<p>Basically the Lucas solution to SMD was the representative agent (which brought its own problems).</p>

<hr>

<p><a href="http://eprints.uwe.ac.uk/38198/1/1806-%20DSGE%20Models%20and%20the%20Lucas%20Critique%20%28WP%29.pdf" rel="nofollow noreferrer">Not everyone</a> agrees that microfounding solves/addresses the Lucas critique:</p>

<blockquote>
  <p>My claim is that the current debate about DSGE models and
  the Lucas Critique should be understood through a historical perspective—
  namely, through the development, during the 1980s and 1990s, of two rival
  interpretations of Lucas (1976). On the one hand, the RBC approach advocated for what I will call a “theoretical interpretation” of the Critique; on
  the other hand, Keynesians championed what I will call an “empirical interpretation” of the Critique. These interpretations were rival with respect
  to their assessment of the following proposition: do microfoundations imply
  parameters’ stability?</p>
  
  <p>[The] RBC approach argues that microfoundations do imply parameters’ stability. [...] Conversely, following the empirical interpretation of the Critique, Keynesians argue that microfoundations do not imply parameters’ stability. </p>
</blockquote>

<p>Now if you're asking about Lucas himself, he <a href="https://books.google.com/books?id=TBUqu6hiHLgC&amp;pg=PA133" rel="nofollow noreferrer">did apparently</a> see microfoundations as the/main answer, well apparently to everything that ailed macroeconomics:</p>

<blockquote>
  <p>The most interesting developments in macroeconomic theory seem to be
  describable as the reincorporation of aggregative problems such as inflation
  and the business cycle within the general framework of 'microeconomic'
  theory. <strong>If these developments succeed, the term 'macroeconomic' will simply
  disappear from use and the modifier 'micro' will become superfluous. We
  will simply speak, as did Smith, Ricardo, Marshall and Walras, of economic
  theory.</strong> If we are honest, we will have to face the fact that at any given time
  there will be phenomena that are well-understood from the point of view of
  the economic theory we have, and other phenomena that are not. We will be
  tempted, I am sure, to relieve the discomfort induced by discrepancies
  between theory and facts by saying that the ill-understood facts are the
  province of some other, different kind of economic theory. Keynesian
  'macroeconomics' was, I think, a surrender (under great duress) to this temptation.
  It led to the abandonment, for a class of problems of great importance,
  of the use of the only 'engine for the discovery of truth' that we have in
  economics. (Lucas 1987, pp. 107-8)</p>
</blockquote>

<p>However the Lucas research programme <a href="https://books.google.com/books?id=Cu_2FVrso44C&amp;pg=PA8" rel="nofollow noreferrer">was hardly without flaws</a>...</p>

<blockquote>
  <p>The theorems of Hugo Sonnenschein, Rolf
  Mantel and Gerard Debreu in the early 1970s established that the restrictions
  that generate well-behaved individual demand functions do not
  constrain aggregate demand functions to exhibit the same properties [...]. <strong>The new classicals sidestepped
  the problem of aggregation either by imagining an economy composed of
  identical individuals or by assuming that there is one individual who
  represents the whole economy, so that the solution to the optimization
  problem of this representative agent gives the aggregate relationships in that
  economy. In fact, they adopted the representative-agent model from the
  optimal-growth literature of the 1960s.</strong></p>
  
  <p><strong>Using such models, Lucas and others developed the characteristic conclusions
  of the new classical school, such as the ineffectiveness of monetary
  policy with respect to the real economy (see Hoover 1988). Policy ineffectiveness
  was widely regarded by Keynesians as a politically conservative
  conclusion.</strong> Initially, it was interpreted as a direct consequence of the
  rational-expectations hypothesis, which was then regarded as politically
  suspect. Later, economists came to see that the assumptions of flexible
  prices and perfect competition were the critical factors in the policy
  ineffectiveness proposition. Once a wedge had been driven between policy
  ineffectiveness and the assumption of rational expectations, the rational expectations
  hypothesis was accepted by a wider spectrum of macroeconomists
  [...]. New Keynesians found that rational
  expectations did not rule out an important role for the government in
  stabilizing the economy.</p>
</blockquote>

