+1 (208) 254-6996 essayswallet@gmail.com
  

In Chapter 15, we learned about DSGE models. Think about one macro-related research question and discuss how you would analyze that question using a DSGE model. 

1Page

Don't use plagiarized sources. Get Your Custom Essay on
DSGE Models: The Frontier Of Business Cycle Research
Just from $13/Page
Order Essay

Chapter 15

DSGE Models: The Frontier of Business Cycle Research

1

15.1 Introduction

In this chapter, we learn

how business cycle models and growth models are connected.

that DSGE models incorporate microfoundations, dynamics, general equilibrium, and shocks.

that DSGE models predict how the economy evolves over time in response to shocks.

Robert Lucas, Finn Kydland, Ed Prescott, Tom Sargent, and Chris Sims revolutionized modern short-run macro models in the 1970s and 1980s.

The class of models they developed are referred to as dynamic, stochastic general equilibrium (DSGE) models.

dynamic: examine the economy over time

stochastic: involve shocks that lead to macroeconomic fluctuations

general equilibrium: multiple markets clear simultaneously

Labor markets and asset markets endogenously determine all prices.

DSGE models make quantitative predictions about how the economy evolves over time in response to shocks.

The short-run model in previous chapters contains many of the key insights of DSGE models.

2

15.2 A Brief History of DSGE Models

Real business cycle models

First DSGE models

Used Solow model of growth to study macroeconomic fluctuations

Introduced total factor productivity (TFP) shocks

Positive shock: new technology, institutions

Negative shock: institutions, taxes

Using the Solow model, the assumption can be made that TFP changes over time, instead of growing at a constant rate or being a parameter.

The introduction of the Internet might represent a positive technology shock that would raise TFP and cause the economy to boom.

Changes in taxes (such as an increase in corporate taxes) or certain institutional changes may cause negative shocks to TFP.

TFP growth from the Solow growth accounting formula shows large fluctuations in TFP.

3

U.S. Total Factor Productivity Growth

4

Figure 15.1, U.S. Total Factor Productivity Growth

Using the growth accounting formula, we can impute the value of TFP over time.

Notice that TFP fluctuates dramatically over time and often becomes negative.

Are these movements important in explaining business cycles?

Source: John Fernald, “A Quarterly, Utilization-Adjusted Series on Total Factor Productivity,” Federal Reserve Bank of San Francisco Working Paper 2012–19, September 2012.

A Brief History of DSGE Models

TFP shocks:

Positive → cause the economy to boom

Negative → cause GDP to decline

Real Business Cycle models

“Real” shocks

Output exhibits fluctuations

Consider augmenting the Solow model with TFP shocks:

A positive TFP shock would increase GDP.

A negative TFP shock would decrease GDP.

The economy would go through cycles because of TFP shocks.

Real Business Cycle (RBC) models:

Shocks to TFP are “real” (as opposed to “nominal”).

Shocks to TFP cause output to fluctuate as in the business cycle.

There are a few obvious shortcomings of this kind of model:

As evidenced in Figure 15.1, not all macroeconomic fluctuations are driven by TFP shocks.

For example, the recession of 2001 had no corresponding negative TFP shock.

Regardless, modeling production and dynamics to study business cycles was novel.

This led to a flood of new macro research.

Economists began to include other shocks and variables.

Note: The Solow model was used by Kydland and Prescott and by Long and Plosser.

5

From Real Business Cycle to DSGE

Components of modern DSGE models

Endogenous variables

Shocks

Features that affect the way shocks impact endogenous variables over time

DSGE models have moved away from the “real” classification by incorporating monetary policy.

6

Endogenous Variables

wages

interest rates

inflation

international trade

foreign debt

government debt

exchange rates

hours worked

GDP

consumption

investment

government purchases

employment

unemployment

capital

DSGE models can be large or small systems.

One important component of almost all DSGE models is the labor market.

