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Our customer services. Advice and contact Do you have any questions? Write to us, call us or visit us in person. Notifications and forms Do you wish to report a claim, notify a change or update a contract? Contact us without delay. When we repeat our main analysis on the poorer state-years by replacing LnCPRatio by the natural log of per capita state lottery sales, the latter variable positively and significantly predicts each of our innovation input and output variables, as shown in row 7b of panel A.

In addition, we conduct several robustness tests aimed at further mitigating a bias coming from potential omitted variables. Well, this subsample contains state-years that are poor only in a relative sense. Moreover, Kumar finds that poorer investors are more likely to buy lottery-type stocks to complement their purchases of state lottery tickets. These tests check for another potential source of endogeneity. Despite a loss of more than 25 percent of our sample when we drop them, the results shown in row 8a remain significant and are in agreement with our main findings.

Moreover, our findings are not driven just by firms in high-tech industries. The results in row 8b are similar when we omit firms in high-tech industries, as defined by Loughran and Ritter The next robustness test examines another potential source of endogeneity. The observed positive relation between innovative activities and LnCPRatio may be driven by common trends in both variables in some locations without any causal relation, if such trends are not adequately captured by our county-level control variables and time fixed effects.

To mitigate this concern, we examine whether our results are driven by clustering of industries in high-tech cities which are also more likely to experience rapid changes in cultural and religious compositions due to immigration. To this end, we exclude the counties that contain the five most high-tech areas in the U.

Our results in row 8c do not materially change when we do so. Alternatively, we exclude the five U. This finding implies that the observed relations are not driven by firms in a few states with a large number of Catholic adherents. We calculate the ratio of Catholic church members to other church members in CORatio , the first year for which ARDA collected data on county-level religiosity. Moreover, since our sample starts in and ends in , this variable represents cross-sectional variation in religious composition from 28 to 54 years ago.

Moreover, it is unlikely that people choose which state and county to live in based on their expectations of corporate policies that far in the future. We next attempt to control for unobserved firm heterogeneity. Ideally, this is done by including firm fixed effects in the regressions. However, our data does not allow us to control for firm fixed effects because the religious composition of a county remains fairly stable over time.

Consequently our main explanatory variable of interest, LnCPRatio, does not have substantial time-series variation within a firm. So, we use the random effects model RE as an alternative. Although the RE model relies on stronger assumptions about the error correlation structure, it can estimate the effects of time invariant explanatory variables, while controlling for unobserved heterogeneity which can be another source of endogeneity due to omitted variables. In row 8g , the estimated coefficient on LnCPRatio in the patent count regression under the RE model turns insignificant in the full sample, but stays significant in the sample of innovative industries.

The point estimates for the innovative industry subsample are larger than for the full sample in all the regressions. Hutton, Jiang and Kumar find that Democratic managers choose riskier corporate policies than Republican managers, so they may invest more in innovation ventures, which tend to be highly risky.

To address this issue, we follow Grullon, Kanatas and Weston and replicate our analysis using only firms that were incorporated after approximated by their first appearance on Compustat , and find similar results. We linearly interpolate the data to obtain estimates for the intermediate years. We then create a dummy variable, Blue County, to indicate whether the Democratic candidate received more popular votes than the Republican candidate in a county in a given year.

When we add the Blue County dummy to our regressions in Table 4, its coefficient is significantly positive in three out of the eight specifications. More importantly, the coefficient of LnCPRatio remains significantly positive in all our regressions, and is larger in the innovative industry sub-sample, as shown in row 8h.

This paper integrates ideas from previous research on two potentially related behavioral attributes, namely gambling preferences and CEO overconfidence. Therefore, a relevant question is how these ideas are conceptually related, and whether LnCPRatio has incremental explanatory power over CEO overconfidence.

CEO overconfidence and lottery preferences can both affect innovation. Overconfidence is a behavioral bias which makes managers underestimate the variance or overestimate the mean of the payoff distribution, leading them to undertake high-risk projects such as innovation.

