Checking the Robustness and Calidity of Model Selection: An

Transcription

Introduction
Macroeconomic contributions
Econometric contributions
Appendix
Checking the Robustness and Validity of
Model Selection: An Application to UK
Wages
Jennifer L. Castle
Department of Economics
Oxford University
17 January 2009
Jennifer L. Castle
RES Fourth PhD Presentation Meeting, UCL
1 / 11
Introduction
Appendix
Motivation
Contributions
Build models of real wage growth over 125 years
Macroeconomic application
Compare feedforward and feedback models of wage in‡ation;
Yield new insights into role of expectations over long-run.
Econometric Methodology
Evaluate robustness of model selection procedure;
Parametric bootstrap to assess selection uncertainty.
Jennifer L. Castle
2 / 11
Introduction
Appendix
Motivation
Models of wage growth
2 main schools of thought:
Forward-looking models where expectations play a key role:
rational expectations – ’NKPC’.
Backward-looking models driven by causal factors
no explicit role for expectations.
Jennifer L. Castle
3 / 11
Introduction
Appendix
Expectations
Measures of expectations
Standard Approach
Replace Et [∆pt +1 ] with actual ∆pt +1 and instrument.
Identi…cation problems
Derive set of rational expectations of in‡ation using price
in‡ation model to obtain recursive one-step ahead predictions
(omitting contemporaneous variables). Equation
Backward-looking expectations:
Exponentially weighted moving average.
Random walk.
Jennifer L. Castle
…gure
4 / 11
Introduction
Appendix
Automatic model selection
Gets – data-based, combining theory at the outset but relying on
statistical characteristics of data to deliver …nal speci…cation.
Initial model of real wage growth includes:
24 conditioning variables including economic and institutional
factors;
expectations measures;
4 dummies (wars, great depression, oil crises).
Jennifer L. Castle
5 / 11
Introduction
Appendix
Non-linear price coe¢ cient
Test of non-linearity: Castle and Hendry (2008).
Non-linearity in real wages; cannot reject linearity in nominal
test results
wages; ) non-linear price coe¢ cient.
Economic theory informed
non-linear speci…cation:
1.0
0.9
0.8
0.7
0.6
fna
fna =
1
1 +1000 (∆p t )2
0.5
0.4
0.3
Sticky information Mankiw and
Reis (2002), slow dissemination of
information.
0.2
0.1
−0.15
−0.10
−0.05
0.00 ∆p
0.05
0.10
0.15
0.20
0.25
As price in‡ation rises, workers are more attentive, act to
prevent further erosion of real wages.
Jennifer L. Castle
6 / 11
Introduction
Appendix
Macroeconomic conclusions
Huge changes: technological innovation, legislative changes, social
reforms, wars, policy regime shifts.
Statistically well-speci…ed, constant parameter model of real
wage growth over 125 years.
No role for replacement ratio, TU power, not much for level of
unemployment.
Expectations, either instrumenting or direct expectations from
price in‡ation forecasts, do not explain real wages.
Model of real wage growth with unit labour costs, productivity
growth, change in unemployment rate, and non-linear price
reaction able to explain much of movement in real wages.
Jennifer L. Castle
7 / 11
Introduction
Appendix
Robustness
Selection criteria
All models selected based on some criteria but reported model is
uncertain:
variables retained by chance when irrelevant
relevant variables omitted
Select models using general-to-speci…c methodology.
Objective: report reliability of selected model using 2 criteria:
1
robustness – parametric bootstrap to assess ability to recover
chosen model in di¤erent draws using same selection algorithm
2
validity – selected model speci…cation is valid
Jennifer L. Castle
8 / 11
Introduction
Appendix
Checking the robustness of wage in‡ation models
How reliable is the preferred real-wage model
Use parametric bootstrap to assess robustness of model selection.
What is the probability that the same model will be selected
for a di¤erent draw using the same selection algorithm?
Gauge – Number of irrelevant variables retained
Potency – Number of relevant variables retained
Results:
Most explanatory variables retained with high probability;
Uncertainty as to timing of e¤ects;
Costs of search over costs of inference small;
Invalid models detected through statistical mis-speci…cation.
Jennifer L. Castle
9 / 11
Introduction
Appendix
Conclusions
Econometric conclusions
Advances in econometric techniques, including:
developments in automatic Gets selection;
use of indicator saturation to identify shifts;
test non-linearity in high dimension, collinear systems.
Monte Carlo simulations demonstrate problems of instrumenting
for forward-looking expectations.
Parametric bootstrap to assess robustness.
Jennifer L. Castle
10 / 11
Introduction
Appendix
Conclusions
Future Research
Automate post-model selection bootstrap
Use selected model as DGP augmented by additional variables
with coe¢ cients drawn from normal distribution with variance
corresponding to general model.
Forecasting
Extend data to see how model forecasts ex ante.
Ex post use bootstrap procedure over forecast horizons to
select forecasting models.
Role of breaks in forward-looking models
Learning models for expectations.
How expectations are formed in periods of high uncertainty.
Jennifer L. Castle
11 / 11
Introduction
Appendix
Route Map
1
Economic theory
2
Data
3
Models of wage in‡ation
1
2
New Keynesian Phillips Curve
Extensions to real wages and additional conditioning variables
– the role of model selection
4
Monte Carlo evidence
5
Robustness testing
6
Conclusions
Jennifer L. Castle
12 / 11

Checking the Robustness and Calidity of Model Selection: An

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