Disclosure Regulation, Intangible Capital and the Disappearance of Public Firms

Finance and Economics Discussion Series Federal Reserve Board, Washington, D.C. ISSN 1936-2854 (Print) ISSN 2767-3898 (Online) Disclosure Regulation, Intangible Capital and the Disappearance of Public Firms Sara Casella, Hanbaek Lee, Sergio Villalvazo 2023-050 Please cite this paper as: Casella, Sara, Hanbaek Lee, and Sergio Villalvazo (2023). “Disclosure Regulation, Intangible Capital and the Disappearance of Public Firms,” Finance and Economics Discussion Series 2023-050. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2023.050. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Disclosure Regulation, Intangible Capital and the Disappearance of Public Firms† Sara Casella Hanbaek Lee Sergio Villalvazo University of Pennsylvania University of Tokyo Federal Reserve Board June 30, 2023 Abstract Since the mid-1990s, the number of listed firms in the U.S. has halved, and their public disclosure has become opaquer. To explain these trends, we developageneralequilibriummodelwherethechoicesofgoingpublicorprivate and the transparency of voluntary disclosure are characterized analytically. In the equilibrium, the stock market with directed search and the private equity market with random search co-exist. According to the estimation, stricter disclosure regulation and increased intangible capital share are the key drivers of the observed patterns. Lastly, we characterize a policymaker’s trade-off between welfare and productivity and analyze the optimal policy. Keywords: Intangible capital, corporate disclosures, technology diffusion. JEL codes: D24, G24, G38. † We are grateful to Manuel Adelino, Ismail Baydur, Santiago Bazdresch, Harold Cole, Jesu´s Fern´andez-Villaverde, Angus Foulis, Luca Guerrieri, Nicolas L. Jacquet, Ryo Jinnai, In Hwan Jo, DirkKrueger,AdrianoRampini,SereneTan,SkanderVandenHeuvel,DavidN.Weil,andtheparticipantsintheseminarattheFederalReserveBoard,HitotsubashiUniversity,SingaporeManagement University, National University of Singapore, Lisbon Macro Workshop, ITAM-PIER conference on macro-finance, and BIS-CEPR WE ARE IN Macroeconomics and Finance conference for their constructive comments and discussions. Compustat and I/B/E/S data were obtained by the authors prior to Villalvazo’s employment at the Federal Reserve Board, while they were PhD candidates at the University of Pennsylvania. The views expressed in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System. All remaining errors are our own. Casella: scas@sas.upenn.edu. Lee: hanbaeklee1@gmail.com. Villalvazo: sergio.villalvazomartin@frb.gov 1

1 Introduction Since the mid-1990s, the number of listed firms in the U.S. has decreased almost by half. Over the same period, we document that listed firms’ performance has become increasingly difficult to predict; reports of listed firms have become significantly more opaque. What are the driving forces for these changes? What are their macroeconomicconsequences? Thispaperanswersthesequestionsthroughthelensofageneral equilibrium model of information disclosure and capital markets, where an analytic solution characterizes a rich set of equilibrium allocations. We then use the model to analyze the optimal disclosure regulation based on the equilibrium. The U.S. Securities and Exchange Commission (SEC) requires listed firms to publicly reveal their annual and quarterly financial information and disclose material events such as transactions involving shareholders and insiders. Moreover, public firms are not allowed to selectively disclose materials to some investors (e.g., Regulation Fair Disclosure of 2000). Disclosure regulation aims to protect investors and facilitate a fair capital market. However, the cost of disclosure is that it may also reveal crucial information to competitors (Bhattacharya and Ritter, 1983). In this paper, we show that stricter disclosure regulation and the increased importance of intangible capital in production are critical factors driving public firms’ disappearance. Support exists for the notion that private firms’ ability to avoid public disclosures is an important factor in their decision to stay private.1 Our second key hypothesis is that, given its nature, intangible capital is one of the most fragile input factors to the information disclosure process. While companies may keep patents and trade secrets, 1For example, Dambra, Casares Field, and Gustafson (2015) study the effect of Title I of the JOBSAct(JumpstartOurBusinessStartupsAct),whichexemptsemerginggrowthcompaniesfrom certain disclosure requirements during the IPO process and allows issuers to disclose information exclusively to investors, but not competitors, until the IPO becomes likely to succeed. They find thattheactincreasedthevolumeofIPOsby25%comparedtotheirpreviouslevel;andthisincrease is concentrated in firms with a high cost of disclosure, such as firms in the tech sector. Aghamolla and Thakor (2022) exploit a shock to disclosure requirements in the biopharmaceutical industry to showthatincreasedmandatorydisclosurerequirementsforprivatefirmssignificantlyincreasestheir propensity of going public. 2

some ideas are simply non-excludable: Once information about intangible capital is revealed, then it is easily mimicked (Crouzet et al., 2022).2 Usingtheestimatedgeneral equilibrium model, weshowthatdisclosureregulation increases the welfare of risk-averse investors through more transparent information disclosure. Regulationcan, however, crowdoutvoluntarydisclosureandevenbackfire throughtheextensive-marginchannel, asmorefirmstendtostayintheprivateequity market, which is more opaque.3 Moreover, as firms adopt more intangible capital, which is subject to imitation risk to a greater extent, they have a stronger incentive to conceal information, leading to an increased tendency to remain privately held. This technological change also leads to less transparent reporting for firms that stay public, as observed in the data. Finally, we show that the disappearance of public firmsandoverallgreateropacityinfinancialmarketssubstantiallyreduceproductivity and technological diffusion across firms. Our approach is motivated by macro- and micro-level empirical evidence. On the macroeconomic side, we revisit some well-known facts in the literature. The level of intangible capital has significnatly risen, and the number of public firms has decreased by almost 50% in the U.S. since 1996. Then, using U.S. Compustat data and data from the Institutional Brokers’ Estimate System (I/B/E/S), we construct a transparency measure of the firm-level disclosure based on earnings surprises. Our measure shows that the average transparency has significantly declined over the same period of the two aforementioned trends. 2We refer to those components of intangible capital that are not well protected by specific legal institutions and thus not necessarily patentable or patented yet. Most importantly, research ideas, early stages innovation and R&D, software, but also certain novel business methods and organizational innovations, branding and marketing strategies, employee training, proprietary information such as some formulas, customer lists, processes, and generally, firms’ strategies and intentions that a public firm cannot selectively disclose. 3This is one of the core issues the SEC is concerned about. For example, in a February 2017 speech, SEC Commissioner Kara Stein posed a question regarding additional disclosures and regulation around private market investment: “We also need to understand why more companies are staying private for longer periods of time. Should we apply enhanced disclosure laws to these private companies? Or perhaps they require a unique set of rules.” See “The Markets in 2017: What’s at Stake?” Commissioner Kara M. Stein, SEC website, https://www.sec.gov/news/speech/steinsecspeaks-whats-at-stake.html 3

Toinvestigatetherelationshipbetweentransparencyandintangiblecapitalfurther we run a panel regression of the transparency on intangible capital with firm-level controls and fixed effects. We find that our measure of transparency, which is based on professional analysts’ forecast errors, is significantly negatively correlated with the firm level of intangible capital. This cross-sectional fact provides an important bridge to link the two macro facts: rising intangible capital and declining transparency. We interpret the result in the following way: the negative relationship between intangible and transparency, proxied by forecast accuracy, can be due to two reasons: one, firms with high levels of intangible tend to be less transparent and, therefore, more difficult to forecast. Two, it may be that, given a certain level of disclosure and transparency, firms with high intangible capital are inherently more challenging to forecast due to their nature (Celentano and Rempel, 2023). Using our model, we set out to disentangle the two forces and their effect. In order to analyze these empirical patterns and their effect on the macroeconomic allocations in a unified framework, we introduce a general equilibrium model of heterogeneous firms where financing decisions are endogenous. In the model, ex-ante homogeneous firms choose whether to go public or private, the level of intangible capital stock, and the transparency of their intangible capital. The disclosed intangible capital is subject to diffusion to other firms as an externality in the form of productivity gain. Ifafirmgoesprivate, transparencyisminimal, andthereisnotechnologydiffusion to the other firms. However, a private firm must search for an investor and is not guaranteed funding if not matched. When a firm chooses to be public, the firm is instead subject to a disclosure obligation, composed of mandated and voluntary components. The minimum mandated portion is enforced by the policymaker. The voluntary portion is endogenously determined by the firm. As the household prefers transparent disclosure, a more voluntarily transparent disclosure leads to a greater value in the funding market. However, a more transparent disclosure undermines 4

the profitability of the firm, especially for high levels of intangible capital. This trade-off endogenously forms a distribution of firms over the transparency domain and determines the mass of the non-listed market in equilibrium. One of the advantages of our model is that these decisions have an analytic solution, which allows us to characterize the model and optimal policy globally and cleanly. The model generates a general equilibrium distribution of endogenous objectsinanalyticform, andassuchresemblestheoneinBurdettandMortensen(1998). In their model, the wage distribution is endogenously determined, as the model captures the endogenous wage postings from the firm side. Similarly, in our model, a risk-averse representative household with CARA utility endogenously chooses the amount of funding for each transparency level. We then conduct a quantitative analysis of the macroeconomic effects of the increasing significance of intangible assets and the impact of information regulation policies. We estimate our model using data from two distinct periods. The first period, spanning from 1992 to 1996, serves as our baseline, while the second period, from 2012 to 2016, is considered as the new steady state. Therefore, we compare a period before the dramatic shift in the number of listed firms with a period several years after the change to assume that it has reached a stationary level. The key structural parameters in the model include intangible capital share and the mandated disclosure rule: the changes in these parameters change the incentive of the voluntary disclosure operating in the listed market. We use the method of simulated moments (MSM) to estimate the parameters, and target moments such as the percentage of listed firms after M&A adjustment, the share of intangiblerelated expenditures over sales, and the fraction of funded private firms. Moreover, one of the advantages of our model is that it is tightly linked with the data: While the distribution of firms’ transparency is not directly observable, the distribution of forecast errors by analysts is both a model output and is observable in our data. Therefore, we target several moments of this distribution over the two periods. 5