Decisions in the labor market determine how much output is produced:

Hours worked

Searching for employment

Job effort

7

Shocks

Shocks to the economy

Cause endogenous variables to fluctuate

Include total factor productivity, government purchases, taxes, monetary policy, energy prices, and financial frictions

Can be temporary or permanent

May be current or anticipated

Uncertainty about the future can slow economic activity today.

Shocks can be temporary or permanent.

For instance, government spending may be temporarily high this year, or there could be a long-lasting change in the size of the government.

Shocks may be current or anticipated.

A shock may occur now or instead we may get news today of a shock that will occur in the future, for example, a change in government policy or even the arrival of a new technology.

Uncertainty about policy of the future can influence economic activity today; for example, during a presidential election in the United States, firms may delay investment or hiring decisions.

8

Features and Mathematics

DSGE model features

Nominal rigidities

Adjustment costs

Heterogeneity

Incomplete markets

DSGE models are complex to solve mathematically because they involve many individual decisions.

Nominal rigidities:

Monetary policy only has real effects if some friction interferes with price adjustment.

Sticky nominal wages and sticky prices are two prominent examples.

Adjustment costs:

It is expensive to change the capital stock by a large amount.

The dynamic response of variables to shocks is often slowed down.

The peak effect of the shock occurs several periods after the shock itself.

This is the opposite of the Solow model, where the effect of the shock is the largest immediately after it hits.

Heterogeneity:

People and firms are different.

Heterogeneity affects the adjustment to shocks.

For example, even if individuals have completely inelastic labor supply, they want to work 40 hours per week or not at all.

The elasticity of labor supply when aggregated across heterogeneous households can be very different.

People may differ according to their reservation wage.

People may require different wages to enter the labor market.

When shocks change the wage, people enter and exit from the labor market.

The aggregate elasticity depends on the distribution of reservation wages rather than on any individual’s elasticity.

Incomplete markets:

Adverse selection and moral hazard may result in some markets missing.

Not all trades between people are permitted if they are separated by time or geography.

Shocks may have larger effects on the economy, and these shocks may be more costly.

For example, unemployment may be concentrated on a subset of the labor force, and those who are unemployed may experience a disproportionate decline in consumption.

Key variables are no longer constant, and these are economic decisions that individuals make each period.

DSGE models can be examined using numerical simulations.

9

15.3 A Stylized Approach to DSGE

Focus on the labor market

Labor demand:

Derived from firm’s profit-maximization problem

Decide how much labor to hire

Negative slope–diminishing MPL

Labor supply:

Decisions by people about how much to work

Most DSGE models contain at least three markets:

Labor

Capital

Output

Many DSGE models have far more markets.

This is what makes it a general equilibrium market.

However, we can learn a lot from just examining the labor market.

The labor demand curve is derived from the firm’s profit maximization problem.

Firms hire labor until the MPL equals the wage.

Maximizing profit according to the production function: 𝑌=𝐴 ̅𝐾^(1/3) 𝐿^(2/3)

Hire until MPL=2/3 (𝐴 ̅𝐾^(1/3))/𝐿^(1/3) =𝑤

Marginal product of labor: the amount of extra output produced by the last worker hired

Because of the assumption that the MPL declines as more labor is hired, the labor demand curve is downward sloping.

Diminishing marginal returns to labor (exponent less than one) implies that each additional unit of labor that is hired produces a smaller and smaller gain in output (holding constant capital and TFP).

The labor supply curve is derived from the individual’s utility maximization problem.

Labor supply: people choose how much to work to maximize utility.

Use the following specification: 𝐿^𝑆=𝑙 ̅ 𝑤/𝑐

where w is the real wage and c denotes consumption per person.

Labor supply is increasing in the wage.

Depends on the wage-to-consumption ratio

Over time, the real wage increases, and consumption per person also rises.

In fact, these growth rates are approximately the same, so that w/c is relatively stable.

