Friday 29 May 2015

A Major Crash is a Matter of Time; the Paradox of Tranquility in Action Again

The financial markets today and the Paradox of Tranquility

Despite a slight pick-up in volatility over the last nine months, the equity and bond markets are very calm. Equities and all forms of bonds have been steadily rising since 2009. Every time they go down, there is a flood of buying interest.

Isn't this a sign that everything is fine? Actually no, it isn't. Equities are rising and credit spreads are falling not because the economy is in rude health and growth means a rising share to everyone. They are rising  because investors are becoming more and more willing to accept a lower yield on the understanding that
  1. Growth is going to be bad.
  2. There exists a 'Central Bank Put' which will continue to add money to the system in the case of any downturn.
Paradoxically the lower economic growth is leading to a rise in asset prices because it is leading people to expect and accept lower yields. High corporate profits as a share of GDP give an illusion of good returns for equities, however they are a symptom of the malaise that has driven salaries down and thereby stunts future economic growth  by increasing structural savings.

Allied to this, there is the feeling that the thus far infallible central bank will always bail them out if something goes wrong. Their share of the future economic pie is protected. Their savings are invincible.

There is, however, a flaw in this argument. The central bank is not infallible, and in fact is reaching the limits of its influence. 

So far, this fallibility has not been tested as there has always been a tool that the central bank could use to save the markets. The fact that there has always been a way in the past gives confidence to people that there will always be a way in the future and this will make the fall even more painful.

The tranquility that we see in the market, as I discuss here, is based on a chimera. It is true only because everyone believes it to be true and will continue to be true as long as that belief holds. But the confidence engendered by this tranquility has only sown the seeds for the mess that awaits us. The more confident everyone is before the crash, the bigger the crash will be.

The solution to this mess (in terms of the economy at any rate, if not the markets) will be Central Bank money given directly to the government, but unfortunately I fear that this solution will be avoided for as long as possible causing untold economic damage.

In order to explain why the central bank has reached its limit, I will once again invoke my Cash Flow model of the economy. It is first summarised and then the important part discussed.

Flows model

The basic model was originally presented here but a summary is below:
Demand Based Cash Flow Model of the Economy

A very simple static model of a closed system will be presented, ignoring, among other things, the government and the financial sector as well as any investment. This will suffice to illustrate the basic idea and draw important conclusions. In this model the economic product (GDP) of time period t creates cash flows. The total of the GDP is paid out either as wages to workers net of mortgage, interest and rental payments (w), interest to bond holders and banks (i)  and dividends and rental payments to landlords (d).

Each receiver of their share of GDP then has their own marginal propensity to consume, α .

There are other sources of spending that are not from the previous period's GDP. The first is spending of existing savings (ES); people or corporations that have previously saved up money will spend a proportion (γ) of these savings during this time period. The second is Net New Loans (L); this is subdivided into government (LG) and private-sector (LP). When a loan is created, a certain proportion (also denoted by α) will be spent on goods and services. This would almost certainly be higher for government loans than for private sector loans. The third other source of spending is new cash created by the central bank (C), which also has its own α.The equation for GDP at time t+1 is thus given as:
GDP(t+1) = αd*d + αi*i + αw*w + αLG*LG + αLP*LP+ αC*C + γ*ES    (1)
 GDPtd + i +       (2)

Now, in a fully healthy economy, with expected trend growth of gt% and inflation rate of it%, we would see the following:

GDP(t+1) = (1 + 0.01*(gt + it))*GDPt              (3)

This is to say that GDP should increase by inflation and growth each year. 

Under ideal circumstances this would be achieved without the help of either further private sector or public sector debt. So equation (1) would become:

GDP(t+1) = αd*d + αi*i + αw*w + αC*C +  γ*ES    (4)

However, for a very long time now, the right hand side of equation (4) has been unable to be high enough to suffice for equation (3). That is to say that there is structurally not enough spending and too much saving in the economy. I call the gap between the right hand side of equation (4) and the right hand side of equation (3) the 'demand gap'.

How, then, was such high economic growth achieved between 1945 and 2008? The demand gap was largely filled by increasing private sector debt. I estimate here that in the period since 1995 approximately 11% of new private sector debt was spent in the economy in the year it was taken out. As an average of 10% of GDP per year has been taken out, this means that approximately 1.1% of economic growth per year can be attributed to private sector debt filling the demand gap. 

