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“Otaki model” is an overlapping generations (OLG) model with fiat money and imperfect competition. It derives Keynesian implications such as involuntary unemployment, welfare-improving fiscal and monetary policy, and money non-neutrality. Though its structure can be applied to other models with productive implications, the Otaki model has not been fully understood by economists. One reason could be that in seminal works about the Otaki model, he implicitly changed the hidden assumptions, and hence, the implications of the model. By employing such assumptions, he aimed at dealing with multiplicity of equilibria in the OLG model. This paper points out the hidden assumptions and reinterprets the Otaki model from the viewpoint of multiple equilibria.

Economist Masayuki Otaki passed away in July 2018. In recent years, he has built a notable Keynesian macroeconomic model that we call as “Otaki model.” Otaki model is an overlapping generations (OLG) model with fiat money and imperfect competition. It derives Keynesian implications such as involuntary unemployment, welfare-improving fiscal and monetary policy, and money non-neutrality. Though its structure can be applied to other models with productive implications, the “Otaki model” has not been fully understood by macroeconomists. This paper sheds lights on an unrecognized but important aspect of Otaki model for economists to understand and apply to other models.

From Otaki’s early career, he had attempted to build a macroeconomic model of dynamic general equilibrium that reflected a Keynesian view of economy. Otaki [

By the Way, The Otaki model has two main implications:

・ Fiscal policy that is financed by seigniorage improves economic welfare.

・ The core concept of Keynesian economics is not based on price rigidity or imperfect competition, but on non-neutrality of money.

The first implication is derived from the early Otaki model, while the second one is derived from the late Otaki model. From the next section, we emphasize the assumption change that can affect the model’s implications.

Mankiw [

The government purchases the firm’s product, and hence, increases the firm’s profit, because it exhibits imperfect competition. The profit is distributed to consumers, and increases the consumers’ income. Then, part of the increased income goes to consumption. Thus, the firm’s profit increases again, which is distributed to consumers and consumers’ income. This cycle continues infinitely.

However, the authors above found that fiscal policy (that is assumed to be a “waste of money” in the sense that does not directly contribute to the consumers’ utility) worsens economic welfare because the profit increase goes with the production increase. Further, the production increase goes with a labor supply increase, which in turn, decreases the consumers’ utility to some extent.

In addition to Mankiw [

・ Overlapping generations with fiat money.

・ Indivisible labor.

・ Imperfect competition.

The main difference between the Otaki model and Mankiw [

Otaki [

To highlight the discussions so far, we introduce a part of the structure of the early Otaki model1. The firm’s profit maximization problem gives

p t = W R 1 − η − 1 . (1)

Here p_{t} represents prices in period t, W^{R} is R reservation wage, and η the parameter. This can be regarded as markup principle. Reservation wage is determined by the labor supply of consumers, and hence, current and future price. So it can be rewritten as

P t = ( A − 1 β 1 − η − 1 ) 1 1 − α P t + 1 , (2)

where A, β , and α are the parameters. P t and P t + 1 are the current and

future price level. We find that the inflation rate ( P t + 1 P t ) is determined only in the

real economy. However, while the inflation rate is determined above, the price levels have not been determined yet. This is one representation of multiple equilibria problems. Multiple equilibria are the typical results in an OLG environment. To determine one equilibrium, additional assumptions are required, including the transversality condition and the interest rate condition. Also in the Otaki model, one more assumption is required. Otaki [

m t + 1 = M t P t ”. Here, m t + 1 is real money balance, M t is money supply. To see

that this is a hidden assumption, we review one equation in Otaki [

Y t P t = α Y t P t + ρ m t + 1 , (3)

here, Y t is output. We can see that real money balance affects Y t through the multiplier effect. The more real money balance (that increases fiscal policy) the government provides, the more output the economy produces. However, it is still undetermined whether the government can control m t + 1 or not. The policy variable is not m t + 1 , but M t . Controlling M_{t} would be equivalent to controlling m_{t}_{+1}, if P_{t} would be fixed. However, as we see in Equation (2), P_{t} is not undetermined because of multiple equilibria, therefore, P_{t} is not necessarily fixed. Then, controlling M_{t} is not equivalent to controlling m_{t}_{+1}. For example, if increasing M_{t} would be followed by increasing P_{t}, m_{t}_{+1} could not be controlled by the government. This is why “If government can arbitrarily control the real money balance m_{t}_{+1}” is an additional assumption.

