How much debt do we need? My answer: 70% of GDP


In a post in 2015 I pointed out that government debt is not a bad thing. Here, I elaborate on that idea and I ask, and answer, a simple question: how much debt do we need? My answer: 70% of GDP is a good guess.

In a recent post, Simon Wren-Lewis asks and answers some of the same questions I discuss here. My focus is narrower than Simon’s. I will focus in on the question: what is the right amount of debt?  I will also abstract from one reason why debt should not be zero. That reason, discussed here by Martin Wolf, and here by Isabella Kaminska, is that the public sector does not only accrue debt; it also owns public assets. I will claim that, even if we did not need to build roads and bridges, it would still be a good idea for the public sector to accumulate debt. My argument is based on a remarkable implication of basic economic theory that was first discussed by Paul Samuelson. If we borrow from our children and our grandchildren, everybody, including all future generations, will be better off.

If a household borrows money to pay for a new car, that debt might be paid back over a period of five years or more. Debt that is accrued to help pay for an investment good, like a car, is widely understood to be a good thing. By borrowing to pay for a car, we arrange for the series of benefits we receive by driving to work or to school every day to be matched with the series of payments we make as we pay back the loan used to purchase the car. Debt accrued by a household to facilitate an investment is widely perceived to be privately beneficial.

Suppose instead, a person borrows to pay for an extravagant lifestyle. Instead of taking out a loan and buying a car, that person maxes out their credit cards to throw expensive parties. To pay back that debt, he or she will need to plan for a period of austere living in future years.  Debt accrued by a household to finance an extravagant lifestyle is widely perceived to be deviant behaviour that is discouraged by social norms. But should we apply those same norms to government behaviour?

If government borrows money to pay for a new road or rail network, the new transportation infrastructure will generate benefits to future generations. It is only fair that those generations should help pay for the investments they enjoy and, for that reason, debt accrued to pay for social investment is widely recognized to be socially beneficial. The principle that all government debt should be used to finance infrastructure investments is sometimes called the golden rule of public finance. It is a commonly held belief that government debt should only finance government investment; but it is a belief that does not survive more careful scrutiny.

Governments are not like households. If a household borrows from a bank it will eventually need to repay the money it borrowed. If a government borrows money from the public, it may never repay that money. It is a myth that government debt is repaid by running public surpluses. In reality, the ratio of outstanding debt to GDP shrinks as the economy grows faster than the interest rate at which the government is borrowing.

In the title to this post I raised the question: How much debt do we need? Economic theory provides an answer to that question and it is never zero. In a series of papers that I am writing with Pawel Zabczyk of the Bank of England, soon to be circulated, we show that a fairly standard model of trade between generations can lead to some very non-standard conclusions. We use Samuelson’s  overlapping generations model, which has been widely used to analyse questions of trade between people of different generations. For a calibrated version that we use as an example, the right answer to my opening question; How much debt do we need? is 70% of GDP.

The main theme of my work with Pawel is that governments are not like households. That point has been made many times by many people. Paul Krugman, for example, makes the case here in a NY Times piece. Although the reason often given is that government expenditure can raise employment through a fiscal multiplier, there is a more fundamental reason why we should not eliminate government debt. And this reason applies even if the economy is always operating at full employment. Debt facilitates trade between current and future generations.  

The figure of 70% that I give in this blog is based on some back of the envelope calculations that Pawel and I use to calibrate our theoretical paper and my subjective confidence bands around that figure are large. The optimal size of public sector debt in the UK might be 5% and it might be 140%. But of one thing I am certain. The right answer to my question; how much debt do we need? is never zero!

Is Unemployment Too Low?

GDP increases over time for two reasons. First, the economy produces more output because we use more labour and more capital. Second, the economy produces more output because we use better techniques over time. Traveling from London to Glasgow on a high-speed train is much faster than travelling there in a horse-drawn carriage. An increase in GDP for this second reason is called productivity growth.

Screen Shot 2017-12-02 at 5.07.05 PM.png

Productivity has been growing at a rate of roughly 1.7% per year since the beginning of the industrial revolution. In the absence of productivity growth, we would have the same standard of living as our grandparents. When productivity grows at 1.7%, our standard of living doubles every forty years or so.  I have graphed US productivity in Box 1.

But although productivity grows on average; it does not grow the same amount every month. Some months are periods when GDP per person grows faster than normal. Other months, are periods when GDP per person grows slower than normal.  In the 1980s, macroeconomists of the real business cycle (RBC) school convinced the profession that these random fluctuations in productivity growth, above or below trend growth, are the main cause of recessions.