This is the predominant, but not the only mechanism that the demand gap was filled. Looking at equation (1) for clues suggests other ways. Equities and bonds have been on a long bull market. This means that existing savings (ES) have been continually rising, giving savers more money to spend. This wealth effect helps to fill the demand gap.

At times when the private sector was unable or unwilling to fund the gap, the government has stepped in, increasing LG

What happens in an economic downturn?

Looking at equation (1), there are a number of ways that  GDP is affected by a downturn. I will use 2008 as an example as I believe that it is a template for what could happen next time.

The first problem is the credit crunch. This means that LP goes negative. More loans are recalled than given. This brings down GDP.

The second problem is that people lose confidence and save more. Thus all the α values and the γ go down. This also significantly brings down GDP.

Equities crash and credit spreads increase, causing ES to go down, thus also having an impact on spending. If people are poorer they will spend less.

Then the feedback loops begin. As demand goes down, workers are made unemployed. This reduces the value of w, thus shrinking demand further.

If fiscal and monetary policy does not apply stabilisers to this then, as in the early 1930s in the US, this downward spiral can continue until a new, much lower equilibrium is reached. 

Fiscal and monetary stabilisers

This is where the government does its part. Government borrowing increases; some naturally in response to lower tax receipts and higher welfare payments, some deliberate. The increase in LG helps to counteract the falls described above. 

At the same time, monetary policy kicks in. A reduction in interest rates stimulates further private sector loans, LP

Up to 2008, this all worked just fine. Unfortunately by 2008 the levels of private sector debt were just too high to stimulate more of it. Interest rates hit the zero lower bound but the poor state of the economy meant that even at these low rates net new debt was not being taken out.

Next came Quantitative Easing. By swapping one form of money (government debt) for another (cash) this is not really printing new money. The large amount of cash swapped for government debt had only a small impact on GDP. This impact came from two main sources.

First, it led to a reduction in long term bond yields which pushed up asset prices. Thus ES went up and spending in the economy marginally increased. 

Second, the low long term bond yields helped to stem the decline in private sector loans.

These are both second order effects, hence the small impact but still there was some improvement in growth in the years of QE.

But what happens next time?

Look at the situation now. We have just had a huge rally in equity and bond prices. Long term bond yields are hitting zero. Credit spreads have shrunk in a desperate scramble for yield. Equities look overpriced by any historical measure. The only way that these prices are justified is if the economy can be kept stable by the central bank.

But it can't.

I don't know when the trigger will come, or what it will be. It could even be years away but I don't think it will be that long. At some point we will get a trigger. Liquidity in the markets is much lower than it has been and especially in higher yield bonds if a crash starts there could be no buyers. The first reaction to a drop may be for buyers to come in. But there will be a time when the buyers will not be there and the drop will continue. 

Now, panic will arise. It will spill over into other asset classes as market participants are forced to liquidate positions taken out during a time of false confidence. The feedback effect of this will cause a market crash as people will be unable to hold their positions in the high volatility, low liquidity environment.

The credit markets will dry up and the process described above in the crash scenario will begin to unfold. 

People will be asking where the Fed put is now? What can it do to stem the crisis?

Interest rates can't be lowered. They are already almost at zero. Quantitative Easing has very limited impact at the best of times, but with long term government bond yields so low already, the long term interest rates can not be reduced much further.

It may decide to buy corporate debt in an attempt to keep these yields lower; but once again the effects are limited.

In fact, the central bank has reached the point where it has very little ammunition left. The full force of the adjustment will need to be carried out by the government using fiscal policy. Since governments in the UK and US are already running a deficit and since monetary policy can't help, the government will have to run deficits at 15%+ of GDP.

The problem here is that government debt to GDP is already, in many countries, running at approximately 100% of GDP. There will be political pushback from politicians who don't understand economics to this level of spending. 

All in all, next time we crash, the starting point will make an appropriate response very difficult to achieve.

The Solution

The solution is to allow the central bank to give government enough money to hit its inflation target. It could be structured as an interest free loan but the best solution would be one that the government can not see this debt at all as it avoids politicians' tendencies to worry about debt problems that are not there.

