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Syllabus Introduction Trend vs. Cycle Facts Model
Lecture 1: Introduction
Advanced MacroeconomicsUniversity of Warsaw
Jacek Suda
March 11, 2019
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Plan of the Presentation
1 Syllabus
2 Introduction
3 Trend vs. Cycle
4 Business Cycle Facts
5 DSGE models
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model Requirements Readings
Website
Class website: http://www.jaceksuda.com/teach/
Email: [email protected]
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model Requirements Readings
Description
The main objective of the course is to introduce fundamental techniquesfor constructing and solving dynamic-stochastic general equilibrium (DSGE)models.
We begin with the basic growth/RBC (Real Business Cycle) model. Themodel (and its extension) will be used to illustrate the concept of equi-librium, market completeness, and solution techniques.We will consider both stochastic Lagrangian multipliers methodologyand dynamic programming.We will also use it to show some properties of the business cycles as wellas its implications for asset prices and macroeconomic policy.
The second part of the course introduces the overlapping generation(OLG) model and, if time permits, incomplete markets model (agentsface idiosyncratic and uninsurable labor income risk).
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model Requirements Readings
Requirements
Three homework assignment with the weight of 30% of final grade.
The class ends either in-class 2 hour long exam or take-home exam.
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model Requirements Readings
Readings
No single textbook but a number of textbooks covers a part of materialdiscussed in class
Frontiers of Business Cycle Research by Thomas Cooley, PrincetonUniversity Press, 1995.Recursive Macroeconomic Theory by Lars Ljungqvist and ThomasSargent, Princeton University Press, 2010.The ABCs of RBCs: An Intoduction to Dynamic Macroeconomic Modelsby Geroge McCandless, Harvard University Press, 2008.
Other texts areDynamic Economics by Jerome Adda and Russel Cooper, MIT Press,2003.Structural Macroeconometrics by David N. DeJong with Chetan Dave,Princeton University Press, 2007.Advanced Macroeconomics by David Romer, McGraw Hill, 1996.Recursive Methods in Economic Dynamics by Nancy Stokey and RobertLucas with Edward Prescott, Harvard University Press, 1989.Bayesian Estimation of DSGE Models by Edward Herbst and FrankSchorfheide, Princeton University Press, 2015.
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Plan of the Presentation
1 Syllabus
2 Introduction
3 Trend vs. Cycle
4 Business Cycle Facts
5 DSGE models
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Lucas critique
Until the 1970s macroeconomic modeling was dominated bylarge-scale models (Cowles Commission approach)
These models consisted of estimated ad-hoc equations, e.g. the Phillipscurve, and lacked cross-equations restrinctions
This approach was criticized by Lucas (1976) (Lucas critique)ad-hoc equation parameters are sensitive to policy modifications ⇒ only,,deep” parameters should be usedexpectations crucial in driving agent’s decisions
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
RBC as DSGE
The general equilibrium (GE) approach to modeling was a response tothe Lucas critique
The RBC model (Kydland and Prescott, 1982) are derived frommicrofoundations:
households solves intertemporal (dynamic) problem (maximize utility)firms maximize profitsthey take into account policy changes
RBC models form the basis of modern macroeconomic modeling
Further advances in DSGE modeling build on the RBC framework
Caveat: it a simple model:simple RBC models explain the business cycle as coming solely fromproductivity shocks⇒ no role for empirically valid demand shocks (e.g. monetary policy)
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Plan of the Presentation
1 Syllabus
2 Introduction
3 Trend vs. Cycle
4 Business Cycle Facts
5 DSGE models
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Business Cycles Stylized Facts
The RBC model is used to explain business cyclesshort and medium term co-movements of macroeconomic variablesfluctuations of output around a long-term growth trend
We need to establish some key business cycle factsfocus on the US in the post-war but pre-financial crisis periodcould look different for emerging countries or specific episodes, e.g. theGreat Depression or the financial crisis
We then build and use an RBC models to understand these facts andguide policy.
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
GDP Time Series
Times series of real output (GDP) in the US
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Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
GDP Time Series
Times series of real output (GDP) in the US, log scale
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Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
GDP Time Series
Times series of the growth of real output (GDP) in the US
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Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
GDP Time Series
Times series of the components of real output (GDP) in the US
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Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
GDP/Output
Output has grown on average, butat variable ratefluctuated around some trend
Recessions and expansions differed in size, length, frequency
Growth rate of GDPvaries over timefeatures changing over time volatility
How to separate the cycle (fluctuations around) from the trend?
