Ebook Financial Implications of Models with Indeterminacy and Variable Capacity Utilization
Starting with the pioneering work of Benhabib and Farmer and Farmer and Guo, a large body of literature has developed in which Real Business Cycle (RBC) models, modified to include increasing returns to scale in production, can result in a continuum of equilibria indexed by agents’ expectations. Models with multiple equilibria successfully replicate essential macroeconomic features of the business cycle. In this regard, these models are similar to the neoclassical RBC model. Prior research has shown that the standard RBC model fails when confronted with the financial market data. In this paper, we examine the asset pricing implications of a model with indeterminacy. To our knowledge, this study is the first to undertake such an analysis.
While fluctuations in the standard RBC model are driven by technology shocks, in our model it is agents’ expectations that cause business cycles. Since financial markets are theorized to be driven, at least in part, by agents’ expectations, one might expect that this model would reflect well the behavior of such markets. If such an improvement is found, it would enhance support for the use of models with self-fulfilling expectations over traditional RBC models without indeterminacy.
In early versions of one-sector models with indeterminacy of equilibria, including Farmer and Guo, the size of increasing returns to scale required for indeterminacy is much higher than empirical estimates suggest. The following example illustrates: Suppose that agents expect the return on capital to increase next period. They will react by increasing next period’s capital stock. Only with very high increasing returns to scale (around 1.5) will the marginal product of capital be increasing in capital and therefore will the expectation be fulfilled.
An alternative specification of the one-sector model, which exhibits indeterminacy with moderate increasing returns to scale (about 1.1), is found in Wen. The model incorporates variable utilization of capital and is very successful in summarizing the key stylized macroeconomic facts. In two-sector versions (see for example Benhabib and Farmer and Harrison), the required returns to scale are also within an empirically acceptable range (about 1.1, which is well within the range of plausibility for sector specific returns in Harrison), as the shifting of resources between sectors affects the relative price of capital, boosting the return on capital. However, also as a result of the increased factor mobility, countercyclical consumption results as agents shift resources into the highly productive investment sector.
While our focus in this research is on financial returns in the context of self-fulfilling expectations, we wish to select an empirically plausible model with adequate macroeconomic performance as a vehicle for our study. We therefore use Wen’s model as the benchmark in our exploration of the financial implications of models with multiple equilibria.
Taking the benchmark model to the financial data, we find an equity premium of 0.09 of one percent. This is 150 times higher than that produced by the standard RBC model; but it is negligible when compared with the equity premium in U.S. data. The risk-free rate is 4.1 percent, which is similar to the risk free-rate generated by traditional RBC models and is much higher than its empirical counterpart. In addition, returns on financial assets, especially the return on equity, do not exhibit realistic volatility. Our results show that although the model with self-fulfilling expectations marginally improves on the financial market performance of models without indeterminacy, this improvement is insufficient to judge it a success on this front.
The question arises whether the poor asset pricing results of the bench-mark model can be improved with modifications which alleviated or resolved financial puzzles in the RBC model. For example, Jermann incorporates habit formation and adjustment costs into a production economy with inelastic labor supply. With these additions, his model is able to match first moments of asset returns and the volatility of the return on equity, but the volatility of the risk-free rate is exaggerated. Avalos combines habit formation with other kinds of adjustment costs, such as time to build or time to plan, and generates a time series of artificial asset returns which replicates the expected returns in the U.S. data but significantly overstates their volatility. Boldrin, Christiano and Fisher introduce habit persistence into a two-sector model with limited capital and labor mobility and obtain similar results.
The combination of habit persistence and capital adjustment costs resolves the asset pricing puzzles in production economies because the agent whose preferences display habit persistence is eager to avoid fluctuations in his consumption level. When frictions such as adjustment costs are present, the equity security becomes an unattractive instrument for consumption smoothing relative to the risk-free asset. As a result, the agent requires a higher return for holding equity and accepts a lower return on bonds. On the other hand, adjustment costs prevent the instantaneous response of the capital stock to exogenous shocks and therefore increase the volatility of the return on equity.
We therefore modify the benchmark model, introducing adjustment costs, habit formation and the combination thereof. First, we need to ensure that these modifications are consistent with indeterminacy in the models. Kim and Wen find that incorporating adjustment costs into the one-sector model without capacity utilization rules out indeterminacy at any realistic value of increasing returns. Our results show that the addition of habit formation, adjustment costs, or both to the benchmark model with variable utilization of the capital stock has negligible effect on the size of returns to scale necessary for indeterminacy. We therefore calibrate and simulate each of the models and compare their macroeconomic and financial properties.
As expected, the proposed modifications do not compromise the macroeconomic performance of the benchmark model. The financial implications, however, are more surprising. Our results show that unlike in traditional RBC models, the inclusion of habit persistence and adjustment costs does not help in matching the stylized asset pricing facts. We attribute this failure to the following tension: For swings in optimism and pessimism to translate into corresponding movements in economic activity there must be enough flexibility in the model economy to allow agents to act on their expecta-tions. In our benchmark model the variable capacity utilization plays this role. This flexibility negates the effect of adjustment costs, allowing agents to smooth their consumption to the desired level.
We therefore conclude that general equilibrium production models with self-fulfilling expectations cannot achieve an accurate representation of the stylized financial markets facts with empirically plausible increasing returns because of two conflicting requirements. On the one hand, in order to generate a sufficient equity premium and volatility of the asset returns we need frictions to restrict the mobility of factors of production, especially of capital. On the other hand, we require flexibility in factor responses to shocks to lower the degree of the increasing returns to an empirically justifiable level. Perhaps a model in which indeterminacy is introduced through channels other than aggregate increasing returns in production will fare better in this regard.
The rest of this paper proceeds as follows: In Section 2 we describe the model and its equilibrium. In Section 3 we choose parameter values and present our results. In Section 4 we conclude.
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