Intangible-Investment-Specific Technical Change, Concentration and Labor Share ∗ Lichen Zhang† Oct. 18, 2019 JOB MAKET PAPER CLICK HERE FOR THE LATEST VERSION Abstract In the past three decades, measured investment in factors such as software and R&D, collectively known as "intangible capital" has risen relative to the total business income. Together with this trend, the U.S. business sector has also been characterized by increased concentration and declined measured labor share. This paper develops a quantitative GE model of firm dynamics, consistent with important aspects of firms’ behavior at micro level, to explore the connection between the three major trends of the U.S. business sector. Individual firms operate at Cobb-Douglas technology, but they aggregate as if the elasticity of substitution among factors in production is above unity, triggered by an intangible-investment-specific technical change (IISTC). The IISTC shifts the firm distribution towards large, intangible-intensive firms with low labor share. I show that an IISTC, targeted to match the decline in the relative price of intangible investment goods, accounts for more than 2/3 of the rise of concentration and around half of the decline in measured labor share. Keywords: Intangible Investment, Concentration, Labor Share, Technical Change JEL Classification: E13, E22, E23, E25, D21, D25, D33 ∗I’m deeply indebted to my advisors Tim Kehoe, Manuel Amador, Loukas Karabarbounis, and Jonathan Heathcote for their invaluable guidance and continuous support. I’m particularly grateful to Ellen McGrattan for her detailed comments and discussions on this project. I also want to thank Hengjie Ai, David Argente, Anmol Bhandari, Jarda Borovicka, Zhifeng Cai, Doirrean Fitzgerald, Tom Holmes as well as participants in the International Macro/Trade Workshop and Quantitative Macro workshop at the University of Minnesota, and the UMN-UW Macro/International graduate workshop for their useful suggestions and comments. The views expressed herein are those of the author and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. All errors are my own. †Affiliation: University of Minnesota and Federal Reserve Bank of Minneapolis. 1925 Fourth Street South, Minneapolis, MN 55455 (email: [email protected]). 1 Introduction In the past three decades, measured investment in factors such as software and R&D, collec- tively known as “intangible capital” has risen relative to the total business income. Together with this trend, the U.S. business sector has been characterized by increased concentration in terms of employment and sales in large firms at the national level as well as declined measured labor share. This paper proposes a theory to explore the connection between the three major trends of the U.S. business sector quantitatively. I show that an intangible-investment specific technical change (IISTC) that drives the intangible investment relative to the total business income can account for the rise of concentration and the declined measured labor share jointly. I highlight the role of intangibles in shaping factor income shares, concentration, and business dynamism at both the micro and aggregate levels. In my model, firms start with zero intangible capital and the same level of wealth in terms of tangible assets, but differ in productivities on producing consumption/physical investment goods and intangible investment goods1. The varied productivity on intangible investment goods leads to heterogeneous factor shares of income across firms in the long run. Firms with high productivity on producing intangibles are large and intangible-capital intensive, and more intangible-capital intensive firms are also less labor-intensive. Hence, my model features a positive correlation between firm size and intangible-intensity, and a negative relationship between firm size and firm-level labor share, which are consistent with the micro evidence2. The IISTC in my model is manifested as a permanent increase in the aggregate productivity on producing intangible investment goods relative to that on producing consumption/physical investment goods, which captures the declined relative price of intangibles, particularly, soft- ware, from the data. Although firms operate at Cobb-Douglas technology, they aggregate as if the elasticity of substitution among factors in production is above one, triggered by the IISTC3. Firms with high productivity on producing intangibles are large and intangible- 1Since firms start with the same endogenous conditions and non-exiting firms can eventually grow to their optimal levels, only the exogenous heterogeneity matters in steady states. 2See Autor et al.(2017) and Crouzet and Eberly(2019) for United States and Lashkari, Bauer, and Boussard (2019) for very similar patterns in France. 3Consider a simple example where there are two perfectly competitive firms in each sector: one labor- intensive firm with production technology Y1 = L and the other is a capital-intensive firm with production technology Y2 = AK. There are constant labor shares within each firm. Suppose there is capital-specific technical change such that A increases. Under certain conditions, as capital becomes relatively cheaper, it is 1 intensive, which benefit disproportionately from this intangible-specific technology advances, thus becoming even larger and more intangible-intensive. More specifically, the IISTC pushes up the equilibrium wage rate. Due to this GE effect together with the negative correlation between firm size and firm-level labor share, output and labor are reallocated from small firms with low productivity on producing intangibles to large firms with high productivity on pro- ducing intangibles. This leads to the increased concentration. The declined aggregate labor share is the consequence of both a within-firm effect and an across-firm effect. Within each firm, the IISTC makes all the firms in the economy become more intangible-capital-intensive, thus being less labor intensive. Across firms, the IISTC shifts the firm distribution towards large firms with low labor share. My approach is to develop a quantitative GE model of firm dynamics for understanding the aggregate long-run impact of an intangible-investment-specific technical change (IISTC) on concentration and measured labor share. I enrich the model with three key features. First, I explicitly incorporate intangible investment and intangible capital into the model. More specifically, I differentiate between two types capital - tangible and intangible, which are both production inputs but intangible capital is accumulated within each firm through costly production for intangible investment goods given the firm’s production ability4. The goal of doing this is to enable this model to explore the role of intangible investment in shaping factor income shares and concentration at both the micro and macro levels. Second, I introduce financial frictions: incumbent firms cannot issue equity, and they face borrowing constraints that restrict leverage to a multiple of collateralizable assets, as in Evans and Jovanovic(1989). Adding such a financial friction contribute to a more realistic firm life cycle since it hinders the births of start-ups and slows the expansion of young firms. Otherwise, firms jump to their optimal level almost immediately after their births. This implies that statistics related to firm dynamics such as entry and concentration generated from a model without financial friction are going to be very sensitive to technology parameters. Since a main goal of this paper is to study the impact of a technical change on firm dynamics, having a model that features realistic firm distribution and life cycle of firms are very important. Third, I allow for endogenous entry and exit of firms. This helps to understand the effects substituted for labor on the aggregate-level. For more details, see Karabarbounis(2018) 4This differentiates with the existing literature on explaining declined measured labor share such as Aghion et al.(2019) that target "intangible share" without explicitly incorporating both tangible and intangible capital. 2 of an IISTC on how heterogenous firms’ behavior shape the aggregates. In the model, firms with high productivity on intangible investment goods account for a disproportionately large fraction of the total employment and total final output. Moreover, endogenous exit, interacting with financial frictions, makes larger firms harder to exit, which makes firm size and firm age distribution in the model closer to the data. I calibrate the model to the U.S. business sector as if it was at the steady state in early 1980s to match a rich set of both macro and micro moments. In particular, I discipline firms’ production technology to target the BEA-measured income shares and their productivity pro- cesses on both consumption/physical investment and intangible investment goods to capture the empirical fact that a small proportion of highly productive firms account for a very large share of total employment and total final output. I then show that the calibrated model can produce firm-level cross-sectional predictions consistent with the micro evidence. The most important one is the negative correlation be- tween firm size and firm-level labor share documented by Autor, Dorn, Katz, Patterson, and Reenen(2017) using census data. As I mentioned above, this relationship is key to generating the declined labor share and the rise of concentration driven by the IISTC. I finally use the calibrated model to quantify the aggregate long-term impact