In the period from 1953 to 1980, productivity and employment moved in the same direction in the US data. When productivity was high, so was employment. That fact supported the RBC theory. But since 1980, this stylized fact has reversed. In more recent data, high productivity goes hand in hand with low employment. How can we explain this reversal?

Screen Shot 2017-12-02 at 5.07.20 PM.png

In Box 2 I plot a graph of US labour productivity (in blue) and the unemployment rate (in red). Both series are expressed as deviations from a flexible trend and the unemployment rate is lagged by four quarters. This figure shows that, when unemployment is low, productivity will be below trend one year later. I will refer to this as the productivity-unemployment puzzle because macroeconomists have operated on the assumption that productivity and employment move in the same direction. That should imply that productivity and unemployment move in opposite directions. The figure shows that, on the contrary, productivity and unemployment move in the same direction once we account for time-lags. The correlation between unemployment in year t, and productivity in year t+1, is strongly positive and has remained stable in the entire post-war period. How can we explain that fact?

In my book Prosperity for All, I provide an explanation for the positive correlation between productivity and unemployment.  When demand is low, firms employ fewer workers and there are more unemployed people searching for jobs. Firms find it easier to fill vacant positions and their overhead costs for recruitment fall. That fall in recruiting costs shows up as higher productivity. I am open to other possible explanations and I invite you to think about how this correlation might be credibly explained.

Screen Shot 2017-12-02 at 5.07.35 PM.png

The unemployment-productivity puzzle is not confined to the US. Last week, Amit Kara and Ana Rincon-Aznar two of my colleagues at NIESR, published a blog on the connection between total factor productivity (TFP) and employment in the UK.* That blog featured the graph in Box 3 that plots total factor productivity on the y-axis against employment on the x-axis. Here is what Amit and Ana said about this graph in their post.

“We find … a long-standing trade-off between employment and productivity such that periods of high productivity are associated with low employment and vice versa. … TFP is thought to capture technological change and efficiency gains and is generally considered to be independent of an increase in the quantity and quality of labour and capital inputs.”

The productivity-unemployment puzzle presents a dilemma for policy makers. If the theory I describe in Prosperity for All is the right explanation for these data, then very low unemployment is as bad for the economy as very high unemployment. This graph suggests an intriguing question: Is unemployment too low? Very low unemployment is achieved by diverting resources from the activity of producing goods, to the activity of filling vacant jobs. Perhaps the UK has moved too far in the pursuit of full employment.

NOTE: *Productivity is measured in two ways. Labour productivity is the ratio of GDP to employment. Total Factor Productivity or TFP, is a more sophisticated measure that takes account of the input not only of labour, but also of capital. For the most part, these measures move closely together.


Making Sense of Chaos with the Windy-Boat


Last week my Rebuild Macro colleague Doyne Farmer, asked “Are Business Cycles Chaotic?”  Doyne’s answer is that economies are complex chaotic systems. He draws an analogy with meteorology and he compares the mathematics of business cycles to the science of the weather. I agree with Doyne on this point. But why do we care?

I wrote a piece on this topic, Not Keen on more Chaos in the Future of Macroeconomics, on my personal blog, Roger Farmer’s Economic Window. Although I agree that economies are chaotic systems, I do not agree with the way that Doyne proposes to address that issue.

Doyne uses the rocking horse metaphor that I discussed in depth in my book How the Economy Works. According to this metaphor, which dates back to Wicksell in the late nineteenth century, the economy is like a rocking horse shocked repeatedly and randomly by a child with a club.  The behaviour of the rocking horse is nothing like the dynamics of the shocks; which are random blows with no intertemporal pattern. Nor is it like the behaviour of the rocker, which displays a smooth cyclical return to its rest point after any single shock. Instead, the rocking horse moves randomly through time in predictable ways. This is the way most conventional economists see the world.

Why is Doyne unhappy with the way most conventional economists see the world?  In his own work, Doyne models complex systems with millions of interacting agents. He sees a parallel between his economic models and meteorological models of the weather. Chaotic systems never return to a single point: they keep moving in ways that, although deterministic, are nevertheless unpredictable. 


In How the Economy Works, I argued that the rocking horse metaphor is a very bad approximation to a chaotic system because it makes a strong prediction that is contradicted by data. The rocking horse, if struck just once, always returns to the same point. The data do not. The US unemployment rate has wandered randomly between 3% and 25% but it does not return to a single point. Central Bank economists construct rocking horse models in which the unemployment rate fluctuates around a unique rate that they call the natural rate of unemployment. The natural rate of unemployment is a myth that does not, and has never, existed in the data.