A preference for skewness, on the other hand, is not necessarily irrational and is justified under a cumulative prospect theory framework. An agent with lottery preferences knows the payoff distribution, but prefers the payoff with greater positive skewness.

Since neither of the two attributes precludes the other, they can co-exist and independently influence innovative decisions. So we next investigate whether gambling preferences have incremental explanatory power over the option-based measure of CEO overconfidence. We add LnCPRatio as an explanatory variable to each of these regressions. We first employ a treatment effect model to mitigate the potential effect of self-selection.

For each year in our sample, we partition the sample firms into two groups based on CPRatio: those in the top tercile, the treatment group and those in the remaining two terciles, the control group. Since location i. As an alternative to the selection-bias model described above, we employ a propensity score matching PSM analysis which, unlike the Heckman selection bias-model, does not depend upon a specific functional form or the choice of the instrument.

We then match each firm located in the high CPRatio subsample with two similar firms in the low CPRatio subsample using the nearest neighborhood approach. Row 9b in Table 4 reports the average treatment effect for the treated ATT.

The results are generally similar to those in our baseline tests. We exclude the year the firm appears in a new state because the relocation takes place at different times during the year for different firms and to allow time for a change in corporate policies. The quintiles are formed every year, starting in , ten years after the beginning year of our sample. The standard errors are robust to heteroskedasticity and clustered at the firm-level.

Kumar argues that stocks with high idiosyncratic volatility, high idiosyncratic skewness and low price tend to have lottery-like characteristics. Investors with a preference for lotteries find such stocks attractive, even if they offer negative expected returns, because these investors expect the extreme positive return events of the past to be repeated in the future. Kumar finds that individual investors in Catholic- Protestant- dominated areas favor lottery-like stocks more less than the rest of the sample.

KPS find that even institutional investors, who generally avoid highly risky stocks, hold higher proportions of lottery-type stocks if they are located in counties with higher concentrations of Catholics. We begin our analysis by identifying stocks that are more likely to be viewed as lottery-like. Motivated by Kumar , we classify a stock as lottery-type if its returns exhibit above-median idiosyncratic volatility and above-median idiosyncratic skewness in a given year.

Idiosyncratic skewness is calculated as the skewness of the residuals obtained by regressing daily returns on a stock on excess market return and excess market return squared see, Harvey and Siddique , and Kumar Following Kumar , Table II , we control for firm-specific variables such as firm size, firm age and market-to-book ratio , variables related to asset pricing such as market beta, SMB and HML and market microstructure variables turnover and illiquidity.

We also include all county-level control variables. In addition, the models include year fixed effects and either industry or firm fixed effects. For brevity, county- level control variables are not tabulated. Column 1 shows the results of a logit regression that predicts the probability of a stock to be lottery-like. This fixed effect logit model examines the determinants of within-firm variability in the lottery-likeness of a stock.

By definition, this regression only includes those firms where the stock switched from being non-lottery type to being lottery type, or vice-versa. The model yields a positive coefficient of 1. The control variables are the same as before. Columns 5 and 6 of Table 5 show the results of regressions of idiosyncratic skewness. Column 6 presents the same regression with firm fixed effects. Following Kumar , we also experiment with adding the cotemporaneous idiosyncratic volatility measure as an additional explanatory variable in the idiosyncratic skewness regressions because volatility and skewness might be simultaneously determined.

The results presented in columns 1 and 2 suggest that stocks with lottery-like features belong mostly to younger firms with significantly smaller market capitalization, lower institutional ownership, higher illiquidity i.

Moreover, lottery stocks earn lower returns and are less likely to be dividend payers. The negative point estimate on price per share suggests that stocks classified as lottery stocks based on idiosyncratic volatility and idiosyncratic skewness also tend to have lower prices, which is the third criterion Kumar uses to identify a lottery stock.

