Quantifying Collateral Constraints' Economic Impact

The paper begins by acknowledging a growing body of research demonstrating the causal link between financing frictions and firm-level outcomes. Studies like Lamont (1997), Rauh (2006), Chaney et al. (2012), and Gan (2007) are cited as examples, highlighting how factors like oil price changes, pension funding rules, and house price fluctuations impact firm investment and labor demand. While these studies convincingly reject the null hypothesis of no financial constraints, they fall short in quantifying the overall economic significance of these constraints. This research paper aims to address this gap by focusing on the macroeconomic consequences of a specific type of friction: collateral constraints.

The study centers its quantitative analysis on collateral constraints, a prevalent source of financing friction. It replicates previous findings by Gan (2007) and Chaney et al. (2012), demonstrating the strong relationship between real estate values and corporate investment for firms owning versus renting properties. The authors replicate these findings using a slightly different model specification, confirming that a $1 increase in real estate value leads to a significant $0.04 increase in both investment and debt. Although this strengthens the evidence of financial constraints, it does not quantify their economic impact, which is the main objective of this study. The authors thus propose two quantification exercises based on these reduced-form estimates to bridge this gap.

The core of the paper involves developing and estimating a dynamic model using the Simulated Method of Moments (SMM). This model incorporates a collateral constraint, mimicking the design of the previous reduced-form estimations. The model simulates how real estate asset values fluctuate randomly, thereby creating variations in the collateral constraint. The SMM estimation procedure explicitly targets the sensitivity of investment to variations in local real estate prices, a key moment differentiating this approach from previous literature that relied on more traditional moments. The successful replication of targeted and non-targeted moments, as well as the model's well-behaved comparative statics, validate the model's robustness. Critically, the authors show how targeting the reduced-form regression coefficient provides different inference on the parameter governing credit friction than using traditional financing moments (like average leverage ratios).

The estimated model is embedded within a simple general equilibrium framework to assess the macroeconomic effects of collateral constraints. By simulating two economies—one with the estimated constraint and another without—the authors quantify the welfare and output losses. This analysis reveals a substantial aggregate welfare loss of 9.4% and an output loss of 11%. The paper clarifies that these losses stem from both input misallocation across heterogeneous producers and a sub-optimal aggregate capital stock, with the latter having a greater impact. Importantly, while the study quantifies the costs of these constraints, it refrains from evaluating their potential benefits or assessing the efficiency of the mechanisms behind these collateral constraints, focusing instead on the pure magnitude of their impact.

This research contributes to the broader literature on corporate finance and the macroeconomic implications of financing frictions, extending previous work by focusing on the aggregate effects of collateral constraints and by employing an innovative methodology. It bridges the gap between reduced-form microeconomic evidence and macroeconomic consequences. The authors emphasize that their results highlight that approximately half of the aggregate losses are attributable to a lower aggregate capital stock compared to a counterfactual economy without collateral constraints, while the remaining losses stem from misallocation of inputs across firms and reduced labor supply. The paper concludes by reinforcing the significant macroeconomic implications of collateral constraints, as calculated using the novel approach of integrating reduced-form findings within a structural model.

The paper employs a Simulated Method of Moments (SMM) approach for structural estimation. The model, incorporating collateral constraints, is solved numerically, a computationally intensive task addressed using GPU processing to handle the large number of optimizations required. The SMM aims to find a parameter set that makes model-generated moments closely match predetermined data moments. Because the model lacks an analytical solution, indirect inference is necessary, involving iterative steps of model simulation and parameter adjustments to minimize the discrepancies between simulated and actual moments. This process is described as finding the parameter set Ωˆ such that model-generated moments m(Ωˆ) closely match the data moments m. The computational details highlight the challenges of achieving high precision in model-generated moments given computational limitations.

A crucial aspect of the estimation is the selection of moments. The paper contrasts a traditional approach relying on moments like short- and long-term volatilities of log sales and mean leverage with a novel approach. The innovative element is the inclusion of the sensitivity of investment and debt to real estate values as targeted moments. This is the coefficient β(Inv, RE) estimated from a reduced-form regression in Section 1, directly linked to financing frictions. The authors demonstrate that incorporating this sensitivity coefficient as a targeted moment is crucial for identifying the strength of financial frictions and the pledgeability parameter (s), which governs the degree to which firms can use their collateral. The authors emphasize that simply rejecting the absence of financing frictions based on positive sensitivity coefficients doesn't provide sufficient information, making their indirect inference method critical for quantifying the magnitude of these frictions.

