NBER WORKING PAPER SERIES CONSTRAINED-EFFICIENT CAPITAL REALLOCATION Andrea Lanteri Adriano A. Rampini Working Paper 28384 http://www.org/papers/w28384 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 January 2021, Revised June 2022 We thank the Editor (Mikhail Golosov) and three anonymous referees for insightful suggestions. We also thank David Berger, Alberto Bisin, Eduardo Dávila, Peter Kondor, Anton Korinek, Pablo Kurlat, Jennifer La’O, Daniel Neuhann, Jaume Ventura, S. “Vish” Viswanathan, Daniel Xu, as well as seminar participants at Duke (economics), the Econometric Society World Congress, Duke (finance), Oxford, the Virtual Australian Macro Seminar, Georgia Tech, the UVA-Richmond Fed Workshop, the PHBS Workshop in Macroeconomics and Finance, Collegio Carlo Alberto, the Search and Matching in Macro and Finance Seminar, the Barcelona GSE Summer Forum on Economic Fluctuations and Growth, University of British Columbia, Northwestern, Columbia, the Federal Reserve Board of Governors, the Finance Theory Group Meeting, CREi, Nottingham, the Theories and Methods in Macro Conference, the SFS Cavalcade, and the FIRS Conference for helpful comments.
Parts of this paper were written while Lanteri was on leave at NYU and Rampini was on sabbatical leave at Princeton University and NYU; their hospitality is gratefully acknowledged. First draft: August 2020. Lanteri is a CEPR Research Affiliate. Rampini is an NBER Research Associate and a CEPR Research Fellow.
Alessandro Villa and Jui-Lin Chen provided excellent research assistance. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.
© 2021 by Andrea Lanteri and Adriano A. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Constrained-Efficient Capital Reallocation Andrea Lanteri and Adriano A.
Rampini NBER Working Paper No. 28384 January 2021, Revised June 2022 JEL No. D51,E22,E44,G31,H21 ABSTRACT We characterize efficiency in an equilibrium model of investment and capital reallocation with heterogeneous firms facing collateral constraints. The model features two types of pecuniary externalities: collateral externalities, because the resale price of capital affects collateral constraints, and distributive externalities, because buyers of old capital are more financially constrained than sellers, consistent with empirical evidence.
We prove that the stationary- equilibrium price of old capital is inefficiently high, because the distributive pecuniary externality exceeds the collateral externality, by a factor of two in our calibrated model. New investment reduces the future price of old capital, providing a rationale for new-investment subsidies. Andrea Lanteri Duke University Department of Economics 233 Social Sciences Building Durham, NC 27708 andrea. Rampini Duke University Fuqua School of Business 100 Fuqua Drive Durham, NC 27708 Durham, NC 27708 and NBER rampini@duke.edu 1 Introduction Collateral constraints distort the level of aggregate investment and the allocation of capital across firms.
What is the nature of the inefficiency induced by these constraints? Is the equilibrium resale price of capital—that is, the value of collateral—inefficiently low or inefficiently high? What is the allocation of capital that maximizes welfare taking collateral constraints as given? To address these questions, we develop an equilibrium model of investment and capital reallocation with collateral constraints. We then characterize the constrained-efficient allocation, that is, the allocation that would arise if a benevolent planner made investment decisions on behalf of firms, using the same markets and subject to the same financing constraints firms face in the competitive equilibrium. We use this benchmark to show that in stationary competitive equilibrium the resale price of capital is inefficiently high and a lower price would facilitate capital reallocation toward the most financially constrained firms. In our framework, heterogeneous firms face collateral constraints on borrowing as well as costs of issuing equity.
They produce output by investing in new capital or by acquiring old capital from other firms. Old capital is reallocated in a competitive secondary market. Importantly, the model is consistent with the key facts about capital reallocation: On average, older assets flow to more financially constrained and more productive firms. These firms have a high marginal value of current net worth.
Thus, they take advantage of the fact that old capital is cheaper and has hence a lower financing need than new capital, because it has a lower future residual value. On the other hand, larger, less financially constrained firms tend to acquire newer investment goods, as they effectively discount the future resale value of capital at a lower rate. These firms account for most of the formation of new capital in the economy, and typically resell their capital on the secondary market as it ages. Because of financial frictions, the competitive-equilibrium price of old capital does not coincide with its social value: Financial frictions manifest themselves as pecuniary exter- nalities.
Specifically, our economy encompasses both collateral externalities, because the resale value of capital affects firms’ ability to borrow, and distributive externalities, be- cause buyers and sellers of old capital have different valuations of internal funds. We show that the price of old capital, which serves as collateral, affects the aggregate value of these externalities with opposite sign. On the one hand, a higher resale price of capital relaxes collateral constraints. On the other hand, because buyers of old capital tend to be more fi- nancially constrained than sellers, a lower price of old capital redistributes resources toward firms with a higher marginal product of capital.
Our main result is that this distributive externality is larger than the collateral exter- 1 nality in stationary equilibrium. As a consequence, the equilibrium price of old capital is higher than the constrained-efficient price. An additional unit of new investment today increases the supply of old capital in the future, thereby reducing its price and creating a positive externality on future constrained firms, who are net buyers of old capital. In the decentralized equilibrium, investing firms do not take this effect into account.
