Macroeconomic Analysis

Aggregate Supply

Assuming the price level P was fixed in the short run. This implies a horizontal SRAS (Short Run Aggregate Supply) curve.

However, let’s consider two models: Sticky-Price Model & Imperfect-Information Model where both models imply:

Aggregate supply implication

Sticky-Price Model

Long-Term Contracts between firms and customers

Menu Costs (If own a restaurant and you wish to change the prices)

Firms not wishing to annoy customers with frequent price chages

Assumption: Firms set their own prices. They have a certain level of market power.

So, let’s start with the behaviour of  a tipcal firm. An individual firm’s desired price level is:

sticky-price level

with positive parameters (where a>0). Small p is individual firm’s price level; capital P is th price level in the economy (overall price level); while (Y-Y bar) is the diviation of the output. So, first look at the overall price level. So, if it is high, we expected that the cost of production increased than we expect to charge more. When we look at the economy activity, we ask ourselves how the economy go. If income increases, it men we will have a higher demand for the particular good.

Suppose two types of firms:

  1. Firms with flexible prices, set prices as above
  2. Firms with sticky prices, must set their price before (setting expectation of a price) they know how P and Y will turn out:

Sticy-price model

 

Let’s assume sticky price firms expect that output will equal its natural level. Then, p=EP.

To derive the aggregate supply curve, first find an expression for the overall price level.

s=fraction of firms with sticky prices (s from sticky). Then, we can write overall price as:

sticky-price model 2

Here we can see s= is the fraction of the fixed price firm.

Therefore, if we want to get an equation for P, we want P in left had side of the equation:

stick-price model 3Then, let’s divide both side by s:

stucky price after divededWe can then find two scenarios:

  1. High EP => High P. If firms expect high prices, then firms that must set prices in advance will set them hig. Other firms respond by setting high prices.
  2. High Y => High P. When income is high, the demand for goods is high. Firms with flexible prices set high prices. The greater the fraction of flexible price firms, the smaller is s and the bigger is the effect of Y on P.

 

Imperfect-Information Model

Assumptions:

  1. All wages and prices are perfectly flexible, all markets are clear.
  2. Each supplier produces one good, consumes many goods.
  3. Each supplier knows the nominal price of the good she produces, but does not know the overall price level.
  4. Supply of each good depends on its relative price: the nominal price of the good divided by the overall price level.
  5. Supplier does not know the relative price at the time she makes her production decision, so uses EP.

 

Suppose P rises but EP does not.

Both models of aggregate supply imply the relationship summarized by the SRAS curve & equation.

Suppose we start at the initial level P1, and suppose a positive AD shock moves output above its natural rate and P above the level people had expected.

SRAS equation

SRAS equation 2

Inflation, Unemployment & Philips Curve

If we have a high inflation, we have a low unemployment. If we increase the output, we will low unemployment.

If we have a high unemployment, we will have low inflation.

The Philips curve states that pi depends on:

  1. Expected inflation Epi
  2. Cyclical unemployment: the derivation of the actual rate of unemployment from the natural rate
  3. Supply shocks

Philips curve

where Beta>0 is an exogenous constant.

Therefore, let’s derive the Philip’s Curve from SRAS:

 

OKUN’S LAW – It is about the negative influence between the output and inflation.

%change in real GDP = 3% – 2 = %change in unemployment rate

 

Let’s practice some few questions here to see if you understood everything:

  • Explain the two theories of aggregate supply. On what market imperfection does each theory rely? What do the theories have in common?

Both models of aggregate supply attempt to explain why, in the short run, output might deviate from its long-run “natural rate”— the level of output that is consistent with the full employment of labour and capital. Both models result in an aggregate supply function in which output deviates from its natural rate Y when the price level deviates from the expected price level:

Y = Y + α(P – EP).

The first model discussed was the sticky-price model. The market imperfection in this model is that prices in the goods market do not adjust immediately to changes in demand conditions — the goods market does not clear instantaneously. If the demand for a firm’s goods falls, some respond by reducing output, not prices.