Our decomposition analysis reveals that stricter SEC regulation and the rising share of intangible capital accounted for a large part of the decline in listed firms and transparency. We also estimate that the same level of disclosure by firms translates into lower information for investors in the more recent period. We interpret this as intangible capital being inherently more opaque and challenging to understand due to its nature, contributing to the decline of listed firms. The model also predicts that access to funds by private investor has become easier, contributing to the reduction of public firms. These findings highlight that stricter regulation, increased intangible capital, and greater opacity in financial markets are important driving factors behind the reduced transparency, number of listed firms, and productivity. Finally, we set out to find an optimal disclosure policy. To evaluate the consequences of the information disclosure policy, we provide three criteria: output, productivity, and investors’ welfare.4 A higher mandated transparency level decreases the incentive to go public, leading to more private firms in the equilibrium. However, a stricter policy lowers uncertainty for investors, achieving greater welfare. In the estimated model, a local policy change from the status quo can achieve only higher output and productivity or higher welfare.5 From the perspective of the protection of investors, we find that the recent regulation has substantially improved welfare. However, we also document that it has led to a loss in productivity in the production sector. Contribution and literature. Our paper delivers two main contributions to the literature. First, we provide a theoretical and quantitative model framework that analyzestheeffectofrisingintangiblecapitalonthefirm-levelfinancingdecision.6 Using 4The mission of the SEC is “to protect investors, maintain fair, orderly, and efficient markets, and facilitate capital formation.” See “Our Goals,” SEC website, https://www.sec.gov/our-goals. 5In the global domain of the policy, there are ranges where welfare and productivity increase simultaneously along with the policy change. We discuss this in the policy analysis. 6Kahle and Stulz (2017) discussed the possibility of the role of intangible capital in the observed declining trends of listed firms. However, the structural analysis of the channel has been missing in the literature. 6

the estimated model, we show that the regulation on disclosure and rising intangible share has been the key driver of the disappearing public firms. Also, the qualitative aspect of our model is worth highlighting as it allows analytic characterization of rich equilibrium allocations, including the distribution of public and private firms. This tractability promotes the transparent illustration of endogenous mechanisms in our model. Also, it enables a fast and accurate quantitative analysis.7 Second, we bring a novel policy angle, information regulation, to the table and analyze its macroeconomic trade-off. From the tractable general equilibrium model, we show that in a reasonable range of parameters, a policymaker faces a trade-off. between welfare and productivity. We believe the analytic closed-form characterization of our model would serve as a useful tool for future research on information regulation policy. Two strands of the literature are closely related to this paper. The first is the literature that studies the rising importance of intangible capital. It was only around a decade ago that intangible capital was first recognized as an important macroeconomic factor that affects economic growth and the business cycle. For example, McGrattan and Prescott (2010) and McGrattan (2020) highlight the importance of intangible capital as a key input factor for production and show how mismeasurement of intangible capital may mislead the neoclassical model predictions in terms of economic growth. Relatedly, Atkeson and Kehoe (2005) and Eisfeldt and Papanikolaou (2014) modeled plant-level intangible capital as an important input for production. Mainly, their intangible capital refers to organizational capital that is partly firmspecific and partly embodied in key labor inputs. We contribute to this literature by analyzing a novel macroeconomic implication of the rising share of intangible capital. Intangible capital has become an important source of competitiveness, leaving firms to put great effort into research and devel- 7The portion of public firms is often substantially smaller than that of private firms in many countries. Then a computation error of 0.1% in the portion of public firms is a significantly large error. Therefore, a highly-computational model is easily subject to a high approximation error in capturing the portion of large firms. 7

opment (R&D) or developing a productive corporate culture. However, intangible capital has a strong spillover effect, which can benefit competitors as well as the owner firm (Crouzet et al., 2022). Therefore, the rising importance of intangible capital has naturally increased a firm’s incentive to stay opaque in its disclosure. Using our model, we theoretically and quantitatively analyze how this change affects the macroeconomy in terms of welfare and productivity. The second literature is about the disappearance of listed firms. Different explanations have been put forward to shed light on this issue. For example, Gao, Ritter, and Zhu (2013) point to the increase in mergers and acquisitions (M&A) among U.S. firms; Doidge, Karolyi, and Stulz (2017) conjecture that as markets have become more globally integrated, the net benefits of going public in the U.S. versus in other markets have decreased; Ewens and Farre-Mensa (2020) argue that the deregulation of securities laws (National Securities Markets Improvement Act of 1996) improved the private equity market, which reduced the incentives for firms to go public. In this paper, we propose a complementary explanation. We argue that the rise of intangible capital, especially the components of intangible capital that could benefit competitors as well as the owner firm, has increased the cost of disclosing information and made staying private more attractive, which is exacerbated by stricter disclosure requirements. The estimated model also predicts that access to funds by venture capital firms, private equity funds, and other private investors has become easier. Finally, one of the papers closest to ours is Celentano and Rempel (2023), which finds that the rising share of intangible capital has amplified public CEOs’ private information compared to outside investors. This rising informational asymmetry between firm insiders and the general public leads to an increase in CEO compensation due to the design of optimal truth-telling compensation contracts, and a decline in the propensity of going public. We abstract from optimal contracts and the principalagent problem; instead, we focus on a different and complementary channel: regulation on information disclosure and its interaction with intangible capital and its 8

spillover to competitors as a positive learning externality. Our model allows us to calculate welfare and the optimal level of regulation. The rest of the paper is structured as follows. Section 2 describes our datasets and empirical results. Section 3 outlines the model. Section 4 describes the equilibrium and model predictions. Section 5 estimates the structural model, conducts counterfactuals, and describes the optimal regulation policy. We conclude in Section 6. 2 Empirical analysis In this section, we empirically analyze the observed patterns in the number of listed firmsandtheintangiblecapitalstocks. Inthefirm-levelanalysis, thekeyvariablesare intangible capital stock and firm transparency. We first explain our measurement of these two variables. Then, using the measured allocations, we analyze the time-series patterns at the macro and sector levels and the cross-sectional relationships at the firm level. 2.1 Data and Measurement In this section, we explain how we measure the intangible capital stock of public firms and firm transparency. We use firm level data on public U.S. firms from Compustat covering the period from 1985 to 2016 to measure firm-level intangible capital stock. Our baseline measure of internally generated intangible capital is the sum of two components: (i) estimated knowledge capital, calculated using research and development expenditure (XRD); and (ii) estimated organizational capital, calculated using selling, general, and administrative expenses (XSGA). The measure is constructed using the perpetual inventory method, which aggregates net investment flows over the life of the 9

firm: [Knowledge capital] : kG = (1−δ )kG +R&D , i,t G i,t−1 it [Organizational capital] : kO = (1−δ )kO +γ SG&A , i,t O i,t−1 O it where R&D is research and development expenditure expenditure; SG&A is selling, general, and administrative expenses. All the intangible flow variables are deflated by the price of intellectual property products from National Income and Product Accounts data (NIPA Table 1.1.9, line 12). δ and δ are the depreciation rates.8 γ G O O is the fraction of selling,general, and administrative (SG&A) expenditure that adds to the intangible capital stock. We assume γ = 0.20 following Falato et al. (2022). O All the empirical results are robust over other reasonable choices of this parameter level. Then, we calculate the net change in the acquired amount of intangibles from changes in the book values of intangibles after the amortization, using Compustat variables INTAN and AM. We obtain the acquired intangible stock kB, applying i,t the perpetual inventory method to the deflated net change in the intangibles. Our final measure of firm-level intangible capital stock kI is obtained by combini,t ing the internally generated intangible stocks and the acquired intangibles stocks: kI = kG +kO +kB i,t i,t i,t i,t In order to get a measure of firms’ transparency, we leverage information on earnings surprises. Every quarter, professional financial analysts produce and disseminate forecasts of firms’ earnings, based on their timely access to all available information on and off the balance sheet. Our assumption is that it is easier to forecast firms that disclose more information, and so we can proxy firm transparency using the accuracy 8Weuseδ =δ =0.15, whichisaroundthelevelsestimatedintheliterature(Corrado, Hulten, G O and Sichel, 2009). 10

of these forecasts.9 Specifically, earnings surprise ES is defined as the difference between a firm’s i,j,t announced actual earnings per share e and the earnings forecast per share ϵ made t,i i,j,t by an analyst for that firm, normalized by the price of a share P : i,t ϵ −e ES := i,j,t i,t i,j,t P i,t where t is the indicator of a quarter; i and j are firm and analyst indicators, respectively. Thus, the surprise is measured at the analyst-firm level. The data on analysts’ forecasts come from the I/B/E/S. The dataset collects quarterly estimates made by professional financial analysts on the future earnings of publicly traded companies. We closely follow Dellavigna and Pollet (2009) for the detailed steps of the earnings surprise calculation. Then, we define two different proxies for the transparency of the balance sheet at the firm level. The first is the inverse of the median absolute value of earnings surprises: 1 Transparency1 := i,t median(|ES |) i,j,t This proxy is based on the intuition that more transparent firms have lower absolute earnings surprise, on average.10 Our second proxy is the inverse of the variance of earnings surprises: 1 Transparency2 := i,t var(ES ) i,j,t The intuition behind this proxy is that more transparent firms have lower dispersion in the earnings surprise among the analysts, on average. Therefore, the second proxy 9Forecast errors may be influenced by other factors as well, namely, idiosyncratic and aggregate risk, analysts coverage and effort, and varying inherent difficulty of the task. We discuss how these factors influence our analysis in the next sections. 10The median is used instead of the average, this is to rule out the outlier’s level effect on the average. 11

is calculated only for firms with multiple analysts’ forecasts available in the data. In our dataset, the average number of analysts covering a firm is three. 2.2 Trends in the number of listed firms, intangible capital, and transparency Figure 1: Time series of aggregate variables. 1985 1990 1995 2000 2005 2010 2015 0008 0007 0006 0005 0004 Year smrif detsil fo rebmuN 1985 1990 1995 2000 2005 2010 2015 (a) Number of listed firms 61.0 41.0 21.0 01.0 80.0 Year smrif lla fo % sa smrif detsiL (b) Listed firms as share of all firms 1985 1990 1995 2000 2005 2010 2015 05 04 03 02 01 Year )%( PDG/kcots latipac elbignatnI 1985 1990 1995 2000 2005 2010 2015 (c) Intangible/GDP 051 001 05 0 Year )001=ycnerapsnarT s'5891( xednI ycnerapsnarT Transparency 1 Transparency 2 (d) Average transparency Notes: This figure shows the trend in the number and share of listed firms, intangible capital, and firm transparency in the U.S. Data comes from Compustat, I/B/E/S, and the World Development Indicators. See Section 2.1 for details on measurement. Figure 1 plots the time series of the variables of interest from 1985 until 2015. Panel (1a) plots the number of listed firms in the U.S. The data is from the World 12