<p>In other words, in order to side-step SMD you can assume the representative agent and "microfound" on that, but that can give you worse headaches in terms of conclusions.</p>

<blockquote>
  <p>The hegemonic claims of microfoundations are most often justified with
  reference to the sort of problems highlighted by the Lucas critique. But
  what justifies the hegemony of the representative agent? Mainstream macroeconomists
  are rarely explicit on this question; but, implicitly, the argument
  seems to be that the assumption of a representative, optimizing, agent
  is mainly technical – both a compromise between the ambitions and the
  computational capacities of the macroeconomist and a convenient way to
  introduce a welfare measure for the evaluation of economic policy. The
  implicit argument is what Hoover refers to as “eschatological justification”:
  “the representative-agent model is but the starting point for a series of fuller
  and richer models that eventually will provide the basis for an adequate
  macromodel, and that, therefore, the current generation of models is
  entitled to credence” (Hoover 2006: 146 [...]</p>
  
  <p>The
  representative-agent program elevates the claims of microeconomics in
  some version or other to the utmost importance, while at the same time not
  acknowledging that the very microeconomic theory it privileges undermines,
  in the guise of the Sonnenschein–Debreu–Mantel theorem, the
  likelihood that the utility function of the representative agent will be any
  direct analogue of a plausible utility function for an individual agent.
  Kirman’s (1992) survey article on the representative agent, which highlights
  the lack of analogy, is well-cited; yet, it is striking that almost all of the
  citations are by critics of the representative-agent program; there is little
  evidence that advocates have even noticed the argument against their
  approach.</p>
</blockquote>

<p>Solow was one of the critics of the representative-agent approach. In response:</p>

<blockquote>
  <p>Chari and Kehoe responded to the criticisms by
  Solow that they considered of substance. They recognize that the challenges
  facing modern macroeconomics are not small, but reject Solow’s
  criticisms to the use of a representative agent and to their claim that
  macroeconomics is now firmly grounded in economic theory. With respect
  to the representative agent hypothesis, Chari and Kehoe (2008: 247) state
  that modern macroeconomics does not end with such hypothesis, and in
  fact it does not end “too far from where Solow prefers”: “Most of macroeconomic
  research over the last 20 years has precisely been about incorporating
  the heterogeneity and the rich interactions that Solow seems to think
  it needs.” They argue that macroeconomists just start with a representative
  agent and then enrich the model “with the detail necessary to answer the
  question at hand” (p. 248). They also criticize Solow for his use in his
  growth papers of a single production function with aggregate labor and
  stock of capital, with which he “sacrificed realism for an abstraction that
  has proven invaluable” (p. 247)</p>
</blockquote>

<p>The more recent works cited there:</p>

<blockquote>
  <ul>
  <li><p>Solow, Robert M. (2008). The State of Macroeconomics. Journal of Economic
  Perspectives, 22 (1):243–6</p></li>
  <li><p>Chari, V. V., and Patrick J. Kehoe (2006). Modern Macroeconomics in Practice:
  How Theory Is Shaping Policy. Journal of Economic Perspectives, 20 (4):3–28.</p></li>
  <li><p>Chari, V. V., and Patrick J. Kehoe (2008). Response from V. V. Chari and Patrick J.
  Kehoe. Journal of Economic Perspectives, 22 (1):247–9.</p></li>
  </ul>
</blockquote>

<p>Also, the representative-agent approach has pretty much become identified with DGSE:</p>

