Innovation Output and Idiosyncratic Volatility: US Evidence

Abstract

Firms engaging in innovative practices have patents to prevent competitive forces from eroding the resulting economic rents; however, there is limited evidence regarding the impact of innovation on risk. We shed new light on how firms’ involvement in innovation activities impacts their volatility, particularly their idiosyncratic volatility. In this paper, we empirically examine the effect of innovation on idiosyncratic volatility. To do so, we empirically examine the impact of innovation, measured by patents weighted by citations and R&D expenditure, on the idiosyncratic volatility of firms. Using a large sample of 8256 US firms, we find that more innovation is associated with lower idiosyncratic volatility. We also find that information uncertainty is the channel through which innovation affects idiosyncratic risk. The results are robust for different measures of idiosyncratic volatility. These results have empirical implications for investors, managers, and firms engaging in innovation-related activities.

1. Introduction

The purpose of this paper is to investigate the impact of innovation output on idiosyncratic volatility (IVOL). Economic theory suggests that innovation contributes positively to firm value and economic growth (Jaffe 1986; Hall 1993; Solow 1957). On the other hand, innovation can also have a “creative destruction” impact on markets. Shiller (2000) suggests that excess volatility increases significantly in periods of rapid technological innovation. An analysis of trends in unsystematic risk shows that it has increased since the 1960s, and this might be attributed to new technologies and listing of riskier companies (Brown and Kapadia 2007).

Firms engage in innovative activities, at first, through investing in R&D projects that are inherently risky due to their low success rate, irreversibility, and high adjustment costs (Holmstrom 1989; Bloom 2007). These investments increase the uncertainty of future economic growth and lead to an increase in stock return volatility (Chan et al. 2001; Kung and Schmid 2015). If R&D projects produce valuable innovations, firms are more likely to apply for patents to secure the economic rent resulting from these projects. A patent provides legal protection for firms and reduces the uncertainty surrounding future cash flows (Balasubramanian and Sivadasan 2011; Hall et al. 2005; Kogan et al. 2017). In addition, applications provide significant details about the invention. Thus, obtaining patents is expected to help reduce the uncertainty associated with R&D projects.

Previous studies have investigated the impact of innovation on firms’ risk levels. Several studies have shown that innovation increases firms’ risk levels (Chan et al. 2001; Zhang 2015; Gu 2016). On the other hand, other studies show that firms’ risk levels decrease as a result of innovative activities (Christensen et al. 1998; Cefis and Marsili 2006). In many of these studies, innovation is measured by R&D expenditure. However, R&D expenditure captures the input part of the innovation process that has different dynamics and is expected to have different impacts on firms’ risk level when compared with innovation output. Mazzucato and Tancioni (2012) use patents to measure innovation in the pharmaceutical industry. Their results show a positive relationship between innovation and volatility.

In this paper, we argue that R&D expenditure and patents have different impacts on firms’ risk, as measured by idiosyncratic volatility. Increasing R&D expenditure increases stock volatility because of the high risk of these projects’ outcomes and the uncertainty surrounding future cash flows. However, if these projects are successful and the innovation output is patented, there will be a higher level of certainty regarding future cash flow and, hence, lower risk.

The main prediction of this paper is that innovation output and IVOL are negatively correlated after controlling for other relevant factors, such as growth, size, age, and industry competition. In addition, based on the information uncertainty argument, we predict that the negative relationship between innovation output and IVOL is stronger for firms with high information uncertainty.

Using a large sample of 8256 US firms from 44 different industries over the 1982 to 2015 period, we use a conventional double sorting approach. We double-sort firms in our sample by patents and R&D expenditure. The tests reveal that, when holding the R&D level constant, the level of IVOL decreases monotonically as the number of patents increases across all R&D quantiles. This indicates that R&D and patents capture different dynamics of the innovation process. Additionally, after double-sorting firms in our sample by information uncertainty and patents, we find that the marginal impact of patents increases at higher levels of information uncertainty.

Furthermore, after controlling for the relevant variables, regression analysis indicates that innovation output has a negative impact on IVOL. The results are robust to alternative IVOL measures and firm and time fixed effects. In addition, we find that the impact of innovation output is more pronounced for firms with higher information uncertainty. The marginal impact of patenting is low on firms with low information uncertainty because patents do not add more information to investors about the firm compared to firms with high information uncertainty.

This paper contributes to the literature on the relationship between innovation and stock price behavior (see, e.g., Cohen et al. 2013; Chambers et al. 2002; Eberhart et al. 2004). The paper adds to the literature regarding innovation and risk by examining the impact of innovation output on IVOL over a large sample from different industries. Second, we identify information uncertainty as the channel through which patents reduce IVOL. We show that patents have a higher impact, in absolute terms, on firms with higher information uncertainty.

This work is related to the literature on understanding the behavior of IVOL. Shleifer and Vishny (1997) suggest that, in the presence of market frictions, IVOL may deter arbitrageurs from exploiting mispricing opportunities. This means that mispricing can exist and persist, which directly affects the cost of capital and the allocation of capital within the firm. Additionally, the behavior of IVOL affects the number of securities that investors must hold to reach full diversification, and this directly affects the value of the options on individual stocks (Campbell et al. 2001). Moreover, empirical results suggest that IVOL is priced in the cross-section of returns (Ang et al. 2006).

The remainder of the article proceeds as follows. Section 2 provides the literature review and develops the hypothesis. Section 3 describes the sample, defines the variables, and presents the summary statistics. Section 4 reports the empirical results. Section 5 concludes the paper.

2. Hypothesis Development

Schumpeter (1934) suggests that firms can achieve long-term success by continuous innovation that creates economic rents that establish a temporary monopoly. The process of capturing these economic rents includes spending on R&D projects and protecting fruitful projects through patenting. Empirical evidence suggests that firms that are more innovative, i.e., those that have patents with more citations, have higher market valuations (Hall et al. 2005).

The economic impact of R&D spending and patenting may differ due to the different nature of these activities. R&D spending is an example of Knightian uncertainty because its benefits are largely unknown (Knight 1921). Thus, as a firm increases its R&D expenditure, its risk level is expected to increase. Zhang (2015) shows that R&D investment increases distress risk. In addition, Bloom (2007) suggests that R&D investment is inflexible and has high adjustment costs. Xu (2006) investigates the reaction of stock price volatility to R&D progress. He shows that stock price volatility decreases proportionally with progress in the R&D process. Patents, on the other hand, work in the opposite direction from R&D spending. When a firm successfully patents its innovative activities, the risk associated with R&D spending and innovative activities is reduced, and this is expected to be reflected in the firm’s stock price volatility. Based on this discussion, we formulate our first hypothesis:

Hypothesis 1a.

IVOL is negatively associated with patents, ceteris paribus.

Although patents decrease IVOL, firms with low information uncertainty would not gain much from patenting their activities because patents do not help market participants to learn more about the future profitability of the firm. In contrast, firms with high information uncertainty are expected to have a higher benefit from their patents because they disseminate information to the market about the future profitability of these firms. As a result, patents should have a higher impact, in absolute terms, on IVOL in firms with higher information uncertainty. This discussion leads us to our second hypothesis:

Hypothesis 1b.

The effect of patents on IVOL is stronger when firms have higher information uncertainty, ceteris paribus.

3. Sample Selection and Research Design

The sample in this study comprises US firms with available data in CompStat, Center of Research in Security Prices (CRSP), and CRSP/CompStat Merged database from 1982 to 2015. In addition, Fama and French 3-factor and Carhart 4-factor data were obtained from the Fama and French & Liquidity Factors database. The patents dataset is constructed from three databases from the United Patent Trademark Office (USPTO) data. The first database is the National Bureau of Economic Research (NBER)’s Patent Data Project database (PDP). This dataset is constructed by Hall et al. (2001). The second database was built by Kogan et al. (2017). The third database was created by Li et al. (2014), and it is used to update the first two databases.

