metadata: authors: 0: author: di Giovanni,Julian
1: author: Garcia Santana,Manuel Jose
2: author: Jeenas,Priit
3: author: Moral Benito,Enrique
4: author: Pijoan-Mas,Josep
count: Spain
docna: 0: docna: Buy Big or Buy Small ? Procurement Policies,
            Firms’ Financing, and the Macroeconomy
docty: Policy Research Working Paper
abstracts: cdata!: This paper provides a framework to study
            how different allocation systems of public procurement
            contracts affect firm dynamics and long-run macroeconomic
            outcomes. It builds a novel panel dataset for Spain that
            merges public procurement data, credit register loan data,
            and quasi-census firm-level data. The paper provides
            evidence consistent with the hypothesis that procurement
            contracts act as collateral for firms and help them grow out
            of their financial constraints. The paper then builds a
            model of firm dynamics with asset- and earnings-based
            borrowing constraints and a government that buys goods and
            services from private sector firms, and uses it to quantify
            the long-run macroeconomic consequences of alternative
            procurement allocation systems. The findings show that
            policies which promote the participation of small firms have
            sizeable macroeconomic effects, but the net impact on
            aggregate output is ambiguous. While these policies help
            small firms grow and overcome financial constraints, which
            increases output in the long run, these policies also
            increase the cost of government purchases and reduce saving
            incentives for large firms, decreasing the effective
            provision of public goods and output in the private sector,
            respectively. The relative importance of these forces
            depends on how the policy is implemented and the type and
            strength of financial frictions.
display_title: Buy Big or Buy Small ? Procurement
            Policies, Firms’ Financing, and the Macroeconomy
listing_relative_url: /research/2023/07/34122163/buy-big-or-buy-small-procurement-policies-firms’-financing-macroeconomy
topicv3: Public Sector Management m1326314 696,Macroeconomic and Structural Policies
            m1327380 439,Financial Sector Development m1327681 1920
publishtoextweb_dt: 2023-07-24T00:00:00Z
dois: 10.1596/1813-9450-10522
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model_extractions: Policy Research Working Paper 10522

# Buy Big or Buy Small?

Procurement Policies, Firms’ Financing, and the Macroeconomy _Julian di Giovanni Manuel García-Santana Priit Jeenas Enrique Moral-Benito Josep Pijoan-Mas_ Development Economics Development Research Group July 2023
Policy Research Working Paper 10522

# **Abstract**

This paper provides a framework to study how different allocation systems of public procurement contracts affect firm dynamics and long-run macroeconomic outcomes. It builds a novel panel dataset for Spain that merges public procurement data, credit register loan data, and quasi-census firm-level data. The paper provides evidence consistent with the hypothesis that procurement contracts act as collateral for firms and help them grow out of their financial constraints. The paper then builds a model of firm dynamics with asset- and earnings-based borrowing constraints and a government that buys goods and services from private sector firms, and uses it to quantify the long-run macroeconomic consequences of alternative procurement allocation systems. The findings show that policies which promote the participation of small firms have sizeable macroeconomic effects, but the net impact on aggregate output is ambiguous. While these policies help small firms grow and overcome financial constraints, which increases output in the long run, these policies also increase the cost of government purchases and reduce saving incentives for large firms, decreasing the effective provision of public goods and output in the private sector, respectively. The relative importance of these forces depends on how the policy is implemented and the type and strength of financial frictions.

This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at mgarciasantana@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Buy Big or Buy Small? Procurement Policies, Firms’ Financing, and the Macroeconomy**<sup>∗</sup>

Julian di Giovanni<sup>☆</sup> Manuel Garc ́ıa-Santana<sup>◇</sup> Priit Jeenas<sup>◽</sup> Enrique Moral-Benito<sup>○</sup> Josep Pijoan-Mas<sup>▵</sup>

## _JEL Classifications_ : E22; E23; E62; G32

_Keywords_ : Government Procurement; Financial Frictions; Capital Accumulation; Aggregate Productivity

> ∗A previous version of the paper circulated with the title “ _Government Procurement and Access to Credit: Firm Dynamics and Aggregate Implications_ ”. We thank Manuel Amador, Wyatt Brooks, Paco Buera, Francesco Decarolis, Thomas Drechsel, Pablo Fajgelbaum, Cosmin Ilut, Joachim Jungherr, Eduardo Morales, Fernando Leibovici, Huiyu Li, Ezra Oberfield, Loukas Karabarbounis, Veronika Penciakova, Yongseok Shin, Kjetil Storesletten, Gustavo Ventura, Gianluca Violante, Daniel Xu, and David Zeke for very useful comments. The authors are also grateful to conference and seminar participants at the Minneapolis FED, Georgetown, Atlanta FED, St.Louis FED, San Francisco FED, World Bank, Richmond FED, USC, Princeton, New York FED, Duke, ASU, ND, CREi, Cornell, ArmEA, UB, and the Bank of Chile for valuable comments. Julian di Giovanni and Manuel Garc ́ıa-Santana acknowledge financial support from Fundaci ́on BBVA. Priit Jeenas acknowledges financial support from the Juan de la Cierva - Formaci ́on Grant by the Spanish Ministry of Science and Innovation. Josep Pijoan-Mas acknowledges financial support by the Spanish Ministry of Science and Innovation. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Banks of New York or any other person affiliated with the Federal Reserve System, the Bank of Spain, or the World Bank.