The estimation process considers different model specifications, including those with and without adjustment costs to capital. The introduction of adjustment costs is significant because these costs generate patterns similar to those observed with financing constraints. Consequently, the authors carefully examine how the inclusion of such costs affects the estimation of the pledgeability parameter (s). Results demonstrate a significant difference in the estimated pledgeability parameter (s) when targeting the investment sensitivity to real estate prices versus traditional leverage moments. In the preferred model specification that includes adjustment costs and uses investment sensitivity as a targeted moment, the authors achieve a precise fit for the targeted investment sensitivity and even the non-targeted debt sensitivity, further validating the chosen moments and their role in accurately identifying the key parameters.

The paper's approach is validated through several checks. The model's comparative statics are well-behaved, implying that the chosen parameters influence the model in a logical and consistent manner. The authors conduct a robustness check by simulating data from an unconstrained model to test the identification strategy. This simulation demonstrates the robustness of using the investment-real estate sensitivity as a targeted moment, unlike estimations that only focus on leverage. When using only leverage as the targeted moment, the model mistakenly identifies the unconstrained model as being constrained, generating misleading inferences about economic losses, in contrast to the correct conclusion obtained using the investment sensitivity. This further highlights the improved identification and robustness of the approach employed in this study. The precision of the estimated pledgeability parameter is also discussed, offering confidence in the estimated macroeconomic effects.

To assess the macroeconomic implications of the estimated model, the researchers embed it within a general equilibrium framework. This framework features heterogeneous firms competing for customers, workers, and capital goods. The key step is simulating two economies: one reflecting the estimated model with collateral constraints, and a counterfactual economy where firms are financially unconstrained. By comparing these two economies, the researchers aim to quantify the aggregate output and welfare losses stemming from the presence of financing frictions, specifically, collateral constraints. The general equilibrium setting allows for a comprehensive analysis of the macroeconomic impact, considering the interconnectedness of various economic agents and markets.

The simulation results reveal substantial macroeconomic consequences of collateral constraints. The study finds an aggregate welfare loss of 9.4% and an output loss of 11% when comparing the constrained economy to the unconstrained counterfactual. This finding highlights the significant economic cost of these financing frictions. The paper further decomposes these aggregate losses, attributing part to the misallocation of inputs across heterogeneous firms (as discussed in Hsieh and Klenow, 2009; Moll, 2014; Midrigan and Xu, 2014) and another part to a suboptimal aggregate capital stock. Remarkably, the analysis indicates that the reduction in the aggregate capital stock accounts for twice the loss compared to input misallocation, demonstrating that this factor is the primary driver of overall macroeconomic losses.

The magnitude of the estimated welfare and output losses is directly related to the choice of moments used in the SMM estimation. The authors compare results obtained by targeting the mean leverage ratio (a traditional approach) with their preferred method of targeting the reduced-form investment sensitivity to real estate values. They demonstrate that targeting mean leverage leads to significantly different estimations of the key parameters, yielding a substantially lower estimate of the macroeconomic losses. The findings emphasize that the choice of moments is critical for accurately reflecting the importance of collateral constraints and, therefore, for precise quantification of aggregate welfare and output losses. Using the sensitivity measure provides a much more accurate picture of the real macroeconomic impact of collateral constraints.

To assess the robustness of the estimated macroeconomic losses, the researchers perform a sensitivity analysis, varying the key parameter 's' (pledgeability) within its 95% confidence interval. The narrow confidence interval (a standard error of 0.008 for a point estimate of 0.189) suggests that the estimated aggregate effects are precise and not significantly altered by small variations in the parameter. This demonstrates the reliability and precision of the study's estimates of the aggregate welfare and output losses from collateral constraints. The analysis visually demonstrates the stable relationship between the parameter 's' and the macroeconomic outcomes within this confidence interval, reinforcing the robustness of the findings.

The study investigates how firm characteristics correlate with the likelihood of being financially constrained. Using the preferred model specification, a firm is defined as constrained if its capital stock falls below 80% of its frictionless counterpart (calculated by removing the no-equity issuance constraint). Analyzing simulated data sorted into bins based on various firm characteristics, the paper finds that more productive firms are generally more constrained, likely due to recent positive productivity shocks exceeding their available capital. Interestingly, the relationship between firm size and constraints is weaker; while larger firms tend to be more productive (and thus more constrained), they also possess more collateral, mitigating the constraint effect. High leverage firms are also more prone to constraints, consistent with the model's assumption of limited debt capacity. Finally, a strong positive correlation exists between the sales-to-capital ratio and the fraction of constrained firms, indicating this ratio serves as a valuable proxy for identifying financially constrained firms, despite acknowledging that it's not a definitive measure of input misallocation in dynamic models.

