Chapter 3

Introduction to Quantitative Macroeconomics

Measuring Business Cycles

Yann AlganMaster EPP – M1, 2010

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)

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

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 ?

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 ?

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

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

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?

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

• « 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

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)

Unemployment fluctuations

US Unemployment rate

Inflation

Unemployment fluctuations

GDP

Wages are a-cyclical or slightly pro-cyclical

What kind of theories do we need to account for such fluctuations ?

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

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)

• 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)

Identifying the cycle part of the series

• Cycle : Output Gap

• Cycle : Growth cycle

But rough filter !!(Jumpy series since all variations of the data longer than

one quarter are filtered out)

• Trend Cycle (1)

• 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

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 !!

• HP Filter

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)

• 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 ?)

2.4 Comovements between output and components

• Comovements between cyclical behavior of output and its component

Contemporaneous correlation and leads and lags

• Strong correlation between consumption, investment and output

Output and Consumption

Output and Investment

What implications for a theory of fluctuations ?

• Little correlation with exports

• Little correlation with governement spending

• 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

• 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)

• High correlation with inflation Phillips curve or Output-inflation gap (which explanation ?)

• 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 ?

2.5 Are all business cycles alike ?

-Volatility and comovement qualitatively similar

- But lower output fluctuations and higher persistency of shocks (unemployment)

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)

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

3.2 The Structural VAR procedure

• How can we back out the structural parameters from the time-series ?

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

• 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 ?

3.4 Applications

-Data: US 1948-2000Output (private sector) and Price series for GNP deflator

Impulse response function

Estimated shocks

Variance decomposition

Variance decomposition

Historical decomposition