1 A Multiple Break Panel Approach to Estimating United States Phillips Curves Bill Russell, Anindya Banerjee, Issam Malki and Natalia Ponomareva Royal.

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A Multiple Break Panel Approach to Estimating United States Phillips Curves

Bill Russell, Anindya Banerjee, Issam Malki and Natalia Ponomareva

Royal Economic Society 2011 ConferenceRoyal Holloway UniversityLondon, 18-20 April 2011

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Graph 1: United States Quarterly InflationSeasonally adjusted, March 1960 – June 2007

0

2

4

6

8

10

12

14

Mar-60 Mar-65 Mar-70 Mar-75 Mar-80 Mar-85 Mar-90 Mar-95 Mar-00 Mar-05

An

nu

alis

ed

Qu

art

erly

Infl

atio

n

March 1960 to June 2007

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What is the ‘true’ statistical process of inflation?

1. Shocks mean zero and no change to MP then inflation varies around the long-run rate of inflation

2. An increase in long-run rate requires a loosening in MP inflation converges on new long-run rate

Implies inflation is stationary around shifting means

Can estimate shifts in mean using Bai-Perron technique for multiple breaks and shown in the inflation slide

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Graph 1: United States Quarterly InflationSeasonally adjusted, March 1960 – June 2007

0

2

4

6

8

10

12

14

Mar-60 Mar-65 Mar-70 Mar-75 Mar-80 Mar-85 Mar-90 Mar-95 Mar-00 Mar-05

An

nu

alis

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Qu

art

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Infl

atio

n

March 1960 to June 2007

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Hybrid Phillips curve

)1(11 ttztbttft zppEp

1:

1;0:

1;0:

0;1:

2001 Salido,-Lopez &Gertler Gali, 1999; Gertler, & Gali

1967 Phelps, 1968; Friedman,

2000 Svensson,1999; Gertler,&GaliClarida,

bf

bf

bf

bf

LRVertical

Hybrid

PF

NKPC

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Remainder of Presentation

1. Demonstrate standard results in the literature are biased using Monte Carlo simulations when we assume inflation is stationary

2. Estimate United States short and long-run Phillips curves assuming inflation is stationary around a shifting mean

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1. Monte Carlo simulations Assuming Inflation is I(0)

006388.0

Generate Phillips curve data with no significant dynamic terms

Forcing variable

‘Inflation series’

Mean shift inflation series

ttt xx 1937967.0

ttt xy 205406.0 004753.0

itt

MSt yy

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Monte Carlo Simulations

0, bf 205406.0z

)1(11 ttztbttft zppEp

– generate 190 observations

– replicate the model 10,000 times

– estimate Phillips curves with GMM using

– report average estimates (inference the same with median)

– ‘true’ model

MSttt yyx and,

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Table 1: Phillips Curve estimates from the generated data

Constant Mean Rate of Inflation

dependent variable ty

Shifting Mean Rates of Inflation

dependent variable MSty

F-P NK Hybrid ND F-P NK Hybrid

1ty 0.0191 (0.0)

0.0186 (0.0)

MSty 1 1.0315

(14.1) 0.9785 (5.2)

1ty - 0.0104 (- 0.2)

- 0.0078 (- 0.1)

MSty 1 0.2984

(4.4) 0.0377

(0.6)

MSty 2 0.2201

(3.1)

MSty 3 0.1923

(3.1)

tx - 0.2076 (- 8.1)

- 0.2017 (- 2.5)

- 0.2034 (- 2.1)

- 0.2052 (- 10.1) tx - 0.0563

(- 1.8) - 0.0146 (- 0.6)

- 0.0158 (- 0.6)

C - 0.0000 (- 0.0)

- 0.0000 (- 0.0)

- 0.0000 (- 0.0)

- 0.0000 (- 0.0)

C 0.0027 (4.0)

- 0.0003 (- 0.4)

- 0.0002 (- 0.1)

2R 0.76 0.77 0.83 0.70 2R 0.75 0.74 0.80

J test 0.4920 0.5185 0.5268 0.4964 J test 0.2911 0.4890 0.4835

LM(4) 0.4357 0.0746 0.0196 0.4478 LM(4) 0.1261 0.0000 0.0000

DW 1.99 2.02 2.01 2.00 DW 2.03 2.90 2.94

ADFR - 6.15 - 6.55 - 6.50 - 6.12 ADFR - 5.92 - 8.35 - 8.43

- 0.0104 [0.0656]

0.0191 [0.4795]

0.0108 [0.6472]

0.7108 [0.0699]

1.0315 [0.0769]

1.0161 [0.0947]

F 0.4230 0.4091 0.4392 0.4524 F 0.0000 0.0000 0.0000

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What do we conclude from the Monte Carlo analysis?

