Definition: Macroeconomics is the branch of economics that studies the behavior of the economy as a whole, focusing on aggregate measures rather than individual entities.
Contrast with Microeconomics:
Microeconomics (1401) focuses on individuals, households, and firms.
Macroeconomics deals with larger economic factors such as national income, inflation rates, and unemployment levels.
Key Questions in Macroeconomics:
What is the overall level of economic activity?
How do various macroeconomic indicators interact?
What are the causes and consequences of economic recessions and expansions?
Gross Domestic Product (GDP): A measure of a country’s economic performance, representing the total value of all goods and services produced over a specific time period.
Unemployment Rate: The percentage of the labor force that is jobless and actively
seeking employment. Defined mathematically as:
$$U = \frac{L -
E}{L} \times 100$$
where U is the
unemployment rate, L is the total labor force, and E is the number of employed individuals.
Inflation Rate: The rate at which the general level of prices for goods and services
is rising, calculated as:
$$\text{Inflation Rate} = \frac{P_t -
P_{t-1}}{P_{t-1}} \times 100$$
where Pt is the price level at time t and Pt − 1 is the price level at the
previous time period.
The relationship between wage growth and inflation is a key interest. Higher wages can lead to increased spending, stimulating demand, which can drive up prices.
We expect inflation to have an inverse connection to unemployment, as described by Okun’s Law, which states that higher unemployment rates are associated with lower inflation rates and vice versa.
Central banks use interest rates to manage economic activity. Generally:
Lowering interest rates typically stimulates the economy by making borrowing cheaper, leading to higher spending and investment.
Raising interest rates generally cools the economy by making borrowing more expensive, which can help to control inflation.
The effect of changes in interest rates on aggregate demand can be modeled as:
AD = C + I + G + (X − M)
where AD is aggregate demand, C is consumption, I is investment, G
is government spending, X is exports, and M is imports.
The global economic landscape exhibits interconnected dynamics.
Changes in one country, significant economies like China, can have widespread repercussions. For example, an increase in China’s growth rate can positively impact commodity exports from Latin America.
Recent higher inflation rates are not confined to the United States; they have become a global phenomenon, often above the central banks’ target rates.
By the end of the course, students should be able to:
Understand and analyze macroeconomic indicators and their relationships.
Read and interpret macroeconomic reports critically, such as the World Economic Outlook and financial journal articles.
Utilize basic equations to explain macroeconomic phenomena.
This introductory lecture aims to provide a foundational understanding of macroeconomics, its core concepts, and the significance of macroeconomic indicators in the context of a dynamic global economy. The subsequent lectures will delve deeper into these topics with a focus on definitions and models essential for macroeconomic analysis.
Current macroeconomic context:
High inflation rates
Supply side issues due to COVID-19
Economic impacts of geopolitical tensions
Importance of understanding definitions in macroeconomics
Challenge in defining output in macroeconomics due to the variety of goods and services produced.
Need for a comprehensive measure: Gross Domestic Product (GDP).
Key measure of aggregate output.
GDP serves as a primary indicator of economic health.
GDP is the total value of all final goods and services produced in an economy over a specified period.
Three methods:
Final Goods Approach:
GDP = Value of Final Goods and
Services
Value Added Approach:
Value Added = Final Goods
Value − Intermediate Inputs Cost
Income Approach:
GDP = Wages + Profits
The GDP measured at current market prices.
$$\text{Nominal GDP} =
\sum_{i=1}^{n} P_i \cdot Q_i$$
where Pi is the price and Qi is the quantity of goods.
Adjusted for changes in price or inflation, using constant prices.
Computed with a base year.
$$\text{Real GDP} = \sum_{i=1}^{n} P_b
\cdot Q_i$$
where Pb
is the base year price.
Importance of distinguishing between nominal growth and real growth.
Employment: Individuals currently holding jobs.
Unemployment: Individuals not holding jobs but actively seeking employment.
Labor Force: Sum of employed and unemployed individuals.
$$\text{Unemployment Rate} = \frac{\text{Number of Unemployed}}{\text{Labor
Force}} \times 100$$
Defined as the sustained increase in the general price level.
The inflation rate is the rate of change in the price level.
Common measures include:
GDP Deflator:
$$\text{GDP Deflator} =
\frac{\text{Nominal GDP}}{\text{Real GDP}} \times 100$$
Consumer Price Index (CPI): Commonly reported measure of price level inflation.
Future lectures will cover models explaining GDP determinants.
The relevance of fiscal and monetary policies will be discussed.
Understanding the potential for a recession is fundamental in macroeconomics. A recession typically refers to a decline in aggregate output, which can be observed through surveys conducted on economists. These economists are often tasked with assessing the probability of recession within a specified timeframe (in this case, 12 months). The prevailing sentiment regarding economic downturns illustrates a significant reliance on models that determine equilibrium output.
Throughout this course, we will explore various models that illustrate how output is determined in different time frames:
Short Run: Focus on the mechanics of output determination typically measured within a year.
Medium Run: Understanding adjustments in prices and their effect on output.
Long Run: Examination of growth determinants and structural factors behind differing growth rates among economies.
Aggregate demand (Z) is composed of the following elements:
Consumption (C): Goods and services purchased by households.
Investment (I): Non-residential and residential investments.
Government Spending (G): Purchases by federal, state, and local governments.
Exports (X): Purchases of U.S. goods by global consumers.
Imports (IM): Purchases of foreign goods by U.S. consumers.
The equation for aggregate demand in a closed economy (disregarding X and IM) can be
expressed as:
Z = C + I + G
For the purposes of this course:
Z = C + 0 + G (Assuming investment and government
spending are constants)
Consumption is defined as an increasing function of disposable income. The function capturing consumption can
be expressed as:
C = C0 + C1(Y − T)
where:
C0 is autonomous consumption.
C1 is the marginal propensity to consume (MPC).
Y is the total income/output.
T is taxes.
It is crucial to note that C1 (MPC) is valued between 0 and 1; as income increases, consumption increases at a diminishing rate.
The equilibrium output in an economy is determined at the point where aggregate demand equals total output:
Y = Z
Inserting the expression for aggregate
demand provides:
Y = C0 + C1(Y − T) + G
Rearranging this yields the fundamental equation for equilibrium output:
$$Y
= \frac{C_0 + G + C_1 T}{1 - C_1}$$
This formula highlights the multiplier effect, which is defined as:
$$\text{Multiplier} = \frac{1}{1 - C_1}$$
The multiplier serves to
amplify the effects of changes in consumption, government spending, or taxes on overall output.
The size of the multiplier indicates the effectiveness of fiscal policies. Higher values of C1 enhance the multiplier, leading to a more significant increase in equilibrium output following a change in expenditures.
Consider the scenario where C0 (autonomous consumption) increases:
The initial increase in consumption leads to an upward shift in aggregate demand.
Output will initially increase by the same amount as the change in C0 due to the short-run nature of the model.
Subsequent iterations of increased income from the initial consumption will further increase demand, showcasing the multiplier effect in action.
While saving is generally encouraged, an increase in overall savings can paradoxically lead to a decrease in equilibrium output when measured macroeconomically. This can occur due to the multiplier effect:
Higher saving decreases consumption for any given level of income.
As consumption falls, demand decreases, leading to lower output.
Ultimately, lower output results in less income, which further decreases consumption.
This insight underscores the complexity of macroeconomic dynamics compared to microeconomic theories.
In summary, this lecture has introduced the foundational concepts of aggregate demand, the nature of consumption, and the mechanics behind equilibrium output. The intricacies of the multiplier effect and the potential paradox of increased savings highlight how interconnected macroeconomic factors can be. Understanding these principles is vital as we delve deeper into macroeconomic analysis in upcoming lectures.
