Discussion of Stock and Discussion of Stock and Watson, “Has Inflation Watson, “Has Inflation

BecomeBecomeHarder to Forecast?”Harder to Forecast?”

Robert J. Gordon (with Ian Dew-Becker)Robert J. Gordon (with Ian Dew-Becker)Northwestern University and NBERNorthwestern University and NBER

QEPD Conference, Fed BOG,QEPD Conference, Fed BOG,Washington, September 30, 2005Washington, September 30, 2005

22

A Paper that Tackles A Paper that Tackles ForecastingForecasting

Opens Up Many New IssuesOpens Up Many New Issues A Basic Distinction between:A Basic Distinction between:

– A macro variable explained A macro variable explained ex post ex post over over some historical intervalsome historical interval

– Versus Forecasting, with no advance Versus Forecasting, with no advance knowledge of coefficients or values of knowledge of coefficients or values of explanatory variablesexplanatory variables

Key differences in forecastingKey differences in forecasting– Must estimate “rolling coefficients”Must estimate “rolling coefficients”– Any right-hand variables in the forecast Any right-hand variables in the forecast

equations must themselves be forecastequations must themselves be forecast

33

We Can Learn from We Can Learn from bothbothEx-post Ex-post Historical Econometrics Historical Econometrics

and and Pure ForecastingPure Forecasting

S-W have done both. What about S-W on history?S-W have done both. What about S-W on history?– With Staiger, their 1997 JEP paper used the “triangle With Staiger, their 1997 JEP paper used the “triangle

model”model” Here, they throw out their own past analysis of Here, they throw out their own past analysis of

history and start from scratchhistory and start from scratch An unanswered puzzle in their paper is the An unanswered puzzle in their paper is the

“permanent stochastic trend” component of “permanent stochastic trend” component of inflationinflation

The answer was already provided by the triangle The answer was already provided by the triangle model in 1980, and in their own 1997 and 2001 model in 1980, and in their own 1997 and 2001 papers, but here they pretend they don’t have a papers, but here they pretend they don’t have a clueclue

44

S-W’s Paper is not an Easy S-W’s Paper is not an Easy ReadRead

Let’s Count the AcronymsLet’s Count the Acronyms Reader already knows: CPI GDP PCE VARReader already knows: CPI GDP PCE VAR Reader is expected to keep track ofReader is expected to keep track of

– ADF ADL AO AR AR(AIC) IMA MA MCMC MSE ADF ADL AO AR AR(AIC) IMA MA MCMC MSE MSFE NAIRU PCED PC PC-MSFE NAIRU PCED PC PC-ΔΔu QLR u QLR RMSFE RMSFE UC-SVUC-SV

““Pseudo” out of sample (what’s “pseudo” Pseudo” out of sample (what’s “pseudo” about it? about it?

Paper has no discussion of real-time data Paper has no discussion of real-time data – PHL and STL FedsPHL and STL Feds

55

Plan of This CommentPlan of This Comment

What we know from historical What we know from historical analysis that might be useful for analysis that might be useful for forecastingforecasting

Exposition of triangle modelExposition of triangle model– Theory, textbooks, econometricsTheory, textbooks, econometrics– Peel the onion of the SSR as we Peel the onion of the SSR as we

transition from A-O’s AR model to the transition from A-O’s AR model to the full triangle model full triangle model

– Interplay of long lags and supply shocksInterplay of long lags and supply shocks

66

What We Learn fromWhat We Learn fromS-W’s Forecasting TestsS-W’s Forecasting Tests

Econometric AR’s are competitive with the Econometric AR’s are competitive with the rectangular distribution of the univariate rectangular distribution of the univariate A-O modelA-O model

What about multivariate models?What about multivariate models?– The triangle model is not tested The triangle model is not tested – What they call testing “multivariate models” is What they call testing “multivariate models” is

nothing more than seeing if alternative activity nothing more than seeing if alternative activity variables improve univariate forecasts, and variables improve univariate forecasts, and their answer is “no”their answer is “no”