Development Indicators (WDI) by World Bank.11 As shown in the figure, there has been a gradually rising trend in the number of listed firms until the mid-1990s. Then, after the peak in the mid-1990s, the number of listed firms steeply declined to almost half the level at the peak year: 8,090 listed firms in 1996 reduced to 4,102 listed firms in 2012. Panel (1b) shows that listed firms have been declining not only in absolute number, but also as a share of all firms in the U.S. Panel (1c) shows the time series of the ratio between the total intangible capital stock of public non-financial corporations and GDP. Over the thirty years, the ratio has dramatically increased from 10% to 50%. This shows how fast intangible capital in the U.S. has grown. Lastly,panel(1d)showsthetimeseriesofthecross-sectionalaveragetransparency. The overall patterns of both transparency measures closely mimic the one in the numberoflistedfirms: transparencyhasincreaseduntilthemid-1990sanddecreasedafter thepeakin1996.12 Thetime-seriescorrelationbetweenthetransparencymeasureand the number of listed firms is 0.80 for the first measure and 0.61 for the second measure, and all are statistically significant. This co-movement between the number of listed firms and the average transparency is the key motivation of this paper: what drives such co-movements? 2.3 The trends by industries In this section we show trends in the number of firms, intangible capital, and transparency by macro industries. Panel 2a shows the trend in the number of firms for the Information and Services sector, excluding trade and transportation, Manufacturing, and other sectors (Trade and transportation, Agriculture and Mining, Construction). All sectors show an initial increase and then a decline after the mid-nineties, and the 11The number of listed firms in WDI is only negligibly different from the one in the Compustat data. 12Recessions and especially the Great Recession represent a big shocks to earnings surprises. In ordertotakethatintoaccount,wealsomeasureaveragetransparencybyexcludingrecessionperiods as measured by the NBER, and we still find that average transparency has been declining. 13

Figure 2: Number of listed firms and intangible intensity by industry. 1985 1990 1995 2000 2005 2010 2015 052 002 051 001 05 Year )001 = rebmun s'5891( xedni mrif fo rebmuN Group Information+Services Manufacturing Others Information+Services (all) 1985 1990 1995 2000 2005 2010 2015 (a) Number of listed firms 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 Year ytisnetni elbignatnI Group Information+Service Manufacturing Others (b) Intangibles intensity Notes: This figure shows the trend in the number of listed firms and intangible capital intensity in theU.S.Intangibleintensityisdefinedastheratioofintangibleassettototalintangibleandtangible assetvalues. ThegroupsaredefinedasInformationandServices,excludingtradeandtransportation, Manufacturing,andothersectors(Tradeandtransportation,AgricultureandMining,Construction). Data comes from Compustat. See Section 2.1 for details on measurement. decline is much more pronounced in the information and service sector. We also plot the normalized number of all non-listed firms in the information and service sector: as can be seen, only listed firms are affected by the large decline during the entire period of 2000 and 2010 (well after the dot-com bubble), while the overall number is only slightly affected by the 2001 and 2008 recessions. Panel 2b shows the intangible intensity, defined as the ratio of intangible asset to total intangible and tangible asset values, for the same industries. Manufacturing had historically a higher intangible intensity, which has been taken over in the early 2000s by the service sector. Finally, Figure 3 shows our transparency measures for the information and service sector, compared to all other sectors. The information and service sector has a lower transparency over the entire period, and both time series of transparency for all sectors have also declined over time. Two main take-aways can be taken by the analysis of industry trends: the information and services sector has seen the largest increase in its intangible intensity, and at the same time the largest decline in the number of listed firms and in transparency. 14

Figure 3: Time series of transparency for information and service industries. 1985 1990 1995 2000 2005 2010 2015 051 001 05 Year )001 = ycnerapsnarT s'5891( xednI ycnerapsnarT Transparency 1: All Transparency 1: Inform.+Service 1985 1990 1995 2000 2005 2010 2015 (a) Transparency 1 051 001 05 Year )001 = ycnerapsnarT s'5891( xednI ycnerapsnarT (b) Transparency 2 Notes: This figure shows the trend in in transparency for information and service industries comparedtoallotherindustries. InformationandServicesexcludestradeandtransportation. Data comes from Compustat and I/B/E/S. See Section 2.1 for details on measurement. In Appendix A, we show the trends for more disaggregated industries. We also report the trends in intangible capital using internally generated R&D only, so that the numbers on intangible intensity can be compared to the ones available in the Bureau of Economic Analysis (BEA). 2.4 Cross-sectional evidence In this section we describe cross-sectional evidence that links high reliance on intangible capital with the value of transparency and earning surprises. We run the following regression on our baseline sample, which includes all firms in Compustat from 1985 to 2016 for which information on earnings forecasts by at least one analysts is available: logy = θ +FEs+β ×Intangible over total assets +γ ×X +ε i,t t i,t i,t i,t where y is either our first or second transparency measure as described in section i,t 2.1. θ areyearfixedeffectsandFEsincludeindustryfixedeffects. X representsfirm t i,t 15

controls.13 The firm-level controls include book-to-market ratio, sales, liquid capital (cash, inventory, and receivables), leverage (total debt over total asset), employment in logs, age (from the IPO year), and the number of analysts. Intangible, sales, and liquid capital are normalized by total asset. Table 1 reports the results for the coefficient on intangible capital asset ratio. We report the full regression table in Appendix B. The regressions show that intangible capital and transparency are inversely related, i.e., firms that have a higher share of intangible capital compared to their size are more difficult to forecast. Specifically, an increase of one percentage point in the intangible capital over assets ratio decreases the value of the first transparency by 0.31 percent, and the value of the second transparency measure by 0.63 percent. We interpret the result in the following way. Given the inclusion of year fixed effects and the number of analysts covering a given firm, we can exclude the effect of a gradual worsening of analysts’ ability and effort, analysts’ coverage, and common changes in idiosyncratic and aggregate risk. Therefore, we can directly link the rise in intangible capital with a decline in the ability of the market to forecast a firm. This relationship can be due to two reasons: one, firms with high intangible intensity tend to be less transparent, and, therefore, more difficult to forecast. Two, it may be that, given a certain level of disclosure and transparency, firms with high intangible intensity are inherently more challenging to forecast due to their nature. We include both possibilities in our model and set out to disentangle the two effects using our structural estimation. 13Firm-level controls and regression specifications are based on Li (2010) and Bird, Karolyi, and Ruchti (2017). 16

Table 1: Regression of transparency proxies on intangibles Dependent Variables: Transparency 1 Transparency 2 Intangible -0.31 -0.627 it (0.046) (0.096) Industry FE Yes Yes Year FE Yes Yes Controls Yes Yes Two-way cluster Yes Yes Observations 256,962 256,962 Adj. R2 0.275 0.289 Notes: This table reports the estimates of the coefficients from the following regression using our baseline sample, which includes all firms in Compustat from 1985 to 2016 for which information on earnings forecasts by at least one analysts is available: logy =θ +FEs+β×Intangible capital over total assets +γX +ε i,t t i,t i,t i,t where y is either the inverse absolute value of earning surprises from the consensus, or the inverse i,t of variance of earning surprises when more than one analyst forecast is present. θ are year fixed t effects and FEs include industry fixed effects. X represents firm controls. i,t 3 Baseline model In this section, we introduce a general equilibrium model, where the firm-level equilibrium allocations are characterized in the closed form. Using this model, we will qualitatively and quantitatively analyze the cause and consequences of the empirical patterns we have shown in the previous section. We consider a stand-in household and a continuum of measure one of the ex-ante 17

homogeneous firms. The model is static.14 A representative household decides its asset portfolio and consumes the payouts from the portfolio. An entrepreneur decides in which market the firm operates between the public and private equity markets. If a firm is listed, the entrepreneur chooses the disclosure level of the firm’s intangible capital to the public, which we define as transparency. On the other hand, the entrepreneur does not disclose any intangible capital to the public if a firm is private. 3.1 Household Astand-inhouseholddecidesontheassetportfolioandconsumestheportfolioreturn. The household is given a wealth level a > 0. The household is risk-averse, and the utility takes the following constant absolute risk aversion form (CARA): u(C) = −e−ΛC, where Λ > 0 is the absolute risk aversion parameter. In the listed market, the household forms a belief about the return r(q) based (cid:101) on the balance sheet information of a listed firm with transparency level q and the mandated transparency level q. The belief about the return is assumed as follows: (cid:18) (cid:19) 1 r(q) ∼ N r(q), (cid:101) iid ξ +(q +q)ψ π(q) s.t. r = , P(q) where q ∈ [0,1−q] is the transparency of the balance sheet information.15 q is the mandated transparency required by the policy maker, ξ is the baseline information level a household has about both listed and non-listed firms, ψ > 0 is the marginal 14The model is intended to capture an equilibrium that is formed over long years. Therefore, the dynamicaspectisabstracted. Also,thestaticsetupgivesagreatdegreeoftractabilityinthemodel, as will be described in the equilibrium analysis. 15The range of transparency is assumed at our convenience. However, the qualitative and quantitative results of this paper are unaffected by this normalization assumption. 18

contribution of transparency to the household’s information about the listed firm.16 π(q) is the profit of the firm with transparency q, and P(q) is the price of the firm with transparency q. In the private equity market, the household forms the following belief about the non-listed firms: (cid:18) (cid:19) 1 rN ∼ N rN, (cid:101) iid ξ πN s.t. rN = , PN where πN and PN are the profit, and price of a non-listed firm. As non-listed firms do not disclose any information publicly, the household does not distinguish one nonlisted firm from another. Then, the household solves the following portfolio choice problem: max E(−e−ΛC) x(q),xN (cid:90) (cid:90) s.t. C = x(q)r(q)dq +xNrN, x(q)dq +xN = a, (cid:101) (cid:101) (cid:101) (cid:101) (cid:101) (cid:101) (cid:101) where x(q) is the funding supply for firms with transparency level q, and xN is the funding supply for non-listed firms. As the model does not include the inter-temporal decision of the household, all the payoffs from the equity investment are consumed. 3.2 Technology A measure one of the ex-ante homogeneous firms produces output using two inputs: tangible capital (k ) and intangible capital (k ). In this economy, there are two types T I of production technologies. One is listed firms’ production technology, and the other 16We regard ψ as the functions of a structural parameter θ, the share of intangible capital in the production function. Intuitively, the importance of intangible capital in the production function affects the information quality household can access from the balance sheet. We do not impose any structural assumption on this function. Instead, we identify the level of ψ in our estimation using the firm-level data. Then, in the quantitative analysis, we interpret a change in ψ is affected by the variation in θ. 19

is non-listed firms’ production technology. 3.2.1 Production function of listed firms A listed firm i operates using the following production function: fL(kT,kI,q ;q,Φex) = z(kT)α(kI(1−q −q ))θ(Φex)γ, i i i i i i where q is the mandated portion of intangible disclosure imposed by the policy maker, q is the voluntarily disclosed portion of intangible, Φex is the shared intangible capi ital from all other firms, z is a constant aggregate productivity level, γ is the scale parameter for the externality, and α and θ are the tangible and intangible capital shares, respectively. We assume α+θ+γ ≤ 1. Importantly, we assume the revealed portion of intangible capital disappears from the private intangible stock. This assumption is to let the revealed intangible capital be symmetrically used between the disclosing firms and the free-riding firms without double counting. If this symmetry is not guaranteed, partial knowledge sharing needs to be specified, which requires an additional intensive margin in the shared information. We simplify the model by assuming pure symmetry to avoid such complications. We assume that a listed firm’s disclosed portion of intangibles can range from q to 1, which does not rule out the possibility of publicly sharing nearly all intangibles. Therefore, the intangible in this model does not include patents or intellectual properties that are legally protected in terms of ownership. Therefore, we treat these assets as tangible assets.17 We assume a firm i’s disclosed intangible q is perfectly substitutable by the other i disclosed intangible. Therefore, the shared intangibles are aggregated in the following additive form: 17Giventheseassetsareevenusedascollateralinreality,theexclusionofthemfromthedefinition intangible is desired for the focus of this paper. In our estimation, we target the intangible share calculated based on the expenditures rather than the stock. Therefore, the protected intangible assets, such as patent do not significantly affect the main results. 20

