This is a very interesting essay addressing a very important decision EAs face. Thank you for writing it!
I think your estimates for the annual financial cost of having children underestimate the real costs, because they don’t account for the time value of money and because they omit opportunity costs.
To account for the time value of money, we can use the formula used to calculate amortization in business. Assuming a present-value cost of £175,000, an interest rate of 5% and 50 periods, the annual cost for each couple turns out to be about £4,700 per parent per year.
To account for opportunity costs, we can use Brian Tomasik’s estimates. He claims that the present-value opportunity costs of parenting are about $380,000, or £225,000. Adding this to the financial costs, we get a total cost of £400,000. Using the formula above, this translates into about £11,000 per parent per year.
However, as Brian notes in private correspondence, the opportunity costs could be much lower if parents outsource them. And parents persuaded by Bryan Caplan’s arguments should be less reluctant to outsource these costs. So for you and Toby, and for many other EAs, the estimate is probably lower than £11,000.
You are right that the £2,000 per year per parent lifetime cost would be better if it included an adjustment for the fact that the cost aren’t evenly distributed over that timespan. However, they are distributed over twenty years of that time and I think the amortization calculator you used assumes it is all paid as a lump sum on year one. I set up a spreadsheet to allocate the costs evenly over the first twenty years and then look for which amount this was equivalent to paying if the costs were spread out over the whole 50 years. This was £3,000 per parent per year, which is higher than the £2,000, but quite a bit less than the £4,700. This is still not perfect as the costs are skewed a bit towards the early and late years, but it should be pretty close to the right model.
I also think that 5% above inflation is substantially higher than the best estimates of the risk adjusted rate of return. Using 3%, the cost per annum drops to £2,500, which is pretty close to the original unadjusted estimate.
(Note that you might want something even higher than 5% if you would really like to spend/donate money a lot sooner, but if so, you should also be taking out loans in order to donate more sooner and I’ve never met anyone doing that).
5% above inflation seems reasonable if you invest in stocks, unless you think (as some do) that stock markets are going to systematically have lower returns in the future than they did in the past. I don’t see why a risk-free rate would be appropriate, since stocks aren’t risky enough to cause problems in many practical situations.
Brian, there are several serious sampling biases in most estimates of long run real returns which tend to overestimate the returns. These include:
(1) Time selection bias. The 20th century was unprecedentedly good for stocks. If we instead averaged over wider periods or over the 21st century so far, we get much lower numbers. It is unclear what is the best period to use, but many estimates use the most optimistic one which is suspect.
(2) Country selection bias. The US has done unprecedentedly well with stocks. International comparisons give lower returns and are probably more representative of the future (we don’t know which country will do best this time round).
(3) Within-index selection bias. The major indices are of the top stocks rather than a fixed set, so for example if all the stocks in the S&P 500 went to zero tomorrow, this would really change the real rate of return, but wouldn’t change the index that much as the next 500 stocks would replace them—we need to adjust for that.
(4) Between-exchange selection bias. Even attempts to adjust for the country selection bias by using a range of stock markets or indices in different countries often overestimate returns because failed stock markets typically don’t appear in the later data for they have ceased to exist. One needs to carefully adjust for this.
I don’t recall the exact real returns when these things are adjusted for and can’t quickly find a good estimate, but I seem to recall it comes down to less than 3%. If someone has a pointer to a good estimate, I’d love to see it.
Regarding risk adjustment, I didn’t mean risk aversion, just that you have to adjust for the chance of losses as well as gains to get an expected rate. Any sensible aggregate will do this.
http://economics.mit.edu/files/637 says the US Social Security Administration used a 7% real rate of return, but the paper goes on to explain why that seems too high.
https://en.wikipedia.org/wiki/Equity_premium_puzzle says the equity premium for stocks “is generally accepted to be in the range of 3–7% in the long-run.” That piece lists reasons to deny an equity premium, similar to those you enumerate, but it also says “most mainstream economists agree that the evidence [for an equity premium] shows substantial statistical power.” I don’t know enough to evaluate this debate without further investigation, but your concerns about biases seem significant.