<blockquote>
  <p>All the different views mainstream macroeconomists have about the state
  of their field and about possible areas of improvement should not diminish
  the degree to which they converged methodologically in studying fluctuations.
  They all analyse such phenomena usually through a dynamic stochastic
  general equilibrium model with a representative agent, firmly
  grounded on microeconomic principles. Moreover, several of them agree
  with Chari (2010: 2) that “any interesting model must be a dynamic
  stochastic general equilibrium model. From this perspective, there is no
  other game in town.” Therefore, he continues, “a useful aphorism in
  macroeconomics is: ‘If you have an interesting and coherent story to tell,
  you can tell it in a DSGE model. If you cannot, your story is incoherent.’”</p>
</blockquote>

<p>See <a href="https://economics.stackexchange.com/questions/29342/what-is-the-appeal-of-dsge-models/29346">What is the appeal of DSGE models?</a> for further on DGSE's success story.</p>

<p>But of course there comes <a href="https://www.ofce.sciences-po.fr/pdf/dtravail/WP2016-11.pdf" rel="nofollow noreferrer">the (nearly standard now, post-2008) critique</a>:</p>

<blockquote>
  <p>The representative-agent (RA) assumption prevent DSGE models to address distributional
  issues, which are one of the major cause of the Great Recession and they are fundamental for
  studying the effects of policies. [...]</p>
  
  <p>The RA assumption coupled with the implicit presence of a Walrasian auctioneer, which
  sets prices before exchanges take place, rule out almost by definition the possibility of interactions carried out by heterogeneous individuals. This prevents DSGE model to accurately study
  the dynamics of credit and financial markets. Indeed, the assumption that the representative
  agent always satisfies the transversality condition, removes the default risk from DSGE models
  (Goodhart, 2009). As a consequence, agents face the same interest rate (no risk premia) and
  all transactions can be undertaken in capital markets without the need of banks. The abstraction from default risks does not allow DSGE models to contemplate the conflict between
  price and financial stability that Central Banks always face (Howitt, 2011): they just care about
  the nth-order distortions caused by price misallignments which can eventually result in inflation
  without considering the huge costs of financial crisis (Stiglitz, 2011, 2015). No surprise that
  DSGE models work fine in normal time but they are unequipped not only to forecast but also
  to explain the current crisis (Goodhart, 2009; Krugman, 2011)</p>
</blockquote>

<p>There is a bit <a href="https://economics.stackexchange.com/a/329/6210">more subtlety to RA</a> than what I've covered here; RA can include some sources of parametric heterogeneity but assumes a sort of "structural" homogeneity, if I understand that correctly.</p>

CC BY-SA 4.0
2019-05-19T18:09:25.870Z
Thanks again for the detailed explanation and helpful material.
Iván
CC BY-SA 4.0
2019-05-18T16:05:32.807Z
2019-05-19T07:12:59.143Z
2019-05-19T07:12:59.143Z
fantastic peace and prosperity
<p>I think that one solution to Lucas' critique is to micro-found your econometric model, but his critique is broader. I think it means that if you don't consider seriously that agents are optimizing, you may assume that some parameters will be invariant to policy changes, when they may not be. If SMD states that when looking at aggregate data, some properties of individual agent models do not follow, then this can be reflected in your econometric model so that your model is still not assuming some parameters to be policy invariant when they are not. I don't really see any tension between these two.</p>

CC BY-SA 4.0
2019-05-18T22:38:23.813Z
Let's say I want to estimate the parameters of the aggregate demand. Lucas critique says I must microfound, ok, I do it, but SMD implies that if I take individual demands and then aggregate demand is not well behaved. Then if I continue estimating I won't estimate a well behaved demand.
Iván
CC BY-SA 4.0
2019-05-18T14:49:17.223Z
2019-05-18T14:49:17.223Z
Regio
<p>One of the consequences of Lucas' critique is that models must be microfounded. On the other side, Sonnenschein-Mantel-Debreu (SMD) theorem claims that microfoundation doesn't have any repercussion on aggregate economics. Then what does Lucas says about SMD? is there a counterargument to SMD? are there any additional conditions at the micro level to generate nice behaved aggregate demand?</p>

