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09-11-2020 | Research Article

Heterogeneous beliefs, monetary policy, and stock price volatility

Author: Katsuhiro Oshima

Published in: Annals of Finance | Issue 1/2021

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Abstract

In this paper, I build a two-agent New Keynesian model in which households with subjective and objective beliefs about capital gains from stock prices exist. The former type of households constructs their beliefs about expected capital gains by Bayesian learning from observed growth rates of stock prices. In a homogenous agent model with only subjective beliefs, the effect of the interest rate on stock prices tends to be unrealistically strong. I show how the presence of heterogeneity improves second moments of stock prices with realistic moments of business cycle properties. This quantitative improvement in stock price behaviors allows me to conduct a realistic analysis of how the stance of monetary policy affects stock price volatilities. Strong inertia of monetary policy provides the stability of stock prices. This is because the near-term real interest rate has dominant effects on stock prices under the presence of subjective beliefs since the presence limits the forward-looking nature in pricing stocks. However, because output depends on the expected path of the real interest rate in the forward-looking manner, strong monetary policy inertia does not necessarily provide stabilities of stock prices and output at the same time.

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See Challe and Giannitsarou (2014) for a summary of empirical studies about the effect of monetary policy shock on stock prices including Bernanke and Kuttner (2005).

Srour (2001) lists an argument that the large surprises in short-term interest rates can cause volatility in financial markets as one reason for smoothing interest rates. Rudebusch (2006) examines a discussion about a rationale for policy gradualism, which is a desire to reduce the volatility in asset prices. González-Páramo (2006) argues that a gradual monetary policy could reduce the likelihood of financial market disruptions. In actual policymaking, FOMC Secretariat (1994) records that there were discussions led by chairman Alan Greenspan on whether a 25 basis point policy tightening was preferable to a 50 basis point tightening because some members considered the larger move to have a higher probability of cracking financial markets. To this question, Bernanke (2004) gives no decisive conclusion on whether gradualism of monetary policy provides stability of financial market or asset prices.

De Paoli et al. (2010) and Challe and Giannitsarou (2014) assume 5 for relative risk aversion rate. The prominent work by Jermann (1998), which is a real model, also assumes 5.

Caines and Winkler (2018) study housing prices in a New Keynesian model with learning about housing price capital gains. Because housing stock quantity is directly included in households’ utility, housing price has wealth effects on business cycles.

The belief structure in Winkler (2019) is also similar. However, Winkler (2019) assumes that agents have “conditionally model-consistent expectations”. Conditionally model-consistent expectations are consistent with all equilibrium conditions of the model, except those that would convey knowledge of the price that clears the asset market, when agents solve for the perceived law of motion. On the other hand, this study follows Adam and Merkel (2018) in which market clearing conditions are known by agents.

On the other hand, external rationality postulates that agents’ subjective probability belief equals the objective probability density of external variables as they emerge in equilibrium.

Both adjustment costs have positive values when the stock and bond holdings deviate from steady state levels. I assume these costs to incorporate demand for stock and bond from the two types of households.

These representations of stock and bond adjustment costs are parsimonious ways to aggregate two types of agents by having a mathematical representation similar to that obtained by the mean-variance optimization under constant absolute risk aversion utility. For example, see Brock and Hommes (1998) and Hanson and Stein (2015). Intuitively speaking, \(\zeta ^S\) and \(\zeta ^B\) represent the variance of expected returns of stocks and bonds, respectively.

The reason why a small value is necessary for the optimal Kalman gain g is that when g is not small enough, the Blanchard-Kahn condition is not satisfied in general equilibrium, as mentioned later. From (15) and (16) shown shortly, g becomes large if I do not assume (13). The calibrated value for g in this model is \(\frac{1}{150}\).

The linearized equation of (50) is given by \(\hat{\pi }_t = \delta E_t \hat{\pi }_{t+1} + \frac{1}{\zeta ^{P}(\mu -1)} \hat{\varOmega }_t + \frac{1}{\zeta ^{P}(\mu -1)} \kappa u_t\).

Winkler (2019) uses the second-order perturbation method to solve his New Keynesian model. I use the first-order perturbation method because the excess return of the stock is out of my interest.

This quarterly value implies 0.5 at an annual rate.

The effect on consumption of the sizes of two parameters does not appear in the homogenous cases with subjective beliefs, \(\alpha =1\). This is because \(S_{s,t}\) is always equal to 1 (or \(S_{ss}\)) in Eq. (18) and \(B_{s,t}\) is always equal to 0 (or \(B_{ss}\)) in Eq. (8) from the market clearing conditions of stock and bond markets, (27), (28), and (30). The same observation applies to the homogenous cases with objective beliefs, \(\alpha =0\).

The sample period almost corresponds to the periods during which the U.S. central bank targeted the interest rate rather than money growth.

In Smets and Wouters (2007), the productivity shock is estimated as 0.45%, monetary policy shock is estimated as 0.24%, preference shock is estimated as 0.24%, and investment-specific shock is estimated as 0.45% in standard deviation on a quarterly basis. The sample period in their study is 1966–2004. Smets and Wouters (2007) use an ARMA(1,1) process for the markup shock process which is different from this study. Levin et al. (2005) estimate that standard deviation of markup shock is 0.2%. The sample period in their study is 1955–2001.

The definition of dividend in the model shown in (53) is not the same as that in the statistics of U.S. Bureau of Economic Analysis because of my model structure. The data are constructed here to be consistent with the definition of dividend in the model.

Due to data accessibility to subjective stock price growth expectations to cover the same data periods with other variables, I did not show \(Corr[\log P^s/d, \log (\alpha m_t + (1-\alpha )E_t[p^s_{t+1}/p^s_{t}])]\) in Table 3.

Castelnuovo and Nistico (2010) claim that incorporating sticky wages helps generate the procyclicality of dividends and their study shows positive responses of stock prices to preference shocks. However, their model does not include investment and capital, which could be crowded out under positive preference shocks and reduce the long-run production capacity. I examined how sticky wages change properties of responses to preference shocks in the model. However, it does not change responses of stock prices qualitatively from what the model without sticky wages presents in this study.

I experimented lower values for g than \(\frac{1}{1000}\). However, results are similar to what I discuss here.

I set \(\alpha =0.95\) instead of 0.94 in this study to match the moments.

In addition, in “Appendix A.2”, I investigate the effects on stock price volatilities under the habit formation parameter \(\phi \) with different values.

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Title: Heterogeneous beliefs, monetary policy, and stock price volatility
Author: Katsuhiro Oshima
Publication date: 09-11-2020
Publisher: Springer Berlin Heidelberg
Published in: Annals of Finance / Issue 1/2021
Print ISSN: 1614-2446
Electronic ISSN: 1614-2454
DOI: https://doi.org/10.1007/s10436-020-00379-9

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