UBI, inflation and labour markets.
Introduction
The aim of this blog is to lay out an argument on how UBI interacts with inflation and labour markets and it requires a few steps to make the point but I hope each step will seem reasonable. I’m trying as much as possible to stay within the standard wheelhouse of economics and only making additional points where I think there is a clear and reasonable rationale for doing so. That said I do have to make some points that are not usually made and you’ll have to judge for yourself whether they are reasonable.
The overall takeaway I intend to work up to is this: This model is consistent with experimental data showing that people do not stop working when they receive a UBI. Instead, it implies that an increase in UBI will, all else equal, put upward pressure on prices but that it is one factor amongst many in the economy and should be thought of as applying pressure, not determining prices in and of itself.
The end result can be significantly affected by not only the total government tax take but via which measures these taxes are collected, overall inequality in a society, interest rates, government spending and investment, business spending and investment, aggregate propensity to save, etc.
To tackle this problem I want to isolate the credit market and labour market elements before recombining them. This is mostly for the sake of clarity. I’m going to start with credit markets as, for the purposes of this discussion, I think that’s the shorter one.
Savings and Loans
Prices of goods and services are usually considered to be a function of how much people are demanding goods vs how much it costs to produce those goods. The crucial point for us here is that we are measuring that demand and supply in units of currency. The way modern currencies work is by aiming for a small but steady decrease in the value of each unit of that currency each year so that the prices of goods and services measured in that currency should increase. This discourages hoarding of the currency itself and encourages just enough demand to keep the economy running full pace without prices spiralling out of control. For the purposes of this blog, we are taking that as a given.
So in a world where nobody ever worked and all goods and services were supplied by machines how would this work? (This is so we can assess credit market effects separately to labour markets for a moment.)
Well, humans would still want things and they would still demand those things using currency. At first glance you can imagine increasing or decreasing the UBI so that inflation continued at the rate that you wanted fairly easily. As long as the amount of goods and services is still limited you can always push up inflation with more currency and decrease it by removing currency. The complication is the addition of savings and investment. Loans expand the supply of currency in circulation while savings remove some of the demand and attempt to store it for use at a later date.
Loans, however, are not made infinitely. Loans are made aiming to receive back the prevailing interest rate, something that at the moment we set via central banks. This is about to be quite important re: UBI.
Imagine a number of possible projects/individuals that can be loaned to and the expected returns on those loans. You can easily imagine that any projects which are expected to yield less than the prevailing interest rate will not receive loans and those that are expected to yield more will receive them. This is what ends up determining the amount of money that gets added to the system via loans. What we do currently is we raise or lower the prevailing interest rate to alter how many of these projects fall into the category of being expected to yield more than the prevailing rate of interest. You can think of UBI and taxes as the other side of the coin, by determining how much people can and do spend on any given project they change how much any given project is expected to make. So even if the interest rate remains constant if the UBI goes up and taxes go down then the expected yield on projects will go up and more loans will be made. On the other hand if UBI goes down and/or taxes go up then projects will yield less and so fewer loans will be made. That is true even if the interest rate remains constant!
What we have isolated here, to my mind, is what I would call passive incomes and expenditures. Nobody had to work for any of the income stated here but nevertheless changes in that passive income (the UBI) vs the passive expenditures (taxes) pushed around, by itself, the amount loaned out even if the interest rate remained constant. Indeed for any given level of inflation there would be pairs of interest rates and passive income vs expenses that would match up. There are other kinds of passive income and expenses too: rent (both as an expense and as an income), loan repayments, cost of necessities like food, inheritances, winning the lottery, investment income on savings, the list goes on. All of these are different to active income, which is dependent on how many hours you spend working and how much you are paid for each hour, and optional expenses, which are the things you could cut down on if you needed to spend less.
So let’s examine UBI and labour markets and then put that together to get an idea of how UBI impacts inflation.