CC BY-SA 4.0
2019-05-19T04:18:46.870Z
By "what does Lucas says" do you mean himself or this critique as interpreted by others?
fantastic peace and prosperity
CC BY-SA 4.0
2019-05-19T04:38:05.813Z
The second (or main?) part of your question (on SMD) has been asked here before https://economics.stackexchange.com/questions/3033/the-sonnenschein-mantel-debreu-results-what-are-the-implications-for-macroecono Althoug the answers leave something to be desired (as in references).
fantastic peace and prosperity
<macroeconomics><microeconomics><general-equilibrium>
SMD and Lucas critique
Iván
# SMD and Lucas critique

(Asked by: username_0 on 2019-05-18)

One of the consequences of Lucas' critique is that models must be microfounded. On the other side, Sonnenschein-Mantel-Debreu (SMD) theorem claims that microfoundation doesn't have any repercussion on aggregate economics. Then what does Lucas says about SMD? is there a counterargument to SMD? are there any additional conditions at the micro level to generate nice behaved aggregate demand?

**Tags:** macroeconomics, microeconomics, general-equilibrium

> **Comments:**
> **username_1**: By "what does Lucas says" do you mean himself or this critique as interpreted by others?  
> **username_1**: The second (or main?) part of your question (on SMD) has been asked here before https://economics.stackexchange.com/questions/3033/the-sonnenschein-mantel-debreu-results-what-are-the-implications-for-macroecono Althoug the answers leave something to be desired (as in references).  

---

## 2 answers

### Answer by username_1 on 2019-05-18. Score: 2 | Accepted answer

Basically the Lucas solution to SMD was the representative agent (which brought its own problems).

---

[Not everyone](http://eprints.uwe.ac.uk/38198/1/1806-%20DSGE%20Models%20and%20the%20Lucas%20Critique%20%28WP%29.pdf) agrees that microfounding solves/addresses the Lucas critique:

> My claim is that the current debate about DSGE models and
> the Lucas Critique should be understood through a historical perspective—
> namely, through the development, during the 1980s and 1990s, of two rival
> interpretations of Lucas (1976). On the one hand, the RBC approach advocated for what I will call a “theoretical interpretation” of the Critique; on
> the other hand, Keynesians championed what I will call an “empirical interpretation” of the Critique. These interpretations were rival with respect
> to their assessment of the following proposition: do microfoundations imply
> parameters’ stability?
>
> [The] RBC approach argues that microfoundations do imply parameters’ stability. [...] Conversely, following the empirical interpretation of the Critique, Keynesians argue that microfoundations do not imply parameters’ stability.

Now if you're asking about Lucas himself, he [did apparently](https://books.google.com/books?id=TBUqu6hiHLgC&pg=PA133) see microfoundations as the/main answer, well apparently to everything that ailed macroeconomics:

> The most interesting developments in macroeconomic theory seem to be
> describable as the reincorporation of aggregative problems such as inflation
> and the business cycle within the general framework of 'microeconomic'
> theory. **If these developments succeed, the term 'macroeconomic' will simply
> disappear from use and the modifier 'micro' will become superfluous. We
> will simply speak, as did Smith, Ricardo, Marshall and Walras, of economic
> theory.** If we are honest, we will have to face the fact that at any given time
> there will be phenomena that are well-understood from the point of view of
> the economic theory we have, and other phenomena that are not. We will be
> tempted, I am sure, to relieve the discomfort induced by discrepancies
> between theory and facts by saying that the ill-understood facts are the
> province of some other, different kind of economic theory. Keynesian
> 'macroeconomics' was, I think, a surrender (under great duress) to this temptation.
> It led to the abandonment, for a class of problems of great importance,
> of the use of the only 'engine for the discovery of truth' that we have in
> economics. (Lucas 1987, pp. 107-8)

However the Lucas research programme [was hardly without flaws](https://books.google.com/books?id=Cu_2FVrso44C&pg=PA8)...