However, they are distributed over twenty years of that time and I think the amortization calculator you used assumes it is all paid as a lump sum on year one.
Yes, this is what I assumed. As I note at the end of my previous comment, I took the £150-200,000 figure to represent the present-value cost of having a child, rather than the unadjusted sum of payments that parents are expected to make over a 20-year period. I think I made that assumption because Brian’s own estimates are adjusted for the time value of money. I agree that, if this assumption doesn’t hold in this case, then the cost per parent per year is £3,000 (excluding opportunity costs).
I’m not familiar with the theory behind the time value of money to appraise it, but it looks to me like your calculation here has taken my per parent figure and come out with a per couple figure, which (I’m sure unintentionally) makes it look at first read like my estimate is <50% of the true cost). But the figure of £4700 per couple is not wildly different from £4000 per couple per annum, given the uncertainty bounds I’d put on it.
Regarding the opportunity costs estimate here I’d dispute that figure with gusto. I think that estimate is inaccurate and probably inflated for two major reasons.
Firstly, I don’t think we have anything like the amount of certainty about that figure—at the very least it deserves some error bars! (Incidentally, I find this is a big problem with back-of-the-envelope calculations that come out with a single figure—the number looks much more authoritative than it should given the uncertainty regarding the factors behind it).
I was deliberately not specific as to the amount of the time cost involved because I was unable to find reliable data to make such an estimate. Brian’s essay does not provide any data from which he draws his estimate of 21 hours per week per parent in time opportunity costs (I think I am correct in believing he’s not a parent). He simply states it after a long list of the types of work that parenting involves. In his account, the following are ‘work’: “playing with your toddler…spending quality time with your kid on the weekends, taking your kid to events and friends’ houses, going to school functions…giving advice on jobs, and everything else in between.” I don’t dispute that some elements of parenting are straightforwardly work—probably unpleasant and with no immediate reward for the individual performing them. However to describe playing with your child, engaging in social activities or giving interested advice to a young person exploring future career options as ‘work’ is a little boggling to me. I suspect that for most people who would class these things as work, parenthood is unlikely to be an attractive prospect.
So I am sceptical of the apparently randomly drawn figure of the hours of work involved. Of course, I’m happy to report back with data on this in a few years.
Secondly (and this criticism also applies to Brian’s figure of 21 hours per parent per week even if it were accurate), I would dispute the assumption that each marginal hour of time can be spent in earning money at the same rate as your basic income.
Depending on your type of work, It may not be practically possible: In my case, though I can increase my earnings by taking on extra shifts, the number I can take is capped as I am not allowed to exceed a set number of hours of clinical duty per week (averaged over a period of time). In fact, just yesterday a colleague was reprimanded for having taken on locum shifts which meant he exceeded these hours, and he has had to come off the ‘on-call’ rota (with a concomitant salary cut) to allow the time to average out. For someone in a full-time salaried position (say a university research appointment), it’s not the case that working longer hours increases your pay. For most people in this position it’s unlikely to be the case that opportunities exist to find an extra 21 hours of paid work per week which will pay them at a professional wage.
In addition to the practical possibility there’s the psychological reality. I don’t know many people who can actually consistently and productively do paid work 50+ hours a week. I recall seeing data (on this blog) that suggested those who estimate their working hours much about the mid-40s were a) overestimating and b) no more productive than those who claimed to work fewer hours. Certainly at a population level an inverse relationship is observed between hours worked and productivity
So even we did work in careers that would theoretically allow us to increase our working hours by nearly 50 and be paid for it, I think it’s highly unlikely we would sustain that working pattern. (I’m sure some people can, I just know I’m not them!)
I’m not familiar with the theory behind the time value of money to appraise it, but it looks to me like your calculation here has taken my per parent figure and come out with a per couple figure, which (I’m sure unintentionally) makes it look at first read like my estimate is <50% of the true cost). But the figure of £4700 per couple is not wildly different from £4000 per couple per annum, given the uncertainty bounds I’d put on it.
