Journal of Monetary Economics 97 (2018) 7187 Contents lists available at ScienceDirect Journal of Monetary Economics journal homepage: p82 Big data in finance and the growth of large firms Juliane Begenau a , b , , Maryam Farboodi c , Laura Veldkamp b , d , e a Graduate School of Business, Stanford University, 655 Knight Way, Stanford, CA 94305 b NBER, 1050 Massachusetts Avenue, Cambridge MA, 02138-5398 c Bendheim Center for Finance, Princeton University, 26 Prospect Avenue, Princeton, NJ 08540 d Leonard N. Stern School of Business, Kaufman Management Center, 44 West Fourth Street, 7-77, New York, NY 10012 e Centre for Economic Policy Research, 33 Great Sutton Street, London EC1V 0DX, UK a r t i c l e i n f o Article history: a b s t r a c t Two modern economic trends are the increase in firm size and advances in information Received 21 April 2018 Accepted 31 May 2018 Available online 15 June 2018 JEL classification: E2 G1 D8 Keywords: Big data Fintech Firm size technology. We explore the hypothesis that big data disproportionately benefits big firms. Because they have more economic activity and a longer firm history, large firms have pro- duced more data. As processor speed rises, abundant data attracts more financial analysis. Data analysis improves investors forecasts and reduces equity uncertainty, reducing the firms cost of capital. When investors can process more data, large firm investment costs fall by more, enabling large firms to grow larger. 2018 Elsevier B.V. All rights reserved. One of the main question in macroeconomics today is why small firms are being replaced with larger ones. Over the last three decades, the percentage of employment at firms with less than 100 employees has fallen from 40% to 35% ( Fig. 1 a); the annual rate of new startups has decreased from 13% to less than 8%, and the share of employment at young firms (less than 5 years) has decreased from 18% to 8% ( Davis and Haltiwanger, 2015 ). While small firms have struggled, large firms (more than 10 0 0 employees) have thrived: The share of the U.S. labor force they employ has risen from one quarter in the 1980s, to about a third today. At the same time, the revenue share of the top 5% of firms increased from 57% to 67% ( Fig. 1 b). One important difference between large and small firms is their cost of capital ( Cooley and Quadrini, 2001 ). Hennessy and Whited (2007) document that larger firms, with larger revenues, more stable revenue streams, and more collateralizable equipment, are less risky to creditors and thus pay lower risk premia. But this explanation for the trend in firm size is challenged by the fact that while small firms are more volatile, the volatility gap between small firms and large firms cash flows has not grown. 1 Alternative, the trend in covariance of firm stock prices with market portfolio, as measured by CAPM , is not significantly different across firms of different sizes. p82 This paper was prepared for the Carnegie-Rochester-NYU conference. We thank the conference committee for their support of this work. We also thank Nic Kozeniauskas for his valuable assistance with the data and Adam Lee for his outstanding research assistance. Corresponding author at: Stanford University Graduate School of Business, 655 Knight Way, Stanford, CA 94305 E-mail address: begenaustanford.edu (J. Begenau). 1 Evidence on the volatility gap between large and small firms is in Appendix A.4 . Other hypotheses are that the productivity of large firms has increased or that potential entrepreneurs instead work for large firms. This could be because of globalization, or the skill-biased nature of technological change as in Kozeniauskas (2017) . These explanations are not exclusive and may each explain some of the change in the distribution of firm size. doi/10.1016/j.jmoneco.2018.05.013 0304-3932/ 2018 Elsevier B.V. All rights reserved. 72 J. Begenau et al. / Journal of Monetary Economics 97 (2018) 7187 Fig. 1. Large Firms Growing Relatively Larger. The left panel uses the Business Dynamics Statistics data published by the Census Bureau (from Kozeniauskas, 2017). It contains all firms with employees in the private non-farm sector in the United States. The right panel uses Compustat/CRSP data. Top x % means the share of all firm revenue earned by the x % highest-revenue firms. If neither volatility nor covariance with market risk has diverged, how could risk premia and thus the cost of capital diverge? What introduces a wedge between unconditional variance or covariance and risk is information. Even if the payoff variance is constant, better information can make payoffs more predictable and therefore less uncertain. Given this new data, the conditional payoff variance and covariance fall. More predictable payoffs lower risk and lower the cost of capital. The strong link between information and the cost of capital is supported empirically by Fang and Peress (2009) , who find that media coverage lowers the expected return on