Abstract
We construct a Bayesian vector autoregressive model with three layers of information: the key drivers of inflation, cross-country dynamic interactions, and country-specific variables. The model provides good forecasting accuracy with respect to the popular benchmarks used in the literature. We perform a step-by-step analysis to shed light on which layer of information is more crucial for accurately forecasting medium-run euro area inflation. Our empirical analysis reveals the importance of including the key drivers of inflation and taking into account the multi-country dimension of the euro area. The results show that the complete model performs better overall in forecasting inflation excluding energy and unprocessed food over the medium term. We use the model to establish stylized facts on the euro area and cross-country heterogeneity over the business cycle.
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Notes
In Sect. 2.2, we provide details on this bottom-up approach.
It consists in an extension of the Phillips curve, realized using inflation data together with its three determinants: inflation persistence, demand-pull inflation and cost-push inflation.
See Appendix A and B for further details.
It is given by the sum of \((26 \times 26) \times 5\) autoregressive coefficients, 26 parameters and \(26 \times 27/2\) parameters of the covariances of the residuals.
The correlation computed on the year-on-year percentage changes is 0.97 for HICPex and 0.99 for HICP.
We also performed a robustness check by using the Minnesota plus sum-of-coefficient prior. The results show that we get an improvement in the forecasting accuracy over the short horizon, but this is reverted over a longer horizon. Further details are available upon requests.
This model does not include the EA inflation aggregate, that is the target variable of our forecasting exercise, which is computed as a weighted average of the four country indices.
The country forecasts are aggregated using normalized country weights to inflation.
The null hypothesis of the test states that the models’ forecasting performance is the same over the entire sample, thus the alternative states that the one model outperforms the other in at least one period.
As noticed by Giannone et al. (2019), this is not a proper structural identification strategy, but rather a statistical method.
The constant term is omitted for conciseness, but it is still included in the exercise.
For readability, we show only the results of the main variables.
The only exception is the European Commission Consumer Survey Expectations since it is a balance statistics providing information on the directional change in prices over the past and next 12 months.
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Acknowledgements
We are very grateful to Michele Lenza and Philippe Weil for their valuable guidance and support. We also would like to thank the editor and two anonymous referees for their useful comments. In addition, we wish to thank Carlo Altavilla, Fabio Busetti, Domenico Giannone, Matteo Luciani, Stefano Siviero, and the participants at the 2019 ITISE Conference in Granada for their helpful comments and suggestions. Angela Capolongo is grateful for the support of the Fonds National de la Recherche Scientifique (FNRS) and the Deutsche Bundesbank. The views expressed in the article are those of the authors and do not involve the responsibility of the Bank of Italy. All remaining errors are ours.
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Appendices
Data
Table 4 reports the definition and data transformations of the \(N (= 26)\) variables included in the analysis. We estimate the model in (log-)levels , by applying the log transformation and then multiplying the variables by four in order to get the annualized log-levels.Footnote 13 Expressing the variables in annual term, allows for simple comparison of growth rates across different periods. As a result, the target variable of our forecasting exercise is expressed as h-period annualized average growth change in prices, that is exactly the way inflation is defined.
The models are expressed in quarterly frequency. In particular for the monthly time series, i.e. HICP, HICPex, PPI, EC Consumer Survey of inflation expectations, oil price and exchange rate, we compute the 3-month average to obtain quarterly values. We adjust all variables for seasonality effect using X-12 ARIMA procedure. The data series are mainly retrieved from Eurostat, except on the oil price, taken from U.S. Energy Information Administration (EIA) database. The sample period considered starts in 1996Q1, which is the first available data for euro area HICP, and end in 2017Q2. Table 5, for each component of the HICP overall index, displays the percentage weights on the overall HICP year-on-year percentage change as of 2017 and the standard deviation in the period 1996Q1-2017Q2. The HICP index is a measure of the prices of consumer goods and services acquired by households. As shown in Table 5, energy and unprocessed food represent the residual part of this indicator, hence, HICPex accounts for about 80% of the entire HICP basket of goods.
European Commission consumer survey of inflation expectations
In Sects. 2 and 3, we use the European Commission’s consumer survey as measure of inflation expectations. It provides freely available country-specific measures of inflation expectations for a long time-span (starting from 1985) at monthly frequency. This survey is indeed conducted at the national level, and the results for the euro area are compiled by aggregating country data. The consumers are asked to indicate whether they expect inflation to rise, fall or remain unchanged. Therefore, the questions are qualitative and provide information on the directional change in prices over the past and next 12 months. The results are summarized using the so-called balance statistic, which shows the difference between the percentage of consumers thinking that consumer prices will increase and the percentage of consumers stating that prices will decrease or remain unchanged.
Specifically, answers are weighted attributing weight 1 to the extreme answers (1) and (5), weight \(\frac{1}{2}\) to the moderate responses (2) and (4) and zero weight to the middle response (3) and the “don’t know” response (6). The balance statistic is thus computed as:
where P(i) is the frequency of response (i) with \(i = 1, 2,\ldots , 6\). The balance statistic ranges between \( \pm 100\).
Since May 2003, the European Commission has been collecting, via this consumer survey, direct quantitative information on consumers’ inflation perceptions and expectations in the euro area. However, these data do not fit the time span of our model.
Diebold and Mariano (1995) test
The tables below show the results of the Diebold and Mariano (1995) test with respect to benchmark models (Table 6) and alternative models (Table 7).
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Capolongo, A., Pacella, C. Forecasting inflation in the euro area: countries matter!. Empir Econ 61, 2477–2499 (2021). https://doi.org/10.1007/s00181-020-01959-4
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DOI: https://doi.org/10.1007/s00181-020-01959-4