– There is no mention of Supply Shocks There is no mention of Supply Shocks

77

What this Comment will What this Comment will ShowShow

The Triangle Model Outperforms A-O and The Triangle Model Outperforms A-O and S-W’s univariate forecastsS-W’s univariate forecasts

The Margin of Superiority of the Triangle The Margin of Superiority of the Triangle Model over A-O and S-W increases, the Model over A-O and S-W increases, the longer ahead is the time horizonlonger ahead is the time horizon

Using a model with long lags, an Using a model with long lags, an unemployment gap, and supply shocks unemployment gap, and supply shocks beats univariate forecasts, especially at beats univariate forecasts, especially at the 8 quarter horizonthe 8 quarter horizon

88

The Triangle Model: Merges The Triangle Model: Merges the NRH Phillips Curve with the NRH Phillips Curve with Inertia and Supply ShocksInertia and Supply Shocks

Theory? Gordon (1975) and Phelps (1978)Theory? Gordon (1975) and Phelps (1978)– Relative price increase of an important price-inelastic Relative price increase of an important price-inelastic

product requires an increase in expenditure share (i.e., on product requires an increase in expenditure share (i.e., on oil)oil)

– Key condition: A wedge must open up between nominal Key condition: A wedge must open up between nominal GDP growth and nominal wage growth to make room for GDP growth and nominal wage growth to make room for this increased expenditure share (i.e., on oil)this increased expenditure share (i.e., on oil)

One Extreme: Flexible nominal wage decline could One Extreme: Flexible nominal wage decline could eliminate any problemeliminate any problem

Other Extreme: Sticky nominal wage growth Other Extreme: Sticky nominal wage growth requires a decline in real nonoil output to reduce requires a decline in real nonoil output to reduce the expenditure share of nonoil sectorthe expenditure share of nonoil sector– ““Inflation Creates Recession” (Inflation Creates Recession” (NYTNYT 1974) 1974)

99

The TextbooksThe Textbooks The diagram: inflation on the vertical, output gap The diagram: inflation on the vertical, output gap

on the horizontalon the horizontal– Short-run Phillips curve slopes up, and is shifted around Short-run Phillips curve slopes up, and is shifted around

by both adaptive expectations and by the oil shockby both adaptive expectations and by the oil shock– Joined with a negative 45 degree line, the “DG” curve, Joined with a negative 45 degree line, the “DG” curve,

the demand-growth curve dependent on nominal GDPthe demand-growth curve dependent on nominal GDP With constant nominal GDP growth, a supply With constant nominal GDP growth, a supply

shock slides the economy northwest along the DG shock slides the economy northwest along the DG curvecurve

Invented by Rudi Dornbusch in a classroom Invented by Rudi Dornbusch in a classroom handout in April, 1975handout in April, 1975– Introduced in two textbooks, Dornbusch-Fischer (1978) Introduced in two textbooks, Dornbusch-Fischer (1978)

and Gordon (1978)and Gordon (1978)

1010

The Econometric Model was The Econometric Model was put into its current form in put into its current form in

19801980 The “triangle model” of inflation dynamicsThe “triangle model” of inflation dynamics

pptt = a(L)p = a(L)pt-1t-1 + b(L)D + b(L)Dtt + c(L)z + c(L)ztt + e + ett

– D is demand (output or unemployment gap), z is D is demand (output or unemployment gap), z is supply shocks, e i.i.d errorsupply shocks, e i.i.d error

– Restrict sum of LDV to unity, DRestrict sum of LDV to unity, DNNtt is natural rate – is natural rate –

implies constant inflationimplies constant inflation

– DDtt, Z, Zt t variables defined relative to zero variables defined relative to zero

Supply shocks in today’s tests are food-energy, Supply shocks in today’s tests are food-energy, imports, Nixon control dummies (“on” and imports, Nixon control dummies (“on” and “off”)“off”)

