### Who Cheats on their Spouse and What Makes Marriages Happy? – Multinomial Logit and Probit Regression Analysis

BACKGROUND

In 1978, Ray C. Fair from Yale University, extended the microeconomic framework to study why people have affairs. The paper creates an econometric model grounded in Utility theory. In economics, Utility Theory describes how people consume goods/services based off their costs, price and availability of substitute goods, price and availability of complementary goods, and explains the well-being people derive from multiple goods consumption. This analysis and theory are extended to the consumption of multiple relationships (i.e. affairs) in Fair’s paper.

The goal of this post is to estimate a probability model, similar to what Fair(1978) used in his paper, that will quantify what socioeconomic factors impact the probability of affairs for married couples. This post will also extend on Fair’s work by analyzing what factors increase happiness in a marriage, which he found to have a significant influences on whether or not a person had an extramarital affair.

ORIGINAL PAPER, DATA, AND STATA PROGRAM USED IN THIS POST

Original Paper (Fair 1978)

Data Affairs (Fair 1978)

STATA PROGRAM – AFFAIRS (1978)

The data are survey data from Psychology Today (1969) and Redbook (1974) magazines. The variables in the data are as follows and contain the following names and labels.

PROBIT REGRESSION MODEL FOR AFFAIRS

The probit regression model assumes that the regression errors will be normally distributed, or more formally:

The results from this regression model are in the table below, followed by an explanation of the results.

REPLICATING WITH SPSS

You can also get these results using SPSS, however SPSS doesn’t have the ability to calculate marginal effect.  Here are the log-odds ratios and syntax to replicate the STATA results above:

plum affair BY kids male  WITH occup educ ratemarr age yrsmarr relig
/print= parameter summary.

INTERPRETATION OF MARGINAL EFFECTS

Happiness

The probability of having an affair is greatly reduced if a person rates themselves happier in a marriage. If a person rates themselves as ‘very happy’ as opposed to ‘average’ on a questionnaire they are 54% less likely to have an affair.

Religion

People who self-identify themselves as more religious also are less likely to have affairs. People who self-identify themselves as “very religious” versus those that say they are “slightly” slightly religious are 38% less likely to have an affair.

Age

Older people are less likely to have extramarital affairs. Every ten years a person’s likelihood of having an affair decreases by 20%. This means that a person who is 30 years old is 20% less likely to have an affair than a person who is 20 years old.

Years Married

The longer people are married the more likely they are to have an affair. A person who has been married 10 years is 25% more likely to have an affair than someone who has been married 5 years.

Statistically insignificant factors…

Education, occupation, sex, and the presence of children are all statistically insignificant when it comes to the likelihood of someone having an affair.

A word of caution about the interpretation of marginal effects after a probit regression: marginal effects are linearized coefficient estimates of a non-linear model evaluated at the mean. Inferences about the probability of affairs are less accurate the farther away from the “X” values a person is in the “mfx” table above.

FURTHER EXPLORATION OF CAUSES OF MARITAL HAPPINESS

Given the importance of marital happiness in determining whether or not a person has an affair, further exploration beyond what Fair did in his paper seems warranted. I estimate a multinomial logit regression, although it can be argued that an ordered logit would be appropriate given the ordinal nature of the marriage rating variable (5 is best and 1 is worst).

The results from a multinomial logit model above show the (rrr) relative risk ratio of marital happiness based on socioeconomic factors. The baseline are people who are very dissatisfied with their marriage (1), each set of possible answers (2-5) is modeled (5 not shown). An rrr of 1 implies equal likelihood of being in the base category. Here is how to interpret these results, look at the second table we see that the rrr for kids is 6.03, hence people with kids are 6 times more likely to say they are “somewhat unhappy” with their marriage (2) than are to say they are very unhappy (1 aka the base).

Overall the statistically significant drivers of happiness are length of marriage and the presence of children. Having children increase a persons chances of going from very unhappy (1) to somewhat unhappy (2), but no other effect is seen past that. In other words, kids increase marital happiness only if a person is miserable. Being in a relationship longer appears to decrease happiness regardless of the level of happiness that exist in the marriage. In other words, satisfaction can decrease over time in even the happiest of marriages. This also means that even the most dissatisfying marriages don’t appear to increase in satisfaction over time.

CRITICISMS

It is important to note that Fair’s paper was a catalyst for much research. Although the paper is based on solid economic theory and tried and true econometrics, there were still some conceptual issues that were a source of criticism. These included…

1) Survivorship Bias – If affairs break up marriages, then the relationship between years married and it’s impact on the likelihood of affairs suffers from survival bias.

2) Sampling Error – People who took the survey are more likely to be aware of their own psychological health. If these people are intrinsicly more likely to cheat as well as have a higher propensity to show other socioeconomic characteristics related to having an affair, bias is introduced through sampling error.

3) Measurement Error – People may be hesitant to admit to affairs. If these sample people also tend to be more religious, then we can be overstating the impact of religion on the probability of affairs because people lied on the survey. This can be true for other variables as well (i.e. occupation).

There are probably a few other criticism out there, but despite the potential issues with Fair’s analysis it did start up a very interesting conversation on extra marital affairs among economists. Affairs destroy relationships and break up families, hence there is a strong social costs affairs as well as the damage they cause to relationships. In the end we all want to be happy, and increasing happiness is a worthy goal for economists in my opinion.