stocks that are more widely covered. This line of reasoning points to an information-related trend in financial markets that has affected the abundance of information about large firms relative to small firms. What is this big trend in financial information? It is the big data revolution. Our goal is to explore the hypothesis that the use of big data in financial markets has lowered the cost of capital for large firms relative to small ones, enabling large firms to grow larger. In modern financial markets, information technology is pervasive and transformative. Faster and faster processors crunch ever more data: macro announcements, earnings statements, competitors performance metrics, export market demand, anything and everything that might possibly forecast future returns. This data informs the expectations of modern investors and reduces their uncertainty about investment outcomes. More data processing lowers uncertainty, which reduces risk premia and the cost of capital, making investments more attractive. To explore and quantify these trends in modern computing and finance, we use a noisy rational expectations model where investors choose how to allocate digital bits of information processing power among various firm risks, and then use that processed information to solve a portfolio problem. The key insight of the model is that the investment-stimulating effect of big data is not spread evenly across firms. Small firms benefit less. In our model, small firms are equivalent to young firms, and large firms to old firms. This is consistent with the data, where age and size are positively correlated. In the model, larger firms are more valuable targets for data analysis because more economic activity and a longer firm history generates more data to process. In contrast, all the computing power in the world cannot inform an investor about a small firm that has a short history with few disclosures. As big data technology improves, large firms attract a more than proportional share of the data processing. Because data resolves risk, the gap in the risk premia between large and small firms widens. Such an asset pricing pattern enables large firms to invest cheaply and grow larger. The data side of the model builds on theory designed to explain human information processing ( Kacperczyk et al., 2016 ), and embeds it into a standard model of corporate finance and investment decisions ( Gomes, 2001 ). In this type of model, deviations from Modigliani-Miller imply that the cost of capital matters for firms investment decisions. In our model, the only friction affecting the cost of capital works through the information channel. The big data allocation model can be reduced to a sequence of required returns for each firm that depends on the data-processing ability and firm size. These required returns can then be plugged into a standard firm investment model. To keep things as simple as possible, we study the big-data effect on firms investment decision based on a simulated sample of firms two, in our case in the spirit of Hennessy and Whited (2007) . The key link between data and real investment is the price of newly-issued equity. Assets in this economy are priced according to a conditional CAPM, where the conditional variance and covariance are those of a fictitious investor who has the average precision of all investors information. The more data the average investor processes about an assets payoff, the lower is the assets conditional variance and covariance with the market. A researcher who estimated a traditional, uncon- ditional CAPM would attribute these changes to a relative decline in the excess returns (alphas) on small firms. Thus, the J. Begenau et al. / Journal of Monetary Economics 97 (2018) 7187 73 widening spread in data analysis implies that the alphas of small firm stocks have fallen relative to larger firms. These asset pricing moments are new testable model predictions that can be used to evaluate and refine big data investment theories. This model serves both to exposit a new mechanism and as a framework for measurement. Obviously, there are other forces that affect firm size. We do not build in many other contributing factors. Instead, we opt to keep our model stylized, which allows a transparent analysis of the new role that big data plays. Our question is simply how much of the change in the size distribution is this big data mechanism capable of explaining? We use data in combination with the model to understand how changes in the amount of data processed over time affect asset prices of large and small public firms, and how these trends reconcile with the size trends in the full sample of firms. An additional challenge is measuring the amount of data. Using information metrics from computer science, we can map the growth of CPU speeds to signal precisions in our model. By calibrating the model parameters to match the size of risk premia, price informativeness, initial firm size and