macro notes: introduction to the short run the birth of modern macroeconomics, ... dickey-fuller...

The Short Run (Business Cycles) Phillps Curve Okun’s Law

Macro Notes: Introduction to the Short Run

Alan G. Isaac

American University


But this “long run” is a misleading guide to currentaffairs. ‘In the long run” we are all dead. Economistsset themselves too easy, too useless a task if intempestuous seasons they can only tell us that whenthe storm is long past the ocean is flat again.J.M. Keynes, 1923 (Tract on Monetary Reform)

As an event, the Depression is largely synonymouswith the birth of modern macroeconomics, and itcontinues to haunt successive generations ofeconomists.R.A. Margo (1993 JEP)


Our long-run model explains potential output Yt and long-runinflation. But deviations from these long-run values areimportant too. Our short-run model explains short-run outputand short-run inflation.Once we have separated out inflation from real growth, we canlook at the behavior over time of real GDP.When we look at real income over time, we not only see theupward trend, we also see large fluctuations around that trend.


Trend and Cycle: Stylized Representation


The theory of business cycles tries to explain such deviations.Contraction (recession, bust): RGDP pc below trend (forenough time).Expansion (boom): RGDP pc above trend (for enough time).The National Bureau of Economic Research (NBERhttp://www.nber.org) is a private, nonprofit, nonpartisaneconomic research organization. Many prominent economistsare members of the NBER. NBER Business Cycle DatingCommitteehttp://www.nber.org/cycles/recessions.html

determines the official business cycle dateshttp://www.nber.org/cycles.html.

http://www.nber.org

http://www.nber.org/cycles/recessions.html

http://www.nber.org/cycles.html


Economists collect macroeconomic data on many variables.We call data collected at regular points in time time seriesdata.Many macroeconomic time series “trend” upward.Can we “detrend” them? I.e., can we separate out the trendsand cycles of a macroeconomic time series?Trend: low frequency componentCycle: high frequency component


When we detrend the log of a variable, we are taking out theaverage percentage growth rate. The best fitting line for thelinear trend is called the low frequency (linear trend, or fitted)values. What is “left over” is the high frequency (linear cycle,or residuals).Linear detrending: best straight line through the points.When macroeconomic series have persistent average growthrates, as many do, we usually use log-linear detrending. (Sometextbooks call this linear detrending.)


Detrending with a Linear Trend

Source: Farmer 2000, Chapter 1, Figure 5


Detrending with a Flexible TrendActual, Potential, and Cyclical Output (Flexible Trend)


Great Depression

US experience:

Unemployment reaches 25%

Output falls 60% (at least 20% below trend)

Problem long lasting: 1930–1941


Coherence and Persistence

Business cycles consist of persistent comovements in thedeviations of certain macroeconomic variables from theirtrends.This comovement is called coherence.E.g., in a boom, RGDP pc above trend and unemploymentbelow trend.Procyclical: rise above trend with RGDP pc. (E.g.,consumption and investment.)Countercyclical: rise above trend when RGDP pc. falls below(E.g., unemployment.)Business cycles tend to persist: macroeconomic variables areautocorrelated.


Coherence and Business Cycles I

The absolute value of the correlation coefficient between twoarbitary time series measures their degree of coherence.Here X and Y are two aribtrary time series.

Correlation Correlation Degree of Scatter plotCoefficient Coherence slope

positive ρXY > 0 +ρXY positivenegative ρXY < 0 −ρXY negative

A variable that is positively correlated with the cycle in realGDP is called procyclical. A variable that is negativelycorrelated with the cycle in real GDP is called countercyclical.Here X is an aribtrary time series and Y is the cyclicalcomponent of real GDP.


Coherence and Business Cycles II

Correlation Scatter plotCorrelation Coefficient Meaning slope

positive ρXY > 0 procyclical positivenegative ρXY < 0 countercyclical negative


Countercyclical Social Indicators



When we look at the linear cycle in (log) real GDP and (log)real C, we find GDP and consumption are highly correlated,with consumption being slightly less volatile.You might have expected the high correlation betweenconsumption and income, since many students first exploreconsumption in terms of a simple linear consumption function:C = a + bY .However economists find this quite surprising, since theyexpect consumption to be much smoother than income. Thepermanent-income/life-cycle hypothesis, tells us thatconsumers smooth their consumption. (Just as you will notspend all your monthly paycheck on the day you receive it.)


Procyclical and Countercyclical Variables



When we look at the the linear cycles in (log) real GDP and(log) real I, we find they are again highly correlated, butinvestment is much more volatile. The volatility in investmenthas led to a lot of scrutiny of investment as a causal factor inbusiness cycles.


RBC economists emphasize technological change as the sourceof I fluctuations. Keynesians emphasize “animal spirits” as asource of I fluctuations. Note a commonality: both linkchanges in I to changes in the perceived profitability of I .


Recall that we tend to find inflation falling during recessions.(Cause or effect?)Stagflation: high inflation and high unemployment.


Is Inflation Countercyclical?


Is Inflation Countercyclical?

Source: FRED


Shock: causes a deviation from the historical trendExamples of shocks: oil price changes, new technologies, fiscalpolicy innovations, natural disasters.Question: are shocks permanent or temporary?Context: we know the cycle component of real GDP is highlyautocorrelated.The idea that shocks are permanent is closely associated withthe real business cycle literature.


Suppose shocks are permanent: then if run a regression of realGDP on its lagged value we should find a coefficient of one.

yt = ρyt−1 + εt (1)

This is something we can test for. Another way to run thesame regression is to subtract yt−1 from each side to get

∆yt = (ρ− 1)yt−1 + εt (2)

and then test if our coefficient (ρ− 1) differs from zero. Thisis the standard way of running what is known as aDickey-Fuller test for a unit root (i.e., for ρ = 1).


This has huge implications for forecasting. If shocks arepermanent (i.e., ρ = 1, the unit root case) then you shouldnot forecast a return to trend even in the distant future. Incontrast, if shocks are transitory (0 < ρ < 1) then you shouldforecast an eventual return to trend.


Phillips Curve: Output Version


Is there a trade-off between output and inflation? In the SR, itseems there is: the Phillips curve. In the LR, no. That is, if wetry to keep output above Y , inflation keeps rising. This issometimes called the accelerationist hypothesis.


Phillips Curve

Output 2% above Y tends to raise inflation about 1percentage point.


Empirical Phillips Curve: Output Version (US)


Empirical Okun’s Law

u − u = −12Yt



Note the unusually big rise in U in 2009.

Source: ERP 2010, Fig 2-16



Internationally also: note the unusually big rise in U in 2009compared to most other OECD countries with similar GDPgrowth.

Source: ERP 2010, Fig 2-16

macro notes: introduction to the short run the birth of modern macroeconomics, ... dickey-fuller...

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