The second model discussed was the imperfect-information model. This model assumes that there is imperfect information about prices, in that some suppliers of goods confuse changes in the price level with changes in relative prices. If a producer observes the nominal price of the firm’s good rising, the producer attributes some of the rise to an increase in relative price, even if it is purely a general price increase. As a result, the producer increases production. In both models, there is a discrepancy between what is really happening and what firms think is happening. In the sticky-price model, some firms expect prices to be at one level and they end up at another level. In the imperfect information model, some firms expect the relative price of their output has changed when it really has not.

 

  • Under what circumstances might it be possible to reduce inflation without causing a recession?

 

The Phillips curve relates the inflation rate to the expected inflation rate and to the difference between unemployment and its natural rate. So one way to reduce inflation is to have a recession, raising unemployment above its natural rate. It is possible to bring inflation down without a recession, however, if we can costlessly reduce expected inflation. According to the rational-expectations approach, people optimally use all of the information available to them in forming their expectations. So to reduce expected inflation, we require, first, that the plan to reduce inflation be announced before people form expectations (e.g., 2 before they form wage agreements and price contracts); and second, that those setting wages and prices believe that the announced plan will be carried out. If both requirements are met, then expected inflation will fall immediately and without cost, and this in turn will bring down actual inflation.

 

  • Suppose that an economy has the Phillips curve: Philips curve exercice

 

a) What is the natural rate of unemployment? 

The natural rate of unemployment is the rate at which the inflation rate does not deviate from the expected inflation rate. Here, the expected inflation rate is just last period’s actual inflation rate. Setting the inflation rate equal to last period’s inflation rate, that is, natural rate of unemployment

we find that u = 0.06. Thus, the natural rate of unemployment is 6 percent.

 

b) Graph the short run and long run relationships between inflation and unemployment.

inflation x unemployment

 

 

 

 

 

 

 

c) How much cyclical unemployment is necessary to reduce inflation by 5%? Using Okun’s Law, calculate the sacrifice ratio.

To reduce inflation, the Phillips curve tells us that unemployment must be above its natural rate of 6 percent for some period of time. We can write the Phillips curve in the form:

Philips curve exercice

 

 

Since we want inflation to fall by 5 percentage points, we want: target inflation

Plugging this into the left-hand side of the above equation, we find:

solution

 

 

Hence, we need 10 percentage points of cyclical unemployment above the natural rate of 6 percent. Okun’s law says that a change of 1 percentage point in unemployment translates into a change of 2 percentage points in GDP. Hence, an increase in unemployment of 10 percentage points corresponds to a fall in output of 20 percentage points. The sacrifice ratio is the percentage of a year’s GDP that must be forgone to reduce inflation by 1 percentage point. Dividing the 20 percentage-point decrease in GDP by the 5 percentage-point decrease in inflation, we find that the sacrifice ratio is 20/5 = 4. d.

d) Inflation is running at 10%. The Central Bank wants to reduce it to 5%. Give two scenarios that will achieve that goal.

One scenario is to have very high unemployment for a short period of time. For example, we could have 16 percent unemployment for a single year. Alternatively, we could have a small amount of cyclical unemployment spread out over a long period of time. For example, we could have 8 percent unemployment for 5 years. Both of these plans would bring the inflation rate down from 10 percent to 5 percent, although at different speeds.

 

  • According to the rational-expectations approach, if everyone believes that policymakers are committed to reducing inflation, the cost of reducing inflation – the sacrifice ratio – will be 4 lower than if the public is skeptical about the policymakers’ intentions. Why might this be true? How might credibility be achieved?