Some variables take the opposite signs while predicting idiosyncratic volatility and idiosyncratic skewness. Similarly, firm age seems to have a negative effect on volatility but a positive effect on skewness. There is also some evidence that the number of eventually granted patent applications is positively related to volatility, but negatively to skewness.

While many of these projects fail, a few can yield ground-breaking inventions with very large returns. This result reinforces our hypothesis that motivating investment in innovation should be easier for firms in which managers and investors possess a taste for gambling. Supporting evidence To improve identification, in this section we examine four secondary implications of our main hypotheses. We argue that firms do so partly because local investors in these areas value lottery-like features in the stock.

Our findings in section 4 support this argument. To test this hypothesis, we examine four indicators of such firms. We create an indicator variable, SmallFirm, which equals one if the market value of the firm is less than the median market value of all firms in a given year, and zero otherwise.

Second, we identify firms located in counties with fewer investment opportunities relative to local investment demand. This effect makes local investors economically more important to firms. Finally, given that individual investors are more likely to be prone to behavioral biases such as gambling preferences see, e. Accordingly, we create a fourth variable, High Indiv Invest, an indicator variable that equals one if a firm has an above-median fraction of individual shareholdings i.

Table 6 presents these results. Column 1 shows the results of the regression using the first indicator variable SmallFirm and its interaction with LnCPRatio. The results support our hypothesis that the influence of local gambling attitudes on innovative input, i. The point estimate of this interaction term, which measures the effect of gambling preferences in small firms, is 0. On the other hand, the point estimate on the rest of the sample is a much smaller 0. To recap, we find that the effect of gambling preferences on innovative input is driven by firms for which the local investor base is more important.

Our findings in section 4 and 5. Consistent with the fact that stock options have lottery-type characteristics, such as a positively-skewed payoff distribution, KPS find that broad-based employee stock option plans are more popular among firms in gambling-tolerant areas.

Second, since the value of an option increases with the volatility and skewness of the underlying asset see, e. For the subsample of our firm-years on Execucomp,31 we start by examining whether stock option holdings of CEOs and the top management team of firms in high CPRatio areas generate higher sensitivity to stock volatility Vega. We then estimate a regression that predicts Vega, where the main explanatory variable of interest is LnCPRatio. The control variables are from Mobbs except for variables related to directors.

The coefficient estimate of LnCPRatio becomes larger in magnitude and statistically more significant after controlling for CEO overconfidence, option Delta and a number of firm-specific and county-specific variables in column 2.

This result implies that consistent with our hypothesis and the findings of KPS about rank and file employees, CEOs of firms in more gambling-tolerant areas have greater exposure to stock volatility and skewness. Even after controlling for additional variables such as overconfidence and option Delta, the coefficient on Vega is significantly positive.

This result is consistent with prior findings see, e. This result suggests that the gambling preference of the top management team, rather than only the CEO, matters for innovation. If gambling preferences instill a corporate culture of tolerating failures with the hope of large gains from potential break- through innovations, this culture would lead to more exploration and experimentation and even some risky long-shots.

To investigate this issue, we conduct two sets of analyses. These results suggest that, while firms in gambling-tolerant areas generate more patents and citations, on average they have lower innovative efficiency. To this end, we modify the regressions of innovation outputs shown in Table 2, Panel A by recognizing two important issues. First, to estimate innovation output i. The two columns in Panel B of Table 8 show the results of regressions of patent applications and technology-adjusted citations, respectively.

The control variables are the same as in column 3 of Table 3, Panel A. As discussed in section A. Firm Valuation We find in sections 3 and 5. Thus, while our empirical results do not do suggest an unambiguous direct effect of gambling preferences on overall firm valuation, we ask a more specific question: Does firm value vary more with local gambling preferences when innovation is more important?

More generally, are firms in areas with a greater preference for gambling more adept at transforming industry growth opportunities into firm value? Theory and empirical evidence by Manso and Tian and Wang suggest that innovative activities require extraordinary tolerance for failure and a strong incentive to explore and experiment. We motivated our thesis with the simple premise that gambling preferences of managers and investors, which make them underweight a large probability of losses and overweight a small probability of large gains, closely resemble the culture of failure-tolerance required for innovation to succeed.