The choice of 1982 as a starting date for the sample is due to the availability of the data needed to construct all the dependent variables. We exclude firms in the banking, utilities, insurance, and other industries (i.e., Fama and French-48 industry classification (44, 31, 45, and 48, respectively). Additionally, we exclude firms with negative net income. The final sample consists of 8256 firms, representing 79,923 firm years. The choice of 2015 as the end date for the sample was in order to account for the number of patent citations.

Table 1. Sample distribution of the sample according to the Fama and French 48-industry classification code.

Fama–French 48-Industry Code	Frequency	%	Cum. Frequency
Agriculture	321	0.4%	0.4%
Food Products	1687	2.1%	2.5%
Candy & Soda	311	0.4%	2.9%
Beer & Liquor	381	0.5%	3.3%
Tobacco Products	80	0.1%	3.4%
Recreation	707	0.9%	4.3%
Entertainment	1215	1.5%	5.8%
Printing and Publishing	741	0.9%	6.7%
Consumer Goods	1596	2.0%	8.7%
Apparel	1305	1.6%	10.3%
Healthcare	1733	2.1%	12.5%
Medical Equipment	3255	4.0%	16.5%
Pharmaceutical Products	5112	6.3%	22.8%
Chemicals	1773	2.2%	25.0%
Rubber and Plastic Products	818	1.0%	26.1%
Textiles	463	0.6%	26.6%
Construction Materials	1855	2.3%	28.9%
Construction	672	0.8%	29.8%
Steel Works, Etc.	1326	1.6%	31.4%
Fabricated Products	345	0.4%	31.8%
Machinery	3432	4.3%	36.1%
Electrical Equipment	1630	2.0%	38.1%
Automobiles and Trucks	1342	1.7%	39.8%
Aircraft	399	0.5%	40.3%
Shipbuilding, Railroad Equipment	153	0.2%	40.4%
Defense	173	0.2%	40.7%
Precious Metals	808	1.0%	41.7%
Non-Metallic and Industrial Metal Mining	542	0.7%	42.3%
Coal	153	0.2%	42.5%
Petroleum and Natural Gas	4394	5.4%	48.0%
Communication	2662	3.3%	51.3%
Personal Services	890	1.1%	52.4%
Business Services	9766	12.1%	64.5%
Computers	3916	4.9%	69.3%
Electronic Equipment	6433	8.0%	77.3%
Measuring and Control Equipment	2253	2.8%	80.1%
Business Supplies	1339	1.7%	81.7%
Shipping Containers	250	0.3%	82.0%
Transportation	2805	3.5%	85.5%
Wholesale	3303	4.1%	89.6%
Retail	4706	5.8%	95.4%
Restaurants, Hotels, Motels	1784	2.2%	97.6%
Real Estate	532	0.7%	98.3%
Trading	1372	1.7%	100.0%
Total	80,733	100.0%

shows the sample’s frequency distribution based on the Frama and French 48-industry classification (Fama and French 1997). The table shows that the sampled firms are classified into 44 industries. The industries with the highest percentage of observations are Business Services (12.1%), Electronic Equipment (8.0%), and Pharmaceutical Products (6.3%).

Table 2. Summary statistics of variables used in the analysis. Variables’ definitions are provided in Appendix A.

	N	Mean	S. D.	p25	Median	p75	Min	Max
$IVOL\_M{M}_{it}$	77,923	0.530	0.357	0.302	0.444	0.644	0.131	2.460
$IVOL\_FF{3}_{it}$	77,923	0.507	0.342	0.288	0.424	0.618	0.125	2.344
$IVOL\_C{4}_{it}$	77,923	0.498	0.336	0.283	0.416	0.607	0.122	2.306
$PA{T}_{it}$	77,923	0.222	0.580	0	0	0.122	0	3.474
$R\&D_{it}$	77,923	0.176	0.859	0	0.001	0.063	0	7.384
$DIS{P}_{it}$	43,827	0.118	0.169	0.028	0.057	0.130	0.001	1.070
$CFVO{L}_{it}$	77,923	0.131	0.120	0.054	0.093	0.164	0.013	0.672
$SIZ{E}_{it}$	77,923	5.449	2.291	3.729	5.326	7.026	0.808	11.111
$AG{E}_{it}$	77,923	2.746	0.678	2.197	2.708	3.258	1.609	4.344
$M{B}_{it}$	77,923	2.801	3.232	1.093	1.821	3.150	0.175	21.60
$LE{V}_{it}$	77,923	0.341	0.228	0.152	0.303	0.496	0.015	0.912
$CAS{H}_{it}$	77,923	0.177	0.201	0.028	0.098	0.258	0	0.868
$DP{O}_{it}$	77,923	0.159	0.382	0	0.015	0.204	−0.973	2.284
$BIDAS{K}_{it}$	77,923	0.031	0.043	0.003	0.015	0.039	0	0.241
$RO{A}_{it}$	77,923	0.079	0.176	0.045	0.111	0.168	−0.768	0.389
$HH{I}_{it}$	77,923	0.068	0.045	0.038	0.054	0.077	0.025	0.259
$TAN{G}_{it}$	77,923	0.285	0.234	0.097	0.215	0.415	0.006	0.903

shows the summary statistics of the dependent and control variables. To minimize the impact of outliers, all variables are winsorized at the 1st and 99th percentiles. The annualized standard deviation of the residuals of the market model using weekly data ($IVOL\_MM)$ is 0.53 over the sample period (the standard deviation of the residuals of the Fama and French three-factor model using weekly data ($IVOL\_FF3$) and the standard deviation of the residuals of the Carhart four-factor model using weekly data ($IVOL\_C4$) are also reported).

The average firm in our sample has weighted patents (PAT) of 0.22 and an R&D expense as a percentage of sales (R&D) of 0.18. On average, the standard deviation of analysts’ expectations of a firm’s EPS scaled by price (DISP) is 0.18, the cash flow volatility (CFVOL) is 0.13, the firm size (SIZE) is 5.43, a natural log of age (AGE) of 2.74, a market to book ratio (M.B.) of 2.80, and a market leverage ratio (LEV) of 0.34. The average cash holding included in our sample (CASH) is 0.18. The average firm has an average dividend payout ratio (DPO) of 0.16, a bid–ask spread (BIDASK) of 0.03, and an ROA of 0.08. Additionally, the average concentration within an industry (HHI) and tangibility of assets (TANG) are 0.07 and 0.29, respectively.

To investigate the impact of innovation on IVOL, we estimate the following panel regression model:

$$\begin{gathered} IVO{L}_{it}=\alpha +{\beta }_{1}PA{T}_{it-1}+{\beta }^{\prime }\times Control{s}_{it-1}+Fir{m}_i+Yea{r}_t \\ +{\epsilon }_{it} \end{gathered}$$

(1)

The dependent variable in the model is IVOL at time $\mathrm{t}$. The primary variable of interest is $PA{T}_{it-1}$. The coefficient of the variable is expected to be negative and significant. $Control{s}_{it-1}$, as discussed previously, is a vector of firm characteristics that could affect the IVOL. $Fir{m}_i$ and $Yea{r}_t$ are firm and year dummies that are available in the model to control for firm and time fixed effects. We acknowledge that a firm’s innovative activities and other included financial variables are contemporaneously determined within the firm. Thus, we follow Mazzucato and Tancioni (2012) and use the lagged values of the control variables. This means that pre-determined values are used to estimate simultaneous relations.

