An SFC Analysis of a Shock to Export Capability

The UK's decision to quit the EU has left a lot of uncertainty over its future trading position.  It will probably be a long time before it becomes clear what kind of arrangements can be negotiated, but the concern is that the UK could suffer damage to export capability, with little reduction in its susceptibility to import penetration.

One immediate consequence of these concerns has been a sharp fall in sterling.  In principle, this should be good news for UK export capability, and there was a case to be made that sterling was overvalued before the referendum.  However, if this indeed reflects a weakened trade position, then assessing the overall impact is more tricky.

As such, I thought it would be interesting to use a stock-flow consistent model to look at how a shock to export capability and consequent exchange rate weakening might impact on overall activity. 

The model I have used here is essentially the same as one described in an earlier post.  It is purely conceptual - no attempt has been made to calibrate it to the UK.  The main difference compared to the earlier version is that I have expanded on the way inflation is determined.  The mechanism here is based on real wage targeting and follows that used in Godley & Lavoie (p 302), incorporating adaptive inflation expectations.  Pricing is a straightforward mark-up to unit labour costs.

Otherwise, the only real departure from what might be found in Godley and Lavoie is the use of forward looking expectations for the exchange rate.  This is useful here, where we want to look at the impact of a change in expectations of future trade prospects.

As usual, I have provided a full equation listing at the end of the post.

The graphs below show the effect on selected variables of a 5% fall in the base level of exports (i.e. before taking account of changes due to relative price).

 

 

One of the first things to note is that although this leads to a fall in actual real exports, there is a much greater fall in real imports.  This is due to the fall in the real exchange rate.  Exports become cheaper which mitigates the impact of the change in the base level of demand.  However, this worsening in the terms of trade means that the level of foreign earnings from exporting has fallen dramatically.  The amount of imports this buys has been significantly reduced.

In itself, the fact that import volumes have fallen by more than export volumes might be expected to provide a boost to domestic production.  However, the worsening of the terms of trade reduces the real value of domestic income, specifically when we measure by reference to the consumer price deflator rather than the GDP deflator.  Consider what happens to the real wage as shown in the graph.  The nominal wage deflated by the price of domestic output is a constant, because of the mark-up pricing.  But, because consumption also includes imports, when the real wage is deflated by the consumer price index it closely reflects changes in the real exchange rate.

This erosion in the value of real income reduces consumer expenditure and this is enough to more than outweigh the boost to output from reduced imports.

Although the scale of this depends on the parameters, the direction of change is a consequence of the stock-flow structure.  In a model like this, GDP tends towards a level which achieves a steady state level of government debt.  This is largely determined by the fiscal stance.  However, inflation will have an impact because it erodes the real value of the government debt.

The decline in the real exchange rate gives an inflationary impulse.  Eventually, this settles down to a higher level of inflation giving a reduced real return on domestic assets compared with overseas assets.  This is necessary because, when valued in the same currency, the fall in the real exchange rate has made the supply of domestic assets lower relative to the supply of foreign assets. (It is, of course, possible that seperate factors might also impact on the relative demand for these assets.  This is not considered here, but is obviously relevant in the context of the fallout from the Brexit vote.)

The higher level of inflation can be seen in graph.  This erodes government debt, requiring the state to run a slightly higher deficit to compensate.  This higher deficit implies lower tax revenues, which in turn implies a lower level of GDP.

Equation Listing

Equations (1) to (15) are as described in the previous model.

(1)        y =  d + g + x

(2)        d = ( C - m . p_f / e ) / p

(3)        C = α₁ . YD  + α₂ . ( Bd_-1 + Fd_-1 / e )

(4)        YD = y . p - T + r_-1 . BD_-1 + rf . Fd_-1 / e

(5)        T = τ .  ( y . p + r_-1 . Bd_-1 + rf . Fd_-1 / e )

(6)        m = d . µ . ( e . p / pf )^σ1

(7)        x = x₀ . ( e . p / pf )^σ2

(8)        V = YD - C + Bd_-1 + Fd_-1 / e

(9)        Fd = e . λ₁ . V. ( rrf / r )^κ1

(10)      Bw = λ₂ . Vf / e . ( rrd / rf )^κ2

(11)      B = B_-1 . ( 1 +r_-1 ) + g . p - T

(12)      Bd = V - Fd / e

(13)      Bw = B - Bd

(14)      rrd = ( 1 + rd ) . E[ e₊₁ ] / e - 1

(15)      rrf = ( 1 + rf ) . e / E[ e₊₁ ] - 1

Employment is proportional to output.

(16)      n = φ . y

The target real wage is based on the level of employment.

(17)      wrt = wrt₀ . ( n / n₀ )^δ

Nominal wage adjustment is based on inflation expectations and the gap between the target real wage and the previous actual real wage.

(18)      w = w_-1 . E[π] . ( wrt . pc_-1  / w_-1 )^ψ

Prices are a straight mark-up to unit labour costs.

