Kobayashi-sensei's Economic Research Picks

Part Six: Information Propagation in the Macroeconomy - Is it not possible to integrally understand asset bubbles and rigidity in wages and prices?

Faculty Fellow

Econo-kun is in his second year of the master's program at a private university, studying hard to become an economist.

Kobayashi Keiichiro's photoKOBAYASHI Keiichiro: This time, instead of taking up a single research paper, I would like to examine information propagation in the macroeconomy and introduce three noteworthy papers on the theme.

An asset bubble, a phenomenon in which land and other asset prices deviate upward from their real earnings or intrinsic value, and nominal rigidity, a phenomenon in which nominal prices and wage remain unchanged despite changes in the real value of goods and labor, are similar in the sense that prices deviate from the actual state of the economy. However, the theoretical structure of macroeconomics, as it stands today, does not allow for understanding these two phenomena within the same framework.

The data reveals interesting commonalities (or what appear to be commonalities) between changes in asset prices and changes in general prices. Nakajima (2003) showed that expectations on the future total factor productivity (TFP) growth rate must be "adaptive expectation" based on past productivity growth in order to properly explain fluctuations in land prices in Japan. With respect to general prices, theoretical models best fit the data observed in reality when the expected inflation rate is assumed to represent adaptive expectations based on past inflation rates.

To integrally understand all these phenomena, we can consider the following research theme: Is it not possible to consider a mechanism for generating asset bubbles and nominal rigidity by explicitly treating problems concerning information propagation and financial constraints in the macroeconomic system? (or: Is it not possible to consider a mechanism in which a certain "adaptive expectations model" can be derived as a reduced-form model concerning asset bubbles and nominal rigidity by examining problems concerning financial constraints and information propagation within the framework of rational expectations models?)

Econo-kun's photoEcono-kun: What sort of mechanisms can we think of?

Kobayashi Keiichiro's photoKOBAYASHI Keiichiro: As shown, albeit incompletely, in Kobayashi and Inaba (2005), we can consider a case in which firms receive "private signals" about the productivity of the land they own in an economy where land is used as collateral. If the private signals suggest lower land productivity in the future, how do the firms behave in response? If they disclose this prospect of decreasing land productivity, the collateral value of the land will decrease, making it difficult for the firms to obtain loans. Naturally, each firm will try to hide from others any private signal indicating lower productivity. Therefore, even when many pieces of private information indicate that land productivity is unlikely to increase in the future, this information is kept private within each firm, and the only information about land productivity circulated throughout the economy is optimistic. The result is a tendency toward bubble-like, inflated land prices.

In the meantime, the cost of hiding private signals gradually rises. And once firms realize that the cost exceeds the benefit, they suddenly reveal their private signals to the whole economy and the bubble bursts. Under the assumption that the cost of hiding private information is incurred in the form of excessive capital investment, Kobayashi and Inaba (2005) attempted to formulate, though incompletely, a model describing a bubble-bursting mechanism, wherein the burden of overinvestment becomes so large it exceeds the present value of future profits, and firms cease making excessive investment and reveal their private information, which triggers the burst of the bubble.

The downward rigidity in wages (probably real wages) might be explained by applying a similar mechanism to wage contracts between firms and their employees. For instance, we can consider a mechanism in which employees, who have certain private signals about their labor productivity, try to hide that information from their employers, thus only optimistic information about labor productivity circulates throughout the economy, resulting in upward pressure on wages.

Econo-kun's photoEcono-kun: Have there been any theoretical studies that are likely to lead to the themes you have just explained?

Kobayashi Keiichiro's photoKOBAYASHI Keiichiro: Many research papers have been written about information propagation in the macroeconomy and, in terms of the likelihood of leading to the specific themes I have discussed, I would point to three areas of theoretical research:

1) "imperfect common knowledge" and "iterated expectations"
2) "herd behavior" or "information trap"
3) "global game" and its development

Among these, 2) herd behavior is closest to the thinking in Kobayashi and Inaba (2005) mentioned above; combining this theory with certain elements of 1) imperfect common knowledge, may produce interesting findings about price rigidity. Also, it may be possible to link 3) global game to 1) and 2) by considering a global game model with two different kinds of agents, instead of one kind of agent as generally assumed.

