<p>This is perhaps a good opportunity to point out that the <strong>"certainty equivalence"</strong> concept means one thing in microeconomics/choice under uncertainty theory, while it means something different in macroeconomics.  </p>

<p><strong>Microeconomics/choice under uncertainty</strong><br>
The Certainty Equivalent of a lottery/gamble, is the amount of wealth which, if given with certainty, provides the same utility as the lottery/gamble. See for example Jehle &amp; Reny's "Advanced Microeconomic Theory" (2011, 3d ed.), p.113.</p>

<p><strong>Macroeconomics</strong><br>
"Certainty Equivalence" is the situation in a stochastic model, where optimal decision rules prove to be identical to those that would have been derived in a deterministic framework (see for example Lungqvist &amp; Sargent's "Recursive Macroeconomic Theory" 2004, 2nd ed, p. 113-115). Informally, this is sometimes described as "agents behave as if the stochastic processes are not stochastic", or "the decision rule is not affected by stochastic variability".</p>

<p>It is a funny coincidence that both references treat the subject in the same page number...</p>

<p>The concepts are evidently linked by the "as if there was no uncertainty" angle, but they are different in essential aspects: the micro-concept is a "buy-out" of uncertainty, providing a certain alternative towards which the agent that faces the gamble is indifferent in terms of utility, while the macro-concept emerges as a property of the solution (and only under restrictive model structures, or linear approximations thereof).</p>

CC BY-SA 3.0
2015-12-02T22:11:55.237Z
I'd like to note that in micro, the word is **equivalent**, indicating that this object is much more specific than the object/phenomenon referred to by **equivalence** `:)`
Herr K.
CC BY-SA 3.0
2015-12-02T18:36:57.757Z
2017-12-30T23:13:37.090Z
2017-12-30T23:13:37.090Z
Alecos Papadopoulos
<p>Expected utility theory is based on valuing expectations. There is more to that than just uncertainty.</p>

<p>First, a risky investment is different from an uncertain investment. Risk is usually defined as future events occurring only with a <strong>measurable probability</strong>, while uncertainty is called upon when the likelihood of future events is <strong>indefinite or incalculable</strong>, but only estimated in itself (it's like a risk on risk). What I'm saying here is actually agreed upon by the author. Note that the first definition of expected utility models did not include any other considerations that risk. Part of the "risk premium" is... a risk premium, rather than an uncertainty premium, and shouldn't be modified by a better understanding of uncertainty.</p>

<p>Another part of the risk premium is the fact that it is usually set outside the micro-economic model, usually at the moment of raising capital. No due diligence can give an investor an "inside" view of the model, and so there will always be a cost of borrowing money, which is to be taken into account in a risk premium for any project that requires money over time.</p>

<p>What the article discusses seems more to me as a motivation to decrease the impact of uncertainty, and so the risk premium, rather than change the way we look at it. Being able to translate uncertainty into risk is great, but won't make risk itself disappear. For some projects so, it is likely to increase the risk premium as risks taken are better quantified, as uncertainty premium is meant to cover hidden/ unknown risk premium only on average.</p>

CC BY-SA 3.0
2015-12-09T06:17:03.783Z
Thanks VicAche for your answer but I don't understand your last paragraph. Why do you mean exactly by "a motivation to decrease the impact of uncertainty"? Is there a section or a page in the paper that suggests this?
emeryville
CC BY-SA 3.0
2015-12-09T10:32:24.853Z
@emeryville it is a (perhaps too personal) deduction from pp164-165, which are saying a) the government use to have such a "risk-premium decrease policy", b) all apparently positive effects of uncertainty on investment are negligible because firms CEO are too tied with their own firms. My deduction was that the paper wants you to deduce that c) uncertainty has exaggerated impact on the economy, and its fluctuations are mostly self-induced, but if the "seems to me as" wasn't enough I can sure edit.
VicAche
CC BY-SA 3.0
2015-12-10T06:37:21.197Z
Yes please if you could edit the last paragraph that would be great because I still do not understand the sentence "a motivation to decrease the impact of uncertainty". Moreover, the pp. 164-165 are simply related to a review of the theory. This is not the main part of the paper.
emeryville
CC BY-SA 3.0
2015-12-02T17:00:25.033Z
2015-12-02T20:37:41.133Z
2015-12-02T20:37:41.133Z
VicAche
<p>Bloom in a recent JEP <a href="https://www.aeaweb.org/articles.php?doi=10.1257/jep.28.2.153">paper</a> considers that "the increase in computing power has made it possible to include uncertainty shocks directly in a wide range of models, allowing economists to abandon assumptions built on “certainty equivalence,” which refers to the amount of money that would be required as compensation for risk." (2nd paragraph of page 154, third point).</p>