(i) Unaccounted mean shifts bias upwards the dynamic inflation coefficients and downward the forcing variable

(ii) Bias is so large that mean shifts alone will generate the ‘standard’ empirical Phillips curve results of the past 35 years

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2. Estimate United States Phillips Curves Assuming inflation is I(0) around shifting means

1. Apply Bai-Perron technique to identify multiple breaks in mean and identify n ‘inflation regimes’ – in our case 9

2. Partition the data into n cross sections of data where each is an individual inflation regime with a ‘constant mean inflation

3. Estimate the 9 short run Phillips curves using 2SLS fixed effects panel estimator

4. Estimate with standard time series panel estimator (2 lags of independent variables as instruments)

nt

ntz

ntb

nt

ntf

nnt zppEp 11

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Estimate United States Phillips Curves

Data

• Quarterly March 1960 – June 2007

• Inflation is ∆ln GDP implicit price deflator at factor cost

• Markup is ln of GDP deflator at factor cost on unit labour costs (national accounts measures)

nt

ntz

ntb

nt

ntf

nnt zppEp 11

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Table 6: Panel Estimates of United States Phillips Curve

All Inflation Regimes

Restricted Constant Fixed Effects

F-P NK Hybrid Markup Only

F-P NK Hybrid Markup Only

ntp 1 0.9835

(14.4) 0.6888 (5.6)

0.0636 (0.2)

0.3819 (1.0)

ntp 1 0.4642

(6.1) 0.2754

(2.7) 0.1263

(1.6) 0.1748

(1.8)

ntp 2 0.1477

(1.8)

ntp 3 0.2805

(3.6)

tmu - 0.0409 (- 2.6)

- 0.0064 (- 0.3)

- 0.0153 (- 0.9)

- 0.2106 (- 9.7)

- 0.0527 (- 2.5)

- 0.0571 (- 2.2)

- 0.0411 (- 1.5)

- 0.0581 (- 2.7)

Constant 0.0205 (2.6)

0.0032 (0.3)

0.0076 (0.9)

0.1094 (10.5)

0.0330 (3.3)

0.0356 (2.6)

0.0236 (1.5)

0.0367 (3.5)

2R 0.786 0.711 0.785 0.340 0.838 0.827 0.816 0.835

AR(1) AR(2) AR(3) AR(4)

[0.031] [0.144] [0.088] [0.068]

[0.000] [0.020] [0.668] [0.197]

[0.000] [0.455] [0.668] [0.151]

[0.000] [0. 000] [0. 000] [0. 000]

[0.844] [0.020] [0.760] [0.551]

[0.575] [0.033] [0.821] [0.542]

[0.000] [0.119] [0.728] [0.285]

[0.195] [0.024] [0.626] [0.729]

DW 2.121 2.769 3.027 0.485 2.048 1.886 2.665 1.82 Wald Tests – probability values

Parameter Constancy

[0.000] [0.209] [0.383] [0.000] [0.134] [0.336] [0.128] [0.413]

0 bf

1 bf

[0.000]

[0.044]

[0.000]

[0.809]

[0.000]

[0.545]

[0.101]

[0.000]

[0.8426]

[0.004]

[0.197]

[0.303]

F Tests – probability values Significant Variables

[0.000] [0.000] [0.000] [0.000] [0.000] [0.000] [0.000] [0.000]

Fixed Effects [0.000] [0.376] [0.977] [0.000]

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Calculating the Long-run Markup

- Define long-run inflation as the mean rate of inflation in each regime

nnbf

n

z

n

nzbf

nn

nbf

n

z

n

zpz

zp

pz

11

1

11

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Calculating the Long-run Markup

- Provides a locus of nine combinations of long-run rates of inflation and the markup

- Can use this locus to look at the shape of the long-run Phillips curve

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Table 6: Estimates of the Long-run Phillips Curve

Linear: 4.133.14

2120.01109.0

zp

, 32.02 R

The estimated coefficient on z is zero is rejected, 1191.17921 , prob-value = 0.0000.

Standard error of the regression: 0.0049.

