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Chapter 3
Introduction to Quantitative Macroeconomics
Measuring Business Cycles
Yann AlganMaster EPP – M1, 2010
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1. Traditional framework for Fluctuations
Undergraduate textbook model
• Divide markets into good market, financial market and labor market• Write equilibrium condition : IS, LM, and Ph. Curve (AD-AS)
IS: C = cY and I = I(Y,r) Y = Y(Y,r,T) +G
LM M/P = L(i,Y)
PC + g(Y,z)
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Implications for understanding fluctuations
• SR: Prices are given, IS-LM determines Demand and Output
• MR : AS is only determined by real factors and Output at its natural level
• Money increases output in the SR but not in the LR
• Fiscal expansion increases output in the SR……. may decrease it in the LR
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What are the shortcuts of this model?
Lack of microfoundations
• Hard to do welfare analysis without explicit utility and motivesof agents
• Key role of uncertainty and expectations
• Leave unexplained a lot of puzzles in SR analysis
Example 1: Boom in the 90’s in the US- Public deficit Contraction ( - 0.2% in 1997, + 2.3% in 2000)- International crisis
and drop in household income (g=7% in 1997 and 4% in 2000)- But consumption remains stable (g=4%): C=cY ? - Increase in investment (g=14%): I=aY ?
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Bring back theories to systematic confrontation with the data
Lucas’ critique
• Example 2: Microfoundations of price rigidities
-Keynesian/Disequilibrium theories rely on nominal rigidities
- But why won’t entrepreneurs adjust their price if they couldincrease their profits? Other argument than irrationality?
What would be the reaction of price-setting and wage-settingto modification in public policies ?
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Major reconstruction
Real business cycle revolution in the 80s
- Theoretical refoundations
Fluctuations as the results of optimal answers of agents to modifications of the environment
+ Technological and real shocks
- Methodological revolution: measuring fluctuations and confrontation to the data
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Real imperfections: information, transaction costs
Wage bargaining and real rigidities
Equilibrium unemployment and Job creation-destructions
Introducing money…but with micro foundations
- Positive analysis of the effect of monetary policy by taking into account of optimal reaction of households and firms
- Normative analysis of the welfare costs of inflation
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2. Measuring Fluctuations
Want to know general characteristics of fluctuations
• How long typical recessions or booms last? • Are fluctuations in output and employment transitory or permanent?• How do C, I, Unemp vary with output?• How do we explain job creation-job destruction process? • How do nominal variables, financial assets move with output?
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Traditional approach:
• Historical approach: ex. of Kondratieff process every 50 years
• Burns and Mitchell (1946): first systematic time series studyof peak and through in history and characterization of the mean lengths and the amplitude of fluctuationsEx. : Friedman and Schwartz (1963): Monetary History
• Modern approach: - Integration of macro-economy and econometrics- Quantification of the statistical properties of the series
2.1 Business Cycles: regularities in fluctuations
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• « Business cycles» : room for characterizing typical facts only if things repeat themselves to a certain extent, with regularities
• Concept of covariance stationaryPossible to estimate the moments, the process of a random variable Y iff it displays covariance stationary, that is
In search for regularities: covariance stationarity
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Reasonable assumptions ?
• Sometimes not: Crisis 2008, Great Depression, Transition Economy, or European Unemployment , Inflation
• Sometime yes:Typical example: post war GDP (not the original time-serie
since it trends up, but a transformation of it)
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Unemployment fluctuations
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US Unemployment rate
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Inflation
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Unemployment fluctuations
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GDP
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Wages are a-cyclical or slightly pro-cyclical
What kind of theories do we need to account for such fluctuations ?
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Question: Why do economists take the log of the series ?
Assume constant growth rate g
The log-GDP reports directly the growth rate as the slopeof the series
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2.2 Trend versus Cycles
Wold Decomposition and ARMA representation
If a series Yt is co-variance stationary, then it can be represented bya Wold decomposition (MA representation)
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• Very convenient !!
