Macroeconomics Slides 7th lecture · Macroeconomics Slides 7th lecture LuisREYES1 Panthéon Sorbonne Master in Economics, Université Paris 1 ... (Krugman). L. Reyes (Paris 1) Macro

MacroeconomicsSlides 7th lecture

Luis REYES1

Panthéon Sorbonne Master in Economics, Université Paris 1

[email protected] or [email protected], www.luisreyesortiz.orgL. Reyes (Paris 1) Macro 7 11/09/2017 1 / 48

Outline

1 Real Business CyclesIntroductionBusiness cycle phenomena and growth modelUsing data to restrict the growth model, i.e. calibration

2 Dynamic Stochastic General Equilibrium modelsIntroductionThe linearized DSGE modelParameter estimates and model properties

L. Reyes (Paris 1) Macro 7 11/09/2017 2 / 48

Outline




Outline




Outline




Introduction (1)Prescott (1986)

The first part of today’s lecture is based on Prescott’s article "Theoryahead of business cycle measurement".

This article is part of a research program by (among others) Kydlandand Prescott (1982, 1987), Hansen (1985) and Bain (1985).The authors computed competitive equilibrium stochastic process forvariants of the constant elasticity, stochastic growth model.The elasticities of substitution and the share parameters of theproduction and utility functions are restricted to those that generatethe growth observations.They ask whether these artificial economies display fluctuations withstatistical properties similar to those which the American economyhas displayed since the Korean War.


https://minneapolisfed.org/research/QR/QR1042.pdf

https://minneapolisfed.org/~/media/files/research/prescott/papers/timetobuild.pdf?la=en

http://www.finnkydland.com/papers/1988_workweekofcapital.PDF

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.295.3865&rep=rep1&type=pdf

https://books.google.fr/books/about/A_Theory_of_the_Cyclical_Movements_of_In.html?id=t5g5GwAACAAJ&redir_esc=y


The first part of today’s lecture is based on Prescott’s article "Theoryahead of business cycle measurement".This article is part of a research program by (among others) Kydlandand Prescott (1982, 1987), Hansen (1985) and Bain (1985).

The authors computed competitive equilibrium stochastic process forvariants of the constant elasticity, stochastic growth model.The elasticities of substitution and the share parameters of theproduction and utility functions are restricted to those that generatethe growth observations.They ask whether these artificial economies display fluctuations withstatistical properties similar to those which the American economyhas displayed since the Korean War.








The first part of today’s lecture is based on Prescott’s article "Theoryahead of business cycle measurement".This article is part of a research program by (among others) Kydlandand Prescott (1982, 1987), Hansen (1985) and Bain (1985).The authors computed competitive equilibrium stochastic process forvariants of the constant elasticity, stochastic growth model.

The elasticities of substitution and the share parameters of theproduction and utility functions are restricted to those that generatethe growth observations.They ask whether these artificial economies display fluctuations withstatistical properties similar to those which the American economyhas displayed since the Korean War.








The first part of today’s lecture is based on Prescott’s article "Theoryahead of business cycle measurement".This article is part of a research program by (among others) Kydlandand Prescott (1982, 1987), Hansen (1985) and Bain (1985).The authors computed competitive equilibrium stochastic process forvariants of the constant elasticity, stochastic growth model.The elasticities of substitution and the share parameters of theproduction and utility functions are restricted to those that generatethe growth observations.

They ask whether these artificial economies display fluctuations withstatistical properties similar to those which the American economyhas displayed since the Korean War.








The first part of today’s lecture is based on Prescott’s article "Theoryahead of business cycle measurement".This article is part of a research program by (among others) Kydlandand Prescott (1982, 1987), Hansen (1985) and Bain (1985).The authors computed competitive equilibrium stochastic process forvariants of the constant elasticity, stochastic growth model.The elasticities of substitution and the share parameters of theproduction and utility functions are restricted to those that generatethe growth observations.They ask whether these artificial economies display fluctuations withstatistical properties similar to those which the American economyhas displayed since the Korean War.








Prescott views the growth model as a paradigm for macro analysis.

Back then he also wondered whether or not this paradigm dominates,with the hope it will

and it did.The early results indicate the model’s power toi organize ourknowledge.The models constructed within this theoretical framework arenecessarily highly abstract.Consequently, they are necessarily false, and statistical hypothesistesting will reject them.The research reviewed in this article is best viewed as a verypromising beginning of a much larger research program.




Prescott views the growth model as a paradigm for macro analysis.Back then he also wondered whether or not this paradigm dominates,with the hope it will

and it did.

The early results indicate the model’s power toi organize ourknowledge.The models constructed within this theoretical framework arenecessarily highly abstract.Consequently, they are necessarily false, and statistical hypothesistesting will reject them.The research reviewed in this article is best viewed as a verypromising beginning of a much larger research program.




Prescott views the growth model as a paradigm for macro analysis.Back then he also wondered whether or not this paradigm dominates,with the hope it will

and it did.





Prescott views the growth model as a paradigm for macro analysis.Back then he also wondered whether or not this paradigm dominates,with the hope it will and it did.





Prescott views the growth model as a paradigm for macro analysis.Back then he also wondered whether or not this paradigm dominates,with the hope it will and it did.The early results indicate the model’s power toi organize ourknowledge.

The models constructed within this theoretical framework arenecessarily highly abstract.Consequently, they are necessarily false, and statistical hypothesistesting will reject them.The research reviewed in this article is best viewed as a verypromising beginning of a much larger research program.




Prescott views the growth model as a paradigm for macro analysis.Back then he also wondered whether or not this paradigm dominates,with the hope it will and it did.The early results indicate the model’s power toi organize ourknowledge.The models constructed within this theoretical framework arenecessarily highly abstract.

Consequently, they are necessarily false, and statistical hypothesistesting will reject them.The research reviewed in this article is best viewed as a verypromising beginning of a much larger research program.




Prescott views the growth model as a paradigm for macro analysis.Back then he also wondered whether or not this paradigm dominates,with the hope it will and it did.The early results indicate the model’s power toi organize ourknowledge.The models constructed within this theoretical framework arenecessarily highly abstract.Consequently, they are necessarily false, and statistical hypothesistesting will reject them.

The research reviewed in this article is best viewed as a verypromising beginning of a much larger research program.




Prescott views the growth model as a paradigm for macro analysis.Back then he also wondered whether or not this paradigm dominates,with the hope it will and it did.The early results indicate the model’s power toi organize ourknowledge.The models constructed within this theoretical framework arenecessarily highly abstract.Consequently, they are necessarily false, and statistical hypothesistesting will reject them.The research reviewed in this article is best viewed as a verypromising beginning of a much larger research program.



Outline




Business cycle phenomena (1)Prescott (1986)

The use of the term business cycle is unfortunate because

(1) it leadspeople to think in terms of a time series’ business cycle componentexplained independently of growth, and (2) it is not accurate; somesystems display key business cycle features without being so.

Following Lucas (1977) EP defines the business cycle phenomena asthe recurrent fluctuations of output about trend and theco-movements among other aggregate time series.(Anecdote) In the words of Lucas: "If the business cycle theorists werecorrect, the short-term manipulation on which much of aggregativeeconomics is now focused only diverts attention from discussion ofstabilization policies which might actually be effective" (p. 9).



http://icm.clsbe.lisboa.ucp.pt/docentes/url/jcn/mabes/LucasUnderstanding.pdf


The use of the term business cycle is unfortunate because

(1) it leadspeople to think in terms of a time series’ business cycle componentexplained independently of growth, and (2) it is not accurate; somesystems display key business cycle features without being so.






The use of the term business cycle is unfortunate because (1) it leadspeople to think in terms of a time series’ business cycle componentexplained independently of growth, and

(2) it is not accurate; somesystems display key business cycle features without being so.






The use of the term business cycle is unfortunate because (1) it leadspeople to think in terms of a time series’ business cycle componentexplained independently of growth, and (2) it is not accurate; somesystems display key business cycle features without being so.






The use of the term business cycle is unfortunate because (1) it leadspeople to think in terms of a time series’ business cycle componentexplained independently of growth, and (2) it is not accurate; somesystems display key business cycle features without being so.Following Lucas (1977) EP defines the business cycle phenomena asthe recurrent fluctuations of output about trend and theco-movements among other aggregate time series.

(Anecdote) In the words of Lucas: "If the business cycle theorists werecorrect, the short-term manipulation on which much of aggregativeeconomics is now focused only diverts attention from discussion ofstabilization policies which might actually be effective" (p. 9).