  (cid:90) 1 Φex = 1 {i∈Listed} ×k I,i q + q i di. 0 (cid:124)(cid:123)(cid:122)(cid:125) (cid:124)(cid:123)(cid:122)(cid:125) Disclosuremandatedbythepolicymaker Voluntarydisclosure A firm chooses first the voluntary disclosure level of the intangible before the operation. Thechoiceproblemofvoluntarydisclosureiselaboratedoninthefollowing section.18 The ex-post profit of a firm with voluntary transparency q is obtained after i taking out the operational costs rkT +pkI from the revenue: i i π(q ;q,Φex) := max z(kT)α(kI(1−q −q ))θ(Φex)γ −rkT −pkI, i i i i i i kT,kI i i where r is the capital rental rate, and p is the R&D cost per unit of intangible capital. For the notational brevity, we assume r and p already include the depreciation rates. 3.2.2 Production function of non-listed (private) firms If a firm is private, it does not disclose the intangible capital publicly. The production function of a non-listed firm i is as follows: fN(kT,kI;Φex) = z(kT)α(kI)θ(Φex)γ. i i i i Except for the disclosure of the intangible capital, the production function is assumed to take the same form and parameters as the one for the listed firms. The profit is also defined similarly to that of listed firms: πN(Φex) := max z(kT)α(kI)θ(Φex)γ −rkT −pkI. i i i i kT,kI i i 3.3 Financial markets In this section, we characterize the financial market in the model. The funding supply is driven by the representative household’s portfolio choice problem. The funding 18The assumption of timing is solely for the descriptive purpose. Even if the decision of input levels and the disclosure level occur simultaneously, the model stays unaffected. 21

demand is determined by each firm’s value maximization problem. 3.3.1 Funding supply: The household’s mean-variance portfolio From the i.i.d assumption of the stock return uncertainty, the consumption (income) satisfies (cid:18)(cid:90) (cid:90) (cid:19) 1 1 C ∼ N x(q)r(q)dq +xNrN, x(q)2 dq +(xN)2 . (cid:101) (cid:101) (cid:101) (cid:101) (cid:101) ξ +ψ(q +q) ξ Then the investors’ expected utility maximization problem is translated into the following form:19 −Λ (cid:16)(cid:82) x(q)π(q(cid:101))dq+xNπN −Λ(cid:82) x(q)2 1 dq−Λ(xN)21 (cid:17) max −e (cid:101) P(q(cid:101)) (cid:101) PN 2 (cid:101) ξ+ψ(q+q) (cid:101) 2 ξ . (cid:82) x(q)dq+xN=a (cid:101) (cid:101) After a strictly-increasing (log) transformation, the problem reduces down to (cid:90) π(q) πN Λ (cid:90) 1 Λ 1 max x(q) (cid:101) dq +xN − x(q)2 dq − (xN)2 . (cid:101) (cid:101) (cid:101) (cid:101) (cid:82) x(q (cid:101) )dq (cid:101) +xN=a P(q (cid:101) ) PN 2 ξ +ψ(q +q) 2 ξ The first-order condition with respect to x(q) yields π(q) 1 −Λx∗(q) −µ = 0, P(q) ξ +ψ(q +q) where µ is the Lagrange multiplier of the wealth constraint. From this equation, we can derive the following supply curve of funding for the listed market: π(q)/P(q)−µ x∗(q) = , Λ/(ξ +ψ(q +q)) where x∗(q) is the funding supply in a dollar amount for firms with the transparency level q. So, the household is willing to invest π(q)/P(q)−µ in the firms with transparency Λ 1 ξ+ψ(q+q) 19Thederivationofthemean-varianceportfolioobjectivefunctionisasfollows: considerarandom variable, y ∼N(µ ,σ2). Then, y y E(−e−Λy)=−E(e−Λy)=−e−Λ(µy−Λ 2 σ y 2). The last equation is derived from the moment generating function of the normal distribution. 22

level q. Similarly, from the first-order condition with respect to xN, the funding supply curve for non-listed firms is characterized as follows: πN/PN −µ xN∗ = . Λ/ξ From this point on, we assume the representative household has a large enough wealth a, as our interest is not in the household’s constrained optimization. Thus, µ = 0. 3.3.2 Funding demand: Listed firms’ value maximization A manager of a firm chooses where to operate to maximize the firm’s price. The price is interchangeable with the value of a firm. The decision problem of where to operate is characterized as follows: max{ max P(q),PN}. q∈[0,1−q] Where P(q) is the price of the firm operating in the listed market with the transparency level at q, and PN is the price of a non-listed firm. In the funding market for the listed firms, the price of a firm, P(q), is determined at the level where funding supply in the number of firms x∗(q) meets funding demand P(q) in the number of firms M(q). Thus, the market-clearing condition is as follows: x∗(q) = M(q). P(q) Recall that a manager needs to determine the transparency level, after going on the listed market: maxP(q). q≥0 Given the funding demand and the market-clearing condition, this problem is equiv- 23

alent to the following form: (cid:115) π(q) max , q≥0 Λ M(q) ξ+ψ(q+q) which is equivalently transformed to π(q) max . q≥0 M(q) ξ+ψ(q+q) Now, we define a net funding intensity ϕL(q) as follows: ξ +ψ(q +q) ϕL(q) := . M(q) Therefore, a listed firm’s problem can be summarized as the following form: (cid:0) (cid:1) JL(M) = max max zkα(k (1−q −q))θ(Φex)γ −rk −pk ϕL(q) T I T I q kT,kI ξ +ψ(q +q) s.t. ϕL(q) = , M(q) where JL is the value of a listed firm given the distribution of listed firms M.20 The solution to this problem characterizes the funding demand in the listed market. 3.3.3 Financial market for non-listed firms The price of a non-listed firm, PN, is determined at the level where funding supply in the number of firms, xN∗ is matched with the demand in a frictional private eq- PN uity market. Especially, we assume the congestion among non-listed firms generates attrition in the funding opportunity in the following way: 1 xN∗ = M , ν PN N N 20Note that the price P is not identical to JL, as one is a monotonically transformed version of the other. Specifically, ΛP(q)2 =JL(q). 24

whereM isthetotalnumberofnon-listedfirmsandν > 1isastructuralparameter N N that captures the congestion effect in the non-listed financial market. Then, we define a net funding intensity ϕN(q) as follows: ϕN := ξ/(ν M ). N N A non-listed firm’s problem can be written down as follows, similar to the listed firm’s problem: (cid:0) (cid:1) JN(M ) = max zkα(k )θ(Φex)γ −rk −pk ϕN N T I T I kT,kI s.t. ϕN = ξ/(ν M ). N N 3.4 Summary of a firm’s problem A firm’s manager decides whether to go listed or non-listed before the operation. If a firm becomes non-listed, the manager does not have to worry about the leakage of their intangibles through disclosure. However, investors penalize the opacity of the non-listed firms by allowing only a low funding intensity. If a firm becomes public, the manager should decide on the level of transparency q ≥ 0. If too many firms choose the same transparency level, it will decrease the firm’s value in the listed market due to demand-side competition. A firm’s problem could be summarized as follows: [Entry decision] max{JL(M),JN(M )}, N (cid:0) (cid:1) [Listed firm] JL(M) := maxmax zkα(k (1−q −q))θ(Φex)γ −rk −pk ϕL(q) T I T I q kT,kI ξ +ψ(q +q) s.t. ϕL(q) = , M(q) (cid:0) (cid:1) [Non-listed firm] JN(M ) := max zkα(k )θ(Φex)γ −rk −pk ϕN N T I T I kT,kI s.t. ϕN := ξ/(ν M ). N N 25

4 Equilibrium Here we define an equilibrium where the economy is given total intangible capital reserve KI (fixed aggregate intangible supply). This equilibrium endogenously determines the R&D cost of intangible capital p. The R&D cost is not a price for a trade. Instead, it is a cost that increases if all the other firms increase their spending in R&D. This captures the intuition that developing new knowledge is harder if more firms seek new knowledge. The rental rate for the tangible capital r is exogenously given. Definition 1. A collection of functions (k ,k ,q,M,M ,p,P,PN,x∗,xN∗,Φex) is T I N an equilibrium if (cid:0) (cid:1) 1. x∗,xN∗ solves the household’s problem. 2. (k (q,M),k (q,M),q(M)) solves the listed firm’s problem. T I 3. The measure of listed firms choosing a transparency level q is consistent with M(q) for all q ∈ [0,1−q]. 4. The measure of non-listed firms is M and satisfies N (cid:90) 1−q M(q)dq +M = 1. N 0 5. R&D cost of intangible capital p is determined by the following equation: (cid:90) 1 KI = k di. I,i 0 6. Aggregate shared knowledge satisfies (cid:90) 1 Φex = 1 ×k (q +q )di. {i∈Listed} I,i i 0 7. Financial market is cleared: 26

x∗(q) 1 xN∗ = M(q) and = M . P(q) ν PN N N 8. Indifference in the extensive-margin decision: P(q) = PN, for ∀q ∈ [0,1−q]. With the endogenously determined distribution M of firms for each q, we can rewritethemarket-clearingconditionforintangiblecapitalandtheexternalitycondition usingM. Inthedefinition,eachfirmisaggregatedalongwithindexi ∈ [0,1]. Instead, we aggregate firms over the distribution of firms at each q. This aggregation is doable since M is endogenously obtained, and k is also a function of q and M. Therefore, I we re-write those two conditions in the following way: (cid:90) 1−q KI = k (q,M)M(q)dq, I 0 (cid:90) 1−q Φex = k (q,M)(q +q)M(q)dq. I 0 Among all possible equilibrium, we are interested in the non-degenerate equilibrium where all the homogeneous firms use mixed strategies over the transparency level q. The mixed strategy leads to the distribution of firms at each level of q. In the equilibrium, this distribution needs to be consistent with the distribution that a firm takes as a given state variable. In the following section, we analytically characterize the equilibrium allocations in this economy. 4.1 A listed firm’s decision First, wesolvealistedfirm’sproblembackwardfromthedecisiononthetransparency level and the other allocations. Then, we solve the firm’s decision on which financial market to enter the public market of the private one. 27

