Dynamics of Unemployment and Inflation

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Mohamed Rehan M S – [email protected]

Dynamics of Unemployment andInflation

An extended Phillips – NAIRU model

Dynamics of Unemployment and Inflation

Mohamed Rehan M S

Center of Excellence in Systems Science

Indian Institute of Technology, Jodhpur13th November 2013

1




Historical inverse relationship between the rateof unemployment and the rate of inflation inan economy

First observed by William Phillips

Cornerstone for Keynesian Economic Policies

Trivia: Seven Nobel Prizes have been awarded for work critical of

the Phillips curve!!!

The Phillips Curve

Dynamics of Unemployment and Inflation 2




The Phillips Curve





Original model deemed to simplistic

The relationship exists only in the short run

Newer models have other factors included in

them, most popular amongst them beingExpectations Augmented Phillips Curves

Imbibes concept of NAIRU (Non AcceleratingInflation Rate of Unemployment) – a level ofunemployment below which inflation rises

Phillip’s Curve today





Comparison of various Phillips Curves





Multiple mathematical models for NAIRUPhillip’s Curves

All models carry the two basic principles

Inflation is inversely proportional to Unemploymentin the short run

In the long run, monetary policy cannot affectunemployment

Mathematical Formulation



http://slidepdf.com/reader/full/dynamics-of-unemployment-and-inflation 7/28Mohamed Rehan M S – [email protected]

Ut+

= Ut i L U

t o

tU

tU = unemployment

i = inflow rate of labor

L = Labor force

o = outflow rate of labor

ot =

+ (−)

Jt = Jobs created at time t

d = Fraction of currently employed people

looking for better jobs

Derivation of our model




Jt = J

s γ m π

t γ = scaling factor

m = money growth rate in the market

πt = Inflation rate at time t

Combining all three equations we get

Ut+= Ut i L Ut Js γ m πt

Ut d 1 Ut

Ut = f(Ut, πt)

Derivation of our model (contd.)




πt =

(πt

e

,−

)πt

e = expected rate of inflation

w,t = real bargained wage

wp = real price determined wage

= price change factor

wp

= 1 μ y

w,t = 1 1 b Ut y





πt+

e = aπt 1 a π

t

e

Substituting all previous equations we obtain

πt =1

δ(πt

e μ (1 b)t

1 μ )

and solving it for πte

πte = δπt

μ (1 b)t

1 μ





Finally, we obtain

πt+ =1

δ[

μ

1 μ aπt 1 a δπt

μ 1 b Ut

1 μ

1 b

1 μUt+]

Which can be expressed as

πt+ =1

δ[

μ

1 μ aπt 1 a δπt

μ 1 b Ut

1 μ

1 b

1 μf(Ut, πt)]

In other words, πt+ = g(Ut, πt)





Ut+= Ut i L Ut

Js γ m πt

Ut d 1 Ut Ut

πt+ =1

δ[

μ

1 μ aπt 1 a δπt

μ 1 b Ut

1 μ

1 b

1 μUt+]

a = 0.5 μ= 0.04

b = 0.5 δ= 2

d = 0.01 γ= 0.5m = 0.03 L= 1

Assumptions for Numerical Analysis




Fixed point obtained at (0.0224,0.03)

Stability analysis for various values of i

i=0.12, λ =-0.8239,0.7356, stable

i=0.16, λ =-1.4104,0.7395, unstable

Stability lost at i=0.131992

Numerical Analysis




Bifurcation Diagram - Unemployment




Bifurcation Diagram - Inflation





Chaotic Attractor





As t tends to infinity, any value is either

Eventually periodic to the fixed point, or

Sucked into an orbit, which may be

• Periodic (i=0.18, all periods possible)

• Chaotic Attractor

Out of 50000 iterations, not a single point isrepeated, when it goes to a chaotic orbit!!!

Chaotic Attractor (Contd.)





Sensitive dependence studied using two initialpoints (0.2,0.15) & (0.2,0.15+10-10)

The points diverge from each other with time,implying that the system shows sensitivedependence on initial conditions

As t tends to infinity, both points converge toentirely different orbits

Sensitive Dependence


( )




Sensitive Dependence (Contd.)


S (C )




Sensitive Dependence (Contd.)


B f A




Basin of Attraction


C l




The NAIRU model exhibits chaotic behaviorafter a certain value of inflow of people tounemployment (approx. 0.18).

Hence large layoffs, population bursts, heavy

migration etc., can have serious impacts onthe economy, and de-stabilize it by leading itto chaos

Existence of chaotic orbits implies that there isno stable tradeoff

Conclusions


C l i (C d )




The chaotic attractor resembles the originalPhillips Curve with a negative slope

However, the curve is composed of unstabledisequilibria, and reaffirms that there is no

feasible inflation-unemployment tradeoff

Long periods of high inflation rates cannotoccur. This should be kept in mind while

designing monetary policy

Conclusions (Contd.)


F P




Conduct analysis for different parameters, oneby one.

Conduct analysis for all parameters varyingtogether and interacting with each other

Instead of fixed values of various parameters,include their values from the actual time series.Try to develop a prediction technique for

values in non-chaotic regionImprove model with other exogenous inputs

Future Prospects


R f




Day, Richard H. "Complex Economic Dynamics Vol. I. An

introduction to dynamical systems and market mechanisms."(1994).

Day, Richard Hollis. Complex economic dynamics: An

introduction to Macroeconomic dynamics. Vol. 2 . Vol. 2. Mit

Press, 1999.Ferri, Piero, Edward Greenberg, and Richard H. Day. "ThePhillips curve, regime switching, and the NAIRU." Journal of

Economic Behavior & Organization 46, no. 1 (2001): 23-37.

Neugart, Michael. "Complicated dynamics in a flow model ofthe labor market." Journal of Economic Behavior &

Organization 53, no. 2 (2004): 193-213.

References




QUESTIONS???


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THANK YOU


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Dynamics of Unemployment and Inflation

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