The use of the term business cycle is unfortunate because (1) it leadspeople to think in terms of a time series’ business cycle componentexplained independently of growth, and (2) it is not accurate; somesystems display key business cycle features without being so.Following Lucas (1977) EP defines the business cycle phenomena asthe recurrent fluctuations of output about trend and theco-movements among other aggregate time series.(Anecdote) In the words of Lucas: "If the business cycle theorists werecorrect, the short-term manipulation on which much of aggregativeeconomics is now focused only diverts attention from discussion ofstabilization policies which might actually be effective" (p. 9).





If the business cycle facts were sensitive to the detrending procedureemployed, there would be a problem.

But the key facts are not sensitive to the procedure if the trend curveis smooth.The curve-fitting method is to take logs of variables and then selectthe trend path {τt} which minimizes the sum of deviations from{Yt}, such that

min{τt}τt=0

T∑t=1

(Yt − τt)2

subject toT−1∑t=2

[(τt+1 − τt) − (τt − τt−1)]2≤ µ

For all series, µ is picked so that the Lagrange multiplier of theconstraint is λ = 1600.




If the business cycle facts were sensitive to the detrending procedureemployed, there would be a problem.But the key facts are not sensitive to the procedure if the trend curveis smooth.

The curve-fitting method is to take logs of variables and then selectthe trend path {τt} which minimizes the sum of deviations from{Yt}, such that

min{τt}τt=0

T∑t=1

(Yt − τt)2


[(τt+1 − τt) − (τt − τt−1)]2≤ µ





If the business cycle facts were sensitive to the detrending procedureemployed, there would be a problem.But the key facts are not sensitive to the procedure if the trend curveis smooth.The curve-fitting method is to take logs of variables and then selectthe trend path {τt} which minimizes the sum of deviations from{Yt}, such that

min{τt}τt=0

T∑t=1

(Yt − τt)2


[(τt+1 − τt) − (τt − τt−1)]2≤ µ






min{τt}τt=0

T∑t=1

(Yt − τt)2


[(τt+1 − τt) − (τt − τt−1)]2≤ µ






min{τt}τt=0

T∑t=1

(Yt − τt)2


[(τt+1 − τt) − (τt − τt−1)]2≤ µ






min{τt}τt=0

T∑t=1

(Yt − τt)2

subject to

T−1∑t=2

[(τt+1 − τt) − (τt − τt−1)]2≤ µ






min{τt}τt=0

T∑t=1

(Yt − τt)2


[(τt+1 − τt) − (τt − τt−1)]2≤ µ






min{τt}τt=0

T∑t=1

(Yt − τt)2


[(τt+1 − τt) − (τt − τt−1)]2≤ µ

For all series, µ is picked so that the Lagrange multiplier of theconstraint is λ = 1600.L. Reyes (Paris 1) Macro 7 11/09/2017 9 / 48


Business cycle phenomena (2’)Parenthesis

Today this procedure is known as the H-P filter, and is widely used inthe economic literature.

However, it should be rather called the Whittaker-Hendersongraduation method (see MacCaulay, 1931).This method is used to decompose economic data into a trend and acyclical component, so that the larger the value of λ the smootherthe resulting filtered series.But the choice of λ is arbitrary (de Alba and Gómez, 2012; Hamilton2016).Not so long ago, the usefulness of the H-P filter was (and still is!) amatter of lively debate.Among others because some people use the HP filtered GDP to arguethat the US economy is already operating near potential, so thatthere is no reason to pursue expansionary policy (Krugman).


https://www0.gsb.columbia.edu/faculty/rhodrick/prescott-hodrick1997.pdf

http://www.nber.org/chapters/c9366.pdf

http://www.inegi.org.mx/rde/rde_07/doctos/rde_07_art3.pdf

http://econweb.ucsd.edu/~jhamilto/hp.pdf

http://bruegel.org/2012/07/blogs-review-hp-filters-and-business-cycles/

https://krugman.blogs.nytimes.com/2012/07/11/filters-and-full-employment-not-wonkish-really/


Today this procedure is known as the H-P filter, and is widely used inthe economic literature.However, it should be rather called the Whittaker-Hendersongraduation method (see MacCaulay, 1931).

This method is used to decompose economic data into a trend and acyclical component, so that the larger the value of λ the smootherthe resulting filtered series.But the choice of λ is arbitrary (de Alba and Gómez, 2012; Hamilton2016).Not so long ago, the usefulness of the H-P filter was (and still is!) amatter of lively debate.Among others because some people use the HP filtered GDP to arguethat the US economy is already operating near potential, so thatthere is no reason to pursue expansionary policy (Krugman).









Today this procedure is known as the H-P filter, and is widely used inthe economic literature.However, it should be rather called the Whittaker-Hendersongraduation method (see MacCaulay, 1931).This method is used to decompose economic data into a trend and acyclical component, so that the larger the value of λ the smootherthe resulting filtered series.

But the choice of λ is arbitrary (de Alba and Gómez, 2012; Hamilton2016).Not so long ago, the usefulness of the H-P filter was (and still is!) amatter of lively debate.Among others because some people use the HP filtered GDP to arguethat the US economy is already operating near potential, so thatthere is no reason to pursue expansionary policy (Krugman).









Today this procedure is known as the H-P filter, and is widely used inthe economic literature.However, it should be rather called the Whittaker-Hendersongraduation method (see MacCaulay, 1931).This method is used to decompose economic data into a trend and acyclical component, so that the larger the value of λ the smootherthe resulting filtered series.But the choice of λ is arbitrary (de Alba and Gómez, 2012; Hamilton2016).

Not so long ago, the usefulness of the H-P filter was (and still is!) amatter of lively debate.Among others because some people use the HP filtered GDP to arguethat the US economy is already operating near potential, so thatthere is no reason to pursue expansionary policy (Krugman).









Today this procedure is known as the H-P filter, and is widely used inthe economic literature.However, it should be rather called the Whittaker-Hendersongraduation method (see MacCaulay, 1931).This method is used to decompose economic data into a trend and acyclical component, so that the larger the value of λ the smootherthe resulting filtered series.But the choice of λ is arbitrary (de Alba and Gómez, 2012; Hamilton2016).Not so long ago, the usefulness of the H-P filter was (and still is!) amatter of lively debate.

Among others because some people use the HP filtered GDP to arguethat the US economy is already operating near potential, so thatthere is no reason to pursue expansionary policy (Krugman).









Today this procedure is known as the H-P filter, and is widely used inthe economic literature.However, it should be rather called the Whittaker-Hendersongraduation method (see MacCaulay, 1931).This method is used to decompose economic data into a trend and acyclical component, so that the larger the value of λ the smootherthe resulting filtered series.But the choice of λ is arbitrary (de Alba and Gómez, 2012; Hamilton2016).Not so long ago, the usefulness of the H-P filter was (and still is!) amatter of lively debate.Among others because some people use the HP filtered GDP to arguethat the US economy is already operating near potential, so thatthere is no reason to pursue expansionary policy (Krugman).








The growth model (1)Prescott (1986)

Filtered variables are the ones used in the computation of thestatistics reported.

The model is a fully articulated, artificial economic system that canbe used to generate economic time series of a set of importanteconomic aggregates.The model is such that

xt + ct ≤ zt f (kt ,nt)

xt is investment, ct is consumption, zt is a technology parameter, ktis capital and nt is labor (both as stocks).The services provided by a unit of capital decrease geometrically at arate 0 < δ < 1.




Filtered variables are the ones used in the computation of thestatistics reported.The model is a fully articulated, artificial economic system that canbe used to generate economic time series of a set of importanteconomic aggregates.

The model is such that






Filtered variables are the ones used in the computation of thestatistics reported.The model is a fully articulated, artificial economic system that canbe used to generate economic time series of a set of importanteconomic aggregates.The model is such that








xt is investment, ct is consumption, zt is a technology parameter, ktis capital and nt is labor (both as stocks).

