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Desirable Effects of Income Taxation IV Dissipative Signaling

From now on, these posts will be reviews of the established literature. I will assume, as is standard, that people are completely selfish. The point is to show that, even if people are selfish, there are desirable incentive effects of income taxation.

As is often the case, the results of 50 year old theory turn out to depend on the assumption of symmetric information. If some agents know things that other agents don’t know, then free market outcomes can easily be Pareto inefficient.

One very old example is due to A Michael Spence who considered a model in which people don’t learn anything useful in college, but get degrees just to prove they can. Spence was dean of Harvard’s faculty of Arts and Sciences, so he should know. Basically the idea is that what matters is having the diploma not knowing how to read it. In fact, I personally possess a diploma signed by a Michael Spence which is written in Latin — a languge which I can’t read (although I can guess that Cantabrigia is the very old word for Cambridge).

Debt and Taxes III

I don’t know if I should try to make my contributions to AngryBear a noahpinion sub substack or if I should put this over at my personal blog, but I am always stimulated by Noah’s posts . His most recent “No one knows how much the government can borrow” is on a topic I’ve mentioned here (and here also Brad all following Blanchard): How much should we worry about the huge and rapidly growing US national debt ?

Noah wrote that he doesn’t know and he doesn’t think anyone else does either. My comment is that Noah assumes things we don’t know. In particular, he assumes that we know something about how much the US Federal Government can borrow while paying record low interest rates. Noah write well, so it is hard to excerpt

If the U.S. federal government keeps borrowing and borrowing and borrowing without limit, eventually foreigners and private companies and citizens are not going to want to buy all of those Treasuries. At that point the U.S. government can basically do one of two things:

It can offer higher interest rates, to make Treasuries more attractive, so that foreigners and U.S. private companies and citizens are willing to absorb larger amounts of debt.

It can have the Fed buy more of the Treasuries at a low interest rate.

But we have no way of knowing if we are anywhere close to the point where “foreigners and private companies and citizens” do not “want to buy all of those Treasuries”. In particular, the titanic gigantic issuance of Treasuries in 2020 did not drive interest rates significantly above record lows.

Covid Vaccination one dose or 2 II

There is evidence from Israel that one dose of the Pfizer vaccine is less effective than was suggested by the few person-days of evidence in the phase III trials. In Israel  “over 12,400 have people tested positive for coronavirus after receiving vaccine shots” Israeli health officials estimate that one shot is about 50% effective after 14 days . The control group is not matched, it’s not a randomized trial, but it is evidence that the second dose provides benefits on the order of the benefits of the first and is evidence against my proposal to delay the second dose.

Debt and Taxes II

This is an extended post on the caveat to debt and taxes 1. It is joint work with Brad DeLong and Barbara Annicchiarico. The point is that, in his Presidential Address, Olivier Blanchard notes that the argument that higher debt causes increased welfare is weaker than the argument that it is feasible.

The Treasury can afford to increase debt D_t just by just giving bonds away and can pay interest and principal without ever raising taxes so long as the safe rate of interest which it has to pay is lower than the trend rate of growth of GDP. In that case it is possible to just roll over the debt forever and the debt (including the additional debt) shrinks to insignificance as a share of GDP.

Following Blanchard we assume zero trend growth and an economy which reaches a steady state. This really just simplifies notation a bit. Also Blanchard works with Rf_t which is 1 plust the safe rate of interest, so bonds mature in one period and pay Rf_t times the amount invested. In contrast investing in productive capital K_t gives a risky return R_t (includng the capital one still has so the ordinary notation is return r = R-1).

The time subscripts are there because, in general, both the safe and the risky return depend on D_t and K_t. This is a major nuisance and I will present a super absurdly simple example (due to Brad) here in which the state is constant.

The model is an overlapping generations model — the young work and get a wage W_t. They consume C_t^y and buy the bonds D_t and the capital K_t from the old. The old get capital income and also sell their bonds and capital to the young. They consume all of that so C_t^o = Rf_tD_t+R_K_t

Importantly, there is a technology shock which makes W_t and R_t stochastic. This is a crazy assumption, which is absolutely standard when one wants to put risk into a macro model and also wants to keep it super simple. The point is that bonds are safe and that ownership of capital (stock) is risky.

The way to make the model absurdly simple involves two steps. First assume that the policy is to increase D and to keep it at the new high level. If Rf_t<1 this involves an additional gift of D(1-Rf) to the young each period. Increased debt finances an increase in this universal basic income so long as Rf_t<1. The point of this is to keep things simple. It is not needed for the increase in debt to help all generations not just the first who get the windfall gift (see below).