<p>My understanding of Bloom's point is the idea that with computing power we can treat and exploit the heterogeneity of data. We can use high-frequency and/or large-scale data, in combination with computing power, to identify the role of uncertainty shock on economic outcomes. </p>

<p>My guess is that Bloom's point could be an implicit criticism of the expected utility theory given the importance of the certainty equivalent concept, and the related concept of risk premium, in this framework. Is this guess/interpretation right?</p>

CC BY-SA 3.0
2015-11-08T09:51:03.323Z
I've rewritten the title, as "big data" was completely irrelevant to the question at hand. Feel free to improve on its current version.
FooBar
CC BY-SA 3.0
2015-11-08T17:49:04.967Z
Thanks. This is a super title, but "big data" is not completely irrelevant because I guess that what Bloom has in mind is the idea that with computing power you can treat the heterogeneity of data, that is big data. You can use high-frequency and/or large-scale data, in combination with computing power, to identify the role of uncertainty on economic outcomes.
emeryville
CC BY-SA 3.0
2015-11-08T18:04:59.343Z
I substituted "will" for "did" in the title because it didn’t happen so much yet!
emeryville
CC BY-SA 3.0
2015-11-13T22:26:43.800Z
I think this is a really interesting question, but you should be specific in what you want to know. Phrases like, "Any thoughts on this?" are an invitation for broad discussion based answers which isn't what we'd like to generate. Could you narrow the scope a little bit and really get at what you'd like to know?
cc7768
CC BY-SA 3.0
2015-11-13T22:27:01.283Z
Also, could you point me to page or section where this is discussed? I looked for a few minutes but couldn't find it -- I'll have another look later, but I'm trying to understand why it would be a criticism of expected utility theory.
cc7768
CC BY-SA 3.0
2015-11-13T22:59:43.317Z
I updated my question based on your comments. Thansk @cc7768.
emeryville
<risk><expected-utility><uncertainty>
Will high computing power substitute the certainty-equivalence assumption?
emeryville
# Will high computing power substitute the certainty-equivalence assumption?

(Asked by: username_0 on 2015-11-08)

Bloom in a recent JEP [paper](https://www.aeaweb.org/articles.php?doi=10.1257/jep.28.2.153) considers that "the increase in computing power has made it possible to include uncertainty shocks directly in a wide range of models, allowing economists to abandon assumptions built on “certainty equivalence,” which refers to the amount of money that would be required as compensation for risk." (2nd paragraph of page 154, third point).

My understanding of Bloom's point is the idea that with computing power we can treat and exploit the heterogeneity of data. We can use high-frequency and/or large-scale data, in combination with computing power, to identify the role of uncertainty shock on economic outcomes.

My guess is that Bloom's point could be an implicit criticism of the expected utility theory given the importance of the certainty equivalent concept, and the related concept of risk premium, in this framework. Is this guess/interpretation right?

**Tags:** risk, expected-utility, uncertainty

> **Comments:**
> **username_1**: I've rewritten the title, as "big data" was completely irrelevant to the question at hand. Feel free to improve on its current version.  
> **username_0**: Thanks. This is a super title, but "big data" is not completely irrelevant because I guess that what Bloom has in mind is the idea that with computing power you can treat the heterogeneity of data, that is big data. You can use high-frequency and/or large-scale data, in combination with computing power, to identify the role of uncertainty on economic outcomes.  
> **username_0**: I substituted "will" for "did" in the title because it didn’t happen so much yet!  
> **username_2**: I think this is a really interesting question, but you should be specific in what you want to know. Phrases like, "Any thoughts on this?" are an invitation for broad discussion based answers which isn't what we'd like to generate. Could you narrow the scope a little bit and really get at what you'd like to know?  
> **username_2**: Also, could you point me to page or section where this is discussed? I looked for a few minutes but couldn't find it -- I'll have another look later, but I'm trying to understand why it would be a criticism of expected utility theory.  
> **username_0**: I updated my question based on your comments. Thansk @username_2.  

