When you see people treating their fur-babies like children, you might be tempted to wonder to what extent people substitute pet ownership for raising children. You wouldn't be alone in considering the relationship between pet ownership and raising children. In 2022, Pope Francis decried the low global birthrate, noting that "dogs and cats take the place of children". But are dogs and cats really taking the place of children?
A new working paper by Kuan-Ming Chen, Ming-Jen Lin (both National Taiwan University), Hau-Hung Yang (Academia Sinica), and Shirley Yu-Hsuan Yen (National Taipei University) provides an answer, using data from Taiwan. They take advantage of dog and cat registry data from 2009 to 2020, matched to tax administration records that identify families and household composition.
To work out whether two goods (in this case, children and pets) are substitutes or complements, we need to look at the cross-price elasticity of demand, which relates the percentage change in quantity demanded of one good to a change in the price of another good. When the cross-price elasticity is a positive number, the two goods are substitutes. When the cross-price elasticity is a negative number, the two goods are complements.
Now, there are two interesting things about this paper that would be familiar to intermediate microeconomics students. First, Chen et al. are careful to distinguish between Marshallian cross-price elasticities (named after late 19th Century economist Alfred Marshall) and Hicksian (compensated) cross-price elasticities (named after 1972 Nobel Prize winner John Hicks). The difference between the two is that Marshallian cross-price elasticities combine both the income and substitution effects, while Hicksian cross-price elasticities look at only the substitution effect (see this post for more on the difference between an income effect and a substitution effect).
The second interesting thing is that Chen et al. effectively use a Slutsky decomposition to identify the cross-price elasticity of children to a change in the price of pets. This essentially involves two equations. The first equation is Slutsky symmetry:
The left-hand-side variables are the share of household spending on pets (spet) multiplied by the Marshallian cross-price elasticity of pets to a change in the 'price' of children. The first term on the right-hand side is the share of household spending on children (schild) multiplied by the Marshallian cross-price elasticity of children to a change in the 'price' of pets. The second term on the right-hand side multiplies the two shares of household spending by the difference in the income elasticity of demand for children and pets.
The second equation is much simpler. The Hicksian cross-price elasticity of children to a change in the price of pets is equal to the equivalent Marshallian cross-price elasticity plus the share of spending on pets multiplied by the income elasticity of demand for children. In other words, this equation adjusts the Marshallian elasticity to remove the income effect, leaving just the substitution effect.
So, the Hicksian cross-price elasticity of children to a change in the price of pets can be calculated using information about all of the other variables in those two equations. And gathering estimates of those other variables is what Chen et al. set about doing.
First, to estimate the cross-price elasticity of pets to a change in the 'price' of children, Chen et al. look at how increases in the 'child bonus' paid by local municipalities affect the registration of pets, since the child bonus affects the up-front cost (or 'price') of having children. Using an event study, they find that:
Both cats and dogs respond, and they respond in an ordered way. In the first post-treatment year, new dog acquisitions rise by 0.067 percentage points on a pre-treatment base of 0.332 percentage points, a 20.1% increase (𝑡 = 2.40); new cat acquisitions rise by 0.0136 percentage points on a base of 0.125 percentage points, a 10.9% increase (𝑡 = 2.36). Cats are therefore complements with children as well, but the proportional response is roughly half as large as for dogs.
...the implied Marshallian cross-price elasticity for cats is approximately −0.68, against −1.24 for dogs.
Remember that the Marshallian cross-price elasticity doesn't remove the income effect of the price change. To calculate the Hicksian cross-price elasticities, Chen et al. therefore need to estimate the other parts of the equation. So, next they estimate the income elasticities of demand for children and pets, making use of an interesting lottery:
Taiwan’s sales tax system provides a natural experiment for income shocks through its uniform invoice lottery program. As part of a nationwide effort to reduce tax evasion, nearly all consumption receipts are eligible for bi-monthly lottery drawings, with prizes reaching up to NTD10 million. Receipt holders are randomly selected, and prizes are distributed regardless of income level or background. These awards thus constitute plausibly exogenous, positive income shocks.
This lottery had already been used by other researchers in an event study (where the treatment is receiving a lottery windfall of at least NTD2 million) to estimate the income elasticity of children, finding it to be 0.15, meaning that children are a normal good. Following the same approach, but looking at the income elasticity of pets, Chen et al. find that the income elasticity of dogs is 0.11. Annoyingly, they don't report the income elasticity of cats (although they use it in their calculations later), although their other estimates suggest that it may be close to zero.
Finally, Chen et al. estimate the share of expenditure on children and pets. Using data from the Family Income and Expenditure Survey, they find the share of household spending on pets is 0.032 (about 3.2 percent). For children, they use an 'equivalence scale approach', which weights children in adult-equivalent terms at 0.3, and noting that would imply a share of spending in a three-person household of about 17 percent, they adopt a conservative share of household spending on children of 0.2.
Now, with all of the pieces together, Chen et al. move on to estimating the Hicksian cross-price elasticity, finding that it is equal to -0.198 for dogs, and -0.089 for cats. In other words, dogs and children are complements, and so are cats and children. The results are also reasonably robust to various alternative assumptions about the income elasticities and expenditure shares.
Chen et al. then go on to explore why pets and children might be complements. By looking at the timing of pet ownership and childbearing, they identify that it is much more common for families to have pets first, and children second. They infer from this that:
Pets may serve as a “starter family,” letting prospective parents rehearse caregiving and learn about their own taste for family life before a birth.
Of course, the mechanism results do not eliminate other explanations. The results are consistent with the 'starter family' channel, but it is also possible that people who are already planning to have children are more likely to register a pet beforehand. Also, these results are based on Taiwan. Perhaps pets and children are substitutes in other countries - we won't know unless further research is done. Nevertheless, these results are a good place to start, and should make us really question whether dogs and cats are taking the place of children.
[HT: Jacques Poot]
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