Introduction to Macroeconomics - University of...

Introduction to Macroeconomics

Martin Ellison

Nuffi eld College

Michaelmas Term 2018

Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 1 / 39

Macroeconomics is Dynamic

Decisions are taken over time

t1 t+1t

Expectations

Expectations make economics special


Macroeconomics is Stochastic

The economy is hit by shocks - Frisch-Slutsky paradigm

Impulses Propagation Fluctuations

Shocks to:

technologymonetary policyconsumer confidenceoil pricesexchange rate…

Microfounded (Lucas) fromdeep parameters:

i) tastes and preferencesii) production technologyiii) market structure

Decisions have to account for uncertainty


Macroeconomics is General Equilibrium

Markets are interconnected

Firms

Goods

Labour

Expenditure(£)

Income (£)

Householdsmaximise

utilitymaximise

profit

Need to analyse all markets together


Dynamic Stochastic General Equilibrium (DSGE)

Work with Frisch-Slutsky paradigm backwards

Impulses Propagation Fluctuations

What do fluctuations look like?

underlying trend

business cycle

seasonality

random fluctuations

measurement error


Macroeconomic data

1940 1950 1960 1970 1980 1990 2000 2010 20207

8

9

10LGNPC96

1940 1950 1960 1970 1980 1990 2000 2010 20207

8

9

10

LPCECC96

Log GNP and non-durable consumption in the US


Filtering

Hodrick-Prescott filter decomposes data yt into trend τt and cycle ct

yt = τt + ct

Trend should be smooth but follow data closely

min{τt}Tt=1

(T

∑t=1(yt − τt )

2 + λT−1∑t=2

[(τt+1 − τt )− (τt − τt−1)]2

)

λ is weighting parameter

λ = 0 means τt = yt and trend is data

λ→ ∞ means ∆2τt = 0 and trend is linear


Hodrick-Prescott filter

2000 2005 2010 2015 20209.4

9.45

9.5

9.55

9.6

9.65

9.7

9.75

LGNPC96LGNPC96( =400)LGNPC96( =800)LGNPC96( =1600)

US GNP and Hodrick-Prescott trends


Hodrick-Prescott as a band-pass filter

λ = 6400 dots; λ = 1600 solid; λ = 400 dashes

λ = 1600 defines business cycle as fluctuations less than about 40 quarters


Comments on filtering

HP is a 2-sided filter that brings future information into the presentand so violates informational assumptions of rational expectations

Identification of cycles not invariant to filter → others may be better

Filtering may induce spurious cycles, e.g. linear detrending of arandom walk

Can remove propagation from a model entirely and still get cycles


Long run properties of macroeconomic data

1940 1950 1960 1970 1980 1990 2000 2010 20207

8

9

10

LGNPC96LGNPC96( =1600)

1940 1950 1960 1970 1980 1990 2000 2010 20200

0.02

0.04

0.06

DLGNPC96( =1600)

Trend growth in US GNP per capita is approximately constant


Long run properties of macroeconomic data

1940 1950 1960 1970 1980 1990 2000 2010 20200.6

0.65

0.7

0.75

labour share

1940 1950 1960 1970 1980 1990 2000 2010 20200

0.2

0.4

0.6

0.8

C/YI/Y

Labour share and the Great Ratios in the US are approximately constant


Kaldor (1957) facts

1 Output per worker grows at a roughly constant rate2 Capital per worker grows over time3 Capital/output ratio is roughly constant4 Rate of return to capital is constant5 Shares of capital and labour in net income are nearly constant6 Real wage grows over time7 Ratios of consumption and investment to GDP are constant


Short run properties of macroeconomic data

Detrended GNP and non-durable consumption

1940 1950 1960 1970 1980 1990 2000 2010 20200.08

0.06

0.04

0.02

0

0.02

0.04

0.06

LGNPC96(hp)LPCECC96(hp)

σY > σC ; strong correlation; C leads Y by a quarter or two?


Short run properties of macroeconomic data

Variable Sd% Cross-correlation of output with:

GNPCNDCDIHAve HLGNP/HAve W

1.720.864.968.241.590.631.140.900.55

t-3 t-2 t-1 t t+1 t+2 t+30.38 0.63 0.85 1.00 0.85 0.63 0.380.55 0.68 0.78 0.77 0.64 0.47 0.270.49 0.65 0.75 0.78 0.61 0.38 0.110.38 0.59 0.79 0.91 0.76 0.50 0.220.30 0.53 0.74 0.86 0.82 0.69 0.520.34 0.48 0.63 0.62 0.52 0.37 0.230.23 0.46 0.69 0.85 0.86 0.76 0.590.20 0.30 0.33 0.41 0.19 0.00 -0.180.21 0.14 0.09 0.03 -0.07 -0.09 -0.09

Cyclical behaviour of the US economy 1954-1991


Stylised facts

Non-durable consumption less volatile than output

Volatility of output and hours similar

Employment more volatile than average hours

Wages less volatile than productivity

Productivity slightly procyclical

Wage acyclical


Vector autoregressions (VARs)

Flexible form that describes wide range of real data sets

Rt = R0 + a11Rt−1 + . . .+ ap1Rt−p + b11πt−1 + . . .+ bp1πt−p + e1tπt = π0 + a12Rt−1 + . . .+ ap2Rt−p + b12πt−1 + . . .+ bp2πt−p + e2t

p-th order vector autoregression in interest rate Rt and inflation πt

Can be estimated by Ordinary Least Squares (OLS)


The identification problem

VAR residuals and fundamental shocks(e1te2t

)=

(θ1 θ2θ3 θ4

)(u1tu2t

);

