IS-LM Model Short-Run Analysis

Historical Context and the Emergency of the IS-LM Model

The Great Depression of the 1930s serves as the primary catalyst for the development of modern macroeconomics. During this era, developed nations, specifically the United States, faced unprecedented economic devastation. In the year 1933, which is considered the worst year of the depression, the United States recorded that $25\%$ of its labor force was unemployed. Furthermore, the real Gross Domestic Product (GDP) had plummeted to $30\text{ percent}$ below the level recorded in 1929. This catastrophic collapse led economists and policymakers to realize that classical economic theory was insufficient. Classical theory posited that national income was strictly dependent on factor supplies, such as capital and labor, and available technology. However, because the physical factors of production in the US had not fundamentally changed between 1929 and 1933, the theory could not explain the sudden downturn. This necessitated a new theoretical framework to explain sudden depressions and suggest government interventions.

In 1936, Maynard Keynes published his landmark book, "The General Theory of Employment, Interest and Money," which revolutionized the field by challenging the classical orthodoxy. Keynes argued that low aggregate demand, rather than factor supply, was the primary driver of low income and high unemployment during economic downturns. While modern economists reconcile these views by applying classical theory to the long run (where prices are flexible), they follow Keynesian logic for the short run, where prices are considered "sticky." The IS-LM model, introduced by Nobel laureate John R. Hicks in his 1937 article "Mr. Keynes and the Classics: A Suggested Interpretation," remains the preeminent interpretation of Keynes' theory. It focuses on how aggregate demand influences income in the short run when the price level is fixed.

Understanding the Components of the IS-LM Framework

The IS-LM model is composed of two primary halves linked by the interest rate. The "IS" portion stands for Investment and Saving, representing equilibrium in the goods market. The "LM" portion stands for Liquidity and Money, representing equilibrium in the financial or money markets. The model illustrates how the interaction between these two markets determines the position, slope, and level of national income in the short run. This framework is essential for understanding business cycles, which are short-run fluctuations that can lead to production and employment falling far below their natural levels.

The Goods Market and the IS Equation

In the goods market, equilibrium is defined by the condition that production, $Y$, must be equal to the demand for goods, $Z$. Previously, demand was defined simply as the sum of consumption, investment, and government spending ($Z = C + I + G$), with consumption typically modeled as a linear function of disposable income ($Y - T$). However, to build the IS-LM model, the assumption that investment is constant must be relaxed. In this expanded view, investment ($I$) depends on two primary factors: the level of sales and the interest rate ($i$). Firms with increasing sales must invest in new capital and machinery to increase production. Conversely, the interest rate represents the cost of borrowing; a higher interest rate makes borrowing to fund new equipment less attractive. It is assumed that all firms borrow at the same rate—the interest on bonds—and no distinction is initially made between nominal and real interest rates.

The expanded investment relation is expressed as $I = I(Y, i)$, where investment is positively related to production ($Y$) and negatively related to the interest rate ($i$). The equilibrium condition for the goods market, known as the IS relation, is thus formulated as:

$Y = C(Y - T) + I(Y, i) + G$

Derivation and Shifts of the IS Curve

The IS curve is derived by observing how changes in the interest rate affect equilibrium output within the goods market. If the interest rate increases from its initial value $i$ to a higher value $i'$, investment decreases. This reduction in investment leads to a decrease in demand, causing the demand curve ($ZZ$) to shift downward. Through the multiplier effect, this initial drop in investment triggers further decreases in consumption and investment, resulting in a lower equilibrium level of output, $Y'$. Consequently, the IS curve is downward sloping: an increase in the interest rate leads to a decrease in output.

Changes in factors other than the interest rate cause the IS curve to shift rather than moving along it. These factors include taxes ($T$) and government spending ($G$). For example, if the government increases taxes while keeping interest rates constant, disposable income falls, leading to decreased consumption and a subsequent drop in demand and output. Graphically, an increase in taxes shifts the IS curve to the left. In general, any factor that decreases the equilibrium level of output for a given interest rate shifts the IS curve to the left, while any factor that increases output shifts it to the right.

The Financial Markets and the LM Equation

The LM relation describes equilibrium in the financial markets, where the supply of money equals the demand for money. The nominal money supply, $M$, is assumed to be directly controlled by the central bank. Money demand is a function of nominal income ($PY$) and the nominal interest rate ($i$). To align this with the goods market analysis, the equation is converted into real terms. By dividing both sides by the price level ($P$), we obtain the LM equation:

$\frac{M}{P} = L(Y, i)$

Here, $\frac{M}{P}$ represents the real money stock (money in terms of goods). Standard economic theory suggests that agents care about real variables, such as real income and real interest rates. If all prices, wages, and the money supply were to increase by $10\text{ percent}$, real variables like consumption and profits would remain unchanged. In the short run, where the price level ($P$) is fixed, the central bank can characterize monetary policy by choosing the money stock ($M$) or the interest rate ($i$). Modern interpretations often assume the central bank chooses a target interest rate and adjusts the money supply to maintain that rate, resulting in a horizontal LM curve.

