GDP and Living Standards
Does GDP Capture Changes in Living Standards? Potential Implications for Our AI Future
If you are like me, you probably are tired of gross domestic product (GDP)-related discourse. If you are not like me, or you are unfamiliar with this discourse, perhaps I should explain.
A lot of the favorite casual criticisms of economics relate to GDP. They typically go something like this. GDP does a bad job of measuring X and X is a thing that really matters, therefore GDP is a bad measure. Often times, these criticisms aren’t necessarily wrong. GDP doesn’t measure X because that is not what it is designed to measure. GDP is designed to measure the total value of newly produced final goods and services in the economy (meaning within the borders of that economy) over a given period of time. Unless that is your definition of X, GDP isn’t going to measure it.
Ironically, however, GDP often tends to be a good proxy for X. For example, some people say that GDP isn’t good because what we really care about is happiness or life expectancy or consumption. It turns out that GDP is actually strongly correlated with all of these things.
Nevertheless, I don’t think that these correlations are something that we as economists should hang our hats on. It is fun to point out that “GDP is fine, actually,” but I also think that sometimes we risk taking this too far. After all, GDP is designed to measure a particular thing. Let’s keep it to that thing. When we want to measure something else, we should try to measure it precisely using the tools that we have.
One thing that we frequently use GDP for is to measure living standards. This seems to make sense. We calculate economic growth by finding the growth rate of the trend in real GDP per capita. As a matter of measuring how much more stuff the economy is producing over time, this seems like a good measure. However, while the phenomenon of economic growth is associated with a corresponding rise in living standards, it isn’t obvious that we can measure improvements in living standards using the growth of real GDP per capita. A recent paper by Philip Trammell and Chad Jones makes this point in an easy to understand way. Allow me to explain.
Preferences, GDP, and Living Standards
Back in the 1970s, Paul Samuelson and Subramanian Swamy wrote a paper that showed that real GDP provides a consistent measure of living standards if preferences are homothetic (a frequent assumption made by economists). I don’t really want to spend any time explaining what homothetic preferences are because I value you, the reader, too much to make you read through that. However, it suffices to say that with homothetic preferences, the income elasticity of all goods is unit elastic and the expenditure shares on each good is constant over time.
To see why that might be important, consider how we measure economic growth when we use a chain-weighted measure. The growth rate of real GDP is just the weighted average of the growth rate of the production of each good. With homothetic preferences, the weights are fixed. Thus, if there are two goods and the production of one good is growing at 4% and the other good is growing at 2% and each make up half of the expenditures, then the growth rate will be 3%.
However, consider the case of non-homothetic preferences. One example of this would be to consider a utility function in which the utility of consuming each good is bounded from above. In other words, consider a world in which there is (at least eventually) diminishing marginal utility for each of the two hypothetical goods already mentioned such that total utility from consuming that good reaches some maximum. Given that the production (and consumption; markets clear) of the first good is growing at 4%, consumers will hit the point of diminishing marginal utility earlier than for the other good. As a result, consumers will start to substitute away from this good and consume more of the other good because the marginal utility of the latter is higher. In fact, in the extreme case in which the consumer ultimately hits the upper bound for utility associated with the first good, all of consumption will be of the second good and thus the growth rate converges to 2%.
Note that the only thing that differs in each of these examples is consumer preferences. The measured growth rate is different just because the expenditure shares are changing over time under one set of preferences, but not the other.
Why does this matter?
As Trammell and Jones note in their paper, when we think about the way in which economic growth improves living standards, we tend not to think about it in terms of just more stuff. Instead, we think about economic growth improving living standards because of a wider variety of goods that are available. We don’t just get more of the same stuff. We get new stuff that is better than the old stuff. An example that they give in their paper is of Nathan Rothschild. Back in the 1830s, this was the richest man in the world. However, he died from something that would have been cured today by cheap antibiotics. The availability of antibiotics would have greatly improved his living standards.
With that in mind, let’s return to our previous example, but instead let’s imagine that the second good doesn’t initially exist. The introduction of the second good makes people better off. It raises total lifetime utility. However, with different assumptions about preferences, we get two different growth trajectories. More importantly, for non-homothetic preferences, the growth trajectory gives us a really perverse result if we think about living standards in terms of real GDP.
The reason for this perverse result is as follows. If only the first good exists, the economy will grow at 4% per year. If the second good is introduced, lifetime utility (and thus living standards) rise for everyone in the economy. However, the growth rate converges to 2%. In other words, projecting this out, real GDP will be lower in the world with the second good even though living standards are higher.
