<p>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).</p>
<blockquote>
<p>What models are currently used to forecast inflation, and what are their empirical accuracies?</p>
</blockquote>
<p>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:</p>
<ul>
<li>Machine learning (ML) models:</li>
</ul>
<p>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 (<a href="https://www.tandfonline.com/doi/full/10.1080/07350015.2019.1637745?needAccess=true" rel="nofollow noreferrer">Medeiros et al, 2019</a>).</p>
<ul>
<li>Univariate time series models:</li>
</ul>
<p>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.</p>
<p>These are not as accurate as ML models but still can have quite high accuracy <a href="https://www.tandfonline.com/doi/full/10.1080/07350015.2019.1637745?needAccess=true" rel="nofollow noreferrer">Medeiros, 2019</a> report RSME/MAE relative to RW of around 0.8 for price level.</p>
<ul>
<li>Multivariate time series models (VAR. BVAR etc):</li>
</ul>
<p>These models are being used although sometimes they have problem beating random walk. However, depending on exact specification they can still do it (see <a href="https://homepage.univie.ac.at/robert.kunst/prognos4.pdf" rel="nofollow noreferrer">Christoffel et al 2010</a>).</p>
<ul>
<li>Structural and mixed DSGE models</li>
</ul>
<p>These are models based on some structural model of an economy. Mixed DSGE models can be showed to perform better than pure VAR <a href="https://homepage.univie.ac.at/robert.kunst/prognos4.pdf" rel="nofollow noreferrer">Christoffel et al 2010</a>, 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.</p>
<p>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).</p>
<hr />
<p><strong>PS:</strong> 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).</p>
<p>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.</p>
<p>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.</p>
<p>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).</p>

CC BY-SA 4.0
2023-03-12T20:04:45.817Z
Hi! Thank you for the model lists! I understand that e.g.; chaotic systems may be perfectly understood and yet they are difficult to forecast. Unfortunately I do not have access to the papers; 1. Medeiros seems to study solely the US; what is the time period? Does it contain periods with high inflation?
Giskard
CC BY-SA 4.0
2023-03-12T20:06:41.847Z
2. Do you agree with the quoted statement that "*macroeconomists actually understand inflation well nowadays*"? If you have an opinion about these, can you please explain to me with what tests is this understanding measured/controlled?
Giskard
CC BY-SA 4.0
2023-03-12T20:14:49.837Z
@Giskard 1. sample period is 1990-2015 that does contain some periods of higher than average inflation. 2. Well that is difficult to answer, lets unpack that statement, what does 'understand inflation well' even mean? With simple QTM you can probably accurately describe 60% of monetary history of US and most other countries (by my guesstimate). Using modern IS-LM-PC state of the art model you can probably explain up to 70%, with some cutting edge theories like FTPL you can probably do 75%, yet there are definitely some periods of inflation that are difficult to explain with current models.
1muflon1
CC BY-SA 4.0
2023-03-12T20:16:49.573Z
so what is your cut-off for understanding something well? I mean do we understand physics well? Einstein's relativity breaks down if you rewind time too much to the past and at extreme heat and pressure, standard model of particle physics also cannot explain everything 100% (and I consider both of the models above as best examples of successful scientific models).  How much variation in data you need to explain before you can claim to understand something well? In Popperian tradition all models are wrong some are just closer to truth than others.
1muflon1
CC BY-SA 4.0
2023-03-12T20:28:18.323Z
if you want to be completely  cynical about it you could simply throw your hands in the air and say we don't understand anything as a result but I would consider that extremely cynical stance. Of course, saying we understand everything about inflation would extremely naive but we do understand quite a lot
1muflon1
CC BY-SA 4.0
2023-03-13T05:24:15.767Z
Thank for your reply. When you [write](https://economics.stackexchange.com/questions/54703/good-inflation-models/54705?noredirect=1#comment89699_54705) "*you can probably accurately describe 60% of monetary history of US and most other countries*" how do you measure this, what counts as an "accurate description"? I understand the number 60% is just a guesstimate; I am trying to understand how macroeconomists assess whether their understanding/model of inflation is good.
Giskard
CC BY-SA 4.0
2023-03-13T05:32:37.137Z
I dislike it when people ask chain questions, so I just [posted this as a new one](https://economics.stackexchange.com/q/54708/1601).
Giskard
CC BY-SA 4.0
2023-03-13T09:47:56.487Z
@Giskard In that guesstimate I measure it as % of years where if you would run lets say long run cointegrated model you would not be able to reject hypothesis that in a model with $\ln p = \alpha \ln m+ \beta \ln v - \gamma \ln y$ that $\beta=\alpha = \gamma =1$ which is what QTM would predict. I will provide fuller answer to your question there
1muflon1
CC BY-SA 4.0
2023-03-12T19:30:40.887Z
2023-03-12T20:23:00.667Z
2023-03-12T20:23:00.667Z
1muflon1
<p>A <a href="https://economics.stackexchange.com/questions/54688/how-is-inflation-logically-possible/54691?noredirect=1#comment89681_54691">well-received comment</a> on this site stated:</p>
<blockquote>
<p>Pundits might not understand inflation but macroeconomists actually understand inflation well nowadays</p>
</blockquote>
<p>What models are currently used to forecast inflation, and what are their empirical accuracies?</p>

