ECONOMIC MODELLING & MACHINE LEARNING...I. Motivation Linear models are constrained where economic...
Transcript of ECONOMIC MODELLING & MACHINE LEARNING...I. Motivation Linear models are constrained where economic...
![Page 1: ECONOMIC MODELLING & MACHINE LEARNING...I. Motivation Linear models are constrained where economic complexity is concerned • Non-linearities • Structural change Machine learning](https://reader033.fdocuments.us/reader033/viewer/2022041607/5e350deda92c8e223f0293b7/html5/thumbnails/1.jpg)
ECONOMICMODELLING & MACHINE LEARNING
A PROOF OF CONCEPT
NICOLAS WOLOSZKO, OECD
NAEC – APRIL 16 2019
![Page 2: ECONOMIC MODELLING & MACHINE LEARNING...I. Motivation Linear models are constrained where economic complexity is concerned • Non-linearities • Structural change Machine learning](https://reader033.fdocuments.us/reader033/viewer/2022041607/5e350deda92c8e223f0293b7/html5/thumbnails/2.jpg)
Motivation
Method
Results
Perspectives
Economic forecasting with Adaptive Trees
I
II
III
IV
![Page 3: ECONOMIC MODELLING & MACHINE LEARNING...I. Motivation Linear models are constrained where economic complexity is concerned • Non-linearities • Structural change Machine learning](https://reader033.fdocuments.us/reader033/viewer/2022041607/5e350deda92c8e223f0293b7/html5/thumbnails/3.jpg)
I. Motivation
Linear models are constrained where economic complexity is concerned
• Non-linearities
• Structural change
Machine learning can provide relevant tools to tackle these challenges
• Modelling without a model: no prior knowledge is required
• Algorithms designed to capture complex patterns in the data
• Use of cross-validation to prevent over-fitting
![Page 4: ECONOMIC MODELLING & MACHINE LEARNING...I. Motivation Linear models are constrained where economic complexity is concerned • Non-linearities • Structural change Machine learning](https://reader033.fdocuments.us/reader033/viewer/2022041607/5e350deda92c8e223f0293b7/html5/thumbnails/4.jpg)
II. ADAPTIVE TREES: A METHOD FOR
ECONOMIC FORECASTING
1. Regression trees
2. Gradient Boosted Trees
3. Adaptive Boosting
![Page 5: ECONOMIC MODELLING & MACHINE LEARNING...I. Motivation Linear models are constrained where economic complexity is concerned • Non-linearities • Structural change Machine learning](https://reader033.fdocuments.us/reader033/viewer/2022041607/5e350deda92c8e223f0293b7/html5/thumbnails/5.jpg)
1. Regression trees
At each node, the algorithm selects the splitting variable + splittingpoint that minimises sub-group variance of GDP growth
![Page 6: ECONOMIC MODELLING & MACHINE LEARNING...I. Motivation Linear models are constrained where economic complexity is concerned • Non-linearities • Structural change Machine learning](https://reader033.fdocuments.us/reader033/viewer/2022041607/5e350deda92c8e223f0293b7/html5/thumbnails/6.jpg)
• Simple regression trees lack robustness, hence the resort to ensemble methods.
• Gradient Boosted Trees (Freidman, 2002):
𝐹𝑚(𝑥) = 𝐹𝑚−1(𝑥) + 𝜈ℎ𝑚(𝑥)
ℎ𝑚(𝑥): regression tree trained on the residual from 𝐹𝑚−1(𝑥)
• Gives more and more weight to observations harder to predict
2. Gradient Boosted Trees
![Page 7: ECONOMIC MODELLING & MACHINE LEARNING...I. Motivation Linear models are constrained where economic complexity is concerned • Non-linearities • Structural change Machine learning](https://reader033.fdocuments.us/reader033/viewer/2022041607/5e350deda92c8e223f0293b7/html5/thumbnails/7.jpg)
2. Gradient Boosted Trees
XGBoost trained on US data, GDP growth shifted by 6 months
Train Test
Gradient Boosted Trees end up giving more weight to observations harder to predict (larger residuals)
![Page 8: ECONOMIC MODELLING & MACHINE LEARNING...I. Motivation Linear models are constrained where economic complexity is concerned • Non-linearities • Structural change Machine learning](https://reader033.fdocuments.us/reader033/viewer/2022041607/5e350deda92c8e223f0293b7/html5/thumbnails/8.jpg)
Adaptive Trees = Gradient Boosting + increasing ex ante observation weights
Ex ante observation weights:
𝑤 𝑡 = 𝑒−𝛾(𝑡𝑁−1)
3. Adaptive Trees
Ex post observation weights:
![Page 9: ECONOMIC MODELLING & MACHINE LEARNING...I. Motivation Linear models are constrained where economic complexity is concerned • Non-linearities • Structural change Machine learning](https://reader033.fdocuments.us/reader033/viewer/2022041607/5e350deda92c8e223f0293b7/html5/thumbnails/9.jpg)
III. RESULTS
FORECAST OF GDP GROWTH
![Page 10: ECONOMIC MODELLING & MACHINE LEARNING...I. Motivation Linear models are constrained where economic complexity is concerned • Non-linearities • Structural change Machine learning](https://reader033.fdocuments.us/reader033/viewer/2022041607/5e350deda92c8e223f0293b7/html5/thumbnails/10.jpg)
