Understanding Household Spending with Stocks and Flows

Household expenditure is the largest component of GDP, so understanding why and how it varies is crucial to understanding recessions.

Mainstream economics tends to look to the real interest rate and a household rate of time preference as the central explanation for such variations.  Stock flow models tend to place greater emphasis on the levels of financial stocks. 

The idea here is that household expenditure is driven by a desire to influence various ratios between financial stocks and the level of income.  Stock-flow models often describe certain target ratios, sometimes called stock-flow norms.   Household expenditure is equal to income[1] less the net acquisition of net financial assets.  If we can explain the acquisition and disposal of financial assets and liabilities in terms of a desire to move towards stock-flow norms, then we can explain why household expenditure might vary.

Looking at the UK, it is useful to divide household net financial assets into the following:

1. Pensions and life insurance

2. Other financial assets

3. Debt (i.e. liabilities of households)

The graph below shows the level of each of these relative to household disposal income.

I'll say something about each of these in turn, dealing first with pensions, then debt, then other financial assets.

Pensions

It seems likely that there should be some kind of target ratio between pension assets and income.  On the whole, people want to achieve a balance between what they can spend during their working years and what they can spend in retirement.  This means they have to save a certain amount whilst working to be run down in later life. This process is naturally going to generate a stable stock-flow ratio.

In fact, we don't need to even postulate that people have a given stock-flow ratio in mind.  Much of the time, the amount of pension contributions will be in a fixed relationship to wage levels, and amounts paid as pensions will be related to the stock level of pension funds.  Institutional arrangements including the tax system influence this.  This process will give rise to a stock-flow norm, even if no-one has such a ratio in mind.

If we look at the graph, however, we can see a clear upward trend in the ratio of pension assets to income.  There are various reasons for this.  The most important is rising life expectancy.  This has reduced the amount of pension income that a given stock of pension assets will buy.  Achieving a similar balance between working and retirement consumption therefore means building a greater stock of pension assets during the working lifetime.

The decline in the yields on government securities has a similar effect.  Pension annuities are priced off fixed income yields, so as these have come down, pension funds need to become larger.

The actual size of pension funds is also impacted by the returns on those funds including stock market gains.  So we should expect to see the actual ratio rising when the stock market is doing well.

Debt

The ratio of debt to income shows less fluctuations than the two asset classes, because it is not subject to the sort of variations in value due to market movements.

With debt levels, it also seems likely that that stock-flow ratios are important.  In particular, credit constraints will tend to limit the amount that can be borrowed relative to income.  The growth in debt levels between around 1999 and 2008 reflect a general relaxation of credit criteria. 

Maximum acceptable debt levels are often assessed by comparing the interest expense to income.  The upper bound to the debt to income ratio is therefore likely to be a function of interest rates to some extent.  At the current low level of rates, interest expense is at its lowest level of this period (see chart below), which partly explains why the debt ratio remains high despite tightening credit conditions.

Credit constraints may impose a cap on this stock-flow ratio, but that is not the same as saying this is a target ratio.  It could be that households prefer a debt ratio below that dictated by credit conditions.  However, it seems likely that credit conditions provide the binding constraint in most cases for new borrowers, and this element is a key driver of the stock-flow ratio.

Other Assets

Whilst there are good reasons for thinking that stock-flow considerations play an important role in determining accumulation of pensions and debt, it is less clear in the case of other assets.  Typical stock-flow consistent models tend to assume that there is a target ratio for holdings of other assets, but I'm not sure this is necessarily the case. 

With pensions and debt, we should be able to predict what sort of target ratios we expect to see from a knowledge of things like life patterns, the tax structures, regulatory issues and so on.  No such considerations determine the holding of other assets, so it's quite possible that any target ratio could develop over time, including in response to changes in the actual.

However, looking at the first graph, the ratio of other assets has actually changed the least over time.  Apart from an apparent slight upward trend, two factors appear to drive the variations.

1. As with pensions assets, the level of other financial assets is subject to variations in asset valuations such as stock market movements.

2. The periods of strong growth in debt levels seems to be associated with an increase in holdings of other financial assets.  There are reasons why we might expect this to be the case.  The largest part of debt is for house purchase, and an increase in debt reflects a greater volume of house purchase and/or higher house prices.  This means that those households receiving property sales proceeds and not repaying debt (otherwise overall debt levels are not increasing) are receiving greater windfalls.  This type of cash receipt, does not get spend all at once, if it gets spend at all, and it therefore adds to the accumulation  of deposits, which makes up the largest part of this catergory of assets.

Once these elements are taken into account, it does appear that there is some reversion-to-norm taking place in this stock-flow ratio.  When the actual ratio is increased or decreased by one of these factors, accumulation reacts to bring it back to a more "normal" level.  It is remains an open question, however, how stable this "normal" level is over time.

Conclusion

 

An analysis of household stock-flow ratios provides a useful insight on what drives changes in household spending.  This is particularly so when we apply a certain level of disaggregation, rather than looking at net finacial assets as a single whole.  Often, we can relate the trends to things that we know are going on.  This approach is likely to be more useful than trying to relate spending to variations in the real interest rate.

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[1] Household disposable income is usually calculated after certain pension contributions and pension income.  To align more closely with the theoretical issues, we need here to think about household income before these items.

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.