The services provided by a unit of capital decrease geometrically at arate 0 < δ < 1.










kt+1 = (1 − δ)kt + xt

Solow completes the specification of his economy by hypothesizingthat 0 < σ < 1 of output is invested, and the remaining 1 − σconsumed:

kt+1 = (1 − δ)kt + σzt f (kt , n)The structure is not yet complete, because in it neither employmentnor the savings rate vary (their behavior is central to the cycle).If we abstract from the labor supply decision and uncertainty (zt = zand nt = n) the utility function is

∞∑t=0βtu(ct) for 0 < β < 1




kt+1 = (1 − δ)kt + xt


kt+1 = (1 − δ)kt + σzt f (kt , n)

The structure is not yet complete, because in it neither employmentnor the savings rate vary (their behavior is central to the cycle).If we abstract from the labor supply decision and uncertainty (zt = zand nt = n) the utility function is

∞∑t=0βtu(ct) for 0 < β < 1




kt+1 = (1 − δ)kt + xt


kt+1 = (1 − δ)kt + σzt f (kt , n)The structure is not yet complete, because in it neither employmentnor the savings rate vary (their behavior is central to the cycle).

If we abstract from the labor supply decision and uncertainty (zt = zand nt = n) the utility function is

∞∑t=0βtu(ct) for 0 < β < 1




kt+1 = (1 − δ)kt + xt


kt+1 = (1 − δ)kt + σzt f (kt , n)The structure is not yet complete, because in it neither employmentnor the savings rate vary (their behavior is central to the cycle).If we abstract from the labor supply decision and uncertainty (zt = zand nt = n) the utility function is

∞∑t=0βtu(ct) for 0 < β < 1




β is the subjective time discount factor, and the function u is twicedifferentiable and concave.

Even with the savings decision endogenous, this economy has nofluctuations.When uncertainty is introduced, the household’s objective is itsexpected discounted utility:

E {∞∑t=0βtu(ct)}

{ct(z1, ..., zt)∞t=0} is the commodity point.

Lucas and Prescott (1971) show that for these homogeneous agenteconomies, the social optimum is also the unique sequence-of-marketsequilibrium allocation.




β is the subjective time discount factor, and the function u is twicedifferentiable and concave.Even with the savings decision endogenous, this economy has nofluctuations.

When uncertainty is introduced, the household’s objective is itsexpected discounted utility:







β is the subjective time discount factor, and the function u is twicedifferentiable and concave.Even with the savings decision endogenous, this economy has nofluctuations.When uncertainty is introduced, the household’s objective is itsexpected discounted utility:





















Consequently, there are equilibrium time-invariant functions for thewage wt = w(kt , zt) and the rental price of capital rt = r(kt , zt),relative to the date t consumption good.

The firm’s period t problem is

maxkt ,nt ≥ 0{yt − rtkt −wtnt}

Subject to the constraint

yt ≤ zt f (kt ,nt)

The household’s problem is more complicated (!) for it must formexpectations about the future.




Consequently, there are equilibrium time-invariant functions for thewage wt = w(kt , zt) and the rental price of capital rt = r(kt , zt),relative to the date t consumption good.The firm’s period t problem is
























If at is its capital stock, its problem is

maxE∞∑t=0βtu(ct)

Subject toct + xt ≤ wt n + rtat

at+1 ≤ (1 − δ)at + xt

Given a0 − k0.In forming expectations, a household knows the relation between theeconomy’s state (kt , zt) and prices, wt and rt .Further, it knows the process governing the evolution of the percapita capital stock (taken as given, like prices).







at+1 ≤ (1 − δ)at + xt








at+1 ≤ (1 − δ)at + xt

Given a0 − k0.

In forming expectations, a household knows the relation between theeconomy’s state (kt , zt) and prices, wt and rt .Further, it knows the process governing the evolution of the percapita capital stock (taken as given, like prices).







at+1 ≤ (1 − δ)at + xt

Given a0 − k0.In forming expectations, a household knows the relation between theeconomy’s state (kt , zt) and prices, wt and rt .

Further, it knows the process governing the evolution of the percapita capital stock (taken as given, like prices).







at+1 ≤ (1 − δ)at + xt





From these elements we define:

The firm’s policy functions y(kt , zt), n(kt , zt) and k(kt , zt).The household’s policy functions x(at , kt , zt) and c(at , kt , zt).A law of motion of per capita capital kt+1 = g(kt , zt),And pricing functions w(kt , zt) and r(kt , zt).

For equilibrium, then

The firm’s policy functions must be optimal given the pricing functions,The household’s policy functions must be optimal given the pricingfunctions and the law of motion of per capita capital,Spot markets clear; that is, ∀kt , zt :

n = n(kt , zt)

kt = k(kt , zt)

x(kt , zt) + c(kt , zt) = y(kt , zt)




From these elements we define:

The firm’s policy functions y(kt , zt), n(kt , zt) and k(kt , zt).The household’s policy functions x(at , kt , zt) and c(at , kt , zt).A law of motion of per capita capital kt+1 = g(kt , zt),And pricing functions w(kt , zt) and r(kt , zt).



n = n(kt , zt)

kt = k(kt , zt)





From these elements we define:The firm’s policy functions y(kt , zt), n(kt , zt) and k(kt , zt).

The household’s policy functions x(at , kt , zt) and c(at , kt , zt).A law of motion of per capita capital kt+1 = g(kt , zt),And pricing functions w(kt , zt) and r(kt , zt).



n = n(kt , zt)

kt = k(kt , zt)





From these elements we define:The firm’s policy functions y(kt , zt), n(kt , zt) and k(kt , zt).The household’s policy functions x(at , kt , zt) and c(at , kt , zt).

A law of motion of per capita capital kt+1 = g(kt , zt),And pricing functions w(kt , zt) and r(kt , zt).



n = n(kt , zt)

kt = k(kt , zt)





From these elements we define:The firm’s policy functions y(kt , zt), n(kt , zt) and k(kt , zt).The household’s policy functions x(at , kt , zt) and c(at , kt , zt).A law of motion of per capita capital kt+1 = g(kt , zt),

And pricing functions w(kt , zt) and r(kt , zt).For equilibrium, then


n = n(kt , zt)

kt = k(kt , zt)





From these elements we define:The firm’s policy functions y(kt , zt), n(kt , zt) and k(kt , zt).The household’s policy functions x(at , kt , zt) and c(at , kt , zt).A law of motion of per capita capital kt+1 = g(kt , zt),And pricing functions w(kt , zt) and r(kt , zt).



n = n(kt , zt)

kt = k(kt , zt)








n = n(kt , zt)

kt = k(kt , zt)






For equilibrium, thenThe firm’s policy functions must be optimal given the pricing functions,

The household’s policy functions must be optimal given the pricingfunctions and the law of motion of per capita capital,Spot markets clear; that is, ∀kt , zt :

n = n(kt , zt)

kt = k(kt , zt)






For equilibrium, thenThe firm’s policy functions must be optimal given the pricing functions,The household’s policy functions must be optimal given the pricingfunctions and the law of motion of per capita capital,

Spot markets clear; that is, ∀kt , zt :

n = n(kt , zt)

kt = k(kt , zt)






For equilibrium, thenThe firm’s policy functions must be optimal given the pricing functions,The household’s policy functions must be optimal given the pricingfunctions and the law of motion of per capita capital,Spot markets clear; that is, ∀kt , zt :

n = n(kt , zt)

kt = k(kt , zt)





Expectations are rational

g(kt , zt) = (1 − δ)kt + x(kt , zt)

This definition still holds if the household values productive time thatis allocated to non-market activities (l).The productive time endowment is normalized to 1, and thehousehold faces constraints:

nt + lt ≤ 1, ∀t

Leisure is introduced as an argument of the utility function, so thehousehold’s objective becomes the maximization of

E∞∑t=0βtu(ct , lt)





g(kt , zt) = (1 − δ)kt + x(kt , zt)

This definition still holds if the household values productive time thatis allocated to non-market activities (l).

The productive time endowment is normalized to 1, and thehousehold faces constraints:

nt + lt ≤ 1, ∀t







g(kt , zt) = (1 − δ)kt + x(kt , zt)


nt + lt ≤ 1, ∀t







g(kt , zt) = (1 − δ)kt + x(kt , zt)


nt + lt ≤ 1, ∀t






Now leisure –and therefore employment– varies in equilibrium.

We now relax the assumption that the technology shocks zt areindependently distributed random variables.They display considerable serial correlation, with their first differencesnearly serially uncorrelated.We assume

zt+1 = ρzt + εt+1

Where the {εt+1} are identically and independently distributed and ρis near 1.




Now leisure –and therefore employment– varies in equilibrium.We now relax the assumption that the technology shocks zt areindependently distributed random variables.

They display considerable serial correlation, with their first differencesnearly serially uncorrelated.We assume

zt+1 = ρzt + εt+1





Now leisure –and therefore employment– varies in equilibrium.We now relax the assumption that the technology shocks zt areindependently distributed random variables.They display considerable serial correlation, with their first differencesnearly serially uncorrelated.