Looking at equation (1) above, this is the only way that the structural demand gap can be filled without further debt being taken out. 

Monday 25 May 2015

Total Wealth and the Obvious Effect on Yields

Savers often complain that, with interest rates at close to zero, they are not rewarded enough for saving. I argue here that, on the contrary, they are actually rewarded too much for what is, at present, a socially and economically damaging activity.

Ben Bernanke recently wondered aloud about the disappearance of term premiums. I believe that it is all linked to the structural excess savings which cause stagnation, inequality and threatens our economic stability.

There is a very simple explanation for low yields. I present you the following graph of total gross financial assets in the UK divided by GDP from ONS data (to 2006 using the statistical annex of this report, and after using other ONS data):

Note that there are questions of double counting here, which would reduce this, but also the foreign sector and property have not been included here. It is merely to give an idea.

We have had an extended period of chronic excess savings, where demand has been too low. The monetary response has been to increase demand by lowering interest rates, stimulating more private sector debt. This has thus increased total assets and total wealth. Interest and dividend payments on this have increased the structural saving further. The economy is now struggling to cope with the loss of demand from the transfers from workers to savers. 

The reason is that the savers (eg pension funds and richer people) have a lower propensity to spend than the workers. This means that the increase in transfers from workers to savers lead to a reduction in demand. And the increase in debt has meant more and more transfers from workers to savers.

As I describe previously, wealth can be looked at as a claim on people's work in the future. We can therefore make a simple model of where future yields should be now, based on total wealth and total GDP. (Actually, to be more correct, it should be based on future GDP including growth estimates  - these are going down - and also how much rent can be extracted from the economy  - this is going up. I assume that these cancel out in the given time period and ignore them in my simple demonstration.)

Let me make the following assumptions:
  1. Interest and dividends remain a fixed share of GDP - for my back of the napkin calculation I will set this at 50%. The rest is shared between wages and investment. 
  2. The average real yield will be 3% above the real government debt yield. This is because people need to be rewarded for productive risk-taking in the economy. No-one would take risk if government bonds paid the same amount.
From these two assumptions, I can make a predicted yield based on total wealth.The total money from the economic activity of the country is apportioned out and 50% is given to the savers. This amount is then divided between the total outstanding wealth. 3% is then taken off to account for the difference between average bond yield and government bond yield.

I now plot my estimate against real yield from 1984 when the Bank of England data starts. The fit is pretty close I think. Possibly in the early 1980s wages and investment were a higher proportion of GDP than they are now - real government yields would not have been 10%. 

Put simply, the more wealth there is, the lower the yield on that wealth must be. Those that talk about an 'equilibrium interest rate' of maybe 3.5% are not taking this into account. 

Any increase in yields will have to come from the broader economy. This implies that either a) wages or investment would have to be reduced to compensate, b) asset values collapse, or c) economic growth increases substantially. 

With the structural excess savings we have, GDP can not go up without private sector debt increasing and thus wealth increasing. Therefore interest rates can not go significantly higher without a collapse in the claims of wealth or even more rent seeking.

All of the wealth amassed, and continually being amassed, is a huge drag on growth. The share of wages is constantly getting lower and thus so is the demand in the economy. As I argue in every other post, we need mild to moderate inflation (maybe 3%) to inflate away some of the wealth, as well as large government deficits (and preferably central bank money given free of charge to the government) in order to get demand sustainably high enough. The current situation is unsustainable and will only lead to economic misery.

Wednesday 20 May 2015

QE4 and the Limits of the Fed Put

For the past year, everyone seems to have been talking about the hiking cycle in the US. When will it start? What will happen to asset prices as interest rates normalise? The US dollar has been hoarded by hedge funds in anticipation of the demand for a higher yielding currency.

The Federal Reserve dot chart predicts interest rates to hit 3% in 2017.

And yet, much as I am loth to go against the wisdom of so many intelligent minds in the market and the Fed, I would place a £1 bet with anyone that we reach QE4 before we reach 3% short term US dollar interest rates.

The reason that I say this is that, as discussed in previous posts, I believe that there is a demand gap. That is to say that for every $1 spent in the economy in time period t, only 99c is spent in period t+1. This means that structurally our economy over-saves. The reasons are discussed here (among other places on my blog). It is largely to do with interest and dividend payments making up too large a proportion of our GDP and the lower marginal propensity to consume of the receivers.

