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Title page 1

Contents 1

Abstract 2

Non-technical summary 3

1. Introduction 4

2. Empirical evidence, theoretical channels and related literature 6

3. Econometric framework 9

3.1. A non-parametric multivariate time series model 9

3.2. Non-linear structural factor models 10

3.3. Structural identification using truncated priors 11

3.4. Bayesian Additive Regression Trees 13

3.5. Priors on the trees and remaining model parameters 15

3.6. Posterior simulation 16

3.7. Computation of the dynamic responses to economic shocks 17

4. Non-linear effects of economic shocks 18

4.1. Data, model specification and identification 18

4.2. The reaction of inflation to economic shocks 21

4.3. The non-linear transmission of energy shocks to inflation 23

4.4. Transmission of energy shocks along the pricing chain 25

4.5. A closer look at the pre-pandemic period 27

5. Predictive evidence for our model 28

6. Conclusions 30

References 31

Appendix: A. Additional Results 34

Acknowledgements 40

Tables 18

Table 1. Data description 18

Table 2. Structural shock identification 19

Table 3. CRPS of BART models relative to CPRS of BVAR model 29

Figures 7

Figure 1. Inflation and energy commodity prices 7

Figure 2. A very simple regression tree for year-on-year inflation 14

Figure 3. Reaction of inflation to the identified structural shocks 22

Figure 4. Reaction of inflation to small, medium, and large energy shocks 23

Figure 5. Reaction of inflation to energy shocks over a sizes grid 25

Figure 6. Transmission of energy shocks of various sizes along the pricing chain 26

Figure 7. Reaction of inflation to large energy shocks over two sub-samples 27

Figure 8. Forecast errors: sfBART versus ECB projections 30

Appendix Figures 34

Figure A1. Reaction of PPI to the identified structural shocks 34

Figure A2. Reaction of PPI energy to the identified structural shocks 35

Figure A3. Reaction of the Synthetic energy commodity price index to the identified structural shocks 36

Figure A4. Reaction of CCI to the identified structural shocks 37

Figure A5. Synthetic energy indicator and contemporaneous reaction to shocks of different sizes 38

Figure A6. Reaction of inflation to negative small, medium, and large energy shocks 38

Figure A7. Estimated energy shocks 39