<p>A variable is exogenous if an equation within the model fully determines its values without recourse to any other endogenous choice variable. Sidenote: More generally, it could also be a set of equations like a VAR.</p>
<p>Your confusion stems from Mankiw not clearly distinguishing between parameters and variables, i.e. essentially conducting comparative statics.
Take your two examples. In the Solow model, the growth rate of technology <span class="math-container">$g$</span> is a fixed parameter. Hence, you can compute every value for technology using just</p>
<p><span class="math-container">$\dot A(t)=gA(t)$</span></p>
<p>without recourse to any other object in the model. This makes technology clearly exogenous. No choice in the model affects its value.</p>
<p>The endogenous growth model of Mankiw with</p>
<p><span class="math-container">$\dot E=guE$</span></p>
<p>looks similar if you treat <span class="math-container">$u$</span> and <span class="math-container">$g$</span> as the fixed parameters that they are. However, Mankiw conducts the thought experiment of changing/chosing the share of workers in the university sector <span class="math-container">$u$</span>. Once you realize that <span class="math-container">$u$</span> is endogenous in this thought experiment, technology <span class="math-container">$A$</span> also becomes endogenous-</p>

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2024-09-22T19:30:38.643Z
If I understand you correctly: That means if I replaced u or (1-u) to L ex  $$\dot{E}(t) = gLE $$, E now will become exogenous if L is considered fixed?     If so, that means only if I replace L with another variable the model specifies is subject to change such as u, 1-u etc  will E become endogenous?
ithoughtso
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2024-09-23T04:12:03.670Z
@ithoughtso my formal academic background is statistics-time series so I'm not claiming that anything is wrong with jpfeifer's answer. The way I think about "endogenous" versus "exogenous" is that the former is a variable that is determined by the value(s) of another variable(s) inside the system.  A simple example would be the variable that represents the response in an ARIMA model. The exogenous variable is determined outside the system. So, in a standard fixed regressor regression, the regressors would be exogenous.
mark leeds
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2024-09-23T04:16:57.670Z
This is the famous paper on exogeneity that is generally referenced when the topic arises. I haven't read it. Most likely it's very theoretical but there may be some useful concepts insights  in it that I've missed out on with my simple take on it. I've never had to really worry about it because it was never an issue as far as what variables fell in which  category. That may be because I really work in econometrics rather than economics.  https://www.jstor.org/stable/1911990
mark leeds
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2024-09-23T17:28:20.037Z
@markleeds The econometrics literature indeed uses a different concept. An AR(1) process for technology is the standard way of representing exogenous TFP in macroeconomics, e.g. the RBC model.  From an econometric time series perspective, it would not be considered exogenous.
jpfeifer
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2024-09-23T17:29:13.287Z
@ithoughtso Yes, if you replace the endogenous choice variable $u$ by an exogenous process for $L$, your are making technology exogenous again.
jpfeifer
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2024-09-24T15:11:13.730Z
@ithoughtso: consider jpfeifer's comment because econometrics defines things differently. thanks jpfeifer.
mark leeds
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2024-09-24T19:21:54.463Z
Thank you for all your input.  It seems after identifying the independent and dependent variables, the economics approach adds an additional layer based on meanings given to variables or parameters in the model which is different from the math approach I am used to.
ithoughtso
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2024-09-22T12:32:29.580Z
2024-09-22T12:32:29.580Z
jpfeifer
<p>I know there were several questions asking about this topic with the definition along the lines of exogenous variables are fixed / independent variables / determined outside the model and endogenous variables are dependent variables / determined inside the model but I am still confused.  Is a variable endogenous in a model due to the set up in the model or due to the definitions given to the variable or both?</p>
<p>For example a simple growth model in which A is endogenous is <span class="math-container">$$Y = AK$$</span>  but is exogenous in the Solow model <span class="math-container">$$Y=K(AL)$$</span> where <span class="math-container">$$\dot{A}(t) = gA(t)$$</span></p>
<p>Why is A endogenous in one model but exogenous in the other?  Is it because in the endogenous growth model A includes human capital which is not fixed but physical capital is fixed?  If it was only physical capital would A in Y = AK be exogenous? If <span class="math-container">$$\dot{A}(t) = gAL$$</span> would A be endogenous because it is now affected by L?</p>
<p>Another question: The Mankiw Intermediate macro book shows an endogenous growth model</p>
<p><span class="math-container">$$ Y = F(K, (1-u)LE)$$</span>  <span class="math-container">$$\dot{E} = guE$$</span>  <span class="math-container">$$\dot{K} = sY-\delta K$$</span></p>
<p>Why is E endogenous here <span class="math-container">$$\dot{E} = guE$$</span> but not in the Solow model here? <span class="math-container">$$\dot{A}(t) = gA(t)$$</span> Is it because in the endogenous model E is now affected by u (share conducting research in universities) or because of initial assumptions that A should be exogenous in the Solow model but not for former model because capital is defined broadly?</p>
<p>Assume the model was <span class="math-container">$$ Y = F(K, (1-u)LE)$$</span>  <span class="math-container">$$\dot{K} = sY-\delta K$$</span> but no definition for growth would E now be exogenous or it depends on if E is narrowly or broadly defined?</p>