A potential concern is the baseline model's inability to perfectly match the observed mean leverage ratio. The authors address this by extending the model to include an additional term (d¯) representing uncollateralized debt capacity, encompassing factors such as unsecured debt, trade credit, and inventories. Re-estimating the model with this addition, the authors find that while the model now matches the observed leverage ratio, this additional debt capacity is primarily used for tax optimization rather than increasing investment. Therefore, the overall binding nature of the borrowing constraint remains largely unaffected, indicating that the initial estimates of aggregate losses due to financing constraints are robust even when considering the additional sources of debt capacity. The inclusion of d¯ helps to complete the model's description of firm leverage without significantly changing the main findings regarding aggregate losses.

The study explores the potential impact of policy interventions, specifically an investment tax credit (ITC), on mitigating the effects of financing constraints. The analysis compares a non-targeted ITC (financed by a lump-sum tax on household income) with a targeted ITC. A 5% non-targeted ITC significantly boosts capital stock (11%), aggregate employment (1.4%), output (4.3%), and welfare (2.9%). This large effect is explained by the high corporate profit tax rate (33%) in the model. However, a targeted ITC, while seemingly more efficient in theory, induces an opportunistic investment strategy, with firms underinvesting until the policy threshold is crossed, and then sharply increasing investment. This contrasts with the smooth investment response to an untargeted ITC. The contrasting effects demonstrate that the design and targeting of policy interventions are crucial for their effectiveness and can lead to unintended consequences unless carefully considered, thus highlighting the importance of appropriate policy interventions to address financing frictions.

The empirical analysis relies on a panel dataset encompassing 2,218 firms observed from 1993 to 2006, resulting in 20,074 observations. The data requirements necessitate that firms provide information on the accounting value and cumulative depreciation of their land and buildings (items ppenb, ppenli, dpacb, dpacli) as of 1993. This information is combined with office prices from the city where each firm's headquarters are located to create a measure of the market value of firms' real estate holdings, normalized by the previous year's property, plant, and equipment. This key variable, labeled REValue, is crucial for the analysis. Note that the panel is unbalanced, with only 676 firms remaining in the dataset by 2006. The availability of REValue for all firms is a critical constraint in defining the sample used in this study.

The firm-level model incorporates several key features consistent with the corporate finance literature. It includes a tax shield for debt, an infinite cost of equity issuance, and importantly, a collateral constraint. Firms' production technology is described by a Cobb-Douglas production function with a capital share α. The model assumes risk-neutral shareholders with a time discount rate of r. Investing entails a convex cost, and there's a one-period time-to-build for capital, a standard assumption in macroeconomic models. The introduction of adjustment costs to capital is particularly important in differentiating financing constraints from other adjustment mechanisms. This is mentioned in relation to studies by Hall (2004), Bloom (2009), and Asker et al. (2014). The model also includes corporate profit taxation at a rate τ, applicable to both positive and negative profits.

The model incorporates a collateral constraint that limits borrowing based on the value of real estate assets. The constraint is specified as (1+r)d_t+1 ≤ d¯ + s(1-δ)k_t+1 + E[p_t+1|p_t]h, where 's' represents the pledgeability of collateral (the fraction of collateral value that can be pledged), and h represents the quantity of real estate assets. This formulation accounts for a potential residual leverage term d¯ that captures the un-collateralized debt capacity not explicitly modeled. A key limitation is the assumption of a constant quantity of real estate (h) across firms and time periods. The paper recognizes this simplification ignores the potentially important heterogeneity in real estate ownership decisions driven by expected productivity, investment opportunities, local factor prices, and financing constraints. It leaves an investigation of these endogeneities for future work.

The model's solution involves numerically solving a Bellman problem to obtain policy functions for debt and capital. The state space is discretized to facilitate numerical computation, acknowledging the potential for numerical errors to affect the magnitude of the estimated aggregate effects of the collateral constraints. To minimize these errors, a fine grid is used, and the authors leverage the computational power of a GPU (Nvidia K80) to accelerate the solution process. The paper emphasizes the computational intensity of solving the model—requiring approximately 4,392,630 optimizations—and the use of the GPU significantly reduces the computation time from several hours on a conventional CPU to only a few minutes. The computational constraints inherent in managing the large arrays during model simulation are also discussed, justifying the use of specific computational techniques.