The cost of reducing inflation comes from the cost of changing people’s expectations about inflation. If expectations can be changed costlessly, then reducing inflation is also costless. Algebraically, the Phillips curve tells us that:

expectations

 

 

If the government can lower expected inflation Eπ to the desired level of inflation, then there is no need for unemployment to rise above its natural rate. According to the rational-expectations approach, people form expectations about inflation using all of the information that is available to them. This includes information about current policies in effect. If everyone believes that the government is committed to reducing inflation, then expected inflation will immediately fall. In terms of the Phillips curve, Eπ falls immediately with little or no cost to the economy. That is, the sacrifice ratio will be very small. On the other hand, if people do not believe that the government will carry out its intentions, then Eπ remains high. Expectations will not adjust because people are skeptical that the government will follow through on its plans. Thus, according to the rational-expectations approach, the cost of reducing inflation depends on how resolute and credible the government is. An important issue is how the government can make its commitment to reducing inflation more credible. One possibility, for example, is to appoint people who have a reputation as inflation fighters. A second possibility is to have Parliament pass a law requiring the Central Bank to lower inflation. Of course, people might expect the Central Bank to ignore this law, or expect the Parliament to change the law later. A third possibility is to pass a constitutional amendment limiting monetary growth. People might rationally believe that a constitutional amendment is relatively difficult to change.

 

So, let’s move to see how we can actually incorporate dynamics into the AD-AS model we previously studied. We will following understanding how to use the dynamic AD-AS model to illustrate long-run economic growth; and moving on to how to use the dynamic AD-AS model to trace out the effects over time of various shocks and policy changes on output, inflation, and other endogenous variables.

 

The dynamic model of aggregate demand and aggregate supply gives us more insight into how the economy works in the short run. It is a simplified version of a DSGE model, used in cutting-edge macroeconomic research.
(DSGE = Dynamic, Stochastic, General Equilibrium)

The dynamic model of aggregate demand and aggregate supply is built from familiar concepts, such as:

  1. the IS curve, which negatively relates the real interest rate and demand for goods & services;
  2. the Phillips curve, which relates inflation to the gap between output and its natural level, expected inflation, and supply shocks’
  3. the adaptive expectations, a simple model of inflation expectations

 

How the dynamic AD-AS model is different from the standard model?

  1. Subsequent time periods are linked together: Changes in inflation in one period alter expectations of future inflation, which changes aggregate supply in future periods, which further alters inflation and inflation expectations.
  2. The vertical axis of the DAD-DAS diagram measures the inflation rate, not the price level.
  3. Instead of fixing the money supply (defined by the central bank), the central bank follows a monetary policy rule that adjusts interest rates when output or inflation change.

The model’s elements has five equations and five endogenous variables (remember the model is just idenfied):

  1. Output (output and GDP is not the same, but we will talk about GDP here as an output).
  2. Inflation
  3. Real interest rate
  4. Nominal interest rate
  5. Expected inflation

output equation

 

 

alpha = measures the interest rate sensitivity of demand

p = “natural rate of interest” – in absence of demand shocks,

Error term = it could be a demand shock, normally random and zero on
average

 

Looking at the graph and the output equation, why when we have a high interest rate, the demand falls?

Because of reduction on investment because the cost of borrowing is high. Drops consumption as well.

Always remember that people have adaptative expectation!!

 

the real interest rate

 

rt => ex ante real interest rate is the real interest rate that the parameter and the lender expect when the loan is made, known at t.

 

Ex. Post reat interest rate (actual_

 

 

 

inflation equation

 

 

 

 

 

 

 

expected inflation equation

 

 

 

 

 

 

 

 

the nominal interest rate equation

 

 

0pi = measures how much the central bank adjusts the interest rate when inflation deviates from its target

0y = measures how much the central bank adjusts the interest rate when output deviates from its natural rate

 

 

Let’s have a look at a particular case study:

  • The Taylor Rule: Economist John Taylor proposed a monetary policy rule very similar to ours.

John Taylor ruleThe Taylor Rule matches Federal policy fairly well.…

RBA and interest rate rules

Does RBA follow an interest rate rule, and if so, what is the rule?