Later, Professor Otaki seems to have recognized that it is an assumption, and additional assumption (one example is the assumption above) is required to solve the model. However, Is this an adequate and realistic assumption? If the

government can choose the cash balance ( M t P t ), is it equivalent to assuming

non-neutrality of money itself? It is clearly a strong assumption. In fact, seminal works including Otaki [

Professor Otaki recognized a hidden assumption, and sought other assumptions to pin down one of multiple equilibria. Then, he focused on the expectation formations since multiple equilibria are consistent with multiple expectation formations. Because each equilibrium arises from its rational expectation, each equilibrium has its specific expectation formation. In this sense, expectation formations can be considered assumptions of the model.

Otaki implicitly changed the assumption of the Otaki model. While the hidden assumption of the early Otaki model is that the government can control the real cash balance, which of the late Otaki model is that people have expectations that money supply does not affect the price level. Otaki called this assumption “credibility of money”. He substituted this assumption for the former one from 2011.

This new assumption implies that consumers do not care about money supply and monetary policy by the central bank, or do not believe that they affect the consumer goods’ prices they face in their daily lives. This may seem to be an irrational assumption from the perspective of neoclassical economics. However, Otaki proves that this expectation is rational, that is, in a particular equilibrium, this expectation comes true.

From 2011, the Otaki model and its variations, such as Otaki [

To observe this, suppose the money supply does not affect the price level.

Then, M t p t can be controlled at any level by the government’s choosing, M t .

Thus, the government decides on the real cash balance. In short, the assumption of “credibility of money” works similar to the assumption of the early Otaki model.

In 2011, the Otaki model’s assumption was implicitly changed from government control of real cash balance to money credibility expectation. This does not change the results of the early Otaki model, but alters its implications. The early Otaki model’s hidden assumption is ambiguous, and hence, he puts emphasis on the results themselves, that is, the multiplier effects arising from government expenditures improve economic welfare. In contrast, the late Otaki model has a meaningful assumption of credibility of money, and hence, he emphasizes both the assumptions and results. From 2011, Otaki insisted that the foundation of Keynesian economics is “credibility of money” or “neutrality of money”.

So far, we have known that the Otaki model has multiple equilibria; one assumption, the expectation of money credibility (money non-neutrality), leads to Keynesian equilibrium in this model. Then, it is natural to consider what the other assumption, the expectation of money neutrality, leads to in this model. Otaki [

・ Expectations of “credibility of money” result in non-neutrality of money and theory of effective demand (multiplier effect and 45-degree analysis).

・ Expectations of “quantity theory of money” result in neutrality of money.

In short, Otaki found another neoclassical equilibrium. In addition, Otaki [

proves the same results in a perfect competition environment. Thus, we can state that the competition conditions do not matter when determining which economy occurs: Keynesian or classical. In other words, imperfect competition and price rigidity are not the core concepts of Keynesian economics. According to Otaki, expectations determine which of the above two economies occur.

Here, we can summarize the implications of the late Otaki model and its variations.

・ Fiscal policy that is financed by seigniorage improves economic welfare.

・ The core concept of Keynesian economics is not price rigidity or imperfect competition, but non-neutrality of money.

Finally, we consider: is credibility of money truly relevant to other economic models or is it only applicable to the Otaki model? Otaki [

The early Otaki model [

An introduction to the Otaki model is difficult; the original article by Otaki [

The author declares no conflicts of interest regarding the publication of this paper.

Tamura, M. (2019) On Otaki’s Keynesian Macroeconomic Model. Theoretical Economics Letters, 9, 119-125. https://doi.org/10.4236/tel.2019.91010