How to Measure Changes in Living Standards
Trammell and Jones suggest that to properly measure living standards, what we really need is lifetime utility. This is a problem since we cannot measure utility. Nonetheless, price theory can help here. Remember that I had a previous post on the statistical value of human life (or the value of a statistical life, VSL, for people who want to butcher the English language). We can estimate the VSL using data from labor markets. People are compensated for taking on risks in particular jobs. The VSL can be measured as the compensation for this risk per change in probability. This gives us a dollar value for human life. Conceivably, this could tell us something about living standards. As living standards improve, life is worth more to people and so they are less likely to take on risk without additional compensation. VSL will capture this change in living standards.
Of course, this is a measure in terms of dollars. To properly measure things, we need to have things in terms of total utility. Fortunately, if one solves an infinite horizon, representative agent problem, it follows that
Or
Where U is total utility from aggregate consumption and MU is the marginal utility of aggregate consumption. In other words, there is a way to convert lifetime utility to dollars to get VSL and correspondingly a way to convert VSL to lifetime utility. Unfortunately, doing so requires having some ability to measure the marginal utility of total consumption. We don’t have a way to do that. Thus, we are back to square one.
Or are we?
Trammell and Jones point out that although we cannot get the level of living standards, we can estimate the growth rate. For example, it follows from our equilibrium condition for VSL that:
where g_u measures the growth rate of lifetime utility, g_VSL measures the growth rate of VSL, and g_mu measures the growth rate of the marginal utility of consumption.
But we know from standard models of consumption that
In words, this means that the growth rate of the marginal utility of consumption is equal to the rate of time preference minus the risk-free interest rate. It therefore follows that
The right-hand side of this expression is all stuff we can measure. Thus, if we can measure the growth rate, we are always able to measure the magnitude of the difference in living standards over different periods of time.
Does This Matter Empirically?
One might wonder whether this matters empirically. Well, using Trammell and Jones’s baseline calculation, they find that the average annual growth rate of total utility from 1940 to 2024 was about 2.3%. This implies that living standards were 6.9 times higher in 2024 than in 1940. As a method of comparison, the average annual growth rate in real GDP per capita from 1940 to 2024 is about 2%. That doesn’t seem like much of a difference, but compound growth makes a difference here. Real GDP per capita would suggest that living standards were 5.4 times higher in 2024 than in 1940.
It is important to note that the estimates depend critically on how we measure VSL. We lack good time series data on VSL. Trammell and Jones splice together estimates from Costa and Khan (which I discussed in my post on VSL) and from the U.S. Bureau of Labor Statistics.
An alternative would be to start with estimates of VSL and then project them forward based on the income elasticity of VSL. Trammell and Jones also do this. They find that if you use the standard BLS assumption that the income elasticity is 1, then this implies that living standards are 5.1 times better in 2024 than 1940. This is pretty close to the estimates implied by the growth in real GDP per capita.
However, Costa and Khan found much higher income elasticity of VSL. When Trammell and Jones use an income elasticity of 1.3, this implies that living standards are 21.1 times higher in 2024 than in 1940!
What this demonstrates is that it is possible that the growth in real GDP per capita might actually understate the rise in living standards associated with economic growth. This shouldn’t necessarily be surprising since its ability to measure living standards requires specific assumptions about preferences that might not hold.
Nonetheless, whether the real GDP per capita is a good proxy ultimately depends on measures of VSL. We need much more frequent and consistent estimates of VSL to make this determination.
Implications for Our AI Future
Why does all of this matter?
Well, one of the things that both Brian and I have been writing about recently is AI and the likely economic effects thereof. To some extent, Brian and I have spent a lot of time throwing cold water on the more provocative claims made by people with respect to AI.
In fact, one argument that I made based on the literature on economic growth is as follows. Some types of production might be easy to automate. AI might be expected to have a huge influence on those types of production. However, other types of production might be hard to automate. If production is a function of both easy-to-automate inputs and hard-to-automate inputs and the elasticity of substitution between those inputs is less than one, then the growth rate of the economy will be determined by the growth in the production of those hard-to-automate inputs.
Nonetheless, in a world of more advanced AI, living standards might increase substantially, in part due to all of that automation, but also due to inventions and innovations that humans might not have discovered in the absence of these AI tools. However, that might imply that real GDP per capita becomes a bad measure of living standards since total utility might be growing substantially faster than measured production.