Equilibrium in the IS-LM Model

The IS-LM model combines the equilibrium conditions of both the goods and money markets to determine the levels of output and interest rate. Graphically, the intersection of the downward-sloping IS curve and the horizontal LM curve represents the unique point (Point A) where both markets are in equilibrium simultaneously. The IS relation ($Y = C(Y - T) + I(Y, i) + G$) and the LM relation ($\frac{M}{P} = L(Y, i)$) together determine the production level ($Y$) and the interest rate ($i$). This model allows for the analysis of how various shocks (sudden, unexpected events affecting output or employment) and policy changes influence the economy.

Fiscal Policy Analysis

Fiscal policy involves changes in government spending or taxes. Fiscal contraction (or consolidation) refers to reducing the budget deficit, often by increasing taxes ($T$) or decreasing spending ($G$). Conversely, fiscal expansion refers to increasing the deficit. If the government increases taxes to reduce a deficit:

1. The increase in taxes reduces disposable income and consumption, shifting the IS curve to the left.
2. Since the central bank does not intervene, the LM curve remains unchanged.
3. The economy moves along the LM curve to a new equilibrium (Point A') where output has decreased from $Y$ to $Y'$.
4. In terms of components, the fall in output and rising taxes lead to a decrease in both consumption and investment.

Monetary Policy Analysis

Monetary policy involves actions taken by the central bank to change the interest rate. Expansionary monetary policy (monetary expansion) involves decreasing the interest rate, while contractionary policy (monetary tightening) involves increasing it. For a monetary expansion:

1. The central bank decreases the interest rate, which shifts the horizontal LM curve downward.
2. The IS curve does not shift because the relationship between output and interest rates defined by the IS equation remains the same.
3. The economy moves downward along the IS curve to a new equilibrium with a higher level of output ($Y'$) and a lower interest rate ($i'$).
4. The lower interest rate stimulates investment, which increases demand and output. The rise in income further increases consumption and investment.

The Monetary-Fiscal Policy Mix

In practice, governments and central banks often implement fiscal and monetary policies simultaneously, a strategy known as the policy mix. These policies can be used in the same direction—for instance, both expansionary fiscal and expansionary monetary policy can be used to combat a recession. This was seen globally, including in South Africa, during the economic collapse caused by the COVID-19 pandemic in 2020. Combining a tax cut (shifting IS right) with an interest rate cut (shifting LM down) leads to a significant increase in output. In other cases, policies might be used in opposite directions; for example, combining a fiscal consolidation (to restore stability in a poorly managed economy) with a monetary expansion to offset the resulting drop in output.

Empirical Evidence and Economic Dynamics

To determine the effectiveness of the IS-LM model, econometrics—the sub-discipline of economics that uses statistical tools to test theories—is employed. A key concept in empirical analysis is dynamics, which refers to the time path the economy takes to reach a new equilibrium following a shock. Economic variables do not adjust instantly; consumers take time to adjust habits to new disposable income levels, and firms take time to adjust production and investment following changes in sales or interest rates.

Research by Christiano, Eichenbaum, and Evans (1996) utilized U.S. data from 1960 to 1990 to estimate the duration of adjustment processes following a $1\text{ percent}$ increase in the federal funds rate (the U.S. policy interest rate). The findings used a confidence band, representing a range with a $60\% \text{ probability}$ of containing the true effect. The empirical results demonstrated the following:

• Output: A $1\%$ increase in the interest rate leads to a decline in output, reaching a maximum decrease of $-0.7\%$ after eight quarters ($2\text{ years}$). This indicates that monetary policy works with long lags.
• Employment: Employment declines similarly to output, with the largest decrease of $-0.4\%$ occurring after $7\text{ quarters}$.
• Unemployment: A $1\%$ interest rate increase leads to an increase in unemployment, peaking with a shorter lag of $4\text{ quarters}$ ($1\text{ year}$) at a change of around $-0.1\%$. The economy typically returns to equilibrium by the $11th \text{ quarter}$.
• Commodity Prices: These peak even faster, with a maximum decline of $-0.2\%$ after only $3\text{ quarters}$, and equilibrium is restored within $10\text{ quarters}$.

These empirical findings confirm that the IS-LM model provides a credible description of how the real world behaves in the short run.