(19)      p = β . w . n / y

Consumer prices are approximated as the deflator between nominal consumer spending and an aggregate volume measure.

(20)      pc = C / ( d + m )

Inflation expectations are adaptive.

(21)      E[π] = E[π]_-1 + ε . ( π_-1 - E[π]_-1 )

Where inflation is taken as the change in consumer prices (expressed as 1 plus the change).

(22)      π = pc / pc_-1

Variables

The variables are listed below.  Uppercase variables denote nominal values.

B	Domestic bonds
Bd	Domestic bonds held by domestic investors
Bw	Domestic bonds held by overseas investors
d	Domestic expenditure by the domestic private sector
e	Exchange rate (units of foreign currency per unit of domestic currency)
Fd	Overseas bonds held by domestic investors (in foreign currency terms)
g	Real government expenditure
m	Real imports
n	Employment
n0	Base level of employment
p	Price of domestic output
pc	Consumer price deflator
pf	Price of foreign output
r	Interest rate on domestic bonds
rf	Interest rate on foreign bonds
rrd	Expected return to foreign investors on domestic bonds
rrf	Expected return to domestic investors on foreign bonds
T	Taxes
V	Net financial wealth of domestic private sector
Vf	Financial wealth of rest of world (in foreign currency terms)
w	Nominal wage
wrt	Target real wage
wrt0	Base level of target real wage
x	Real exports
x0	Base level of real exports
y	Real output
YD	Disposable income of domestic private sector
π	Consumer price inflation

Policy variables are the level of government expenditure, the tax rate (τ) and the domestic interest rate.  Foreign variables (Vf, x₀ and rf) are taken as exogenous in accordance with the "small" economy assumption.  E[  ] denotes the expected value of a variable.  Expected values of exchange rates are set equal to actual outcomes, except for the period of the shock.

Helicopter Money and the Denial of the Importance of Sound Fiscal Policy

A recent article on VOX has prompted more commentary on Helicopter Money.

In principle, HM should appeal to anyone who believes that more stimulus is needed.  To those of a post-Keynesian mindset, HM is just expansionary fiscal policy; the fact that it is financed by money rather than bonds being of secondary importance.  But those that believe fiscal policy is impotent and it all comes down to monetary policy can view HM as being another monetary tool.

Given that it should appeal to both points of view, it's perhaps odd that it should cause so much argument.  Yet, as someone whose perspective tends to fall in the former camp, I find myself strangely irritated by the approach of many in the latter.  Where additional stimulus is needed, I think debt-financed fiscal expansion is best, but I'd still see HM as a pretty good substitute.  So what's the problem?

I think the issue is that portraying HM as monetary policy looks to me like a pretence and worse, it looks like a rather desperate attempt to defend the idea that monetary policy is sufficient to regulate demand in the economy, regardless of what fiscal policy is doing.  In my opinion, if we think we need HM, that  is an indication that we have got fiscal policy wrong.  Furthermore, it is an indication that when we get fiscal policy wrong, regular monetary policy is not capable of providing anything other than a temporary fix.  Monetary policy enthusiasts like to think of the zero lower bound as a special case where regular monetary policy might be insufficient.  However, they fail to acknowledge that if the fiscal stance is misjudged, attempts by monetary policy to compensate will inevitably end up at the zero lower bound anyway (see here).

So what I don't like about this debate is the way that it is used to avoid recognising how important fiscal policy is.  Fiscal policy is, on the whole, an unwieldy tool for day-to-day management, but it is critical that it is used with a view to its impact on demand, not to managing the public debt.  If this is not the case, monetary policy is stuffed.  It might provide a temporary fix, but only through stoking private sector debt bubbles.  The notion that HM may now be beneficial should be a recognition of this, not an attempt to pretend that monetary policy is still what it's all about.

The Importance of Manufacturing: Productivity Growth or Trade?

In a recent article, Ha-Joon Chang highlights the decline of manufacturing as a source of stagnating living standards in the UK.  I would agree that Britain's manufacturing decline is a cause for concern, but what interested me in the article was the discussion of the role of productivity growth.

The basic argument here is: 1) there is greater scope for productivity growth in manufacturing than in services; 2) greater concentration of economic production in activities with high productivity growth means higher aggregate productivity growth; 3) the higher a country's overall productivity growth, the higher its per capita real income growth.  In fact, for a small open economy like the UK, I think the latter point is a bit more complicated than that.

To help see why, imagine that you were about to choose your future career and had the choice between going to work on a production line making TVs - an area with scope for high future productivity growth - or becoming a hairdresser - an area with little scope for productivity growth.  Now, obviously, there are lots of considerations here.  However, the argument that you could expect to see much higher personal income growth as a production line worker than as a hairdresser because of the productivity issue should sound a little suspect.