Why am I so confident of this? Because, in the US since 1965, in order to have the economy running at capacity we have needed an average of 8.5% of GDP per year of private sector debt to be added to the economy to keep demand up. We have needed an average of 2.7%  of GDP government deficit per annum (and the trend is rising). We have had a stock market rising at 7.5% per year to increase wealth and spending. And recently those rises have been caused more by monetary policy than by expectation of economic growth. 

All of these have been necessary to keep growth at capacity. Had they not been there then demand would have been lower.

There must be a demand gap because all of this was needed in the past. And most of it is unsustainable.

As the private debt rises (as I discuss here) so does the demand gap. The amount of money needed to keep the economy growing gets larger and larger. 

At the moment we can see broadly trend growth in the US. We have a Federal deficit of 2.8%, we have asset prices at record highs making people feel wealthier and thus spending more, and we have monetary policy as accommodative as possible to stimulate even more private sector debt.

Whilst an economy is an extremely complex system, in many ways it can be simplified to say that if there is enough money spent, then the economy can run at capacity. If too much is spent we will get inflation. If too little is spent then growth will be lower than capacity.

In this way, GDP can be estimated using some other very basic data. Below, using regression, I build a proxy for GDP growth. This proxy is based on only the following: 1) change in short term interest rate during the year, 2) change in stock market the year before, 3) total private debt at the start of the year, and 4) change in private debt during the year.

This gives the following GDP prediction vs actual GDP:

Here, the share price movement the year before and interest rate changes are an indicator of sentiment. The change in debt gives a boost to/drag on the economic growth, and the size of private sector debt gives a measure of the drag on the economy caused by the structural over-saving discussed above. The share price movement in the previous year also creates a wealth effect which stimulates spending of savings.

Although this test is just for the US (and covers a larger time period), I find a similar effect of stimulus and drag from private sector debt as I do here. In this regression, the stimulus is 15% of the increase in private sector debt and the drag is 1.9% per year. This compares to my previous findings across 28 countries since 1995 of 11% stimulus and 1.5% drag.

So, why do I think that we will have QE again?

Because, at the current levels of private sector debt then, without help from rising asset prices or increased private sector debt, trend growth is at 0.65% per year. 

I just don't believe that enough private sector debt can be stimulated at considerably higher interest rates than we are seeing now, given the low expectations of future growth. For this reason I am happy to make the small bet that we will have QE4 before we hit 3% Fed Funds rate. I may be wrong about this; the capacity of private sector debt to grow can be surprising. But if it does, the pain at the end will be larger.

As discussed previously, as shown by my flows model, there are only 3 direct ways to close the demand gap: 
1) increase private sector debt,  
2) increase public sector debt and  
3) print more Central Bank money. Note that I do not mean QE here; I mean printing money that is put into the real economy rather than swapped for existing monetary instruments. 

Since (3) is, unfortunately, viewed as heresy by the mainstream economics community we are left with only the choice of more debt. This can not go on forever.

The other, indirect method, is through increasing asset prices, increasing wealth and thus increasing spending of existing savings. In the regression above, a 20% rise in the S&P creates a wealth effect (or helps predict GDP - it is not clear which) corresponding to 1.2% GDP growth in the next year. Eventually the Fed's powers to raise equity prices will stop. This also can not go on forever.

The Fed is reaching the limits of its powers. Once the long term bond yields hit close to zero there is nothing more it can do to stimulate asset prices or private sector lending. 

The only way within the current framework would be if a rational government decided to use the Fed buying of government debt as a free pass to spend the necessary money (which is effectively method (3) above). Unfortunately government debt is not always seen rationally.

In any case, if we do hit that debt ceiling I feel that we are really in trouble.

As mentioned in every previous post, the only conclusion I can draw from all of this is that in order to achieve sustainable future demand, the Central bank needs to print money and give it to the government. This is the only way to regulate money supply that sustainably keeps demand high enough for the economy to run at capacity. On top of this, it counters the instability as well as the inequality and rent-seeking caused by ever-rising private sector debt.

Saturday 16 May 2015

Is Economic Growth Fake if it is Fuelled by Exponentially Increasing Debt?

