the term structure of inflation expectations · 2010. 11. 19. · page 10 summary of findings...
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The Term StructureOf Inflation Expectations
Mikhail Chernov, London Business School and CEPR
Philippe Mueller, London School of Economics
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Monetary policy effectiveness
Monetary policy (MP) matters for the real economy– How effective is MP in the US?
“...[the] economic system will work best when producers and consumers, employers and employees, can proceed with full confidence that the average level of prices will behave in a known way in the future -- preferably that it will be highly stable.” -- Friedman (1968)
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Monetary policy effectiveness
Monetary policy (MP) matters for the real economy– How effective is MP in the US?
“...[the] economic system will work best when producers and consumers, employers and employees, can proceed with full confidence that the average level of prices will behave in a known way in the future -- preferably that it will be highly stable.” -- Friedman (1968)
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Optimal monetary policy
In the rational expectations equilibrium (REE) , the optimal MP entails a response to shocks in inflation and outputIf private sector expectations deviate from rational expectations, then REE optimal MP will lead to instabilityOptimal MP should respond to private sector expectations or their determinants
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Questions
Is there any evidence that US MP responds to private sector expectations?
If yes, does it lead to anchored expectations?
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Are private sector expectations observed?
Nominal yields are noisy measures of expectations
Survey forecasts are supposed to be direct measures
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The Term Structure of Inflation Forecasts
1970 1975 1980 1985 1990 1995 20000
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14Michigan Forecast
4q
1970 1975 1980 1985 1990 1995 20000
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14Livingston Forecasts
2q4q8q40q4q (2q fw)4q (4q fw)
1970 1975 1980 1985 1990 1995 20000
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14SPF Forecasts
1q4q40q1q (1q fw)1q (2q fw)1q (3q fw)
1970 1975 1980 1985 1990 1995 20000
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14Blue Chip Forecasts
1q1q (1q fw)1q (2q fw)1q (3q fw)1q (4q fw)1q (5q fw)1q (6q fw)
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Are private sector expectations observed?
Nominal yields are noisy measures of expectations
Survey forecasts are supposed to be direct measures
Is information in yields consistent with that of the surveys?
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Approach
We build a joint model of survey forecasts and UST yieldsMeasure private sector inflation expectationsEstablish the determinants of these expectationsDoes the policy respond to these determinants?Are expectations anchored?Implication: Out-of-sample inflation forecasting
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Summary of findings
Private sector expectations measurement requires information from both yields and surveys The expectations are driven by inflation, output, and an independent “survey” factor that is needed to model all the inflation expectations at all maturitiesThe interest rate rule loads on the “survey” factor, that is, MP responds to variables outside of the standard setMonetary policy appears to be more effective recentlyInflation expectations outperform those of a “standard”macro-finance model
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Modeling strategy
It is natural to investigate these issues in a model that incorporates macro variables, forecasts and yieldsMacro-finance term structure model with a twistWe accommodate macro variables ( -measure), yields ( -measure), and surveys ( -measure)– Allows for multiple surveys– State-dependent biases– Can establish the “marginal” expectations
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States of the economy
Objective probability measure
Factors – Gaussian VAR(1):
Inflation forecast:
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Yields
Spot interest rate:
Stochastic discount factor:
Risk-neutral probability measure
Essentially-affine risk premia:Bond yields:
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Incorporating survey forecasts
How do we include the forecast data given this framework?
Look quite different from each other and realized inflation– Biases?– Errors?
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Different signals
Forecaster i believes that only her signal is correlated with state variables The forecast is computed under subjective measure – Related to the heterogeneous agents framework (Harrison
and Kreps, 1978; Scheinkman and Xiong, 2003; Dumas, Kurshev and Uppal, 2007; …)
– In the reduced-form framework, we do not have to assume that forecasters coincide with consumers → links between and are muted
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Asymmetric loss functions
Forecasters have asymmetric (and different) loss functions– Linex– The optimal forecast is biased– Forecast errors are autocorrelatedUnder regularity, there exist a measure under which– The optimal forecast is unbiased– Forecast errors are iid
(Patton and Timmerman, 2007)
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Subjective Forecasters
Survey forecasters may have different private signals, loss functions:
Survey-specific probability measure:
Reported forecasts:
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What should we expect to see?
Measure private sector inflation expectations– How do they behave over time?– Do subjective and objective expectations coincide?Establish the determinants of these expectations– How do expectations load on the model factors?– Are the factor related to interesting objects?Does monetary policy respond to these determinants?Evaluate effectiveness of the monetary policy– Inflation premia– Changes in inflation’s persistence– How do medium- and long-term expectations behave out-of-sample?Out-of-sample inflation forecasting
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Data and Methodology1970-2004, quarterly frequency (140 quarters)Macro variables : GDP and CPIInflation forecasts: Michigan, Livingston, SPF, Blue ChipUnsmoothed Fama-Bliss zero yields with 8 maturities ranging from 3 months to 10 yearsEstimation: – ML with Kalman filter– Allow for missing observations (for forecasts)
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Term Bias: hjkkkkkkk
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Additional Models
AO
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Additional Models
NF
AO
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Additional Models
NF
OF
AO
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Factor loadings
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Determinants of Forecasts: Simple Filters
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Determinants of Forecasts: Simple Filters
Model Factor mt yt(τ) pt(s, t) corr
AO x1 g, π — LS(0,4), SPF(0,4) 0.99x2 — 1, 40 LS(0,4), SPF(0,4) 0.98
f1 continues to have strong correlation with forecasts
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Determinants of Forecasts: Simple Filters
Model Factor mt yt(τ) pt(s, t) corr
AO x1 g, π — LS(0,4), SPF(0,4) 0.99x2 — 1, 40 LS(0,4), SPF(0,4) 0.98
f1 continues to have strong correlation with forecasts– where ft is orthogonal to Mt (mt and its history)
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Does the interest rate respond to f1?
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The Fisher equation
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Changing impulse responses
0 2 4 6 8 10−0.05
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0.05
0.1
0.15
0.2
0.25
0.3
0.35
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1987:11989:22000:12004:4
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Changing conditional expectations
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Out-of-sample inflation forecasting
AO outperforms NF by 25% to 60% (RMSE ratios)AO is very similar to the survey forecastsBut, AO is available for any horizon of interest at any point in time
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Conclusions
We construct a no-arbitrage model that incorporates macro variables, yields and inflation forecasts in a internally consistent mannerBoth yields and surveys are required to construct inflation expectationsInflation expectations are driven by the history of macro variables and “survey” factorThe implied term structure of inflation expectations is:– Reasonable– Instrumental in identifying real yields and inflation premia– Suggests that monetary policy became more effective over time– Forecasts inflation and yields well