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Plan of the Presentation
1 Syllabus
2 Introduction
3 Trend vs. Cycle
4 Business Cycle Facts
5 DSGE models
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Detrending data
Several methods for detrending (filtering) the data
Most popular filters:Linear trendHP (Hodrick-Prescott) filterBandpass filterBeveridge-Nelson decomposition
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Trend and Cycle
Denote log of actual GDP (or any other variable of interest) as yt
yt = logGDP
Let yt be the trend (or growth) component of yt
Let yt be cyclical (or detrended) component of yt
yt ≡ yt − yt
Sometimes trend is viewed as “potential” GDP
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Linear trend
Define linear trend asyt ≡ g · t
where g is the average growth rate
Until the late 70s:fit a linear trend: yt is the residual of regressing yt on t.define the stochastic part of the time series as deviations from this trend
Conceptually simple but not that useful if low-frequency movementsare different than exact deterministic linear trend (e.g., demographics,secular stagnation)
Example: problem in late 70s:The “trend” (potential) GDP growth rate slowed down
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
HP Filter
Hodrick-Prescott filter: define trend as the solution to minimization ofthe loss function:
L =∑
t
(yt − yt)2 + λ
∑t
((yt+1 − yt)− (yt − yt−1))2
λ is the parameter that governs the punishment for the variations in thegrowth component
Trend converges to a linear trend when λ → ∞Trend converges to actual data as λ → 0
Standard value for λ for quarterly data is λ = 1600Ravn and Uhlig (2002) suggests that λ should equal the fourth power ofthe frequency observation ratio
Hamilton (2017) suggests we should never use HP filter:
“A regression of the variable at date t + h on the four most re-cent values as of date t offers a robust approach to detrending thatachieves all the objectives sought by users of the HP filter with noneof its drawbacks.”
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Example - linear trend to level data
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Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Example - HP trend to log data
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Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Band-pass Filter
Baxted and King (1999) proposed band-pass filter to isolate the sourcesof variation that operate at particular frequencies
“A linear filter which eliminates very slow moving (“trend”) com-ponents and very high frequency (“irregular”) components whileretaining intermediate (“business cycle”) components.”
⇒ similarly to HP, BP removes low-frequency movement but, incontrast to HP, it also removes high-frequency “noise”Common practice is look at the band-pass filter that keeps frequenciesbetween 6 and 32 quarters (8 years)Bank-pass filter can be defined in frequency domain[see Stock and Watson (1998) for further discussion]
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
In Practice
Use either H-P or B-P:→ both give very similar picture for most macro variables
Introduction Cycle vs. Trend Business Cycle Facts Conclusion
In Practice• the next figure illustrates the similarity of the cyclical componentsof GDP that we obtain if we apply either the HP or the BP filter.
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• clearly, there isn’t much difference in the case of output. note,however, that there could be more noticeable differences for othervariables. think, e.g., of stock prices.
Source: King and Rebelo (2000)
not much difference in case of output but could be more noticeabledifferences for other variables, e.g., stock prices
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
In Practice
Use either H-P or B-P:→ both give very similar picture for most macro variables
Alternative: look at the cyclical properties of the changes (growth rates)
yt ≡ yt − yt−1
But ‘first differences” gives too much emphasis on very short-livedmovements (“noise”)
to some extent the HP filter also keeps this noise while band-pass filterremoves it.