No, sorry: I took the middle value of your £150-£200,000 estimate (£175,000) then divided this figure by two and used one of the many amortization schedule calculators found online to reach the £4700 figure, assuming a 5% interest rate and 50 annual periods. So £4700 is what each parent would need to pay at the end of each year, over the following 50 years, to cover the costs of having the child. (This assumes £175,000 is the present-value cost of parenthood, rather than the nominal cost.)
I have nothing to add to your comments about Brian’s estimates, and I agree with much of what you write. I relied on those estimates because I knew of no better ones. I do however think that if you believe his calculations are inflated you should, if possible, use figures that match your own estimates, rather than no estimates at all. But I grant that this may be quite complicated, since the opportunity costs of parenting may be highly sensitive to factors that vary significantly among different people, as Brian himself acknowledges in his comment.
Bernadette makes some good criticisms, and I’ve updated my piece in response. I now put the opportunity-cost figure around $100K of present value, which seems low but not obviously too low if much of the parenting time is not “work.” I also changed the opportunity cost from being about extra income to being about how much you value what you would have been doing instead.
Individual differences seem big here. While there are some people like Bernadette and Julia who give extensive thought to this issue, there are others who don’t actually care about kids as much but just go along with social custom, spousal pressure, or the results of carelessness with birth control. It’s this latter group that my piece is mainly intended to speak to. I don’t know the relative proportions of different types of people in the population.
If this is still linking to the correct Economist article, it notes that Greece is poorer than other parts of Europe but Greeks work more hours per week. However, I have not seen evidence for causation, that is if the rest of Europe worked more hours, its GDP per capita would actually fall. Has anyone seen this?
You could outsource the costs if that’s something you’re inclined to do. I would probably feel guilty about doing so myself.
The opportunity costs can vary a lot based on what your alternative career might have been (e.g., for a would-have-been CEO they’re much bigger than for a would-have-been librarian), as well as whether the parenting time comes from your existing leisure time or your existing work time.
This is a very interesting essay addressing a very important decision EAs face. Thank you for writing it!
I think your estimates for the annual financial cost of having children underestimate the real costs, because they don’t account for the time value of money and because they omit opportunity costs.
To account for the time value of money, we can use the formula used to calculate amortization in business. Assuming a present-value cost of £175,000, an interest rate of 5% and 50 periods, the annual cost for each couple turns out to be about £4,700 per parent per year.
To account for opportunity costs, we can use Brian Tomasik’s estimates. He claims that the present-value opportunity costs of parenting are about $380,000, or £225,000. Adding this to the financial costs, we get a total cost of £400,000. Using the formula above, this translates into about £11,000 per parent per year.
However, as Brian notes in private correspondence, the opportunity costs could be much lower if parents outsource them. And parents persuaded by Bryan Caplan’s arguments should be less reluctant to outsource these costs. So for you and Toby, and for many other EAs, the estimate is probably lower than £11,000.
Hi Pablo,
You are right that the £2,000 per year per parent lifetime cost would be better if it included an adjustment for the fact that the cost aren’t evenly distributed over that timespan. However, they are distributed over twenty years of that time and I think the amortization calculator you used assumes it is all paid as a lump sum on year one. I set up a spreadsheet to allocate the costs evenly over the first twenty years and then look for which amount this was equivalent to paying if the costs were spread out over the whole 50 years. This was £3,000 per parent per year, which is higher than the £2,000, but quite a bit less than the £4,700. This is still not perfect as the costs are skewed a bit towards the early and late years, but it should be pretty close to the right model.
I also think that 5% above inflation is substantially higher than the best estimates of the risk adjusted rate of return. Using 3%, the cost per annum drops to £2,500, which is pretty close to the original unadjusted estimate.