> The theorems of Hugo Sonnenschein, Rolf
> Mantel and Gerard Debreu in the early 1970s established that the restrictions
> that generate well-behaved individual demand functions do not
> constrain aggregate demand functions to exhibit the same properties [...]. **The new classicals sidestepped
> the problem of aggregation either by imagining an economy composed of
> identical individuals or by assuming that there is one individual who
> represents the whole economy, so that the solution to the optimization
> problem of this representative agent gives the aggregate relationships in that
> economy. In fact, they adopted the representative-agent model from the
> optimal-growth literature of the 1960s.**
>
> **Using such models, Lucas and others developed the characteristic conclusions
> of the new classical school, such as the ineffectiveness of monetary
> policy with respect to the real economy (see Hoover 1988). Policy ineffectiveness
> was widely regarded by Keynesians as a politically conservative
> conclusion.** Initially, it was interpreted as a direct consequence of the
> rational-expectations hypothesis, which was then regarded as politically
> suspect. Later, economists came to see that the assumptions of flexible
> prices and perfect competition were the critical factors in the policy
> ineffectiveness proposition. Once a wedge had been driven between policy
> ineffectiveness and the assumption of rational expectations, the rational expectations
> hypothesis was accepted by a wider spectrum of macroeconomists
> [...]. New Keynesians found that rational
> expectations did not rule out an important role for the government in
> stabilizing the economy.

In other words, in order to side-step SMD you can assume the representative agent and "microfound" on that, but that can give you worse headaches in terms of conclusions.

> The hegemonic claims of microfoundations are most often justified with
> reference to the sort of problems highlighted by the Lucas critique. But
> what justifies the hegemony of the representative agent? Mainstream macroeconomists
> are rarely explicit on this question; but, implicitly, the argument
> seems to be that the assumption of a representative, optimizing, agent
> is mainly technical – both a compromise between the ambitions and the
> computational capacities of the macroeconomist and a convenient way to
> introduce a welfare measure for the evaluation of economic policy. The
> implicit argument is what Hoover refers to as “eschatological justification”:
> “the representative-agent model is but the starting point for a series of fuller
> and richer models that eventually will provide the basis for an adequate
> macromodel, and that, therefore, the current generation of models is
> entitled to credence” (Hoover 2006: 146 [...]
>
> The
> representative-agent program elevates the claims of microeconomics in
> some version or other to the utmost importance, while at the same time not
> acknowledging that the very microeconomic theory it privileges undermines,
> in the guise of the Sonnenschein–Debreu–Mantel theorem, the
> likelihood that the utility function of the representative agent will be any
> direct analogue of a plausible utility function for an individual agent.
> Kirman’s (1992) survey article on the representative agent, which highlights
> the lack of analogy, is well-cited; yet, it is striking that almost all of the
> citations are by critics of the representative-agent program; there is little
> evidence that advocates have even noticed the argument against their
> approach.

Solow was one of the critics of the representative-agent approach. In response:

> Chari and Kehoe responded to the criticisms by
> Solow that they considered of substance. They recognize that the challenges
> facing modern macroeconomics are not small, but reject Solow’s
> criticisms to the use of a representative agent and to their claim that
> macroeconomics is now firmly grounded in economic theory. With respect
> to the representative agent hypothesis, Chari and Kehoe (2008: 247) state
> that modern macroeconomics does not end with such hypothesis, and in
> fact it does not end “too far from where Solow prefers”: “Most of macroeconomic
> research over the last 20 years has precisely been about incorporating
> the heterogeneity and the rich interactions that Solow seems to think
> it needs.” They argue that macroeconomists just start with a representative
> agent and then enrich the model “with the detail necessary to answer the
> question at hand” (p. 248). They also criticize Solow for his use in his
> growth papers of a single production function with aggregate labor and
> stock of capital, with which he “sacrificed realism for an abstraction that
> has proven invaluable” (p. 247)