This lecture addresses the determination of interest rates, particularly in the context of monetary policy and financial markets. The discussion pertains to the aggressive monetary policies implemented by central banks, specifically the United States Federal Reserve (Fed), to combat inflation.
Central banks, such as the Federal Reserve in the US and the Bank of Japan, play a crucial role in setting interest rates. The current chair of the Federal Reserve is Jerome Powell.
Interest Rates: The rates at which interest is paid by borrowers for the use of money they borrow from lenders.
Monetary Policy: A tool used by central banks to influence the economy by controlling the money supply and interest rates.
Money: Liquid assets used for transactions that typically do not earn interest (e.g., cash).
Bonds: Instruments that pay interest and are used as an alternative to cash. They are less liquid than money.
The relationship between money demand (Md) and the interest rate (r) can be described as follows:
Md = Md(r, Y)
where Y is nominal income, and the demand for money decreases as the interest rate increases (downward sloping curve).
The demand for money can be affected by: 1. Interest rate changes. 2. Shifts in nominal income.
The equilibrium interest rate occurs where money demand equals money supply, depicted by the equation:
Md = Ms
where Ms is the money supply determined by the central bank.
In case the central bank increases the money supply, the equilibrium interest rate will fall as shown:
If Ms ↓ → r↓
Expansionary Monetary Policy: Increases in money supply lead to lower interest rates.
Contractionary Monetary Policy: Decreases in money supply lead to higher interest rates.
In practice, central banks conduct operations through:
Expansionary Open Market Operation: The central bank buys bonds, increasing money supply and lowering interest rates.
Contractionary Open Market Operation: The central bank sells bonds, reducing money supply and increasing interest rates.
The relationship between bond prices (PB) and interest rates (r) is inversely related. The interest rate of a bond can be expressed as:
$$r = \frac{C}{P_B}$$
where C is the cash flow received from the bond (e.g., payoff at maturity).
The market for reserves is essential for understanding how central banks implement monetary policy. The Federal Reserve targets the Federal Funds Rate, the rate at which banks lend reserves to each other overnight.
The demand for reserves can be expressed as:
Hd = θMd
where θ is the required reserve ratio.
The central bank influences the interest rate through the supply of reserves (H):
Hs = monetary policy actions
If demand for reserves exceeds supply, the interest rate will rise:
r ↑ if
Hd > Hs
The lecture concludes by reiterating the roles of central banks in influencing interest rates through monetary policy. The practices have evolved with an understanding of the complexities of financial markets today.
Before delving into the IS-LM model, let’s examine the current state of the U.S. economy and its impact on aggregate demand.
Household wealth, composed primarily of net worth, shows a general upward trend, with notable declines during recessions, including the COVID-19 recession. However, post-recession, there has been a significant recovery in asset prices, including:
Recovery in equity markets
Surging house prices
Despite the downturn in 2022, the overall wealth increase is notable. Increased household wealth typically leads to increased consumption and hence higher aggregate demand.
Asset Prices: Rapid increases in stock and real estate prices contribute significantly to wealth.
Government Transfers: Large governmental monetary transfers helped maintain incomes, particularly for lower-income households during COVID-19, leading to increased savings.
The personal saving rate increased dramatically during the COVID-19 recession, peaking at $2.7 - $2.8 trillion in excess savings.
As the economy reopens, pent-up demand manifests as increased spending, especially in sectors like travel and hospitality, further pressuring aggregate demand.
Aggregate demand is influenced by both consumer wealth and spending behavior. The relationship can be
summarized as:
AD ∝ C + I + G + NX
Where AD is aggregate demand, C is consumption, I is
investment, G is government spending, and NX is net exports.
The IS-LM model combines the goods market (IS) and money market (LM) to find equilibrium output and interest rate.
The IS curve represents the equilibrium in the goods market:
Investment (I): A function of output (Y) and inversely related to the interest rate (i).
I = I(Y, i)
- I is positively related to output Y (higher output leads to higher demand for investment). -
I is negatively related to interest rate i (higher interest rates make borrowing more expensive).
Goods Market Equilibrium:
Y = C + I + G
Where C is consumption, I is investment, and G is government spending.
The IS curve slopes downward: An increase in the interest rate reduces investment for a given level of output, moving the economy to a lower equilibrium output.
The LM curve represents the equilibrium in the money market:
Money Demand (L): Dependent on income (Y) and interest rates (i):
L = L(Y, i)
This implies:
M/P = L(Y, i)
Where M is nominal money supply and P is the price level, leading to the real money supply
(M/P).
The LM curve slopes upward: When output increases, the demand for money rises, necessitating a higher interest rate to restore equilibrium.
The intersection of the IS and LM curves determines the equilibrium levels of output (Y*) and interest rate (i*).
Fiscal Policy Changes: Increasing taxes or reducing government spending shifts the IS curve left (lower output).
Expansionary Fiscal Policy: Increased government expenditure or transfers shifts the IS curve right (higher output).
Monetary Policy: The LM curve is shifted through changes in money supply M, which can be controlled by the central bank.
When the IS curve shifts due to fiscal policy changes:
If the curve shifts left due to a contractionary fiscal policy:
Y′ < Y
If the curve shifts right due to an expansionary fiscal policy:
Y′ > Y
The IS-LM model provides a foundational understanding of how output and interest rates are determined in an economy influenced by fiscal and monetary policies. It allows for deeper analysis of the impacts of various shocks and government interventions, particularly in a complex environment like the post-COVID U.S. economy.
The IS-LM model is a foundational concept in macroeconomics, illustrating the interaction between the goods market (IS) and the money market (LM). This model helps analyze economic policy responses, particularly during shocks such as the COVID-19 pandemic.
The IS curve represents the combinations of output (Y) and interest rate (i) that satisfy equilibrium in the goods market. The following components contribute to the IS relation:
Investment (I): A function of both output
and the interest rate:
I = I0 − b ⋅ i + c ⋅ Y
With b > 0 and c > 0, indicating:
Investment increases with output due to rising sales.
Investment decreases with higher interest rates.
The IS curve is downward sloping because higher interest rates reduce investment and hence total demand (Y).
Equilibrium is achieved when:
Y = C(Y − T) + I + G + NX
Where:
C = consumption
T = taxes
G = government expenditure
NX = net exports
A movement along the IS curve occurs when only the interest rate changes.
A shift in the IS curve happens when there are changes in any other variables (e.g., taxes, spending).
The LM curve reflects equilibrium in the money market, where real money supply equals real money demand:
$$\frac{M}{P} = L(Y, i)$$
Where:
M = nominal money supply
P = price level
L = liquidity preference (money demand)
Assuming P is constant in the short run leads to:
M = L(Y, i)
The LM curve is typically upward sloping, indicating that as output (Y) increases, the interest rate (i) must rise to maintain money market equilibrium.
In the current context, central banks set interest rates directly rather than targeting money supply. This results in a flat LM curve at the target interest rate set by the central bank.
Combining the IS and LM curves allows the determination of equilibrium output: - The point at which both
curves intersect signifies the equilibrium interest rate and output level (Y*, i*).
Equilibrium:
(Y*, i*)
Fiscal policy can be expansionary or contractionary:
Expansionary Fiscal Policy: Increasing government spending (G) or lowering taxes (T) shifts the IS curve to the right.
Contractionary Fiscal Policy: Decreasing government spending or increasing taxes shifts the IS curve to the left.
Monetary policy involves changes in the interest rate, affecting investment:
Expansionary Monetary Policy: Decreasing interest rates shifts the LM curve down, leading to higher output.
Contractionary Monetary Policy: Increasing interest rates shifts the LM curve up, leading to lower output.
The multiplier effect amplifies the impact of changes in spending:
$$\text{Final Output Change} = \frac{1}{1 - MPC} \cdot \Delta G$$
Where is the marginal propensity to consume, and ΔG is
the change in government spending.
