Monetary shocks, equity returns and volatility: a firm-level panel data analysis

ABSTRACT

This article studies the impact of monetary policy shocks on equity returns and their volatility among nine industries and their affiliated firms in the United States. We use an extension of the traditional CAPM as the analytical framework and approximate policy shocks with the unexpected component of the federal funds rate. Data on the characteristics of firms and industries are obtained from Compustat and the Center for Research in Security Prices, covering a sample period from 1987 to 2009. Our results clearly show that responses to policy shocks vary by industry and across firms. Furthermore, credit availability matters in certain industries, and small, financially constrained, and bank-dependent firms are found to be more vulnerable to unexpected federal funds rate shocks.

KEYWORDS:

• Monetary shock
• firm characteristics
• Taylor rule
• Markov switching
• GARCH
• financial accelerator model

JEL CLASSIFICATION:

• E44
• G1

Notes

¹ ‘Though small, federal funds rate shocks are estimated to have a highly persistent positive effect on excess returns. Discounting these future positive excess returns back using a discount factor near unity yields a large negative impact on the current excess return.…’ (Bernanke and Kuttner 2005, 31).

² For a survey, see Piazzesi and Swanson (2008).

³ The difference between the realized and implied FFR reflects only current and past information. As both the agents and the Fed are forward looking, Fed’s policy may influence the economy and also be affected by future economic conditions, creating the so-called endogeneity problem in estimation. We attempted to address this issue by regressing the expected FFR derived from the Taylor rule on an index of some forward-looking variables such as the composite index of 10 leading indicators compiled by the Conference Board. We then used the difference between the actual FFR and predicted FFR as an alternative measure of monetary shocks. However, the predicted FFR created this way has a unit root. Additional steps to address the issue are possible, but the interpretations of the shocks would be very different from Konrad (2009). Thus, we stick to Konrad’s (2009) version of monetary shocks.

⁴ The St. Louis Fed set ${\pi }^{\ast }$ at five different rates, i.e. ${\pi }^{\ast }=0,1,2,3,4$, and calculated the implied FFR for each case. $r^{\ast }$ was set at 2% before April 2000 and it was changed to 2.5% in later periods.

⁵ To understand whether monetary shocks have any impact on equity returns, cross-sectional regression (CRS) proposed by Black, Jensen, and Scholes (1972) and Fama and Macbeth (1973) are typically conducted (Chen, Roll, and Ross 1986). However, by following Ehrmann and Fratzscher’s (2004) panel OLS approach, our model can accommodate two additional testable implications. First, firm characteristics are usually time-varying. Our model allows this flexibility. Second, our model offers the flexibility for incorporating a latent variable (state of credit availability), a topic to be discussed in the next section. It should be noted that if our firm-characteristic variables are not time varying, the panel OLS and CRS give identical estimates (Cochrane 2005, Section 12.3).

⁶ The monthly data on the percentage changes in business loan (BUSLOAN) are from the Federal Reserve Bank of St. Louis. It has mean of 0.626 and variance of 0.863. The sample period is from 1947/01 to 2013/08.

⁷ The log-likelihood is invariant to switching of ${\mu }_{s_t}$, the state-dependent parameters and $s_t$, credit states. Markov chain Monte Carlo will explore the permutations of ${\mu }_{s_t}$ and $s_t$. Therefore, we impose this prior restriction to avoid biased posterior estimates. Any parameter draws that violates this restriction is discarded.

⁸ We use the Gibb’s sampling to simulate three groups of parameters $M=\{{\mu }_1,{\mu }_2\},\mathrm{\Sigma }=\left\{{\sigma }^{2}I\right\}$, and two diagonal elements of P. Let $\theta =\left\{M,\mathrm{\Sigma },P\right\}$. In addition, we treat the states $S=$ {$s_1,s_2\}$ as a set of parameters and derive its posterior (e.g. see Maheu, McCurdy, and Song 2012). For a linear model, the conditionally conjugate priors are well known and each row of transition matrix follows a Dirichlet distribution. We set the independent priors as ${\mu }_1\sim N\left(-1,1\right)$, ${\mu }_2\sim N\left(1,1\right)$, ${\sigma }^{-2}\sim Gamma\left(0.5,0.5\right)$, $\left\{p_{11},p_{12}\right\}\sim Dir\left(0.6,0.4\right)$ and $\left\{p_{21},p_{22}\right\}\sim Dir\left(0.4,0.6\right)$. Given the observations on the percentage change in business loans $L_T=\left\{L_1,\dots ,L_T\right\}$, Gibbs sampling is conducted on the following conditional densities given initial parameter values. Chib (1996) shows that $S|M,\mathrm{\Sigma },P$ can be sampled backwards. Define $S_n=\left\{s_1,\dots ,s_t\right\}$, $S^{t+1}=\left\{s_{t+1},\dots ,s_n\right\}$ we decompose $p(S_n|L_T,\theta )$ = $\prod _{j=1}^{n}p(s_j|L_T,S^{j+1},\theta )$ with $S^{T+1}=\left\{\mathrm{\varnothing }\right\}$, where a typical element of this expression is $p\left(s_t|L_T,S^{t+1},\theta \right)\propto p$($s_{t+1}|s_t,\theta )p(s_t|L_t,\theta )$. The first term is the transition probability and the second term is the Hamilton filter, which provides a recursive formula to obtain $p(s_t|L_t,\theta )$. This filter involves two steps: an update step and a predictive step. The latter step is the variable of our interest.

⁹ We assume that firms will not pay prescheduled dividends by external financing.