Do Americans work more because of status concerns? Maybe, but in all honesty, it's hard to tell
First, how much people want to work - labor supply - can be all kinds of weird, even without assuming any kind of "status effects". Labor supply curves can slope downwards (if the income effect dominates the substitution effect), they can bend backwards (same, except different at different wage levels), they can be discontinuous because of household specialization, and relatedly, there's two margins that people operate on when it comes to labor supply. Whether to play in the labor market in the first place (labor force participation) and then, if so, how much (hours worked). Add to that the various institutional structures which constrict the flexibility of labor supply and you can get pretty much anything.
The second reason why this is more complicated than the savings case is that now we have two "goods" (things which are desirable) which are subject to the "status effect" to a different degree. With saving and consumption the trade-off was between keeping up with the Joneses today, or keeping up with the Joneses tomorrow. In both periods there were status effects. However, the usual story with respect to work time is told differently:
Your annoying neighbor Jones works more and with his extra income goes out and purchases a Cadillac ("he means a Lexus but he don't know it") with a vanity license plate that says "YouAintGot1". At this point you start thinking "maybe I should have one" but the only way to afford it - given that you want to keep your level of savings constant so that we don't mix up our various "status effects" here - is to work more, slave like an ant and buy a Cadillac too. What ends up happening is that you end up working more than you'd like to just to keep up with the Joneses and you consume a (sub-optimal) amount of leisure.
The difference between this story and the one about consumption/saving one is that what is being implicitly assumed is that only one type of good - consumption of physical goods - is subject to "status effects". The other good - leisure - is not a "status good". Right at the start this is sketchy. Why couldn't leisure be a status good too? Obviously if I can show off to my neighbors that "I don't have to work hard for my income" by goofing off in conspicuous ways, why doesn't that involve status? Mr. Veblen, I'll see your Conspicuous Consumption and raise you some InYourFace Conspicuous Leisure! From what I understand (according to my reading of Victorian novels) that's how "status goods" used to play out. The merchant that was richer than an aristocrat was still looked down upon because, well, he still had to work for his money, whereas the aristocrat simply inherited it.
But never mind. From a theoretical point of view, the difference is that now not all goods are subject to the "status effect". Before, both "consumption today" and "consumption tomorrow" were both subject to status. In fact if both consumption of physical goods and leisure are status goods then we can just relabel:
consumption today = consumption of physical goods
consumption tomorrow = consumption of leisure
and then everything in the last post goes through - i.e. status effects essentially don't matter.
So let's consider the case where one good - consumption of physical goods - is a "status good", but the other - leisure - is not. If people for some goofy reasons are driven to compete in terms of their consumption of physical goods are they going to supply more or less labor? Will they work more or less?
Here it is actually plausible that the answer is "more", but not necessarily. Which is why a model which incorporates status effects on labor supply needs to be empirically tested. Them parameters need to be estimated. How do you know if some peoples care about status, rather than just having a lower disaffection for work (i.e. a lower marginal utility of leisure)?. The point here is that it's gonna be pretty much impossible to estimate this kind of thing.
Alright, so how do we go about analyzing this? Well, let's suppose that we've got a person whose welfare depends on their level of leisure, their consumption of some physical good ("trinkets") and also the consumption of trinkets by other people.
where c denotes consumption, l denotes leisure and c_J denotes the consumption of them annoyin' Joneses. Since our person has no power over how the Joneses choose their consumption level she regards c_J as a parameter and optimizes u over c and l.