volatility, we can determine whether the effect of big data on firms cost of capital is trivial or if it is a potentially substantial contributor to the missing small firm puzzle. Contribution to the existing literature Our model combines features from a few disparate literatures. The topic of changes in the firm size distribution is a topic taken up in many recent papers, including Davis and Haltiwanger (2015) , Kozeniauskas (2017) , and Akcigit and Kerr (forthcoming) . In addition, a number of papers analyze how size affects the cost of capital, e.g. Cooley and Quadrini (2001) , Hennessy and Whited (2007) , and Begenau and Salomao (forthcoming) . We explore a very different force that affects firm size and quantify its effect. Another strand of literature explores the feedback between information in financial markets and investment: Maksimovic et al. (1999) models the relationship between a firms capital structure and its information acquisition prior to capital budgeting decisions. Bernhardt et al. (1995) studies the effect of different levels of insider trading on investment. Ozdenoren and Yuan (2008) studies a setting where asset prices influence fundamentals through coordinated buying and thus self-fulfilling beliefs. Furthermore, there are papers that focus on long run data or information trends in finance: Asriyan and Vanasco (2014) , Biais et al. (2015) and Glode et al. (2012) model growth in fundamental analysis or an increase in its speed. The idea of long-run growth in information processing is supported by the rise in price informativeness documented by Bai et al. (2016) . Over time, it has gotten easier and easier to process large amounts of data. As in Farboodi et al. (2017) , this growing amount of data reduces the uncertainty of investing in a given firm. But the new idea that this paper adds to the existing work on data and information frictions, is this: Intensive data crunching works well to reduce uncertainty about large firms with long histories and abundant data. For smaller firms, who tend also to be younger firms, data may be scarce. Big data technology only reduces uncertainty if abundant data exists to process. Thus as big data technology has improved, the investment uncertainty gap between large and small firms has widened, their costs of financing have diverged, and big firms have grown ever bigger. 1. Model We develop a model whose purpose is to understand how the growth in big data technologies in finance affects firm size and gauge the size of that effect. The model builds on the information choice model in Kacperczyk et al. (2016) and Kacperczyk et al. (2015) . 1.1. Setup This is a repeated, static model. Each period has the following sequence of events. First, firms choose entry and firm size. Second, investors choose how to allocate their data processing across different assets. Third, all investors choose their portfolios of risky and riskless assets. At the end of the period, asset payoffs and utility are realized. The next period, new investors arrive and the same sequence repeats. What changes between periods is that firms accumulate capital and the ability to process big data grows over time. Firm Decisions. We assume that firms are equity financed. Each firm i has a profitable 1-period investment opportunity and wants to issue new equity to raise capital for that investment. For every share of capital invested, the firm can produce a stochastic payoff f i , t . Thus total firm output depends on the scale of the investment, which is the number of shares x i,t , and the output per share f i , t : y i,t = x i,t f i,t . (1) The owner of the firm chooses how many shares x i,t to issue. The owners objective is to maximize the revenue raised from the sale of the firm, net of the setup or investment cost ( x i,t , x i,t1 ) = 0 1 (| Delta1x i,t | 0) + 1 | Delta1x i,t | + 2 (Delta1x i,t ) 2 , (2) where Delta1x i,t = x i,t x i,t1 , 1 | Delta1x i,t | 0 is an indicator function taking the value of one if | Delta1x i,t | is strictly positive and 0 , 1 , 2 0. This cost function represents the idea that issuing new equity (or buying equity back) has a fixed cost 0 and a 74 J. Begenau et al. / Journal of Monetary Economics 97 (2018) 7187 marginal cost that is increasing in the number of new shares issued. Each share sells at price p i , t , which is determined by the investment market equilibrium. The owners objective is thus E v i,t = E x i,t p i,t ( x i,t , x i,t1 ) |I t1 , (3) which is the expected net revenue from the sale of firm i . The firm makes its choice conditional on the same prior information that all the investors have and understanding the equilibrium behavior of investors in the asset market. But the firm does not condition on p i , t . In other words, it does not take prices as given. Rather, the firm chooses x i,t , taking into account its impact on the equilibrium price. Assets. The model features 1 riskless and n risky assets. The price of the riskless asset is n