<p>Depends on what exactly you mean by backward looking component. When people talk about agents being 'backward looking' they often mean adaptive expectations, if that is what you have in mind then answer would be no.</p>
<p>However, rational expectations really just require agents to have model consistent expectations (see Snowdon, Vane, &amp; Wynarczyk,(1994). A modern guide to macroeconomics). So if by 'backward looking components' you mean that agents utilize past information in some way answer is yes. This is especially true if the underlying model predicts that expected variable has some structural relationship to its past realizations. This being said there are not many situations where this occurs.</p>
<p>There can also be mixed expectations models that assume that portion of agents follows adaptive expectations for example and rest rational expectations, but these would not strictly be called rational expectations models.</p>

CC BY-SA 4.0
2020-08-08T19:26:38.730Z
Hi: I'm not clear on what backward looking components means (  but I would probably say yes because expectations are  based on the past ), but to get a decent idea of what RE models do, gets Lucas' book : "Studies In Business Cycle Theory". IMHO, he is the clearest of all the RE authors when it comes to academic type RE papers. The book contains most , if not all of his important papers and was a real eye opener for me.
mark leeds
CC BY-SA 4.0
2020-08-09T06:23:41.013Z
I would add to this answer that if the underlying laws of motion are Markovian (a benchmark assumption) or 2-period Markovian (by extending the state), then Forward-looking models will be trivially backward-looking haha.
Debreu
CC BY-SA 4.0
2020-08-10T02:16:55.247Z
@Beck Batucada : I looked and I think you may be referring to the type of solution in an RE model ? When the coeff in the  expectational difference equation, $a$, is less than 1.0, then the terminology is that the solution to the difference equation is "forward-looking". When $a$ is greater than 1.0, then the corresponding solution is said to be "backward looking". But, as before, I'm not sure if this is what you are referring to in your question ? If yes, the answer is no, the solution can't be both forward and backward looking because the estimate of $a$ has to be in one range or the other.
mark leeds
CC BY-SA 4.0
2020-08-10T12:54:05.663Z
I just mean backward looking components an sich, adaptive expectations are an example of a forecasting rule with backward components indeed as you mention.

So, the answer seems to be yes, although in most models, rational expectations seems to be only forward looking because the underlying model predicts that expected variables has NO structural relationship to its past realizations?

Yes I know about the mixed models.

This is a question to finalize my master thesis about boundedly rational expectations.
Beck Batucada
CC BY-SA 4.0
2020-08-10T12:55:37.297Z
@mark leeds: sorry, I really do not understand your second comment
Beck Batucada
CC BY-SA 4.0
2020-08-10T12:58:06.793Z
To clarify backward looking component: if your forecast for the next period, either directly,  or indirectly, takes into account information that is extracted from past realisations, I would call it back-ward looking. Examples are naive, adaptive, trend following, anchor and adjustment, AR(1) based on sample mean and autocorrelation forecasting heuristics.
Beck Batucada
CC BY-SA 4.0
2020-08-10T13:00:54.960Z
if the underlying model postulates that the to-be forecasted variables have some structural relationship to their past realizations
Beck Batucada
CC BY-SA 4.0
2020-08-10T13:09:57.390Z
This sentence if really important, I would like to include it in my thesis:

"if the underlying model predicts that the to-beforecasted variable has some structural relationship to its past realizations"

What would be examples of such a relationship? Or can you eleborate on that? You say most models assuming RE do not include such a structural relationship.
I get the main idea. But it remains an rather abstract understanding so far.
Beck Batucada
CC BY-SA 4.0
2020-08-10T13:11:56.583Z
If I understand correctly, this particular structural relationship to its past, should be part of the forecasting rule? As such, it would be an adjustment of the RE assumption, no? Not the standard RE assumption?
RE agents know the structure of the economy, so if this  particular structural relationship to its past would be part of the model, the RE prediction would capture it. 
Seems like the chicken or the egg problem :)
Beck Batucada
CC BY-SA 4.0
2020-08-10T13:18:56.393Z
@BeckBatucada a simple example would be some models where variables are based markovian motion as Flintro mentioned in his excellent comment. For example, let’s suppose we have state variable $y_t$ that depends on some information set $I$. In such case the rational expectation would be $E[y_t]=E[y_t|I_t]$ however if we use markovian property and present realizations of $I_t$ are based on past realizations that is $I_{t-i}={y_j, j=0,1..i-t}$ then by law of iterating expectations it must also hold that $E[y_t]= E[y_t | I_{t-1}] = E[E[y_t | I_t] | I_{t-1}$ these are rational expectations
1muflon1
CC BY-SA 4.0
2020-08-10T13:24:42.330Z
But take into account past information as well. Also I don’t really see that chicken and egg problem there. You are not adjusting your RE assumption- the knowledge of the model is part of it. The problem is that often in many economic models past is useless for predicting future. Knowing past profit might not be useful for knowing future one. So many models do not have that structural dependence. However, if they have it there then RE naturally incorporate it.
1muflon1
CC BY-SA 4.0
2020-08-10T13:52:36.803Z
Thanks for this clarification. When Flintro mentions "trivially backward-looking", he actually means a high degree of backward looking, right? This would be in line with your answer.
Beck Batucada
CC BY-SA 4.0
2020-08-10T13:53:00.467Z
no idea how to cite you on this one though :), is there a good reference for this point?
Beck Batucada
CC BY-SA 4.0
2020-08-10T13:55:47.587Z
@BeckBatucada I think by trivially he means that it’s obvious/easy to prove that they are backward looking. Also usually people don’t use the terminology high/low degree of backward looking but it’s true that in the example I set up the rational expectations would completely take into account all past information and I also think that he had in mind this kind of example.
1muflon1
CC BY-SA 4.0
2020-08-10T13:57:19.257Z
I guess I could refer to it as Markov-Switching Rational Expectations Models? As in this reference:

Minimal State Variable Solutions
to Markov-Switching Rational Expectations Models
Roger E.A. Farmer, Daniel F. Waggoner, and Tao Zha
Working Paper 2008-23a
September 2010
Beck Batucada
CC BY-SA 4.0
2020-08-10T13:59:02.190Z
For my conclusion, it seems that  high/low degree of backward looking determines stability properties of models under learning, as well as the sign of the backward looking components.
Beck Batucada
CC BY-SA 4.0
2020-08-10T14:17:40.230Z
@BeckBatucada yes you shouldn't cite stack exchange. This kind expectations are not just exclusive to markow switching models though. Good source is Introduction to Quantitative Macroeconomics Using Julia from Carani (2019) - you can skip all the julia stuff unless you are interested in the new program and just look in the theory and sources cited therein. You should be able to get the book free through university VPN.
1muflon1
CC BY-SA 4.0
2020-08-10T20:30:08.653Z
@Beck Batucada:  I'm still not clear on the meaning of backward and forward components but I'll try to find notes on the meaning that I was referring to. It's clearly not what you're looking but it's useful to know about because it's talked about a lot in RE.  I'll look on the net and get back to you. As far as the rest of the discussion, I'm staying out of it because I don't follow it.
mark leeds
CC BY-SA 4.0
2020-08-10T20:48:31.637Z
I don't think it's relevant to your question (and I don't claim deep understanding of it either ) but, just so you know that I'm not just making this stuff up :), check out part II at this link titled. "Single Stochastic Difference Equations". https://www.karlwhelan.com/MAMacro/part6.pdf
mark leeds
CC BY-SA 4.0
2020-08-08T18:50:01.937Z
2020-08-08T18:50:01.937Z
1muflon1
<p>Are rational expectations (Muth, Lucas, Kyland and Prescott) in economics purely forwards looking, or can they have backward looking components?</p>

<macroeconomics><rational-expectations><adaptive-learning>
Are rational expectations in economics purely forwards looking, or can they have backward looking components?
Beck Batucada
# Are rational expectations in economics purely forwards looking, or can they have backward looking components?

(Asked by: username_0 on 2020-08-08)

Are rational expectations (Muth, Lucas, Kyland and Prescott) in economics purely forwards looking, or can they have backward looking components?

**Tags:** macroeconomics, rational-expectations, adaptive-learning

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## 1 answers

### Answer by username_1 on 2020-08-08. Score: 2 | Accepted answer

Depends on what exactly you mean by backward looking component. When people talk about agents being 'backward looking' they often mean adaptive expectations, if that is what you have in mind then answer would be no.

However, rational expectations really just require agents to have model consistent expectations (see Snowdon, Vane, & Wynarczyk,(1994). A modern guide to macroeconomics). So if by 'backward looking components' you mean that agents utilize past information in some way answer is yes. This is especially true if the underlying model predicts that expected variable has some structural relationship to its past realizations. This being said there are not many situations where this occurs.

There can also be mixed expectations models that assume that portion of agents follows adaptive expectations for example and rest rational expectations, but these would not strictly be called rational expectations models.