To test H1b, we estimate the following panel regression model:

$$\begin{gathered} IVO{L}_{it}=\alpha +{\beta }_{1}PA{T}_{it-1}+{\beta }_{2}PA{T}_{it-1}\times DIS{P}_{it-1}+{\beta }^{\prime }\times Control{s}_{it-1}+Fir{m}_i \\ +Yea{r}_t+{\epsilon }_{it} \end{gathered}$$

(2)

In this model, we interact the PAT with DISP to investigate the marginal impact of innovation output on firms with different levels of information uncertainty. We expect the coefficient on the interaction variable to be negative and statistically significant.

Variables’ Definitions

To estimate IVOL, we use the annualized standard deviation of the residuals of the market model. The model is estimated using the following regression equation:

$$r_{it}={\alpha }_i+{\beta }_i{R}_{m,t}+{\epsilon }_{i,t}$$

(3)

where $r_{it}$ is the excess return for stock i at time t, and $R_{m,t}$ is the value-weighted excess market return at time t. The model is estimated using weekly returns. We require at least 6 weeks to compute the IVOL. The IVOL that is calculated from the market model is denoted $IVOL\_MM$.

Additionally, we employ the Fama and French (1993) three-factor model and the Carhart (1997) four-factor model. All the models are estimated using weekly returns. We require at least six observations to compute the IVOL. The Fama and French three-factor model is calculated using the following regression equation:

$$r_{it}={\alpha }_i+b_i{R}_{m,t}+s_{i}SM{B}_{i,t}+h_{t}HM{L}_{i,t}+{\epsilon }_{i,t}$$

(4)

where $SM{B}_{i,t}$ and $HM{L}_{i,t}$ are the size premium (small minus big) and the value premium (high minus low). The Carhart four-factor model is estimated using the following regression model:

$$r_{it}={\alpha }_i+b_i{R}_{m,t}+s_{i}SM{B}_{i,t}+h_{t}HM{L}_{i,t}+u_{i}UM{D}_{i,t}+{\epsilon }_{i,t}$$

(5)

where $UM{D}_{i,t}$ is the momentum premium (up minus down). The IVOL values that are computed from the Fama and French three-factor model and the Carhart four-factor model are denoted $IVOL\_FF3$ and $IVOL\_C4$, respectively.

Two variables are used in the literature to measure a firm’s innovation: R&D expenditure and number of patents. The former only captures an observable input of innovation rather than the quality of innovation. However, the latter measure captures the firm’s utilization of observable and unobservable innovation inputs and turning them into outputs. For innovation, we use the natural log of the number of patents weighted by citations (PAT) to capture a firm’s innovation output. Following He and Tian (2013) and Fang et al. (2014), we use the natural log of one plus. The number of patents weighted by citations as a measure of corporate innovation output is used to avoid losing observations from the sample.

To address truncation bias, we follow Squicciarini et al. (2013) and count citations over seven years after the publication date. Thus, most patents have the same window of time to be cited regardless of their application year. Moreover, we follow Atanassov (2013) and drop the last two years of the sample because they exhibit severe forms of bias.

We control for several variables that have been shown to affect IVOL. We control for operations risk using the standard deviation of the operating cash flow over the last three years (Zhang 2006). Cao et al. (2008) show that growth opportunities positively correlate to IVOL. Thus, we include the market-to-book ratio (MB) as a proxy for growth opportunities. Larger firms tend to have lower IVOL (Pástor and Pietro 2003). Therefore, we control for size (SIZE), which is measured by the natural log of the market value of equity. Brown and Kapadia (2007) suggest that the dividend payout ratio is negatively correlated to the IVOL. Therefore, we control our model’s dividend payout ratio (DPO). Pástor and Pietro (2003) show a negative association between a firm’s age and IVOL, so we include the natural log of a firm’s age (AGE) as a control variable. Chan et al. (2001) show that firms with high R&D expenditure exhibit higher volatility. Therefore, we include R&D expenditure scaled by total assets to control for R&D spending.

In addition, we control for information uncertainty measured by the standard deviation of the analysts’ forecasts of firms’ EPS (DISP) and information asymmetry proxied by bid–ask spread (BIDASK). We follow Zhang (2015) and control for cash holdings (CASH) and profitability, which are measured by cash divided by total assets and ROA, respectively. These two variables are expected to be negatively correlated with firms’ risk. Prior literature suggests that competition is an essential determinant of IVOL (Gaspar and Massa 2006; Irvine and Pontiff 2009). Therefore, we control market competition by including the Herfindahl–Hirschman Index (HHI). Additionally, we follow Zhang’s (2015) control for asset tangibility. Furthermore, we add the lagged values of the IVOL to account for volatility persistence (Wei and Zhang 2006). Detailed variable descriptions are provided in Appendix A.

4. Empirical Results

4.1. Univariate Analysis

This section conducts a univariate analysis to examine the relationship between IVOL and patents. To further explore our sample, we divide our sample into firms that invest in R&D projects and firms with no R&D expenditure (firms that report no R&D activities).

Table 3. Comparison of means test. Panel A shows the comparison of means t-test after classifying the firms in our sample as No-R&D firms or R&D firms. Panel B shows the comparison of means t-test after classifying the firms in our sample into firms with no patents and firms with patents. The t-statistic is adjusted for unequal variance. The sample period is from 1982 to 2015. ***, **, and * denote significant two-tailed p-values ≤ 1%, 5%, or 10%, respectively.