A subsidy on new investment may thus lead to a more efficient allocation. Importantly, a low price of old capital is optimal, despite its negative effect on the value of collateral. The economic intuition is that the buyers of old capital are the most constrained firms, whereas the firms that purchase new capital and borrow against its collateral value are less constrained or unconstrained. Thus, the marginal value of net worth of firms that benefit from the distributive externality of a lower price of old capital is higher than the marginal value of net worth of the firms that are negatively affected by the collateral externality of a lower price of old capital.
To formalize this result, we consider a planner who faces the same constraints and has access to the same markets as private firms, but, crucially, internalizes all pecuniary externalities. The planner needs to respect all individual budget constraints and cannot re- distribute net worth across firms, that is, cannot “remove” financial frictions. We solve for the constrained-efficient allocation and compare it with the stationary competitive equi- librium. We show, both analytically and quantitatively, that the price of old capital is inefficiently high in competitive equilibrium.
The constrained-efficient allocation induces a lower price of old capital, allowing financially constrained firms to produce at larger scale. Our analysis is organized in three parts. First, we consider a stylized infinite-horizon model of capital reallocation and pecuniary externalities with over-lapping generations of firms and capital that lasts for two periods. In this model, we characterize the stationary equilibrium analytically and obtain a formal result on the sign of the inefficiency in equi- librium: The distributive externality is larger than the collateral externality.
Importantly, this result holds independently of specific assumptions about the distribution of net worth. We then provide a closed-form solution for the constrained-efficient allocation, as well as a Ramsey implementation of this allocation with proportional subsidies on investment in new capital and taxes on investment in old capital, rebated in a lump-sum fashion to each firm. We also consider several alternative restrictions on the set of policy instruments available to the planner. All of these policy experiments confirm that the planner aims to reduce the price of old capital.
Second, we consider three relevant generalizations of the assumptions of the stylized model, namely entrepreneurial risk aversion, heterogeneity in firm productivity, and when both firms and capital goods are long-lived. We show that our main analytical results 2 obtain in these more general models, as well as under a different timing assumption for the collateral constraint. We highlight the essential role of heterogeneity and equilibrium reallocation for these results and show how to apply these insights to an environment with productive assets in fixed supply. We also provide explicit guidance on the role of different assumptions for the comparison of collateral and distributive externality, connecting to other results in the literature on pecuniary externalities.
In particular, we discuss how modifying our assumptions on collateralizability of new and old capital, on discount rates vs. the interest rate, or on the type of market incompleteness may lead to different implications for the relative size of the two types of externalities. Third, we consider a richer quantitative model with persistent idiosyncratic productiv- ity shocks and long-lived firms and capital, which nests our stylized model. We calibrate the model to match empirical moments related to US firm dynamics and financing costs, and use it to perform a quantitative efficiency analysis, with a main focus on the stationary equilibrium.
We find that the distributive externality is over twice as large as the collateral externality in competitive equilibrium. Moreover, output and consumption are respectively 10% and 7% lower than in the first-best allocation. The constrained-efficient allocation re- covers approximately 70% of these losses (7 percentage points of output and 5 percentage points of consumption), by substantially decreasing the price of old capital. This outcome can be implemented in competitive equilibrium, with a mix of subsidies on new investment and taxes on purchases of old capital.
We also perform several additional policy experi- ments with restricted sets of policy instruments, which buttress our main conclusion on the desirability of policy interventions to stimulate new investment and reduce the resale price of capital. The paper proceeds as follows. Section 2 discusses the related literature. Section 3 presents our main theoretical results in a stylized model of capital reallocation.
Section 4 provides analytical results in more general models and discusses the role of different assump- tions. Section 5 introduces the quantitative model with idiosyncratic productivity shocks and characterizes the constrained-efficient allocation. Section 6 presents our quantitative results. Section 7 discusses additional analyses.
2 Related Literature This paper contributes to several strands of the literature, specifically on capital reallocation and the role of secondary markets, on pecuniary externalities with collateral constraints, on constrained efficiency in dynamic heterogeneous-agent economies, and on the effect of 3 financial frictions on capital misallocation.1 Capital reallocation and secondary markets. Several papers study the reallocation of durable assets across heterogeneous producers, starting with Eisfeldt and Rampini (2006). A ro- bust empirical finding of this literature is that financially constrained agents tend to buy assets in the secondary market. In particular, Eisfeldt and Rampini (2007) analyze invest- ment in new and used capital in the presence of financial frictions, and present empirical evidence that more financially constrained firms tend to acquire older investment goods, using both the Annual Capital Expenditure Survey and micro data on commercial trucks.
More recently, Ma, Murfin, and Pratt (forthcoming) leverage a large dataset on equipment transactions to document a negative correlation between firm age and capital age. We relate our quantitative results to their estimates. Gavazza, Lizzeri, and Roketskiy (2014) provide a quantitative analysis of the welfare gains due to secondary markets for durable goods in the presence of consumer heterogeneity. Gavazza and Lanteri (2021) emphasize the role of secondary markets in reallocating used consumer durable goods from wealthier to poorer households and argue that this mechanism contributes to the transmission of credit shocks.