  1. The mandate of RBA (1996): keep ‘underlying inflation’ between 2-3%.
  2. RBA does not say that it follows a rule. However, evidence suggests that the RBA behaved as if it followed a rule that includes targets for both inflation and unemployment (probably a type of Taylor’s rule).

endogenous variables

 

 

 

 

 

 

exogenous variables

 

 

 

 

 

 

parameters

 

 

 

 

 

 

 

The model’s long-run equilibrium

The normal state around which the economy fluctuates. Two conditions required for long-run equilibrium:

two conditions

Plugging the preceding conditions into the model’s five equations and using algebra yields these long-run values:

long run equations

Finally, we are going to move and have a look at The Dynamic Aggregate Supply Curve (DAS). The DAS curve shows a relation between output and inflation that comes from the Phillips Curve and Adaptive Expectations:

DASDAS graph

Now, let’s have a look at the The Dynamic Aggregate Demand Curve (DAD). To derive the DAD curve, we will combine four
equations and then eliminate all the endogenous variables other than output and inflation. Let’s start with the demand for goods and services:

deriving DADderiving DAD2The Dynamic Aggregate Demand Curve:

 

DAD curveThe short-run equilibrium:

the short run equilibrium

 

 

 

 

 

 

Long-run growth:

long run growth

 

 

 

 

 

 

 

Let’s practice some questions here to see if you understood everything:

 

  • On a carefully labeled graph, draw the dynamic aggregate supply curve. Explain the slope of this curve.The equation for the dynamic aggregate supply curve is:

DASRecall that φ is a positive parameter that measures how rapidly firms adjust their prices in response to output fluctuations. When output in the economy rises above its natural level, firms experience rising marginal costs and will increase prices. There is therefore a positive
relationship between the level of output and inflation in the economy. The dynamic aggregate supply curve is upward sloping. The steepness of the dynamic aggregate supply curve depends on how quickly marginal costs rise when output is above its natural level and on how quickly firms respond to the rising marginal cost with an increase in prices. The dynamic aggregate supply curve will be steeper if marginal costs rise more quickly and if firms respond by increasing prices more quickly. The dynamic aggregate supply curve is illustrated in figure below.

DAS graph labeled

  • Suppose a central bank does not satisfy the Taylor principle; that is, θπ is less than zero. Use a graph to analyze the impact of a supply shock. Does this analysis contradict or reinforce the Taylor principle as a guideline for the design of monetary policy?The equation for the dynamic aggregate demand curve is given below:

DADcurve equation

The parameter θπ measures the central bank’s responsiveness to changes in the inflation rate. When θπ is large, the central bank aggressively responds to changes in the inflation rate. When θπ is small but still positive, the central bank has a weak response to changes in the inflation rate, and the dynamic aggregate demand curve becomes very steep. If θπ becomes negative, the dynamic aggregate demand curve actually has a positive slope, as can be seen in the equation above. In this case, a supply shock that shifts the dynamic aggregate supply curve up and to the left will lead to ever-increasing inflation, even if the shock is temporary. This is due to the fact that output remains above its natural level since the central bank’s increase in nominal interest rates is not enough to increase real interest rates.
The supply shock will shift the dynamic aggregate supply curve up and to the right as rising production costs increase the inflation rate. Since nominal interest rates rise by less than the inflation rate, real interest rates will fall and therefore output will rise. In figure below, this is shown as a movement from point A to point B. Since output is above the natural rate, inflation will continue to rise, and the dynamic aggregate supply curve will continue to shift up and to the left as people adjust their expectations about inflation. This analysis reinforces the Taylor principle as a guideline for the design of monetary policy in that the central bank wants to maintain low and stable inflation.

impact of the supply shock

  • Use the dynamic AD-AS model to solve for inflation as a function of only lagged inflation and the supply and demand shocks (assuming target inflation is a constant).

AD-AS model

a) According to the equation you have derived, does inflation return to its target after a shock? Explain.

A supply or demand shock will lead to an increase in current inflation. As the economy adjusts and returns to long-run equilibrium, the inflation rate will return to its target level. Note that the coefficient on the lagged inflation variable in the equation above is positive but less than 1. This means that inflation in time t + 1 will be less than inflation in time t, and that inflation will eventually return to its target rate.
b) Suppose the central bank does not respond to changes in output but only to changes in inflation, so that θy = 0. How, if at all, would this fact change your answer to part (a)?