Panel A
	1	2	3	4	(2–4)
	No R&D Firm		R&D Firms
Variable	N	Mean	N	Mean	Difference
$\mathit{I}\mathit{V}\mathit{O}\mathit{L}\_\mathit{M}{\mathit{M}}_{\mathit{i}\mathit{t}}$	38,610	0.512	39,313	0.548	−0.0359 ***
$\mathit{I}\mathit{V}\mathit{O}\mathit{L}\_\mathit{F}\mathit{F}{3}_{\mathit{i}\mathit{t}}$	38,610	0.491	39,313	0.524	−0.0330 ***
$\mathit{I}\mathit{V}\mathit{O}\mathit{L}\_\mathit{C}{4}_{\mathit{i}\mathit{t}}$	38,610	0.482	39,313	0.514	−0.0325 ***
$\mathit{P}\mathit{A}{\mathit{T}}_{\mathit{i}\mathit{t}}$	38,610	0.035	39,313	0.407	−0.372 ***
$\mathit{D}\mathit{I}\mathit{S}{\mathit{P}}_{\mathit{i}\mathit{t}}$	21,120	0.105	22,707	0.108	−0.003
$\mathit{C}\mathit{F}\mathit{V}\mathit{O}{\mathit{L}}_{\mathit{i}\mathit{t}}$	38,610	0.124	39,313	0.139	−0.0152 ***
$\mathit{S}\mathit{I}\mathit{Z}{\mathit{E}}_{\mathit{i}\mathit{t}}$	38,610	5.360	39,313	5.537	−0.177 ***
$\mathit{A}\mathit{G}{\mathit{E}}_{\mathit{i}\mathit{t}}$	38,610	2.744	39,313	2.749	−0.005
$\mathit{M}{\mathit{B}}_{\mathit{i}\mathit{t}}$	38,610	2.322	39,313	3.272	−0.950 ***
$\mathit{L}\mathit{E}{\mathit{V}}_{\mathit{i}\mathit{t}}$	38,610	0.403	39,313	0.280	0.123 ***
$\mathit{C}\mathit{A}\mathit{S}{\mathit{H}}_{\mathit{i}\mathit{t}}$	38,610	0.112	39,313	0.241	−0.129 ***
$\mathit{D}\mathit{P}{\mathit{O}}_{\mathit{i}\mathit{t}}$	38,610	0.165	39,313	0.154	0.0103 ***
$\mathit{B}\mathit{I}\mathit{D}\mathit{A}\mathit{S}{\mathit{K}}_{\mathit{i}\mathit{t}}$	38,610	0.034	39,313	0.027	0.007 ***
$\mathit{R}\mathit{O}{\mathit{A}}_{\mathit{i}\mathit{t}}$	38,610	0.110	39,313	0.048	0.0623 ***
$\mathit{H}\mathit{H}{\mathit{I}}_{\mathit{i}\mathit{t}}$	38,610	0.067	39,313	0.069	−0.002 ***
$\mathit{T}\mathit{A}\mathit{N}{\mathit{G}}_{\mathit{i}\mathit{t}}$	38,608	0.370	39,313	0.200	0.1702 ***
Panel B
	No Patents Firm		Firms with Patents		(2–4)
Variable	N	Mean	N	Mean	Difference
$\mathit{I}\mathit{V}\mathit{O}\mathit{L}\_\mathit{M}{\mathit{M}}_{\mathit{i}\mathit{t}}$	51,602	0.553	26,321	0.484	0.070 ***
$\mathit{I}\mathit{V}\mathit{O}\mathit{L}\_\mathit{F}\mathit{F}{3}_{\mathit{i}\mathit{t}}$	51,602	0.531	26,321	0.462	0.069 ***
$\mathit{I}\mathit{V}\mathit{O}\mathit{L}\_\mathit{C}{4}_{\mathit{i}\mathit{t}}$	51,602	0.521	26,321	0.453	0.068 ***
$\mathit{R}\&{\mathit{D}}_{\mathit{i}\mathit{t}}$	51,602	0.103	26,321	0.320	−0.217 ***
$\mathit{D}\mathit{I}\mathit{S}{\mathit{P}}_{\mathit{i}\mathit{t}}$	25,994	0.111	17,833	0.100	0.0112 ***
$\mathit{C}\mathit{F}\mathit{V}\mathit{O}{\mathit{L}}_{\mathit{i}\mathit{t}}$	51,602	0.135	26,321	0.125	0.010 ***
$\mathit{S}\mathit{I}\mathit{Z}{\mathit{E}}_{\mathit{i}\mathit{t}}$	51,602	5.018	26,321	6.296	−1.278 ***
$\mathit{A}\mathit{G}{\mathit{E}}_{\mathit{i}\mathit{t}}$	51,602	2.684	26,321	2.868	−0.183 ***
$\mathit{M}{\mathit{B}}_{\mathit{i}\mathit{t}}$	51,602	2.584	26,321	3.228	−0.644 ***
$\mathit{L}\mathit{E}{\mathit{V}}_{\mathit{i}\mathit{t}}$	51,602	0.367	26,321	0.291	0.076 ***
$\mathit{C}\mathit{A}\mathit{S}{\mathit{H}}_{\mathit{i}\mathit{t}}$	51,602	0.155	26,321	0.221	−0.066 ***
$\mathit{D}\mathit{P}{\mathit{O}}_{\mathit{i}\mathit{t}}$	51,602	0.147	26,321	0.183	−0.036 ***
$\mathit{B}\mathit{I}\mathit{D}\mathit{A}\mathit{S}{\mathit{K}}_{\mathit{i}\mathit{t}}$	51,602	0.036	26,321	0.020	0.017 ***
$\mathit{R}\mathit{O}{\mathit{A}}_{\mathit{i}\mathit{t}}$	51,602	0.082	26,321	0.073	0.008 ***
$\mathit{H}\mathit{H}{\mathit{I}}_{\mathit{i}\mathit{t}}$	51,602	0.068	26,321	0.068	−0.000
$\mathit{T}\mathit{A}\mathit{N}{\mathit{G}}_{\mathit{i}\mathit{t}}$	51,602	0.553	26,321	0.484	−0.217 ***

, panel A compares the mean IVOL and other control variables for both groups. The analysis shows that firms investing in R&D projects have higher IVOL, size, market to book ratio, cash holdings, and cash flow volatility, indicating that such firms that engage in risky long-term projects are large firms with more growth opportunities and higher cash flow volatility. On the other hand, positive R&D firms have lower leverage, dividend payout ratio, bid–ask spread, profitability, and asset tangibility. These results are consistent with the finding of Phillips and Zhdanov (2013).

Similarly, we conduct the same analysis after classifying firms in our sample into patent and no-patent firms. As shown in Table 3, panel B, firms with patents have lower volatility, leverage, cash flow volatility, bid–ask spread, and ROA, indicating that firms producing patents have a healthy financial status, rely less on debt, and have lower volatility and bid–ask spread. These findings are consistent with the results of Balasubramanian and Sivadasan (2011).

Table 4. Pearson correlations between the variables included in the analysis. The sample period was from 1982 to 2015. The correlations in bold are at least significant at the 1% level, and ^a and ^b denote correlations significant at the 10% and 5% level, respectively (the other measures of IVOL were removed due to space limitations; the full correlation matrix is available upon request).

	Variable	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
1	$IVOL\_M{M}_{it}$	1
2	$PA{T}_{it}$	−0.150	1
3	$R\&D_{it}$	0.147	0.012	1
4	$DIS{P}_{it}$	0.284	−0.070	−0.153	1
5	$CFVO{L}_{it}$	0.351	−0.084	0.145	0.221	1
6	$SIZ{E}_{it}$	−0.472	0.420	−0.480	−0.228	−0.281	1
7	$AG{E}_{it}$	−0.296	0.215	−0.298	−0.090	−0.198	0.300	1
8	$M{B}_{it}$	0.070	0.070	0.069	−0.044	0.176	0.190	−0.075	1
9	$LE{V}_{it}$	0.112	−0.056	0.111	0.204	0.021	−0.232	0.075	−0.344	1
10	$CAS{H}_{it}$	0.129	0.029	0.126	0.101	0.161	−0.043	−0.189	0.234	−0.468	1
11	$DP{O}_{it}$	−0.203	0.094	0.350	−0.121	−0.124	0.213	0.148	0.031	−0.083	−0.007 b	1
12	$BIDAS{K}_{it}$	0.430	−0.169	−0.203	0.157	0.194	−0.645	−0.185	−0.107	0.260	−0.101	−0.145	1
13	$RO{A}_{it}$	−0.388	0.081	0.439	−0.379	−0.342	0.335	0.177	−0.136	−0.035	−0.336	0.202	−0.180	1
14	$HH{I}_{it}$	−0.029	0.008	−0.384	−0.014	0.005	−0.076	0.041	−0.033	0.036	−0.076	−0.010	0.085	0.031	1
15	$TAN{G}_{it}$	−0.095	−0.054	−0.026	0.100	−0.133	0.110	0.066	−0.128	0.219	−0.408	−0.015	0.027	0.183	−0.037	1

shows the Pearson correlation matrix for all the variables. The negative association between IVOL measures and PAT provides preliminary evidence that is consistent with our first hypothesis. However, this univariate analysis is only suggestive because it does not consider other variables. Thus, we rely on the subsequent analyses to make an inference about the proposed hypotheses. In addition, the bivariate correlations between the independent variables are low; hence, multicollinearity is not a problem in our analyses.

Table 5. Double sorting. Panel A reports the average (median) IVOL of firms grouped and sorted based on R&D and patent quantiles over the sample period. The reported t-statistic (chi-squared) is for the difference between the mean (median) of the average IVOL in the lowest and highest quantiles. Panel B reports the comparison means (median) test based on the variance of analyst forecasts and patent quantiles. The sample period is from 1982 to 2015. *** denotes that the difference between the highest and the lowest quantile is significant p-value at the 1% level.