Non-linear Exponential Model

1.58.2

2860.228436.5

zpLn

, 34.02 R

The estimated coefficient on z is zero is rejected, 1511.2621 , prob-value = 0.0000.

Standard error of the regression: 0.4920.

Notes: Numbers in ( ) are t statistics . The models are estimated using ordinary least squares in Eviews 7.1 with Newey-West HAC standard errors on 7 combinations of the long-run rate of inflation and long-run markup calculated from column 12 of Table 5.

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Graph 3: United States Inflation and the Markup

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.4 0.45 0.5 0.55

Markup

Qu

arte

rly

Infl

atio

n

SRPC 1 (squares)

SRPC 2(triangle)

SRPC 3 (diamonds)

Regime 5 (circles)

Regime 4 (dash)

SRPC 6 (plus)

SRPC 7 (solid dot)

SRPC 9 (solid triangle)

LRPC

Note: SRPC 2, 7 and 9 overlap.

SRPC 8 (solid diamond)

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Conclusions

i. If inflation is stationary around shifting means then no support for any of the ‘modern’ theories

ii. No evidence that the lead in inflation plays a significant role in inflation dynamics

iii. Marginal evidence that any lags in inflation are significant in the inflation-markup Phillips curve

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Conclusions

iv. Given ii & iii then no support for F-P, NK & hybrid models and markup should be thought of as ECM and a proxy for the firm’s profit margin

v. Friedman/Phelps remarkable empirical insight appears true to a first approximation

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Spare slides from here

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Monte Carlo on the panel methodology

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Table 3: Monte Carlo Bai-Perron Estimates of the Inflation Regimes

Estimated Number of Breaks k

Implied Number of Inflation Regimes

Frequency

1 2 3

2 3 365

3 4 1146

4 5 2286

5 6 2768

6 7 1893

7 8 1037

8 9 387

9 10 115

Statistical analysis of the number of breaks k . Mean: 4.99, Median: 5, Standard Deviation: 1.469, Skewness: 0.225, Kurtosis: - 0.194.

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Table 4: Monte Carlo Panel Estimates of the Phillips Curve using the Generated Mean Shift Variable MS

ty and the Forcing Variable tx

Restricted Constant Fixed Effects

F-P NK Hybrid F-P NK Hybrid ND

MSty 1 0.9683

(8.0) 0.9400 (4.4)

0.1567 (0.3)

0.1408 (0.3)

MSty 1 0.5198

(8.0) 0.0260

(0.4) 0.0211 (0.3)

0.0188 (0.2)

tx -0.0920 (-2.5)

-0.0237 (-0.5)

-0.0230 (-0.5)

- 0.1095 (- 2.5)

- 0.1060 (- 1.6)

- 0.1100 (- 1.4)

-0.1113 (-2.7)

Constant 0.0044 (5.6)

0.0003 (0.2)

0.0003 (0.3)

0.0090 (24.1)

0.0077 (18.9)

0.0077 (18.4)

0.0092 (24.6)

2R 0.415 0.231 0.216 0.599 0.477 0.433 0.598

LM(1) LM(2) LM(3) LM(4)

[0.007] [0.011] [0.009] [0.006]

[0.000] [0.000] [0.000] [0.000]

[0.000] [0.000] [0.000] [0.000]

[0.588] [0.540] [0.529] [0.521]

0.061 [0.076] [0.084] [0.085]

[0.025] [0.035] [0.038] [0.039]

[0.355] [0.394] [0.412] [0.420]

DW 2.339 2.928 2.954 2.004 2.169 2.171 1.960

Wald Tests – probability values

0 bf

1 bf

[0.000]

[0.000]

[0.000]

[0.880]

[0.000]

[0.934]

[0.662]

[0.000]

[0.724]

[0.343]

[0.845]

[0.528]

W [0.000] [0.000] [0.000] [0.164] [0.218] [0.255] [0.141]

F Tests – probability values

Significant Variables

[0.000] [0.000] [0.000] [0.000] [0.000] [0.000] [0.000]

Fixed Effects [0.000] [0.001] [0.000] [0.000]

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Reassessing Cogley and Sbordone slides from here

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Graph 3: Cogley and Sbordone AER 2008 Inflation Data

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Mar-60 Mar-68 Mar-76 Mar-84 Mar-92 Mar-00 Mar-08

An

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In

flati

on

Inflation

Trend Inflation

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Graph 4: Cogley and Sbordone Inflation Gap and Implicit Ratio of Actual over Trend Price Levels

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Table 9: Estimates of the Hybrid United States Phillips Curves