The question in the title relates to the period leading up to the crash of 2008 where economic growth in the UK and US coincided with rises on house prices, rising levels of private sector debt and a general financial sector boom. The idea of this post is to ask whether this growth was real and sustainable or whether it was based on borrowing growth from the future and that we are suffering the inevitable comedown now.

This post is part a response to my own previous thoughts on this subject (as well as others whom I have seen propounding the same view) and in part a continuation of my previous call to look at money in a different way. In the current paradigm, my previous thinking was correct but if we can change our mentality it need not be.

Economists often draw a straight line through trend economic growth, which goes through 2008 and continues upwards as if there had been no crash. They point out the gap between where we are now and where we would be now - often arguing that austerity has caused the gap. But that's unfair, I used to say, because the growth in the period leading up to 2008 was debt fuelled growth and now we are deleveraging so we are paying some of that growth back. The idea behind this was that by using debt we were in some way borrowing from future growth.

From one point of view, this was completely correct. In this post, I discuss my empirical study that shows how private sector debt causes a stimulative increase in GDP in the year that it is borrowed. This amounts to around 11% of the amount of debt taken out - so if private sector debt rises by 10% of GDP then we could expect a 1.1% increase in GDP that year. 

But this growth is not cost free. The increase in debt creates changes in structure of the economy so that money flows to people with a lower propensity to spend, as I discuss here. Higher levels of debt correspond to lower GDP growth (all else being equal) as it causes a structural reduction in demand. In fact for just that 10% of GDP of private sector debt, the demand in future is lowered so much that the GDP growth of a country with that extra debt is lowered by 0.15% per year for every year. The only way around this was to lower interest rates and encourage even more debt to replace the missing demand

In that sense, every increase in private sector debt bought trend growth in that year, but caused a loss in future years. So it was borrowing from the future.

However, my thinking has evolved since then. The belief above is only true if one uses the standard money paradigm - which unfortunately is also the one used by every major government and central bank in the world. In this paradigm there are two ways of regulating the amount of money flowing through an economy:
1) Fiscal policy; using government borrowing and repayment of debt to put money in or take it out of the economy.
2) Interest rate policy; either by setting the short term rate or also, as more recently because demand has become so low, using Quantitative Easing to reduce the long term rate. This then encourages/discourages private sector borrowing which increases the money supply to the economy.
Unfortunately, partly because of the very high level of debt and partly because of the increased ability of the corporate sector to extract rents (maybe through technology, patents, offshoring etc.), this has led to what we have now, which is a structural deficit in demand. 

If, for every £1 spent in the UK economy, 1p gets saved and only 99p is spent next time around then the result is a shrinking economy and unemployment. I have built a flows model which shows in a simplified way how this happens. The only way for the government to stop this shrinking economy is to increase demand in one of the two ways above and put the 1p of spending back into the economy. By creating approximately 10p of mortgage debt to put that 1p back, the government is making the demand next year lower and the problem larger.

I believe that unless we add a third tool to the box then we will not be able to easily and quickly extract ourselves from this low demand spiral. This third tool is:
3) Central Bank Cash. The Central Bank is able to regulate demand by printing new money which it gives to the government for public spending or tax cuts. The Central Bank can also demand a return of money from the government to reduce the money supply; leading to tax rises or spending cuts. No interest is charged on this money.
The reason that it is vital is that we need to break out of the debt spiral we are in. There is no other obvious way out, short of large default, revolution or other major event. Unless we wish to wait it out - but it could be a very long wait.

In my flows model, I show why this is no more dangerous than using interest rates to control the economy. This is also discussed here

One sometimes sees frankly idiotic comparisons to Zimbabwe. It is a bit like saying that you should never eat meat because if you ate a whole cow you would burst and die. A credible Central Bank removes any risk from this. The only way to get an economy similar to Zimbabwe's is to put in place a policy that takes away most of the productive capacity of your economy, while at the same time needing money to fight a war abroad. Then, if you are printing money to pay the soldiers and government employees and there is nothing to buy in the shops - guess what? You get inflation. But this is a symptom of a collapsed economy, not a cause. 

We need to stop thinking about money as a stock - a fixed quantity. We need to start thinking about money as a flow that keeps the economy at full capacity. 

Yes, money as a stock is a store of value. But as I argue here, we can not simply protect this value regardless of the costs. The store of value can only be as a share of the future economic activity - not a fixed amount when that amount is unpayable.

