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First published: January 2016

The universal income is gaining ground those days in Europe. After Finland, some cities in the Netherlands might adopt it in a near future. No need to recall that France has offered such a quasi-universal income – young people are not eligible to it – since 1988. The recent report by the CNNum handed over to the French minister of Labor suggests that due to the huge transformations in the economy implied by technologies it is high time considering such a proposal. Yet, those measures raise moral, social and economic issues. 

In this post I explore in a neoclassical model the macroeconomic implications of increasing the level of universal income. As it is often argued, such a reform is expected to lower the supply of labour, on the intensive margin – working people supplying less – and on the extensive margin – some people dropping from the labor force. Both partial and general equilibrium effects contribute to its decline. As a consequence, the amount of capital in the economy, output and utility – happiness in this model – decrease. However, those results are highly debatable.

The RANG model

The first benchmark is our friend RANG – Representative Agent Neo-classical Growth – model that features one – but yet price-taking ! – agent optimally smoothing consumption over time by accumulating capital and supplying labor in a flexible price economic system. In this version of the model, the single agent chooses how many hours to supply.

The universal income is unconditional, that is to say, it is given regardless of the working status of the agent. Notice the sharp contrast with the French universal minimum – RSA – which is conditional on “not working too much”. However, as the after-transfers net income of the latter is increasing in the number of hours worked – “working always pays off” -, it is not a bad first approximation to consider that it is unconditionally given.

The financing of the universal income is based on income taxes (capital and labor) and consumption taxes. We alternatively study the case where all the burden lies on income taxes and where all the burden lies on consumption taxes.  

The equations of the steady-state flexible price economy write as follows:

They are respectively: the optimal labor supply decision l, as a function of the wage, w ; the long term interest rate, r, as a function of the rate of time preference ρ and rate of depreciation δ ; the demand for capital K; the demand for labor, L ; the good market clearing condition that determines consumption, c, the State-budget equations that ensures that the universal income T is financed by taxes on labor, capital and consumption and the definition of the level of the universal income. κ is the percentage of national income per capital that is guaranteed as universal income.

The equilibrium

Financing through income taxes

The figure below plots the general equilibrium for κ going from 0 to 40% of national income per capita. The key insight is that the supply of labor and capital and therefore output decreases a lot. Output decreases by 30% when increasing the universal income from 0 to 40% of national income per capita.  This is due to the fact that in partial equilibrium, increasing the universal income amounts to increasing taxes on labor and capital which deters the supply of those factors – I discuss this strong reaction below. 

Financing through consumption taxes

When the universal income is financed through a tax on consumption, the partial equilibrium effect goes through the consumption vs leisure trade-off: by increasing the relative price of consumption, the tax on consumption makes people consume less and have more leisure, and therefore work less. In general equilibrium, this implies a decrease in output and in the return to capital. However, notice that the decline in output is much smaller.  

The effect is not very different – contrary to the level – as the (inverse of the) Frisch elasticity θ increases (from dark to light grey).    

The HANG model

To talk about unemployment one has to move away from RANG that features only one agent and to introduce Heterogeneous Agents (this is how RA became HA). I modify the previous model along two dimensions. First I consider an economy with a continuum of agents that are heterogeneous in their productivity. Second, the labor choice is no longer on the intensive margin – how many hours to work – but whether to work or not.

The key insight in such a framework is that the less productive agents in the economy will not find worth working and will prefer staying unemployed. As the figure below shows, as the universal income rises, the unemployment rate increases. Again, the effect is magnified when the financing goes through income taxes. 

The higher the cost of working φ the stronger the reaction of unemployment and all macroeconomic variables to the increase in the universal income.

Summary and Limits

In a RANG model, we showed that output and consumption decrease with the amount of universal income and that the decrease is magnified when the financing is through income taxes. In a HANG model, a larger portion of the population drops from the labor force.

However, those results are conditional on both the structure of the model and the chosen parameters – chosen to be consistent with conventional value in the academic literature, which is of course not a good justification.

Regarding the RANG model with income taxes, the most important concern is the elasticity of labor and capital to their respective net income. We know that those models imply a far too large long run elasticity of capital to interest rate. Regarding the elasticity of labor to wages, the literature is still struggling to get sensible elasticity of labor supply to wages at a macroeconomic level.