Then the key extreme very convenient assumption just for a simple example.

Agents choose C_t^y to maximiz

1) C_t^y + beta ln(C_{t+1}^o)

The extreme extraordinary assumption is that utility is linear in consumption when young, so young people are risk neutral. The assumption that utility is logarithmic in consumption when old is fairly conventional but it is not innocent either. Together they make everything simple, because it means that people always save beta

so

2) K_{t+1}+D_{t+1} = beta

Then the assumption that the state keeps Debt constant implies that capital is constant.

This implies that Rf and E(R) and the stochastic distribution of R are all constant and everything is simple.

After the jump I will discuss other cases. Here I just note that the extreme assumptions don’t just make all the math simple. They actually matter, because constant Rf_t gaurantees that it stays below 1. In general (and certainly for independent technology shocks) Rf_t is sometimes greater than 1. I will put all this off to the after the jump appendix.

The super simple model shows three beneficial effects of increased debt. First there is the gift to the old at the time D is increased, second there is the gift of (1-Rf) to the young each period. Third debt causes higher Rf which is nice for the citizens so long as the new higher Rf is less than 1.

There is, however, a fourth effect which alarmed Blanchard. In the olg model debt crowds out capital. In the super simple model

3) K=beta-D

The reduction in K causes lower wages W_t and higher returns R_t (still with time subscripts because both depend on the technology shock).

This transfer from the young to the old is risky and it reduces expected welfare so long as the steady state risky rate is greater than 1. In the super simple model that means it reduces expected welfare s long as E(R) >1 when K = beta. Blanchard shows this at some length.

I am now going to do some algebra. I am going to set population + labor supply to 1 just to simplify notation.

With constant returns to scale, perfect competition implies

4) W_t + R_t K = Y_t

taking the derivative with respect to K

5) d W_t/dK + (dR_t/dK)K + R_t=R_t

so

6) d W_t/dK = – (dR_t/dK)K

7) K+D=Beta so dK/dD=-1 so

8) d W_t/dD = – (dR_t/dD)K

Now consider the following policy. D is increased by a small amount deltaD and a small tax on capital income of Tau is introduced so that

9) (1-tau)(R_t + deltaD dR_t/dD) = R_t

That is the tax is calculated so that the after tax income from ownership of risky capital of the old is unchanged.

The revenues tau(R_t + deltaD dR_t/dD)K are given to the workers. Equation 8 implies that their income is unchanged. The tax and transfer policy eliminates the fourth effect of incrased D.

This means that the policy of increasing debt and eliminating the effect on wages and the return on capital by taxing capital income and giving the proceeds to workers makes every generation better off and is a Pareto improvement.

In general in public economics a reform is said to increase efficiency if it is possible to combine the reform with taxes and transfers such that everyone is better off. So in the simple model, the standard use of the term implies that issuing debt and giving the proceeds to citizens would increase efficiency.

This is a very standard analysis of the absolutely standard model used to analyze the welfare effects of public debt. The conclusion really shouldn’t be controversial (but it will be).

Debt and Taxes I

There might be such a thing as a free lunch.

There will soon be a Democrat in the White House and Republicans will soon rediscover their hatred of deficits (which were no problem when they were cutting taxes on firms and rich individuals). We are going to read a lot of arguments about irresponsibly burdening our children with debt (which ignore the fact that they will also inherit most of the bonds). We will be reminded that sooner or later we will have to pay.

I am not sure if Milton Friedman will be quoted saying “to spend is to tax”. There will be arguments about how deficit spending creates the illusion of wealth (as consumer/investors we forget that we owe the money as well as owning the bonds just as citizens we forget that we are (most of) the creditors as well as the owners of the indebted Federal Government). There will be arguments about how we can pay now or pay later and it will be more costly if we pay later.

All of this is based on the assumption that the Federal Government’s intertemporal budget constraint is binding. Arguments that you can’t get more now without having less later are arguments about a binding budget constraint. The argument that an increase in spending must be financed by increased taxes in the present or in the future of the same present value is the argument that the intertemporal budget constraint is binding (in fact it is a better explanation of the concept than “the intertemporal budget constraint is binding” the two statements are equivalent and “increased spending … increased taxes …” is written in plain English).

It is true that in standard models, the intertemporal budget constraint is binding (this is called the transversality condition just to type more big words). This is a condition for *optimality* — an aspect of the solution to an intertemporal optimization problem. It is not a given or an assumption about the problem agents face. This is embarrassingly simple. In standard models, you can’t get something for nothing, because if you were in a situation in which you could get something for nothing, then you made a mistake not getting it, and it is assumed that you didn’t make a mistake.

