# Keynesian Model

## Keynes's Basic Toolkit of Fiscal Policy

Since its publication in 1936, John Maynard Keynes’s General Theory of Employment, Interest and Money has provided an essential conceptual framework for analyzing the influence of fiscal policy Opens in new window on aggregate demand Opens in new window.

The standard Keynesian model Opens in new window assumes price stickiness in the short term. The supply of goods and services is supposed to be elastic, and the level of aggregate demand determines output. When demand is insufficient, this results in the underemployment of labor and capital.

A fundamental role of macroeconomic policy—be it fiscal Opens in new window or monetary Opens in new window—is to ensure that aggregate demand is such that the economy remains at or close a level corresponding to equilibrium employment.

In response to a negative demand shock, this can be done by increasing public spending Opens in new window or by cutting taxes.

This framework rests on two key assumptions:

that because of price stickiness, the macroeconomic balance is not reached through changes in prices and that the response of private spending does not offset the rise in public spending.

In the elementary Keynesian model, nominal rigidity and the income-demand relationship are simply postulated. An exogenous increase in aggregate demand (a demand shock) results in an increase in the level of output. The ratio between output variation and the initial exogenous variation of aggregate demand is called the Keynesian multiplier

A Primer on the Keynesian Multiplier

Suppose that household consumption C is a linear function of current income Y:
C = ɑY + b with ɑ,b >0       (eqn. 1)

The parameter ɑ is the marginal propensity to consume (meaning that out of one additional euro of disposable income, the representative household spends ɑ and saves 1 - ɑ).

Let us assume, for example, that ɑ = 0.8, so that households consume 80% of any additional unit of income, and that households own companies, so that any profit is treated by them as income.

Suppose that supply is perfectly elastic, so that output adjusts to the level of aggregate demand at constant prices. The closed economy product market equilibrium is given by:
Y = C + Ī + G       (eqn. 2)

where Ī is aggregate investment and G is government demand. Both are assumed to be exogenous.

Suppose the government increases by one unit public spending while keeping taxes constant. This will initially lift output, and thus income distributed to households, by one euro.

Out of this additional unit, 80 cents will be consumed and will lift output — thus disposable income — further. At the end of the process, the total increase in output is:
1 + ɑ + ɑ2 + ɑ3 + … = 1 + 0.8 + 0.8 X 0.8 + 0.83 + …
= 1/(1 – ɑ) = 1/(1 – 0.8) = 5.

The same result can be obtained by solving the two-equation system directly, leading to:
Y =   ∆G
1 – ɑ       (eqn. 3)

In this example, the multiplier is excessively large, and fiscal policy is therefore implausibly powerful. There are, however, many factors that may lower the multiplier:

First, not all the additional income accrues to consumers because a fraction of it is taxed away by the government. So Equation (eqn. 1) needs to be rewritten C = ɑ (1–t)Y + b, where t is the tax rate. The multiplier becomes 1/[1 – ɑ (1 – t)].

Second, in an open economy, an additional euro of disposable income leads households to consume more of both domestic and imported products and firms to import more intermediate goods. Assuming that the marginal propensity to import is m (meaning that an additional unit of income will lead to m units of imports), the Keynesian multiplier becomes 1/ 1 – ɑ[(1 – t ) + m].

Third, the assumption of complete price rigidity is extreme. If prices adjust upward, part of the increase in demand does not result in an increase of the volume of products consumed but in an increase in their price. This especially applies over time, as prices adjust gradually.

Fourth, the central bank may respond to an increased demand for products by an increase in the interest rate. In this case investment (from firms) declines because firms compare the yield of investment projects with the financing cost or with the return to financial investments.

A crowding-out effect Opens in new window appears: part of the increase in public demand results in lower private investment (due to the interest rate increase, private investment is crowded out by public demand). Conversely, an interest rate reduction by the central bank in response to a public spending cut partially offsets its negative impact — unless there is no room for cutting the policy rate because it has already reached the “zero lower bound”.

All these factors weaken the impact of fiscal expansion on aggregate demand and income.