Panel A: firms grouped and sorted on R&D and patents.
	Patents Quantile		No Patents	Lowest	2	3	4	Highest	H-L	t-stat/χ2	p-Value
(a) Full sample	$IVOL\_M{M}_{it}$	Means	0.551	0.545	0.531	0.507	0.455	0.360	−0.184 ***	−33.854	0.000
	$IVOL\_FF{3}_{it}$		0.529	0.521	0.506	0.484	0.433	0.343	−0.178 ***	−34.282	0.000
	$IVOL\_C{4}_{it}$		0.519	0.512	0.497	0.475	0.424	0.335	−0.177 ***	−34.632	0.000
	$IVOL\_M{M}_{it}$	Medians	0.460	0.467	0.456	0.442	0.391	0.299	−0.168 ***	1152.331	0.000
	$IVOL\_FF{3}_{it}$		0.440	0.446	0.433	0.421	0.371	0.283	−0.163 ***	1167.140	0.000
	$IVOL\_C{4}_{it}$		0.432	0.438	0.425	0.414	0.364	0.278	−0.161 ***	1184.536	0.000
	N		53,537	7122	5173	4559	5019	5323
	Patents Quantile		No Patents	Lowest	2	3	4	Highest	H-L	t-stat/χ2	p-Value
(b) No R&D firms	$IVOL\_M{M}_{it}$	Means	0.520	0.464	0.425	0.433	0.378	0.331	−0.132 ***	−6.989	0.000
	$IVOL\_FF{3}_{it}$		0.499	0.444	0.406	0.413	0.362	0.319	−0.124 ***	−6.870	0.000
	$IVOL\_C{4}_{it}$		0.490	0.436	0.399	0.405	0.355	0.313	−0.122 ***	−6.866	0.000
	$IVOL\_M{M}_{it}$	Medians	0.428	0.390	0.364	0.363	0.317	0.272	−0.118 ***	67.809	0.000
	$IVOL\_FF{3}_{it}$		0.410	0.372	0.348	0.346	0.303	0.261	−0.111 ***	63.539	0.000
	$IVOL\_C{4}_{it}$		0.402	0.365	0.341	0.339	0.298	0.257	−0.108 ***	61.456	0.000
	N		35,393	2156	1080	674	419	258
	Patents Quantile		No Patents	Lowest	2	3	4	Highest	H-L	t-stat/χ2	p-Value
(c) R&D (Q1)	$IVOL\_M{M}_{it}$	Means	0.499	0.440	0.404	0.381	0.349	0.292	−0.148 ***	−12.239	0.000
	$IVOL\_FF{3}_{it}$		0.480	0.421	0.386	0.364	0.333	0.277	−0.144 ***	−12.337	0.000
	$IVOL\_C{4}_{it}$		0.471	0.413	0.378	0.357	0.327	0.271	−0.142 ***	−12.381	0.000
	$IVOL\_M{M}_{it}$	Medians	0.422	0.376	0.348	0.328	0.295	0.244	−0.132 ***	182.295	0.000
	$IVOL\_FF{3}_{it}$		0.404	0.357	0.325	0.314	0.279	0.232	−0.125 ***	187.777	0.000
	$IVOL\_C{4}_{it}$		0.397	0.351	0.319	0.311	0.276	0.224	−0.127 ***	176.894	0.000
	N		4304	1049	705	684	789	631
	Patents Quantile		No Patents	Lowest	2	3	4	Highest	H-L	t-stat/χ2	p-Value
(d) R&D (Q2)	$IVOL\_M{M}_{it}$	Means	0.550	0.483	0.466	0.433	0.359	0.304	−0.179 ***	−16.682	0.000
	$IVOL\_FF{3}_{it}$		0.529	0.464	0.447	0.415	0.342	0.290	−0.174 ***	−16.941	0.000
	$IVOL\_C{4}_{it}$		0.520	0.457	0.439	0.407	0.335	0.283	−0.174 ***	−17.157	0.000
	$IVOL\_M{M}_{it}$	Medians	0.472	0.406	0.397	0.375	0.308	0.263	−0.143 ***	243.941	0.000
	$IVOL\_FF{3}_{it}$		0.450	0.393	0.381	0.356	0.293	0.249	−0.144 ***	241.249	0.000
	$IVOL\_C{4}_{it}$		0.443	0.389	0.378	0.349	0.288	0.242	−0.147 ***	243.941	0.000
	N		3574	918	768	703	904	1285
	Patents Quantile		No Patents	Lowest	2	3	4	Highest	H-L	t-stat/χ2	p-Value
(e) R&D (Q3)	$IVOL\_M{M}_{it}$	Means	0.616	0.575	0.530	0.511	0.438	0.348	−0.227 ***	−19.933	0.000
	$IVOL\_FF{3}_{it}$		0.591	0.552	0.507	0.489	0.419	0.333	−0.219 ***	−20.143	0.000
	$IVOL\_C{4}_{it}$		0.580	0.542	0.497	0.480	0.412	0.326	−0.216 ***	−20.226	0.000
	$IVOL\_M{M}_{it}$	Medians	0.536	0.512	0.467	0.449	0.384	0.284	−0.228 ***	368.925	0.000
	$IVOL\_FF{3}_{it}$		0.516	0.488	0.447	0.434	0.368	0.272	−0.216 ***	378.864	0.000
	$IVOL\_C{4}_{it}$		0.506	0.481	0.436	0.428	0.364	0.267	−0.214 ***	378.864	0.000
	N		3488	963	815	752	878	1256
	Patents Quantile		No Patents	Lowest	2	3	4	Highest	H-L	t-stat/χ2	p-Value
(f) R&D (Q4)	$IVOL\_M{M}_{it}$	Means	0.654	0.624	0.582	0.567	0.505	0.396	−0.228 ***	−18.588	0.000
	$IVOL\_FF{3}_{it}$		0.626	0.597	0.554	0.541	0.479	0.377	−0.220 ***	−18.840	0.000
	$IVOL\_C{4}_{it}$		0.616	0.587	0.544	0.531	0.469	0.368	−0.219 ***	−19.153	0.000
	$IVOL\_M{M}_{it}$	Medians	0.566	0.543	0.514	0.511	0.445	0.337	−0.206 ***	267.952	0.000
	$IVOL\_FF{3}_{it}$		0.544	0.526	0.487	0.494	0.420	0.323	−0.203 ***	285.189	0.000
	$IVOL\_C{4}_{it}$		0.536	0.517	0.476	0.486	0.408	0.315	−0.202 ***	299.963	0.000
	N		3455	942	804	775	932	1244
	Patents Quantile		No Patents	Lowest	2	3	4	Highest	H-L	t-stat/χ2	p-Value
(g) R&D (Q5)	$IVOL\_M{M}_{it}$	Means	0.774	0.762	0.743	0.650	0.609	0.505	−0.257 ***	−13.663	0.000
	$IVOL\_FF{3}_{it}$		0.741	0.726	0.707	0.618	0.576	0.477	−0.249 ***	−13.915	0.000
	$IVOL\_C{4}_{it}$		0.728	0.715	0.695	0.608	0.564	0.465	−0.250 ***	−14.184	0.000
	$IVOL\_M{M}_{it}$	Medians	0.659	0.654	0.653	0.576	0.543	0.444	−0.210 ***	157.917	0.000
	$IVOL\_FF{3}_{it}$		0.631	0.626	0.625	0.546	0.514	0.421	−0.205 ***	160.417	0.000
	$IVOL\_C{4}_{it}$		0.621	0.610	0.611	0.538	0.507	0.408	−0.201 ***	155.436	0.000
	N		3323	1094	1001	971	1097	649
Panel B: firms grouped and sorted based on standard deviation of analyst’s forecasts and patent quantiles.
	Patents Quantile		No Patents	Lowest	2	3	4	Highest	H-L	t-stat/χ2	p-Value
(a) DISP (Q1)	$IVOL\_M{M}_{it}$	Means	0.384	0.387	0.382	0.389	0.355	0.299	−0.089 ***	−9.863	0.000
	$IVOL\_FF{3}_{it}$		0.367	0.370	0.364	0.371	0.339	0.285	−0.085 ***	−9.805	0.000
	$IVOL\_C{4}_{it}$		0.361	0.364	0.357	0.365	0.333	0.279	−0.085 ***	−9.880	0.000
	$IVOL\_M{M}_{it}$	Medians	0.345	0.340	0.326	0.352	0.298	0.242	−0.097 ***	111.829	0.000
	$IVOL\_FF{3}_{it}$		0.329	0.327	0.309	0.334	0.286	0.229	−0.098 ***	101.714	0.000
	$IVOL\_C{4}_{it}$		0.324	0.322	0.306	0.322	0.280	0.223	−0.099 ***	113.910	0.000
	N		5211	747	570	577	729	945
	Patents Quantile		No Patents	Lowest	2	3	4	Highest	H-L	t-stat/χ2	p-Value
(b) DISP (Q2)	$IVOL\_M{M}_{it}$	Means	0.403	0.417	0.411	0.425	0.395	0.323	−0.093 ***	−9.516	0.000
	$IVOL\_FF{3}_{it}$		0.385	0.398	0.391	0.404	0.375	0.309	−0.089 ***	−9.444	0.000
	$IVOL\_C{4}_{it}$		0.379	0.391	0.384	0.397	0.366	0.303	−0.088 ***	−9.592	0.000
	$IVOL\_M{M}_{it}$	Medians	0.363	0.372	0.368	0.370	0.346	0.263	−0.110 ***	114.346	0.000
	$IVOL\_FF{3}_{it}$		0.344	0.357	0.347	0.349	0.326	0.254	−0.102 ***	110.178	0.000
	$IVOL\_C{4}_{it}$		0.338	0.353	0.344	0.340	0.317	0.247	−0.106 ***	118.591	0.000
	N		5099	778	612	623	770	883
	Patents Quantile		No Patents	Lowest	2	3	4	Highest	H-L	t-stat/χ2	p-Value
(c) DISP (Q3)	$IVOL\_M{M}_{it}$	Means	0.431	0.451	0.457	0.462	0.422	0.356	−0.095 ***	−8.528	0.000
	$IVOL\_FF{3}_{it}$		0.411	0.431	0.435	0.441	0.401	0.337	−0.093 ***	−8.798	0.000
	$IVOL\_C{4}_{it}$		0.404	0.422	0.427	0.433	0.393	0.330	−0.092 ***	−8.895	0.000
	$IVOL\_M{M}_{it}$	Medians	0.383	0.400	0.404	0.418	0.367	0.300	−0.100 ***	97.455	0.000
	$IVOL\_FF{3}_{it}$		0.368	0.380	0.386	0.395	0.350	0.285	−0.096 ***	101.484	0.000
	$IVOL\_C{4}_{it}$		0.360	0.373	0.380	0.392	0.344	0.280	−0.093 ***	109.787	0.000
	N		5106	772	709	634	745	797
	Patents Quantile		No Patents	Lowest	2	3	4	Highest	H-L	t-stat/χ2	p-Value
(d) DISP (Q4)	$IVOL\_M{M}_{it}$	Means	0.486	0.513	0.526	0.516	0.482	0.411	−0.103 ***	−7.556	0.000
	$IVOL\_FF{3}_{it}$		0.463	0.488	0.500	0.491	0.455	0.386	−0.102 ***	−7.996	0.000
	$IVOL\_C{4}_{it}$		0.454	0.479	0.491	0.483	0.444	0.376	−0.103 ***	−8.256	0.000
	$IVOL\_M{M}_{it}$	Medians	0.427	0.463	0.467	0.466	0.428	0.360	−0.102 ***	36.980	0.000
	$IVOL\_FF{3}_{it}$		0.408	0.436	0.446	0.448	0.404	0.338	−0.098 ***	47.732	0.000
	$IVOL\_C{4}_{it}$		0.400	0.427	0.438	0.439	0.395	0.334	−0.093 ***	46.313	0.000
	N		5098	822	685	678	797	685
	Patents Quantile		No Patents	Lowest	2	3	4	Highest	H-L	t-stat/χ2	p-Value
(e) DISP (Q5)	$IVOL\_M{M}_{it}$	Means	0.580	0.613	0.635	0.620	0.590	0.503	−0.110 ***	−5.387	0.000
	$IVOL\_FF{3}_{it}$		0.553	0.583	0.603	0.590	0.559	0.476	−0.107 ***	−5.516	0.000
	$IVOL\_C{4}_{it}$		0.540	0.573	0.592	0.578	0.547	0.464	−0.110 ***	−5.747	0.000
	$IVOL\_M{M}_{it}$	Medians	0.499	0.531	0.551	0.555	0.530	0.447	−0.084 ***	24.164	0.000
	$IVOL\_FF{3}_{it}$		0.475	0.510	0.527	0.531	0.499	0.417	−0.092 ***	27.784	0.000
	$IVOL\_C{4}_{it}$		0.465	0.502	0.518	0.521	0.487	0.415	−0.086 ***	33.003	0.000
	N		5480	846	631	683	685	430