Therefore, the amount of labor supplied (per person) would be stable as well.

𝑙 ̅ is the parameter that governs the overall magnitude of labor supply.

10

The Labor Market in the DSGE Model

L

0

w

0

w

c

L

d

:

w

=

2

3

A

K

1

/

3

L

1

/

3

.

Animated Figure 15.2, The Labor Market in the DSGE Model

The labor demand curve slopes downward, reflecting the declining marginal product of labor as firms expand employment.

Also, notice that an increase in TFP or capital will cause the labor demand curve to shift out.

The labor supply curve slopes upward, as people work harder when the wage is higher.

Figure 15.2 shows the basic equilibrium in the labor market.

Where labor supply equals labor demand determines the real wage and the amount of labor that gets used in production.

We do not formally model how the level of consumption is determined at each point in time.

The main thing that makes DSGE models hard to solve mathematically is the forward-looking consumption problem.

So, we assume consumption is exogenous.

This is not an unreasonable assumption. The permanent income hypothesis tells us that consumption should not move much over the business cycle.

11

15.4 Using the Stylized DSGE Model

Examine the following:

a negative TFP shock

a change in taxes

a rise in the size of government purchases

a shock to monetary policy

We now use this stylized DSGE framework to study business cycles through a series of examples.

12

A Negative TFP Shock in the DSGE Model

L

9

w

9

L

0

A

w

0

L

s

,

·

L

d’

w

c

L

d

:

w

=

2

3

A

K

1

/

3

L

1

/

3

.

B

Animated Figure 15.3, A Negative TFP Shock in the DSGE Model

Suppose there is a negative shock that temporarily reduces the TFP parameter, A-bar.

Firms do not want to produce due to low demand, so labor demand shifts down.

Note: TFP only enters the demand curve.

Lower A decreases the amount of output that an extra worker can produce.

The MPL is lower for any given L.

The TFP shock is temporary, so effects on consumption are small.

The equilibrium in the labor market moves from point A to point B.

In response to a negative TFP shock, employment falls, and the equilibrium wage falls as well.

This looks a lot like a recession.

The basic patterns explain why early DSGE models focused on TFP shocks.

They lead the economy to respond in ways that look similar to the business cycle.

13

The Imposition of a Sales Tax in the DSGE Model

L

L

0

A

w

9

w

0

L

s

,

·

w

c

L

d

:

w

=

2

3

A

K

1

/

3

L

1

/

3

.

L

d’

:

w

(1

)

2

3

A

K

1

/

3

L

1

/

3

.

τ

B

14

Animation: bring in axes, Ls and Ld , and point A. Add Ld’ and point B.

Suppose firms must pay a tax for every dollar of output they sell.

Assume the policy change is a temporary rise in the tax rate from zero to some positive value, t.

Since firms pay the tax, the labor demand curve shifts.

Firms now hire until the after-tax marginal product of labor falls to equal the wage.

(1−𝑡)2/3 (𝐴 ̅𝐾^(1/3))/𝐿^(1/3) =𝑤

This reduces the amount that the firm earns at any given level of employment, lowering the MPL and shifting the labor demand curve in.

Wages and employment decline.

Notice that the effects here are similar to a negative TFP shock (also similar to a recession).

A Rise in Government Purchases

L’

L

0

A

w’

w

0

L

d

:

w

=

2

3

A

K

1

/

3

L

1

/

3

.

L

s’

B

15

Animated Figure 15.5, A Rise in Government Purchases

Consider an increase in government purchases, financed through a rise in lump-sum taxes at some unspecified point in the future.

The implied tax burden lowers permanent income and therefore reduces consumption today.

Consumption is the variable in our DSGE model that allows future events to affect the economy today.

A general principle in microeconomics is that as people get richer, they generally consume more of all goods, including leisure.

This means that consumption and leisure will typically move in the same direction.

This means the labor supply curve shifts to the right.

The equilibrium effect of this shock is to increase employment and reduce the real wage.