The more recent works cited there:

> * Solow, Robert M. (2008). The State of Macroeconomics. Journal of Economic
>   Perspectives, 22 (1):243–6
> * Chari, V. V., and Patrick J. Kehoe (2006). Modern Macroeconomics in Practice:
>   How Theory Is Shaping Policy. Journal of Economic Perspectives, 20 (4):3–28.
> * Chari, V. V., and Patrick J. Kehoe (2008). Response from V. V. Chari and Patrick J.
>   Kehoe. Journal of Economic Perspectives, 22 (1):247–9.

Also, the representative-agent approach has pretty much become identified with DGSE:

> All the different views mainstream macroeconomists have about the state
> of their field and about possible areas of improvement should not diminish
> the degree to which they converged methodologically in studying fluctuations.
> They all analyse such phenomena usually through a dynamic stochastic
> general equilibrium model with a representative agent, firmly
> grounded on microeconomic principles. Moreover, several of them agree
> with Chari (2010: 2) that “any interesting model must be a dynamic
> stochastic general equilibrium model. From this perspective, there is no
> other game in town.” Therefore, he continues, “a useful aphorism in
> macroeconomics is: ‘If you have an interesting and coherent story to tell,
> you can tell it in a DSGE model. If you cannot, your story is incoherent.’”

See [What is the appeal of DSGE models?](https://economics.stackexchange.com/questions/29342/what-is-the-appeal-of-dsge-models/29346) for further on DGSE's success story.

But of course there comes [the (nearly standard now, post-2008) critique](https://www.ofce.sciences-po.fr/pdf/dtravail/WP2016-11.pdf):

> The representative-agent (RA) assumption prevent DSGE models to address distributional
> issues, which are one of the major cause of the Great Recession and they are fundamental for
> studying the effects of policies. [...]
>
> The RA assumption coupled with the implicit presence of a Walrasian auctioneer, which
> sets prices before exchanges take place, rule out almost by definition the possibility of interactions carried out by heterogeneous individuals. This prevents DSGE model to accurately study
> the dynamics of credit and financial markets. Indeed, the assumption that the representative
> agent always satisfies the transversality condition, removes the default risk from DSGE models
> (Goodhart, 2009). As a consequence, agents face the same interest rate (no risk premia) and
> all transactions can be undertaken in capital markets without the need of banks. The abstraction from default risks does not allow DSGE models to contemplate the conflict between
> price and financial stability that Central Banks always face (Howitt, 2011): they just care about
> the nth-order distortions caused by price misallignments which can eventually result in inflation
> without considering the huge costs of financial crisis (Stiglitz, 2011, 2015). No surprise that
> DSGE models work fine in normal time but they are unequipped not only to forecast but also
> to explain the current crisis (Goodhart, 2009; Krugman, 2011)

There is a bit [more subtlety to RA](https://economics.stackexchange.com/a/329/6210) than what I've covered here; RA can include some sources of parametric heterogeneity but assumes a sort of "structural" homogeneity, if I understand that correctly.

> **Comments:**
> **username_0**: Thanks again for the detailed explanation and helpful material.  

---

### Answer by username_2 on 2019-05-18. Score: 0

I think that one solution to Lucas' critique is to micro-found your econometric model, but his critique is broader. I think it means that if you don't consider seriously that agents are optimizing, you may assume that some parameters will be invariant to policy changes, when they may not be. If SMD states that when looking at aggregate data, some properties of individual agent models do not follow, then this can be reflected in your econometric model so that your model is still not assuming some parameters to be policy invariant when they are not. I don't really see any tension between these two.

> **Comments:**
> **username_0**: Let's say I want to estimate the parameters of the aggregate demand. Lucas critique says I must microfound, ok, I do it, but SMD implies that if I take individual demands and then aggregate demand is not well behaved. Then if I continue estimating I won't estimate a well behaved demand.  

---