Regarding the RANG model with consumption taxes, who would believe a story in which by making consumption more expensive, people are going to opt for more leisure and work less? (remember that everybody receives the universal income, irrespective of whether she or he is working). I don’t. All this suggests that, should the universal income be financed by VAT, the intensive margin impact on labor should be minimal.

The limits of the HANG model are essentially the same.

This model disregards important issues:

1-it is a supply-side model that cannot say anything about short-run effects – that may have long-run impacts in models that feature hysteresis effects – of such redistributive measure which is expected to boost demand in the short-run. To my knowledge, unfortunately and surprisingly, no model in the literature can rationalize this old Keynesian idea.

2-would labor and capital fly away from the country? This ever-harped on refrain – surprisingly sung from those who are the most likely to be net financial contributors – is relevant – yeah, who knows, I might become rich one day -, has received some attention recently in the academic literature – suggesting that the missing wealth is huge but also that the elasticity to taxes is not that high – and western States are now undertaking measures to cope with this issue.      

3-will the decrease in hours supplied decrease output? It may be that the efficiency of labor use will increase to compensate the decrease in hours. As it is often argued, the rate of utilization of labor is far from 100% and in many instances the same amount of labor could be make in a shorter amount of time, even without more effort.

4-should the income taxes increase, how would innovation and creative efforts react? In the long run, this would be my major concern. But again, we have no idea what the elasticity of (interesting) innovations to (financial) rewards is.  

Conclusion

The main intuition that labor, both on the extensive and intensive margin, and output might decrease and unemployment rise with the increase in the universal income is justified within a neoclassical framework. However, the decrease in labor heavily depends on its elasticity to wages as well as the reaction of the rate of utilization of labor which are two key unknowns; the elasticity of capital is also crucial for the magnitude of the general equilibrium effect but is far too large in those models; short-run effects might have important positive long-run impacts which are overlooked; creative efforts might suffer from the compression of the income ladder. Overall, there are a lot of uncertainties regarding the macroeconomic impact of increasing the universal income.

Although the macroeconomic questions are important, my major concern regards the social consequences of such a measure. Its proponents argue that it is a necessary step towards an ideal society of idleness in its noble sense, where social interaction, leisure, arts, enriching activities would have replaced working at the center of one’s existence. But the way to it is, to say the least, very long – what is the timing to change mentalities and cultural habits? -, and in the current context, it might, more than anything else, reinforce the division of societies between those who are included – through a stable decently paid job – and those who are on the peripheries of the labor market. Unless one argues that with a higher universal income, being on the peripheries will no longer be going with lower happiness, lesser social integration and health conditions and that the peripheries will merge into the core. Would you believe it?

First published: december 2015

Most models used in macroeconomics, especially in the policy-making sphere, are linear DSGE – Dynamic Stochastic General Equilibrium – models. They feature rational expectations and require, for the determinacy of their equilibrium path, a set of stability conditions. In this post I would like to briefly review how one solves such models and shed light on three major questions: first what are the justifications for the stability conditions – the assumption that the macroeconomic system has to return to a steady-state ; second what are the justifications for the uniqueness of the equilibrium path ; and third what is the meaning in words of such a solution concept.

I would like to show how crazy those solution concepts – direct descendants of the rational expectations assumption – are. Just to give a little glimpse of the funniest part: in those models, the economy jumps and evolves on a unique stable path because agents who are perfectly forward looking and knows the model are able to forecast that if they sit away from the saddle path, they will make the economy explode and violate the stability conditions ; and that’s what keep the economy on track. That’s crazy!

Let’s start with a little bit of math. A DSGE can be written as a system of dynamic equations – either a system of difference equations in discrete time or a system of differential equations in continuous time. In continuous time, the model in a deterministic setup is summarized by the following matrix equation:

X’(t)=AX(t)

Where X is the vector of variables of size n, X’ is the time derivative of X and A is an n*n matrix that is independent of time. And a set of initial conditions that describes where the system starts

Y(0)=Y0

Where Y is a subvector of X: X=(Y Z)’.

Example: the neoclassical growth model

It features capital, K, and consumption, C, as variables. X=(K C)’ where K(0)=K0 is the predetermined variable of the system. Consumption which is not predetermined is called the jump variable. The linearized model is described by:

K’=aK– b C

C’=ρ C

So that it can be written as X’(t)=A X(t). The system runs from 0 to infinity.

The solution to such a system involves eigendecomposing A. The details of it can be found either here (a good treatment done by Moll) or here (by Sims if the reader looks for something more technical).