We assumezt+1 = ρzt + εt+1





Now leisure –and therefore employment– varies in equilibrium.We now relax the assumption that the technology shocks zt areindependently distributed random variables.They display considerable serial correlation, with their first differencesnearly serially uncorrelated.We assume

zt+1 = ρzt + εt+1





Now leisure –and therefore employment– varies in equilibrium.We now relax the assumption that the technology shocks zt areindependently distributed random variables.They display considerable serial correlation, with their first differencesnearly serially uncorrelated.We assume

zt+1 = ρzt + εt+1




Outline




Growth model restrictions (1)Prescott (1986)

In this model both growth and micro observations can be used todetermine its production and utility functions.

The key parameters of the growth model are the intertemporal andintratemporal elasticities of substitution.Lucas (1980): "On these parameters, we have a wealth ofinexpensively available data from census cohort information frompanel data describing the reactions of individual households to avariety of changing market conditions, and so forth".A fundamental thesis is that the measures obtained from aggregateseries and those from individual panel data must be consistent.Secularly in the U.S., capital and labor shares of output have beenapproximately constant, as has rt .




In this model both growth and micro observations can be used todetermine its production and utility functions.The key parameters of the growth model are the intertemporal andintratemporal elasticities of substitution.

Lucas (1980): "On these parameters, we have a wealth ofinexpensively available data from census cohort information frompanel data describing the reactions of individual households to avariety of changing market conditions, and so forth".A fundamental thesis is that the measures obtained from aggregateseries and those from individual panel data must be consistent.Secularly in the U.S., capital and labor shares of output have beenapproximately constant, as has rt .




In this model both growth and micro observations can be used todetermine its production and utility functions.The key parameters of the growth model are the intertemporal andintratemporal elasticities of substitution.Lucas (1980): "On these parameters, we have a wealth ofinexpensively available data from census cohort information frompanel data describing the reactions of individual households to avariety of changing market conditions, and so forth".

A fundamental thesis is that the measures obtained from aggregateseries and those from individual panel data must be consistent.Secularly in the U.S., capital and labor shares of output have beenapproximately constant, as has rt .




In this model both growth and micro observations can be used todetermine its production and utility functions.The key parameters of the growth model are the intertemporal andintratemporal elasticities of substitution.Lucas (1980): "On these parameters, we have a wealth ofinexpensively available data from census cohort information frompanel data describing the reactions of individual households to avariety of changing market conditions, and so forth".A fundamental thesis is that the measures obtained from aggregateseries and those from individual panel data must be consistent.

Secularly in the U.S., capital and labor shares of output have beenapproximately constant, as has rt .




In this model both growth and micro observations can be used todetermine its production and utility functions.The key parameters of the growth model are the intertemporal andintratemporal elasticities of substitution.Lucas (1980): "On these parameters, we have a wealth ofinexpensively available data from census cohort information frompanel data describing the reactions of individual households to avariety of changing market conditions, and so forth".A fundamental thesis is that the measures obtained from aggregateseries and those from individual panel data must be consistent.Secularly in the U.S., capital and labor shares of output have beenapproximately constant, as has rt .




However, the real wage has increased greatly. So that, for theseresults to hold, the model’s production function must beapproximately Cobb-Douglas

zt f (kt ,nt) = ztk(1−θ)t nθt

θ is the labor’s share, which has been around 64% in the postwarperiod, whereas leisure per capita lt has shown virtually no seculartrend.This implies that the elasticity of substitution between consumptionand leisure is near 1.δ is chosen to be 10%.






θ is the labor’s share, which has been around 64% in the postwarperiod, whereas leisure per capita lt has shown virtually no seculartrend.

This implies that the elasticity of substitution between consumptionand leisure is near 1.δ is chosen to be 10%.






θ is the labor’s share, which has been around 64% in the postwarperiod, whereas leisure per capita lt has shown virtually no seculartrend.This implies that the elasticity of substitution between consumptionand leisure is near 1.

δ is chosen to be 10%.






θ is the labor’s share, which has been around 64% in the postwarperiod, whereas leisure per capita lt has shown virtually no seculartrend.This implies that the elasticity of substitution between consumptionand leisure is near 1.δ is chosen to be 10%.




The restricted utility function is now

u(ct , lt) =(c1−φ

t lφt )1−γ − 11 − γ

where 1/γ > 1 is the elasticity of substituting between different datecomposite commodities c1−φ

t lφt .This leaves γ and the subjective time discount factor β to bedetermined.The steady-state interest rate is

i = 1β− 1 + γ c

c






t lφt )1−γ − 11 − γ


t lφt .

This leaves γ and the subjective time discount factor β to bedetermined.The steady-state interest rate is

i = 1β− 1 + γ c

c






t lφt )1−γ − 11 − γ


t lφt .This leaves γ and the subjective time discount factor β to bedetermined.

The steady-state interest rate is

i = 1β− 1 + γ c

c






t lφt )1−γ − 11 − γ


t lφt .This leaves γ and the subjective time discount factor β to bedetermined.The steady-state interest rate is

i = 1β− 1 + γ c

c




The average annual interest rate is about 4%.

The growth rate of per capita consumption c/c has averaged nearly2%.Based on findings from other authors’ works, γ is chosen to be near 1.Taking the limit as γ → 1 yields

u(ct , lt) = (1 − φ)logct + φloglt

This leaves β and φ still to be determined.Assuming λ = 0, the average interest rate approximately equals thesubjective time discount rate, so that β = 0.96 per year or 0.99 perquarter.Again based on previous empirical works, EP defines φ = 2/3.




The average annual interest rate is about 4%.The growth rate of per capita consumption c/c has averaged nearly2%.

Based on findings from other authors’ works, γ is chosen to be near 1.Taking the limit as γ → 1 yields






The average annual interest rate is about 4%.The growth rate of per capita consumption c/c has averaged nearly2%.Based on findings from other authors’ works, γ is chosen to be near 1.

Taking the limit as γ → 1 yields






The average annual interest rate is about 4%.The growth rate of per capita consumption c/c has averaged nearly2%.Based on findings from other authors’ works, γ is chosen to be near 1.Taking the limit as γ → 1 yields








This leaves β and φ still to be determined.

Assuming λ = 0, the average interest rate approximately equals thesubjective time discount rate, so that β = 0.96 per year or 0.99 perquarter.Again based on previous empirical works, EP defines φ = 2/3.






This leaves β and φ still to be determined.Assuming λ = 0, the average interest rate approximately equals thesubjective time discount rate, so that β = 0.96 per year or 0.99 perquarter.

Again based on previous empirical works, EP defines φ = 2/3.









Measuring technological change (1)Prescott (1986)

Solow’s method consists in

∆ln(zt) = ∆ln(yt) − θ∆ln(nt) − (1 − θ)∆ln(kt)

For the U.S. economy between 1955q3 and 1984q1, the s.d. of thischange is 1.2%.Furthermore, ρ1 = −0.21, ρ2 = −0.06, ρ3 = 0.04, ρ4 = 0.01 andρ5 = −0.05.To a first approximation, the process on the percentage change in thetechnology process is a random walk with drift plus some seriallyuncorrelated measurement error (on a yearly basis).The process that resembles such r.w. is thus

zt+1 = 0.9zt + εt+1






For the U.S. economy between 1955q3 and 1984q1, the s.d. of thischange is 1.2%.

Furthermore, ρ1 = −0.21, ρ2 = −0.06, ρ3 = 0.04, ρ4 = 0.01 andρ5 = −0.05.To a first approximation, the process on the percentage change in thetechnology process is a random walk with drift plus some seriallyuncorrelated measurement error (on a yearly basis).The process that resembles such r.w. is thus

zt+1 = 0.9zt + εt+1






For the U.S. economy between 1955q3 and 1984q1, the s.d. of thischange is 1.2%.Furthermore, ρ1 = −0.21, ρ2 = −0.06, ρ3 = 0.04, ρ4 = 0.01 andρ5 = −0.05.

To a first approximation, the process on the percentage change in thetechnology process is a random walk with drift plus some seriallyuncorrelated measurement error (on a yearly basis).The process that resembles such r.w. is thus

zt+1 = 0.9zt + εt+1






For the U.S. economy between 1955q3 and 1984q1, the s.d. of thischange is 1.2%.Furthermore, ρ1 = −0.21, ρ2 = −0.06, ρ3 = 0.04, ρ4 = 0.01 andρ5 = −0.05.To a first approximation, the process on the percentage change in thetechnology process is a random walk with drift plus some seriallyuncorrelated measurement error (on a yearly basis).