Data from Cogley and Sbordone 2008

Panel Estimation Time Series

Restricted Constant Fixed Effects

1 tgapp 0.9327 (4.0)

ntgapp 1 1.0839

(4.6) 0.0696 (0.1)

1 tgapp 0.0224 (0.1)

ntgapp 1 0.0207

(0.1) - 0.0073 (- 0.1)

tgapmu -0.0391 (- 0.6)

ntgapmu 0.0021

(0.1) - 0.0347

(0.6)

Constant - 0.0001 (- 0.1)

Constant 0.0000 (0.0)

0.0040 (1.7)

2R 0.503 0.4980 0.626

DW 2.895 3.051 2.124

Wald Tests – probability values

0 bf

1 bf

[0.000]*

[0.537]*

[0.000]

[0.325]

[0.898]

[0.109]

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Inflation Persistence

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Alternative Hypothesis: The estimated low persistence is due to the over-breaking of highly persistent data

• Generate 190 observations

assuming and

• Estimate fixed effects OLS using the cross-section panel methodology imposing breaks 0 to 15

ttt ww 1

0.1 844559.0

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True Model AR(1) = 1.0 and Zero Breaks

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Number of Breaks

Mea

n E

stim

ated

Co

effi

cien

ts

True Model AR(1) = 0.844559 and Zero Breaks

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Number of Breaks

Mea

n E

stim

ated

Co

effi

cien

ts

Graph 2: The Impact of Over-breaking on Estimates of the AR(1) Coefficients

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Graph 2: The Impact of Over-breaking on Estimates of the AR(1) Coefficients

True Model AR(1) = 0.2 and Zero Breaks

-0.2

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Number of Breaks

Me

an E

stim

ated

Co

effi

cien

ts

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Table 7: Panel Estimates of United States Phillips Curve

Stationary and Non-stationary Inflation Regimes

Stationary Inflation Regimes Non-stationary Inflation Regimes

F-P NK Hybrid Markup Only

F-P NK Hybrid Markup Only

ntp 1 0.2392

(0.5) 0.4186 (0.9)

1.3338 (2.2)

1.0890 (2.2)

ntp 1 0.0573

(0.7) 0.0845

(0.8) 0.7218

(2.1) 0.6563

(2.3)

ntp 2

ntp 3

tmu - 0.0441 (- 2.2)

- 0.0438 (- 1.8)

- 0.0365 (- 1.4)

- 0.0469 (- 2.3)

- 0.4409 (- 1.7)

0.8562 (1.7)

0.5250 (1.3)

- 0.1455 (- 0.6)

Constant 0.0288 (2.9)

0.0272 (2.1)

0.0215 (1.4)

0.0306 (3.2)

0.2050 (1.8)

0.2331 (- 1.7)

- 0.2510 (- 1.3)

0.0853 (0.7)

2R 0.810 0.795 0.774 0.810 0.645 0.672 0.806 0.534

AR(1) AR(2) AR(3) AR(4)

[0.429] [0.065] [0.546] [0.399]

[0.012] [0.090] [0.227] [0.305]

[0.000] [0.152] [0.245] [0.292]

[0.708] [0.068] [0.555] [0.403]

[0.199] [0.480] [0.134] [0.181]

[0.795] [0.019] [0.328] [0.038]

[0.743] [0.011] [0.368] [0.452]

[0.154] [0.062] [0.007] [0.243]

DW 2.051 2.378 2.747 1.94 2.624 1.812 1.839 1.306 Wald Tests – probability values

Parameter Constancy

[0.253] [0.669] [0.393] [0.261] [0.867] [0.972] [0.527] [0.566]

0 bf

1 bf

[0.481]

[0.000]

[0.527]

[0.046]

[0.326]

[0.332]

[0.064]

[0.432]

[0.075]

[0.610]

[0.019]

[0.203]

F Tests – probability values Significant Variables

[0.000] [0.000] [0.000] [0.000] [0.006] [0.023] [0.015] [0.010]

Fixed Effects [0.000] [0.600] [0.946] [0.000] [0.064] [0.152] [0.464] [0.007]

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A2. Monte Carlo simulations assuming inflation is I(1)

ADF univariate unit root test statistic = - 2.615, CV5% = - 2.877

Difference the data and the model

‘True’ model remains

ttztbttft zppEp 12

122

0, bf 205406.0z

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Table 2: Phillips Curve estimates from the differenced generated data

