Harnessing sectoral information for improved aggregate inflation forecasts

Stabilising inflation is an objective of monetary policy in the USA, and the primary objective of policy in countries targeting inflation, such as the UK, many OECD countries and emerging market countries, like South Africa (SA). As inflation targeting is a forward-looking approach, with monetary policy based on the likely path of inflation, it is important that the central bank has a reliable forecasting framework. However, forecasting presents significant challenges. Not only can there be large and unpredictable shocks in oil and other commodity prices, but structural changes in the inflation process and variations in the frequency of price changes with the size of recent inflation shocks can lead to forecast failure. Stock and Watson (2003) conclude that simple autoregressive models, in which the inflation rate depends only on its own recent history, are hard to beat. These models then provide a benchmark for more sophisticated models to surpass.

Recently there has been renewed interest, mainly by central banks, in the potential for greater accuracy from forecasting the component indices of the overall consumer price index (CPI) and aggregating these forecasts, as against forecasting the aggregate CPI itself. Modelling the individual components makes sense as different information sets apply to different sectors, and hypotheses about sectoral transmission of policy and shocks are often more specific than hypotheses about overall transmission. Trends in components differ, e.g. because of technical progress, taxation regimes and consumers’ preferences. This diversity is well illustrated for SA in Figure 1a and b, with price components plotted relative to the targeted measure of CPI, the so-called CPIX that excludes mortgage interest rates (see Aron and Muellbauer, 2008a, 2009a on the inflation targeting monetary framework adopted in SA in 2000). For instance, the downward trend in clothing and furniture components is largely due to rapid liberalisation of trade policy from 1990; by contrast, the sharply rising trend in the ‘beverages and tobacco’ component reflects greater taxation of alcohol and tobacco under the new government after 1994. The dynamic properties of individual components may be better captured by modelling them separately, and econometric specifications be allowed to vary across disaggregated components. Non-linearities may be more important for some components, such as asymmetric reactions to changes in oil prices.

Theory suggests that aggregating sub-component forecasts is superior to directly forecasting the aggregate if the data generating process is known. When aggregating sub-component forecasts, the forecast errors may in part cancel out (Clements and Hendry 2002), but this is not necessarily the case as exogenous shocks might drive the forecast errors of some disaggregate variables in the same direction. Models for the disaggregated variables may not be correctly specified. Predictive improvements can also be off-set by model selection uncertainty, estimation uncertainty, changing collinearity, structural breaks over the forecast horizon and measurement errors (see Hendry and Hubrich 2006). Further, a well-specified model in sample does not necessarily imply higher forecast accuracy.

The review in our US paper (Aron and Muellbauer 2008b, see also 2008c) shows that there have been surprisingly few empirical studies exploiting sectoral information. The majority apply to Euro area countries, two to the USA, but none for the UK, other OECD countries or emerging market countries. A rather mixed view on the effectiveness of the method is presented by these studies. Most of the models in the literature have adopted the ‘accelerationist’ restriction embodied in a hybrid New Keynesian Phillips curve (see Angeloni et al (2006) for an open economy extension): models are estimated in first differences, omitting long-run relationships and the key role of relative prices. In practice, many determinants of inflation are excluded in simple VAR models that are constrained by degrees of freedom. Regime changes, e.g. increased openness to trade, are rarely treated. Although differencing can help avoid the forecast failure from structural breaks (e.g. unanticipated shifts in long-run relationships), a common source of forecast failure (Hendry and Clements 2003), the feedback relationships that help tie down sectoral price behaviour in the medium run are missing.

Our recent ESRC project aimed to develop a novel and more comprehensive framework for estimating sub-component prices than hitherto used in the literature. This framework would be applied in multistep estimation and forecasting of aggregate and sub-component price indices for several countries, including SA. Forecast performance would be compared with the benchmark differenced models used in the literature. In addition to investigating a range of informational hypotheses, the direct forecast of aggregate inflation would be compared with an indirect forecast, obtained by aggregating the forecasts of the individual components benefiting from sectoral information.

The exercise for South Africa involved a considerable amount of data construction. For instance, as the CPIX data were only policy-relevant from 2000, and only constructed by Statistics South Africa back to 1997, we relied on updating our own consistent construction of monthly CPIX data back to 1970 (Aron and Muellbauer 2004). We had to construct HX, the housing component less the mortgage interest cost, back to the start of the sample, using the methods of Aron and Muellbauer (2004) and appropriate weights. We also constructed measures of trade openness for SA (Aron and Muellbauer 2007), which make a big difference in modelling and forecasting inflation after 1990 (see also Aron and Muellbauer 2009b, c).