When the nominal interest rate is effectively zero, monetary policy becomes ineffective, known as the liquidity trap:
In a liquidity trap, increasing the money supply will not lower interest rates further.
Central banks may resort to unconventional monetary policies (e.g., quantitative easing).
During the COVID-19 pandemic:
The Fed cut interest rates to near zero.
Massive fiscal expansions occurred, with government spending rising significantly to address the recession.
The IS-LM model provides insights into how various macroeconomic policies affect equilibrium output and interest rates. Understanding the interactions between fiscal and monetary policy is vital for effective economic management, especially during periods of economic shock.
The IS-LM model is foundational in macroeconomics and provides insight into the interactions between the goods market (IS) and the money market (LM). This lecture will extend the IS-LM model in two key dimensions: the distinction between nominal and real interest rates, and the incorporation of credit spreads in corporate borrowing.
Nominal Interest Rate (i): The interest rate expressed in monetary terms (in dollars). For example, if the nominal interest rate is 10%, an investment of $100 will yield $10 in interest after one year.
Real Interest Rate (r): The interest rate
adjusted for inflation, reflecting the true cost of borrowing in terms of a basket of goods. The
real interest rate can be approximated as:
r ≈ i − πe
where πe is the expected inflation
rate.
The real interest rate influences significant investment decisions in the private sector. For durable goods consumer purchases and physical investment, it is the real rate, not the nominal rate, that matters because it represents the opportunity cost of investment adjusted for inflation.
To derive the real interest rate, we equate the returns from nominal bonds and real goods:
$$1 + r = (1 + i) \frac{P_t}{P_{t+1}}^e$$
From this, we can rearrange
to express it in terms of expected inflation:
r ≈ i − πe
Most corporate bonds are considered risky. The interest rate on these bonds can be represented as:
rf = r + xt
where xt is the risk premium reflecting the
higher borrowing costs associated with corporate lending compared to treasuries.
The risk premium, xt, increases in response to:
An increased probability of default (p).
Heightened risk aversion from investors.
During recessions, both factors can amplify, causing a significant increase in the credit spread.
The modifications include: 1. Replacing the nominal interest rate in the investment function with the real
interest rate adjusted by credit risk:
I = f(r − xt, Y)
An increase in expected inflation (π) or a decrease in credit
spreads (xt) will shift the ZZ curve upwards,
mimicking the effects of expansionary monetary policy:
ΔY = f(Δπ, − Δxt)
Conversely, during financial crises: Increases in the risk premium and declines in expected inflation shift the ZZ curve downwards.
The Great Recession (2008-2009) where nominal rates were reduced aggressively while real rates remained high due to declining expected inflation.
The COVID-19 economic shock led to a similar drop in expected inflation but also required central banks to reduce nominal rates to near zero.
Recently, the interplay between nominal interest rates, real interest rates, and credit spreads has resulted in challenges for monetary policy, particularly as expected inflation has begun to rise again.
Understanding the dynamics between nominal and real interest rates and the implications of credit spreads is crucial for effective investment decisions and policy formulation. The IS-LM model, while foundational, requires these extensions to accurately reflect contemporary economic conditions.
The labor market plays a critical role in macroeconomics due to its influence on key indicators such as:
The unemployment rate, which is essential for assessing the macroeconomic health of a country.
The inflation rate, where labor market conditions significantly affect inflation drivers.
As of recent data, the following statistics illustrate the labor market dynamics:
Total U.S. population: approximately 330 million.
Non-institutional civilian population: around 260 million (excluding youths under 16, incarcerated individuals, and military personnel).
Civilian labor force: about 162 million, with approximately 6 million unemployed.
Unemployment rate: approximately 3.4%, a historical low.
Employment-population ratio: approximately 60%.
The unemployment rate is calculated as:
$$\text{Unemployment Rate} =
\frac{\text{Number of Unemployed}}{\text{Civilian Labor Force}} \times 100$$
Labor markets exhibit large monthly flows amid static stock statistics:
Monthly movements include approximately 3 million job-to-job transitions, as well as transitions between employment and unemployment.
Significant flows indicate that labor market conditions can change rapidly, affecting wage dynamics and employment stability.
Wage determination can be influenced by several factors:
Collective bargaining or individual negotiations depending on the industry and employment level.
Skills required for jobs; higher skill levels often lead to individual negotiations.
The concept of the reservation wage, which is the minimum wage level at which a worker would prefer to be employed rather than unemployed, is crucial. Workers typically demand wages above their reservation wages for various economic and psychological reasons.
Wages can be represented as an increasing function of the expected price level and decreasing function of
unemployment. Mathematically, we can express this as:
W = f(Pe, U, z)
where:
W = nominal wage
Pe = expected price level
U = unemployment rate
z = a catch-all variable that represents workers’ bargaining strength.
The price that firms are willing to charge can be represented by:
P = (1 + M)W
Here:
M = markup over wages
Thus, the real wage offered by the firm can be expressed as:
$$W_r =
\frac{W}{P} = \frac{W}{(1 + M)W} = \frac{1}{1 + M}$$
The natural rate of unemployment (Un) reflects
labor market conditions where expected prices equal actual prices:
Un occurs when
Pe = P
The relationship between the unemployment
rate, price expectations, and wages can be shown graphically, where the intersection of the wage-setting and
price-setting equations determines the natural rate of unemployment.
1. Increase in Bargaining Power z:
Higher z leads to increased wage demands, subsequently raising Un to restore equilibrium.
2. Increase in Markup M:
Higher markups lower firms’ willingness to pay wages, requiring a rise in Un to reach equilibrium.
These foundational concepts illustrate the interplay between labor market dynamics, wage setting, and macroeconomic variables such as inflation and unemployment. The next step involves examining the Phillips Curve to understand how deviations between expected and actual prices influence inflation.
In today’s lecture, we will explore the Phillips curve and its relationship to inflation. The Phillips curve represents a central concept in macroeconomics, particularly its implications on the relationship between unemployment and inflation. This will extend beyond mere empirical analysis to theoretical underpinning using established economic models.
The Phillips curve was first introduced by economist A.W. Phillips in 1958, where he observed a negative correlation between unemployment rates and inflation in the United States from historical data. This empirical relationship was later popularized by Paul Samuelson and Robert Solow.
The Phillips curve is commonly visualized as a downward-sloping curve. That is:
If U (unemployment) decreases, then π (inflation)
increases.
We start with two key equations from the previous lectures:
1. Wage Setting Equation:
W = F(u, z)
where W is the nominal wage, u
the unemployment rate, and z represents labor market institutions
(increasing function).
2. Price Setting Equation:
P = (1 + m)W
where P is the price level and m
is a markup.
The wage-setting equation reflects that as unemployment u rises, wage demand W decreases, and as z increases, wage demand increases.
Starting with the relationship between inflation and the price level:
$$\pi
= \frac{P_t - P_{t-1}}{P_{t-1}} = \frac{P_t}{P_{t-1}} - 1$$
Rearranging this in terms of
expected inflation gives:
Pt = (1 + πe)Pt − 1
where πe is expected inflation.
Substituting in both the wage and price equations ultimately leads us to the relation:
π = πe − α(u − un)
where un is the natural rate of unemployment,
a key concept in understanding inflation dynamics.
The natural rate of unemployment un satisfies
the conditions where expected inflation equals actual inflation. Mathematically:
un = F − 1(π, z)
This means that higher z or m leads to an increase in un due to changes in bargaining power of
workers.
An increase in z leads to a higher required wage from workers, but firms can only afford to pay a lower wage, leading to higher unemployment un to reach equilibrium.
At the core of the Phillips curve is the assumption about inflation expectations:
πe = E[πt + 1]
Where E[ ⋅ ] denotes the expectation operator. When expectations
are well anchored, especially at low values of inflation, the Phillips curve maintains its downward slope.