Modelling labour markets
First, we need to briefly talk about how labour markets are traditionally modelled. Here economists tend to assume that hours worked is a product of the hourly wage and your own personal preferences for more income vs more leisure time. You can see that discussed in this lecture from the MIT Microeconomics course: https://www.youtube.com/watch?v=-5XT0Mzl72E&list=PL61533C166E8B0028&index=7
I want to talk about the same thing but using a slightly different model.
Whereas in the original model you work out how much people like any particular combination of total income and total leisure time and map that into a series of curves where every point on the curve is equally good (that’s what economists call a utility curve) I want to do something very similar but mapping utility slightly differently in order to more easily incorporate the ideas about passive income and expenses. Conveniently that also means my graph is going to look more like other demand and supply graphs for goods and services which is a nice bonus.
I’m going to map wage/hour against number of hours worked. So this will eventually look like a cost per unit vs number of units graph but we need to go through a couple of stages to get there. The reason for that is that I want to use a specific utility function (that’s just a representation of how a hypothetical person feels about different combinations of hours worked and pay). I want to do that so we can incorporate passive income and expenses into our utility function.
So what I have gone with is intended to be illustrative of some real-life things we might care about. It looks at how much you need to survive in each period of time subtracted from your passive income in that time. It then assesses how good a particular combination of hours worked times by wage/hour is for you based on how much income you have left to spend during your free time.
The assumption here is that free time is worth more to you if you have income to spend during that free time and to know how much income that is we need to know how much you have to spend on necessities and how much money you have coming in both from money you get without working at all and how much you get coming in from hours worked.
So it looks something like this: Hours of free time (leisure time) are given a value.
That value is assumed to be slightly less for each additional hour of free time and each £ earned. So, a hypothetical example, you can take the square root of: ((hours worked x wage + passive income — passive expenses) divided by number of hours of leisure) and times all that by the number of hours of leisure.
I.e:
-You work out the income you have left over to spend after expenses divided by the number of hours of leisure time.
-You then square root it to make it diminishing, so that each additional £/hour is worth slightly less than the one before
-Then you times that by the number of hours of leisure time to get a number that represents utility.
That’s a utility function.
So let’s make it look more “mathy” for a moment. Make utility U, hours worked H, Leisure hours L, wage per hour W, passive income P and passive expenses E you get:
Now if you want to get fancier you can put in additional factors like: the innate value of each hour of leisure time, even if you don’t have any money to spend in it; the innate value of work; and the diminishing marginal utility of income overall. You could also use some other function than a square root to create the diminishing marginal utility effect. Whatever floats your boat. For simplicity I’ve just kept the equation above here. Here is a table laying out what that looks like and I’ve colour coded utility from low (red) to high (green).
These particular numbers are based on Passive Income minus Passive Expenses of zero so whatever passive income they get perfectly matches expenses and the only remaining income is from wage labour a wage of zero, therefore, yields neither a positive nor a negative utility value. I’ve also not included an innate value to either work or leisure (or for that matter income which might exist due to prestige for example). That’s why zero hours of work produces zero utility.
Any two squares which have the same colour also have the same utility score. You can see by looking at the colour gradient how those equal scores form curves of the same colour/utility. If you take the lowest (in terms of wages) point on each curve then that is the ideal number of hours someone would work for a particular wage per hour.
Now in this example for any given wage the optimum number of hours to work a day is 6. This is just a sample utility function though- I’m not saying that this implies any magical truth about that specific number of hours! However, this particular function does something interesting if you change the passive income mins passive expenses part of the equation. If you have more passive income than passive expenses then the curve moves to look more like a traditionally drawn upward-sloping labour supply curve, where the less pay you are offered per hour the fewer hours you will want to work and the higher the hourly wage the more hours you will want to work. Conversely if you make passive expenses larger than passive income then the curve shifts the other way and slopes downwards so that the less you are paid per hour the MORE hours you want to work. Why? Because you want to be able to pay your bills of course!
I want to take a moment to consider the assumptions in the utility function I’m using and whether we are making the right ones before looking at some of the results it throws up.
Firstly I am effectively taking the lowest point on each utility curve, i.e the highest utility score for any given hourly wage, as the implicit labour supply curve. Is this right?