The process that resembles such r.w. is thus

zt+1 = 0.9zt + εt+1






For the U.S. economy between 1955q3 and 1984q1, the s.d. of thischange is 1.2%.Furthermore, ρ1 = −0.21, ρ2 = −0.06, ρ3 = 0.04, ρ4 = 0.01 andρ5 = −0.05.To a first approximation, the process on the percentage change in thetechnology process is a random walk with drift plus some seriallyuncorrelated measurement error (on a yearly basis).The process that resembles such r.w. is thus

zt+1 = 0.9zt + εt+1




Solow growth accounting finds that the process on the technologyparameter is highly persistent with the s.d. of change being about 0.9(overstated).

To summarize, there is overwhelming evidence that technologicalshocks are highly persistent.But tying down the s.d. of the technology change is difficult(estimated here as 0.763.The author finds that his calibrated series mimic the movement of theobserved (filtered) series.The story goes on and on, but these are the main elements of theRBC model that makes up the basis of the DSGE model seen next.

But before that, the summary and policy implications.




Solow growth accounting finds that the process on the technologyparameter is highly persistent with the s.d. of change being about 0.9(overstated).To summarize, there is overwhelming evidence that technologicalshocks are highly persistent.

But tying down the s.d. of the technology change is difficult(estimated here as 0.763.The author finds that his calibrated series mimic the movement of theobserved (filtered) series.The story goes on and on, but these are the main elements of theRBC model that makes up the basis of the DSGE model seen next.





Solow growth accounting finds that the process on the technologyparameter is highly persistent with the s.d. of change being about 0.9(overstated).To summarize, there is overwhelming evidence that technologicalshocks are highly persistent.But tying down the s.d. of the technology change is difficult(estimated here as 0.763.

The author finds that his calibrated series mimic the movement of theobserved (filtered) series.The story goes on and on, but these are the main elements of theRBC model that makes up the basis of the DSGE model seen next.





Solow growth accounting finds that the process on the technologyparameter is highly persistent with the s.d. of change being about 0.9(overstated).To summarize, there is overwhelming evidence that technologicalshocks are highly persistent.But tying down the s.d. of the technology change is difficult(estimated here as 0.763.The author finds that his calibrated series mimic the movement of theobserved (filtered) series.

The story goes on and on, but these are the main elements of theRBC model that makes up the basis of the DSGE model seen next.





Solow growth accounting finds that the process on the technologyparameter is highly persistent with the s.d. of change being about 0.9(overstated).To summarize, there is overwhelming evidence that technologicalshocks are highly persistent.But tying down the s.d. of the technology change is difficult(estimated here as 0.763.The author finds that his calibrated series mimic the movement of theobserved (filtered) series.The story goes on and on, but these are the main elements of theRBC model that makes up the basis of the DSGE model seen next.





Solow growth accounting finds that the process on the technologyparameter is highly persistent with the s.d. of change being about 0.9(overstated).To summarize, there is overwhelming evidence that technologicalshocks are highly persistent.But tying down the s.d. of the technology change is difficult(estimated here as 0.763.The author finds that his calibrated series mimic the movement of theobserved (filtered) series.The story goes on and on, but these are the main elements of theRBC model that makes up the basis of the DSGE model seen next.





Solow growth accounting finds that the process on the technologyparameter is highly persistent with the s.d. of change being about 0.9(overstated).To summarize, there is overwhelming evidence that technologicalshocks are highly persistent.But tying down the s.d. of the technology change is difficult(estimated here as 0.763.The author finds that his calibrated series mimic the movement of theobserved (filtered) series.The story goes on and on, but these are the main elements of theRBC model that makes up the basis of the DSGE model seen next.But before that, the summary and policy implications.



Summary and policy implicationsPrescott (1986)

The match between theory and observation is excellent, but far fromperfect.

The key deviation is that the empirical labor elasticity of output isless than predicted by theory.An important part of this deviation could very well disappear if theeconomic variables were measured in conformity with theory.The policy implication of this research is that costly efforts atstabilization are likely to be counterproductive.Economic fluctuations are optimal responses to uncertainty in the rateof technological change.Attention should be focused NOT on fluctuations in output butrather on determinants of the average rate of technological advance.




The match between theory and observation is excellent, but far fromperfect.The key deviation is that the empirical labor elasticity of output isless than predicted by theory.

An important part of this deviation could very well disappear if theeconomic variables were measured in conformity with theory.The policy implication of this research is that costly efforts atstabilization are likely to be counterproductive.Economic fluctuations are optimal responses to uncertainty in the rateof technological change.Attention should be focused NOT on fluctuations in output butrather on determinants of the average rate of technological advance.




The match between theory and observation is excellent, but far fromperfect.The key deviation is that the empirical labor elasticity of output isless than predicted by theory.An important part of this deviation could very well disappear if theeconomic variables were measured in conformity with theory.

The policy implication of this research is that costly efforts atstabilization are likely to be counterproductive.Economic fluctuations are optimal responses to uncertainty in the rateof technological change.Attention should be focused NOT on fluctuations in output butrather on determinants of the average rate of technological advance.




The match between theory and observation is excellent, but far fromperfect.The key deviation is that the empirical labor elasticity of output isless than predicted by theory.An important part of this deviation could very well disappear if theeconomic variables were measured in conformity with theory.The policy implication of this research is that costly efforts atstabilization are likely to be counterproductive.

Economic fluctuations are optimal responses to uncertainty in the rateof technological change.Attention should be focused NOT on fluctuations in output butrather on determinants of the average rate of technological advance.




The match between theory and observation is excellent, but far fromperfect.The key deviation is that the empirical labor elasticity of output isless than predicted by theory.An important part of this deviation could very well disappear if theeconomic variables were measured in conformity with theory.The policy implication of this research is that costly efforts atstabilization are likely to be counterproductive.Economic fluctuations are optimal responses to uncertainty in the rateof technological change.

Attention should be focused NOT on fluctuations in output butrather on determinants of the average rate of technological advance.




The match between theory and observation is excellent, but far fromperfect.The key deviation is that the empirical labor elasticity of output isless than predicted by theory.An important part of this deviation could very well disappear if theeconomic variables were measured in conformity with theory.The policy implication of this research is that costly efforts atstabilization are likely to be counterproductive.Economic fluctuations are optimal responses to uncertainty in the rateof technological change.Attention should be focused NOT on fluctuations in output butrather on determinants of the average rate of technological advance.



Outline




Outline




Introduction (1)

The presentation of DSGE models is based on a single article that hasbeen considered a major reference in this field.

Other DSGE models may look different, but the basic structure andproperties are basically the same or do not differ greatly from the onepresented here.Thus, a new generation of small-scale monetary business cycle modelswith sticky prices and wages has become popular in monetary policyanalysis.These models are called New Keynesian or New NeoclassicalSynthesis (NNS).


Introduction (1)

The presentation of DSGE models is based on a single article that hasbeen considered a major reference in this field.Other DSGE models may look different, but the basic structure andproperties are basically the same or do not differ greatly from the onepresented here.

Thus, a new generation of small-scale monetary business cycle modelswith sticky prices and wages has become popular in monetary policyanalysis.These models are called New Keynesian or New NeoclassicalSynthesis (NNS).


Introduction (1)

The presentation of DSGE models is based on a single article that hasbeen considered a major reference in this field.Other DSGE models may look different, but the basic structure andproperties are basically the same or do not differ greatly from the onepresented here.Thus, a new generation of small-scale monetary business cycle modelswith sticky prices and wages has become popular in monetary policyanalysis.

These models are called New Keynesian or New NeoclassicalSynthesis (NNS).


Introduction (1)

The presentation of DSGE models is based on a single article that hasbeen considered a major reference in this field.Other DSGE models may look different, but the basic structure andproperties are basically the same or do not differ greatly from the onepresented here.Thus, a new generation of small-scale monetary business cycle modelswith sticky prices and wages has become popular in monetary policyanalysis.These models are called New Keynesian or New NeoclassicalSynthesis (NNS).


Introduction (2)Smets and Wouters, 2007

The objectives of the authors are threefold

1 As the NNS models have become the standard workhorse for monetarypolicy analysis, it is important to verify whether they can explain themain features of the U.S. macro data.

2 The introduction of a large number of fictions raises the questionwhether each of these are really necessary to describe the 7 data series.