> **Comments:**
> **username_2**: Hi: I'm not clear on what backward looking components means (  but I would probably say yes because expectations are  based on the past ), but to get a decent idea of what RE models do, gets Lucas' book : "Studies In Business Cycle Theory". IMHO, he is the clearest of all the RE authors when it comes to academic type RE papers. The book contains most , if not all of his important papers and was a real eye opener for me.  
> **username_3**: I would add to this answer that if the underlying laws of motion are Markovian (a benchmark assumption) or 2-period Markovian (by extending the state), then Forward-looking models will be trivially backward-looking haha.  
> **username_2**: @Beck Batucada : I looked and I think you may be referring to the type of solution in an RE model ? When the coeff in the  expectational difference equation, $a$, is less than 1.0, then the terminology is that the solution to the difference equation is "forward-looking". When $a$ is greater than 1.0, then the corresponding solution is said to be "backward looking". But, as before, I'm not sure if this is what you are referring to in your question ? If yes, the answer is no, the solution can't be both forward and backward looking because the estimate of $a$ has to be in one range or the other.  
> **username_0**: I just mean backward looking components an sich, adaptive expectations are an example of a forecasting rule with backward components indeed as you mention.  So, the answer seems to be yes, although in most models, rational expectations seems to be only forward looking because the underlying model predicts that expected variables has NO structural relationship to its past realizations?  Yes I know about the mixed models.  This is a question to finalize my master thesis about boundedly rational expectations.  
> **username_0**: @mark leeds: sorry, I really do not understand your second comment  
> **username_0**: To clarify backward looking component: if your forecast for the next period, either directly,  or indirectly, takes into account information that is extracted from past realisations, I would call it back-ward looking. Examples are naive, adaptive, trend following, anchor and adjustment, AR(1) based on sample mean and autocorrelation forecasting heuristics.  
> **username_0**: if the underlying model postulates that the to-be forecasted variables have some structural relationship to their past realizations  
> **username_0**: This sentence if really important, I would like to include it in my thesis:  "if the underlying model predicts that the to-beforecasted variable has some structural relationship to its past realizations"  What would be examples of such a relationship? Or can you eleborate on that? You say most models assuming RE do not include such a structural relationship. I get the main idea. But it remains an rather abstract understanding so far.  
> **username_0**: If I understand correctly, this particular structural relationship to its past, should be part of the forecasting rule? As such, it would be an adjustment of the RE assumption, no? Not the standard RE assumption? RE agents know the structure of the economy, so if this  particular structural relationship to its past would be part of the model, the RE prediction would capture it.  Seems like the chicken or the egg problem :)  
> **username_1**: @BeckBatucada a simple example would be some models where variables are based markovian motion as Flintro mentioned in his excellent comment. For example, let’s suppose we have state variable $y_t$ that depends on some information set $I$. In such case the rational expectation would be $E[y_t]=E[y_t|I_t]$ however if we use markovian property and present realizations of $I_t$ are based on past realizations that is $I_{t-i}={y_j, j=0,1..i-t}$ then by law of iterating expectations it must also hold that $E[y_t]= E[y_t | I_{t-1}] = E[E[y_t | I_t] | I_{t-1}$ these are rational expectations  
> **username_1**: But take into account past information as well. Also I don’t really see that chicken and egg problem there. You are not adjusting your RE assumption- the knowledge of the model is part of it. The problem is that often in many economic models past is useless for predicting future. Knowing past profit might not be useful for knowing future one. So many models do not have that structural dependence. However, if they have it there then RE naturally incorporate it.  
> **username_0**: Thanks for this clarification. When Flintro mentions "trivially backward-looking", he actually means a high degree of backward looking, right? This would be in line with your answer.  
> **username_0**: no idea how to cite you on this one though :), is there a good reference for this point?  
> **username_1**: @BeckBatucada I think by trivially he means that it’s obvious/easy to prove that they are backward looking. Also usually people don’t use the terminology high/low degree of backward looking but it’s true that in the example I set up the rational expectations would completely take into account all past information and I also think that he had in mind this kind of example.  
> **username_0**: I guess I could refer to it as Markov-Switching Rational Expectations Models? As in this reference:  Minimal State Variable Solutions to Markov-Switching Rational Expectations Models Roger E.A. Farmer, Daniel F. Waggoner, and Tao Zha Working Paper 2008-23a September 2010  
> **username_0**: For my conclusion, it seems that  high/low degree of backward looking determines stability properties of models under learning, as well as the sign of the backward looking components.  
> **username_1**: @BeckBatucada yes you shouldn't cite stack exchange. This kind expectations are not just exclusive to markow switching models though. Good source is Introduction to Quantitative Macroeconomics Using Julia from Carani (2019) - you can skip all the julia stuff unless you are interested in the new program and just look in the theory and sources cited therein. You should be able to get the book free through university VPN.  
> **username_2**: @Beck Batucada:  I'm still not clear on the meaning of backward and forward components but I'll try to find notes on the meaning that I was referring to. It's clearly not what you're looking but it's useful to know about because it's talked about a lot in RE.  I'll look on the net and get back to you. As far as the rest of the discussion, I'm staying out of it because I don't follow it.  
> **username_2**: I don't think it's relevant to your question (and I don't claim deep understanding of it either ) but, just so you know that I'm not just making this stuff up :), check out part II at this link titled. "Single Stochastic Difference Equations". https://www.karlwhelan.com/MAMacro/part6.pdf  

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