I argue here that it is an economic crime to run the economy at lower than full capacity. It is clearly better for everyone if everyone has a suitable full time job. This makes the economic product of the country at a maximum. 

Note that I say a maximum. This brings me back to the initial argument. I would now argue that no, the economic growth leading up to 2008 was not fake. An economy can only grow at the maximum that it is allowed to by certain constraints. These constraints are that you can not have more than full employment, you can not take more from the environment than is allowed by regulation, you can not grow unless you have invested time in developing technology that increases productivity. All of these are not related to money. 

The economy needs enough money to be flowing through it in order to achieve the full capacity. Too much spending relative to productivity and the result is inflation. There is a maximum to the amount of growth that can be achieved and this is called full capacity. And there is no reason not to be there except mismanagement of money. Too little money, and the result is an economy running under capacity. 

In the period up to 2008 the growth was very real because the economy was running at capacity and real productivity growth was achieved. The problem with it was that the way that we chose to keep the economy at full capacity was with private sector debt. 

But it need not have been. It could have been with Central Bank money or government spending. The only problem we have for the future is that the ways of the past are unsustainable as they create structural shortfalls in demand. If we were to start printing Central Bank money now, then we can continue to enjoy an economy running at full capacity and growing at trend growth in the future. 

Thursday 14 May 2015

Bernanke: This is the Real Reason that the Taylor Rule is Dangerous

A couple of weeks ago Ben Bernanke argued in his blog against John Taylor's suggestion that the making of monetary policy should be rule based, and that the rule it should be based on is Taylor's eponymous Taylor Rule. 

This rule was based on looking at past interest rate decisions and placing a line of best fit through the response of policy makers to changes in inflation and growth expectations. It was set up to be descriptive of past monetary policy decisions and Taylor believes that it provides a good basis for monetary policy going forwards.

Like any man faced with his job being replaced by a computer, Bernanke responded by voicing the opinion that human discretion would trump robot decision making. Most people tend to agree with Bernanke on this. 

It is not that I disagree with Bernanke here, but it brought to mind a study of university admission processes which I now can't find (I have found this one instead which is similar). If you ask any professor who conducts university admission interviews, they will normally state without doubt that their interview adds value to the admissions process. However the study showed that, in the subjects in the sample group, the interview score added no value in terms of predicting the prospective student's final grade. Thus including the interview in the process alongside other hard data such as exam results gave a worse selection of students. The human discretionary input made the selection process worse.

However, when the researchers, instead of taking the actual individual interview scores, did a regression of the qualities that the admissions tutors looked for (using interview scores regressed against qualities shown) - and then they applied a interview score based on the implicit weightings given by the professors - they found that the qualities-weighted interview score proxy was actually a good indicator of performance. So the problem was not that the admission professors did not know what to look for. The problem was inconsistent application of the rules they had in their head but had not formalised.

One could argue, as Taylor does, that the inconsistency of human decision making is sub-optimal and a rule that describes the average decision making gives better results.

How relevant is this idea here? I don't know. For one thing, the researchers had a lot more data than John Taylor had formulating his rule. For another, the experiment assumes that the overall environment is the same in the past as the future (that it is ergodic). It is not clear that the economic situation now can be compared to that when the rule was trained. The third criticism would be that when a descriptive rule becomes prescriptive it can change the reaction of the system that it is supposed to describe.

Overall, I am probably more on Bernanke's side here. But actually that whole discussion was something of a digression. The main point here is to talk about the real danger of using the Taylor rule - a danger that is orders of magnitude larger than that described by Bernanke.

To do so, I need to go back to my flows model of the economy first discussed here. It takes nominal GDP at the end of one time period and looks at money spent during the next time period to give nominal GDP at the end of the next time period. It is very simple and, because it is set up as an accounting identity, unless I have made an error in setting it up, it should be correct.

The flows model connects GDP at time t to GDP at time t+1 like this:

At the beginning of every time period all the money is paid out and then during the time period it is either spent or saved. At the beginning of next time period we start again.

The sources of money are: 

1) 'GDP' from work done the previous time period.

2) 'New Cash' printed by the Central Bank, C. This could, in theory, be negative.