Econo-kun's photoEcono-kun: Could you briefly explain each of these theoretical approaches?

Kobayashi Keiichiro's photoKOBAYASHI Keiichiro: Let me explain in the order listed above.

1. Imperfect Common Knowledge and Iterated Expectations

Revived as a theory for explaining nominal price rigidity by information imperfections is the one assuming imperfect common knowledge. (This theory, first developed by Edmund Phelps, winner of the 2006 Nobel Prize in Economics, and others in the 1970s, has been revived and a series of research studies are underway to further refine it.)

A typical example of such research studies is:

Amato, J. D. and H. S. Shin (2006), "Imperfect Common Knowledge and the Information Value of Prices," Economic Theory, 27: 213-241.

Others include: Ui (2003), Chwe (1998), and Morris and Shin (2006)

These studies show that price rigidity emerges from the fact that iterated expectations, in the presence of imperfect common knowledge, are not reduced to a single expectation.

Consider a situation where common knowledge shared by an entire economy is imperfect because each person has private information. Where X is a random variable, E_i(X) represents the expectation of an agent i with respect to the value of X. In the presence of imperfect common knowledge, E_i(X) does not equal E_j(X). When E(X) = (1/N) Σ_i E_i(X) is defined as the sample average of the E_i(X) values, E(X) does not equal E(E(X)). (When there is perfect common knowledge, E(X) = E(E(X)), that is, iterated expectations are reduced to a single expectation.)

Assume that a firm i is engaged in Stiglitz-Dixit type monopolistic competition, and describe the pricing strategy of the firm i as q_i = (1-w)E_i(q)+wE_i(z), in which q and z respectively represent the general price level and economic fundamentals while w is a parameter (the economy is more competitive when the value of w is closer to zero). The sample average of this function can be described as q = (1-w)E(q)+wE(z). When E0(X) = E(X) and Ek(X) = E(Ek-1(X)), this function can be written as follows:

q=Σw(1-w)k-1 Ek(z)

When w→0, the weights on higher-order beliefs (i.e., Ek(z)) increase. Meanwhile, when k→∞, Ek(z)→μ (in which μ is the expectation of z calculated based on public information). Therefore, the more competitive the economy, the less reflective q is of z which represents economic fundamentals, and the closer it is to μ which represents the least precise expectation. This can be deemed as one mechanism of generating price rigidities.

Studies in this field deal with cases involving only one type of agents (e.g. firms competing under monopolistic competition). It would be interesting to consider the possible implications of these theories of imperfect common knowledge and iterated expectations when two or more different types of agents with conflicting interests (e.g. firms and employees; banks and firms) are involved.

2. Herd Behavior or Information Trap

Assume an economy where private information is given gradually and individually to agents and each agent is to infer the private information received by others by observing their behavior (investment decisions, etc.). When placed in a certain situation, uninformed agents begin to act en masse without waiting for more information. This phenomenon is called herd behavior (particularly when the behavior is socially inefficient by some standards).

Literature addressing this phenomenon includes:

Chari, V. V. and P.J. Kehoe, (2003), "Financial Crises as Herds: Overturning the Critiques," NBER Working Paper 9658.

"Common knowledge" evolves as uninformed agents infer the private information given to a certain agent by observing that agent's behavior; thus inferred information accumulates. Since one piece of private information is to be given to one agent at one date (or time), the longer an agent waits, the greater the accuracy of common knowledge. At the same time, however, the benefit from acting (in terms of present discounted value) is decreased by waiting longer. Because of this trade-off, all agents suddenly stop waiting and take action when faced with a certain situation.

In investment decision models developed by Chari et al., k is provided as an integer equal to the balance between the number of dates in the past, in each of which an investment was implemented and the number of dates in each of which no investment was implemented. When k = 1 or k > 1, all agents are to make investments; when k = 0 or k = -1, uninformed agents are to wait and change their k based on their observation of the behavior of informed agents; when k = -2 or k < -2, all uninformed agents choose to never invest.

