Central Banks as Control Systems or Can We Replace Ben Bernanke with a Computer?

Being in a technical field I encounter control systems all the time.  But that is because everyone encounters control systems all the time.  They make elevators stop at the right floor in a comfortable fashion, your car humming along efficiently and presumably keeps your oven at the specified temperature, though they never seem to actually be correct.  You are a control system when you adjust your shower water knob for maximum pleasure.  In short, modern life would suck without control systems.

For those unfamiliar with control systems, the basic principle is you measure a variable and apply some sort of forcing to the system based on what you want the variable to be.  It is really that simple.  The standard is a PID controller or proportional-integral-derivative controller.  You have a process variable which you measure and you compare that to your desired setpoint to create an error value.  The proportional part of the controller applies a force, wait for it, proportional to the error value.  Next up the integral part integrates the error over a period of time and applies a force proportional to that.  Lastly, the derivative part looks at how quickly the error changes and forces according to that.  By far the most important is the P part, but I is also important since with just P you will only asymptotically reach the setpoint (the dreaded droop).  D is great for increasing the speed of you control system, but is also sensitive to noise and is a pain to set.

Now as the title implied I was going to tie this into central banks.  Central banks look at some set of economic variables and then nudge the economy with various tools, most importantly the open market operation.  The process variable is in most places inflation and in the U.S. its setpoint is 2%.  In fact economics has a simple rule called the Taylor rule that provides guidelines on how to adjust interest rates to maintain desired inflation.  In fact if you look at it is basically a P controller where a_pi is the proportional gain on an error signal generated by the difference in desired and current inflation.

Great, so central banks have a P controller and all is well, right?  Well, no.  As I said earlier without an I term you will always undershoot your setpoint.  Evidence of that is quite explicit in our current predicament.  We still have a weak economy six years after the financial crisis and the Fed is currently beginning to taper its bond purchases.  This is a clear sign of a P-only droop.  For maximum speed in arriving at the setpoint you actually want to overshoot.  In contrast, central banks seem to regard their inflation targets as ceilings, yet there is no argument for being afraid of breaching the inflation target.  On the other hand, there is an argument for returning the economy to normal as quickly as possible.  Every year of high unemployment is another year of millions of people suffering.

The other problem is that the Taylor Rule targets two variables: inflation and the output gap.  Now these have a “divine coincidence” in some economic models, but in the real world it is likely that you cannot hit an inflation target and close the output gap simultaneously.  Thus, one should switch to targeting nominal GDP growth which is something of a combination of the two.  This has worked quite well under Stanley Fischer at the Israeli central bank and there are some detailed theoretical arguments for why it is better than an inflation target.  In my mind, it just makes sense to target the growth of the economy than some ancillary variable like inflation.  Anyways this makes designing a control system a bit easier.

If I were designing a rule then I would make an error signal that is the difference in nominal GDP and the target nominal GDP (lets say 6%).  Then we would determine the amount of our open market operations by an amount proportional to that error signal and proportional to the error signal added up over lets say the last two years.  All you need to do is set the gain coefficients for the two terms and then you don’t even need a board to determine monetary policy, it’s just an algorithm.  Ben Bernanke is obsolete.

The nice thing about a PID controller is that you don’t need to know anything about the system you are controlling.  You just need to look at how it reacts to your forcing.  However, we have an entire discipline called macroeconomics that attempts to model the economy and with that knowledge we could make our control system more sophisticated.  Now feedforward is possible.  Or we could just add a differential term that responds to the severity of the shock.  It makes relying on the simple P controller of the Taylor Rule look monumentally stupid when easy modifications abound.

Ideally, the people in charge of the central bank are already a control system.  Yet an analysis showed that most central bank operations are described fairly well by just the Taylor Rule.  Also, history shows that humans are really bad at the job.  They either don’t do enough (Great Depression, Great Recession) or don’t put on the brakes (70s inflation in the U.S.).  Some of this is political pressure, some of this is that most central bankers are drawn from a culture that is deathly afraid of any bit of inflation for reasons they can never articulate cogently.  Therefore I propose that we just automate it.  Publish the coefficients so everyone knows what will happen.  This actually implements something the Krugman/DeLong axis of economists have been shouting about.  Namely, that in a liquidity trap we need to credibly commit to higher inflation.  The integral term basically does that.  It follows the engineering maxim of “if it doesn’t work, apply more force.”  That is, if the economy is consistently underperforming it just keeps shoveling more and more money at the problem.  However, I suspect like Switzerland when it fixed its exchange rate briefly, the credible commitment to a policy anchors expectations such that you don’t actually need to do much.  I am not saying we wont have recessions (or bubbles) but I suspect they will be much shallower just because people know that our control system central bank will do whatever it takes to bring the economy back.

As far as I can tell, nobody has made this analogy between central banks and control systems.  Furthermore, I don’t think anyone has proposed removing human agency from how they operate.  Well I just did and I think it is the future of central banking.