1111

Allowing the NAIRU to VaryAllowing the NAIRU to Vary

The Kalman smoother:The Kalman smoother: pptt = a(L)p = a(L)pt-1t-1 + b(L)(U + b(L)(Utt – U – UNN

tt) + c(L)z) + c(L)ztt + e + ett

UUNNtt = U = UNN

t-1t-1 + + ννtt , E( , E(ννtt)=0, var()=0, var(ννtt)=)=σσ 22

SSW implemented this in JEP 1997 SSW implemented this in JEP 1997 using the Gordon “triangle model” and using the Gordon “triangle model” and Gordon adopted the SSW innovation Gordon adopted the SSW innovation simultaneously, a true “merger”simultaneously, a true “merger”

What the TV-NAIRU looks like now What the TV-NAIRU looks like now compared to 1998compared to 1998

1212

The “Unexplained Permanent The “Unexplained Permanent Component”Component”

1313

Stock-Watson Current Stock-Watson Current ApproachApproach

Leaves Both Big Questions Leaves Both Big Questions UnansweredUnanswered

#1 Big Question: Why did the #1 Big Question: Why did the “Permanent Stochastic Trend “Permanent Stochastic Trend Component” of Inflation rise 1972-83 Component” of Inflation rise 1972-83 and then fall?and then fall?

#2 Big Question: Why is their version #2 Big Question: Why is their version of the TV-NAIRU so low in the 1960s and of the TV-NAIRU so low in the 1960s and so high in 1978-83?so high in 1978-83?

Triangle Model Answers Triangle Model Answers bothboth Questions Questions

1414

Post-Sample Dynamic Post-Sample Dynamic Simulations (this is Figure 6 in Simulations (this is Figure 6 in

BPEA paper)BPEA paper)

0

1

2

3

4

5

6

7

8

9

10

1984:01 1989:01 1994:01 1999:01 2004:01

Simulated

Predicted Column 1

Column 2

Column 5Actual

1515

Historical Analysis, SSRs and Historical Analysis, SSRs and U Coefficients, 1962:Q1 to U Coefficients, 1962:Q1 to

2004:Q42004:Q4 A-OA-O 237.2237.2 AR(4)AR(4) 235.4235.4 16 lags16 lags 257.0257.0 Add UAdd U 204.1204.1 -0.53-0.53 Add TVNAdd TVN 166.3166.3 -0.89-0.89 Nixon/offNixon/off 158.6158.6 -0.91-0.91 Food-energyFood-energy 74.7 74.7 -0.59-0.59 ImportsImports 70.1 70.1 -0.63-0.63

1616

Interplay Between Supply Interplay Between Supply ShocksShocks

and Long Lags on LDVand Long Lags on LDV U4 no SS LDV 1-4U4 no SS LDV 1-4 233.9233.9 -0.23-0.23 U4 no SS LDV 1-16U4 no SS LDV 1-16 222.5222.5 -0.52-0.52 U4 with SS LDV 1-4U4 with SS LDV 1-4 81.481.4 -0.32-0.32 U4 with SS LDV 1-16U4 with SS LDV 1-16 70.170.1 -0.63-0.63

Substitute S-W current treatment of Substitute S-W current treatment of TV-NTV-N

U4 with SS LDV 1-16U4 with SS LDV 1-16 87.487.4 -0.65-0.65

1717

That’s Enough about History, That’s Enough about History, Now It’s Time for a Forecasting Now It’s Time for a Forecasting

ContestContest Aim is to compare A-O, SW AR(8), and the Triangle Aim is to compare A-O, SW AR(8), and the Triangle

ModelModel Method for Triangle Model Method for Triangle Model

– Instead of eliminating zero-lag variables from triangle Instead of eliminating zero-lag variables from triangle model, each RHS variable is forecast using a AR(8) rolling model, each RHS variable is forecast using a AR(8) rolling forecastforecast