The Keynesian framework can be represented within the aggregate supply, aggregate demand (AS – AD) model. The price stickiness assumption implies that the aggregate supply (AS) curve is upward sloping but not vertical in the short run.

In the elementary model, the slope of AS is low, so that production can increase without having a major impact on prices. The aggregate demand curve is downward-sloping due to the negative impact of inflation on demand for goods and services, either through a wealth effect or because of the impact of a rise of the interest rate engineered by the central bank.

A fiscal expansion (either a rise in public spending or an exogenous cut in taxes) results in the demand curve moving to the right: production increases. If the slope of the supply curve is low, the adjustment takes place through a variation in the level of output (movement of E1 to E2 in Figure I).

Here, we have simply postulated the AD curve that summarizes the demand side of the economy. It can be derived from the IS-LM model introduced by Hicks (1937) and Hansen (1953) to formalize Keynes’s General Theory Opens in new window.

This model, which has been widely used ever since, consists of two curves that relate output and the interest rate: the IS curve describes the product market equilibrium and the LM curve the money market equilibrium, both for a given product price (Figure I):

• The IS curve gives the combination of output and interest rate that results in a product market equilibrium. It is downward-sloping since a higher interest rate results in a lower demand for products;
• For a given money supply, the LM curve gives the combination of output and interest rate that results in money market equilibrium.

With a fixed money supply, the positive relationship between output and the interest rate relies on the demand for money, which is supposed to be an increasing function of output (as output grows, more money is needed for transactions) and a decreasing function of the interest rate (as the interest rate grows, private agents prefer to hold interest-bearing assets rather than cash). Figure I Effect of a Keynesian fiscal expansion in an IS-LM framework

In an IS-LM model Opens in new window, a fiscal expansion is represented by a shift of the IS curve to the right (because of the additional demand for goods, output is larger at any given interest rate).

This fiscal expansion entails an increase in the interest rate, which reduces the interest-sensitive components of private demand: there is partial crowding-out of private demand by public demand.

Modern analysis of interest rate formation no longer starts from the assumption that the central bank targets money supply.

Rather, the interest rate is supposed to be set by it in response to economic developments in order to ensure price stability (or more generally macroeconomic stability) in the medium run.

In other words, most central banks nowadays do not follow a money supply rule, but rather an interest-rate rule. This has led to several reformulations of the IS-LM framework that result in substituting for the LM curve an interest-rate reaction function (Romer, 2000; Bofinger, Wollmerhäuser, 2002).

However, such reformations generally result in representations that make the interest rate dependent on the level of output, as in the LM curve.

Because monetary and fiscal policies are to a certain extent substitutable, the Keynesian approach naturally leads to thinking in terms of policy mix (i.e., in terms of the combination of monetary and fiscal policies). Fiscal policy Opens in new window is indeed more effective when supported by monetary policy Opens in new window. At the limit, a perfectly accommodative monetary policy that keeps the interest rate constant in response to a fiscal expansion results in a maximum multiplier effect Opens in new window.

This may lead governments to put pressure on the central bank so that it contributes to maximizing fiscal expansion and possibly submitting monetary policy to fiscal dominance. When the central bank is independent, however, it may choose not to accommodate the effects of fiscal policy if it perceives it as potentially inflationary. In Figure I, the LM curve does not shift to the right, so the interest rate increases.

This does not imply that an independent central bank always reacts to a fiscal expansion.

For example, monetary policy Opens in new window can have hit the “zero lower bound” where the policy-determined interest rate remains at or near zero, whereas the economic situation would justify setting it at a significantly negative level. In such a situation, monetary policy does not respond to a fiscal expansion and is therefore fully accommodative without being subject to fiscal dominance.

A context of this sort magnifies the impact of fiscal policy because, instead of resulting in a policy-induced increase in the real interest rate, a fiscal expansion results in its lowering (since the nominal interest rate stays constant while price inflation accelerates).

Another case where the interest rate may not react to a fiscal expansion can be found within a monetary union, when the country carrying out the fiscal expansion is small enough to have negligible impact on the aggregate inflation rate.  