(u1tu2t

)∼ N

[0;(1 00 1

)]Problem is that both u1t and u2t may affect both e1t and e2t

Not identified


Causal ordering

Assume Rt reacts to πt with a lag

VAR residuals and fundamental shocks(e1te2t

)=

(θ1 0θ3 θ4

)(u1tu2t

)∼ N

[0;(

σ1 σ12σ12 σ2

)]Unique identification σ1 = θ21, σ12 = θ1θ3, σ2 = θ23 + θ24


Notes on causal ordering

Identified VAR is a structural vector autoregression (SVAR)

Ordering could be so πt reacts to Rt with a lag → not unique

Known as Wold decomposition or Choleski ordering

Generalisable to more than two variables


Impulse response functions

Shock to u2t

t Rt πt−1 0 00 0 θ41 b11θ4 b12θ42 a11b11θ4 + b11b12θ4 + b21θ4 a12b11θ4 + b12b12θ4 + b22θ4...

......


Sims (1992)

Six variable VAR for UK 1965q4 to 1990:12

Causal ordering1 Short interest rate R2 Index of foreign exchange value of domestic currency XR3 Commodity price index PC4 Monetary aggregate M5 Consumer price index P6 Industrial production index Y

Innovations only affect variables lower in causal ordering


Sims (1992)


Christiano, Eichenbaum and Evans (2005)

Nine variable VAR for US 1965:3 to 1995:3

Causal ordering1 Real GDP, real consumption, GDP deflator, real investment, real wage,labour productivity

2 Interest rate3 Real profit and growth rate of M2

R shocks only affect real profit and M2

R affected by all shocks except real profit and M2 shocks



Solid lines with plus signs are VAR-based estimates



Results suggest that after an expansionary monetary policy shock:

1 output, consumption, and investment respond in a hump-shape,peaking after about one and a half years and returning to pre-shocklevels after about three years

2 inflation responds in a hump-shape, peaking after about two years3 interest rate falls for roughly one year4 real profits, real wages, and labor productivity rise5 growth rate of money rises immediately


Problems with causal orderings

Sims (1992) and Christiano, Eichenbaum and Evans (2005) findprices ↑ for a while after an unexpected ↑ in RtCould be a cost channel effect (firm borrowing costs rise so theyincrease prices) but more likely faulty identification

Sign restriction VARs designed to rule out such anomalies


Mapping all identifications

Relationship between residuals and fundamental shocks

e1t = (θ1 cosλ) u1t + (θ1 sinλ) u2te2t = (θ3 cosλ− θ4 sinλ) u1t + (θ3 sinλ+ θ4 cosλ) u2t

λ = 0 recover standard causal ordering

λ = tan−1(

θ3θ4

)recovers alternative causal ordering

By looking at λ ∈ [−π,π] can map all possible identifications


Mapping all identifications

Matrix form(e1te2t

)=

(θ1 0θ3 θ4

)(cosλ sinλ− sinλ cosλ

)(u1tu2t

)Distribution of residuals(

e1te2t

)∼ N

[0;(

θ21 θ1θ3θ1θ3 θ23 + θ24

)]for all λ ∈ [−π,π]

In linear algebra we are rotating matrices


Sign restrictions

First variable is Rt and second variable is inflation πt

Standard VAR with causal ordering identifies θ1, θ3, θ4

All possible rotations

e1t = (θ1 cosλ) u1t + (θ1 sinλ) u2te2t = (θ3 cosλ− θ4 sinλ) u1t + (θ3 sinλ+ θ4 cosλ) u2t

Monetary policy shock raises Rt and lowers πt

Search for rotations that satisfy

θ1 cosλ > 0

θ3 cosλ− θ4 sinλ < 0


Illustrative example

Suppose standard VAR identifies θ1 = θ3 = θ4 = 1

Permissible rotations

θ1 cosλ > 0 θ3 cosλ− θ4 sinλ < 0

λ is in region[

π4 ,

π2

]


Canova (2007)

Responses to a US policy shock, 1964:1-2001:10


Canova and Paustian (2010)

Sign restrictions


Canova and Paustian (2010)

Response intervals to monetary shocks


Identification using high frequency information

ECB monthly press conference January 15, 2009

Traders expect interest rate cut on February 5, 2009

Trichet announces no policy change expected next meeting

Traders revise up expectations


Rosa (2008)

Link

Time zero when Trichet starts answering a journalist’s question

Mid-quote on 3-month Euribor future expiring in March 2009


https://www.youtube.com/watch?feature=player_embedded&v=3y8H4xqzShI

Kuttner (2001)

Spot-month futures rate on day t of month s interpreted asconditional expectation of the average funds rate in month s plusterm premium

f 0s ,t = Et1m

∑i∈sri + µ0s ,t

Policy surprise measure computed from the 1-day change in thespot-month future rate

∆r̃ut =m

m− t(f 0s ,t − f 0s ,t−1

)Policy surprise is proxied by change in futures rate → proxy VAR


Proxy

Correlated with u1t so E (u1tzt ) = φ

Uncorrelated with u2t so E (u2tzt ) = 0

Correlated with both residuals

E[(

e1te2t

)zt

]= E

[(θ1 θ2θ3 θ4

)(u1tu2t

)(φu1t + νt )

]=

(θ1φθ3φ

)Proxy VAR identified by restriction

θ1θ3=E (e1tzt )E (e2tzt )

for known E (e1tzt ) and E (e2tzt )


Kuttner (2001)

1-month response of interest rates to Fed funds surprises


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