A differential equation without boundary condition admits an infinite number of solutions. Therefore, for each dynamic equation, we need a boundary condition or a stability condition. Either one needs an initial condition – this is what the predetermined variables, Y, such as capital, have – or a stability condition that imposes that the variable goes back to its steady-state. All jump variables get impose such a stability condition.

These conditions most of the time imply that the equilibrium path is determinate, i.e. unique and stable. They will force the vector of variables X to lie on the saddle path of the system, the only path that is compatible with convergence back to the steady-state. There are many other paths but all of them are divergent or explosive[1].  

I would like to stress three important points. One is about the justification of the stability conditions. The second is about the justification of the uniqueness requirement. The third is about the economic intuition underlying such a solution concept.

1)      The justification of the stability conditions are twofold.

The first justifications stem from the economic model itself. In many instances, stability conditions look like “natural” conditions given the specification of the model: the transversality condition for the capital stock for example prevents any upward explosion of capital and the non-negativity constraint prevents any downward explosion. However in most instances stability conditions are stronger than the requirements of the model. For example in the previous model, the transversality condition does impose that the rate of growth capital be smaller than some constant but not that it cannot explode upward. In some other instances, there are even nothing in the model that may look like a stability condition. Still we impose the stability of the solution.

The second justification is much more realistic and simple although scientifically less sound: economists like stable solutions because the actual macroeconomic system has never exploded (not yet at least). That is we restrict a priori the set of solutions not because the model we have in mind would necessarily require it but because the match with reality requires it.

2)      The justification of uniqueness is a little more subtle and less robust to criticism. The main justification is purely utilitarian: if a model generates multiple equilibria, we – economists – cannot say anything sensible about the implications of a given policy in a given model. If we want to say something, we need uniqueness. Fortunately, most model spontaneously generate a unique equilibrium path.     

3)      The economic intuition behind the stability condition and the uniqueness of the saddle path is at the same time fascinating for its depth and worrying for the weakness of the solution’s robustness.

The reason why the economy jumps onto the saddle-path from the beginning of time until the end and cannot walk away from it is because the rational agents that populate the economy form rational expectations, so that they know the model and can perfectly forecast what is going to happen in a far remote future for any starting point of the economy. Consequently, should the economic system be away from its saddle path, the forward-looking rational agent would see that the path is divergent and would eventually violate the stability conditions, which contradicts the conditions of the model. Therefore the agent will refuse to sit on such a path. The only path on which the agent would accept to sit is one that he expects to converge to the steady-state. That’s crazy, isn’t it?

That’s rational expectations combined with stability requirement in DSGE models.

[1] Although beyond the scope of this post, there are important instances in which the stability conditions are not enough to get uniqueness of the saddle path. Such case are called “indeterminate”. We assume here that uniqueness is not an issue.

First published: December 2015

In a 1999 paper, Buiter argues that the fiscal theory of the price level is a fallacy.

Two years ago (so in 2013), before joining the resisting village governed by the wise Chris Sims, I would have naively agreed with the assertion of the title without even feeling the need to endure the pain of reading his paper. The Fiscal Theory of the Price Level looked so much unrealistic to me, so far-fetched, that there must have been a fallacy somewhere into the foundations of the intellectual construction. No need to check it.

Surprisingly enough, I find now myself in the position of defending it, not because I have come to the idea that the theory captures some interesting dimension of reality – I hope Chris Sims wouldn’t disagree with me on this point, for I fear his wrath – but because I think it is misunderstood by many people. 

The criticisms of Buiter are of 4 types but only the first one is really serious.

1)  The first criticism is about the key underlying economic assumption: “only those models of a market economy are well-posed, in which, if default is ruled out, budget constraints (including the government budget constraint), must be satisfied for all admissible values of the economy-wide endogenous variables [and not only in equilibrium].”

As we explained in a previous post, models of Fiscal Theory assume that the government doesn’t adjust its taxes and spending to meet its budget constraint and can’t default on its debt so that the prices have to move to make the real value of the debt equal to the expected discounted stream of future revenues.

I agree with Buiter that this assumption doesn’t make sense from an economic point of view. If only this was the first time economists make unreasonable assumptions…

2) Because the level of prices should remain positive, there are some restrictions on the admissible set of debt and sequence of revenue and spending.