Paying for the GBI: Optimal Tax Policy

Now it should be noted that whatever your country’s preferred tax scheme is, be it VAT or income or something else, it is without a doubt terrible.  Like so many things governments do, they managed to find the worst possible way to do something and then stick with it indefinitely despite the obvious flaws.  So while technically you could pay for a GBI just by increasing rates on existing taxes, if we are going to reform the welfare state why not at the same time reform how we pay for it?

What is the problem with existing taxation systems?  Well in the case of the income tax it actively discourages saving compared to a consumption tax since since you are taxed on your income and then the appreciation of your investments.  Instead, in the U.S. we have very complicated systems designed to allow you to save money tax free for retirement or health costs, etc.  It seems simpler to just switch to a consumption tax and drop the exceptions.

A VAT is a consumption tax, but has no progressiveness.  Ideally, you would just have people report their income-savings and be taxed at progressive rates on their consumption.  However, another goal of tax reform is that we want to reduce the burdens of the tax code and reporting all sources of income and savings is quite burdensome.  Thus there are things like the X-tax where you have a VAT and businesses deduct wages which are then taxed progressively.   I see two problems.  One it basically leaves non-wage income untaxed.  This is a boon for rich people who usually earn most of their money from financial investments, but not exactly fair to the average worker.  Secondly, it still leaves the enormous burden of assessing VATs around.  Since most countries already have an income tax apparatus that requires the same information in place, the ideal tax mentioned earlier seems like a better option.

Similarly, corporate taxes are ubiquitous despite being a dubious source of revenue.  This is true for three reasons.  One, you have added yet another entity to audit on top of all the individuals you tax.  This also causes double taxation as corporate profits are being taxed at the corporate level and then taxed again when distributed to shareholders.  Two, the incidence of the tax is ambiguous.  That is, are shareholders paying the tax or are the consumers of the corporation’s products?  A good tax should be levied on the people/things we want taxed and the incidence of a corporate tax probably varies wildly by industry.  Third, at least in the U.S. it is a blatantly unfair tax.  Walmart pays almost the full corporate tax rate, whereas G.E. has enough negative tax liability to roll some of it over to the next year.  This is an effective subsidy to certain industries that can avoid tax liabilities more deftly and encourages resources to be spent on tax shenanigans (either through better accountants or better lobbyists).  In my opinion the corporate tax should be among the first to go.

However, all of these are bad taxes when there are so many low hanging fruit out there.  By this I mean, all of the above cause a deadweight loss to the economy whereas there exist taxes that have no associated deadweight loss or even make our economy more efficient.

One such tax that seems to have grown popular in the policy sphere is the land value tax.  That is where you tax land based only the value of the land for its best use and not on the improvements built upon the land.  The best discussion of this is I think found here or elsewhere on the internet if you do not want to register.  What makes the land value tax so appealing is that there is no deadweight loss because the supply of land is essentially inelastic which means the full incidence of the tax is on landowners.  Wikipedia has a nice graphic illustrating this.

This is of course the primary benefit of an LVT, but it also brings parcel development forward in time.  Since you have to pay the tax no matter what, it behooves you to either develop it or sell it to someone who will.  The Lincoln Institute paper claims the tax is time-neutral and it is, in a narrow technical sense, but in terms most people understand, it is not.  This also dampens speculation because as the gains from holding onto land in hope of appreciation must be larger than the LVT in order to profit.  In the ideal case you would set the LVT at 100% of the land’s value and that would deter all speculation.  This pressure to develop land also helps alleviate urban sprawl as land parcels will be developed to maximize the profits of the improvements which in general means denser developments.  This is in contrast to a property tax where intense development of land is taxed at a higher amount, thus reducing the benefits of using land for its best use.

The major criticism of an LVT is assessing it, but it is the same challenge we already surmount when assessing property taxes.  The hardest part is determining “best use” and the ambiguity here suggests we tax at less than 100% in order to alleviate penalizing owners for overestimating “best use.”

The LVT is great, but people are ignoring that many other things share the key fact that allows an LVT to work so well.  That is, the inelasticity of supply of the good being taxed.  There are in fact a lot of goods that are like that, foremost among them being natural resources.  By this analysis we should tax oil at up to 100% of its value and so on.

This brings up arguments about the justice of taxing someone’s property at such high rates.  I counter by saying that land and the natural resources are the wealth of a nation and those that own them are merely extracting rents (rents as in the economic definition of a bad thing).  Or to put it another way, the owners are deriving profits without providing any value added.  Should a landlord be entitled to a profit for merely owning land?  Most of the value of land is created by society, from the other people living there and the infrastructure governments build around it.  When a new metro stop is built and the value of the property near the stop goes up, should the landlords in the area be entitled to increased wealth?  I would say no and an LVT reclaims the increased land value and gives it back to the State that created it.