If inflation expectations are disanchored (such as during the 1970s), the relationship can break down, as seen from historical data where inflation accelerated despite high unemployment due to expected inflation catching up with realized inflation.
In a dynamic world, expected inflation can be modeled as:
πe = θπt − 1 + (1 − θ)π̄
where π̄ is the target inflation rate (often around 2
The implication is that if θ approaches 1, expected inflation becomes much more responsive to previous inflation shocks, leading to persistent inflation against earlier Phillips curves.
Understanding the Phillips curve provides essential insight into monetary policy and inflation targeting. The dynamics of inflation expectations, the natural rate of unemployment, and economic shocks interact to determine inflation outcomes.
As we continue exploring macroeconomic models, this foundation will aid in addressing contemporary economic challenges such as rising inflation pressures.
The IS-LM-PC model combines various economic concepts discussed in previous lectures. It serves as a central model to analyze the interactions between the goods market (IS), money market (LM), and inflation dynamics (Phillips Curve, PC).
Recent failure of Silicon Valley Bank (SVB), a significant event affecting economic confidence.
SVB’s rapid growth led to vulnerability, with heavy reliance on the tech sector.
Withdrawals were triggered by capital-raising efforts, leading to panic among depositors and a bank run.
The Federal Reserve faced pressure to mitigate potential systemic risks.
A bank run occurs when depositors lose confidence, leading to mass withdrawals. The key factors in SVB’s situation:
Large withdrawals spurred by the nature of depositors (tech startups).
Deposits largely uninsured (above $250,000).
Poor timing in purchasing Treasury bonds just prior to interest rate increases.
The IS-LM-PC model consists of three core components: the IS curve, the LM curve, and the Phillips Curve.
Y = C(Y − T) + I(r) + G
where:
Y = output (income),
C = consumption function,
T = taxes,
I = investment function dependent on the real interest rate r,
G = government spending.
The IS curve represents equilibrium in the goods market.
M/P = L(r, Y)
where:
M = nominal money supply,
P = price level,
L = liquidity preference (money demand).
The LM curve represents equilibrium in the money market, linking the real interest rate and output.
π − πe = − β(Y − Yn)
where:
π = actual inflation,
πe = expected inflation,
β = sensitivity parameter,
Yn = potential output.
The Phillips curve depicts the trade-off between inflation and unemployment/output.
The short run analysis focuses on the immediate reactions to shocks in the economy, where the IS-LM model governs the output and inflation behavior.
In the initial phases, the model assumes expected inflation is influenced by previous inflation rates.
Over time, the economy adjusts toward the natural rate of output and interest.
The natural rate, r*, is defined such that monetary
policy does not create inflationary or deflationary pressures:
Yn = C(Yn − T) + I(r*) + G.
As inflationary pressures build, central banks must react:
Central banks raise interest rates to bring inflation down.
The real interest rate is incrementally adjusted until stability is reached.
In the medium run, monetary policy determines nominal variables while real variables are determined by real factors.
Credibility of the central bank is essential to anchor expected inflation. A loss of credibility can lead to significant economic distortions and necessitate severe corrections.
The IS-LM-PC model offers a comprehensive framework for understanding the interplay between monetary policy, output fluctuations, and inflation dynamics. The recent events in the banking sector highlight the fragility of financial institutions and the critical importance of sound regulatory practices.
The IS-LM-PC model integrates the IS-LM analysis with the Phillips Curve (PC). It provides insights into the relationship between output, interest rates, inflation, and unemployment, particularly in the context of monetary policy and economic shocks.
The IS-LM model represents the goods market (IS curve) and the money market (LM curve):
IS Curve: Represents equilibrium in the goods market, where investment equals savings.
LM Curve: Represents equilibrium in the money market, where money supply equals money demand.
The Phillips Curve shows the inverse relationship between inflation and unemployment:
π = πe − β(u − un)
where:
π: actual inflation rate
πe: expected inflation rate
u: actual unemployment rate
un: natural rate of unemployment
β: parameter indicating sensitivity of inflation to unemployment gap
The output gap is defined as the difference between actual output (Y) and potential output (Yn):
Output
Gap = Y − Yn
Potential output is achieved when unemployment is at its natural rate, defined as:
Yn = L ⋅ (1 − un)
where:
L: labor force
un: natural rate of unemployment
The IS-LM-PC model combines the output and inflation aspects by replacing unemployment with the output gap in
the Phillips Curve, yielding:
π − πe = α(Y − Yn)
where α is a sensitivity parameter.
In the short run, changes in the interest rate by the central bank affect the equilibrium level of output. If output exceeds potential output, inflation will rise:
Positive Output Gap (Y > Yn): Inflation rises as firms face upward wage pressures.
Negative Output Gap (Y < Yn): Inflation falls, and prices are under pressure to decrease.
When inflation rises, a responsible central bank typically raises interest rates, which can lead to a
decrease in output over time. The implicit natural interest rate (Rn) is the rate that stabilizes the output at
its potential level:
Rn = implied rate for
equilibrium output
Expectations about future inflation greatly impact the economy’s response to shocks:
Anchored Expectations: Stable expectations help maintain current inflation levels without requiring drastic policy changes.
Unanchored Expectations: If inflation expectations rise uncontrollably, the central bank may need to enact contractionary policy, potentially leading to recession.
Aggregate demand shocks, such as fiscal consolidations, move the IS curve:
Fiscal Consolidation (Contraction): Reduces output in the short run, leading to declining inflation.
Supply side shocks, such as oil price increases, influence the Phillips Curve directly, shifting it outwards:
Natural Rate of Unemployment Increases: Results in a decrease of potential output.
Recent shocks, such as the situation at Silicon Valley Bank, illustrate how credit shocks can shift the IS curve leftward. The bank’s event resulted in reduced investment and increased inflationary pressures.
The markets have responded to these shocks with anticipated changes in inflation:
Expected inflation rates have dropped due to the negative shock and anticipated central bank responses.
Implied interest rates suggest that the Federal Reserve will need to reconsider its rate hike strategy in light of recent financial instability.
Understanding the IS-LM-PC model enables analysts to navigate the complexities of macroeconomic dynamics, especially during periods of economic turbulence. The interplay between interest rates, output, and inflation, as illustrated in this model, is critical for effective monetary policy formulation.
This lecture focuses on macroeconomic growth, which examines phenomena occurring over decades rather than short-term business cycles. The discussion includes the significance of monetary policy, particularly in regard to interest rates and financial crises.
Macroeconomic policies are complex and must be managed carefully.
Policymakers should respond to financial crises with large and rapid actions.
Gradualism is preferred in other economic settings to avoid breaking the economy.
Monetary policy’s impact is highlighted through historical episodes of interest rate hikes and their consequences. Key events include:
U.S. Interest Rate Hike: Aggressive interest rate hikes led to a financial crisis in emerging markets, including a significant crisis in Chile.
Lost Decade of Latin America: Result of U.S. policies that financially destabilized emerging markets.
Savings and Loan Crisis (1980s): Interest hike impacted small regional banks, leading to broader economic repercussions.
Japanese Real Estate Bubble Burst: Resulted from U.S. monetary policy; Japan has since struggled to regain prior economic growth.
The Great Recession (2008): Preceded by aggressive interest hikes, ultimately led to a housing market crash and subsequent global financial crisis.
The International Monetary Fund (IMF) provides growth forecasts reflecting cyclical and structural factors. These forecasts show emerging markets typically grow faster than advanced economies.
In 2022, global growth was approximately 3.4% with advanced economies growing at 2.7% and emerging markets at 3.9%. Forecast for 2024 suggests a slowdown in growth due to economic conditions.