CC BY-SA 4.0
2023-03-12T17:49:45.903Z
? This question seems to be off. Understanding =/= ability to forecast. For example, physics of weather is pretty well understood by physicists to the point that there is very little if anything to be learned about how weather operates. Yet forecasting what weather will be in future is quite a challenge. What even more, **ability to forecast something provides no indication of understanding** the subject matter. There are numerous variables that can be forecasted without understanding them. For example, most of the top line machine learning models used for short term forecasting
1muflon1
CC BY-SA 4.0
2023-03-12T17:53:14.367Z
give excellent forecast without telling us how the forecasts were made and without having any structural parameters that would explain how things works. For example, an alien via statistical analysis might be able to forecast with 100% accuracy post-Christmas sale with 0 socio-economic understanding why the sale occurred or even why humans have sales at all. PS: you seem to link to some random user rather than to comment
1muflon1
<macroeconomics><inflation>
Good inflation models
Giskard
# Good inflation models

(Asked by: username_0 on 2023-03-12)

A [well-received comment](https://economics.stackexchange.com/questions/54688/how-is-inflation-logically-possible/54691?noredirect=1#comment89681_54691) 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?

**Tags:** macroeconomics, inflation

> **Comments:**
> **username_1**: ? This question seems to be off. Understanding =/= ability to forecast. For example, physics of weather is pretty well understood by physicists to the point that there is very little if anything to be learned about how weather operates. Yet forecasting what weather will be in future is quite a challenge. What even more, **ability to forecast something provides no indication of understanding** the subject matter. There are numerous variables that can be forecasted without understanding them. For example, most of the top line machine learning models used for short term forecasting  
> **username_1**: give excellent forecast without telling us how the forecasts were made and without having any structural parameters that would explain how things works. For example, an alien via statistical analysis might be able to forecast with 100% accuracy post-Christmas sale with 0 socio-economic understanding why the sale occurred or even why humans have sales at all. PS: you seem to link to some random user rather than to comment  

---

## 1 answers

### Answer by username_1 on 2023-03-12. Score: 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](https://www.tandfonline.com/doi/full/10.1080/07350015.2019.1637745?needAccess=true)).

* 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](https://www.tandfonline.com/doi/full/10.1080/07350015.2019.1637745?needAccess=true) 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](https://homepage.univie.ac.at/robert.kunst/prognos4.pdf)).

* 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](https://homepage.univie.ac.at/robert.kunst/prognos4.pdf), 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).

---

**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).

> **Comments:**
> **username_0**: Hi! Thank you for the model lists! I understand that e.g.; chaotic systems may be perfectly understood and yet they are difficult to forecast. Unfortunately I do not have access to the papers; 1. Medeiros seems to study solely the US; what is the time period? Does it contain periods with high inflation?  
> **username_0**: 2. Do you agree with the quoted statement that "*macroeconomists actually understand inflation well nowadays*"? If you have an opinion about these, can you please explain to me with what tests is this understanding measured/controlled?  
> **username_1**: @username_0 1. sample period is 1990-2015 that does contain some periods of higher than average inflation. 2. Well that is difficult to answer, lets unpack that statement, what does 'understand inflation well' even mean? With simple QTM you can probably accurately describe 60% of monetary history of US and most other countries (by my guesstimate). Using modern IS-LM-PC state of the art model you can probably explain up to 70%, with some cutting edge theories like FTPL you can probably do 75%, yet there are definitely some periods of inflation that are difficult to explain with current models.  
> **username_1**: so what is your cut-off for understanding something well? I mean do we understand physics well? Einstein's relativity breaks down if you rewind time too much to the past and at extreme heat and pressure, standard model of particle physics also cannot explain everything 100% (and I consider both of the models above as best examples of successful scientific models).  How much variation in data you need to explain before you can claim to understand something well? In Popperian tradition all models are wrong some are just closer to truth than others.  
> **username_1**: if you want to be completely  cynical about it you could simply throw your hands in the air and say we don't understand anything as a result but I would consider that extremely cynical stance. Of course, saying we understand everything about inflation would extremely naive but we do understand quite a lot  
> **username_0**: Thank for your reply. When you [write](https://economics.stackexchange.com/questions/54703/good-inflation-models/54705?noredirect=1#comment89699_54705) "*you can probably accurately describe 60% of monetary history of US and most other countries*" how do you measure this, what counts as an "accurate description"? I understand the number 60% is just a guesstimate; I am trying to understand how macroeconomists assess whether their understanding/model of inflation is good.  
> **username_0**: I dislike it when people ask chain questions, so I just [posted this as a new one](https://economics.stackexchange.com/q/54708/1601).  
> **username_1**: @username_0 In that guesstimate I measure it as % of years where if you would run lets say long run cointegrated model you would not be able to reject hypothesis that in a model with $\ln p = \alpha \ln m+ \beta \ln v - \gamma \ln y$ that $\beta=\alpha = \gamma =1$ which is what QTM would predict. I will provide fuller answer to your question there  

---