3 They use the estimated NNS model to address a number of key issues.These issues are:

(1) the main driving forces of output developmentsin the U.S., (2) prove that productivity shocks have a significantshort-run negative impact on hours worked, (3) inflationdevelopments are mostly driven by the price mark-up shocks in theshort run and the wage mark-up in the long run.


https://www.ecb.europa.eu/pub/pdf/scpwps/ecbwp722.pdf


The objectives of the authors are threefold1 As the NNS models have become the standard workhorse for monetary

policy analysis, it is important to verify whether they can explain themain features of the U.S. macro data.


















3 They use the estimated NNS model to address a number of key issues.

These issues are:
























3 They use the estimated NNS model to address a number of key issues.These issues are: (1) the main driving forces of output developmentsin the U.S.,

(2) prove that productivity shocks have a significantshort-run negative impact on hours worked, (3) inflationdevelopments are mostly driven by the price mark-up shocks in theshort run and the wage mark-up in the long run.







3 They use the estimated NNS model to address a number of key issues.These issues are: (1) the main driving forces of output developmentsin the U.S., (2) prove that productivity shocks have a significantshort-run negative impact on hours worked,

(3) inflationdevelopments are mostly driven by the price mark-up shocks in theshort run and the wage mark-up in the long run.







3 They use the estimated NNS model to address a number of key issues.These issues are: (1) the main driving forces of output developmentsin the U.S., (2) prove that productivity shocks have a significantshort-run negative impact on hours worked, (3) inflationdevelopments are mostly driven by the price mark-up shocks in theshort run and the wage mark-up in the long run.



Outline




The linearized DSGE model (1)Smets and Wouters, 2007

This is an extension that is consistent with a balanced steady stategrowth path driven by deterministic labor-augmenting technologicalprogress.

Households maximize a non-separable utility function with twoarguments (goods and labor effort) over an infinite horizon.Consumption appears in the utility function relative to a time-varyingexternal habit variable.Labor is differentiated by a union, so that there is some monopolypower over wages.Households rent capital services to firms and decide how much capitalto accumulate given the capital adjustment costs they face.




This is an extension that is consistent with a balanced steady stategrowth path driven by deterministic labor-augmenting technologicalprogress.Households maximize a non-separable utility function with twoarguments (goods and labor effort) over an infinite horizon.

Consumption appears in the utility function relative to a time-varyingexternal habit variable.Labor is differentiated by a union, so that there is some monopolypower over wages.Households rent capital services to firms and decide how much capitalto accumulate given the capital adjustment costs they face.




This is an extension that is consistent with a balanced steady stategrowth path driven by deterministic labor-augmenting technologicalprogress.Households maximize a non-separable utility function with twoarguments (goods and labor effort) over an infinite horizon.Consumption appears in the utility function relative to a time-varyingexternal habit variable.

Labor is differentiated by a union, so that there is some monopolypower over wages.Households rent capital services to firms and decide how much capitalto accumulate given the capital adjustment costs they face.




This is an extension that is consistent with a balanced steady stategrowth path driven by deterministic labor-augmenting technologicalprogress.Households maximize a non-separable utility function with twoarguments (goods and labor effort) over an infinite horizon.Consumption appears in the utility function relative to a time-varyingexternal habit variable.Labor is differentiated by a union, so that there is some monopolypower over wages.

Households rent capital services to firms and decide how much capitalto accumulate given the capital adjustment costs they face.




This is an extension that is consistent with a balanced steady stategrowth path driven by deterministic labor-augmenting technologicalprogress.Households maximize a non-separable utility function with twoarguments (goods and labor effort) over an infinite horizon.Consumption appears in the utility function relative to a time-varyingexternal habit variable.Labor is differentiated by a union, so that there is some monopolypower over wages.Households rent capital services to firms and decide how much capitalto accumulate given the capital adjustment costs they face.




Prices are set in function of current and expected marginal costs, butare also determined by the past inflation rate.

SW introduce a time-varying demand elasticity which depends on therelative price (more reasonable degree of price and wage stickiness).The aggregate resource constraint is:

yt = cyct + iy it + zyzt + εgt

Output (yt) is absorbed by consumption (ct), investment (it),capital-utilization costs that are a function of the capital utilizationrate (zt), and exogenous spending (εg

t ).cy is the ss share of consumption in output (1− gy − iy ), where gy andiy are respectively the ss exogenous spending-output andinvestment-output ratios.




Prices are set in function of current and expected marginal costs, butare also determined by the past inflation rate.SW introduce a time-varying demand elasticity which depends on therelative price (more reasonable degree of price and wage stickiness).

The aggregate resource constraint is:







Prices are set in function of current and expected marginal costs, butare also determined by the past inflation rate.SW introduce a time-varying demand elasticity which depends on therelative price (more reasonable degree of price and wage stickiness).The aggregate resource constraint is:










t ).

cy is the ss share of consumption in output (1− gy − iy ), where gy andiy are respectively the ss exogenous spending-output andinvestment-output ratios.











The ss investment-output ratio equals (γ − 1 + δ)ky , where γ is the ssgrowth rate, δ is the depreciation rate of capital and ky is the sscapital-output ratio.

zy = Rk∗ky where Rk∗ is the ss rental rate of capital.We assume that exogenous spending follows a AR(1) process withi.i.d. normal error term, and is affected by the productivity shock asfollows

εgt = ρgε

gt−1 + η

gt + ρgaη

at

In estimation, εgt also includes net exports, which may be affected by

domestic productivity developments.




The ss investment-output ratio equals (γ − 1 + δ)ky , where γ is the ssgrowth rate, δ is the depreciation rate of capital and ky is the sscapital-output ratio.zy = Rk∗ky where Rk∗ is the ss rental rate of capital.

We assume that exogenous spending follows a AR(1) process withi.i.d. normal error term, and is affected by the productivity shock asfollows

εgt = ρgε

gt−1 + η

gt + ρgaη

at






The ss investment-output ratio equals (γ − 1 + δ)ky , where γ is the ssgrowth rate, δ is the depreciation rate of capital and ky is the sscapital-output ratio.zy = Rk∗ky where Rk∗ is the ss rental rate of capital.We assume that exogenous spending follows a AR(1) process withi.i.d. normal error term, and is affected by the productivity shock asfollows

εgt = ρgε

gt−1 + η

gt + ρgaη

at






The ss investment-output ratio equals (γ − 1 + δ)ky , where γ is the ssgrowth rate, δ is the depreciation rate of capital and ky is the sscapital-output ratio.zy = Rk∗ky where Rk∗ is the ss rental rate of capital.We assume that exogenous spending follows a AR(1) process withi.i.d. normal error term, and is affected by the productivity shock asfollows

εgt = ρgε

gt−1 + η

gt + ρgaη

at






The dynamics of the consumption function follows from theconsumption Euler equation

ct = c1ct−1 + (1 − c1)Etct+1 + c2(lt − Et lt+1) − c3(rt − Etπt+1 + εbt )

ct depends on a weighted average of past and expected futureconsumption, and on expected growth in hours worked, the ex-antereal interest rate and a disturbance term.The parameters c1, c2 and c3 are calibrated.If we assume that there is no external habit formation (λ = 0) and thelog utility in consumption (σc = 1), c1 = c2 = 0, and the purelyforward-looking consumption function is obtained.






ct depends on a weighted average of past and expected futureconsumption, and on expected growth in hours worked, the ex-antereal interest rate and a disturbance term.

The parameters c1, c2 and c3 are calibrated.If we assume that there is no external habit formation (λ = 0) and thelog utility in consumption (σc = 1), c1 = c2 = 0, and the purelyforward-looking consumption function is obtained.






ct depends on a weighted average of past and expected futureconsumption, and on expected growth in hours worked, the ex-antereal interest rate and a disturbance term.The parameters c1, c2 and c3 are calibrated.

If we assume that there is no external habit formation (λ = 0) and thelog utility in consumption (σc = 1), c1 = c2 = 0, and the purelyforward-looking consumption function is obtained.






ct depends on a weighted average of past and expected futureconsumption, and on expected growth in hours worked, the ex-antereal interest rate and a disturbance term.The parameters c1, c2 and c3 are calibrated.If we assume that there is no external habit formation (λ = 0) and thelog utility in consumption (σc = 1), c1 = c2 = 0, and the purelyforward-looking consumption function is obtained.




εbt represents the wedge between the interest rate controlled by thecentral bank and the return on assets held by households, and followsan AR(1) process.