Well, this is true. For example, if tomorrow, the debt of the French State becomes negative – i.e. if the government becomes a net creditor – , the price level should become negative to maintain its intertemporal budget constraint. It is not a serious criticisms, because for most realistic parametrizations, the price level would remain positive.

3) The theory of the price level can determine the price of money in a model without money.

This is not exactly true. Without money, the price level remains the relative price between the nominal unit of account/numeraire and real goods and the numeraire becomes the public bond.

4) Buiter then gives many instances where a non-Ricardian fiscal rule gives rise to overdeterminacy of the price level: in finite-horizon with a monetary rule for the government, in finite-horizon with a taylor rule and price rigidities, in infinite horizon…..  This over-determinacy is easy to understand: when one adds additional restrictions on the dynamic system, the price level is determined both by the intertemporal solvency condition and the other parts of the model.

Well, this is obviously true, but I really don’t see how this criticism – which can be made to any model – weaken the intellectual construction of the fiscal theory of the price level.

 To conclude, only the first criticism is really serious: the key assumption that the government doesn’t adjust its taxes and spending to meet its budget constraint and can’t default on its debt so that the prices have to move, an assumption on “fiscal benign neglect”, is not realistic at all. But again, remember, if one makes the government Ricardian, then the price level becomes undetermined unless the monetary authority becomes active…

Buiter’s paper can be found here: http://www.nber.org/papers/w7302

First published: December 2015

A New View on the absolute and relative effectiveness of monetary and fiscal policies is now emerging from the recent work of Kaplan, Moll and Violante (2015). This paper is by far the most realistic model macroeconomics has ever got. Not very surprisingly, the conclusions that one can draw from reading it carefully is that fiscal policy is more effective than monetary policy…as original keynesians thought.

The authors show in a paper entitled “Monetary Policy according to HANK’ (Heterogenous Agents New Keynesian) that a model with heterogenous agents, liquidity constraints, liquid and illiquid assets and sticky prices implies that :

-Monetary policy is (about 10 times!!) less effective than in the usual representative agent model. The key intuition is that in those models – and in the actual economy – people respond much less to changes in the interest rate than it is traditionally assumed because many people are “optimally” Hand-to-Mouth, i.e. simply consuming their current income.

-Fiscal policy is more effective because many people in this economy are Non-Ricardian in the sense that the timing of the fiscal adjustment now matters for their saving decision. For example, a decrease in taxes today offset by an increase in taxes tomorrow would have a real effect on the economy because Non-Ricardian agents will consume part of the tax rebate – contrary to a Ricardian economy in which all the additional income would have been saved. 

The idea that liquidity constraints make both the economy less responsive to changes in the interest rates and more responsive to changes in fiscal policy is not radically new but the novelty is to put those ideas into a quantitative model that features a realistic distribution of income, assets and marginal propensities to consume and get more credible figures for the macroeconomic impact of policies.  

That we are back to the original beliefs of old keynesians should not make us conclude that economics has wasted its time over the past 30 years. The large and long detour the universal mind has done is not useless: in the HANK model, one has microfounded what was left ad hoc in the original keynesians model – mainly the hand-to-mouth and the non-ricardian behaviors. Those models are also far richer as they allow for multiple assets and the description of the distribution of households.

The paper can be found here:

http://scholar.princeton.edu/gkaplan/publications/monetary-Policy-According-Hank

First published: December 2015

The absolute and relative effectiveness of “monetary policy” and “fiscal policy” is a matter of intense debates. The prevailing views have evolved since the State and the Central Bank really started to use those instruments – 80 years ago.  

From the Great Depression to the 70’s

The Great Depression is a landmark decade as the States in developed countries – for the first time explicitly in their history – used new tools to regulate the state of the macroeconomic equilibrium such as wage increase and government spending. From the 1950’s to the 1970’s, the State explicitly led full-employment policies using both fiscal and monetary policy. 

On the academic/ideological side, keynesianist ideas are captured by the simple IS-LM framework: individuals consume a proportion of their current income Y and at first order independently from the interest rate. Investment is supposed to be a decreasing function of the interest rate. The equilibrium on the market for goods requires that that what is produced is either consumed by households or the State or invested, so that

Y=C+I+G

and finally the money market requires that money demand which is decreasing in the interest rate and increasing in output be equal to the exogenous money supply:

Regarding the relative effectiveness of the two instruments, the common wisdom was that the propensity to consume out of temporary increase in income was large, which implies a large macro multiplier from government spending, and that the elasticity of consumption and investment to the interest rate was very low. Overall the consensus was that fiscal policy was more effective than monetary policy to boost output in recession.