The rocking horse is the wrong way to approximate a complex dynamical system. Is there a better one?  I believe so. In my book How the Economy Works I provide an alternative narrative that I call the windy-boat metaphor. In this narrative, the economy is a sailboat on the ocean with a broken rudder. The wind blows the boat here and there and after a strong gust it never returns to the same point. The windy-boat metaphor leads to approximations to complex systems that, although simple, do not predict that the system is self-stabilizing. Instead it leads to models that display what mathematicians call hysteresis. Perhaps we will eventually have good models of the non-linear dynamics of real world economies. In the meantime, our simple models should provide good approximations to those dynamics that are not obviously contradicted by the facts.  

Conventional macroeconomists approximate the world with the rocking horse model. That is one way of cutting the Gordian knot of complexity theory. But, as Doyne points out, it leads to some pretty silly conclusions. In my work, I replace the rocking horse model with a simple alternative. The windy-boat metaphor makes sense of chaos. It predicts many of the simple correlations we see in data and it provides a viable model of real-world economies that fits the facts.

Tax Reform: A Proposal for the Chancellor

Given the upcoming autumn budget, I have a proposal for the Chancellor to consider. Replace taxes on dividends, capital gains and inheritance with a tax on wealth. Currently these three taxes combined raise £41b in revenue. A 1.2% wealth tax on those with net wealth greater than £700,000 would raise approximately this amount with £2b to spare to help pay down the deficit. A 2% wealth tax would raise £72b and give the Chancellor breathing room to lower taxes on wage income or to provide much needed additional resources for our nurses, firefighters and police men and women.

Chart 1: Source, Office for Budget Responsibility and Authors Calculations (c) Roger Farmer 2017

Chart 1: Source, Office for Budget Responsibility and Authors Calculations (c) Roger Farmer 2017

In 2017-2018 the Office for Budget Responsibility (OBR) expects that tax revenues will be equal to 37% of national income. Chart 1 breaks this down by whether those revenues came from taxes on labour, capital or sales.

To construct this chart, I took the major sources of revenue from OBR’s tax by tax – spend by spend data and I allocated each major revenue source to either labour, capital or sales taxes. Sales taxes include VAT and petrol and taxes on alcohol and tobacco.<1>

The UK generates approximately £1.9 trillion in income of which 2/3 is paid as wages and 1/3 goes to the owners of capital in the form of profits, rents, dividends and capital gains. If tax revenues were raised in proportion to these two sources of income, we would expect that the revenue raised from capital should be approximately 1/3 of the revenue from income taxes. In reality, taxes on labour income account for 61% of tax revenues and taxes on capital for only 8%. 

To put my proposal for a wealth tax in context, let me revisit some of the principles of the public finances. For at least two hundred years, there has been a public consensus in favour of progressive taxation. In other words, a rich person should not only pay a higher amount in taxes; that person should also pay a higher percentage of his or her income in taxes. That principle is encoded into the current system of income taxation whereby those earning less than £11,500k pay nothing and those earning more than £11,500 pay income tax at a graduated rate. That rate increases in steps with the highest rate currently set at 45%.

So far so good. But there is a growing consensus that the very wealthy are not paying their fair share. The offshore schemes unearthed in the recent Paradise Papers scandal, may all be legal. But to many, they do not seem just. It is relatively easy to raise taxes from wage income. It is much harder to raise taxes from capital income.

Suppose that you own shares in a company that pays little or no dividends. The company nevertheless makes a healthy profit that it reinvests. Because you receive no dividends, you pay no income tax. But because the company is profitable, its shares keep appreciating and, when you sell those shares, you will make a capital gain. Currently, the maximum tax you will pay on that capital gain is 20%.  The very rich earn little of their income from wages and thus the top marginal rate of 45% never applies.

The Office for National Statistics estimates UK wealth to be roughly £9 trillion of which £3.5 trillion is in the form of factories and machines and £5.5 trillion is in the form of property. The Institute for Fiscal Studies (IFS) estimates that 40% of that wealth is held by the top 5% of wealth owners and 20% is held by the top 1%. £9 trillion generates an annual flow of income of roughly £450 billion. 40% of £450 billion is £180 billion. Assuming that the top five percent of wealth owners are in the 45% tax bracket, one could argue that the Chancellor should be receiving an income of £81 billion from those individuals. My proposal is more modest.