We use two alternate measures of IndGrowthOpp. First, we use industry innovativeness Innovative Ind which equals one for 4-digit SIC industries whose citations per patent exceed the median for all industries in a given year; it equals zero for other industries. As HLT point out, PE is a noisy measure of growth opportunities because it is influenced by both growth potential and discount rate changes, biasing our tests against finding a significant result.

Firm-level control variables are the same as in HLT In addition, we control for all the county-level variables used in our earlier analyses. If firms in areas with a greater preference for gambling are more adept at transforming industry growth opportunities into firm value, we expect b3 to be positive.

However, we do not have a prior on the sign on b2. Our finding in section 3. But our finding in section 5. Table 9 shows estimates of four variants of this regression. For brevity, we do not report estimates of the county-level control variables and the intercept. Models 1 and 3 include alternate measures of industry growth opportunities, without firm-level controls.

The coefficient estimates of both measures are positive and highly significant, consistent with the idea that firms in industries with higher growth opportunities command higher valuations. Models 2 and 4 include LnCPRatio, a measure of industry growth opportunities, their interaction, and firm-level controls. The coefficient estimate of LnCPRatio is ambiguous: it is positive in model 2 and negative in model 4. This result suggests that firms in areas with greater preference for gambling are more successful at converting their potential growth opportunities into realized firm value.

Conclusion Because innovation is critical for firm value and economic growth, recent academic research and public policy discussion have both focused on identifying factors that lead to more and better innovation. While most prior research investigates rational factors related to firms and financial markets as contributors to innovation, we examine a behavioral determinant of innovation.

The economic magnitudes of these effects are larger for firms in more innovative industries. Our results are consistent with the view that gambling preferences instill a corporate culture of tolerating failures for the possibility of very large gains, which leads to more spending on exploration and experimentation, and eventually to more innovation. These results are robust to several alternative empirical specifications and treatments of endogeneity, both via economic reasoning and econometric techniques.

Moreover, they are supported by analyses of firms 1 that relocate their corporate headquarters, and 2 located in counties that experience large changes in religious composition over time. In addition, we empirically confirm four secondary implications of our hypothesis. Second, gambling preferences of both local investors and managers appear to matter. In our Execucomp subsample, we find that in high CPRatio areas, top executives create large personal exposures to stock volatility and skewness via higher Vega of their stock option holdings.

Our findings suggest that innovative endeavors, like many other financial decisions, are partly a product of human behavior. Our findings are congruent with the rich literature on investor behavior, particularly regarding their preference for local stocks, gambling and skewness. However two caveats are worth noting. First, our finding of a strong positive relation between local gambling preferences and innovation activities is open to two plausible explanations.

The first is the causal explanation that local gambling preferences cause firms to pursue more innovative ventures. The second is the endogenous matching explanation that firms that need more innovation to succeed tend to get matched with investors and managers with greater tastes for gambling. Although none of these analyses are perfect, they consistently support the causal explanation. The second caveat is regarding the normative interpretation of our results.

We examine one consequence of gambling preferences, namely firm innovation. However, we recognize that gambling has many other consequences on individuals and society, and do not argue that gambling is necessarily optimal for a society in an overall sense.

But nurturing some aspects of gambling preference such as a tolerance for early failure, a focus on the maximum payoff and perhaps the ability to endure and enjoy some risk might be beneficial for innovation, which is an activity that is crucial for economic growth. Atanassov, Julian, , Do hostile takeovers stifle innovation? Evidence from antitakeover legislation and corporate patenting, Journal of Finance 68, Balkin, David B.

Markman, and Luis R. Barberis, Nicholas, and Ming Huang, , Stocks as lotteries: The implications of probability weighting for security prices, American Economic Review 98, Barro, Robert J. Bates, Thomas W. Stulz, , Why do U.