(Note that you might want something even higher than 5% if you would really like to spend/donate money a lot sooner, but if so, you should also be taking out loans in order to donate more sooner and I’ve never met anyone doing that).
5% above inflation seems reasonable if you invest in stocks, unless you think (as some do) that stock markets are going to systematically have lower returns in the future than they did in the past. I don’t see why a risk-free rate would be appropriate, since stocks aren’t risky enough to cause problems in many practical situations.
Brian, there are several serious sampling biases in most estimates of long run real returns which tend to overestimate the returns. These include:
(1) Time selection bias. The 20th century was unprecedentedly good for stocks. If we instead averaged over wider periods or over the 21st century so far, we get much lower numbers. It is unclear what is the best period to use, but many estimates use the most optimistic one which is suspect. (2) Country selection bias. The US has done unprecedentedly well with stocks. International comparisons give lower returns and are probably more representative of the future (we don’t know which country will do best this time round). (3) Within-index selection bias. The major indices are of the top stocks rather than a fixed set, so for example if all the stocks in the S&P 500 went to zero tomorrow, this would really change the real rate of return, but wouldn’t change the index that much as the next 500 stocks would replace them—we need to adjust for that. (4) Between-exchange selection bias. Even attempts to adjust for the country selection bias by using a range of stock markets or indices in different countries often overestimate returns because failed stock markets typically don’t appear in the later data for they have ceased to exist. One needs to carefully adjust for this.
I don’t recall the exact real returns when these things are adjusted for and can’t quickly find a good estimate, but I seem to recall it comes down to less than 3%. If someone has a pointer to a good estimate, I’d love to see it.
Regarding risk adjustment, I didn’t mean risk aversion, just that you have to adjust for the chance of losses as well as gains to get an expected rate. Any sensible aggregate will do this.
Thanks for those notes. :)
http://economics.mit.edu/files/637 says the US Social Security Administration used a 7% real rate of return, but the paper goes on to explain why that seems too high.
https://en.wikipedia.org/wiki/Equity_premium_puzzle says the equity premium for stocks “is generally accepted to be in the range of 3–7% in the long-run.” That piece lists reasons to deny an equity premium, similar to those you enumerate, but it also says “most mainstream economists agree that the evidence [for an equity premium] shows substantial statistical power.” I don’t know enough to evaluate this debate without further investigation, but your concerns about biases seem significant.
Hi Toby,
Yes, this is what I assumed. As I note at the end of my previous comment, I took the £150-200,000 figure to represent the present-value cost of having a child, rather than the unadjusted sum of payments that parents are expected to make over a 20-year period. I think I made that assumption because Brian’s own estimates are adjusted for the time value of money. I agree that, if this assumption doesn’t hold in this case, then the cost per parent per year is £3,000 (excluding opportunity costs).
I’m not familiar with the theory behind the time value of money to appraise it, but it looks to me like your calculation here has taken my per parent figure and come out with a per couple figure, which (I’m sure unintentionally) makes it look at first read like my estimate is <50% of the true cost). But the figure of £4700 per couple is not wildly different from £4000 per couple per annum, given the uncertainty bounds I’d put on it.
Regarding the opportunity costs estimate here I’d dispute that figure with gusto. I think that estimate is inaccurate and probably inflated for two major reasons.
Firstly, I don’t think we have anything like the amount of certainty about that figure—at the very least it deserves some error bars! (Incidentally, I find this is a big problem with back-of-the-envelope calculations that come out with a single figure—the number looks much more authoritative than it should given the uncertainty regarding the factors behind it).
I was deliberately not specific as to the amount of the time cost involved because I was unable to find reliable data to make such an estimate. Brian’s essay does not provide any data from which he draws his estimate of 21 hours per week per parent in time opportunity costs (I think I am correct in believing he’s not a parent). He simply states it after a long list of the types of work that parenting involves. In his account, the following are ‘work’: “playing with your toddler…spending quality time with your kid on the weekends, taking your kid to events and friends’ houses, going to school functions…giving advice on jobs, and everything else in between.” I don’t dispute that some elements of parenting are straightforwardly work—probably unpleasant and with no immediate reward for the individual performing them. However to describe playing with your child, engaging in social activities or giving interested advice to a young person exploring future career options as ‘work’ is a little boggling to me. I suspect that for most people who would class these things as work, parenthood is unlikely to be an attractive prospect.