For our immediate purposes I think it is but I will be adjusting this later once we have covered the basics and are in a position to open ourselves up to more complexity. For now we can assume that any individual person is stuck accepting whatever the prevailing hourly rate is for labour but that they can choose to work for any number of hours they wish within a given time period (for us 1 day) at that prevailing hourly wage (not how the real world works of course but this is consistent with the simple models of labour markets you’ll learn in an economics lecture). I will talk more later on about more realistic labour market assumptions but we can work up to that.
Secondly, are we really saying that the only value anyone has in relation to work or leisure is a depreciating utility of income per leisure hour? We have assumed that here but we don’t have to. Utility functions can be arbitrarily complex but to avoid going too overboard I’m only going to be adding in two further things: how much someone enjoys their job and how much someone enjoys leisure time innately, even if there is no money for them to spend that hour. I will also be assuming that these depreciate for each hour of work or leisure. I.e. you might like your job quite a lot and that counts for a lot in hour 1 of work but less so in hour 23! Ditto for leisure, the first hour of having a rest is probably worth a lot to you but at hour 23 of sitting around doing nothing because you don’t have any money to spend you’re probably reasonably bored.
Adding in those two factors we can adjust them for how quickly they depreciate and how important they are relative to our original measure of utility. Then we can add the three values together to get a new utility score that incorporates the innate enjoyment of work, innate enjoyment of leisure and how much you can enjoy your income in your leisure time after you’ve paid all your bills. That seems to be more than enough for a basic model.
This also helps address the unusual straightness of the original model when passive expenses = passive income. Why does the passive income minus passive expenses equalling zero result in it being suboptimal for them to work any more hours than 6?
Well in the original example that’s because they don’t need any further income than they have to make their rent/mortgage/etc. They prefer not to work more than their optimum number of hours. What adding in values for innate enjoyment of work and leisure does is it pushes around the lower part of the graph where wages are low and thus not a major fact but then the graph still curves up to the same point (in this case 6) that it did originally. This is the same point it curved up towards in the original utility calculation when passive income and passive expenses did not match as well. In each scenario it tended towards 6 hours as wages got larger and larger. This matches well onto a sensible perception we might have that, although more income is always good, it’s going to take more and more income to persuade us to give up our leisure time and ultimately for any given hourly wage there is a maximum number of hours that it is optimal to work. We might work more hours if it’s the only way of getting a higher wage/hour but given any set hourly wage there’s probably a prefered maximum that each of us has for how many hours we would choose to work at that rate.
Given this and taking the highest utility number of hours to work for any given wage/hour we can create some interesting labour supply curves that can give us an intuition of what we really wanted to know: how will a different level of UBI affect inflation? In fact, even better, what we talked about at the beginning around income that comes passively rather than from labour/hours worked is now conveniently baked into this new labour supply function!
So I’ve taken the new utility function and used it to plot graphs for multiple individuals and added them together to show a particular pattern. Again I want to stress this isn’t fitted to data, but rather serves as an illustrative example to demonstrate how we might model an intuitive story about the labour market. The way this works is that, generally speaking, individuals will pay for their required expenses first, but then the curve bends back into a more traditional shape where more pay/hour means the person is more willing to give up their free time and work more hours, up to a point. So in a world where everyone is paid the one universal market wage, but everyone sets the number of hours they choose to work in a day, this graph now tells us how many hours someone with this specific utility function will choose to work. We can take that exact same utility function and put together samples of people who have different personal circumstances and by putting them together we can create a labour supply curve for the whole market. We are assuming that every person in this hypothetical market is identically effective at their job and identically driven to succeed. None of them is any better at their job, any more or less lazy, any more or less deserving. The only difference is that they have different starting circumstances in terms of passive income minus passive expenses (P - E). Let’s look at some examples of how that might affect their behaviour and how that can give us a simple mental model to use in considering UBI and labour markets.