If the central bank does not respond to changes in output so that θy is zero, then the economy will still return to its target inflation rate after a supply or demand shock because the coefficient on the lagged inflation variable in the equation above is still positive but less than 1. In this case, inflation should return more quickly to its target rate. This is because the coefficient on lagged inflation has become smaller (the change in the numerator is larger in comparison to the change in the denominator). The dynamic aggregate demand curve is relatively flat when the central bank only cares about inflation.
c) Suppose the central bank does not respond to changes in inflation but only to changes in output, so that θπ = 0. How, if at all, would this fact change your answer to part (a)?

If the central bank does not respond to changes in inflation so that θπ is zero, then the coefficient on lagged inflation in the above inflation equation equals 1. In this case, the economy will not return to its target inflation rate after a demand or supply shock. The
demand or supply shock will increase inflation in time t. When θπ is zero, inflation in time t + 1 is equal to inflation in time t.

 

 

d) Suppose the central bank does not follow the Taylor principle but instead raises the nominal interest rate only 0.8 percentage point for each percentage-point increase in inflation. In this case, that is θπ? How does a shock to demand or supply influence the path of inflation?

The Taylor rule says that a one-percentage-point increase in inflation will increase the nominal interest rate by 1 + θπ percentage points. If the central bank increases the nominal interest rate by only 0.8 percentage points for each one-percentage-point increase in the nominal interest rate, then this means θπ is equal to –0.2. When θπ is negative, the dynamic aggregate demand curve is upward sloping. A shock to demand or supply will set the economy on a path of ever-increasing inflation. This path of ever-increasing inflation will occur because real interest rates will continue to fall and output will remain above the natural level. You can see this phenomenon in the above
equation for inflation: If θπ is negative, the coefficient on lagged inflation is greater than 1. That larger-than-one coefficient is the mathematical manifestation of explosive inflation.

 

Consumption Behavior – how people behave

Let’s talk about some very important economic work by:

  1. John Maynard Keynes: consumption and current income
  2. Irving Fisher: intertemporal choice
  3. Franco Modigliani: the life-cycle hypothesis
  4. Milton Friedman: the permanent income hypothesis
  5. Robert Hall: the random-walk hypothesis
  6. David Laibson: the pull of instant gratification

 

Keynes’s conjectures were:

1. 0 < MPC < 1

Where MPC is the marginal propensity to consume. Higher income households will consume more and MPC > than low income household. People with high income will save more than low income earners.

2. Average propensity to consume (APC) falls as income rises. (APC = C/Y )

3. Income is the main determinant of consumption. It might have other factors but income will be the main one.

The Keynesian consumption function

*If we don’t have any income, we still consume C bar as we have to eat to live. So, there will always be an initial consumption.

The Keynesian consumption as income rises

*Remember from math that every slope = the rise/the run

Consumption Puzzle

 

Irving Fisher and Intertemporal Choice:

  1. The basis for much subsequent work on consumption.
  2. Assumes consumer is forward-looking and chooses consumption for the present and future to maximize lifetime satisfaction.
  3. Consumer’s choices are subject to an intertemporal budget constraint, a measure of the total resources available for present and future consumption.

The basic two-period model

Period 1: the present

Period 2: the future

Notation

Y1, Y2 = income in period 1, 2

C1, C2 = consumption in period 1, 2

S = Y1 – C1 = saving in period 1 (S < 0 if the consumer borrows in period 1)

First, we want to derive budget constraint:

Period 2 budget constraint:

 

budget constrain derivation

The intertemporal budget constraint

intertemporal budget constraint 2

 

*If C2 = 0, it means that we actually consume everything today.

intertemporal budget constraint 3

 

Consumer preferences

 

consumer preference 2

 

Optimization

 

How C responds to changes in Y

 

Now, we would like to compare both models:

Keynes vs. Fisher

Keynes: Current consumption depends only on current income.