Growth is crucial for evaluating the health of an economy. Gross Domestic Product (GDP) is often measured in constant prices (e.g., 2012 dollars) to accurately reflect economic changes over time.
The following observations reflect long-term economic growth:
The U.S. GDP increased significantly from 1890 to 2017, demonstrating a 50 times increase.
Business cycle fluctuations appear small in the context of long-term growth.
Changes in GDP per person (per capita) are also significant, showing a 10 times increase from 1890 levels.
The increase in the population from 63 million to 320 million in the U.S. correlates with economic growth, raising crucial questions regarding ongoing population changes in the global context.
When comparing GDP per capita across countries, adjustments are necessary to account for price level differences using Purchasing Power Parity (PPP). The main principles of PPP can be illustrated with the following hypothetical scenario:
Assume two economies:
U.S.: Household consumption includes one car ($10,000) and food ($10,000), totaling $20,000.
Russia: Household consumption is 0.07 cars per year (costing 40, 000 rubles) and food (costing 80, 000 rubles), totaling 120, 000 rubles.
Given an exchange rate of 60 rubles/USD:
$$\text{US Consumption: } 20,000 \text{ USD}, \quad \text{Russian Consumption: }
\frac{120,000 \text{ rubles}}{60 \text{ rubles/USD}} = 2,000 \text{ USD}$$
This suggests
that without adjustments, it appears Russia is 10 times poorer than the
U.S. However, real consumption must account for lower price levels in Russia.
Using U.S. market prices:
Russian Household Consumption: (0.07
cars × 10, 000) + (1 food bundle × 10, 000) = 10, 700 USD
This indicates that the Russian
household is actually 53% of the U.S. household’s purchasing power rather
than 10 times poorer.
An analysis of growth rates from 1950 to 2017 reveals trends such as:
Countries like Japan experienced higher growth rates (4.1%) compared to the U.S. (2%).
The correlation between higher initial GDP and slower growth rates is identified as a significant economic pattern.
This suggests that poorer countries tend to grow faster than richer ones, aiding in the understanding of global economic convergence.
Long-run growth can be represented through a production function, typically expressed as:
Y = F(K, N)
Where Y is output, K is capital,
and N is labor.
Constant Returns to Scale: Doubling inputs leads to a doubling of output.
Decreasing Returns to Capital: Increasing K while holding N constant leads to progressively smaller increases in Y.
Understanding the factors behind changes in per capita output is crucial. The two mechanisms driving changes are:
Capital Accumulation: More capital per worker results in higher output per worker.
Technological Progress: Improvements in technology shift the production function upward, enabling greater output for the same amount of capital and labor.
The Solow Growth Model, developed by Robert Solow, focuses on long-term economic growth driven by capital accumulation, labor or population growth, and advances in technology. This model outlines key mechanisms for understanding how economies grow over time.
Factors of Production: The primary factors are labor (N) and capital (K).
Output: Output (Y) is a function of capital and labor, represented as Y = f(K, N).
Output per Capita: Output per person is defined as $\frac{Y}{N}$.
Capital Accumulation: Investment (I) is the key driver of capital accumulation, where I = S (savings) in equilibrium.
The production function exhibits constant returns to scale, leading to:
$$\frac{Y}{N} = f\left(\frac{K}{N}\right)$$
This function is
increasing and concave due to the property of diminishing marginal returns to capital.
Assuming savings is proportional to income:
S = sY, where s = saving
rate ∈ [0, 1]
Investment in a closed economy is equal to savings.
The evolution of capital per worker over time is described by the equation:
Kt + 1 = Kt + It − δKt
where:
Kt = capital stock at time t
It = investment at time t
δ = depreciation rate of capital
Dividing by N for per worker terms gives:
$$\frac{K_{t+1}}{N} = \frac{K_t}{N} + \frac{I_t}{N} - \delta
\frac{K_t}{N}$$
In the steady state, output per worker and capital per worker remain constant. This results in:
$$0 = s f\left(\frac{K}{N}\right) - (\delta + g_N)\frac{K}{N}$$
Where
gN is the population growth rate.
The steady-state capital per worker is given by:
$$\frac{K^*}{N} =
\frac{s}{\delta + g_N}$$
When the savings rate increases:
The green line (investment curve) shifts upward.
The capital stock increases over time until reaching a new steady state.
Upon reaching this steady state, growth returns to zero.
This leads to a transitional growth phase with increased output per worker until a new steady state is achieved.
If the population grows at a rate gN > 0,
the steady state changes:
$$K^* = \frac{s}{\delta + g_N}$$
This indicates that output per worker may stabilize or decline depending on the growth of the population
relative to output.
The Solow Growth Model provides a framework for analyzing how capital accumulation and population growth affect output in an economy. It emphasizes the role of savings for investment and the implications of diminishing returns in the growth process.
Today, we will discuss the relationship between technological progress and economic growth. This topic is essential for understanding how economies develop and how human well-being is enhanced through innovation.
In the previous lecture, we focused on the role of capital accumulation in economic growth. We began with a production function that demonstrates constant returns to scale in capital and labor.
Labor refers to the total labor force or population.
Output per person is an increasing function of the capital per person but exhibits diminishing returns.
For a closed economy without fiscal deficit, investment equals savings.
The key equation derived was the capital accumulation equation:
kt + 1 = kt − δkt + it
where kt + 1 is the capital stock tomorrow,
δ is the depreciation rate, and it is investment.
If we allow for population growth, we adjust the equation:
$$\frac{k_{t+1}}{n_{t+1}} = (1 - \delta - g_n) \frac{k_t}{n_t} + \text{Investment
function}$$
where gn is the
population growth rate.
When population (n) grows, the capital per person (k/n) can decrease, even when the total capital remains constant. The introduction of gn (population growth rate) highlights this relationship. For instance, a greater gn means that more investment is needed just to maintain the capital per person.
If population growth is high, the investment must keep pace to maintain the capital-labor ratio.
The next step is to integrate technological progress (denoted as ga) into our growth model.
a: represents the level of technology, and its growth rate (ga) indicates how effectively labor is utilized.
Technological progress allows for producing more output from the same amount of capital and labor, leading to higher efficiency.
We can model technological progress as an increase in effective labor, represented as an. The effectiveness of labor increases, similar to having more workers.
The production function now becomes:
Y = F(K, aN)
where K is the capital and N is
the labor force.
Dividing by effective labor:
$$y = f\left(\frac{K}{aN}\right)$$
where y is output per effective worker.
The new equation regarding capital accumulation under technological progress becomes:
$$\frac{k_{t+1}}{a_t n_{t+1}} = \left(1 - \delta - g_a - g_n\right) \frac{k_t}{a_t
n_t}$$
This equation demonstrates that the effective capital per worker changes over time
based on both population growth and technological change.
As ga increases, the economy can potentially experience higher growth rates over time:
Transitionally, if ga increases, output will grow faster until it reaches a new steady state.
Essentially, long-run growth is determined by the growth rate of technology (ga) in the steady state.
Because technological progress allows for higher productivity, it becomes the principal driver for sustainable increases in output per person, beyond what capital accumulation can achieve alone.
We have explored how population growth and technological progress interrelate and their effects on economic growth. The next steps will further detail how to model these interactions more robustly.
The understanding of these dynamics is critical, especially as economies face challenges such as declining population growth rates in various regions across the world.
In this lecture, we will summarize the key elements of growth theory, focusing on what our models can and cannot explain regarding the great dispersion we observe in income per capita across the world.
A balanced growth model assumes that all relevant variables grow at the same rate. This can be illustrated
through the following:
1. Normalized Variables:
Yt = At ⋅ Ht ⋅ Kt1 − α ⋅ (At ⋅ Nt)α
Where:
Yt = Output
At = Technology level
Ht = Human capital
Kt = Physical capital
Nt = Labor force
α = Output elasticity of labor
2. Growth Rates: - The growth rate of output per effective worker is given by:
gY = (1 − α)gK + α(gA + gH)
In balanced growth, gA and gH remain constant.