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
In Practice: trend matters matters for cycle
Use the HP filter with caution, especially around large shocks: they candistort estimates of the underlying trends, both before and after theshockJames Bullard, “Housing in America: Innovative Solutions to Addressthe Needs of Tomorrow ”, 5 June 2012
Bullard (2012)
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Plan of the Presentation
1 Syllabus
2 Introduction
3 Trend vs. Cycle
4 Business Cycle Facts
5 DSGE models
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Business Cycle Facts
We report facts from King and Rebelo (2000)King and Rebello (2000) use the HP filter and concentrate on realquantitiesStock and Watson (1998) use BP filter
As RBC is concerned exclusively with real quantities we abstact fornow from nominal variables
See Stock and Watson (1998) for a more detailed discussion of all thekey business cycle facts
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
ConsumptionIntroduction Cycle vs. Trend Business Cycle Facts Conclusion
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Introduction Cycle vs. Trend Business Cycle Facts Conclusion
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Source: King and Rebelo (2000)
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Consumption
Consumption is positively correlated with output (pro-cyclical)
Spending on durables is more volatile than output
Spending on non-durables is less volatile than output
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Investment
Investment is strongly pro-cyclical and more volatile than output
Introduction Cycle vs. Trend Business Cycle Facts Conclusion
Investment
• Investment is strongly pro-cyclical and more volatile than output
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Source: King and Rebelo (2000)
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Labor
The labor input (total hours) is pro-cyclical and as volatile as output
Introduction Cycle vs. Trend Business Cycle Facts Conclusion
Labor
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Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Employment vs. Hours
Most of the labor-input fluctuations are in total employment (number ofworkers employed) rather than in hours per worker
Introduction Cycle vs. Trend Business Cycle Facts Conclusion
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Source: King and Rebelo (2000)
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Labor Productivity
Labor productivity (y/n) and real wages are only mildly pro-cyclical
Introduction Cycle vs. Trend Business Cycle Facts Conclusion
Labor Productivity• Labor productivity (y/n) and real wages are only mildly procyclical
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Introduction Cycle vs. Trend Business Cycle Facts Conclusion
Labor Productivity• Labor productivity (y/n) and real wages are only mildly procyclical
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Source: King and Rebelo (2000)
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Capital
The capital stock moves very slowlyCapital utilization is highly pro-cyclical⇒ effective capital input is highly pro-cyclical
Introduction Cycle vs. Trend Business Cycle Facts Conclusion
Capital• The capital stock moves very slowly, but capital utilization is highlyprocyclical, so that effective capital input is highly pro-cyclical
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Introduction Cycle vs. Trend Business Cycle Facts Conclusion
Capital• The capital stock moves very slowly, but capital utilization is highlyprocyclical, so that effective capital input is highly pro-cyclical
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Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
The Solow Residual
The Solow residual (a proxy from TFP) is strongly procyclical
Introduction Cycle vs. Trend Business Cycle Facts Conclusion
The Solow Residual
• The Solow residual (a proxy from TFP) is strongly procyclical
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Source: King and Rebelo (2000)
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Sidenote: How is the Solow Residual defined?
Assume that output is produced using a Cobb-Douglas productionfunction
Yt = AtKαt N1−α
t .
TFP can be computed from data on output Yt , capital Kt , and totalhours Nt as follows:
logAt = SolowResidualt ≡ log Yt − α logKt − (1− α) logNt
where α is the income share of capital.
The Solow residual is just a residual.
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Variances and Co-variances
Basic business-cycle statistics for the US economy from King andRebelo (2000).(all variables expect for the interest rate are HP filtered)
Introduction Cycle vs. Trend Business Cycle Facts Conclusion
Variances and Co-variances
• Basic business-cycle statistics for the US economyfrom King and Rebelo (2000).
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• all variables except the interest rate are HP filtered
Source: King and Rebelo (2000)
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Summary
King and Rebelo (2000) reported following business cycle stylizedfacts
Consumption, Investment, and Labor are all strongly pro-cyclical
Durables are more pro-cyclical than non-durables
Employment fluctuates more than hours
Capital moves slowly
Labor productivity and wages are only mildly pro-cyclical
The Solow residual (proxy for TFP) is strongly pro-cyclical
Next step: think about models that may account for these patterns!
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Plan of the Presentation
1 Syllabus
2 Introduction
3 Trend vs. Cycle
4 Business Cycle Facts
5 DSGE models
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
Plan of the Presentation
1 Syllabus
2 Introduction
3 Trend vs. Cycle
4 Business Cycle Facts
5 DSGE models
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
The problem
DSGE models are derived from microeconomic problems
Write down the problems1 households maximize utility s.t. budget constraint2 producers maximize profits s.t. technology3 markets clear
Construct Lagrangeans (or Bellman equations)
Lecture 1
Syllabus Introduction Trend vs. Cycle Facts Model
The solution
Derive first order conditions
Derive steady state
Log-linearize the equations
Solve
Check stability
Lecture 1
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