Fisher: Current consumption depends only on the present value of lifetime income. The timing of income is irrelevant because the consumer can borrow or lend between periods.

 

How C responds to changes in r

 

How C responds to changes in r

  1. Income effect: If consumer is a saver, the rise in r makes him better off, which tends to increase consumption in both periods.
  2. Substitution effect: The rise in r increases the opportunity cost of current consumption, which tends to reduce C1 and increase C2.
  3. Both effects: Increase C2.

Whether C1 rises or falls depends on the relative size of the income & substitution effects.

Constraints on borrowing

  • In Fisher’s theory, the timing of income is irrelevant: Consumer can borrow and lend across periods. However, if consumer faces borrowing constraints (aka “liquidity constraints”), then she may not be able to increase current consumption.

 

*If you can save the money…

Constraints on borrowing

*If you cannot save the money…

constrain on borrowing 2

 

consumer constraint 3

 

consumer constraint 4

 

Franco Modigliani – The Life-Cycle Hypothesis:

Fisher’s model says that consumption depends on lifetime income, and people try to achieve smooth consumption. The Life Cycle Hypothesis (LCH) says that income varies somewhat predictably over the phases of the consumer’s “life cycle,” and saving and borrowing allows the consumer to achieve smooth consumption.

The basic model:

W = initial wealth

Y = annual income until retirement (assumed constant)

R = number of years until retirement

T = lifetime in years

Assumptions:

  •  zero real interest rate (for simplicity)
  • consumption-smoothing is optimal

life cycle hypothesis model

Implications of the Life-Cycle Hypothesis:

The LCH can solve the consumption puzzle:

The life-cycle consumption function implies APC = C/Y = a(W/Y ) + B”beta”.

Across households, income varies more than wealth, so high-income households should have a lower APC than low-income households. Over time, aggregate wealth and income grow together, causing APC to remain stable.

 

Milton Friedman – The Permanent Income Hypothesis

Y = YP + YT

where Y = current income

YP = permanent income average income, which people expect to persist into the future

YT = transitory income temporary deviations from average income

 

Consumers use saving & borrowing to smooth consumption in response to transitory changes in income. The PIH consumption function:

C = aY^P where a is the fraction of permanent income that people consume per year.

The PIH can solve the consumption puzzle:

The PIH implies APC = C/Y = aY^P/Y

If high-income households have higher transitory income than low-income households, APC is lower in high-income households. Over the long run, income variation is due mainly (if not solely) to variation in permanent income, which implies a stable APC.

 

PIH vs. LCH

Both: people try to smooth their consumption in the face of changing current income.

LCH: current income changes systematically as people move through their life cycle.

PIH: current income is subject to random, transitory fluctuations.

Both can explain the consumption puzzle.

 

Robert Hall – The Random-Walk Hypothesis (very common in Econometrics)

Based on Fisher’s model & PIH, in which forward-looking consumers base consumption on expected future income. Hall adds the assumption of rational expectations, that people use all available information to forecast future variables like income.

If PIH is correct and consumers have rational expectations, then consumption should follow a random walk: changes in consumption should be unpredictable (could be caused by shocks).

A change in income or wealth that was anticipated has already been factored into expected permanent income, so it will not change consumption.

Only unanticipated changes in income or wealth that alter expected permanent income will change consumption.

Implication of the R-W Hypothesis: If consumers obey the PIH and have rational expectations, then policy changes will affect consumption only if they are unanticipated. 

The Psychology of Instant Gratification:

Theories from Fisher to Hall assume that consumers are rational and act to maximize lifetime utility. Recent studies by David Laibson and others consider the psychology of consumers.

Consumers consider themselves to be imperfect decision-makers. In one survey, 76% said they were not saving enough for retirement. Laibson: The “pull of instant gratification” explains why people don’t save as much as a perfectly rational lifetime utility maximizer would save.

 

Reference:

Reserve Bank of Australia –

Mankiw 9th edition, Chapters 14, 15 & 16

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