3. Steady State Growth: In steady state, the growth rates for key variables are:
gK = gA + gN
gY = gA + gN
4. Implications:
Capital per effective worker remains constant.
Output per worker grows at the rate gA + gN.
To measure the rate of technological change (gA), we can utilize the following formula based
on the contributions of labor and capital:
1. Contribution from Labor:
gY|N = α ⋅ gN
Where:
gY|N = Growth of output due to growth
in employment
2. Contribution from Capital:
gY|K = (1 − α) ⋅ gK
The total growth of output can be decomposed as follows:
gY = gY|N + gY|K + gA
The residual (gA) represents technological
progress.
Avg. Output Growth: 7.2%
Population Growth gN: 1.7%
Capital Stock Growth gK: 9.2%
Residual gA: 4.2%
These contributors can be expressed in terms of the relative output and saving rates.
Transitional growth occurs when a country is below its steady-state level, leading to faster growth due to
capital accumulation.
1. If a country has below-steady-state levels of capital:
gOutput > gA + gN
Example: Post-war economies often experience transitional growth.
2. For China during growth episodes:
gK > gY > (gA + gN)
In the context of an extended model to include human capital (H):
1. Human capital model:
Y = A ⋅ Hh ⋅ K1 − α
2. Steady states will still yield gA and gH as before. If education is increased, the
model predicts higher output without changing the growth dynamics fundamentally.
Education plays a crucial role in explaining differences in income per capita across countries. A rise in
average years of schooling contributes positively to human capital:
gH = 0.1 ⋅ ΔYears of Schooling
Empirical findings suggest that countries with higher education often exhibit higher income per capita:
Yi = A ⋅ Hiα ⋅ Ki1 − α
Despite accounting for savings rates and education, significant income disparities remain. The Solow Residual continues to play a vital role, indicating that technology levels vary drastically worldwide.
1. The relative technology output levels across countries:
$$A_i =
\frac{Y_i}{K_i^{1-\alpha}H_i^{\alpha}}$$
This allows for considerable insights into how much of the output per worker disparities can be attributed to technology differences.
While models like the Solow model provide substantial insight, they struggle to account for variations in growth rates and income levels as affected by diverse factors, particularly those relating to institutions and technology adoption rates.
Future discussions will encompass the dynamics of open economies and integrate these modern growth theories into broader economic models.
As economies begin to reopen from the COVID-19 pandemic, there has been excess demand over supply. The expected potential output, as described in the IS-LM-PC model, was slow to recover due to:
Supply chain bottlenecks
Labor market constraints (some workers reluctant to return to work)
This resulted in a positive output gap, defined as output exceeding potential output (represented mathematically as Y > Y*), thereby exerting inflationary pressures described by the Phillips Curve.
Phillips
Curve: π = πe − β(Y − Y*)
Where:
π is inflation
πe is expected inflation
β is a parameter representing sensitivity
Initially, the Federal Reserve (Fed) underestimated the persistence of inflation due to strong demand fueled
by fiscal and monetary policies. As inflation rose:
Output:
Y > Y* ⟹ i↑
Where i is the interest rate. As such, policymakers prefer gradual
changes, especially when hiking rates to prevent systemic failures in the banking sector.
The resilience of large banks was initially reassuring. However, rapid deposit outflows led to a significant banking failure, most notably exemplified by the collapse of Silicon Valley Bank.
Depositors began relocating funds to safer investments (e.g., U.S. Treasuries), leading to:
Decline in Lending ⇒ Credit Crunch
Small and medium-sized banks, which primarily serve local businesses, faced much sharper declines in deposits, ultimately affecting their ability to lend. This created a contraction in the economy with a disproportionate impact on small businesses.
Banks in Gray (Small/Medium) ⇒ High Share of Loans to Small
Businesses
This leads to:
Y = C + I + G + NX (AggregateDemand)
Where C is consumption, I is investment, G is
government spending, and NX is net exports.
Despite low unemployment rates, underlying wage pressures remain. The labor force participation declined during the pandemic but is now recovering.
The change in labor force participation influences wage pressure, as follows:
$$\text{Wage Pressure} \propto \frac{W}{L} \quad \text{(where \(W\) is wages
and \(L\) is labor supply)}$$
Immigration affects labor input significantly, with disruptions during COVID. The recovery in immigration can alleviate wage pressures.
The next section details how these concepts apply in an open economy framework.
Exchange Rate E: Price of domestic currency in terms of foreign currency.
Trade Balance TB: The difference
between exports and imports:
TB = X − M
The U.S. generally has a trade deficit, meaning it imports more than it exports.
When discussing currency valuation, we define appreciation and depreciation:
Appreciation:
Ecurrent > Epast
Depreciation:
Ecurrent < Epast
A real exchange rate R can be defined as:
$$R = \frac{E \cdot P_d}{P_f}$$
Where:
Pd is domestic price level
Pf is foreign price level
This metric allows for comparisons of relative prices between goods across countries.
As economies integrate through trade and finance, synchronizing business cycles becomes more prevalent. The U.S. demonstrates remarkably synchronized cycles, especially during significant global events like the 2008 financial crisis and the COVID-19 pandemic.
Through intra-country trade and capital mobility, countries become increasingly exposed to each other’s economic conditions. This is particularly relevant as global events can have amplified impacts across integrated economies.
The U.S. economy is currently at a critical juncture, balancing the need for continued rate hikes to combat inflation while navigating the implications of a potential credit crunch that could lead to a slowdown. Understanding these dynamics in both closed and open economy contexts is vital for policymakers and economists alike.
The lecture focuses on the IS-LM model, revisiting it within the context of an open economy. The key concepts discussed will include openness in goods and capital markets, real exchange rates, and demand for domestic versus foreign goods.
Openness in an economy can be defined in two major aspects:
Goods Market Openness: The ability to buy goods from both home and abroad, which introduces the concept of relative prices and the real exchange rate.
Financial Market Openness: The ability to invest in both domestic and foreign assets, requiring an understanding of expected relative returns.
The real exchange rate (ϵ) is defined as:
$$\epsilon = \frac{P^*}{P} \cdot E$$
where:
P* = Price level abroad
P = Price level domestically
E = Exchange rate (price of domestic currency in terms of foreign currency)
A rise in ϵ indicates a real appreciation of the domestic currency, meaning domestic goods become more expensive than foreign goods. Conversely, a fall in ϵ indicates a depreciation.
When considering investments, comparing the expected returns on domestic assets with foreign assets is crucial:
For a domestic bond with interest rate i, the future value
is:
FVdomestic = (1 + i) ⋅ P
For a foreign bond with interest rate i*, after
converting currency at expected future exchange rate E*:
$$FV_{foreign} = \frac{(1 + i^*) \cdot P^*}{E^*}$$
The equilibrium condition for investors is given by:
$$(1 + i) = (1 + i^*)
\cdot \frac{E}{E^*}$$
Where it states that interest rates must be equal when adjusted for
expected changes in exchange rates.
In an open economy, we distinguish between:
Domestic Demand (DD): Consumption
(C) + Investment (I) + Government Expenditure (G)
DD = C + I + G
Demand for Domestic Goods (ZZ):
ZZ = DD − M + X
Where:
M: Imports (function of Y, domestic output)
X: Exports (function of Y*, foreign output)
- Exports increase as foreign output (Y*) increases and
decrease with an increase in the real exchange rate (ϵ):
X = f(Y*, ϵ)
-
Imports increase with domestic output (Y) and also with the real
exchange rate (ϵ):
M = f(Y, ϵ)
To find equilibrium output, we use:
Y = ZZ
Where the intersection of the ZZ (demand for domestic goods) and the 45-degree line gives
us equilibrium output.