Given a net funding intensity function, ϕL and the externality, Φex, a listed firm’s problem is characterized as follows: Interimproblem (cid:122) (cid:125)(cid:124) (cid:123) (cid:20) (cid:21) (cid:0) (cid:1) max max zkα(k (1−q −q))θ(Φex)γ −rk −pk ϕL(q) T I T I q kT,kI ξ +ψ(q +q) s.t. ϕL(q) = . M(q) From the optimality conditions of the interim problem, we can derive the relationship among the transparency q, the regulation parameter q, and the intangible capital k . I The relationship is formally stated in the following proposition: Proposition 1. (Intangibles and the transparency) Given α+θ < 1, kI(q,M;q) decreases in both q and q. Specifically, (cid:32) (cid:18) αz(Φex)γ(cid:19) 1−α 1 −θ (cid:18) rθ (cid:19) 1− 1− α α −θ (cid:33) θ k I (q,M;q) = (1−q −q)1−α−θ. r pα Proof. See Appendix D. ■ If a firm is in a state where the knowledge has to be transparently revealed to the public, it naturally disincentivizes the firm to accumulate less knowledge. Therefore, the marginal increase in voluntary or mandatory transparency leads to a marginal decrease in the deployment of intangible capital stock. This result is consistent with the empirical observation we document in the empirical analysis section. Moreover, the incentive to reveal the information interacts with the importance of the intangible in the production function, θ. When the intangible becomes more important in production, the negative association between the intangible and transparencystrengthens. Inotherwords, giventhefixedintangiblecapitalstock, agreater θ is associated with a stronger incentive to conceal the information (lower q). Proposition 2 theoretically shows this relationship. 28

Proposition 2 (Intangible share and the transparency). Given α+θ < 1, the sensitivity of kI(q,M;q,θ) to the changes in q and q increases in θ. Proof. See Appendix D. ■ Then, from the optimality condition with respect to the transparency, q, we can characterize an ordinary differential equation (ODE) where the function of interest is the net funding intensity function ϕ(q). The ODE is specified in Appendix D. Solving the ODE, we characterize the transparency distribution M in the analytic form. We state the analytic form of M in the following proposition: Proposition 3. (Transparency distribution) The unnormalized probability density function M of transparency q has the following analytic form: 1 θ M(q) = (ξ +ψ(q +q))(1−q −q)1−α−θ . ϕN Proof. See Appendix D. ■ In the multiplicative form of the closed-form endogenous distribution in Proposition 3, each component is directly interpretable.21 1 θ M(q) = (ξ +ψ(q +q)) (1−q −q)1−α−θ . ϕN (cid:124) (cid:123)(cid:122) (cid:125)(cid:124) (cid:123)(cid:122) (cid:125) (cid:124)(cid:123)(cid:122)(cid:125) fundingsupply fundingdemand eq. normalizer The first component is the household’s preference for transparent firms. For a higher q, the household is willing to provide greater funding to the firm. This behavior generates an incentive for a firm to choose high q. In contrast, the second term captures 21It is worth noting that the endogenous distribution is independent of the productivity level z. Thus, the firm-level productivity heterogeneity does not matter in this setup. In the quantitative analysis, we normalize the productivity z at 1. 29

firms’ incentive to reveal less information. This is consistent with the intuition that a greater revelation only benefits competitors at the firm’s own cost. The third term is the equilibrium object that balances the measure of listed and non-listed firms. The following corollary establishes that the equilibrium distribution is unique for the given support of the transparency [0,1−q]. Corollary 1. (Uniqueness of the transparency distribution) Given the support [0,1−q], the equilibrium unnormalized probability density function M is unique. Proof. The result is immediate from the uniqueness of the ODE solution that satisfies the boundary condition. ■ The probability density function M(q) belongs to a variant of a well-known class ofdensityfunctions: Betadistribution. Inthefollowingcorollary, weprovethatM(q) follows a shifted truncated beta distribution and provide the closed-form characterization of the net funding intensity of the private firms, ϕN. For brevity of notation, we define B := θ . 1−α−θ Corollary 2. (Truncated normalized Beta distribution) The gross transparency, y := q +q, follows a truncated normalized Beta distribution where the shape parameters are B +1 and 2, and the support is [q,1]. I{q ∈ [0,1−q]} q +q ∼ ×Beta(B +1,2), 1−M N where B = θ . 1−α−θ Proof. See Appendix D. ■ It is worth noting that the probability density of q depends on the net funding intensity of non-listed firms, ϕN. This net funding intensity is determined by the 30

following identity that requires the total measure of firms is unity: 1 (cid:90) 1−q (cid:18) ξ (cid:19) (ξ +ψ(q +q))(1−q −q)Bdq = 1− . (1) ϕN ν ϕN 0 N Equivalently, we can write down the identity in terms of the mass of non-listed firms as follows: ν (cid:90) 1−q(cid:18) ξ (cid:19) ψ N M +(q +q) (1−q −q)Bdq = 1−M . (2) N N ξ ψ 0 Therefore, we have the following closed-form solution for M : N 1 M = . (3) N 1+ψνN (cid:82)1−q (ξ +(q +q))(1−q −q)Bdq ξ 0 ψ Equation (3) is the fundamental component of the model, which captures how the total measure of non-listed firms, M , behaves when the policy parameter q N changes. Using Corollary 2, we can integrate out the M(q) in the right-hand side of the equation in the following steps, using y = 1−q−q ∈ [0, 1−q ]: 1+ξ/ψ 1+ξ/ψ 1 M = . N 1+ψνN(1+ ξ)B+2 (cid:82) 1+ 1− ξ/ q ψ(1−y)(y)Bdy ξ ψ 0 Then, we divide the numerator and the denominator by a beta function, B(B+1,2).22 1/B(B +1,2) M = . N 1/B(B +1,2)+ψνN(1+ ξ)B+2B(B +1,2) (cid:82) 1+ 1− ξ/ q ψ yB(1−y)dy ξ ψ 0 We integrate the denominator using the cumulative distribution function of beta 22The beta function is defined as follows: Γ(a)Γ(b) (a−1)!(b−1)! (cid:90) 1 B(a,b):= = = xa−1(1−x)b−1dx. Γ(a+b) (a+b−1)! 0 31

distribution, F: 1/B(B +1,2) M = . N (cid:16) (cid:17) 1/B(B +1,2)+ψνN(1+ ξ)B+2F 1−q;B +1,2 ξ ψ 1+ξ By multiplying B(B + 1,2) on the numerator and the denominator, we obtain the following analytic form: 1 M = . (4) N (cid:16) (cid:17) 1+ψνN(1+ ξ)B+2B(B +1,2)F 1−q;B +1,2 ξ ψ 1+ξ Equation (4) characterizes the measure of private firms in the analytic form. Importantly, the equation does not include either the price of the intangible or the externality. That is, the measure of private firms is independently determined from thegeneralequilibriumeffectsandexternality. Theintuitionbehindthisresultisthat both the productivity shift through the externality and the general equilibrium effect uniformly affect the operating profit of each firm, so they do not affect the decision of how to finance their operating activities.23 Due to this separation, a measure of private firm M is determined directly by Equation (4). M determines the funding N N intensity of private firm ϕN. Then, from Proposition 3, the distribution of firms over transparency is also independently determined from the general equilibrium effect and the externality. Therefore, the mandated transparency q affects the firm-level distribution directly through Equation (4) without any feedback effects in the general equilibrium. Also, it is worth noting that Equation (4) theoretically predicts that M increases in q. N Proposition 4. (The relationship between the policy and the measure of listed firms) M strictly increases in q ∈ [0,1]. N Proof. 23For the same logic, the heterogeneous firm-level productivity does not affect the analytic form in the current setup. 32

See Appendix D. ■ As the policymaker requires a stricter disclosure regulation on financial information, the measure of non-listed firms increases. The reason is that a firm does not internalize the productivity gain from the shared information. As can be observed from Equation (2), the measure of non-listed firms is independent of the externality effect, Φex. The total measure of listed or non-listed firms, however, cannot solely serve as an objective of the disclosure regulation. The desired objective is stated clearly in the following mission of the SEC in the U.S.: “The mission of the SEC is to protect investors, maintain fair, orderly, and efficient markets, and facilitate capital formation.”24 Consistent with the view of the SEC, we investigate the effect of regulation on the investors’ welfare, productivity, and output in the following section. 4.2 The scoreboards: Welfare, productivity, and output In this section, we define the three objectives of the disclosure regulation: welfare, productivity, and output. First, we define the welfare measure. Besides the performance of firms, the investor values the transparency of the disclosed information, as it is helpful for the investor’s portfolio. The representative investor’s utility can be 24See “Our Goals,” SEC website https://www.sec.gov/our-goals. 33

monotonically transformed into the following mean-variance form: (cid:90) π(q) πN Λ (cid:90) 1 Λ 1 Objective = x(q) (cid:101) dq +xN − x(q)2 dq − (xN)2 welfare (cid:101) p(q) (cid:101) PN 2 (cid:101) ξ +ψ(q +q) (cid:101) 2 ξ (cid:101) (cid:90) Λ (cid:90) x(q)P(q)M(q) ΛxNν PNM = M(q)π(q)dq +ν MNπN − (cid:101) dq − N N (cid:101) (cid:101) (cid:101) N (cid:101) 2 ξ +ψ(q +q) 2 ξ = (cid:90) M(q)π(q)dq +ν MNπN − Λ (cid:90) Λ/ π (ξ (q + ) ψ /P (q ( + q) q)) P(q)M(q) dq − Λ πN Λ / / P ξ N ν N PNM N (cid:101) (cid:101) (cid:101) N (cid:101) 2 ξ +ψ(q +q) 2 ξ (cid:90) (cid:90) 1 1 = M(q)π(q)dq +ν MNπN − π(q)M(q)dq − ν πNM . (cid:101) (cid:101) (cid:101) N (cid:101) (cid:101) (cid:101) N N 2 2 (cid:90) 1 ν = M(q)π(q)dq + N MNπN. (5) (cid:101) (cid:101) (cid:101) 2 2 Therefore, the welfare measure is equivalent to the expected profit in equilibrium. The second measure is the productivity in the production sector that is defined as follows: Objective = (Φex)γ productivity (cid:18)(cid:90) 1−q (cid:19)γ = (q +q)k (q,M;q)M(q)dq , I 0 where A(cid:101):= (cid:18) (cid:0) αz (cid:1) 1−α 1 −θ (cid:16) rθ (cid:17) 1− 1− α α −θ (cid:19) . The productivity is identical to the externality r pα effect, which is the total shared knowledge in the economy. From the regulator’s perspective, there is a trade-off in the productivity measure for increasing the strictness of the disclosure requirement. For higher q, the amount of shared information is greater, while the pool of listed firms to share the information shrinks due to the firm-level extensive-margin responses. Also, the size of intangible k to be shared I declines as in Proposition 1. The third measure is the aggregate output in the economy. The output measure is defined in the following form: (cid:90) 1−q Objective = zk (q)α(k (q)(1−q −q))θ(Φex)γM(q)+zkα kθ (Φex)γM . output T I DT DI N 0 34