Friedman, Lucas and the rational expectations revolution

In the 1960 and 1970’s, Friedman criticized full-employment policies for their ineffectiveness. He mentioned the delays with which the State could react to the macroeconomic fluctuations and regarding the effectiveness of monetary policies he was supportive of a monetarist view of the economy according to which, in the long run, money is neutral and changes in monetary aggregates only translate into changes in the price level.

Lucas and the rational expectation expectations revolution that he led went further and has completely annihilated the regulationist view. Because people are assumed to be rational optimizers, forward-looking and to dislike variation in consumption over time, they smooth consumption over their life-time so that their marginal propensity to consume their current income is very low – about 4%, much lower than the one traditionally assumed in keynesian models.

Moreover the Ricardo-Barro equivalence result tells us that any change in the balance-sheet of the State is fully understood and internalized by private agent so that a decrease in taxes to boost aggregate demand is offset by an increase in saving by private agent who rationally anticipate future increases in taxes (the State is always satisfying its intertemporal budget constraint).

On the monetary policy side, the rational expectation assumption – as well as the flexible price assumption – implies that one cannot boost output by decreasing the interest rate or creating unexpected inflation. In a nutshell, the Phillips curve is a vertical line: the real side of the economy is unaffected by monetary variables.  

Overall this view makes both instrument ineffective to regulate output fluctuations. But according to this view this ineffectiveness is not a problem, because fluctuations are efficient and the results of optimal response of agents to aggregate productivity shocks!

The New Keynesian View

Three main assumptions are at the core of the new classical revolution: rational optimization, rational expectation and flexible prices. In the 1980-1990’s, many economsts dissatisfied with the neoclassical view brought back the idea of inefficient fluctations by relaxing the assumption of flexible prices and allowing for sticky prices. Because prices and wages are sticky, a decrease in aggregate demand led by a contractionary monetary policy has an effect in the short run because agent cannot straight-away decrease their price/wages.

This view justifies a role for monetary policy in the regulation of the macroeconomic fluctuations in the short run. Those models constitute the formal justification and the tools of most monetary authorities and policies in the world until today.

Monetary policy in these frameworks is, most of the time, a strictly better instrument than fiscal policies. This is because these models break neither from he Ricardian equivalence, nor from the very low marginal propensity to consume out of temporary increase in income. Fiscal cannot have a boosting effect, and it is mostly harmful because wasteful.

These views are changing as I will explain in a future blog post.

The Euro Area is not in deflation. Not yet, but not far. The reassuring news is that the EA is not alone to sink in a deflationary spiral. The US, the UK, Japan and the EA share the same inflation rate which has been on a downward trend for 5 years: the price level will probably not increase by more than 0.5% in 2015.

Although at a microlevel people tend to like a decrease in the price level as they feel richer, there is a general consensus in the economic profession that it leads to perverse and harmful macroeconomic dynamics that tend to depress activity and increase unemployment.

1. Unexpected deflation amounts to a  rise in the real rate of interest: it depresses demand

Deflation has a substitution effect: it gives an incentive for people to postpone consumption and to save. A decrease in inflation amounts to an increase in the interest rate: future good becomes cheaper. For those who are indebted, it gives them an incentive to reimburse rapidly their debt – i.e. to increase their saving – to avoid the increase in the real value of their debt. The implied additional aggregate saving is expected to depress the economy in the short-run.

It has a (likely) positive income effect: as the households are positive net creditors on aggregate, an unexpected increase in the real rate increases the value of their assets, which makes them richer and therefore consume more – provided consumption is a normal good, which is a reasonable assumption. However this effect is often expected to be small.

Deflation has a redistribution effect between debtors and creditors as it increases the value of nominal debt as we explained here. This is the Fisher channel. It means that unexpected deflation is an unexpected wealth transfers from debtors to creditors. If creditors have a lower propensity to consume than debtors, this redistribution of wealth depresses aggregate consumption and therefore aggregate demand as we explain here.

It also has a more subtle redistribution effect between people with different maturities exposure. Those who are long on the economy, i.e. those who have long term assets and short term liabilities will suffer from deflation/increase in the real interest rate as they now have to pay a higher interest rate on their debt and keep a relatively low interest rate on their long term asset. Symmetrically, those who have long liabilities and short term assets will benefit. If this distribution of maturities exposure is correlated with the marginal propensities to consume, then it can also have an aggregate effect [1].     