<economic-growth><definition><solow><endogenous-growth>
Endogenous vs exogenous variables
ithoughtso
# Endogenous vs exogenous variables

(Asked by: username_0 on 2024-09-22)

I know there were several questions asking about this topic with the definition along the lines of exogenous variables are fixed / independent variables / determined outside the model and endogenous variables are dependent variables / determined inside the model but I am still confused. Is a variable endogenous in a model due to the set up in the model or due to the definitions given to the variable or both?

For example a simple growth model in which A is endogenous is $$Y = AK$$ but is exogenous in the Solow model $$Y=K(AL)$$ where $$\dot{A}(t) = gA(t)$$

Why is A endogenous in one model but exogenous in the other? Is it because in the endogenous growth model A includes human capital which is not fixed but physical capital is fixed? If it was only physical capital would A in Y = AK be exogenous? If $$\dot{A}(t) = gAL$$ would A be endogenous because it is now affected by L?

Another question: The Mankiw Intermediate macro book shows an endogenous growth model

$$ Y = F(K, (1-u)LE)$$ $$\dot{E} = guE$$ $$\dot{K} = sY-\delta K$$

Why is E endogenous here $$\dot{E} = guE$$ but not in the Solow model here? $$\dot{A}(t) = gA(t)$$ Is it because in the endogenous model E is now affected by u (share conducting research in universities) or because of initial assumptions that A should be exogenous in the Solow model but not for former model because capital is defined broadly?

Assume the model was $$ Y = F(K, (1-u)LE)$$ $$\dot{K} = sY-\delta K$$ but no definition for growth would E now be exogenous or it depends on if E is narrowly or broadly defined?

**Tags:** economic-growth, definition, solow, endogenous-growth

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## 1 answers

### Answer by username_1 on 2024-09-22. Score: 1 | Accepted answer

A variable is exogenous if an equation within the model fully determines its values without recourse to any other endogenous choice variable. Sidenote: More generally, it could also be a set of equations like a VAR.

Your confusion stems from Mankiw not clearly distinguishing between parameters and variables, i.e. essentially conducting comparative statics.
Take your two examples. In the Solow model, the growth rate of technology $g$ is a fixed parameter. Hence, you can compute every value for technology using just

$\dot A(t)=gA(t)$

without recourse to any other object in the model. This makes technology clearly exogenous. No choice in the model affects its value.

The endogenous growth model of Mankiw with

$\dot E=guE$

looks similar if you treat $u$ and $g$ as the fixed parameters that they are. However, Mankiw conducts the thought experiment of changing/chosing the share of workers in the university sector $u$. Once you realize that $u$ is endogenous in this thought experiment, technology $A$ also becomes endogenous-

> **Comments:**
> **username_0**: If I understand you correctly: That means if I replaced u or (1-u) to L ex  $$\dot{E}(t) = gLE $$, E now will become exogenous if L is considered fixed?     If so, that means only if I replace L with another variable the model specifies is subject to change such as u, 1-u etc  will E become endogenous?  
> **username_2**: @ithoughtso my formal academic background is statistics-time series so I'm not claiming that anything is wrong with jpfeifer's answer. The way I think about "endogenous" versus "exogenous" is that the former is a variable that is determined by the value(s) of another variable(s) inside the system.  A simple example would be the variable that represents the response in an ARIMA model. The exogenous variable is determined outside the system. So, in a standard fixed regressor regression, the regressors would be exogenous.  
> **username_2**: This is the famous paper on exogeneity that is generally referenced when the topic arises. I haven't read it. Most likely it's very theoretical but there may be some useful concepts insights  in it that I've missed out on with my simple take on it. I've never had to really worry about it because it was never an issue as far as what variables fell in which  category. That may be because I really work in econometrics rather than economics.  https://www.jstor.org/stable/1911990  
> **username_1**: @markleeds The econometrics literature indeed uses a different concept. An AR(1) process for technology is the standard way of representing exogenous TFP in macroeconomics, e.g. the RBC model.  From an econometric time series perspective, it would not be considered exogenous.  
> **username_1**: @ithoughtso Yes, if you replace the endogenous choice variable $u$ by an exogenous process for $L$, your are making technology exogenous again.  
> **username_2**: @ithoughtso: consider jpfeifer's comment because econometrics defines things differently. thanks jpfeifer.  
> **username_0**: Thank you for all your input.  It seems after identifying the independent and dependent variables, the economics approach adds an additional layer based on meanings given to variables or parameters in the model which is different from the math approach I am used to.  

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