---

## 2 answers

### Answer by username_3 on 2015-12-02. Score: 5

This is perhaps a good opportunity to point out that the **"certainty equivalence"** concept means one thing in microeconomics/choice under uncertainty theory, while it means something different in macroeconomics.

**Microeconomics/choice under uncertainty**  
The Certainty Equivalent of a lottery/gamble, is the amount of wealth which, if given with certainty, provides the same utility as the lottery/gamble. See for example Jehle & Reny's "Advanced Microeconomic Theory" (2011, 3d ed.), p.113.

**Macroeconomics**  
"Certainty Equivalence" is the situation in a stochastic model, where optimal decision rules prove to be identical to those that would have been derived in a deterministic framework (see for example Lungqvist & Sargent's "Recursive Macroeconomic Theory" 2004, 2nd ed, p. 113-115). Informally, this is sometimes described as "agents behave as if the stochastic processes are not stochastic", or "the decision rule is not affected by stochastic variability".

It is a funny coincidence that both references treat the subject in the same page number...

The concepts are evidently linked by the "as if there was no uncertainty" angle, but they are different in essential aspects: the micro-concept is a "buy-out" of uncertainty, providing a certain alternative towards which the agent that faces the gamble is indifferent in terms of utility, while the macro-concept emerges as a property of the solution (and only under restrictive model structures, or linear approximations thereof).

> **Comments:**
> **username_4**: I'd like to note that in micro, the word is **equivalent**, indicating that this object is much more specific than the object/phenomenon referred to by **equivalence** `:)`  

---

### Answer by username_5 on 2015-12-02. Score: 2

Expected utility theory is based on valuing expectations. There is more to that than just uncertainty.

First, a risky investment is different from an uncertain investment. Risk is usually defined as future events occurring only with a **measurable probability**, while uncertainty is called upon when the likelihood of future events is **indefinite or incalculable**, but only estimated in itself (it's like a risk on risk). What I'm saying here is actually agreed upon by the author. Note that the first definition of expected utility models did not include any other considerations that risk. Part of the "risk premium" is... a risk premium, rather than an uncertainty premium, and shouldn't be modified by a better understanding of uncertainty.

Another part of the risk premium is the fact that it is usually set outside the micro-economic model, usually at the moment of raising capital. No due diligence can give an investor an "inside" view of the model, and so there will always be a cost of borrowing money, which is to be taken into account in a risk premium for any project that requires money over time.

What the article discusses seems more to me as a motivation to decrease the impact of uncertainty, and so the risk premium, rather than change the way we look at it. Being able to translate uncertainty into risk is great, but won't make risk itself disappear. For some projects so, it is likely to increase the risk premium as risks taken are better quantified, as uncertainty premium is meant to cover hidden/ unknown risk premium only on average.

> **Comments:**
> **username_0**: Thanks username_5 for your answer but I don't understand your last paragraph. Why do you mean exactly by "a motivation to decrease the impact of uncertainty"? Is there a section or a page in the paper that suggests this?  
> **username_5**: @username_0 it is a (perhaps too personal) deduction from pp164-165, which are saying a) the government use to have such a "risk-premium decrease policy", b) all apparently positive effects of uncertainty on investment are negligible because firms CEO are too tied with their own firms. My deduction was that the paper wants you to deduce that c) uncertainty has exaggerated impact on the economy, and its fluctuations are mostly self-induced, but if the "seems to me as" wasn't enough I can sure edit.  
> **username_0**: Yes please if you could edit the last paragraph that would be great because I still do not understand the sentence "a motivation to decrease the impact of uncertainty". Moreover, the pp. 164-165 are simply related to a review of the theory. This is not the main part of the paper.  

---