All these effects tend to depress aggregate consumption. We now turn to the firm side, then to the feedback effects and finally to the ZLB issue.

2. Deflation will likely raise real wages

A first order effect of deflation is the impact on real wages. For nominal wages exhibit downward rigidities, deflation implies a rise of real wages over time. As a result, the cost of labor increases: demand for labor is expected to decrease as well production, employment and profits. But the income of the employed population rises. 

All the effects coming from the rise in the real interest rate described on the consumer side play a similar role on the firm side. Firms will delay their investments and orders (substitution effect). Their balance sheet exposure will also impact their wealth: as an aggregate they are net debtor, so they will feel poorer, and there can be redistribution of wealth depending on their maturity exposure. All these effects plus the decrease in profits caused by the supply shock will depress investments, especially so if their access to financing is constrained by their net wealth.

3.  Vicious circles: investment accelerator and job uncertainty further depress demand.

Besides there are some vicious feedback effects: as a byproduct of the decrease in aggregate consumption, firms will also decrease their investments – as we know that the first determinant of investment is aggregate demand rather than the cost of capital – which further depresses aggregate demand.

The rise in unemployment caused by depressed aggregate demand and the supply shock further depresses demand as consumption is pushed down by the increase in unemployment and job uncertainty – although it is also pushed up by the rise in real wages, the aggregate effect is usually expected to be negative, as the propensities to consume correlate with job uncertainties.

4.  Zero Lower Bound

Finally and most importantly, the policy-makers are not well-equipped to navigate in a deflationary world (or even in a low-inflation environment): the Central Bank will find it difficult to boost the economy by decreasing interest rates as it is constrained by the Zero Lower Bound on the nominal interest rate – i. Indeed the latter implies that the monetary authority cannot cut the short term real interest rate – r – lower than the negative of the rate of inflation.

i >0 => r>-pi  

This has two potential consequences that the academic literature is now exploring. First because of the ZLB, the Central Bank might lose its ability to smooth the economic fluctuations and in particular recessions could become longer and deeper. We come back on this issue in a paper to come.

Second, it can lead to permanent underemployment is the natural rate of return is negative. Many people have argued that the so-called natural rate of interest – the real rate of interest that would guarantee full-employment – should now be negative [2].  But the Central Bank can no longer implement negative real rate if there is deflation. The ZLB, the low inflation/deflation environment together with a negative natural rate of interest implies that the economy may be permanently stuck in underemployment. We explain the very important “Secular Stagnation” issue in a paper to come.

Conclusion

Two important points. One should keep in mind is that there is no discontinuity between low inflation and deflation. None of the channels are particular to deflation, they were also playing when there has been a decrease in inflation in the past – like the quick disinflation in the 1980s – and it also plays in the reverse direction when inflation surprisingly increases. And there is no reason to expect non-linearities in the behavior of households and firms when it comes to deflation. As for the ZLB, as the current situation suggests, it may also bind in a low inflation environment. 

A second crucial point is “how afraid should we be about the contractionary forces?” It is an empirical question I still don’t have a clear answer for. To compare with recent history, many people would argue that the disinflation period of 1980s and the high real interest rates in the 1990s – partly because of the reunification – has had long term impact on unemployment in Europe. Besides high real wages are also often pointed out as responsible for the high unemployment rate in Europe. The different channels I have described suggests that these problems – and the associate underemployment situation – may only be expected to last if not worsen in the coming decade because of the fall in the inflation rate and in the natural rate of interest if we don’t do anything about it.    

[1] A. Auclert, http://www.princeton.edu/~aauclert/mp_redistribution.pdf

[2] https://research.stlouisfed.org/publications/economic-synopses/2015/06/05/liftoff-and-the-natural-rate-of-interest/

First published: October 2015

Some have invoked inflation as the goddess that would relieve us from the burden of high public debt. We have argued here that although theories exist showing mechanisms according to which public debt was a burden, the empirical evidence were mixed. It is therefore not perfectly clear why one might want to reduce public debt in the current context. Anyway, assume we are willing to reduce public debt.

As argued here, inflation can help the government reduce the real stock of debt. But how much inflation would be necessary today to stabilize or even reduce the total real value of public debt? This article does the simple calculation for the main developed countries.

