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.

Sticky Prices, Unexpected Inflation and Ricardian Equivalence

An interesting point came up in my recent discussion with Stephen Williamson (referred to in my last post, but there's no need to read that to understand what I'm going to say here.)  It is to do with the interpretation of Ricardian Equivalence, when there are unexpected policy changes.  I actually thought the point was obvious, but from Williamson's response I am left thinking that it's either not obvious or I'm wrong.  If anyone wishes to enlighten me either way, I'd be grateful.

To look at this, I need to make some of the standard assumptions for Ricardian Equivalence to apply, so I'm going to assume homogenous households with infinite horizons and no issues like liquidity constraints.  Under this assumption, the long-run government budget constraint is binding.  This says that the present value of taxes cannot be less than the value of current debt plus the present value of government spending.

The usual way to interpret this is to suppose that any change in tax now must be offset by a change in tax at some future time.  So, for example, if there is a one-off tax reduction today, then this will need to be financed by issuing debt.  That additional debt, plus the interest, must be repaid at some point and this requires future taxes.

This analysis is usually set out in real (non-monetary) terms, with bonds paying a real rate of interest.  In this case, there is no way other than a future tax increase for the government budget constraint to be met.

However, in reality, public debt is generally issued in nominal terms, paying a nominal rate of interest.  This means that the actual rate of return will vary from the expected rate of return if there is unexpected inflation.  What matters for the government's budget constraint is the actual rate of return.

So, consider a case where the government makes an unexpected tax cut.  One possibility we have to consider is that this will lead to a higher inflation than was expected before the tax cut was known about.  The result would be that the actual rate of return on outstanding government debt is lower than previously expected.  This represents a kind of unexpected inflation tax on bondholders, which must be factored into the government budget constraint.  The need for future taxes is correspondingly lower.

In a model with perfectly flexible prices, we might have a position where an immediate jump in the price level produces an inflation tax that completely offsets the impact of the tax reduction.  In this case, the tax reduction would have no impact, simply because it would make no net difference to households' real position.  The Ricardian Equivalence result holds, albeit somewhat trivially.

With sticky prices, it's a different matter.  Any inflation shock that occurs in response to a tax reduction must be correlated with inflation in subsequent periods, whether under a forward-looking or backward-looking relationship.  So, if a current tax reduction is to be recouped through an inflation tax, that must take place over time.  And, throughout the period of higher inflation, expected real interest rates are higher, which will impact on the pattern of household spending.  So, in this case, the choice between taxation or bond issuance does make a difference.

It needs to be stressed that this is fully consistent with rational expectations, provided we are considering an unexpected change in taxation (or equivalently a change in actual taxation, following a known rule, but in response to some other unexpected event).  The standard New Keynesian Phillips curve has current inflation as a function of expected inflation.  We can equate expected inflation to the actual outcome for every point in time where there are no unexpected tax policy changes.  But, if a new policy is announced we have to allow for expectations to be revised accordingly.

In a standard New Keynesian model, therefore, we seem to have two options as to how an unexpected tax reduction might play out:

We can assume that people do not revise their inflation expectations and that they believe that the government will increase taxes again in the future to pay off (with interest) the debt incurred to finance the tax cut.  In this case, the model-consistent expectation solution is that there is no inflation shock, and indeed the only way the government budget constraint can be met is by increased future taxes.

Alternatively, we can assume that people do not believe that the government will raise future taxes and that they revise their inflation expectations to take this into account.  In this case, the model-consistent expectation solution is an (unexpected) jump in inflation, followed by a steady fall in inflation back to its baseline level.  This inflation erodes the value of outstanding debt and the government budget constraint is indeed met without any future taxes.

If we were using a non-monetary model, we would have no choice but to go the first route, because there is no unexpected inflation.  But once we think in terms of monetary debts, there is no good reason for saying that the former should hold rather than the latter.  The first gives us the classic Ricardian Equivalence result; the second does not.

The path of output, inflation and (nominal) interest rate in this second case would be something like that shown below (model details at end of post).  The shock occurs when the announcement is made.  It makes no difference whether the tax reduction is actually applied now or in the future.  In that sense, the result is still Ricardian.

A key point here is we are relying on the fact that, under the government budget constraint, a current tax reduction can be made whole either by an increase in future taxes or by a change in the rate at which future taxes are discounted.  The usual approach is to assume that there needs to be a rise in futures taxes.  This leads to a self-fulfilling loop:

a) Because there is an offsetting rise in future taxes, there is no change in household spending and real interest rates remain unchanged.

b) Because real interest rates remain unchanged, there needs to be a increase in future taxes to meet the government budget constraint.

The trick is to recognise that when we have expectation shocks and sticky prices, there is an alternative:

a) Because there is no offsetting rise in future taxes, households spend more currently, causing a temporary, but drawn out, reduction in real interest rates.

b) Because of the reduction in future real interest rates, the present value of future taxes is increased and so there is no need for additional taxes to meet the government budget constraint.

In my view, this is actually quite an important point of departure between mainstream and more heterodox approaches.  If we come at this from a mindset that sees the government budget constraint as something that dictates policy, rather than simply an accounting identity, then we might naturally assume the former.  But, if we take the view that the government will just do what it thinks appropriate from time to time and we just need to work out how the economy responds, then we might be more inclined to the latter.  And, in my opinion, the latter is more plausible.

Model

The model I've used here is a standard three equation NK model with an additional equation showing the evolution of the government debt and the further condition that the level of debt is bounded (this is equivalent to the government budget constraint). 

(1)          y_t = E[y_t+1] . ( β . i_t+1 / E[π_t+1] )^-σ

(2)          π_t = E[π_t+1]^β . y_t^κ

(3)          i_t+1 = i* + φ_π . ( E[π_t+1] - 1 ) + φ_y . ( E[y_t+1] - 1 )

(4)          b_t = b_{t-1 .} i_t / π_t - τ_t

where y is output, π is inflation (both normalised to 1), i is the nominal interest rate, τ is tax and b is the real value of government debt.  Parameter values used are β = 0.97, σ = 1, κ = 0.2, φ_π = 0.5, φ_y = 0.4 and i* is set at 1/β.  The baseline level of tax is 0.2 and the shock is a one-off reduction by 0.05.

The usual approach would be to take equation (4) and the boundary condition simply to place a constraint on the level of taxes, in which case it has no bearing on the other variables.  What we are doing here is allowing taxes to be freely set, letting expectations adjust when a change in tax policy is announced and using equation (4), plus the boundary condition, to pin those expectations down.