Inthequantitativeanalysis, wewillquantitativelyanalyzethevariationinthesethree measures. 5 Quantitative analysis Using the model we developed in the theory section, we conduct a quantitative analysisofthemacroeconomiceffectsresultingfromtheincreasingsignificanceofintangible assetsandtheimpactofinformationregulationpolicies. Weestimateourmodelusing data from two distinct periods. The first period, spanning from 1992 to 1996, serves as our baseline, while the second period, from 2012 to 2016, is considered as the postchange period. As our model is static, we cannot examine the dynamic response that may have occurred immediately after a change in structural parameters. Therefore, we compare a period just before the year of the dramatic shift in the number of listed firms with a period several years after the change to assume that it has reached a stationary level. 5.1 Estimation In this section, we elaborate on how we fit the firm-level data into the model. The core parameters to be estimated are the following: {q,θ,ξ,ψ,ν }, N where q is the mandated transparency of disclosure; θ is the intangible capital share; ξ is the baseline information level a household has about both listed and non-listed firms, ψ isthetransparency’scontributiontothehousehold’sinformationaboutlisted firms; and ν is the efficiency parameter of the private equity market. N To generate ourbaselineestimates, wematchtheaveragetargetmomentsbetween 1992 and 1996. For the estimates of the post-change periods, we match the average 35

targetmomentsbetween2012and2016. Thetargetmomentsandsimulatedmoments are reported in Table 2. The parameter q is identified based on the adjusted fraction of listed firms out of the total number of firms with more than 100 employees. To accountformergersandacquisitions(M&As)byanotherpublicfirm(Doidge,Karolyi, and Stulz, 2017) we adjusted the target fraction of listed firms. Starting from 1975, we sequentially updated the exit rate, which is the number of delistings minus M&As, over the number of listed firms, plus new entries and minus M&As. Our adjustments showthatthetotaldropinlistedfirmswasabout52%,butafteraccountingforM&As, the drop is only 31%. This means that the adjusted fraction of listed firms went from 11.08% in the baseline period to 7.60% in the post-change period. Regarding the share of intangible capital, θ is identified from the intangible to tangible ratio. Since in the model the households form a belief on a stock return that follows a normal distribution: (cid:18) (cid:19) 1 r(q) ∼ N r(q), . (cid:101) ξ +ψ(q +q) Analysts’ forecast dispersion is a natural data counterpart to the dispersion in the ex-ante stock return. Specifically, earnings surprise is defined as: (cid:18) (cid:19) 1 ES(q) := r(q)−r(q) ∼ N 0, . (cid:101) ξ +ψ(q +q) Hence, in our analysis, we identify ψ using the average standard deviation value of the returns of all firms, while ξ represents the equivalent value for the top 1% opaque firms. We assume that opaqueness in non-listed firms is comparable to that of the top 1% of opaque listed firms, which allows us to identify ξ. Lastly, ν for the baseline D period is identified using the 30% fraction of private firms that get funded, and for the post-change period, we use the 4 percentage points estimate of improvement in the private equity market friction following Ewens and Farre-Mensa (2020). We use the method of simulated moments to estimate the parameters. The weight 36

matrix is chosen to be an identity matrix. However, the choice of the weight matrix is not an issue in our estimation, as the parameters are exactly identified at the level where the level of moments is exactly matched. Table 2: Fitted Moments Moments Data Model Reference Baseline (1992∼1996) Fraction of listed after M&A adj. (%) 11.08 11.08 Compustat & BDS (cf. without M&A adj. (%)) (8.30) Intangible Exp./Sale (%) 2.906 2.906 Compustat Average sd(r) (%) 12.53 12.53 Compustat (cid:101) Average sd(r) of top 1% (%) 25.52 25.52 Compustat (cid:101) Portion of funded non-listed firms (%) 30.30 30.00 Ewens and Farre-Mensa (2020) Post-change (2012∼2016) Fraction of listed after M&A adj. (%) 7.60 7.60 Compustat & BDS (cf. without M&A adj. (%)) (4.01) Intangible Exp./Sale (%) 5.356 5.356 Compustat Average sd(r) (%) 28.00 28.00 Compustat (cid:101) Average sd(r) of top 1% (%) 84.81 84.81 Compustat (cid:101) Portion of funded non-listed firms (%) 34.30 34.00 Ewens and Farre-Mensa (2020) Table 3 reports the estimated parameters. In the post-change period, the estimated mandated transparency parameter, q, slightly increased, indicating that information regulation has become stricter, consistent with the intended direction of the reform. Theshareofintangibleassets, θ, hasincreasedbyapproximately50%, reflectingthesignificantriseintheimportanceofintangibleinput. Thebaselineinformation level a household has about both listed and non-listed firms, ξ, has decreased substantially, and the transparency’s contribution to the household’s information about the listed firms, ψ, has decreased, both changes indicating an increase in the return variance on both listed and non-listed markets. Furthermore, the friction parameter ν has decreased, indicating an improvement in the private equity market, which re- N flects the impact of the National Securities Markets Improvement Act of 1996 (Ewens 37

and Farre-Mensa, 2020). Table 3: Estimated parameters Param. Description Baseline Post-change (1992 ∼ 1996) (2012 ∼ 2016) q Mandated transparency 0.981 0.995 θ Intangible share 0.029 0.054 ξ Baseline information level 25.520 1.390 ψ Transparency’s contribution to public info. 38.539 11.394 ν PE market friction 3.300 2.915 N Besides the estimated parameters, we fix the following parameters before the estimation: {α,γ,KI}. Capital share, α, is set to be 0.30. Because our model is abstract from a labor input, the capital share in the model needs to be interpreted as an after-labor-adjustment capital share, as in the following formulation: Akα = maxA(cid:101)kα (cid:101)Lϵ −wL L (cid:16) ϵ (cid:17) ϵ = (1−ϵ)A(cid:101)1− 1 ϵ 1−ϵ k1− α(cid:101) ϵ = Ak1− α(cid:101) ϵ, w where A = (1−ϵ)A(cid:101)1− 1 ϵ (cid:0) ϵ (cid:1) 1− ϵ ϵ. Therefore, our model’s α is equivalent to a standard w model’s α (cid:101) . We assume α = 0.12, and ϵ = 0.6, leading to α = 0.30. The public 1−ϵ (cid:101) intangible share, γ, is assumed to be equal to the private intangible share, θ. The total intangible capital stock, KI, is normalized to 1. Figure 4 shows the non-normalized distribution of listed firms over the transparency level for the baseline and the post-change periods. The distribution shrinks in the post-change period due to the reduced number of listed firms, and shifts leftward, indicating a decrease in the average transparency level. 38

Table 4: Fixed parameters Parameters Description Value α Capital share 0.30 −θ γ Public intangible share = θ r Rental rate tangible capital plus depreciation 0.10 KI Total intangible supply 1 z TFP level 1 Figure 4: Distribution of listed firms over transparency 16 14 12 10 8 6 4 2 0 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 5.2 Decomposition analysis In this section, we calculate the average contributions of each parameter to the decrease in the measure of listed firms and the decrease in the average transparency. We obtained these contributions by first keeping the estimated parameters at their baseline values and changing only one parameter to its post-change value to obtain the counterfactual measure of listed firms and average transparency if only that specific parameter changed. Second, we kept the estimated parameters at their post-change values and changed only one parameter to its baseline value to obtain the counterfactual measure of listed firm and average transparency if only that specific parameter remained at the baseline value. We performed this calculation for all five estimated parameters and then averaged both numbers from each parameter to obtain the average contributions to the decrease in the measure of listed firms and the decrease in 39

the average transparency. Table 5 reports the results of the decomposition analysis in annualized percentage.25 Table 5: Decomposition of the channels in the macroeconomic changes Contribution to the change (p.a.): Param. Channel #listed transparency productivity welfare Total change -1.88 -1.85 -0.42 -1.42 q SEC regulation -6.22 -6.18 -0.25 0.20 θ Rising intangible share -0.89 -0.89 -0.37 -0.81 ξ Baseline information level 8.62 8.62 0.34 -0.92 ψ Harder to forecast public firms -3.72 -3.72 -0.16 0.16 ν PE market friction -0.56 -0.56 -0.02 -0.59 N Table 5 presents the results of a decomposition analysis examining the factors contributing to the observed decline in the number of listed firms over the past two decades. The analysis reveals that the percentage of listed firms decreased from 11.08% in the baseline period to 7.60% in the post-change period, representing a 31% drop over 20 years, with an average annual change of -1.88. Furthermore, transparency, productivity, and welfare have also exhibited annual changes of -1.85, -0.42, and -1.42, respectively. The decomposition analysis identifies several factors contributing to the observed decline in the number of listed firms. Specifically, the stricter SEC regulation accounted for the majority of the change, contributing -6.22 percentage points. The rising share of intangible capital contributes to the declining transparency through two channels. One is through the direct effect of the firms’ declining willingness for transparent disclosure, and the other is through the transparency’s contribution to listed firms’ information ψ. Each intangible channel contributed -0.89 and -3.72 percentage points, marking the intangible share as the second most important factor for the observed decline of the listed firms. We obtain similar decomposition outcomes for the observed declining transparency. 25The two periods of comparison are 20 years apart from each other. So, we annualized the total change by a division of 20. 40