Below is a graph with seven different labour supply curves. They are not seven individuals but seven groups of individuals. Each curve represents a different scenario. Each group has the same number of individuals and all the individuals have the same utility function but each individual has a different Passive Income minus Passive Expenses (P - E). Each of the seven groups is made up of individuals who have different P - E to each other. In some groups the P - E of the people in that group is pretty consistent and in other groups there is a large amount of inequality between individuals. That gives us seven example labour market supply curves made up of individuals who have the same underlying utility curve but different personal circumstances in terms of Passive Income minus Passive Expenses.
The Y axis is wages/hour and the X axis is the number of hours of labour supplied by the entire labour market.
For the record I know the graph seems like a lot to take in at first glance but I’m going to go through it steadily and cover each relevant part.
As you can see the 7 supply curves are broken down into two clusters. Each cluster is a group of three or four supply curves where each curve in that group has a similar total amount of passive income minus passive expenses. In cluster 1 the total amount of passive income minus passive expenses in each supply curve is positive, i.e. the group of individual people who make up each supply curve as a whole have more passive income than passive expenses. That’s why the labels for the curves have positive numbers next to them. The differences between the supply curves are down to inequality within the group of people that make up the curve. Some curves are a group of more equal people who make up that curve and some curves are a group of people with higher inequality. Note: this is specifically inequality in passive income minus passive expenses. That’s why the labels for the curve label them as higher or lower inequality. Cluster 2 is also a set of curves where the total passive income minus passive expenses is generally consistent across the cluster of curves but each curve has a different level of inequality to the other curves but this time the cluster is made up of curves where, in total, passive expenses are greater than passive incomes, leading to the negative number next to the label for each curve.
Implications of the model
Ok so that’s the graph and that’s what the different curves are but what are the implications?
The first is that I appear to have accidentally created a graph of a terrifying disembodied walking hand in the vein of ‘Thing’ from the Adams Family but there are also some interesting economic implications.
Something that stands out right away is how all the curves, regardless of inequality and regardless of passive incomes minus passive expenses, tend towards the same number of hours worked at high wages/hour, while with lower wages/hour they can all be quite different. This is reflecting the idea that if you have a large income coming in then your passive outgoings are relatively less of a concern and also it’s increasingly difficult to get you to give up your last few hours of leisure time regardless of your passive income minus passive expenses.
In the lower section of the graph however there are noticeable differences between the curves. The curves on the left-hand side look very much like any traditional labour supply curve and we’ll come back to them in a moment. The curves in the centre and on the left look noticeably different though, being bent backwards right at the very bottom before curving around to come around to a more traditional upward sloping shape as you move up in wages/hour. This is because at lower wages people will work however many hours are required to afford their necessary expenses because they want to continue to survive and live in their home. The bulge above that point where the graph curves back comes about because I have added in an innate value for leisure time on top of the value given by the initial formula around leftover income available in leisure hours. The shape of the graph at this point is very dependent on the relative values you choose to give to leisure and work time and how quickly you make that depreciate for each additional hour of work or additional hour of leisure.
What is unaffected by those particular variables is that the higher the amount of necessities that must be covered by labour income the more the bottom of the graph is pulled to the right in an attempt to cover them. I.e. people will work long hours for low pay if it’s the only way to survive/feed their kids! This seems like an incredibly obvious human point but I haven’t seen it properly discussed in economics lectures so I wanted to really hammer it home.
On the other hand the higher someone’s passive income relative to their necessary expenses the more their labour supply curve looks like a traditional upward sloping graph. Ultimately that’s what this whole essay is really about. UBI advocates have made the point that covering people’s essential costs increases their bargaining power in the labour market for a long time but this graph gives a model of what that might look like and the important insight that it is the level of UBI relative to those necessities that will determine UBI’s impact on people’s behaviour. You may reasonably argue “It’s only a model” (Monty Python reference very much intended) and that’s entirely reasonable BUT models are really useful in helping us think about problems and imagining the impacts of policies. We can and should then test the assumptions underlying the model, of course, but we do need a model as a starting point, as a framework to think about the issue.