, panel A reports the differences in the means and medians of subsamples double-sorted based on R&D spending and PAT. Panel B reports double sorting based on PAT and DISP. Table 5, panel A (a) shows the difference in the means and medians of the entire sample. The results indicate that IVOL is negatively correlated to PAT. The lowest patent quantile has an average (median) $IVOL\_MM$ of 0.545 (0.467) compared to 0.455 (0.391) in the highest quantile. The difference between the two averages is significant at the 1% level. Panel A (b) through panel A (g) show similar results across all R&D quantiles. An important observation is that the mean (median) IVOL monotonically declines as the number of patents increases across all R&D quintiles. These results provide preliminary evidence that IVOL is negatively correlated to patents after controlling for R&D spending, supporting our first hypothesis. Additionally, this shows that R&D and patents capture different dynamics of the innovation process. These results are consistent with those of previous studies (e.g., Czarnitzki and Toole 2011).

Similarly, Table 5, panel B reports the mean and the median of the sample double sorting based on DISP and PAT quantiles. The first observation is an inverse relationship between IVOL and PAT across all DISP quantiles. For the lowest DISP quantile (Q1), as is shown in panel B (a), the average (median) $IVOL\_MM$ declines from 0.387 (0.340) to 0.299 (0.242). The difference between the two averages (medians) is −0.089 (−0.097) and is significant at the 1% level. In the highest DISP quantile (Q5), panel B (e), average (median) $IVOL\_MM$ declines from 0.613 (0.531) in the lowest PAT quantile to 0.503 (0.447) in the highest PAT quantile. The difference is also significant at the 1% level. Interestingly, the difference between the average (median) IVOL in the lowest PAT quantile and the highest PAT quantile increases as we move up the DISP quantile. This indicates that the impact of patents is higher for firms with higher information uncertainty as measured by DISP, which is consistent with Hypothesis 1b.