So I am sceptical of the apparently randomly drawn figure of the hours of work involved. Of course, I’m happy to report back with data on this in a few years.
Secondly (and this criticism also applies to Brian’s figure of 21 hours per parent per week even if it were accurate), I would dispute the assumption that each marginal hour of time can be spent in earning money at the same rate as your basic income.
Depending on your type of work, It may not be practically possible: In my case, though I can increase my earnings by taking on extra shifts, the number I can take is capped as I am not allowed to exceed a set number of hours of clinical duty per week (averaged over a period of time). In fact, just yesterday a colleague was reprimanded for having taken on locum shifts which meant he exceeded these hours, and he has had to come off the ‘on-call’ rota (with a concomitant salary cut) to allow the time to average out. For someone in a full-time salaried position (say a university research appointment), it’s not the case that working longer hours increases your pay. For most people in this position it’s unlikely to be the case that opportunities exist to find an extra 21 hours of paid work per week which will pay them at a professional wage.
In addition to the practical possibility there’s the psychological reality. I don’t know many people who can actually consistently and productively do paid work 50+ hours a week. I recall seeing data (on this blog) that suggested those who estimate their working hours much about the mid-40s were a) overestimating and b) no more productive than those who claimed to work fewer hours. Certainly at a population level an inverse relationship is observed between hours worked and productivity
http://www.economist.com/blogs/freeexchange/2013/09/working-hours.
So even we did work in careers that would theoretically allow us to increase our working hours by nearly 50 and be paid for it, I think it’s highly unlikely we would sustain that working pattern. (I’m sure some people can, I just know I’m not them!)
Thanks for the reply. You write:
No, sorry: I took the middle value of your £150-£200,000 estimate (£175,000) then divided this figure by two and used one of the many amortization schedule calculators found online to reach the £4700 figure, assuming a 5% interest rate and 50 annual periods. So £4700 is what each parent would need to pay at the end of each year, over the following 50 years, to cover the costs of having the child. (This assumes £175,000 is the present-value cost of parenthood, rather than the nominal cost.)
I have nothing to add to your comments about Brian’s estimates, and I agree with much of what you write. I relied on those estimates because I knew of no better ones. I do however think that if you believe his calculations are inflated you should, if possible, use figures that match your own estimates, rather than no estimates at all. But I grant that this may be quite complicated, since the opportunity costs of parenting may be highly sensitive to factors that vary significantly among different people, as Brian himself acknowledges in his comment.
Bernadette makes some good criticisms, and I’ve updated my piece in response. I now put the opportunity-cost figure around $100K of present value, which seems low but not obviously too low if much of the parenting time is not “work.” I also changed the opportunity cost from being about extra income to being about how much you value what you would have been doing instead.
Individual differences seem big here. While there are some people like Bernadette and Julia who give extensive thought to this issue, there are others who don’t actually care about kids as much but just go along with social custom, spousal pressure, or the results of carelessness with birth control. It’s this latter group that my piece is mainly intended to speak to. I don’t know the relative proportions of different types of people in the population.
If this is still linking to the correct Economist article, it notes that Greece is poorer than other parts of Europe but Greeks work more hours per week. However, I have not seen evidence for causation, that is if the rest of Europe worked more hours, its GDP per capita would actually fall. Has anyone seen this?
You could outsource the costs if that’s something you’re inclined to do. I would probably feel guilty about doing so myself.
The opportunity costs can vary a lot based on what your alternative career might have been (e.g., for a would-have-been CEO they’re much bigger than for a would-have-been librarian), as well as whether the parenting time comes from your existing leisure time or your existing work time.