What in fact is likely to happen is that, over time, TVs become cheaper relative to haircuts.  The productivity growth in TV production benefits both the production line worker and the hairdresser.  Exactly how much each benefits depends on how the terms of trade develop between the two which depends on various demand and supply elasticities.

In a world with significant global trade, the same point applies to whole economies.  Productivity gains in one country are to the benefit of all countries, even those which are themselves seeing no productivity growth.  Exactly which countries benefit depends on their trading positions - the elasticities in the goods they export and import.

Now, this does not mean that the UK's decline in manufacturing does not matter.  It does matter, but the point is that it matters as much because of the role of manufacturing in providing exports and import substitutes as it does in providing productivity growth.  To benefit from global productivity growth, a country has to be well positioned in traded markets.  Cutting hair is a useful activity, but has limited export potential.  Of course some services can act as exports and, in principle, it is possible for a country which exports the right services to see substantial growth in living standards without any material domestic productivity growth.  But this is probably not an option for the UK.

Why the Inter-temporal Government Budget Constraint Cuts Both Ways

There are some heterodox economists who get very worked up over the notion of the inter-temporal government budget constraint (IGBC).  In my opinion, this is unjustified.  For a couple of reasons.

In the first place, where the constraint does hold, it is in itself little more than an accounting identity and not a limit on policy as we normally understand it.  If there is any kind of non-accounting constraint, it arises for other reasons such as resource constraints or the imposition of other objectives.  Secondly (and I rarely see this mentioned) the IGBC sometimes imposes a strong imperative for the use of active fiscal policy.

The IGBC says that the real discounted value of future primary surpluses is equal to the real value of current outstanding debt (where discounting takes place at the real effective rate of interest on government debt).

With regard to the first point, we can easily see that this condition will hold in a typical SFC model[1].  Such models settle down into a steady state where the real value of debt remains constant, with a primary surplus exactly offsetting the interest charge on outstanding debt.  This is a position which meets the IGBC, so the IGBC must hold for each preceding period as well.

In the typical SFC model, the policy instruments are the level of real government expenditure, the rate of tax and the nominal rate of interest.  The IGBC does not itself limit the choice of these variables.  This is because the models allow for the level of real output and/or the rate of inflation to be determined, with the mix depending on what is assumed about Phillips curve relationships.  Given the policy variables, both of these are relevant for the IGBC.  The level of output determines the tax take and hence the level of primary surpluses.  The level of inflation impacts on the real discount rate.

The upshot of this is that all the IGBC does in this type of model is limit the possible sets of solutions for output and inflation.

The assumptions of different types of model may combine to place more of a constraint on policy.  For a start, if taxes are assumed to be lump sum, then there is no scope for primary surpluses to be determined endogenously.  Even without lump sum taxes, the assumption that real output is supply side determined in the long run (a common, if questionable, assumption) will limit the endogeneity of the tax take.   Additionally, if the model assumptions incorporate a unique natural rate of interest, then it may be that the discount rate used for the IGBC must also be tightly constrained (although this does depend on what is assumed about how monetary policy is conducted).  A typical DSGE model will tend to incorporate these sorts of assumptions and will therefore impose a greater constraint on fiscal policy.

However, this constraint cuts both ways.  The usual message is to say that, given the exogenous output level and natural rate of interest, there is no scope for increased government expenditure now without requiring correspondingly higher taxes later.  But this is not in fact true in all circumstances and, in some cases, expansionary fiscal policy is exactly what is required.

Specifically, we can consider what happens if there is a permanent fall in the natural rate of interest (or at least a fall that everyone expects to be permanent), something that in Keynesian terms we might interpret as an increased propensity to save.  The DSGE response required of the central bank is a reduction in actual interest rates in an attempt to bring these in line with the lower natural rate.

This has consequences within the IGBC.  As the current level of debt is given, then a reduction in the long-term discount rate requires a reduction in future real primary surpluses.  If we assume that long-term  surpluses are to remain the same, then what is required is a short-term period of expansionary fiscal policy.

The IGBC plus the other assumptions of DSGE dictate that something  like this is required.  Monetary policy alone is inadequate.  This raises the question of what happens if the government declines to respond and instead decides to pursue a policy of austerity.  In fact, the only solution in the model [2] involves a period of deflation with the nominal interest rate hitting the zero lower bound.  This gives a period of higher real interest rates which increase the real value of outstanding government debt until it is equal to the future surpluses discounted at the new lower rate.

New Keynesian economists will generally recognise the need for fiscal policy when monetary policy is constrained by the zero lower bound.  They are usually only thinking of scenarios where there are temporary drops in the natural rate of interest that appears in their models.  But there are other possibilities, such as a permanent fall in the natural rate, that monetary policy can never deal with alone even unconstrained by the lower bound.  These situations require a fiscal policy response and the IGBC shows us why.

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[1] Not necessarily in growth models which may be dynamically inefficient.

[2] That I can see, at any rate, but I'd be interested if anyone knows differently.