Assumptions and results
So what are the assumptions here and what does this model show?
Well, it assumes that people will generally work for however many hours it takes to earn enough to survive even if wages are extremely low. I think that is entirely reasonable and plausible.
It assumes that people put some innate value on leisure time and on work but that the value placed on leisure hours is greater and falls off more slowly than the value placed on work hours. This I think is also plausible but even if you alter these values considerably, or alter their fall-off rates, or remove them altogether, the main outcomes of the model don’t change. All that changes is the shape of the bulge part of the curve.
It assumes that people value their income they receive above and beyond their necessities, that more is generally better but that how much more valuable any increase in this income is depreciates as the amount increases and as the number of leisure hours it is spread over increases. More income and more leisure are always better here but the amount each additional unit of income and each additional hour of leisure brings is less than the previous one.
The exact numbers this formula produces in terms of units of utility for any given amount of income and number of hours of work/leisure is not intended to perfectly reflect reality. Nor are the nuances of the shape of the curve. They are hopefully roughly right but it is the overall implications and overall shape of the curves in relation to each other that is hopefully accurate and informative.
What the curves show then is that the aggregate supply of labour is affected in the first instance by the aggregate amount of passive income minus necessities. This is the numerical value listed on the key next to each curve and we can clearly see that the two clusters of curves have similar values within the cluster and very different values between the two clusters. Consequently one cluster is clearly to the left of the other. This implies that as passive incomes relative to necessary expenses rise across a population you would expect people to demand higher wages for the same amount of work, all else equal. That seems reasonable. What it does not show, it is relevant to point out, is that having a passive income like UBI that covers necessities removes all incentive to work at all. It just increases the wages required to get people to work the same number of hours. This is especially true at the lower end of the spectrum. That’s why inequality between the individuals who make up the different aggregate labour supply curves also makes a difference. More equal curves do see the relatively wealthier individuals within that curve willing to work more hours for less than the wealthier individuals in the unequal groupings, however the effect on the most desperate individuals in the group is more profound and so the aggregate effect is that when the group of individuals making up one of these curves is more equal the curve overall shifts to the left. Inequality in this context is entirely within passive income minus necessities as labour income is the output of the graph and not an input. No attempt is made here to address income taxation either, if the individuals in this model are receiving UBI or other government income the taxes collected are coming from other sources. If an income tax were to be added it would be equivalent to lowering the wages/hour. If the income tax were progressive the effect would be a more substantial shift to the left for the wealthier individuals, i.e. they would demand more pay for the same number of hours or else would reduce their hours. This is in contrast to taxes that show up as part of the necessary spending portion of the formula which, if they were still targeted to wealthier individuals, would push the labour supply curves for those individuals down and to the right causing them to work for longer hours and lower pay than they otherwise would.
What the model implies in that context is that people’s supplied labour will be affected by a UBI but not in the simplified way portrayed in people’s critique of UBI. Instead UBI will be one force within a system of different pressures on labour supply and, in turn, one force in a system of forces affecting inflation both via people’s incomes and via how much people create in terms of goods and services to be sold within the economy. The overall implication is that higher UBI will push labour supply to higher wages/hour for the same amount of work. To examine how that will affect inflation we need to finally add back in some more realistic assumptions about how labour markets work.
More realistically thinking about the model out in the real world
In the real world this is unlikely to manifest as one single price per hour of labour across the whole economy where each worker chooses an optimum number of hours for them but instead with relatively flexible hours in a minority of jobs and more regulated hours in the majority of jobs. This means labour is more likely to be hired in a 40-hour workweek than one hour at a time but the overall shape of the labour supply curve and the pressures are likely similar. Instead we should think of multiple prices for labour and how a UBI affects the labour supply curve at those different wage levels.