Sticky Wages

Distinguish between nominal and real variables

W is the nominal wage

P is the price level

W/P = w is the real wage

Introduce nominal wage rigidity (sticky wages)

To study the effect of monetary policy in the DSGE framework, we need to distinguish between real and nominal variables.

If the classical dichotomy holds, then changes in monetary policy will only affect nominal variables in the economy and have no real effects.

For monetary policy to have real effects on the economy, we must introduce frictions in the adjustment of prices.

We introduce frictions in two steps:

First, suppose there is nominal wage rigidity (sticky wages).

That is, nominal wages are slow to change in the economy, particularly in the downward direction.

Assume

16

Sticky Wages in the DSGE Model

L

0

A

L

s

W

P

0

L

d

Unemployment

17

Animated Figure 15.6, Sticky Wages in the DSGE Model

Wages, W, are stuck at W-bar, above the market equilibrium wage.

More people would like to work at that wage than firms are willing to hire, so there is involuntary unemployment.

Employment is set by the demand side, as both sides of the trade must be willing participants.

This mechanism is one of the key ways that DSGE models incorporate unemployment.

A Monetary Expansion with Sticky Wages

A

L

0

L

d

L

B

18

Figure 15.7, A Monetary Expansion with Sticky Wages

Now, consider what happens when there is expansionary monetary policy.

Lowering the federal funds rate increases other prices (only wages are sticky).

The overall price level P rises to some new level P’.

With the nominal wage stuck at W, the price increase leads the real wage W/P to decline.

At this lower real wage, labor demand is higher and labor supply is lower.

The result is a move to point B, where employment is higher and unemployment is lower.

A change in monetary policy leads the real wage and employment to move in opposite directions.

This is not the signature pattern we would expect.

For example, booms are not generally thought of as times when real wages are low, and recessions are certainly not thought of as times when real wages are high.

As we see next, this pattern changes when we consider nominal stickiness in prices instead of wages.

A Monetary Expansion with Sticky Prices

A

L

0

L

d

L

d’

L

W’

P

W

0

P

B

19

Animated Figure 15.8, A Monetary Expansion with Sticky Prices

It is usually assumed that output is determined by the demand side of the market.

Then, from the production function, the amount of labor that firms must demand is whatever amount is needed to produce the required output.

In this case, the labor demand curve is now vertical.

In other words, labor demand is now insensitive to the wage.

Firms have agreed to produce whatever output is demanded of them, regardless of the wage.

Now consider the effect of an expansionary monetary policy (a lower fed funds rate) under sticky prices.

The monetary expansion increases demand in the economy since prices are fixed.

Firms need to produce a higher level of output and therefore require more labor: the labor demand curve shifts to the right.

To induce more people to work, the wage must rise (recall that the nominal wage is flexible in this case), and with sticky prices, this leads to an increase in real wages, as the economy moves to point B.

Models in which sticky prices and monetary shocks play an important role are sometimes called new Keynesian models.

15.5 Quantitative DSGE Models

Full DSGE models incorporate the complete dynamic response of all economic variables to all shocks.

The Smets–Wouters model

Incorporates shocks previously discussed

Includes both sticky prices and sticky wages

In this section, we illustrate the richness and quantitative nature of modern DSGE models.

By “estimated,” we mean that the parameters of the DSGE model are chosen to make the model match the data for the U.S. economy as accurately as possible.

The particular model we present here was originally estimated by Frank Smets and Rafael Wouters.

Versions of this model are now used by macroeconomic forecasters and central banks around the world—including the Federal Reserve and the European Central Bank.

20

Impulse Response Functions

An impulse response function shows how one macroeconomic variable of interest responds over time to an economic shock.

The next slide shows the impulse response function for GDP in the estimated Smets-Wouters model.

By what percent does GDP change after a temporary 1 percentage point increase in the fed funds rate?