4.2. Baseline Results

Table 6. Innovation and idiosyncratic volatility. This table shows the relationship between innovation, measured by the natural log of the number of patents weighted by citations (${\mathrm{PAT}}_{\mathrm{it}-1}$), and different proxies of idiosyncratic volatility ($IVOL\_{\mathrm{X}}_{\mathrm{it}}$). The definitions of the variables are provided in Appendix A. Fixed effects are included. The standard errors are clustered by firm and year and are reported in parentheses. The sample period is from 1982 to 2015. ***, **, and * denote significance at the 1, 5, and 10% level, respectively.

	(1)	(2)	(3)	(4)	(5)	(6)
	$\mathit{I}\mathit{V}\mathit{O}\mathit{L}\_\mathit{M}{\mathit{M}}_{\mathit{i}\mathit{t}}$	$\mathit{I}\mathit{V}\mathit{O}\mathit{L}\_\mathit{F}\mathit{F}{3}_{\mathit{i}\mathit{t}}$	$\mathit{I}\mathit{V}\mathit{O}\mathit{L}\_\mathit{C}{4}_{\mathit{i}\mathit{t}}$	$\mathit{I}\mathit{V}\mathit{O}\mathit{L}\_\mathit{M}{\mathit{M}}_{\mathit{i}\mathit{t}}$	$\mathit{I}\mathit{V}\mathit{O}\mathit{L}\_\mathit{F}\mathit{F}{3}_{\mathit{i}\mathit{t}}$	$\mathit{I}\mathit{V}\mathit{O}\mathit{L}\_\mathit{C}{4}_{\mathit{i}\mathit{t}}$
$\mathit{P}\mathit{A}{\mathit{T}}_{\mathit{i}\mathit{t}-1}$	−0.099 ***	−0.096 ***	−0.095 ***	−0.026 ***	−0.025 ***	−0.024 ***
	(0.002)	(0.002)	(0.002)	(0.007)	(0.006)	(0.006)
$\mathit{R}\&{\mathit{D}}_{\mathit{i}\mathit{t}-1}$	0.053 ***	0.050 ***	0.050 ***	−0.001	0.000	0.000
	(0.002)	(0.002)	(0.002)	(0.002)	(0.002)	(0.002)
$\mathit{D}\mathit{I}\mathit{S}{\mathit{P}}_{\mathit{i}\mathit{t}-1}$				0.057 ***	0.055 ***	0.057 ***
				(0.021)	(0.020)	(0.018)
$\mathit{C}\mathit{F}\mathit{V}\mathit{O}{\mathit{L}}_{\mathit{i}\mathit{t}-1}$				0.066 ***	0.064 ***	0.060 ***
				(0.024)	(0.021)	(0.021)
$\mathit{S}\mathit{I}\mathit{Z}{\mathit{E}}_{\mathit{i}\mathit{t}-1}$				−0.027 ***	−0.026 ***	−0.027 ***
				(0.007)	(0.007)	(0.006)
$\mathit{A}\mathit{G}{\mathit{E}}_{\mathit{i}\mathit{t}-1}$				−0.063 ***	−0.059 ***	−0.058 ***
				(0.012)	(0.011)	(0.011)
$\mathit{M}{\mathit{B}}_{\mathit{i}\mathit{t}-1}$				0.009 ***	0.009 ***	0.009 ***
				(0.002)	(0.002)	(0.002)
$\mathit{L}\mathit{E}{\mathit{V}}_{\mathit{i}\mathit{t}-1}$				0.183 ***	0.175 ***	0.165 ***
				(0.028)	(0.026)	(0.024)
$\mathit{C}\mathit{A}\mathit{S}{\mathit{H}}_{\mathit{i}\mathit{t}-1}$				−0.02	−0.02	−0.022 *
				(0.014)	(0.013)	(0.013)
$\mathit{D}\mathit{P}{\mathit{O}}_{\mathit{i}\mathit{t}-1}$				−0.027 ***	−0.025 ***	−0.025 ***
				(0.004)	(0.003)	(0.003)
$\mathit{B}\mathit{I}\mathit{D}\mathit{A}\mathit{S}{\mathit{K}}_{\mathit{i}\mathit{t}-1}$				0.560 ***	0.618 ***	0.642 ***
				(0.187)	(0.178)	(0.174)
$\mathit{R}\mathit{O}{\mathit{A}}_{\mathit{i}\mathit{t}-1}$				−0.146 ***	−0.135 ***	−0.132 ***
				(0.029)	(0.027)	(0.025)
$\mathit{H}\mathit{H}{\mathit{I}}_{\mathit{i}\mathit{t}-1}$				0.073	0.082	0.079
				(0.094)	(0.088)	(0.086)
$\mathit{T}\mathit{A}\mathit{N}{\mathit{G}}_{\mathit{i}\mathit{t}-1}$				0.063 ***	0.058 ***	0.054 ***
				(0.017)	(0.017)	(0.016)
$\mathit{I}\mathit{V}\mathit{O}\mathit{L}\_{\mathit{X}}_{\mathit{i}\mathit{t}-1}$				0.072 ***	0.069 ***	0.067 ***
				(0.007)	(0.007)	(0.007)
$\mathit{C}\mathit{o}\mathit{n}\mathit{s}\mathit{t}\mathit{a}\mathit{n}\mathit{t}$	0.381 ***	0.369 ***	0.363 ***	0.524 ***	0.500 ***	0.505 ***
	(0.030)	(0.029)	(0.029)	(0.052)	(0.047)	(0.045)
Year FE	Yes	Yes	Yes	Yes	Yes	Yes
Firm FE	Yes	Yes	Yes	No	No	No
Industry FE	No	No	No	Yes	Yes	Yes
N	77,923	77,923	77,923	37,587	37,587	37,587
$\mathit{A}\mathit{d}\mathit{j}. {\mathit{R}}^2$	0.162	0.159	0.159	0.523	0.520	0.520
No. of firms	8256	8256	8256	5548	5548	5548

shows the results of the regression model, Equation (1), where IVOL proxies are regressed on the control variables. We hypothesized that IVOL would be negatively correlated to a firm’s innovation after we control for fixed effects. Consistent with our hypothesis, the results show that innovation output has a significant negative relationship with idiosyncratic volatility. In model (1), the coefficient for PAT (${\mathsf{\beta }}_1=-0.09$) in the regression on IVOL is significant at the 1% level. The result is robust to alternative measures of IVOL.

In models (4), (5), and (6), we regress IVOL proxies on $PA{T}_{it}$. Fixed effects are introduced to the model to mitigate the impact of endogeneity issues that might arise due to the omitted variables bias and the other control variables besides industry and year fixed effects. The results of the fixed effects regression are similar to the results presented in models (1), (2), and (3). This indicates that these results are not driven by time-variant or time-invariant unobserved heterogeneity.

The results in Table 6 show that the coefficients of most of the control variables are significant and have the predicted sign. Consistent with the previous literature, firms that are larger ($SIZE$), are older ($AGE$), have higher payout ratios ($DPO$), have higher cash holdings ($CASH$), and are more profitable ($ROA$) have a lower IVOL. On the other hand, firms with higher information uncertainty ($DISP$), growth opportunities ($M{B}_{it}$), leverage ($LE{V}_{it}$), and information asymmetry ($BIDAS{K}_{it}$) have higher IVOL.

In an unreported previous robustness check, we repeat the analysis using the subsample of firms with positive R&D firms, positive patents, and firms with positive R&D AND positive patents. The results are similar to the reported results, suggesting that the negative association between IVOL and patents is not driven by the jump from no patents to having positive patents or by innovative firms that have lower IVOL in the first place.