On the contrary, the decline in the household’s baseline information level about listed and non-listed firms contributed positively to the changes by 8.62 percentage points. This is because the declined information level makes the household provide little funding to the non-listed market, which makes the firms tend to go listed. Overall, the results suggest that the key drivers of lowered transparency, productivity, andwelfarearethestricterSECregulationandtheincreasedshareofintangible capital. These results provide valuable insights for policymakers and market participants seeking to understand the underlying factors contributing to the decline in the number of listed firms and the associated macroeconomic implications. 5.3 Optimal Policies In this section, we use the proposed model to analyze the optimal level of imposed transparency for welfare maximization. As shown in the previous section, the policy makercanchoosetheimposedtransparencylevelq¯. However,sincewelfareisobtained from the utility maximization problem of the household, q¯ will have two effects on welfare. On the one hand, lower imposed transparency increases the measure of listed firms that will have more access to finance relative to private firms, increasing output and consumption. On the other hand, lower imposed transparency also increases the output’s variance, lowering the welfare of the risk-averse household. Hence there is a trade-off between the level of consumption and its volatility. In Figure 5, we show the Laffer-type curve for the transparency policy for both periods. The estimated level of transparency in the pre-change period is 0.981 (Table 3) and the optimal level is 0.992, suggesting the mandated transparency was below the optimal level in the pre-change period. In the post-change period estimation, the results suggest that both the estimated and the optimal level of transparency increased to 0.994 and 0.995, respectively (Table 3). It is worth mentioning that output and productivityarealsonon-monotonicwithrespecttotheimposedtransparencylevel.26 26Figure 5 shows only the region where output and productivity decrease monotonically with 41

Figure 5: Optimal level of mandated transparency 1.4 1.4 1.4 1.4 1.3 1.3 1.2 1.2 1.2 1.2 1.1 1.1 1 1 1 1 0.8 0.8 0.9 0.9 0.6 0.8 0.6 0.8 0.9 0.92 0.94 0.96 0.98 1 0.9 0.92 0.94 0.96 0.98 1 (a) Baseline estimation (b) Post-change estimation This property of the model suggests that depending on the value of the estimated parameters, moving q¯ towards the welfare-optimal point could increase both output and productivity as well, achieving a divine coincidence. With the current estimated parameters, such a divine coincidence happens when q¯ is above the welfare optimal point: Decreasing q¯toward the optimal would increase welfare, output, and productivity. 6 Concluding remarks Thispaperanalyzesthedrivingforcesofthedisappearinglistedfirms,andrisingopacity of the disclosed balance sheets, and the macroeconomic consequences through a lens of the general equilibrium model. Our empirical analysis shows the presence of such trends and a negative correlation between the transparency and the intangible intensity of a firm. Then, we develop a general equilibrium model where the household determines the funding level for non-listed and listed markets depending on the transparency of disclosure, and firms determine which market to operate in and the transparency level. The policymaker’s disclosure regulation parameter is considered respect to q¯. 42

in the model, which allows an equilibrium-based analysis of the disclosure policy. In the equilibrium, a listed market based on directed search and a non-listed market based on random match endogenously co-exist. Notably, the model allows the analytical characterization of a rich set of equilibrium allocations. Using the model, we theoretically show that a stricter disclosure regulation leads to fewer listed firms. Also, a greater intangible share leads to a lower willingness for transparent disclosure. Using the estimated model, we show that the stricter disclosure regulation and the rising intangible share mainly drive the recently observed macroeconomic trends we document. Then, we quantify the macroeconomic implications of the observed trends. According to the estimated model, overall trends have led to a 0.42 percentage point productivity loss annually due to the reduced knowledge spillover and a 1.42 percentage point annual welfare loss. The stricter regulation has helped mitigate the welfare loss through the transparent information disclosure of the listed firms. Our approach broadens the scope of structural policy analysis to the regulation of information disclosure. According to our policy analysis, the recent change in the disclosure regulation almost achieved the optimum with respect to the welfare criterion. Still, the policy change has intensified the productivity loss, as the change made it costlier for firms to stay in the listed market. References Aghamolla, Cyrus and Richard T. Thakor. 2022. “Do Mandatory Disclosure Requirements for Private Firms Increase the Propensity of Going Public?” Journal of Accounting Research 60 (3):755–804. Atkeson, AndrewandPatrickJ.Kehoe.2005. “ModelingandMeasuringOrganization Capital.” Journal of Political Economy 113 (5):1026–1053. Bauguess, Scott, Rachita Gullapalli, and Vladimir Ivanov. 2015. “Capital Raising in the U.S.: An Analysis of the Market for Unregistered Securities Offerings, 2009- 2014.” U.S. Securities and Exchange Commision . 43

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Appendix: For Online Publication Contents 1 Introduction 2 2 Empirical analysis 9 2.1 Data and Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Trends in the number of listed firms, intangible capital, and transparency 12 2.3 The trends by industries . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4 Cross-sectional evidence . . . . . . . . . . . . . . . . . . . . . . . . . 15 3 Baseline model 17 3.1 Household . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.2 Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2.1 Production function of listed firms . . . . . . . . . . . . . . . 20 3.2.2 Production function of non-listed (private) firms . . . . . . . . 21 3.3 Financial markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.3.1 Funding supply: The household’s mean-variance portfolio . . . 22 3.3.2 Funding demand: Listed firms’ value maximization . . . . . . 23 3.3.3 Financial market for non-listed firms . . . . . . . . . . . . . . 24 3.4 Summary of a firm’s problem . . . . . . . . . . . . . . . . . . . . . . 25 4 Equilibrium 26 4.1 A listed firm’s decision . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.2 The scoreboards: Welfare, productivity, and output . . . . . . . . . . 33 5 Quantitative analysis 35 5.1 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 5.2 Decomposition analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 39 46

5.3 Optimal Policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 6 Concluding remarks 42 A Additional figures 48 B Cross-sectional evidence: Full table 53 C Comparative Statics 54 D Proofs 56 D.1 Proof for Proposition 1. . . . . . . . . . . . . . . . . . . . . . . . . . 56 D.2 Proof for Proposition 2. . . . . . . . . . . . . . . . . . . . . . . . . . 57 D.3 Proof for Proposition 3. . . . . . . . . . . . . . . . . . . . . . . . . . 57 D.4 Proof for Corollary 1. . . . . . . . . . . . . . . . . . . . . . . . . . . 59 D.5 Proof for Proposition 4. . . . . . . . . . . . . . . . . . . . . . . . . . 60 47

A Additional figures Figure A.1 plots the time series of the total number of firms in the united states. In contrast to the declining trend of the number of listed firms, the total number of firms has been steadily rising. Figure A.1: Number of all firms 1985 1990 1995 2000 2005 2010 2015 2.5 0.5 8.4 6.4 4.4 2.4 Year ).lim( smrif fo rebmuN Notes: This figure plots the time series of the number of all firms using the Business Dynamics Statistics (BDS) data from the U.S. Census Bureau. Figure A.2 plots the time series of (a) the number of listed firms and (b) the intangible intensity measured by using R&D only for multiple industries. Panel (a) showstheindustryandserviceindustrieshavedisplayedthemostdramaticdeclinesin recentyearsintermsofthenumberoflistedfirms. However, thetotalnumberoffirms intheseindustries(solidthinline)hassteadilyrisenoverthesampleperiod. Panel(b) showsthattheinformationandserviceindustrieshaveshownafastincreaseinreliance on intangible assets. However, compared to Figure 2, the difference between the information and service industries and the manufacturing industry is not as drastic. Figure A.3 plots the time series of the number of listed firms for different industries. Specifically, we report the trends for (a) natural resources and mining, (b) 48

Figure A.2: Number of listed firms and intangible intensity by industry (internal R&D only). 1985 1990 1995 2000 2005 2010 2015 052 002 051 001 05 Year )001 = rebmun s'5891( xedni mrif fo rebmuN Group Information+Services Manufacturing Others Information+Services (all) 1985 1990 1995 2000 2005 2010 2015 (a) Number of listed firms 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 Year )D&R lanretnI( ytisnetni elbignatnI Group Information+Services Manufacturing Others (b) Intangibles intensity Notes: This figure shows the trend in the number of listed firms and intangible capital intensity in the U.S. Intangible intensity is defined as the ratio of intangible asset, excluding acquired intangibleandorganizationalcapital,tototalintangible(againexcludingacquiredintangibleandorganizational capital) and tangible asset values.The groups are defined as Information and Services, excluding trade and transportation, Manufacturing,and other sectors (Trade and transportation, AgricultureandMining, Construction). DatacomesfromCompustat. SeeSection2.1fordetailson measurement. construction, (c) manufacturing, trade, (d) transportation, and utilities, (e) information, (f) professional and business services, (e) education and health services, and (f) leisure and hospitality industries. Figure A.4 plots the time series of the intangible intensity of listed firms for different industries. Specifically, we report the trends for (a) natural resources and mining, (b) construction, (c) manufacturing, trade, (d) transportation, and utilities, (e) information, (f) professional and business services, (e) education and health services, and (f) leisure and hospitality industries. Figure A.5 plots the time series of the transparency measures for all firms and for only survivors. Here, the survivor is ex-post conditioned by the firms of which observations are available at the end of the sample period. 49

Figure A.3: Trends in the number of public firms by industry 1985 1990 1995 2000 2005 2010 2015 002 051 001 05 Natural Resources and Mining Year )001 = rebmun s'5891( xedni mrif fo rebmuN 1985 1990 1995 2000 2005 2010 2015 002 051 001 05 Construction Year )001 = rebmun s'5891( xedni mrif fo rebmuN 1985 1990 1995 2000 2005 2010 2015 002 051 001 05 Manufacturing Year )001 = rebmun s'5891( xedni mrif fo rebmuN 1985 1990 1995 2000 2005 2010 2015 002 051 001 05 Trade, Transportation, and Utilities Year )001 = rebmun s'5891( xedni mrif fo rebmuN 1985 1990 1995 2000 2005 2010 2015 006 005 004 003 002 001 Information Year )001 = rebmun s'5891( xedni mrif fo rebmuN 1985 1990 1995 2000 2005 2010 2015 002 051 001 05 Professional and Business Services Year )001 = rebmun s'5891( xedni mrif fo rebmuN 1985 1990 1995 2000 2005 2010 2015 002 051 001 05 Education and Health Services Year )001 = rebmun s'5891( xedni mrif fo rebmuN 1985 1990 1995 2000 2005 2010 2015 002 051 001 05 Leisure and Hospitality Year )001 = rebmun s'5891( xedni mrif fo rebmuN 50

Figure A.4: Trends in intangible intensity by industry 1985 1990 1995 2000 2005 2010 2015 08 06 04 02 0 Natural Resources and Mining Year )%( ytisnetnI elbignatnI All intangible Internal R&D 1985 1990 1995 2000 2005 2010 2015 08 06 04 02 0 Construction Year )%( ytisnetnI elbignatnI All intangible Internal R&D 1985 1990 1995 2000 2005 2010 2015 08 06 04 02 0 Manufacturing Year )%( ytisnetnI elbignatnI All intangible Internal R&D 1985 1990 1995 2000 2005 2010 2015 08 06 04 02 0 Trade, Transportation, and Utilities Year )%( ytisnetnI elbignatnI All intangible Internal R&D 1985 1990 1995 2000 2005 2010 2015 08 06 04 02 0 Information Year )%( ytisnetnI elbignatnI All intangible Internal R&D 1985 1990 1995 2000 2005 2010 2015 08 06 04 02 0 Professional and Business Services Year )%( ytisnetnI elbignatnI All intangible Internal R&D 1985 1990 1995 2000 2005 2010 2015 08 06 04 02 0 Education and Health Services Year )%( ytisnetnI elbignatnI All intangible Internal R&D 1985 1990 1995 2000 2005 2010 2015 08 06 04 02 0 Leisure and Hospitality Year )%( ytisnetnI elbignatnI All intangible Internal R&D 51

