5+6 - The New Keynesian Model I and II

Question 1

What is the New Keynesian model?

Answer 1

DSGE model with sticky prices and monopolistic competition

Question 2

What are the assumptions of classical DSGE models?

Answer 2

fully flexible prices and wages

firms act under monopolistic competition

Question 3

How can the New Keynesian Model break classical dichotomy?

Answer 3

by integrating price stickiness into the analysis

Question 4

What is Calvo price setting?

Answer 4

• θ denotes probability of prices “sticking” in a certain period.
• Each firm may reset its price with a probability of 1 - θ in any given period.

Question 5

What is the average price duration in Calvo price setting?

Answer 5

Average duration of a price:

1 / (1-θ)

Question 6

What is special about this firm’s maximization problem?

Answer 6

• price-setting is forward-looking (sticky prices)
• assumptions/restrictions are same as in normal setting

Question 7

What is the interpretation of Qₜ,ₜ₊ₖ?

Answer 7

it is the stochastic discount factor for nominal payoffs (SDF), that makes sure that firms behave in the best interests of housholds

Question 8

How does the Lagrangian of the firm’s maximization problem in the NKM use the “Calvo assumption”?

Answer 8

It takes into account that future prices will only affect current decisions when the price sticks

Question 9

What is p* in the steady state of the staggered price setting (NKM)?

Answer 9

p* = 1

Question 10

What is the equation for the New Keynesian Phillips Curve?

Answer 10

Question 11

What is this:

Answer 11

output gap = output - natural output

Note: An economy’s natural level of output occurs when all available resources are used efficiently. It equals the highest level of production an economy can sustain. It is “natural” because an economy returns to its natural level of output following a recession or overheated period.

Question 12

How to interpret this equation? What does it mean and what does it suggest?

Answer 12

• It is the new keynesian phillips curve, reformulated through forward substitution of inflation
• It suggests that inflation leads the output gap = the current inflation predicts the future output gap (-> forward looking nature of inflation)

Question 13

What does this graph show?

Answer 13

• Correlation between output gap + inflation
• Lead of the output gap (as measured by Fuhrer and Moore) over inflation would be inconsistent with the New Phillips Curve.

Question 14

What are problems with this graph?

Answer 14

1. Issue 1: How to measure the output gap? Fuhrer and Moore (1995), QJE use detrended output, i.e., the deviation of output from a smooth trend. But there is no theoretical reason to believe that yₜ is a smooth function of time.
2. Issue 2: Potential Misspecification? The NPC relies on many assumptions (technology, labor market, aggregate demand).

Question 15

What does this graph show, which problem does it address?

Answer 15

The graph looks at the different assumptions/predicted relationships: movements in our measure of real marginal cost (described below) tend to lag movements in output, in direct contrast to theidentifying assumptions that imply a co-incident movement.

• Comparing Fig 1+3: neg. correlation on the right disappear (with theory consistent derived measure for marginal costs)
• Fig 2: at point 0: negative correlation -> output gap is measuring opposite of what it is supposed to measure

Question 16

What is the output gap in the New Keynesian Model?

Answer 16

the difference between the observed (sticky price) output and the theoretical flexible price output

Question 17

What is the New Keynesian Phillips Curve (in words)?

Answer 17

The NKPC describes a simple relationship between inflation, the expectation that firms hold about future inflation, and real marginal costs (=the real resources that firms must spend to produce an extra unit of their good or service)

Question 18

What is the inflation equation in the New Keynesian model?

Answer 18

Question 19

Show that the output gap, ỹₜ, is proportional to the log-deviation of the real marginal cost from its steady state.

Answer 19

Question 20

Explain the forward looking nature of inflation.

Answer 20

Inflation on period t, depends entirely on current and expected future economic conditions. This results from the aggregate consequences of purposeful price-setting decisions by individual firms, which adjust their prices in light of current and anticipated cost conditions, since they know that they might not be able to reset their prices at will in the future given the Calvo assumption.

Question 21

What are the advantages of the rearrangement of the inflation equation for its estimation, as Galí & Gertler did?

Answer 21

1. Inflation now depends on observables (not on Eₜ{π ₜ₊₁})
2. ξₜ₊₁ ≡ (π ₜ₊₁ - Eₜ{π ₜ₊₁}) is the rational expectations forecast error which is zero in expectation. This corresponds nicely to the stochastic error term in a regression model.

Question 22

What advantages does it have to estimate the inflation equation as Galí+Gertler (below) instead of the New Keynesian Phillips Curve?

Answer 22

Deriving the relationship between real marginal cost and output gap requires additional assumptions that might not hold in reality:

• technology
• labor market (perfectly competitive, no extra costs to extra labor)
• aggregate demand

Question 23

Why would estimating the inflation equation with OLS (Ordinary Least Squares) neither be consistent nor unbiased?

Answer 23

• For OLS to be unbiased and consistent several conditions have to be satisfied. Among them: E{xᵢ, єᵢ} = 0 (regressors have to be uncorrelated with the error term)
• But in the current example as πₜ₊₁ is at the same time a regressor and part of the error term, this condition is clearly violated.

Question 24

Instead of OLS, Galí and Gertler estimate the equation using an instrumental variable (IV) approach. What is the idea of IV estimation?

Answer 24

IV replaces the regressors that are correlated with the error terms by other variables (instruments). The instruments have to fulfill two conditions:

• They must not be correlated with the error term: Eₜ{ξₜ₊₁ zₜ} = 0.
• They have to be correlated with the regressors they replace: Eₜ{zₜ xₜ} ≠ 0

Note: OLS is a special case of IV in which the instruments (Zₜ) are the regressor themselves (Xₜ):

Question 25

Instead of OLS, Galí and Gertler estimate the equation using an instrumental variable (IV) approach. How?

Answer 25

Galí and Gertler replace the regressor πₜ₊₁ with several instruments. The procedure of using more instruments than regressors (and weighing them optimally) is called General IV Estimation.

Question 26

How do you go about the derivation of the expected duration of a price (according to Calvo)?

Answer 26

1. In each period, a fraction of (1-θ) of producers reset their price, while a measure θ keep prices unchanged.
2. Therefore, the expected duration of a price is given by 1*(1-θ) + 2*(1-θ)θ + 3*(1-θ)θ² + 4*(1-θ)θ³ + …
3. The expected duration of a price can be rewritten in the following way:

Question 27

What is MPNₜ?

Answer 27

marginal product of labor

∂Yₜ / ∂Nₜ

Question 28

What do the assumptions

• wages taken as given by firms,
• no costs of labor adjustment

impy about the nominal marginal costs?

Answer 28

Question 29

What does this notation mean?

Answer 29

marginal costs (linearized around steady state):

mcₜ - mc