According to my calculations, a wealth tax of 1.2% levied on net assets greater than £700,000 would raise approximately £43b in revenue, enough to replace existing taxes on capital and still have £2b to spare. I chose a threshold of £700,000 because the IFS estimates that it is the cut-off for the top 5% of the UK wealth distribution. A person with net assets of £700k is at the 95th percentile and his or her assets would, under this plan, be tax free.  There is, of course, no need for a new proposed tax to be revenue neutral. A tax of 2% on net wealth greater than £700k would raise £72 billion and allow the Chancellor to lower the top rate of income tax on earned income or to fund important spending programmes such as defence, education or health care.

Any major tax reform is likely to have unforeseen consequences and this plan is no exception. One major change from existing policy is that the wealth tax I am proposing would apply not only to wealth held in the form of factories and machines, but also to wealth held in the form of residential property. Currently, those with net assets of £700,000 or more own property worth £2.2 billion (40% of £5.5b) for which they are receiving no income. It is likely that a wealth tax would provide incentives to convert housing wealth into income earning assets. That would put downward pressure on property prices and increase investment in productive capital thereby making houses more affordable and increasing labour productivity at a single stroke.

The British people are tired of austerity and there is a growing concern that our nurses, firefighters and police men and women deserve better. Mr Hammond, I respectfully ask that you consider my proposal for tax reform. It might just provide a simple and popular way to balance the books. 

<1> The three major sources of government revenues are pay as you earn (PAYE) income taxes, 20%, National Insurance (NI) contributions, 17.5%, and VAT 16.9%.  Together, these three taxes make up 54% of all treasury receipts. To get to the labour tax data I added two-thirds of self-employment income and two-thirds of corporation tax. To get to the capital tax figure I added one-third of self-employment income, one-third of corporate taxes and all of capital gains taxes and inheritance taxes. The two-third, one-third division is based on the rough calculation that two-thirds of national income goes to labour and one-third to capital. 

Macroeconomics: Religion or Science?


Writing in 1999 in a widely cited paper “The Science of Monetary Policy”, three leading economists, Richard Clarida, Jordi Galí and Mark Gertler, CGG, make the case that monetary policy is a science. Although there is some truth to that claim, CGG could equally well have titled their paper; “Macroeconomics: Religion or Science?”

Science and religion are strange bedfellows. Science dates from the enlightenment. Religion has been around since the dawn of history. Science is supported by rationalism. Religion is supported by dogma. Science is challenged by experiment. Religion is codified by scholars and protected by a priesthood. Macroeconomics has aspects of both.                                                           

Macroeconomists build theories codified by systems of equations. We use those equations to explain patterns in economic data. Unlike experimental sciences, chemistry and physics for example, macroeconomists cannot easily experiment. That does not mean that we cannot challenge existing theories; but it makes it much harder. Like astronomers waiting for the next supernova to explode; macroeconomists must wait for big recessions or large bouts of stagflation to help us sort one theory from another.

The inability to experiment is more serious than most macroeconomists realise. When CGG wrote their paper on monetary policy they put forward a New Keynesian (NK) theory. That theory was  codified by three equations that they used to explain GDP, the interest rate and inflation. The NK equations are widely used today by policy makers in every major central bank to help guide policy. What if those equations are wrong?

Economists select one theory over another using a statistical procedure called maximum likelihood. We say that theory A is better than theory B if the data we observe has a higher probability of being generated by A than B. In research with my co-author Andreas Beyer of the European Central Bank, (Beyer and Farmer 2008) we showed how to produce theories that cannot be distinguished in this way. If you come up with theory A to explain data set X, our procedure will produce another, theory B, that has the identical probability of having generated the observed data as theory A.

It gets worse. We provide an example of this problem where theory A and theory B provide contradictory policy conclusions. The only way to tell them apart would be for a policy maker to experiment by changing the way they react to economic data. The Bank of England could, for example, raise the Bank Rate while, at the same time, the Federal Open Market committee lowers the US Federal Funds Rate.

Macroeconomists can explain past data relatively well. But we are not very good at explaining new events and our theories are always evolving. In that sense, economics is a science. The way that our models are allowed to evolve is controlled by a group of high-priests who maintain doctrinal purity. In that sense, economics is a religion. The religious aspect is important during normal times, when we have not recently experienced a big event. At other times, after we observe an economic supernova, the grip of the high-priests becomes counterproductive and it is a fertile time to explore ideas that the priesthood considers heretical. Now is one of those times.