When discussing fiscal policy, Friedman et al assumed that it is optimal while criticizing it as suboptimal. This is a plain contradiction and simple error. All of the discussion of fiscal policy which is used to rule out more deficit spending now assumes that policy is optimal which rules out any change by assumption.

This is not a quibble. The condition for a binding intertemporal budget constraint is that r>n that the interest rate the Treasury must pay is greater than the trend growth of GDP. if r<n then debt can be rolled over forever with new bonds sold to pay interest and principle on the old bonds. The debt to GDP ratio shrinks to zero if r<n and debt is rolled over. This is how the USA handled World War II debt. The US did not pay it off by running primary surpluses. The USA rolled the debt over until it was small and then elected Reagan and began the modern era of huge deficits.

The relevant r in the inequality is the interest rate the Treasury pays on it’s debt. This is always much lower than many other interest rates and has historically usually been very very low. It is now exceedingly low, and it has been extremely low since 2008. It was also very low until the 70s and, when corrected for inflation, remained very low until Reagan and Volcker began working with each other.

This is well known to economists. A masterful explanation and empirical demonstration was given as an American Economic Association Presidential address by OJ Blanchard in 2019 . Read it if you doubt my claims (also if you don’t — it is very good).

For a while after 2008, it was assumed that this was temporary and things would return to normal (normal meaning as they were from 1980 to 2000 but never were before 1980 nor have been after 2000). Many economists now agree that this is the new normal (same as the old normal and different from the situation of extremely loose fiscal policy combined with extremely tight monetary policy).

Importantly this is *not* entirely a forecast. The yield on 30 year inflation indexed bonds is currently -0.24% — the US Federal Government can borrow for 30 years paying a negative real interest rate. Pessimists think that the trend of real GDP growth has fallen to 2% a year (from 3% historically). But it is definitely growth not shrinking.

It is true that investors might change their minds and interest rates might shoot up. If the US financed it’s spending with 30 inflation indexed bonds, this would not be a problem for the Treasury for 30 years. Investors who bought the bonds would lose money, but the Treasury would still have to pay the same coupons and face value. There is even a discussion of introducing extremely long duration bonds — 50 year bonds to lock in interest rates longer or even consols (bonds which last forever and pay a constant interest rate — obviously a multiple of the CPI because the old 19th century nominal consols are silly collectors’ items now))..

But basically the main hugely important point is that there is every reason to think that the US Federal Government can get something for nothing, because it has a slack intertemporal budget constraint.

Failing to take advantage of that would be failing to solve an intertemporal optimization problem. It is one of the few (very difficult) ways to fail my Macroeconomics course.

Caveat after the jump

Desirable Incentive Effects of Income Taxation III

This is the third post in a series. I will discuss advantages of income taxation different from the obvious advantage that taking from people with high income hurts them less than taking from people with low income. Here again, I will assume that, in equilibrium, income tax is returned to the people who pay it as a lump sum. I do this to focus on the incentive effects of income taxation.

The first two posts are here and here.

In standard models, these effects are undesirable and amount to a deadweight loss which is second order in the tax rate. However, the standard models rely on standard assumptions which are completely implausible. They are used, because it is guessed that the policy implications don’t depend on the absurd assumptions. The policy implications always, in fact, follow from the assumptions.

In this post, for the third and last time, I will relax the assumption that people are 100% purely selfish and care only about their own consumption and leisure. Instead I will assume that people maximize the sum of their pleasure from consumption and leisure plus a constant far less than one times other people’s pleasure from consumption and leisure.

Desirable Incentive Effects of Income Taxation II

This is the second post in a series. I will discuss advantages of income taxation different from the obvious advantage that taking from people with high income hurts them less than taking from people with low income. Here again, I will assume that, in equilibrium, income tax is returned to the people who pay it as a lump sum. I do this to focus on the incentive effects of income taxation.

In standard models, these effects are undesirable and amount to a deadweight loss which is second order in the tax rate. However, the standard models rely on standard assumptions which are completely implausible. They are used, because it is guessed that the policy implications don’t depend on the absurd assumptions. The policy implications always, in fact, follow from the assumptions.

In this post, for a second time, I will relax the assumption that people are 100% purely selfish and care only about their own consumption and leisure. Instead I will assume that people maximize the sum of their pleasure from consumption and leisure plus a constant far less than one times other people’s pleasure from consumption and leisure.

Covid Vaccine Dosing Trials ?

I asked if, given the data collected in Phase III trials, it might be wise to delay second doses of the Pfizer and Moderna Covid 19 vaccines until supplies are ample.