A positive shock to this wedge increases the required return on assetsheld by households.At the same time, it increases the cost of capital and reduces thevalue of capital and investment (net-worth shocks).The dynamics of investment comes from the investment Eulerequation

it = i1it−1 + (1 − i1)Et it+1 + i2qt + εit

A higher elasticity of the cost of adjusting capital reduces thesensitivity of investment (it) to the real value of existing capital stock(qt).




εbt represents the wedge between the interest rate controlled by thecentral bank and the return on assets held by households, and followsan AR(1) process.A positive shock to this wedge increases the required return on assetsheld by households.

At the same time, it increases the cost of capital and reduces thevalue of capital and investment (net-worth shocks).The dynamics of investment comes from the investment Eulerequation






εbt represents the wedge between the interest rate controlled by thecentral bank and the return on assets held by households, and followsan AR(1) process.A positive shock to this wedge increases the required return on assetsheld by households.At the same time, it increases the cost of capital and reduces thevalue of capital and investment (net-worth shocks).

The dynamics of investment comes from the investment Eulerequation






εbt represents the wedge between the interest rate controlled by thecentral bank and the return on assets held by households, and followsan AR(1) process.A positive shock to this wedge increases the required return on assetsheld by households.At the same time, it increases the cost of capital and reduces thevalue of capital and investment (net-worth shocks).The dynamics of investment comes from the investment Eulerequation






εbt represents the wedge between the interest rate controlled by thecentral bank and the return on assets held by households, and followsan AR(1) process.A positive shock to this wedge increases the required return on assetsheld by households.At the same time, it increases the cost of capital and reduces thevalue of capital and investment (net-worth shocks).The dynamics of investment comes from the investment Eulerequation






The arbitrage equation for the value of capital is given by

qt = q1Etqt+1 + (1 − q1)Etrkt+1 − (rt − πt+1 + ε

bt )

The current value of the capital stock (qt) depends positively on itsexpected future value and the expected rental rate on capital (Etrk

t+1).And negatively on the ex-ante real interest rate and the risk premiumdisturbance.The aggregate production function is

yt = φp(αkst + (1 − α)lt + εa

t )

Output is produced using capital (kst ) and labor services (hours

worked lt).






bt )


t+1).

And negatively on the ex-ante real interest rate and the risk premiumdisturbance.The aggregate production function is


t )


worked lt).






bt )


t+1).And negatively on the ex-ante real interest rate and the risk premiumdisturbance.

The aggregate production function is


t )


worked lt).






bt )




t )


worked lt).






bt )




t )


worked lt).




Total factor productivity (εat ) is assumed to follow an AR(1) process.

α captures the share of capital in production and φp is one plus theshare of fixed costs in production.As newly installed capital becomes only effective with a one-quarterlag, current capital services used in production (ks

t ) are a function ofcapital installed in the previous period (kt−1) and the degree ofcapital utilization

kst = kt−1 + zt

Cost minimization by the households that provide capital servicesimplies that zt is a positive function of the rental rate of capital

zt = z1rkt





α captures the share of capital in production and φp is one plus theshare of fixed costs in production.

As newly installed capital becomes only effective with a one-quarterlag, current capital services used in production (ks


kst = kt−1 + zt


zt = z1rkt







kst = kt−1 + zt


zt = z1rkt







kst = kt−1 + zt


zt = z1rkt




The accumulation of installed capital (kt) is a function of the flow ofinvestment and the relative efficiency of inv. expenditures

kt = k1kt−1 + (1 − k1)it + k2εit

The price mark-up (µpt ) (difference between average price and

nominal marginal cost) equals the difference between the marginalproduct of labor (mplt) and the real wage (wt)

µpt = mplt −wt = α(ks

t − lt) + εat −wt

Prices adjust sluggishly to their desired mark-up.





kt = k1kt−1 + (1 − k1)it + k2εit










kt = k1kt−1 + (1 − k1)it + k2εit









Profit maximization by price-setting firms gives rise to theNew-Keynesian Phillips curve

πt = π1πt−1 + π2Etπt+1 − π3µpt + ε

pt

The price mark-up disturbance is assumed to follow an ARMA(1,1)process

εpt = ρpε

pt + η

pt − µpη

pt−1, with ηp

t ∼ i .i .d .

The assumption that all prices are indexed to either lagged inflationor the ss inflation ensures that the Phillips curve is vertical in thelong-run.Cost minimization by firms implies that the rental price of capital isnegatively associated to the capital-labor ratio and positively to thereal wage.






pt


εpt = ρpε

pt + η

pt − µpη

pt−1, with ηp

t ∼ i .i .d .







pt


εpt = ρpε

pt + η

pt − µpη

pt−1, with ηp

t ∼ i .i .d .

The assumption that all prices are indexed to either lagged inflationor the ss inflation ensures that the Phillips curve is vertical in thelong-run.

Cost minimization by firms implies that the rental price of capital isnegatively associated to the capital-labor ratio and positively to thereal wage.






pt


εpt = ρpε

pt + η

pt − µpη

pt−1, with ηp

t ∼ i .i .d .





rkt = −(kt − lt) +wt

Due to nominal wage stickiness and partial indexation of wages toinflation, real wages only adjust gradually to the desired mark-up

wt = w1wt−1 + (1−w1)(Etwt+1 +Etφt+1)−w2πt +w3πt−1 −w4µwt + εw

t

If wages are perfectly flexible, the real wage is a constant mark-upover the marginal rate of substitution between consumption andleisure.The wage mark-up disturbance follows an ARMA(1,1) process.







t








t

If wages are perfectly flexible, the real wage is a constant mark-upover the marginal rate of substitution between consumption andleisure.

The wage mark-up disturbance follows an ARMA(1,1) process.







t





Finally (!) the model is closed by adding the empirical monetarypolicy reaction function

rt = ρrt−1 + (1− ρ)[rπ + rY (yt − ypt )]+ rw [(yt − yp

t )− (yt−1 − ypt−1)]+ ε

rt

We assume that the monetary policy shocks (εrt) follows an AR(1)

process with i.i.d. error term (εrt = ρRε

rt−1 + η

rt ).

The stochastic behavior of the system of linear rational expectationsequations is driven by seven exogenous disturbances:

(1) total factorproductivity (εa

t ), (2) investment-specific technology (εit), (3) risk

premium (εbt ), (4) exogenous spending (εg

t ), (5) price mark-up (εpt ),

(6) wage mark-up (εwt ) and (7) monetary policy shocks (εr

t).






t )− (yt−1 − ypt−1)]+ ε

rt



rt−1 + η

rt ).







t).






t )− (yt−1 − ypt−1)]+ ε

rt



rt−1 + η

rt ).







t).






t )− (yt−1 − ypt−1)]+ ε

rt



rt−1 + η

rt ).







t).






t )− (yt−1 − ypt−1)]+ ε

rt



rt−1 + η

rt ).

The stochastic behavior of the system of linear rational expectationsequations is driven by seven exogenous disturbances: (1) total factorproductivity (εa

t ),

(2) investment-specific technology (εit), (3) risk




t).






t )− (yt−1 − ypt−1)]+ ε

rt



rt−1 + η

rt ).


t ), (2) investment-specific technology (εit),

(3) riskpremium (εb

t ), (4) exogenous spending (εgt ), (5) price mark-up (εp

t ),(6) wage mark-up (εw

t ) and (7) monetary policy shocks (εrt).






t )− (yt−1 − ypt−1)]+ ε

rt



rt−1 + η

rt ).



premium (εbt ),

(4) exogenous spending (εgt ), (5) price mark-up (εp

t ),(6) wage mark-up (εw

t ) and (7) monetary policy shocks (εrt).






t )− (yt−1 − ypt−1)]+ ε

rt



rt−1 + η

rt ).




t ),

(5) price mark-up (εpt ),


t).






t )− (yt−1 − ypt−1)]+ ε

rt



rt−1 + η

rt ).






t).






t )− (yt−1 − ypt−1)]+ ε

rt



rt−1 + η

rt ).





(6) wage mark-up (εwt )

and (7) monetary policy shocks (εrt).






t )− (yt−1 − ypt−1)]+ ε

rt



rt−1 + η

rt ).






t).



