Are Pornography and Marriage Substitutes for Young Men?

Abstract

Substitutes for marital sexual gratification may impact the decision to marry. Proliferation of the Internet has made pornography an increasingly low-cost substitute. We investigate the effect of Internet usage, and of pornography consumption specifically, on the marital status of young men. We show that increased Internet usage is negatively associated with marriage formation. Pornography consumption specifically has an even stronger effect. Instrumental variables and a number of robustness checks suggest that the effect is causal.

Appendices

Appendix A

Mathematical results from theoretical model

The utility function for a single man is U^S(x, z), where x represents extra-marital sexual activities and z represents other consumption. The utility function is concave and increasing in both arguments. The price of consumption z is normalized to 1 and the cost of extra-marital sexual activities is p. When income is m, a single man solves the following constrained maximization problem:

The corresponding indirect utility function V^S(p, m) gives the maximized value of utility. It is increasing in m but decreasing in p.

The utility function for a married man is U^M(x, z)+θ, where θ is non-pecuniary utility specific to marriage. The utility function U^M(x, z) is also assumed to be concave and increasing in both arguments, although the marginal utility of x may be different than that for a single man. A married man solves a similar constrained maximization problem to that given above, and his corresponding indirect utility function is V^M(p, m)+θ.

Recall that income in the first period is m₁ and income in the second period is m₂. Where future payoffs are discounted at rate β, a man who chooses not to marry enjoys lifetime utility:

For men who marry, their monetary income available for consumption is αm. Thus, men who marry and remain married through the second period enjoy lifetime utility:

Men who marry but divorce in the second period face a cost of c associated with divorce, reducing their incomes, which generates lifetime utility of:

Thus, where divorce occurs with probability μ, expected lifetime utility at the beginning of period 1 for a man who chooses to marry is:

An expected utility maximizer will marry during the first period whenever EV _lifetime ^M exceeds V _lifetime ^S. Solving this inequality, the minimal level of marital utility θ that justifies marriage is:

Anything that increases threshold spousal quality θ* leads to a decline in marital probability (the probability that a single man will encounter a potential mate who satisfies the threshold), and conversely anything that reduces threshold quality level θ* leads to more marriage.

The marginal effect of an increase in the cost of paid sexual activities p on threshold spousal quality level is:

This can be either positive or negative, because an increase in p has marginal effects on the utility of both single and married men. For a benchmark case, let us begin by assuming that only single men use pornography (i.e. that marital sex is a perfect substitute for pornography). In that case, the marginal effect is:

Even in this case, the sign of the derivative is ambiguous. A reduction in the value of p raises the value of being single but it also raises the value of being divorced. As income is reduced by c as a result of divorce, concavity of the utility function implies that the marginal utility of a reduction in p has a stronger impact for a divorced single man than for a never-married single man. Thus, when divorce is expensive and likely, a reduction in the cost of pornography can increase the man’s propensity to marry by making it less costly to get divorced.

In the more general model, where paid sexual activities x can contribute utility both for divorce and for marriage, there are additional ambiguities in the sign of the comparative static because a reduction in p can add to utility both for married and single men.

For the other comparative statics, inspection of the expression for threshold quality θ* shows that it is declining in bargaining share α but increasing in separation cost c. The impact of changes in income is ambiguous in income from both periods. Precisely:

Higher income contributes utility both to married and to single people. Married people typically are able to consume only a lower share of their incomes (when α<1), but whatever share they do claim has higher marginal value.

In the body of the paper, we have raised the possibility that the divorce probability μ may not be exogenous, but may itself be a function of a married man’s consumption of extra-marital sexual opportunities. Precisely, μ(x₁^m) depends on a married man’s choice of x in the first period during which he is married. Thus, μ depends indirectly on p since the maximized value of paid sexual activity x* for a married man is itself a function of p. For a small, marginal change in p, the envelope theorem allows us to ignore this indirect effect in computing the derivative, and the results will be the same as above (as long as the dependence is smooth). We discuss discrete changes heuristically in the main text.

Appendix B

Table B1

Table B1 First-stage OLS regression results