Benjamin, Daniel J. Blalock, Garrick, David R. Just, and Daniel H. Simon, , Hitting the jackpot or hitting the skids: Entertainment, poverty, and the demand for state lotteries, American Journal of Economics and Sociology, 66, — Boyer, Brian H.

Carhart, Mark M. Chan, Louis K. Cohen, Lauren, Umit G. Gurun, and Christopher J. Core, John E. Coval, Joshua D. Moskowitz, , Home bias at home: Local equity preference in domestic portfolios, Journal of Finance 54, Diaz, Joseph D. Dittmann, Ingolf and Ernst Maug, , Lower salaries and no options? On the optimal structure of executive pay, Journal of Finance 62, Edmondson, Brad, , Demographics of gambling, American Demographics 8, — Fama, Eugene F.

French, , Common risk factors in returns on stocks and bonds, Journal of Financial Economics 33, 3— Fang, Vivian W. Friedman, Milton, and Leonard J. Savage, , The utility analysis of choices involving risk, Journal of Political Economy 56, Grichting, W.

Weston, , Religion and corporate mis behavior, Working paper, Rice University. Hall, Bronwyn H. Harvey, Campbell R. Innovative efficiency and stock returns, Journal of Financial Economics , — Just, David R. Kahneman, Daniel, and Amos Tversky, , Prospect theory: An analysis of decision under risk, Econometrica 47, Kumar, Alok, , Who gambles in the stock market?

Vishny, , Trust in large organizations, American Economic Review 87, Manso, Gustavo, , Motivating innovation, Journal of Finance 66, Myers, Stuart, and Nicholas Majluf, , Corporate financing and investment decisions when firms have information that investors do not have, Journal of Financial Economics 13, — Stulz, and Rohan Williamson, , The determinants and implications of corporate cash holdings, Journal of Financial Economics 52, 3— Griliches, ed.

Pirinsky, Christo, and Qinghai Wang, , Does corporate headquarters location matter for stock returns? Journal of Finance 61, Rapoport, John, , The anatomy of product-innovation process: Cost and time, in E. Mansfield, ed. Schneider, Christoph, and Oliver Spalt, , Acquisitions as lotteries: do managerial gambling attitudes influence takeover decisions? Eric Yeung, , Local religious beliefs and mutual fund risk-taking behaviors, Management Science 58, Solow, Robert M. Sorescu, Alina B.

Journal of Marketing 72, Spalt, Oliver G. Tversky, Amos, and Daniel Kahneman, , Advances in prospect theory: Cumulative representation of uncertainty, Journal of Risk and Uncertainty 5, Wagner, Leonore U. Replaced by zero if missing. LnPatent Natural logarithm of one plus Patent Applications.

Citations Per Patent The total number of citations received during the sample period on all patents filed and eventually received by a firm in a given year, scaled by the number of the patents filed and eventually received by the firm during the year. The number of citations is adjusted by the weighting index of Hall, Jaffe and Trajtenberg , Replaced by zero if citation counts are missing. LnCitePerPat Natural logarithm of one plus Citations Per Patent Tech-Adjusted Citations Total number of technology class-adjusted citations received during the sample period on all patents filed and eventually received by a firm during the year.

LnCPRatio Natural logarithm of one plus the ratio of the number of Catholic adherents to the number of Protestant adherents in a county in a given year. LnFirmAge Natural logarithm of firm age, approximated by current fiscal year minus the year the firm first appears in Compustat. Skewness Idiosyncratic skewness, computed as the skewness of residuals obtained by regressing daily returns on a stock on excess market return and excess market return squared over a year.

KZ Index Kaplan and Zingales index for a given year calculated as LnAnalysts Natural logarithm of one plus the number of analysts following a firm in a given year. Younger An indicator variable that equals one if the median age of the people in a firm- county is less than the median age for all the firm-counties in a given year, and equals zero otherwise.