Since then the UK government has decided to give second doses three months after the first dose. The reason is explicitly to get first doses in more people quickly. This is highly controversial. I’m just going to name drop (actually link drop) to show I am not the only person outside of the UK who supports this.

Another approach to vaccinating more people with limited supplies of vaccine is to reduce the dose. This was proposed by the now former head of the US program formerly known as Warp Speed. Here the logic is based on a clinical trial — with a sample size of 42 — the Moderna Phase 1 trial . The trial includes an estimate of the amount of infection blocking antibodies in participants serum. The measure is the blocking antibody titer — how much the serum has to be diluted before it blocks only half of the virus from infecting cells. After the first dose and before the second, a dilution of 8:1 (the lowest) allowed more than half of the control infection (of cells in vitro). However, even with a dose of vaccine of 25 micrograms per kilogram (half of the dose of 100 micrograms per kg which people are getting) there was a high average titer by day 43 soon after the second dose.

The phase 1 results explain why 2 doses were used in the phasee III trial (and in Pfizer phase 1-2-3 all merged to speed things up trial). It also makes the rareness of infection in the phase III trials more than 10 days after the first dose a bit surprising. My guess is that the rapid induction of blocking antibodies after the second exposure is enough to block infection even if the second exposure is infection with Sars Cov2 and not a second vaccination. However note that I am not an immunologist (my dad is an immunologist and he said better half the dose twice than the full dose once back when I started talking about this — as usual he knew what he was talking about).

The 14 who got 25 compared to the 14 who got 100 strongly suggest giving 50 micrograms per kg twice is a better way to spread out the vaccine.

However, there is no way either will be done in the USA without a large clinical trial. Also there is no way that there will be a large clinical trial (who would pay for it for one thing). But the point of this post is to ask how such a trial could be ethical if it were financed (the cost is negligible compared to Federal Covid relief spending and roughly equal to the cost of a delay of effective herd immunity of about one hour). I’d say if people are given the chance to get a first dose sooner than they otherwise could (and the second dose as soon as they would be allowed to get the first if they weren’t in the trial) then it is ethical. The trial can’t be double blind (or at least people who get a second shot have to be told if their first was placebo so they should get a third shot which will be the second of actual vaccine).

Similarly people can be invited to get half a dose if the alternative is no dose (with option to get full dose when it would be granted even if they weren’t in the trial). I think this can be done. I think it should be done. I am sure this won’t be done.

update: There is evidence from Israel that one dose of the Pfizer vaccine is less effective than was suggested by the few person-days of evidence in the phase III trials. In Israel  “over 12,400 have people tested positive for coronavirus after receiving vaccine shots” Israeli health officials estimate that one shot is about 50% effective after 14 days . The control group is not matched, it’s not a randomized trial, but it is enough evidence that it’s hard to argue for clinical trials (as I did above).

Desirable incentive effects of income taxation I

Cases in which income taxation is preferable to lump sum taxation with the same ex post net transfers.

The main reason for progressive taxation is that the welfare cost of taking money from wealthy people is lower, because they have a lower marginal utility of consumption. I would like to discuss other advantages of income taxation, that is cases in which it can cause an increase in money metric welfare, or, in other words cases in which a distortionary tax and transfer policy is desirable even if, in the end (in the Nash equilibrium) everyone gets a transfer equal to taxes paid.

The incentive effects of taxation can be desirable for many reasons. I will try to list them in a series of posts. One very simple reason is that lower income is typically obtained by providing a goods and services to poorer people. This means that the signal from the market is not ideal – even if people obtain income by providing useful goods and services, the income depends on the usefulness divided by the consumers marginal utility of consumption.

For example, lawyers income depends on the wealth of their clients separately from the validity of their clients cases. For another doctors income depends on insurance coverage of their patients as well as the effectiveness of therapy and the need of the patience. I will address these issues in the second post in the series. In this post, I will assume that agents sell goods not services and that they sell them for the same price to all customers. Even in this case, there is a difference between the income maximizing choice and the most socially useful choice. Some people obtain more income selling luxuries that no one needs, but for which high income people are willing to pay a lot rather than selling necessities which poor people really want, but for which they can pay little.

People often perceive a difference between maximizing income and contributing as much as they can to society. There is nothing odd about this – it follows from absolutely standard assumptions about market prices and simple utilitarianism – economists most standard approach to welfare economics ( which is an approach to social welfare often considered to underestimate the importance of equality).