21

The Response of GDP to a Monetary Policy Shock

22

Figure 15.9, The Response of GDP to a Monetary Policy Shock

A 1 percentage point increase in the fed funds rate causes GDP to fall by about 0.2 percent in the first quarter after the shock.

At its peak three to four quarters after the shock, GDP is lower by 0.33 percent.

GDP then gradually recovers back to normal over the next several years.

Source: Frank Smets and Rafael Wouters, “Shocks and Frictions in U.S. Business Cycles: A Bayesian DSGE Approach,” American Economic Review, vol. 97, no. 3 (2007), pp. 586–606.

The Dynamic Effects of a Monetary Policy Shock

23

Figure 15.10, The Dynamic Effects of a Monetary Policy Shock

Because DSGE models also include consumption, hours worked, and inflation, we can study how each of these variables responds to a shock.

The response of a representative set of macro variables to the monetary policy shock is shown in Figure 15.10.

The response of the economy looks very much like the response we saw in our AS/AD framework in earlier chapters.

In terms of the labor market version of the DSGE model, it also looks like the version of that framework with sticky prices.

That is, GDP, consumption, and hours worked all decline in response to the surprise tightening of monetary policy, which causes inflation to decline as well.

Source: Frank Smets and Rafael Wouters, “Shocks and Frictions in U.S. Business Cycles: A Bayesian DSGE Approach,” American Economic Review, vol. 97, no. 3 (2007), pp. 586–606.

A TFP Shock

Quantitative DSGE models incorporate multiple shocks simultaneously.

The Smets-Wouters model features

Productivity shocks

Shocks to government purchases

Financial frictions

Investment shocks

Labor market shocks

Shocks to markups in product markets

24

The Dynamic Effects of a TFP Shock

25

Figure 15.11, The Dynamic Effects of a TFP Shock

This figure shows the response of four macro variables to a temporary increase in total factor productivity.

The initial size of the shock is 1 percent, and the shock decays slowly to zero.

Source: Frank Smets and Rafael Wouters, “Shocks and Frictions in U.S. Business Cycles: A Bayesian DSGE Approach,” American Economic Review, vol. 97, no. 3 (2007), pp. 586–606.

The Dynamic Effects of a Shock to Government Purchases

26

Figure 15.12, The Dynamic Effects of a Shock to Government Purchases

This figure shows the response of four macro variables to a temporary increase in government purchases.

The initial size of the shock is 1 percent, and the shock decays slowly to zero.

Source: Frank Smets and Rafael Wouters, “Shocks and Frictions in U.S. Business Cycles: A Bayesian DSGE Approach,” American Economic Review, vol. 97, no. 3 (2007), pp. 586–606.

The Dynamic Effects of a Financial Frictions Shock

27

Figure 15.13, The Dynamic Effects of a Financial Frictions Shock

This figure shows the response of four macro variables to a temporary rise in financial frictions.

The initial shock raises the interest rate faced by consumers by 1 percentage point above the fed funds rate.

The shock decays quickly to zero.

Source: Frank Smets and Rafael Wouters, “Shocks and Frictions in U.S. Business Cycles: A Bayesian DSGE Approach,” American Economic Review, vol. 97, no. 3 (2007), pp. 586–606.

15.6 Conclusion

Macroeconomists argue about the importance of various shocks and various frictions in accounting for economic fluctuations.

These arguments often center around the extent to which certain frictions are quantitatively important.

How sticky are wages and prices?

How important are credit market frictions?

How elastic is labor supply in the economy?

28

Conclusion—1

The basic framework we should use to understand macroeconomic fluctuations developed over the past 50 years.

A key element is a basic growth model like the Solow model.

Another key element is that the model is populated by individual economic agents.

29

Conclusion—2

The basic DSGE framework has been enriched in many ways recently.

The models make precise quantitative predictions about the complete dynamics of a host of endogenous variables.

30

Order your essay today and save 10% with the discount code ESSAYHELP