3) 'New Loans' created by private banks, L. This could also be written as New Deposits. This can be positive or negative.

4) Money taken 'From Existing Savings' to be spent in the economy. Eg pensioners spending their private pension. In terms of the Stocks model, the existing savings, ES,  can be seen as the sum of CB cash, equity and debt.

The GDP is divided into three flows:

a) Dividends - this includes eg. rental payments on houses. It is any return on equity as defined in my post on Stocks. This is denoted by d.

b) Interest, i.

c) Wages, w.

There is not much more required for this simple system in order to calculate the path of nominal GDP. Real GDP depends on actual productivity increases, but nominal GDP in this closed system is just how much money is spent (if there is more money spent but no increase in productivity then it is just inflation). To calculate the nominal GDP and net new savings/debt, I just need to put in how much is spent on consumption.

I will call α the coefficient of consumption. So αd is the proportion of the dividends paid that are spent in the economy. Similarly, αi, αwαL  and α are the coefficients of consumption of interest, wages, new loans and new cash. Also, I will define γ as the proportion of existing savings that are spent in the year.

We can then find the next year's nominal GDP and the amount of net savings by using the following:

GDP(t+1) = αd*d + αi*i + αw*w + αL*L + αC*C + γ*ES     (1)

And we can define Unspent Income (UI) as:

UI  = (1-αd)*d + (1-αi)*i + (1-αw)*w + (1-αL)*L + (1-αC)*C - γ*ES  (2)
In order to proceed further, I will need to provide a new concept of equilibrium. This is not a Neo-Classical equilibrium; it is the equilibrium of an economy that does not need further debt to achieve GDP potential. For this equilibrium, the following must apply:


 γ*ES  = (1-αd)*d + (1-αi)*i + (1-αw)*w + (1-αC)*C  (3)

This means that the spending of existing savings exactly matches the amount being saved without any new debt being taken out. 

This is the true equilibrium in an economy that we need to aim for.

In any case, you can see how the dividends, interest and wages from GDP at time t, as well as the external sources of money (from existing savings, new loans and new central bank money) make up the next period nominal GDP.

What has gone wrong:

I would say that during the 1945 to 1975 period, a period of excellent growth across the developed world, we were broadly in equilibrium (or at least the total private debt levels were low enough that it didn't matter). The savings broadly matched the spending of exisiting savings. Governments, using Keynesian policy tools would increase their spending (the government component of L) when savings were too high and reduce when more savings were being spent than new savings made. It all worked pretty well.

What changed in the 1970s was the rise of credit. Looking at the Equilibrium equation (3) above, the share of GDP going to interest and dividends went up relative to the share going to wages. The coefficients of consumption (α) for the interest and dividends is lower than that for wages so we had the following inequality:

γ*ES  < (1-αd)*d + (1-αi)*i + (1-αw)*w + (1-αC)*

This means that the economy is out of equilibrium. The GDP shown in figure 1, will now go down because of the excess savings. 

Previously fiscal policy would have been used to stimulate growth and return the system to equilibrium. 

Increased government debt is far more efficient at stimulating the economy than increased private sector debt. I show here that a 10% net increase in private sector debt stimulates the economy and adds approximately 1.1% to GDP growth in the year that the debt is taken out. So the multiplier of private sector debt to GDP here is 11%. However, the cost in future years due to the increase of interest repayments at the expense of wages is 0.15% of GDP for every year going forwards. 

The same amount of increased government debt costs only 0.9% of GDP going forwards, but crucially the multiplier on this spending is much higher. Therefore much less government debt is needed to create the same amount of economic stimulus as private sector debt. In fact, I estimate that government debt is an order of magnitude more efficient.

But from the early 1980s, policy makers deregulated markets and switched to monetary policy as the tool of demand moderation. They used something equivalent to a Taylor rule before the Taylor rule was invented.