Our method can be summarised as follow. We estimated four-quarter-ahead multistep models for each price index sub-component and for the aggregate index itself, with increasingly richer information sets. Equilibrium correction models included trade openness and split trends to handle structural shifts, and permitted the adjustment of prices to trends in relative prices and to input costs to be part of the inflation process. (The shape of split trends was suggested by earlier work in a stochastic framework, see Aron et al. 2006). We applied plausible restrictions to overcome the ‘curse of dimensionality’. Automatic model selection (Doornik 2008) was used to select parsimonious models from general unrestricted models over an initial period, 1979–2002, in the case of SA. We then generated recursive pseudo out of sample forecasts for the components and the aggregate index for each date in the forecast period, to the end of 2007. We aggregated the individual component forecasts using their weighting in the overall index. In SA these weights change typically every five years. Finally, we compared the root mean square forecasting error (RMSFE) performance of the aggregate model (direct forecast) and the aggregated sub-components models (indirect forecast) with each other, and with standard benchmark reference models, such as autoregressive models.
We found that for one year ahead inflation forecasting, using naïve models based only on CPIX price data, the weighted indirect forecast does not improve on the direct forecast for aggregate CPIX inflation. Then, more comprehensive information sets were examined. Incorporating changes in the wholesale price index, unit labour costs, the real exchange rate, import prices, terms of trade, oil prices, the output gap and trade balance to GDP ratio, and the level of trade openness, an aggregate CPIX equation achieves a 28 per cent reduction in root mean squared forecast error relative to the best of the naïve models. Applying the same methods to each of the inflation components, and weighting the forecasts using the CPIX weight to obtain an indirect forecast for CPIX, brings a further gain of 4 per cent relative to the naïve model benchmark. At the aggregate CPIX level, we find long lags in strongly significant equilibrium correction terms with respect to unit labour costs and to oil prices, and also in the terms of trade and the output gap. Indeed, we more generally find that far longer lags are relevant than conventionally considered in VAR modelling.

Further extending the data to bring in equilibrium correction terms in relative prices, and the level of the output gap, trade balance, terms of trade, the real exchange rate, and split trends, forecasts from the aggregate CPIX equation have an RMSFE 32.5 per cent lower than the best of the naïve models. Applying the extensions to the individual CPIX components and, in addition, bringing in specific sectoral information such as house prices in the housing cost equation and the wholesale price index for food manufacturing in the food equation, we can obtain a further 8 per cent reduction in RMSFE relative to the naïve benchmark.

There is considerable potential for further improvements in model specification. For example, explicit treatment of tax policy and regulatory information, such as in the car industry, is likely to improve some of these equations considerably. In practical real-time forecasting, there is often information on announced planned price rises, for example for electricity prices, going forward a year or more. Combining this kind of information with forecasts from the models should make it possible to improve further on these forecasting methods.

We have concentrated on forecasting four-quarters ahead: exactly the same exercise could be executed at shorter, less challenging horizons, one- and two-quarters ahead. This has further practical policy connotations. Corresponding to each horizon, an estimate of the RMSFE could be obtained for the selected forecasting period. These could be used to calibrate the fan chart for inflation forecasts over different horizons using these methods. Central Banks, such as SA’s, regularly publish such fan charts to indicate the probabilities associated with different levels of future inflation.

The models lend insight into inflationary pressures for particular components of the basket of consumer spending, and clarify the different monetary transmission channels. In revising the work we will explore non-linearities, such as whether the speed of price adjustment falls in a lower inflation volatility environment, if asymmetries matter in price adjustment and if changing regimes, e.g. the adoption of inflation targeting, contribute to a lower inflation environment.


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Figure 1a:       Relative prices of CPIX components to CPIX: services
Figure 1a: Relative prices of CPIX components to CPIX: services

Figure 1b:       Relative prices of CPIX components to CPIX: goods
Figure 1b: 	Relative prices of CPIX components to CPIX: goods

Notes: RAT refers to the ratio of the component to total CPIX, the consumer price index excluding mortgage interest costs: HX is the ‘housing’ sub-component of CPI with the mortgage interest component subtracted; TS, transport services; OS, other services; FD, food; FR, furniture; CL, clothing; VH, vehicles; BT, beverages and tobacco; TG, transport goods; OG, other goods, sub-components of CPI. CPIX pre-2000 and HX are constructed as in Aron and Muellbauer (2004).