– Rolling coefficients. Consider a 4q forecast for 1990:Q4Rolling coefficients. Consider a 4q forecast for 1990:Q4 Coeffs in triangle equation estimated thru 1989:Q4Coeffs in triangle equation estimated thru 1989:Q4 TV-NAIRU estimated thru 1989:Q4TV-NAIRU estimated thru 1989:Q4 Coeffs in AR(8) for RHS variables also thru 89:Q4Coeffs in AR(8) for RHS variables also thru 89:Q4 Values of RHS variables use these 89:Q4 coefficients iteratively Values of RHS variables use these 89:Q4 coefficients iteratively

to forecast 90:Q4 valuesto forecast 90:Q4 values 4Q Forecasts start in 1977:Q1 (My 1977 BPEA Paper), 4Q Forecasts start in 1977:Q1 (My 1977 BPEA Paper),

8Q Forecasts start in 1978:Q18Q Forecasts start in 1978:Q1

1818

Contest for the 4-quarter-Contest for the 4-quarter-aheadahead

Forecasts (Cumulative Sq Forecasts (Cumulative Sq Errors)Errors)

0

50

100

150

200

250

300

1977:01 1982:01 1987:01 1992:01 1997:01 2002:01

A-O

1980 Triangle

AR(8)

1919

Contest for theContest for the8-quarter-ahead forecasts8-quarter-ahead forecasts

0

100

200

300

400

500

600

700

1978:01 1983:01 1988:01 1993:01 1998:01 2003:01

1980 Triangle

AR(8)

2020

Summary Statistics of the Summary Statistics of the Contest between AO, AR(8), Contest between AO, AR(8),

and Triangleand Triangle Four-quarter-ahead RMSEFour-quarter-ahead RMSE

– 1977-2004 AO 1.54 AR(8) 1.45 TR 1.271977-2004 AO 1.54 AR(8) 1.45 TR 1.27– 1977-1989 AO 2.05 AR(8) 1.77 TR 1.471977-1989 AO 2.05 AR(8) 1.77 TR 1.47– 1990-2004 AO 1.08 AR(8) 1.18 TR 1.111990-2004 AO 1.08 AR(8) 1.18 TR 1.11

Eight-quarter-ahead RMSEEight-quarter-ahead RMSE– 1977-2004 AR(8) 2.17 TR 1.321977-2004 AR(8) 2.17 TR 1.32– 1977-1989 AR(8) 3.03 TR 1.581977-1989 AR(8) 3.03 TR 1.58– 1990-2004 AR(8) 1.30 TR 1.111990-2004 AR(8) 1.30 TR 1.11

2121

Conclusions, #1Conclusions, #1

In historical mode, the “triangle In historical mode, the “triangle model” invented in 1980 is strongly model” invented in 1980 is strongly supported in many dimensionssupported in many dimensions– Performance in dynamic simulations Performance in dynamic simulations

(1995-2005)(1995-2005)– Survives sample split (1962-83 vs. 1984-Survives sample split (1962-83 vs. 1984-

2005)2005)– No variable has a significant shift pre-post No variable has a significant shift pre-post

1984 except for FAE. The slope of the PC 1984 except for FAE. The slope of the PC is stableis stable

2222

Conclusions, #2Conclusions, #2 Can we learn from historical econometric Can we learn from historical econometric

equations as we attempt to forecast?equations as we attempt to forecast?– S-W emphatically say “no”! We must reject all S-W emphatically say “no”! We must reject all

knowledge gained from three decades of research on knowledge gained from three decades of research on inflation dynamicsinflation dynamics

But the triangle model But the triangle model can be used for forecastingcan be used for forecasting– Forecast the RHS variables by AR(8)Forecast the RHS variables by AR(8)– Triangle model has RMSE’s in rolling forecasts 1977-Triangle model has RMSE’s in rolling forecasts 1977-

2004 that are 12% lower for q4 forecasts but 40 percent 2004 that are 12% lower for q4 forecasts but 40 percent lower for q8 forecasts (48% lower for 1977-89)lower for q8 forecasts (48% lower for 1977-89)

Concluding suggestion: Future papers both on Concluding suggestion: Future papers both on forecasting and on counterfactual history should forecasting and on counterfactual history should start from the triangle model as a baseline, not start from the triangle model as a baseline, not from univariate autoregressions that leave most from univariate autoregressions that leave most of the interesting questions unanswered.of the interesting questions unanswered.