Upload
emily-adair
View
215
Download
0
Tags:
Embed Size (px)
Citation preview
1
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
2
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
3
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
4
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
5
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
6
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
7
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
8
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,
9
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
10
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
11
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
12
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
13
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]
14
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
15
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
16
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.
17
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)
18
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
19
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
20
Spare slides from here
21
Monte Carlo on the panel methodology
22
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.
23
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]
24
Reassessing Cogley and Sbordone slides from here
25
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
nu
ali
sed
In
flati
on
Inflation
Trend Inflation
26
Graph 4: Cogley and Sbordone Inflation Gap and Implicit Ratio of Actual over Trend Price Levels
27
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]
28
Inflation Persistence
29
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
30
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
31
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
32
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]
33
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
34
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
35
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).
36
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
37
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
38
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
40
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