How does the Taylor Rule work - using the Flows model:

As Wikipedia will explain it better than me, I will give their definition of the Taylor Rule:
According to Taylor's original version of the rule, the nominal interest rate should respond to divergences of actual inflation rates from target inflation rates and of actual Gross Domestic Product (GDP) from potential GDP:
i_t = \pi_t + r_t^* + a_\pi  ( \pi_t - \pi_t^* )  + a_y ( y_t - \bar y_t ).
In this equation, \,i_t\, is the target short-term nominal interest rate (e.g. the federal funds rate in the US, the Bank of England base rate in the UK), \,\pi_t\, is the rate of inflation as measured by the GDP deflator\pi^*_t is the desired rate of inflation, r_t^* is the assumed equilibrium real interest rate, \,y_t\, is the logarithm of real GDP, and \bar y_tis the logarithm of potential output, as determined by a linear trend.
In this equation, both a_{\pi} and a_y should be positive (as a rough rule of thumb, Taylor's 1993 paper proposed setting a_{\pi}=a_y=0.5).[7] That is, the rule "recommends" a relatively high interest rate (a "tight" monetary policy) when inflation is above its target or when output is above its full-employment level, in order to reduce inflationary pressure. It recommends a relatively low interest rate ("easy" monetary policy) in the opposite situation, to stimulate output. Sometimes monetary policy goals may conflict, as in the case of stagflation, when inflation is above its target while output is below full employment. In such a situation, a Taylor rule specifies the relative weights given to reducing inflation versus increasing output.

So the Taylor rule states that the nominal short term interest rate should be a function of the difference between current inflation and desired inflation and the difference between the current rate of GDP growth and the potential GDP growth - which is GDP when the economy is at full capacity (to get this he suggests linear trend extrapolation). Using Taylor's rule of thumb above, it suggests that a 1% increase in inflation should correspond to a 1.5% increase in interest rates and a 1% decrease in growth should correspond to a 0.5% increase.

How does this work in our Flows model? Looking at the equation for GDP (1) we can see that if the right hand side of the equation gives a GDP lower than potential, the monetary policy needs to adjust the right hand side to increase the total.

How would lowering interest rates increase the total GDP. There are three ways:
1) It would increase the appetite for new borrowing - making L go up.
2) It would increase the value of assets - making ES go up. 
3) It would increase the spending of existing savings - making γ go up.
I would say that the biggest impact here is 1); it increases the amount of debt in the economy.

But by increasing the amount of debt what does it do? It pushes the system further away from equilibrium in equation (3). Interests payments in the next period go up, and so demand is further reduced. And GDP goes further from potential in the next time period. So interest rates need to be reduced further next time. This continues until we reach the lower bound. Here is a graph of the US 10 year government bond rate since 1975 - the trend is clear apart from the spike in the early 1980s, and we now have the lowest interest rates ever:

One more minor point which I disagree on, is that the inflation targeting does not separate inflation with a domestic source compared to that with a foreign source. I discuss the error that I believe that they are making here.

But the main problem is that, as with the whole orthodox macroeconomic profession it seems, is that IT IGNORES PRIVATE SECTOR DEBT.

I can not stress how obviously important this is. It assumes that debt can grow indefinitely. It assumes that previous debt has no impact on growth. It ignores financial instability. And ultimately, it creates a positively reinforcing feedback mechanism that ends in the zero lower bound and economic stagnation.

This is the real danger of the Taylor rule, Dr Bernanke. 

And the solution, once again I point out, is to regulate the money supply not using interest rates but by using central bank cash. I describe here why it is an economic crime for an economy to be running under capacity because of lack of money. And I describe here why printing money for government expenditure is essentially the same as the government borrowing to spend in a Keynesian framework, just at 0% interest rate indefinitely. There is nothing to fear from allowing the government to create money instead of relying purely on private sector debt to fuel the economy. The sooner we realise this, the better for us all.

This is not even ideological. The money could be spent on research, infrastructure, education and other investment; in my opinion this is the most sensible place to start. But it could be given in tax cuts to lower income workers. Or it could be given as tax cuts to top rate tax payers  - although more money would be needed to keep the spending at the same level due to the higher rate taxpayers' lower propensity to consume. The important part is to work out a multiplier on the spending and make sure that total spending of money created matches the amount taken out of the economy by savings.

It is my view that, due to the debt levels and corporate rent seeking, we have a structural and chronic problem of excess savings in the economy. We have only three choices to keep demand up. 1) Private Sector Debt, 2) Government Debt and 3) New Government money. By refusing to use choice (3), we are forcing upon ourselves (1) and (2). And the eventual consequences will not, I fear, be pleasant.

Unfortunately I worry that it will take a long stagnation before we work it out.