Her consumption is equal to her income which is given by
where h is amount of hours worked and w is the wage. Normalizing the time endowment to 1, h=1-l, so
Graphing that sucker in consumption/leisure space you get your usual budget constraint:
The fact that both leisure and consumption are desirable, and assuming that there's diminishing marginal utility to both gives us a standard indifference curve. Since no one person has power over what average consumption is, c_J is just an argument in the utility function:
This means that one way to analyze what happens if people care about status in consumption is to see how the indifference curve changes when other people's consumption (here average consumption) changes. In other words, what happens to the slope of the indifference curve when, say, average consumption goes up. There's two possibilities. The indifference curve either gets flatter or steeper. If it gets flatter then the amount of leisure will fall and consumption will rise. If it gets steeper then the opposite will happen:
On the other hand it could be the case that your consumption gets "crowded" or "congested" by the status seeking of others. Every time you buy a damn Cadillac, Jones does too and you get no utility from it (this is another way of saying that other people's purchases mess with your marginal utility of consumption of physical goods). At some point you might decide to not bother and switch to the one good that is not affected by others' choices - leisure. In that case your indifference curve will become steeper rather than flatter and you will increase your leisure and decrease your consumption:
So which one is it? Well, to see what happens we can look at how the slope of the indifference curve changes when there's a rise in average (Jones') consumption. Of course if someone doesn't care about status at all then there won't be a change. Your econ 101 (or maybe 201 in some places) tells you that the slope of the indifference curve is given by the ratio of marginal utilities:
where the top is the marginal utility of leisure and the bottom the marginal utility of own consumption. To see the role of status effects we take a total derivative of (absolute value) that with respect to average consumption:
If that equation above is negative then we have the first case with the indifference curve gettin' flatter. If it's positive then we have the second case, with an increase in average consumption INCREASING leisure.
are just cross derivatives of leisure and consumption with other people's consumption:
Are these guys positive or negative? If Jones buys his Cadillac how does that affect your enjoyment of leisure? On the other hand it's somewhat plausible that your MARGINAL utility of consumption would go up if c_J increases - you not only get the extra benefit of consumption for its own sake but also you catch up with the Joneses. But it' not clear. Still, I'm willing to concede here that the relevant parameters work out so that the net effect of an increase in average consumption is to raise labor supply. But that's exactly why this is the sort of thing that you'd wanna estimate empirically. And that's gonna be messy.
To illustrate, take a simple specification of utility with own consumption, others' consumption and leisure:
where c is own consumption, c_J is others' consumption, h is own hours worked, w is own wage, h_J is others' hours worked and w_J is others' wage. Gamma measures the dis utility of work effort. Phi, like before, measures the extent of the "status effect".
Maximizing that sucker wrt to h gives you a labor supply function:
If phi=0 - no status effects - then this would just collapse to
at which point you could just log that monkey and run some regressions in order to estimate alpha and gamma.
This is what it looks like for the average person (Jones):
and if you can find some variation in h and w then you could, at least in theory run a regression like this:
The problem with this is that both gamma - the disutility of work - and phi - the status effect - all wind up in the constant. In other words, there's no way to know - even if you can estimate this thing - whether people in a given economy work more because they care more about status, or because they just dislike working less. If you got some taxes, or labor market distortions running around that's gonna be in there too. And it could be very well the case that what looks like "Americans work more because they care about status" is really "the freakin' income taxes are lower". Or maybe Americans are just "more hardworking" for them, anthropological, sociological, psychological, and English Studies reasons. How would you know?
We can actually use the equation above for average/Jones' hours worked to plug into any ol' person's labor supply function. In that case we get a very nonlinear equation. We could still estimate it - to be honest I'm not up to my nonlinear econometrics - but I'm pretty sure you'd get the same problem. Work it through yourself. What you'll get is that with nonlinear methods you can estimate two parameters but you've got three variables you care about. In other words, one of your parameters will be a (nonlinear) combination of alpha and gamma, and the other a (nonlinear) combinations of alpha and phi. Which, again, means that even when you get all kinds of fancy statistically it's next to impossible to separate the "status effect" (phi) from just plain ol' "don't like to work effect" (gamma).
So how would you know? And anyway, isn't worry about "status" an Old World type of thing?
A final note here. You could get some estimates by considering some kind of variation in wages and labor supply levels. But this is going to get you thinking about exactly what kind of status people worry about. You could estimate the above equation across different countries. But that brings up the alpha/gamma problem mentioned above. You could assume that people care about status within their own status, zip code or county. Or maybe educational groups. At each point the same issue will arise. I could explain all this better, but god damn, I'm tired after writing all this.