Identities Do Not Imply Equilibrium

In macroeconomics, it is often useful to start from accounting identities between aggregate magnitudes. Since identities are true by definition, they offer a good way to organize concepts. However, it is important to keep in mind that identities in themselves say nothing about causation. In order to build a theory on the basis of accounting identities, it is necessary to make behavioral assumptions. Unlike the identities themselves, these behavioral assumptions are of course contestable.

Consider, initially, a simple two-sector closed-economy model with no government or external sector. For such an economy, actual saving, S, equals actual investment, I:

S = I

This is an identity, true by definition. However, it does not necessarily imply an equilibrium situation. Macroeconomic equilibrium can be defined as a situation in which plans are realized. In the simple two-sector model, equilibrium requires that desired saving, Sd, be equal to desired investment, Id:

Sd = Id

The significance of desires (or plans) is that when they go unrealized there will be disequilibrium and an impetus for changed behavior. Aggregate demand, AD, will differ from output or aggregate supply, AS, and firms will experience unanticipated variations in inventory levels. These unexpected changes in inventories are counted in national accounting as part of actual investment. However, the changes were not intended, so can be thought of as unintended investment, Iu. In a disequilibrium situation, the excess demand or excess supply will equal unintended investment by definition: Iu = AS – AD.

Summarizing the situation:

Excess supply implies Iu > 0; excess demand implies Iu < 0.

Likewise, Iu > 0 implies I > Id; Iu < 0 implies I < Id.

Equilibrium requires AS – AD = 0, which occurs when Iu = 0 and I = Id.

Equilibrium also requires actual saving to equal desired saving (S = Sd). Otherwise, households will be motivated to alter spending and saving behavior.

To theorize further it is necessary to make behavioral assumptions. For example, it is relevant to ask how firms will respond to unanticipated variations in inventories.

Economists influenced by Keynes or Kalecki assume that firms will respond to a situation of excess supply in which they experience an unexpected buildup in inventories mainly by cutting back production. There might also be price reductions but output adjustments are assumed to dominate. Modern day neoclassicals generally take the same view in the short run, although they suppose that the price mechanism would restore full-employment output in the long run if it wasn’t for various so-called ‘rigidities’ in the system such as minimum-wage laws, unions or monopolistic firms.

In the case of excess demand and an unanticipated dwindling of inventory stocks, the response of firms is assumed by Keynes and Kalecki influenced economists to depend on whether there is excess capacity. If there is, firms are thought to expand output to meet the stronger demand. This includes an increase in desired investment to restore inventories to the preferred level. The extra desired investment will cause a multiplied increase in income. As a result, desired saving will also rise. Income will continue to adjust until desired saving is equal to desired investment. As output nears full employment, there may also be some price effects but the output response is assumed to dominate. It is only at full capacity that ‘pure inflation’ could occur, a situation in which only prices could rise in response to further increases in demand. Modern day neoclassicals also generally accept this logic in the short run.

It is behavioral assumptions such as these that are at the heart of disagreements among macroeconomists. When Keynesian and Kaleckian economists hold that investment determines saving through income adjustments, they are not talking about actual investment and saving, but desires. They are referring to the kind of multiplier process described in the previous paragraph in which planned saving adjusts passively to planned investment through income adjustments. Likewise, when neoclassicals maintain that in the long run investment adjusts to saving via interest-rate adjustments, they are referring to desires, not actual saving and investment.

Similar logic applies to more elaborate models. For example, in a three-sector closed economy with government but no external sector the following identity holds:

(G – T) = (S – I)

On the left-hand side, G is government spending and T is tax revenue. The difference between them is the government (or fiscal) deficit. In words the identity says:

Government Deficit = Net Private Saving

This identity refers to actual net private saving and says nothing in itself about desires, equilibrium or causation.

Equilibrium in this model requires that desired net private saving equals the government deficit. Otherwise, even though the identity holds, there will be impetus for behavioral change.

As in the two-sector model, any disequilibrium is captured in the definition of unintended investment and unintended saving. If desired net private saving, (I – S)d, exceeds the fiscal deficit, economists assuming Keynesian or Kaleckian causation suppose that there will be negative income adjustments. This is argued to occur because the private sector is attempting to hit a net saving target that is incompatible with the fiscal deficit. Faced with weak demand conditions, firms will cut back production (and desired inventory investment), impacting negatively on income and the government’s tax revenues. This will be exacerbated if households attempt to maintain their level of planned saving alongside weak demand. This is possible in a model with more than two sectors because it is now Sd + T that adjusts passively to Id + G rather than simply Sd adjusting to Id. If the private sector resists the government’s fiscal stance by attempting to maintain high net private saving, the fiscal balance will endogenously move further into deficit. The result will be unemployment and a “bad deficit” (one caused endogenously by weak economy activity) rather than a “good deficit” (one that sustains demand and income).

Conversely, if the fiscal deficit exceeds desired net private saving, the effects will depend on whether there is excess capacity. If there is, there will be an expansion of output and income in response to stronger private spending. If there isn’t, pure inflation will occur.

Again, most modern day neoclassicals would expect similar in the short run even if they don’t couch the argument in terms of the sectoral balances.

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