The open economy has a lower multiplier effect due to:
Part of any increase in demand being satisfied by imports
Hence the multiplier effect is tempered by the leakages to imports.
If a country faces a trade deficit and seeks to improve it through currency depreciation:
Depreciation improves net exports, shifting the net export function up.
However, this is also expansionary, potentially increasing domestic output.
To balance the expansion caused by depreciation, a government may choose to reduce spending or implement fiscal contraction.
The main learnings from this lecture include: - Differentiation between domestic demand and demand for domestic goods. - Understanding how exchange rates influence exports and imports. - Recognizing the implications of an open economy on multipliers and trade balances.
This lecture prepares us for the upcoming integration with financial markets in the context of the Mundell-Fleming model, emphasizing the interconnectedness of goods markets and financial markets in an open economy.
The Mundell-Fleming model is a critical tool for understanding the interactions between exchange rates, interest rates, and output in an open economy. The model is particularly important for short-term economic analysis and is likely to be a key focus for quizzes and examinations.
In this course, we define an increase in the exchange rate as an appreciation of the domestic currency (the dollar). Conversely, a decrease signifies a depreciation.
The dollar has appreciated significantly relative to the euro and depreciated regarding the Japanese yen over recent years.
Fluctuations in exchange rates are influenced by investors’ perceptions of interest rate policies across different regions.
The Uncovered Interest Parity (UIP) condition is fundamental to the Mundell-Fleming model, expressing the
relationship between exchange rates and interest rates.
$$E_t =
\frac{(1+i_d)}{(1+i_f)}E_{t+1}$$
Where:
Et = nominal exchange rate today
id = domestic interest rate
if = foreign interest rate
Et + 1 = expected nominal exchange rate next period
The principle behind UIP is that the expected rate of return on domestic assets must equal that of foreign assets when adjusted for exchange rate expectations.
Net exports (NX) influence aggregate demand. The NX function is influenced by three factors:
NX = NX(Yd, Yf, RER)
Where:
Yd = domestic output
Yf = foreign output
RER = real exchange rate
The function suggests:
NX is decreasing in domestic income (Yd)
NX is increasing in foreign income (Yf)
NX is decreasing in the real exchange rate (RER)
Higher domestic income leads to increased imports, reducing net exports.
Higher foreign income leads to increased demand for exports, enhancing net exports.
The model integrates the IS-LM framework by incorporating the effects of exchange rates:
The IS curve represents equilibrium in the goods market:
Y = C(Y − T) + I(r) + G + NX
Where:
C = consumption
T = taxes
I = investment
r = interest rate
G = government spending
NX = net exports
Revised aggregate demand accounts for the open economy context:
Y = C(Y − T) + I(r) + G + NX(Yd, Yf, RER)
The LM curve remains consistent with the closed economy, driven by monetary policy:
M/P = L(r, Y)
Where:
M = money supply
P = price level
L = liquidity preference (function of interest rate and income)
An increase in the domestic interest rate will lead to:
A contraction in output (reduced aggregate demand).
An appreciation of the domestic currency (increase in exchange rate).
Expansionary fiscal policy (increased government spending) without a change in interest rates leads to:
Higher output.
No immediate effect on the exchange rate, as the interest rate remains stable.
An increase in the expected exchange rate will:
Shift the IS curve left due to reduced net exports.
A decline in foreign output will:
Shift the IS curve left due to decreased demand for exports.
An increase in foreign interest rates will:
Shift the UIP condition, requiring a depreciation of the exchange rate to maintain equilibrium.
The Mundell-Fleming model serves as a foundational component in international economics, offering insights into how monetary and fiscal policies affect exchange rates, output, and net exports in an open economy.
This document summarizes the key concepts discussed in the lecture concerning exchange rate regimes and the Mundell-Fleming model. We explore how different economic factors interact in open economies and the implications of various exchange rate systems.
The Mundell-Fleming model extends the IS-LM model to include international trade and finance.
The modified IS curve includes a net export term, influenced by:
Foreign output/income
Real exchange rate
The real exchange rate is determined by the Uncovered Interest Parity (UIP) condition:
$$E_t = \frac{(1 + i_t)}{(1 + i^*_t)} E_{t+1}$$
where:
Et is the current exchange rate
it is the domestic interest rate
it* is the foreign interest rate
Et + 1 is the expected exchange rate for the next period
If the expected exchange rate Et + 1 increases:
The current exchange rate Et must rise
The IS curve shifts left due to a contraction in aggregate demand.
If foreign output decreases:
Net exports decrease
The IS curve shifts left, indicating a recession.
If the international interest rate rises while domestic interest rate remains constant:
The current exchange rate Et must depreciate
IS curve shifts right due to an increase in net exports.
Exchange rate arrangements can be broadly classified into floating (flexible) and fixed (pegged) regimes.
In a floating exchange rate regime, currency values are determined by market forces. Advantages include:
Monetary policy autonomy.
The ability to absorb external shocks via exchange rate adjustments.
Disadvantages include:
Increased volatility in exchange rates, complicating international trade and investment.
A fixed exchange rate regime involves pegging a currency to another major currency.
If credible, the expected exchange rate is constant:
Et = Efixed
Leads to alignment of domestic and foreign interest rates:
it = it*
Results in loss of monetary policy autonomy.
Countries often use hybrid exchange rate systems that incorporate elements of both fixed and floating regimes.
Examples include selective pegging or interventions during periods of high volatility.
In a recession, countries in different regimes respond differently:
Expansionary fiscal policy is pursued alongside lowering interest rates, leading to currency depreciation and increased net exports.
Fiscal policy can be expansionary, but the country cannot pursue independent monetary policy.
During a recession not aligned with the economic cycle of the pegged currency, the country cannot effectively respond with monetary tools.
Countries with fixed exchange rates may face speculative attacks if markets do not believe in the sustainability of the peg. To defend against such attacks:
Interest rates must be raised to maintain the fixed exchange rate, which can lead to domestic recession.
The choice between exchange rate regimes is multifaceted and involves a trade-off between stability and policy autonomy. Countries may choose fixed exchange rates to combat inflation or stabilize their economy, while flexible regimes provide greater policy freedom but expose countries to excess volatility.
Expectations play a crucial role in economics, influencing decisions made by firms, consumers, and governments. Most economic and financial calculations involve evaluating future outcomes. Understanding how to assess the value of assets based on anticipated future cash flows is fundamental.
Recent bank collapses, such as Silicon Valley Bank and First Republic Bank, exemplify the power of expectations in finance. The rapid withdrawal of deposits indicates that people’s expectations can influence the stability of financial institutions.
The S&P 500 serves as a primary equity index in the U.S. market, capturing movements of large companies. Major swings in the index can be attributed to changes in expectations about:
Future economic conditions
Federal Reserve actions (e.g., interest rate hikes)
Risk appetite among investors
For instance, the index dropped by 35% at the onset of COVID-19 and rallied by 114% by late 2021, only to decline again due to inflation concerns and subsequent interest rate increases.
To determine if the price of an asset today is fair, we calculate its expected present discounted value (EPDV). This concept combines several critical elements:
Expectation: Anticipated future returns.
Present Value: Current worth of future cash flows.
Discounting: Future cash flows are considered less valuable than cash flows received today, typically utilizing the current interest rate.
The present value of a cash flow Zt, received
at time t, can be generally represented as:
$$PV = \sum_{t=0}^{n} \frac{Z_t}{(1+i_t)^t}$$
Where:
it is the interest rate applicable at time t.