The model is the same as that of Kobayashi and Inaba (2005) in that common knowledge is to be inferred by observing the behavior of informed agents. But Chari et al. did not incorporate a mechanism to account for informed agents' propensity to hide their private information. Consideration of what would happen when each agent tries to hide private information may result in interesting findings.

The information structure assumed in Avery and Zemsky (1998) may be more closely related what concerns us here. According to their definition, herd behavior is a phenomenon in which informed agents act in line with the trend even contrary to their respective private information. This is similar to the definition of firm behavior in Kobayashi and Inaba (2005).

3. Global Game and its Development

In the herd behavior models developed by Chari et al., one piece of private information is given to one agent at one time and the other agents infer that private information by observing the behavior of that agent. In contrast, global game models assume that private information is given to all agents at one time and each agent acts based on that information, which aggregates into major macroeconomic changes (regime changes such as bank runs and currency crises). In global game models, individual agents decide their own behavior, while expecting that changes in their behavior will result in a major regime change; this is where "higher-order beliefs" come into play.

The following paper has been drawing attention in this field of studies:

Angeletos, G.-M., I. Werning (2004), "Crises and Prices: Information Aggregation, Multiplicity and Volatility," NBER Working Paper 11015.

Some global models, such as that of Morris and Shin (1998), assume that both common knowledge and private information are given exogenously. Under this setting, equilibrium is uniquely determined. Meanwhile, Angeletos and Werning incorporated a financial asset, the price of which is observable from each agent, into their global game model. The price of the asset is determined in the market (through the aggregate interaction of behavioral responses of individual agents). That is, the asset price as common knowledge is endogenously determined by aggregating private information. This is where Angeletos-Werning model differs from the original global game model of Morris and Shin (1998) in which common knowledge is an exogenous variable.

This difference also affects the nature of the equilibrium; Angeletos-Werning model demonstrates the existence of multiple equilibria (one with the equilibrium asset price at a high level and another with the equilibrium asset price at a lower level, i.e., an equilibrium in which a regime change is hardly probable and one in which it is highly probable).

As a model that deals with regime change, global games have been often applied to various phenomena in developing countries, such as bank runs and currency crises. These models of regime change, though not very convenient for analyzing price rigidities, nevertheless offer some important implications concerning the aggregation of private information.

As stated in 1 above, we can consider a two-party global game, as a new model based on global games, involving two heterogeneous groups of players (e.g., borrowers and lenders; employees and firms) with each group engaged in different types of actions. For instance, assume that borrowers make "capital investments" and lenders "appraise the value" of collateral assets pledged by borrowers (and lend them money). The lenders infer changes in economic fundamentals (borrowers' productivity) by observing the overall behavior of borrowers and, based on these inferences, decide their own actions. Borrowers base their actions on private information concerning their own productivity and the overall behavior of lenders that they observe. Also, it is assumed that each group depends on the actions of the other group for the payoff of its own actions.

If we can find in this model an equilibrium path where informed agents wait some time before revealing their private information, it means that we have developed a model that explains the mechanism of an asset bubble by attributing the phenomenon to a sort of information trap.

October 23, 2006
  • Avery, C. and P. Zemsky (1998) "Multidimensional Uncertainty and Herd Behavior in Financial Markets," American Economic Review 88(4): 724-748.
  • Chwe, M. S.-Y. (1999). "The reeded edge and the Phillips Curve: Money Neutrality, Common Knowledge, and Subjective Beliefs," Journal of Economic Theory 87: 49-71.
  • Kobayashi, K., and Masaru Inaba (2005). "'Irrational Exuberance' in the Pigou cycle under collateral constraints." RIETI Discussion Paper 06-E-015.
  • Morris, S. and H. S. Shin (2006) "Inertia of Forward-Looking Expectations," American Economic Review 96(2): 152-157.
  • Morris, S. and H. S. Shin (1998) "Unique Equilibrium in a Model of Self-Fulfilling Currency Attacks," American Economic Review 88(3): 587-597.
  • Nakajima, T. (2003) "Asset Price Fluctuations in Japan: 1980-2000," Working Paper, Kyoto University
  • Ui, T. (2003) "A Note on the Lucas Model: Iterated Expectations and the Neutrality of Money," unpublished manuscript, Yokohama National University

October 23, 2006

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