> ☆Federal Reserve Bank of New York, CEPR, juliandigiovanni@gmail.com;

> ◇World Bank, mgarciasantana@worldbank.org;

> ◽Universitat Pompeu Fabra, Barcelona School of Economics, CREI, priit.jeenas@upf.edu;

> ○Bank of Spain, enrique.moral@bde.es; ▵CEMFI, CEPR, pijoan@cemfi.es
# **1 Introduction**

Governments play a key role in economic activity. They are large employers, they set taxes and transfers, and they purchase goods and services from the private sector. These purchases are done by awarding _public procurement contracts_ to private firms. The size of public procurement varies over time and across countries, but it consistently represents a large fraction of GDP —12.8% in the OECD countries, 14% in EU countries, and 9.3% in the United States.<sup>1</sup> Because of its large size and high level of discretion, many governments use the public procurement process to allocate resources to specific firms. In the U.S., for example, the Small Business Act aims to “ensure that a fair proportion of federal contracts is awarded to small business”.<sup>2</sup> Similarly, in the EU, promoting the participation of small firms is at the core of the European Commission’s agenda for public procurement regulation.<sup>3</sup> A common justification for these policies is that small firms may face demand or financial constraints, preventing them from reaching their full potential and hence negatively affecting aggregate economic outcomes. Given the wide presence of these types of policies worldwide, it is surprising how little we know about their macroeconomic impact. This paper aims to fill this gap by asking if it is possible to achieve better aggregate outcomes when changing the composition of firms from which governments buy their goods and services.

Our research question is the following: how would the level of aggregate output, TFP, and provision of public goods be affected if governments change the composition of firms from which they buy while keeping total expenditure fixed? In order to address this question, we carry out an analysis that integrates a novel firm-level dataset with a macroeconomic model of firm dynamics. Our dataset merges administrative data on public procurement, credit allocation at the bank-firm level, and firm outcomes for the Spanish economy over the 2000-2013 period. Our model builds on the canonical framework of firm dynamics with financial frictions (e.g., Midrigan and Xu, 2014) and incorporates two novel elements. First, there is a government that purchases goods and services from private sector firms. Firms that are willing to sell to the government must make a risky investment in advance, which reflects the costs of preparing a good proposal and increasing the chances to win the contract. Second, we allow for earnings-based borrowing constraints where the pleadgeability of firms’ earnings from procurement may differ from that from selling to the private sector.<sup>4</sup> And third, we allow for the pleadgeability of firms’ earnings from procurement to differ

> 1See EU Commission’s web and OECD for details.

> 2See Report from Congressional Research Service for details. Policies promoting small firms’ participation in public procurement are widely spread worldwide. Some other examples are Australia and Brazil.

> 3See the Public Sector Directive 2014/24/EU for details. There has been strong support from the European Parliament for explicit regulation that discriminates in favor of small firms: “From this House, we must insist that...administrative bodies incorporate terms into their tender specifications that facilitate positive discrimination in favor of SMEs and remove contractual provisions that hinder their participation.” See EU Parliament Debate.

> 4Other recent papers that embed earning-based borrowing constraints into macro models are Drechsel (2023), Brooks and Dovis (2020), and Li (2022). The importance of earning-based borrowing constraint is also supported by direct evidence, see Lian and Ma (2020).

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from that from selling to the private sector.

We analyze the interplay between procurement and the macroeconomy by calibrating the model to reproduce several macro moments and, crucially, micro moments related to firm selection into procurement and to firm dynamics after winning a procurement contract (treatment).

We document a selection pattern where firms that participate in procurement are 72% larger exante in terms of value-added. We refer to this difference as the “procurement size premium.” Our model generates this procurement size premium through two firm-level state variables: productivity (TFPQ) and net worth. As it is standard in heterogeneous firm models, the value of participating in a given market —the procurement market in this case— depends on firms’ ability to deliver large projects (e.g., Melitz, 2003, in the context of international trade). In our model, this ability uniquely depends on firms’ TFPQ in the case of financially unconstrained firms. However, for constrained firms, it also depends on their financing capacity, which itself depends on firms’ net worth (e.g., Chaney, 2016, also in the context of international trade). In our baseline calibration, where we match the 72% value-added procurement size premium, our model implies a procurement premium of 35% in terms of TFPQ and 44% in terms of net worth.

Regarding treatment, the model is able to reproduce several facts related to the evolution of firms’ credit and firms’ sales, which we document by estimating local projections with our micro data.