Rural Urban Continuum A classification scheme that distinguishes metropolitan i. Scaled from 1 to 9, where a higher number means more rural 1 to 3: metro areas; 4 to 9: non-metro areas. Minority Population Percentage of non-White population in a county. Married Household Percentage of population living in a household of married couples in a county. Male to Female Ratio Ratio of male population to female population in a county. LnAdherentsPer Natural logarithm of the number of religious adherents in a county per residents.

Amihud Illiquidity Absolute daily returns per unit of trading volume, averaged over the number of trading days in a year. Dividend Payer An indicator variable that equals one if the firm pays a cash dividend in a given year, and equals zero otherwise. Turnover Average monthly shares traded divided by the number of shares outstanding during a year.

Stock Return Holding period stock return for a year. Price Per Share Price per share at the end of a fiscal year. Market Beta Loadings on market risk premium estimated by a factor model using the prior sixty monthly returns. SmallFirm An indicator variable that equals one if a firm in a given year has a smaller market capitalization than the median of all firms, and zero otherwise.

High Indiv Invest An indicator variable that equals one if a firm has above-median fraction of individual investors i. CEO Mgmt. Holder67 Option-based measure of overconfidence based on HLT Innovative Ind An indicator variable that equals one for 4-digit SIC industries whose citations per patent exceed the median for all industries in a given year; it equals zero for other industries.

Business Segments Number of business segments from Compustat segment file. Table 1 Summary statistics The table reports the summary statistics of our key variables of interest. Panel A shows county-related variables at the county-level for the latest year that a county appears in our sample. Panel B shows variables at the firm-year level. The sample consists of U.

All the variables used in the regression analyses are defined in the Appendix. Panel A: County-level summary statistics 25th 75th Mean Std. Volatility 0. Skewness 0. Own 0. Team Vega 0. Team Option Delta 0. All the variables are defined in the Appendix. All firm- level independent variables are lagged by one year. County-level control variables are contemporaneous.

Panel A shows the results of regressions on the full sample and panel B shows the results on sub-samples partitioned by industry innovativeness, where a 4-digit SIC code industry is defined as innovative if its average citations per patent exceed the median of all industries in a given year.

All regressions include year and industry dummies, where industry is defined based on 2-digit SIC codes. Intercepts are not reported. Standard errors are corrected for heteroscedasticity and are clustered at the firm-level, and t-statistics are in parentheses. Own LnCPRatio 0. All regressions include year and industry dummies where industry is defined based on 2- digit SIC codes. The first three columns in each set are for the full sample and the next three columns are for the sub-sample of innovative industries.

A 4-digit SIC code industry is defined as innovative if its average citations per patent exceeds the median value for all industries in a given year. In both panels, all regressions include year and industry dummies, where industry is defined based on 2-digit SIC codes.

Standard errors are corrected for heteroscedasticity and are clustered at the firm-level, except that they are Newey-West corrected in row 4 in Panel A, are double-clustered by firm and county-year pairs in row 5, and clustered at the county-level in row 6 in Panel A. Full Sample Innovative Ind. All independent variables at the firm-level are lagged by one year. County-level control variables not reported for brevity are contemporaneous.

Models 1 and 2 are logit and fixed effects logit models where the dependent variable is a dummy variable for a lottery stock. Models 3 and 4 are OLS and firm fixed effects panel regressions with idiosyncratic volatility as the dependent variable. Models 5 and 6 are OLS and firm fixed effects panel regressions with idiosyncratic skewness as the dependent variable.

All regressions include year dummies, and all regressions except those with firm fixed effects include industry dummies. Industry is defined by 2-digit SIC codes. SmallFirm equals one if the market value of a firm is below the median of all firms in a given year. High Indiv Invest is an indicator variable that equals one if a firm has above-median fraction of individual investors i.

Control variables are the same as in column 2 of Table 4, Panel A. All the independent variables at the firm-level are lagged by one year. Standard errors are corrected for heteroscedasticity and clustered at the firm-level and t-statistics are in parentheses.

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