La théorie du stimulus fiscal: comment le stimulus financé par la dette affectera-t-il l'avenir ?

The Theory of the Fiscal Stimulus: How will a Debt-financed Stimulus affect the Future?

This paper takes a close look at the Keynesian theory underlying the policy of fiscal stimulus being undertaken or considered in many countries, led by the United States. A central question is whether a debt-financed fiscal stimulus now must adversely affect future taxpayers owing to the debt burden being created. There are many interesting issues considered, for example, the role of automatic stabilizers, and the basis for Keynes’ paradox of thrift. The model used is for a single country with a floating exchange rate. It is assumed that, for various reasons, monetary policy cannot eliminate high unemployment and a resultant output gap. In fact, there is a market failure, which government action needs to compensate for, at least temporarily.

I

The Main Story

We start with an output gap. Actual output is below potential output. The latter can be defined as maximum output consistent with low inflation. Aggregate demand is insufficient. There are various possible reasons for this, one being that there is a credit crisis of the kind that initiated the current world output gap, and that prevents monetary policy on its own from eliminating it. The aim of the fiscal stimulus is to reduce or eliminate the output gap.

I am assuming – realistically for the United States and for Britain in 2009 – that the average levels of domestic prices of goods and services and of nominal wages are (more or less) constant. I am also assuming that the interest rate is at a very low level and cannot be lowered any further. This has also been the case for the US and Britain in 2009.

The Stimulus and the Leakages

Let us assume that the fiscal stimulus consists of government expenditure on infrastructure and similar capital works. These public investments are of two kinds, namely I1 and I2. I1 has a significant positive marginal social return. By contrast, I2 consists of building “bridges to nowhere” and other useless expenditure, thus having a zero rate of return. The latter are justified by their employment creating or vote getting potential.

The fiscal stimulus creates a budget deficit that is additional to any existing deficit or surplus. We are concerned here purely with the effects of the fiscal stimulus and not the existing situation, except that the latter yielded an output gap. The new deficit has to be financed, and this will be achieved by selling government bonds. But who will buy them? I shall come to that important issue below.

Next we come to the Keynesian multiplier. The stimulus will increase demand for domestic private sector output, and so raise incomes by Y1. This will lead to further spending on domestic goods, and so on. This is a textbook story. At each stage there are leakages from the income stream, namely into taxation, into savings and into imports. What is left after the leakages leads to further spending on domestic goods and hence a further rise in Y, and hence a further decline in the output gap. In the final equilibrium (as any good textbook explains) the sum of the leakages – namely the sum of all the increases in tax revenue (dT), savings (dS) and imports (dM) – will be equal to the original “injection” into the income stream, namely the new budget deficit caused by the fiscal stimulus (dF).

dF = dT + dS + dM

The additional tax revenue that is raised will reduce the financing need of the original stimulus, yielding the “net” stimulus. This tax revenue can thus be subtracted from both sides of the equation, so that the net stimulus is equal to the sum of additional saving and of additional imports.

dF – dT = dS + dM

We now come to an assumption and an argument that is crucial – and not unrealistic – at this stage. I assume that the country has a market-determined floating exchange rate, that net international capital flows as a result of the stimulus are zero, and that, therefore, the exchange rate will ensure that the current account balance stays in its original position. Any increase in imports must then lead to depreciation of the exchange rate, which will bring about a rise in exports, as well as some reversal of the rise in imports, so that there is no change in net exports. It follows that any reduction in demand for domestic goods caused by a leakage into imports will be offset by an increase in demand for domestic goods caused by a rise in exports. At every stage of the multiplier process the exchange rate will depreciate because of the rise in imports, and thus exports will also increase. These two effects together – the rise in imports and the rise in exports – will then have a zero effect on the multiplier. We thus get the simple relationship

dF – dT = dS

where dF is the initial stimulus, dT is the increase in tax revenue, so that the LHS is the net stimulus that has to be financed, while dS is the total increase in savings. The savings assumption is the standard Keynesian one that there is a positive marginal propensity to save. It does not have to be constant, but it must be positive and (at this stage of the analysis) below 100%. Various alternative savings assumptions will be considered in Part II of this paper. Here it might be noted that if the marginal propensity to save were zero the multiplier would be infinite: in that case demand would implausibly expand to an unlimited extent as a result of an initial stimulus.

The Financial Flows

So far there has been an increase in public investment but no change in private investment. The increase in private demand has gone wholly into private consumption. Together the rise in public investment and the rise in private consumption have absorbed the increase in output brought about by the fiscal stimulus.

Let us now consider the financial flows. When the government sells the bonds that finance the fiscal stimulus the buyers could be on the world market – if there were international capital mobility – they could be domestic savers, or they could be the central bank. As for the savers, they could buy the government’s bonds, or buy foreign bonds or equities. They could also buy private domestic bonds, though these will already be held somewhere in the private sector. The main conclusions at this stage are two. (1) Because of the budget deficit resulting from the net fiscal stimulus the taxpayers will acquire a liability in the form of having eventually to redeem the bonds that were issued to finance the deficit. (2) Private savers will acquire assets in the form of bonds or equities as a result of the increases

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