Good inflation models

Question

A well-received comment on this site stated:

Pundits might not understand inflation but macroeconomists actually understand inflation well nowadays

What models are currently used to forecast inflation, and what are their empirical accuracies?

Answer 1

Before providing answer, you should note forecasting is separate discipline from standard empirical economics. Even the word model has slightly different meaning in lets say theoretical economics, applied economics and forecasting where the latter uses purely statistical definition. As a result forecasting models are not a measure of our understanding of economic phenomena, and what even worse ability to forecast variable can be completely orthogonal on level of knowledge or actual 'deep' understanding of a variable (more on this in PS if you are interested).

What models are currently used to forecast inflation, and what are their empirical accuracies?

Since you are talking about forecasting there is extremely large number of models, since the way how modern 21st century forecasting is being done is that you on purpose construct multiplicity of models (even very similar ones) like for example multiple DSGE models, and then you aggregate forecasts. Since, it is beyond scope of stack exchange to cover every single model I will cover 4 big categories:

• Machine learning (ML) models:

These are models that are currently quite a 'hit' with central bankers. Generally having quite small forecasting errors. For example, LASSO or Random Forest ML methods were shown to be able to achieve RSME/MAE relative to random walk (RW) benchmark of approximately 0.7 in some specification for price level (change of which gives you inflation) which is quite accurate (Medeiros et al, 2019).

• Univariate time series models:

These include simple things such as AR models. This category somewhat overlaps with previous one as ML models can be based on some simple time series regression if you look deep enough under the hood, but in this category I include simply direct use of univariate time series models without.

These are not as accurate as ML models but still can have quite high accuracy Medeiros, 2019 report RSME/MAE relative to RW of around 0.8 for price level.

• Multivariate time series models (VAR. BVAR etc):

These models are being used although sometimes they have problem beating random walk. However, depending on exact specification they can still do it (see Christoffel et al 2010).

• Structural and mixed DSGE models

These are models based on some structural model of an economy. Mixed DSGE models can be showed to perform better than pure VAR Christoffel et al 2010, they typically don't work as well as ML models but they are used as they actually are able to provide us with some structural insight beside just providing in-sightless forecasts.

To sum it up, there are actually quite decent models for forecasting price level/deflator and thus by extension inflation, which are able to beat random walk (which is considered benchmark for success). However, again ability to forecast variable has nothing to do with understanding why something happens (people were able to forecast lunar cycle long before they had even rudimentary present day high school level understanding of astrophysics).

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PS: Your question seems to be motivated about some comment about understanding inflation. You should note that forecasting accuracy can be completely orthogonal on our understanding of subject matter. That is we can have excellent understanding of a topic but poor forecasting ability (e.g. weather) or excellent forecasting ability but extremely poor understanding (e.g. random walk is often quite good forecasting model).

Hence it is impossible to judge someone's understanding of topic by forecasts. For example, even ancient humans could forecast rain quite accurately using frogs in jar yet ancient scientists had laughable understanding of climate or biology (e.g. Aristoteles believed that life is conceived when semen mixes with menstrual blood) or Ptolemy was able to forecast natural phenomena with excellent accuracy unmatched prior to modern era with his (in hindsight) preposterous model of solar system with epicycles.

If you are actually interested in knowing which models offer good understanding on the economy, you should ask which models fit best historical data, or which models yield causal predictions (as opposed to forecasts) or mechanics that can be matched to real life data, using some appropriate method (e.g. forecasting models generally can't even tell you what direction of causality is as opposed to lets say quasi experimental methods such as diff-in-diff or RDD that can tell you what causality exists but would be terrible forecasting models) not which models are best able to forecast future.

Forecasting models are made by construction in such a way that they often completely disregard our understanding of subject matter (e.g. some price forecasting models completely ignore endogeneity issue which is important for lets say understanding optimal pricing). In fact structural models that offer good understanding are at great disadvantage because if you have a structural model where x causes y, and you want to use such model for forecasting you need to forecast x first! Hence, with any reasonable structural model where something is causally explained by multiple variables you would have to pile forecasts upon forecasts to use it to forecast the variable of interest compounding forecasting errors (as forecasting errors for x will affect forecasts of y). This can quickly lead to models that are bad at forecasting even if they might be real life accurate (meaning real life causal relationships are accurately modeled).