So far, there is no hint of any reason why the incentive effects of income taxation might be useful. The novel assumption is that people are not perfectly completely selfish. If you would rather see well fed than starving children, then standard economic theory does not apply to you. It is very important to avoid the false dichotomy between the assumption that people are perfectly selfish and that they are perfectly altruistic. I have often read read proofs that people are not perfectly selfish presented as an argument against the assumption that people are partially altruistic. Before going on, the assumption I need can be that people care 100% as much about their own interests as about anyone else’s. Such people would strike us as extraordinarily selfish, but they are not selfish enough for standard theory.

No one argues that people are selfish. Selfishness is almost always assumed in economic models. I can think of a number of justifications. One is that we should hope for the best but plan for the worst – hope that people are altruistic, but design a system which will work if they are perfectly selfish. I see no merit in this argument. In particular, we don’t have to guess, we know people are partially altruistic. Another is that a system designed on the assumption that people are partially altruistic also works if they are selfish – it just isn’t true that if one fears something might be true, then one should assume that it is. Another argument for assuming selfishness is that economists focus on arms length interaction, and altruism is important in interactions other than buying and selling. This post aims to demonstrate that that argument is invalid. A third argument for assuming selfishness is that altruism has benefits which are separate from the benefits of good policy. The main point of this post is that policies which are optimal if people are selfish and Pareto inefficient if people are partially altruistic.

The key paper in the literature on this topic is “” by Lester Thurow. Thurow’s point is that if people are slightly altruistic, then redistribution from the rich to the poor can make everyone happier, can be a Pareto improvement. Rich person A likes the fact that money is taken from rich person B and given to a poor person. The small loss for person B bothers him a tiny amount, the large gain for person C pleases him a small amount. Person A does not want his money to go to the poor, but in a large society the huge amount of benefit to the poor from transfers from all the other rich people can make up for his (not totally) selfish desire to keep what he has. This means that rich people who support progressive taxation and welfare but don’t give all of their money away are not necessarily hypocrites.

Thurow points out that even partial altruism is an externality and if people are partially altruistic, then equality is a public good. Standard arguments combined with the clearly true assumption that people are not completely 100% selfish imply that redistribution from the rich to the poor can be Pareto improving.

These posts are not simply a reiteration of Thurow’s point. I will assume no net redistribution. The tax and transfers will not help the poor directly, however, their incentive effects may help the poor.

This post will assume that people produce goods and can choose whether to produce a necessity or a luxury good. Caring about the benefit of their product for the consumer, they will prefer, other things equal, to produce the necessity. In equilibrium, other things won’t be equal because they can make more money producing the luxury. By reducing that incentive, income taxation can shift production from luxuries to necessities. This can increase welfare. This, in turn, can please everyone because people are partially altruistic (the last point is exactly Thurow’s point).

A tiny simple model after the jump

Is an Increased Federal Deficit good or bad ?

As the Senate decides whether to send an additional $1400 to US residents, there are two macroeconomic policy issues. One is whether aggregate demand stimulus would be useful. The other is whether we should be concerned about the budget deficit.

I think that the case for fiscal stimulus is medium strong and the case for higher Federal Debt is very strong. Thus I agree with Donald Trump and Bernie Sanders and disagree with Larry Summers.

The case for stimulus is only medium strong. Unemployment is fairly high, but part of this is an efficient response to the risk of Covid Transmission. There are two ways to argue that demand is undesirably slack. One is below peak employment in sectors which are not especially directly affected by Covid 19 such as construction. The other is that core inflation is below target and falling. Both are enough to convince me that general stimulus is OK.

But mostly the amazing fact is that the 30 year TIPS real interest rate is negative. This means that investors are willing to pay the US Federal Government to store their wealth safely. Given this, I think there is a very strong case for selling more long term bills and giving the money to residents. The interest rates assert that the US Federal Government intertemporal budget constraint is slack. This can’t be Pareto efficient.

I anticipate the concern that interest rates might rise. That is why I graphed the 30 year rate, which is locked in now. If interest rates rise, investors will lose money, but it won’t create a new problem for the Treasury. Also these are real rates (paid in multiples of the consumer price index) so deflation wouldn’t be a problem for the Treasury (although it would be a catastrophe for the economy).

Given the market interest rate, the ration of the debt to GDP should fall roughly in half over the life of the bonds. If the rates lasted, rolling over the debt would be a source of income indefinitely. The argument is absurdly simple. It is also valid.

The only concern is that public debt might crowd out private investment. This could cause higher returns on capital and lower wages with undesirable distributive effects. This problem can be managed by shifting taxation from labor to capital.

I am convinced that raising the subsidy to $2000 is an improvement.