Figure A.5: Time series of transparency: all firms vs. survivors 1985 1990 1995 2000 2005 2010 2015 002 051 001 05 Year )001 = ycnerapsnarT s'5891( xednI ycnerapsnarT Transparency 1: All Transparency 1: Survivor Transparency 2: All Transparency 2: Survivor Notes: This figure shows the trend in in transparency for all firms vs. survivors. Data comes from Compustat and I/B/E/S. See Section 2.1 for details on measurement. 52

B Cross-sectional evidence: Full table Table B.1: Regression of transparency proxies on intangibles Dependent Variables: Transparency 1 Transparency 2 Intangible -0.31 -0.627 it (0.046) (0.096) Sale -0.145 -0.303 it (0.049) (0.096) CurrentAsset -0.738 -1.392 it (0.099) (0.198) Leverage -1.594 -3.362 it (0.265) (0.516) B/M -1.003 -2.045 it (0.127) (0.263) log(emp ) 0.249 0.497 it (0.04) (0.08) Age -0.001 -0.002 it (0.004) (0.007) #Analysts 0.019 0.012 it (0.008) (0.02) Industry FE Yes Yes Year FE Yes Yes Controls Yes Yes Two-way cluster Yes Yes Observations 256,962 256,962 Adj. R2 0.275 0.289 Notes: This table reports the estimates of the coefficients from the following regression using our baseline sample, which includes all firms in Compustat from 1985 to 2016 for which information on earnings forecasts by at least one analysts is available: logy =θ +FEs+β×Intangible capital over total assets +γX +ε , i,t t i,t i,t i,t where y is either the inverse absolute value of earning surprises from the consensus, or the inverse i,t of variance of earning surprises when more than one analyst forecast is present. θ are year fixed t effects and FEs include industry fixed effects. X represents firm controls. i,t 53

C Comparative Statics Figure C.6 plots the comparative static results of optimal disclosure regulation (vertical axis) for different parameters (horizontal axis). The optimal regulation displays a strict monotone variation with each parameter change. Figure C.6: Comparative statics on optimal transparency level with respect to each parameter 0.996 0.998 0.994 0.997 0.996 0.992 0.995 0.99 0.994 0.993 0.988 0.992 0.991 0.986 0.99 0.984 0.989 0 10 20 30 40 50 60 70 80 0.988 0 10 20 30 40 50 60 (a) Transparency’s contribution to public information ψ (b) Baseline information level ξ 1 1 0.99 0.998 0.98 0.996 0.97 0.994 0.96 0.992 0.95 0.99 0.94 0.988 0.93 0.986 0.92 0.984 0.91 0.982 0.9 0.98 1 2 3 4 5 6 7 0 0.01 0.02 0.03 0.04 0.05 0.06 (c) PE market friction ν (d) Intangible share θ N Notes: We change each single parameter, keeping the others constant at their baseline value, and calculate the resulting optimal transparency level. Figure C.7 plots the comparative static results of the equilibrium mass of listed firms (vertical axis) for different parameters (horizontal axis). The equilibrium mass of listed firms displays a strict monotone variation with each parameter change. 54

Figure C.7: Comparative statics on fraction of listed firms with respect to each parameter 0.18 0.3 0.16 0.25 0.14 0.12 0.2 0.1 0.15 0.08 0.1 0.06 0 10 20 30 40 50 60 70 80 0.05 0 10 20 30 40 50 60 (a) Transparency’s contribution to public information ψ (b) Baseline information level ξ 0.2 0.135 0.18 0.13 0.16 0.125 0.14 0.12 0.12 0.115 0.1 0.11 0.08 0.105 0.06 0.1 0.04 0.095 0.02 0.09 1 2 3 4 5 6 7 0 0.01 0.02 0.03 0.04 0.05 0.06 (c) PE market friction ν (d) Intangible share θ N 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0.9 0.92 0.94 0.96 0.98 1 (e) Mandated minimum transparency q¯ Notes: We change each single parameter, keeping the others constant at their baseline value, and calculate the resulting number of listed firms. 55

D Proofs D.1 Proof for Proposition 1. Proposition 1. (Intangibles and the transparency) Given α+θ < 1, kI(q,M;q) decreases in both q and q. Specifically, (cid:32) (cid:18) αz(Φex)γ(cid:19) 1−α 1 −θ (cid:18) rθ (cid:19) 1− 1− α α −θ (cid:33) θ k I (q,M;q) = (1−q −q)1−α−θ. r pα Proof. From FOC [k ] : zαkα−1(k (1−q −q))θ(Φex)γ = r T T I [k ] : zθkα(k (1−q −q))θ−1(Φex)γ(1−q −q) = p I T I + (cid:0) zkα(k (1−q −q))θ(Φex)γ −rk −pk (cid:1) ϕ′L(q) = 0. T I T I From the first-order conditions with respect to k and k , we obtain T I r (cid:16)α(cid:17) k I = . p θ k T Substituting this relation into the first-order condition with respect to k , we get T (cid:16)αp(cid:17)α−1 r = αz (k )α+θ−1(1−q −q)θ(Φex)γ. I θr Thus, (cid:32) (cid:18) αz(Φex)γ(cid:19) 1−α 1 −θ (cid:18) rθ (cid:19) 1− 1− α α −θ (cid:33) θ θ k I = (1−q −q)1−α−θ = A(1−q −q)1−α−θ, r pα (cid:18) (cid:16) (cid:17) 1 (cid:16) (cid:17) 1−α (cid:19) whereA := αz(Φex)γ 1−α−θ rθ 1−α−θ . Asα+θ < 1, thepropositionisimmediate r pα from the last equation. ■ 56

D.2 Proof for Proposition 2. Proposition 2 (Intangibles and the transparency). Given α+θ < 1, the sensitivity of kI(q,q,θ) to the changes in q and q increases in θ. Proof. (cid:12) (cid:12) (cid:12) (cid:12) (cid:18) (cid:19) ∂ (cid:12) ∂ (cid:12) ∂ (cid:12) ∂ θ (cid:12) (cid:12) log(K )(cid:12) = (cid:12) log(1−q −q)(cid:12) ∂θ(cid:12)∂q I (cid:12) ∂θ(cid:12)∂q 1−α−θ (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:18) (cid:19) ∂ 1−α 1 = −1+ ∂θ 1−α−θ 1−q −q 1−α 1 = > 0. (1−α−θ)21−q −q ■ D.3 Proof for Proposition 3. Proposition 3. (Transparency distribution) The probability density function M of transparency q has the following closed form: 1 θ M(q) = (ξ +ψ(q +q))(1−q −q)1−α−θ . ϕN Proof. 57

We derive the following equations using the first-order condition with respect to q:27 ϕ′L(q) zθkα(k (1−q −q))θ−1(Φex)γk = T I I ϕL(q) zkα(k (1−q −q))θ(Φex)γ −rk −pk T I T I zθkα(k (1−q −q))θ−1(Φex)γk = T I I (1−α−θ)zkα(k (1−q −q))θ(Φex)γ T I (cid:18) (cid:19) θ 1 = . 1−α−θ 1−q −q From ∂ log(ϕL(q)) = ϕ ′L(q), the solution of the first-order differential equation is as ∂q ϕL(q) follows: ϕL(q) = (1−q −q)nC(cid:101), for some n ∈ R and some C(cid:101) ∈ R. From the indifference condition in the equilibrium, πL(q)ϕL(q) does not depend on q. (cid:16) (cid:16)αp(cid:17)α (cid:17) πLϕL(q) = z(1−α−θ) Aα+θ(1−q −q)1−α θ −θΦγ (1−q −q)nC(cid:101). θr Therefore, θ n = − . 1−α−θ This leads to ϕL(q) = (1−q −q)− 1−α θ −θ C(cid:101). Then, the distribution of listed firms is as follows: M(q) = (ξ +ψ(q +q))/ϕL(q) 1 θ = (ξ +ψ(q +q))(1−q −q)1−α−θ . C(cid:101) 27Here the proof is based on the first-order conditions that are simultaneously obtained for k , T k , and q for the brevity of notations. The equilibrium allocations stay unaffected in this problem I even if the solution is solved sequentially (interim problem first (k and k ), and then q) T I 58

From the indifference condition between listed and non-listed, πL(q)ϕL(q) ϕN = πN (cid:16) (cid:17) z(1−α−θ) (cid:0)αp(cid:1)α Aα+θ(1−q −q)1−α θ −θΦγ (1−q −q)− 1−α θ −θ C(cid:101) θr = (cid:0) z(1−α−θ) (cid:0)αp(cid:1)α Aα+θΦγ (cid:1) θr = C(cid:101). Therefore, M(q) = (ξ +ψ(q +q))(1−q −q)1−α θ −θ 1 . ϕ(cid:102)N In the equilibrium, ϕN(= C(cid:101)) is determined at the level where the following equation holds: (cid:90) 1−q M(q)dq = 1−M . N 0 ■ D.4 Proof for Corollary 1. Corollary 1. (Truncated Beta distribution) The gross transparency, y := q + q, follows a truncated Beta distribution where the shape parameters are 2 and B +1, and the support is [q,1]. I{q ∈ [0,1−q]} q +q ∼ ×Beta(B +1,2), 1−M N where B = θ . 1−α−θ Proof. WedefineM (y)astheprobabilitydensityfunctionoftherandomvariabley = 1−q−q. Y 1+ξ/ψ (cid:20) (cid:21) 1−q M (y) ∝ (1−y)yB and y ∈ 0, . Y 1+ξ/ψ Also, (cid:82) 1+ 1− ξ/ q ψ M (y)dy = 1−M . Therefore, y ∼ I{q∈[0,1−q]} ×Beta(B +1,2). ■ 0 Y N 1−MN 59

D.5 Proof for Proposition 4. Proposition 4. (The relationship between disclosure regulation and the measure of listed firms) M strictly increases in q ∈ (0,1). N Proof. We have 1 M = . N (cid:16) (cid:17) 1+ψνN(1+ ξ)B+2B(B +1,2)F 1−q;B +1,2 ξ ψ 1+ξ F decreases in q, and M decreases in F. Thus, M increases in q. ■ N N 60