4.3. Patents and Information Uncertainty

If patents help investors to predict future firm performance and reduce risk, we should expect this effect to be more pronounced for firms with higher information uncertainty. This is because patents disseminate positive information and reduce the information uncertainty in these firms. To test this hypothesis, we follow Diether et al. (2002) and Zhang (2006) and use DISP as a proxy for information uncertainty. We interact the variable with PAT and add the interaction term to the regression analysis. We expect the parameter estimate to be significant and negative.

Table 7. The interaction between innovation, information uncertainty, and idiosyncratic volatility. This table shows the interaction between innovation and information uncertainty and their relationship’s effect on idiosyncratic volatility. The definitions of the variables are provided in Appendix A. Fixed effects are included. Standard errors clustered by firm and year are reported in parentheses. The sample period is from 1982 to 2015. ***, **, and * denote significance at the 1, 5, and 10% level, respectively.

	(1)	(2)	(3)	(4)	(5)	(6)
	$\mathit{I}\mathit{V}\mathit{O}\mathit{L}\_\mathit{M}{\mathit{M}}_{\mathit{i}\mathit{t}}$	$\mathit{I}\mathit{V}\mathit{O}\mathit{L}\_\mathit{F}\mathit{F}{3}_{\mathit{i}\mathit{t}}$	$\mathit{I}\mathit{V}\mathit{O}\mathit{L}\_\mathit{C}{4}_{\mathit{i}\mathit{t}}$	$\mathit{I}\mathit{V}\mathit{O}\mathit{L}\_\mathit{M}{\mathit{M}}_{\mathit{i}\mathit{t}}$	$\mathit{I}\mathit{V}\mathit{O}\mathit{L}\_\mathit{F}\mathit{F}{3}_{\mathit{i}\mathit{t}}$	$\mathit{I}\mathit{V}\mathit{O}\mathit{L}\_\mathit{C}{4}_{\mathit{i}\mathit{t}}$
$\mathit{P}\mathit{A}{\mathit{T}}_{\mathit{i}\mathit{t}-1}$	−0.036 ***	−0.034 ***	−0.034 ***	−0.021 ***	−0.021 ***	−0.020 ***
	(0.005)	(0.004)	(0.004)	(0.005)	(0.004)	(0.004)
$\mathit{P}\mathit{A}{\mathit{T}}_{\mathit{i}\mathit{t}-1}*\mathit{D}\mathit{I}\mathit{S}{\mathit{P}}_{\mathit{i}\mathit{t}-1}$	−0.089 ***	−0.087 ***	−0.083 ***	−0.067 **	−0.066 **	−0.062 **
	(0.031)	(0.029)	(0.028)	(0.030)	(0.028)	(0.028)
$\mathit{R}\&{\mathit{D}}_{\mathit{i}\mathit{t}-1}$	0.011 **	0.011 **	0.011 **	(0.001)	0.000	0.000
	(0.005)	(0.005)	(0.005)	(0.005)	(0.005)	(0.005)
$\mathit{D}\mathit{I}\mathit{S}{\mathit{P}}_{\mathit{i}\mathit{t}-1}$	0.207 ***	0.199 ***	0.197 ***	0.070 ***	0.068 ***	0.069 ***
	(0.020)	(0.019)	(0.019)	(0.020)	(0.019)	(0.019)
$\mathit{C}\mathit{F}\mathit{V}\mathit{O}{\mathit{L}}_{\mathit{i}\mathit{t}-1}$				0.067 ***	0.064 ***	0.061 ***
				(0.022)	(0.021)	(0.021)
$\mathit{S}\mathit{I}\mathit{Z}{\mathit{E}}_{\mathit{i}\mathit{t}-1}$				−0.027 ***	−0.026 ***	−0.027 ***
				(0.003)	(0.003)	(0.003)
$\mathit{A}\mathit{G}{\mathit{E}}_{\mathit{i}\mathit{t}-1}$				−0.063 ***	−0.059 ***	−0.058 ***
				(0.007)	(0.007)	(0.007)
$\mathit{M}{\mathit{B}}_{\mathit{i}\mathit{t}-1}$				0.009 ***	0.009 ***	0.009 ***
				(0.001)	(0.001)	(0.001)
$\mathit{L}\mathit{E}{\mathit{V}}_{\mathit{i}\mathit{t}-1}$				0.183 ***	0.175 ***	0.165 ***
				(0.014)	(0.014)	(0.014)
$\mathit{C}\mathit{A}\mathit{S}{\mathit{H}}_{\mathit{i}\mathit{t}-1}$				−0.02	−0.02	−0.022 *
				(0.013)	(0.012)	(0.012)
$\mathit{D}\mathit{P}{\mathit{O}}_{\mathit{i}\mathit{t}-1}$				−0.027 ***	−0.025 ***	−0.025 ***
				(0.003)	(0.003)	(0.003)
$\mathit{B}\mathit{I}\mathit{D}\mathit{A}\mathit{S}{\mathit{K}}_{\mathit{i}\mathit{t}-1}$				0.557 ***	0.615 ***	0.639 ***
				(0.163)	(0.156)	(0.153)
$\mathit{R}\mathit{O}{\mathit{A}}_{\mathit{i}\mathit{t}-1}$				−0.146 ***	−0.136 ***	−0.132 ***
				(0.020)	(0.019)	(0.019)
$\mathit{H}\mathit{H}{\mathit{I}}_{\mathit{i}\mathit{t}-1}$				0.074	0.083 *	0.080 *
				(0.049)	(0.047)	(0.046)
$\mathit{T}\mathit{A}\mathit{N}{\mathit{G}}_{\mathit{i}\mathit{t}-1}$				0.062 ***	0.056 ***	0.049 ***
				(0.017)	(0.017)	(0.016)
$\mathit{C}\mathit{o}\mathit{n}\mathit{s}\mathit{t}\mathit{a}\mathit{n}\mathit{t}$				0.063 ***	0.058 ***	0.054 ***
				(0.010)	(0.010)	(0.010)
Year FE	Yes	Yes	Yes	Yes	Yes	Yes
Firm FE	Yes	Yes	Yes	No	No	No
Industry FE	No	No	No	Yes	Yes	Yes
N	37,587	37,587	37,587	37,587	37,587	37,587
$\mathit{A}\mathit{d}\mathit{j}. {\mathit{R}}^2$	0.493	0.489	0.489	0.524	0.520	0.520
No of firms	5548	5548	5548	5548	5548	5548

shows the results. Consistent with hypothesis H1.b, the parameter estimate on the interaction term is negative and statistically significant at the 1% level in all specifications. The coefficient on $PA{T}_{it}$ continues to be negative and statistically significant. These results support the hypothesis that the impact of patents is higher for firms with higher information uncertainty.

5. Conclusions

In this paper, we examine the impact of innovation output on IVOL. Using alternative measures of IVOL for a large sample of US firms, we find that IVOL is negatively associated with innovation output after controlling for several firm characteristics under different model specifications. In addition, we show that the impact of innovation output on IVOL is more pronounced in firms with higher information uncertainty, as captured by dispersion in analysts’ forecasts. This is consistent with our conjecture that patenting improves information dissemination.

The findings of this paper advance our knowledge of how innovation output affects a firm’s risk and how innovative activities are evaluated by the capital market. Our results can help managers to better understand the impact of innovative projects on a firm’s risk profile and its capital market implications. This will help them allocate capital effectively and efficiently to their available investment opportunity set. Additionally, our results contribute to our understanding of the behavior of IVOL, which affects portfolio diversification, options pricing, and market efficiency.

Similar to other studies, this study has the following limitations. There might be firm-specific or market variables that impact firms’ IVOL but are not included in the model. Additionally, the paper does not address the impact of innovation characteristics (radical and incremental innovation) on firms’ risk levels. Future research should investigate this issue as it may have importance to investors and corporate executives.