We know from the same article that the level of inflation that stabilizes the ratio of debt over GDP is

Pi= d/B-g+i

Just for fun, let’s take the data and forecasts from the OECD and compute the required inflation rate necessary to stabilize the debt of GDP ratio in every OECD countries. The projection of g, i, d/B are based on averages over 2002-2016 (14y) or alternatively averages over 2015-2016 (2y). The results are reported in the table below. The data in the first four columns are averages over 2015-2016 except for inflation and computed required inflation for which we report the two values.

Comparing the actual and required inflation rate for the recent period, we conclude that Greece is in a worrying situation followed by Japan and the US who both lack one percentage point of inflation to stabilize debt – although current inflation for the US might be a bad estimate of long-run future inflation. If Japan is on an equilibrium path, I would be curious to know which one… One good news, the EA as a whole could afford deflation up to -1% thanks to their overall public surplus. But that the EA is “a whole” remains to be shown… 

Country	g	B/Y	Surplus/GDP	i	Pi (14 y)	Pi (2 y)	Required Pi (14y)	Required Inflation (2y)
France	1,37	122	-4,03	0,6615	1,21	0,393	3,44	0,69
Germany	1,94	74	-1,44	0,346	1,286	0,9955	0,93	-3,81
Greece	1,21	187	-7,58	9,3395	1,70	-0,227	9,66	7,67
Italy	1,05	158	-3,23	1,5645	1,81	0,45	3,28	-0,49
Japan	1,07	231	-6,31	0,3565	-0,50	0,6305	2,74	1,65
UK	2,35	113	-5,17	2,3965	2,18	0,8115	4,59	0,77
US	2,38	111	-6,48	2,7645	1,80	0,945	4,98	1,92
EA	1,75	109	-2,95	0,9665	1,56	0,6745	2,87	-0,98

First published: October 2015.

The fiscal theory is one of these theories that would leave my mother speechless. No way I can make it convincing. No way she will understand it. I can’t blame her, nobody understands it. Nobody? A little village is resisting, this village is governed by an old wise man, Chris Sims. The fiscal theory of the price level is a revolutionary theory, really.

There is the key to the mystery: while most of the economic tradition has attributed the determination of the price level to monetary policy, the fiscal theory tells you that when taxes and expenditures don’t respond to keep the government solvent, the price level is determined by the government’s ability to repay its debt. As a result, if the government is expected not to be able to meet its obligations, inflation will have to erode away part of the nominal value of the debt. In a nutshell, the price level adjusts so that the government remain solvent, or in other words, so that it meet its intertemporal budget constraint. Why does it “have to”? And what is the economic mechanism behind it?

Why does it ‘have to’? In Sims’ world, the government fully repays its debt, so that if it were to become insolvent, something in the economy would have to adjust to bring public debt back onto a sustainable path. This something could be taxes or expenditures, but by assumption they don’t react strongly enough. So prices and inflation have to adjust. That’s as simple as that.   

What is the economic mechanism? The key ingredient consists in assuming that people deeply believe the government will always remain solvent and will repay its debt – in other words it cannot default on its debt. We also assume the public knows more or less the amount of taxes that will be collected and the amount of expenditures in the future. Therefore the public knows how much it will be taxed and by how much the total amount of tax exceed the amount of debt. Imagine now a situation in which the government is accumulating too large a stock of debt to be repaid and that it is not going to increase taxes. Because the public believes debt will be repaid, and because it knows the future amount of tax, it will consider the part of the debt that cannot be repaid as net wealth, will feel richer and crucially will consume more. In a world of flexible prices, the latter will raise prices, thereby inflating away the debt.

Notice the schizophrenic thinking of consumers. They know the government is about to be insolvent because they know the future path of taxes as well as the current level of debt. Yet, they still buy the debt, believe it will be repaid, feel richer because of the gap between current assets and future liabilities and therefore consume more. And we dare call these people rational…

This is often the difficulty with macroeconomic models: equilibrium paths are exactly the sequence of states that makes compatible all the relationships that constitute the system. As for our example, the price increase is the only outcome that makes compatible the fact that the intertemporal budget constraint of the government holds and is believed to hold, that the government is insolvent and that it is not expecting to raise taxes in the future and that people anticipate future liabilities (taxes) rationally and compare it their current asset when choosing upon consumption. If prices didn’t increase, then one of these relationships would have to break down: for example the government could be forced to default or the consumer don’t believe anymore that the government budget constraint has to hold.