Outline




Parameter estimates and model properties (1)Smets and Wouters, 2007

The model is estimated with Bayesian estimation techniques using sevenkey macroeconomic quarterly U.S. time series:

log difference of real GDP (dlGDPt),log difference of real consumption (dlCONSt),log difference of real investment (dlINVt),log difference of the real wage (dlWAGt),log hours worked (lHOURSt),log difference of GDP deflator (dlPt),and the federal funds rate (FEDFUNDSt).





log difference of real GDP (dlGDPt),

log difference of real consumption (dlCONSt),log difference of real investment (dlINVt),log difference of the real wage (dlWAGt),log hours worked (lHOURSt),log difference of GDP deflator (dlPt),and the federal funds rate (FEDFUNDSt).





log difference of real GDP (dlGDPt),log difference of real consumption (dlCONSt),

log difference of real investment (dlINVt),log difference of the real wage (dlWAGt),log hours worked (lHOURSt),log difference of GDP deflator (dlPt),and the federal funds rate (FEDFUNDSt).





log difference of real GDP (dlGDPt),log difference of real consumption (dlCONSt),log difference of real investment (dlINVt),

log difference of the real wage (dlWAGt),log hours worked (lHOURSt),log difference of GDP deflator (dlPt),and the federal funds rate (FEDFUNDSt).





log difference of real GDP (dlGDPt),log difference of real consumption (dlCONSt),log difference of real investment (dlINVt),log difference of the real wage (dlWAGt),

log hours worked (lHOURSt),log difference of GDP deflator (dlPt),and the federal funds rate (FEDFUNDSt).





log difference of real GDP (dlGDPt),log difference of real consumption (dlCONSt),log difference of real investment (dlINVt),log difference of the real wage (dlWAGt),log hours worked (lHOURSt),

log difference of GDP deflator (dlPt),and the federal funds rate (FEDFUNDSt).





log difference of real GDP (dlGDPt),log difference of real consumption (dlCONSt),log difference of real investment (dlINVt),log difference of the real wage (dlWAGt),log hours worked (lHOURSt),log difference of GDP deflator (dlPt),

and the federal funds rate (FEDFUNDSt).





log difference of real GDP (dlGDPt),log difference of real consumption (dlCONSt),log difference of real investment (dlINVt),log difference of the real wage (dlWAGt),log hours worked (lHOURSt),log difference of GDP deflator (dlPt),and the federal funds rate (FEDFUNDSt).




The measurement equation is

Yt =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

dlGDPtdlCONStdlINVtdlWAGtlHOURSt

dlPtFEDFUNDSt

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

=

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

γγγγ

lπr

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

+

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

yt − yt−1ct − ct−1it − it−1wt −wt−1

ltπtrt

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

γ = 100(γ − 1) is the common quarterly trend growth rate to realGDP, consumption, investment and wages, π = 100(Π∗ − 1) is thequarterly ss inflation rate and r = 100(β−1γσc Π∗ − 1).




The measurement equation is

Yt =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

dlGDPtdlCONStdlINVtdlWAGtlHOURSt

dlPtFEDFUNDSt

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

=

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

γγγγ

lπr

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

+

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

yt − yt−1ct − ct−1it − it−1wt −wt−1

ltπtrt

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

γ = 100(γ − 1) is the common quarterly trend growth rate to realGDP, consumption, investment and wages, π = 100(Π∗ − 1) is thequarterly ss inflation rate and r = 100(β−1γσc Π∗ − 1).




The model is estimated for 1966q1 - 2004q4, as well as the "GreatInflation" (1966q1 - 1979q2) and the "Great Moderation" (1984q1 -2004q4).

The authors distinguish between priors on the stochastic processes(assumed distributions of the disturbance terms) and posteriorestimates (estimated values obtained after assumptions).SW mention that their tightly parameterized DSGE model performsmuch better than an unconstrained VAR in the same vector ofobservable variables.It can also compete with standard BVAR models (Sims and Zha,1998) in terms of empirical one-step-ahead prediction performance.





The model is estimated for 1966q1 - 2004q4, as well as the "GreatInflation" (1966q1 - 1979q2) and the "Great Moderation" (1984q1 -2004q4).The authors distinguish between priors on the stochastic processes(assumed distributions of the disturbance terms) and posteriorestimates (estimated values obtained after assumptions).

SW mention that their tightly parameterized DSGE model performsmuch better than an unconstrained VAR in the same vector ofobservable variables.It can also compete with standard BVAR models (Sims and Zha,1998) in terms of empirical one-step-ahead prediction performance.





The model is estimated for 1966q1 - 2004q4, as well as the "GreatInflation" (1966q1 - 1979q2) and the "Great Moderation" (1984q1 -2004q4).The authors distinguish between priors on the stochastic processes(assumed distributions of the disturbance terms) and posteriorestimates (estimated values obtained after assumptions).SW mention that their tightly parameterized DSGE model performsmuch better than an unconstrained VAR in the same vector ofobservable variables.

It can also compete with standard BVAR models (Sims and Zha,1998) in terms of empirical one-step-ahead prediction performance.





The model is estimated for 1966q1 - 2004q4, as well as the "GreatInflation" (1966q1 - 1979q2) and the "Great Moderation" (1984q1 -2004q4).The authors distinguish between priors on the stochastic processes(assumed distributions of the disturbance terms) and posteriorestimates (estimated values obtained after assumptions).SW mention that their tightly parameterized DSGE model performsmuch better than an unconstrained VAR in the same vector ofobservable variables.It can also compete with standard BVAR models (Sims and Zha,1998) in terms of empirical one-step-ahead prediction performance.




Main driving forces of output (1)Smets and Wouters, 2007

In the short run, movements in GDP are primarily driven by theexogenous spending shock and the two shocks that affect theintertemporal Euler equations:

The risk premium shock which affects both consumption andinvestment, andThe investment-specific technology shock which affects theinvestment Euler equation.These are demand shocks that have a positive effect on output,hours worked, inflation and the nominal interest rate under theestimated policy rule.However, it is mostly two supply shocks that account for most of theoutput variations in the medium to long run:

productivity and wagemark-up.




In the short run, movements in GDP are primarily driven by theexogenous spending shock and the two shocks that affect theintertemporal Euler equations:The risk premium shock which affects both consumption andinvestment, and

The investment-specific technology shock which affects theinvestment Euler equation.These are demand shocks that have a positive effect on output,hours worked, inflation and the nominal interest rate under theestimated policy rule.However, it is mostly two supply shocks that account for most of theoutput variations in the medium to long run:





In the short run, movements in GDP are primarily driven by theexogenous spending shock and the two shocks that affect theintertemporal Euler equations:The risk premium shock which affects both consumption andinvestment, andThe investment-specific technology shock which affects theinvestment Euler equation.

These are demand shocks that have a positive effect on output,hours worked, inflation and the nominal interest rate under theestimated policy rule.However, it is mostly two supply shocks that account for most of theoutput variations in the medium to long run:





In the short run, movements in GDP are primarily driven by theexogenous spending shock and the two shocks that affect theintertemporal Euler equations:The risk premium shock which affects both consumption andinvestment, andThe investment-specific technology shock which affects theinvestment Euler equation.These are demand shocks that have a positive effect on output,hours worked, inflation and the nominal interest rate under theestimated policy rule.

However, it is mostly two supply shocks that account for most of theoutput variations in the medium to long run:





In the short run, movements in GDP are primarily driven by theexogenous spending shock and the two shocks that affect theintertemporal Euler equations:The risk premium shock which affects both consumption andinvestment, andThe investment-specific technology shock which affects theinvestment Euler equation.These are demand shocks that have a positive effect on output,hours worked, inflation and the nominal interest rate under theestimated policy rule.However, it is mostly two supply shocks that account for most of theoutput variations in the medium to long run:





In the short run, movements in GDP are primarily driven by theexogenous spending shock and the two shocks that affect theintertemporal Euler equations:The risk premium shock which affects both consumption andinvestment, andThe investment-specific technology shock which affects theinvestment Euler equation.These are demand shocks that have a positive effect on output,hours worked, inflation and the nominal interest rate under theestimated policy rule.However, it is mostly two supply shocks that account for most of theoutput variations in the medium to long run:





In the short run, movements in GDP are primarily driven by theexogenous spending shock and the two shocks that affect theintertemporal Euler equations:The risk premium shock which affects both consumption andinvestment, andThe investment-specific technology shock which affects theinvestment Euler equation.These are demand shocks that have a positive effect on output,hours worked, inflation and the nominal interest rate under theestimated policy rule.However, it is mostly two supply shocks that account for most of theoutput variations in the medium to long run: productivity and wagemark-up.



Last slide

End of the seventh lecture.


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Macroeconomics Slides 7th lecture · Macroeconomics Slides 7th lecture LuisREYES1 Panthéon Sorbonne Master in Economics, Université Paris 1 ... (Krugman). L. Reyes (Paris 1) Macro