If cash flows are known and consist of constant payments Z over
n periods with a constant interest rate i, then the present value can be simplified to:
$$PV = Z \cdot \frac{1 - (1+i)^{-n}}{i}$$
If you expect $1 one year from now, it can be discounted at the interest rate i:
$$PV(1 \text{ year}) =
\frac{1}{1+i}$$
Extending this, for $1 received two years from now, we have:
$$PV(2 \text{ years}) = \frac{1}{(1+i)^2}$$
Bonds have varying maturities and coupon structures. The price of a bond can be determined using the present discounted value framework.
Yield to maturity (YTM) is defined as the constant annual interest rate that equates the present value of a
bond’s future cash flows to its current price. It can be calculated using:
$$P = \sum_{t=1}^{n} \frac{C_t}{(1 + YTM)^t}$$
Where Ct represents cash flows (coupon and face value
payments).
The yield curve illustrates the relationship between the yield and maturity of bonds. It can become inverted, indicating expectations of falling interest rates or economic downturns.
If the interest rates are expected to remain constant, the yield to maturity can be approximated as an
average of the expected future rates:
$$YTM_2 \approx \frac{i_1 +
E(i_1)}{2}$$
Understanding expectations and their impact on financial assets is vital for evaluating investments and managing economic policies. Future classes will build upon these concepts and explore their applications in various financial contexts.
Asset pricing is centered on the notion that the payoff from an asset occurs in the future. This involves three key elements:
Valuation of Future Returns: We need to establish a method to express future returns in terms of today’s dollars.
Expectations: Since payoffs are in the future, we must hold expectations about them.
Risk: Given that numerous events may occur between now and the payoff, assets carry an inherent risk.
To value a future cash flow, we need to understand its present value (PV). The present value calculation hinges on the idea that money today can earn interest.
To value $1 received next year:
$$PV = \frac{1}{1 + r}$$
where
r is the interest rate. If you have $1 today, investing it at rate
r yields:
FV = 1(1 + r) = 1 + r
Consequently, the present value of a future cash flow is discounted by the interest rate.
For cash flows over n years, the present discounted value of cash
flows Zt for t years would be:
$$PV =
\sum_{t=0}^{n} \frac{Z_t}{(1 + r)^t}$$
If we introduce uncertainties in payoffs and interest rates, we adjust our calculations based on
expectations, such that:
$$PV = \sum_{t=0}^{n} \frac{\mathbb{E}[Z_t]}{(1 +
\mathbb{E}[r])^t}$$
where 𝔼[Zt] and 𝔼[r] denote the expected cash flows and interest rates,
respectively.
If the interest rate r is constant.
If the cash flows Zt are constant.
If both are constant (for bonds maturing in n years).
For perpetuities, where cash flows extend indefinitely.
Bonds promise fixed cash flows over time. For a simple bond paying $100 at maturity with a price denoted as
Pt:
$$P_t =
\frac{100}{1 + r}$$
For multi-period bonds, say a two-year bond:
$$P_t = \frac{100}{(1 + r_1)(1 + r_2)}$$
where r1 and r2 are the one-year interest rates at times t and t + 1, respectively.
Two instruments with the same maturity should yield comparable returns. This leads to the principle of
arbitrage:
Return from a one-year bond = Expected return from holding a
two-year bond for a year
The yield on a bond is the constant interest rate that equates the present value of expected cash flows to
the price of the bond:
$$P_t = \frac{100}{(1 + y)^2}$$
The
yield is often interpreted as an average of expected future interest rates.
Stocks differ from bonds primarily:
Stocks pay dividends rather than fixed interest payments.
Stocks don’t have a fixed maturity, and their cash flows can extend indefinitely.
For a stock priced Q with expected dividend D and price P after one
year, the expected return on equity can be modeled as:
$$Q = \frac{D}{(1 +
r + x_s)} + \frac{P_{t+1}}{(1 + r + x_s)}$$
where xs is the risk premium for equity investments.
The price Q can be rearranged to capture the expected dividends and
future price:
$$Q = \sum_{t=1}^{\infty} \frac{D_t}{(1 + r +
x_s)^t}$$
An expansionary monetary policy (a decrease in interest rates) influences the price of both bonds and stocks by reducing discount rates. Thus:
The price of bonds increases as the discounting on future cash flows diminishes.
The price of stocks also tends to rise due to similar discounting effects, as well as enhanced expected future revenues due to increased consumer spending.
An increase in consumer spending may have a dual effect:
Positive: Higher expected revenues and dividends.
Negative: Anticipation of an interest rate hike by the Federal Reserve to manage inflation, leading to higher interest rates and lower prices.
The risk premium, particularly in equity markets, is sensitive to economic conditions, which can lead to significant fluctuations in asset prices, indicating high market volatility especially during economic crises.
Asset prices can exhibit irrational exuberance leading to bubbles, characterized by unsustainable price increases. Historical examples show that when asset prices soar without fundamental backing, they often decline sharply, emphasizing the importance of market psychology in asset pricing.
Expectations play a significant role in economics, especially in asset pricing and the broader economic models discussed throughout the course. This document provides a detailed exploration of how expectations affect consumption and investment using the IS-LM model as a framework.
Economics heavily relies on expectations about the future. All economic actors—investors, consumers, firms, and governments—base their decisions on anticipated future conditions rather than solely current conditions.
Permanent Income Hypothesis (Milton Friedman): Consumption decisions depend more on expected lifetime income than on current income.
Life-cycle Hypothesis (Franco Modigliani): Individuals plan for their consumption based on expected income over their lifetime rather than short-term fluctuations.
Traditionally, consumption (C) was modeled as a function of current
disposable income (Yd):
C = C0 + c ⋅ Yd
where C0 is autonomous consumption and c is the marginal propensity to consume.
Real expectations indicate that consumers smooth consumption over their lifetime, treating temporary income fluctuations differently:
Consumption is related to total wealth rather than just current Yd.
Financial Wealth (Wf)
includes liquid assets, and Human Wealth (Wh) represents expected future labor
income:
W = Wf + Wh
A more realistic consumption function includes both current income and total wealth:
C = C0 + c1 ⋅ Yd + c2 ⋅ W
where c1 and c2 reflect the impacts of current income and wealth on
consumption decisions, respectively.
Investment decisions depend on expected future cash flows from capital assets and current economic
conditions:
I = f(V, Y, r, future
variables)
where:
I = Investment
V = Expected present discounted value of future cash flows
Y = Current output (as a proxy for sales)
r = Interest rate
The value of an investment depends on:
Expected profits over the lifetime of the asset (geometric depreciation model)
Interest rates influencing the present value of future cash flows:
$$\text{Present Value} = \sum_{t=1}^{n} \frac{CF_t}{(1 +
r)^t}$$
where CFt are the cash flows in year
t.
A firm’s ability to borrow is often constrained by its current profitability, leading to the necessity of retaining earnings.
Incorporating expectations into IS-LM, aggregate demand is now a function of both current and expected future
variables:
AD = f(Yt, Yf, G, Tt, Tf, rt, rf)
where Yf, Tf, and rf are expected future values of income, taxes,
and interest rates, respectively.
The modified IS curve will shift more or less based on the permanence of changes in economic variables:
A temporary tax increase will shift IS less than a permanent tax increase.
Expectations of higher future income can mitigate the impact of current tax increases.
The effectiveness of monetary policy lies in managing expectations:
A cut in interest rates has a greater impact when it is perceived as lasting.
Expectations of low future interest rates boost consumption and investment.
Fiscal contractions can lead to expansionary outcomes if they are perceived as reducing future risks or if they are associated with future monetary easing.
Historical cases, such as the fiscal consolidation in Ireland in the late ’80s, illustrate how positive expectations can result in economic growth despite short-term austerity measures.
Expectations play a critical role in shaping economic behavior, influencing investment, consumption, and overall aggregate demand. Understanding the expectations framework enhances the predictive power of economic models like the IS-LM model while showcasing the importance of managing expectations in effective monetary and fiscal policy.