• Simulations in pseudo-real time of a forecast of GDP growth in G6 countries
• Using the exact same data as benchmark OECD IndicatorModel (housing prices, indutrial production, PMI…) so as to provide a methodological benchmark
Setting of forecast simulations
![Page 11: ECONOMIC MODELLING & MACHINE LEARNING...I. Motivation Linear models are constrained where economic complexity is concerned • Non-linearities • Structural change Machine learning](https://reader033.fdocuments.us/reader033/viewer/2022041607/5e350deda92c8e223f0293b7/html5/thumbnails/11.jpg)
Comparison with OECD Indicator Model
1. USA, M+3
Accuracy: + 5 %
2. UK, M+6
Accuracy: + 22 %
![Page 12: ECONOMIC MODELLING & MACHINE LEARNING...I. Motivation Linear models are constrained where economic complexity is concerned • Non-linearities • Structural change Machine learning](https://reader033.fdocuments.us/reader033/viewer/2022041607/5e350deda92c8e223f0293b7/html5/thumbnails/12.jpg)
• The method could be extended to broader sets of variables, as it can be applied in high dimension
• That may include financial indicators or big data
• Machine learning also has promising applications in inference and causal analysis. Exisiting methodsaddress non-linearities and causal heterogeneity
Perspectives
![Page 13: ECONOMIC MODELLING & MACHINE LEARNING...I. Motivation Linear models are constrained where economic complexity is concerned • Non-linearities • Structural change Machine learning](https://reader033.fdocuments.us/reader033/viewer/2022041607/5e350deda92c8e223f0293b7/html5/thumbnails/13.jpg)
THANK YOU
![Page 14: ECONOMIC MODELLING & MACHINE LEARNING...I. Motivation Linear models are constrained where economic complexity is concerned • Non-linearities • Structural change Machine learning](https://reader033.fdocuments.us/reader033/viewer/2022041607/5e350deda92c8e223f0293b7/html5/thumbnails/14.jpg)
ADDITIONAL MATERIAL
![Page 15: ECONOMIC MODELLING & MACHINE LEARNING...I. Motivation Linear models are constrained where economic complexity is concerned • Non-linearities • Structural change Machine learning](https://reader033.fdocuments.us/reader033/viewer/2022041607/5e350deda92c8e223f0293b7/html5/thumbnails/15.jpg)
• Modelling complexity requires more complex models
• Trade off simplicity/accuracy:
– Too much simplicity: fail to capture important variations
– Too much complexity: fail to produce a sensible story
Problem: interpretability
![Page 16: ECONOMIC MODELLING & MACHINE LEARNING...I. Motivation Linear models are constrained where economic complexity is concerned • Non-linearities • Structural change Machine learning](https://reader033.fdocuments.us/reader033/viewer/2022041607/5e350deda92c8e223f0293b7/html5/thumbnails/16.jpg)
Interpretability
𝑌 = 0.9% + 𝐹𝑒𝑎𝑡𝑢𝑟𝑒 𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛𝑠
We can easily decompose in variable’s contribution
![Page 17: ECONOMIC MODELLING & MACHINE LEARNING...I. Motivation Linear models are constrained where economic complexity is concerned • Non-linearities • Structural change Machine learning](https://reader033.fdocuments.us/reader033/viewer/2022041607/5e350deda92c8e223f0293b7/html5/thumbnails/17.jpg)
Variable contributions, Italy M+3
![Page 18: ECONOMIC MODELLING & MACHINE LEARNING...I. Motivation Linear models are constrained where economic complexity is concerned • Non-linearities • Structural change Machine learning](https://reader033.fdocuments.us/reader033/viewer/2022041607/5e350deda92c8e223f0293b7/html5/thumbnails/18.jpg)
• For each variable: – What relevant lag : M-1, M-2, M-12, M-24 ?
– In level ? In growth rate ?
• Data-driven variable selection:– Based on variable importance
– Variable importance: a variable is all the more important that it is high in the tree, close to the root
– Accounts for multiple interactions (can keep a variable that is loosely correlated with the GDP but that provides relevant interactions. Ex: price of gold)
Variable selection
![Page 19: ECONOMIC MODELLING & MACHINE LEARNING...I. Motivation Linear models are constrained where economic complexity is concerned • Non-linearities • Structural change Machine learning](https://reader033.fdocuments.us/reader033/viewer/2022041607/5e350deda92c8e223f0293b7/html5/thumbnails/19.jpg)
• In a regression with 10 variables, should we want to test all possible multiple interactions : 1010 possibilities
• With tree-based approaches, we explore all possible interactions with 120 variables
• Amount of prior knowledge:– Linear econometrics: we know the form of the relationship
– Bayesian econometrics: we know the relationship can take any of the know forms
– Machine learning: we know nothing
Complexity v. Bayesian econometrics