As good as taxes on rents are, the best taxes are Pigouvian.  Externalities are things created by someone but the value of which is not capture by the creator.  The primary example is carbon emissions that contribute to global warming.  This is massively costly for the planet, but this cost is not fully born by the entities that produce it.  A Pigouvian tax would then tax carbon emissions at a rate such that the marginal emission of carbon dioxide would provide the same benefit to society as the costs to society as a whole from emitting that carbon.  That is, if I were deciding whether to make a plastic Barbie doll, I would include the cost of the carbon emissions associated with making it and all the other costs and compare it to the joy imparted on the next youngster to receive a doll.  Without a Pigouvian tax, we would make more Barbie dolls than we as a society want since the full costs are not taken into account.

Thus, taxing negative externalities is actually improving the efficiency of our economy.  It’s also a great source of revenue as a carbon tax in the U.S. could raise a trillion dollars.  On the flip side we should subsidize positive externalities, which is primarily what the government should do.  It creates parks under the assumption that parks are great but no private enterprise could capture all of the value of a park as revenue.  Same with roads and education and the list goes on.  So if we implicitly accept subsidizing positive externalities then we should tax the negative ones.

With Georgian taxes on rents and Pigouvian taxes, we would be well on our way to funding a GBI and building a more efficient economy too.


Guaranteed Basic Income Revisited

Wonkblog is getting on the bandwagon and discussing a guaranteed basic income.  The comments suggest that many detractors and even some of the proponents think that a GBI will accompany a cessation of normal market capitalism.  That is the only way to explain the slippery slopes and straw men that pop up everywhere.

As a sidenote, someone misinterpreted a land value tax as taxing a rural homeowner more than Lloyd Blankfein (head of Goldman Sachs) seemingly thinking the tax would be independent of location.  It is of course based on the value of the land, as the name implies, so land in Manhattan would be taxed at much higher amounts.

Lets tackle a few of these misconceptions and then maybe imagine the shape of the economy after a GBI.  I think this page provides a good defense of a GBI except for the allowance that inflation might run amok after it is implemented.  The example they give is landlords raising rent in response to the fact that everyone has a GBI.  Now the prices of everything will change after a GBI is implemented, there is no denying that.  However, the article makes no attempt at explaining why market forces are suspended under a GBI.  A landlord could cut prices to increase his occupancy and make more money.  This would in turn induce other landlords to lower their prices, so on and so forth.  You need an explanation for why the market is so badly imperfect.  You could talk about inelastic supply, but that is a problem with housing/zoning policy, not a GBI.

Now the author compares this to a child care credit in the UK that did indeed cause price inflation.  This problem is specific to in-kind welfare benefits.  The UK was basically saying here is money you can only use on child care, i.e. they are subsidizing and as we should know subsidies cause us to consume more of that product.  This obviously increases the demand for child care immediately increasing the price.  In-kind benefits have a number of such drawbacks.  Walmart gets a huge amount of our food stamp money as that is where a lot of poor people shop.  On the employment end, stuff like food stamps allows them to pay a lower wage to their employees who can count on the government to make up the difference so to speak.  So means-tested benefits are a subsidy to low wage jobs.  The GBI has no market distorting effects as it subsidizes no particular industry or occupation.

Finally, lets tackle the lazy moocher problem and potential impact on prices in one go.  The GBI to a zero order approximation would immediately cut all salaries by the amount of the GBI.  This has little effect on people making considerably more than the GBI and I would say the same even for most of the middle class.  After all, theoretically they could work less and earn less if they valued leisure.  Instead they either enjoy their jobs or the extra consumption enough to continue to work full time.

No, the important cohort are people that who once made about the same amount as the GBI now provides.  The amount of money they get from their marginal hour of work is virtually nothing and thus it makes sense that they would consume leisure as an economist would put it.  Who then would man our local Walmarts?  Quite simply the market jumps in to the rescue.  Wages will rise until the wage for an hour of work is greater than the utility of a marginal hour of leisure.  At this point you have induced people back into the workforce.

Oh noes you say, wont everything cost a bunch more?  Actually on the face of it everything should be cheaper since wages are almost assuredly lower than they were before the GBI.  The only way this is not the case would be if the utility of leisure was higher than the wage before the GBI was implemented.  However, this is unlikely as we are talking about people on the border of poverty, not people deciding whether to work to buy a fourth jetski.  The real culprit for any real price increases (as opposed to inflation) will come from how you pay for the GBI.  This, however, is a topic for a later post.

Lets say a country implements a GBI.  It is either too high or too low.  If it is too low you basically have the current situation where it ameliorates suffering but must be supplemented by some amount of work.  It’s probably still better than our current welfare system.  If it is too high you will immediately see a general price inflation in all lower class goods as the demand curve is pushed outward and the supply curve contracts as people leave the workforce to retire on their overgenerous benefits. However, wages will go up as well and the price inflation will help settle the economy into an equilibrium where the GBI is not too high.

Thus, I think that fears about making it too generous are mostly overblown.  The worst possible scenario is that the price inflation is large enough to trivialize the GBI.  However, I am having difficulty imagining the dynamics that would lead to such a situation.  Our current welfare system triggered no such price spiral and remains relatively generous for low income workers.  Instead I believe the economy will self-correct to neutralize the objections to a GBI.

Up next is how to pay for a GBI.