causal arrow might point. It could be that voters who have more marital problems of their own are more inclined to deny the right of marriage to same-sex couples.

But that doesn’t make sense.  They’re anti-gay, after all.  Why would they want to save gays from an institution that they personally find intolerable?  The much more plausible explanation is that they honestly think gay marriage is immoral and they want to preserve matrimony as a sacramental relationship.

Matthew Yglesias:

At any rate, one seriously doubts that this sort of research would be persuasive to anyone. Certainly if the sign on the coefficient of correlation had gone the other way, I wouldn’t suddenly become an opponent of marriage equality. But if anyone you know seems genuinely concerned about this aspect of the issue, please urge them to check out Silver’s table.

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1 Comment

Filed under Families, Gay Marriage

One response to “Correlation, Causation, Nate Silver’s Calculations

  1. Pierre

    Nate Silver is the one I believe who was completely wrong with his projections on the vote in Maine.
    Now he is also wrong with his analysis on divorce.
    His propaganda is eagerly promoted by his homosexual audience and is fueling misinformation that will take years to be corrected.
    He has to know it.
    The average marriage age in Mass is almost 30 years old. This alone as with different levels of powerty and races ratios from other states brings a lot more variables than the fact that gay “marriage” is legal.
    Nate Silver need to let go of his bias before he spreads any more misinformation

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