If our simplified model here is that an increasing UBI “pulls” the bottom of the labour supply curve across from right to left and then upwards, then we can talk about a UBI putting a larger upward pressure on wages for the lowest-paid and a far more moderate upward pressure at the higher end of the wage scale. If UBI is paid for via taxation on passive income (like on capital gains or a Land Value tax) but those taxes are nonetheless progressive it can even put downward pressure on higher wages. If UBI is paid for via progressive taxation then it can also create some upwards wage pressure at the top, although less than at the bottom, although this depends on demand as those wages may be inflated via shortages of a particular type of worker and thus affected by the same effects as taxes on monopoly income, i.e. the tax does not actually reduce the willingness to supply and would not produce upwards wage pressure. If financed via a tax on business, like a VAT, then this would create upwards pressure on the prices that the tax was applied to (e.g. a VAT that does not apply to food but does apply to electronics would put upward price pressure on electronics but not food.)
Please note that this is often talking about wage pressure and not always inflation pressure. It is entirely possible for progressive income taxes to cause a wealthy person’s spendable income to drop while the UBI raises the spendable income of someone at the bottom and so have no net change on aggregate demand. Equally the wealthy person could end up spending less than before but the amount that gets transferred to the people on lower incomes then gets spent at a higher rate by people on lower incomes and saved less than it would have been had it stayed in the hands of the wealthy person and so it does create some upward pressure on aggregate demand. The level of inequality and propensity to save in society directly affect the end result of inflation. That is why we can talk about an increase in UBI being, in general, an upward force on inflation and a decreasing UBI being, in general, a downward force on inflation but we can not talk about it by itself wholly deciding what inflation is. Context matters. (It could hypothetically be used to offset those other factors by changing the UBI level as those other factors change, much as we currently use interest rates, but we can not say increasing UBI will always increase inflation regardless of the context as the context may be deflationary and increasing the UBI will merely stop that deflation. It depends.)
The last point is how inflation affects the labour supply curve. Inflation in the price of necessities acts like an increase in passive costs and shifts the labour supply curve to the right, more acutely at the bottom, less at higher wages. Inflation in luxuries functions like reducing the effective amount that can be spent after the cost of necessities, during leisure time. This shifts any part of the curve that is upwards sloping (like a traditional labour supply curve) to the left, i.e. higher wages will be demanded for the same work.
Conclusions
Overall the take-away is this: This model is consistent with experimental data showing that people do not stop working when they receive a UBI. Instead it implies that a UBI will, all else equal, put upward pressure on prices but that it is one factor amongst many in the economy and should be thought of as applying pressure, not determining prices in and of itself. Also that it is the increase in the UBI that puts upward pressure as a UBI that is just the status quo doesn’t push the curve one way or the other. Only a change in UBI changes the shape of the curve.
The end result can also be significantly affected by not only the total government tax take but via which measures these taxes are collected, overall inequality in a society, interest rates, government spending and investment, business spending and investment, aggregate propensity to save, etc.
UBI will be a factor in what loans are made and which are not by increasing the nominal amount of currency that any given economic actor is capable of paying back and so for any given interest rate a rise in UBI should, in general, increase loans made and a decrease in UBI should, in general, decrease loans made. This means that in our current economic system a UBI that is increasing too fast would result in central banks raising interest rates. In a system where the UBI itself was used to moderate inflation at a constant interest rate, which would likely be possible, increasing a UBI too fast would push up inflation beyond the target rate.
Additionally, a UBI kept stable in its nominal value/amount will reduce in value as inflation increases, especially inflation in necessities. As such with a positive rate of inflation a UBI that is kept at the same nominal amount will, in effect, be falling over time and so have a deflationary effect on the economy. Only a UBI rising faster than the rate of inflation could be expected to increase inflation and even then this effect may be swallowed up and counteracted by economic growth, rising interest rates, increasing inequality, increasing propensity to save, etc.
There are a number of issues I would like to explore in more detail in future posts such as UBI’s effect on aggregate demand, particularly in this case for labour, the interaction with interest rates, etc. For those reading this who want to get a better understanding of traditional economics of labour markets I’d suggest the MIT Microeconomics course linked above and this much more accessible course from Khan Academy: https://www.youtube.com/watch?v=Cm69zTuUzMI