F-P NK Hybrid

MSty 1 - 0.3772

(- 0.5) - 0.4464 (- 0.7)

MSty 1 - 0.6013

(- 6.6) - 0.6006

(- 4.6)

MSty 2 - 0.2869

(- 3.3) - 0.3005

(- 2.3)

tx 0.0129 (- 0.8)

- 0.2089 (- 0.3)

0.0375 (- 0.1)

Constant 0.0000 (0.1)

0.0000 (0.5)

0.0001 (0.1)

2R 0.71 0.56 0.84

J test 0.2397 0.2298 0.3955

LM(4) 0.0405 0.0000 0.0029

DW 2.05 2.44 2.07

ADFR -7.13 - 7.54 - 7.23

- 0.8882 [0.1890]

- 0. 3772 [1.1864]

- 1.3475 [5.3564]

F 0.0052 0.1725 0.2447

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United States Phillips Curves

Long-run Phillips Curve

Inflation = 0.2964 ue2 - 1.5445 ue + 2.5189

R2 = 0.938

-4

-2

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10 12

Unemployment Rate (percent)

An

nu

ali

se

d Q

ua

rte

rly

In

fla

tio

n

SRPC 1 (pink)

SRPC 2 (turquoise)

SRPC 3 (brown)

SRPC 4 (red)

SRPC 5 (green)

SRPC 6 (blue)

SRPC 7 (purple)

SRPC 8 (orange)

LRPC

From Russell (2007). Non-stationary Inflation and Panel Estimates of United States Short and Long-run Phillips Curves.

Price index is all urban CPI.

Assumes inflation is stationary around shifting means.

Same data as Russell and Banerjee (2008).

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From Russell and Banerjee (2008). The Long-run Phillips curve and Non-stationary Inflation, Journal of Macroeconomics, vol. 29, pp. 355-67.

Price index is all urban CPI.

Assumes inflation and markup are integrated.

Graph 9: United States Long-run Phillips Curve

-5

0

5

10

15

20

0 2 4 6 8 10 12

Unemployment Rate (per cent)

Infl

atio

n (

ann

ual

ised

qu

arte

rly

log

ch

ang

e)

1

2

3

45

LR

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Issues: long-run Phillips curve has a positive slope

• Ross and Wachter (1973)

• Friedman’s (1977) Nobel Lecture

• Akerlof, Dickens and Perry (2000)

• Markup and inflation are negatively related in the long-run

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UNITED STATESDecember 1961 - June 1997

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

90 95 100 105 110

Markup (100=period average)

Ann

ualis

ed Q

tly I

nfla

tion

LogChange

D1961-J1964 (cross)S1964-S1972 (square)D1972-J1982 (circle)S1982-J1991 (dash)

S1991-J1997 (triangle)

Banerjee, A. and B. Russell (2001). ‘Inflation and the Markup in the G7 Economies and Australia’, Review of Economics and Statistics, vol. 83, no. 2, May, pp. 377-87.

39

Three Issues

1. Are the coefficients constant across ‘regimes’

2. Estimating dynamic panels when n is large relative to t

- Arellano & Bond (1991), Arellano & Bover (1995), Blundell and Bond (1998), Bond (2002)

- ‘rule-of-thumb’ says it is ok if t is large enough to estimate each cross section separately

nt

ntz

ntb

nt

ntf

nnt zppEp 11

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Three Issues

3. Endogeneity of u/e rate and expected inflation term

- 2SLS

- instruments are two lags of inflation and unemployment rate

nt

ntz

ntb

nt

ntf

nnt zppEp 11

41

1 (i) Inflation is not stationary

Inflation stationary with constant mean implies that

(i) The question ‘what is the long-run rate of inflation?’ is valid. Average

March 1952 – September 2004 3.7%March 1952 – September 1994 4.1%Last 10 years 2.4%

(ii) Institutional arrangements have no impact on the long-run rate of inflation

42

1 (i) Inflation is not stationary

(iii) All monetary economics and macroeconomics literature on the dynamics of inflation with changes in money growth is at best ‘misplaced’

(iv) Long-run Phillips curve in an applied sense is a single point

- If you do not accept (i) to (iv) then you have to conclude that inflation is not stationary with a constant mean

43

Consider now the last 50 years of US Inflation Data

• What is the ‘true’ statistical process of ?

- not integrated

- not trend stationary

- not stationary with constant mean

therefore stationary with shifting means

tp

)1(11 ttxtbttft xppEp