-The Wold representation may be not the true process but evenhighly non-linear process have an infinite MA Wold decomposition
- Infinite MA cannot be estimated but can be approximated by ARMA(n,m) process or AR(n) process, thus allowing to estimatethe process of the series: correlations, cross-correlations…
Ex.: AR(1)
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Identifying the cycle part of the series
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• Cycle : Output Gap
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• Cycle : Growth cycle
But rough filter !!(Jumpy series since all variations of the data longer than
one quarter are filtered out)
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• Trend Cycle (1)
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• Trend Cycle (2)…. Some key flaws !!
Trend stationarity versus Difference Stationarity
Nelson-Plosser (1982): Spurious identification if the seriesis stationary in first difference rather than in level
In this case: no clean separation between trend and cycle
Ex. DS : Random Walk with drift
With
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Thus
Stochastic trend
Implications• Trend Stationary: a one-period shock has only a transitory effect• Difference stationary: a one-period shock has a permanent effect
Sources of long-term growth (technological progress) andshort-term fluctuations are indistinguishable
• We need a filter that eliminates long-run components !!
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• HP Filter
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2.3 Fluctuations in GDP and components
• Representation of the output fluctuation processy: log deviation from a trendCyclical part well fitted by an AR(2)
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• Volatility of output components
- Lower volatility of consumption: smoothing effect ?
- Investment five times more volatile than output: key dimension of fluctuations
- Hours less volatile (hiring or destructions costs ?)- Wages much less volatile (wage rigidity ?)
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2.4 Comovements between output and components
• Comovements between cyclical behavior of output and its component
Contemporaneous correlation and leads and lags
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• Strong correlation between consumption, investment and output
Output and Consumption
Output and Investment
What implications for a theory of fluctuations ?
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• Little correlation with exports
• Little correlation with governement spending
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• Comovement with employment
-Correlation high and positivePuzzling ? Think about the leisure consumption trade-off
- Highly positive lags: movement in output, then employment
- Adjustment on the intensive margin first (correlationis the same as output) and extensive margins (hiring) second
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• High correlation with factor productivity (TFP and labor productivity)
• Wages a-cyclicalPuzzling ? Keynes/Tarshis discussion. Inconsistent with movementonly along a labor curve or a supply curve
Do we need a mix of the two? Or a new theories: foundations for real wages rigidities and largemovement in employment (job creation-destruction margins)
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• High correlation with inflation Phillips curve or Output-inflation gap (which explanation ?)
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• What is the impact of money on output? Hotly debated question (Great Depression, Competetive desinflation…)
-Correlation really high (nominal and real)But what is the causality at work ?
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2.5 Are all business cycles alike ?
-Volatility and comovement qualitatively similar
- But lower output fluctuations and higher persistency of shocks (unemployment)
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3. Identifying the sources of FluctuationsSVAR approach
Motives• Identifying and quantifying promising classes of business cyclemodels using a simple time series procedures
• Run vector autoregressions in the data and impose identifying assumptions based on theory to back out the role of structural shocks
• Ex.: Test the AD-AS model : Blanchard and Quah (AER, 1989) and Gali (QJE, 1992)
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3.1 Identification and Economic Interpretation
• Blanchard and Quah type analysis to evaluate the relativeimportance of supply and demand shocks
Decompose any movement in the economy as the consequence of two orthogonal demand and supply shocks
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3.2 The Structural VAR procedure
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• How can we back out the structural parameters from the time-series ?
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3.3 Some summary statistics and tests
• From the VMA representation, output is given by:
• Impulse response (IRF)-Demand shock : - Supply shock :
• Forecast error in predicting output one period ahead
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• Share of the variance of FE due to demand shock is
- One-period ahead
- At horizon k
• Historical decomposition Counter-factual: what would have happen if only demand or supply
shock had occured ?
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3.4 Applications
-Data: US 1948-2000Output (private sector) and Price series for GNP deflator
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Impulse response function
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Estimated shocks
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Variance decomposition
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Variance decomposition
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Historical decomposition
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