First, we show a positive and persistent effect of participating in procurement on firms’ credit. Importantly, the effect on impact is completely explained by an increase in loans for which no tangible collateral is posted. This finding points towards the importance of earnings-based constraints. The subsequent effects over time, however, are partly explained by loans that require capital as collateral. This finding points towards the presence of asset-based constraints playing an important role, and the fact that firms’ ability to accumulate capital increases as a result of participating in procurement. In the calibration, we reproduce a structural regression in which the change in firms’ leverage, i.e., total credit divided by fixed assets, depends on two variables: the change in total earnings divided by fixed assets and the change in total earnings from procurement divided by fixed assets. The coefficient associated with the former ratio pins down the parameter that governs the pledgeability of firms’ earnings from selling to the private sector, whereas the coefficient associated with the latter pins down the difference in the pledgeability of earnings from procurement relative to the pledgeability of private earnings.<sup>5</sup> We run this regression for firms that are likely to be financially constrained, both in the model and in the data, and find that firms can pledge 10% of their annual earnings from selling to the private sector and 15% of their annual earnings from procurement.

> 5This structural identification of the earnings-based constraints is similar to the one used by Li (2022) for the case of private sector earnings only.

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Second, we also show that sales to the private sector decline upon obtaining a procurement contract (a “crowding-out” effect) and increase afterward (a “crowding-in” effect) leading to firm growth in the medium run. In our model, this crowding-out effect on impact of the procurement shock occurs because financially constrained firms have to split their scarce collateral to serve both procurement and private sector operations. The fact that government sales can be collateralized partly alleviates but does not eliminate this problem. Importantly, we show that the crowding-out effect is particularly stronger for firms that are more likely to be financially constrained, which suggests that the financial frictions at play in the model are also relevant in the data.

To assess the interplay between procurement and the macroeconomy, we use our calibrated model to perform some _expenditure-neutral_ counterfactual experiments that consist of reallocating procurement contracts across firms while keeping government expenditure unchanged. In particular, we compare our benchmark economy with counterfactual economies in which a higher share of procurement contracts is allocated to small firms. Our preferred counterfactual, which consists of promoting small firms’ participation by directly targeting them in the procurement allocation system, aims to reproduce the “set-aside” policies for small businesses implemented by the U.S Small Business Administration.

Our main result is that promoting the participation of small firms in government procurement generates sizeable macroeconomic effects through three main channels. First, the policy generates the positive effect of helping small firms grow and overcome financial constraints. The high pledgeability of procurement contracts together with the extra profits generated by them reinforces the self-financing channel previously emphasized in the literature (Moll, 2014). In this respect, public procurement is a powerful policy tool to help small firms overcome financial frictions and achieve closer to optimal size in the long run. We find that, through this channel, GDP would go up by around 3% as a result of the policy reform.

Second, there is an unintended consequence related to the change in capital accumulation incentives of relatively big firms (those for which the expected value of procurement decreases) and their responses to general equilibrium price changes. In particular, one of the main reasons firms accumulate financial wealth in our model is that they expect to obtain a public procurement contract at some point. Obtaining a procurement contract acts as a large demand shock in response to which firms want to expand their capital stock, causing even relatively big firms to accumulate precautionary savings. Intuitively, productive firms want to have enough net worth to minimize the probability of being constrained in case an opportunity for a big procurement contract is realized. A procurement policy that aggressively targets smaller firms will remove savings incentives for middle-sized and large firms. This channel shrinks the positive aggregate effect on GDP by 2 percentage points, from 3% to 1%.

Third, there is a second unintended consequence of the size-dependent policy related to the 3
government’s underlying production of public goods. By buying relatively more from the pool of small firms, the government also buys from firms that are fundamentally less productive and thus charge higher prices. Under a constant government expenditure, this phenomenon inevitably translates into a higher price index paid by the government and a lower provision of public goods. When accounting for this reduction in the amount of real final goods provided by the government, the overall effect on GDP shrinks further from 1% to 0.05%.

We also conduct an alternative policy experiment that consists in promoting small firms’ participation by reducing the average size of contracts. This reform aims to mimic the European Commission’s strategy to increase the presence of small firms in public procurement in Europe.<sup>6</sup> Our main finding is that this alternative policy counterfactual would reach a higher number of small firms than in our preferred counterfactual but would actually generate a fall in aggregate GDP of 0.85%. The reason for this decline in GDP is that the reduction in incentives of relatively big firms to accumulate capital – the _long-run general equilibrium effect_ – is particularly high due to the fall in the average size of procurement contracts. Our results hence imply that the particular way in which the promotion of small firms is implemented is crucial to understand its aggregate effects.

# **1.1 Related literature**

There is practically no literature that analyzes how the microeconomic aspects of public procurement can affect the macroeconomy. One recent exception is Cox, Muller, Pasten, Schoenle and Weber (2021), who document several new facts using micro-level data on public procurement contracts awarded by the U.S federal government, and investigate how accounting for these facts— in particular that government spending is concentrated in sectors where prices are more sticky— can affect the short run fiscal transmission mechanism in a New Keynesian model. Our interest differs in that we focus on quantifying the long-run macroeconomic effects of different procurement allocation systems through their impact on firm dynamics.

Governments may harm the long-run economic performance of countries through the implementation of policies that distort the allocation of resources across firms. Some examples are credit subsidies to state-owned-enterprises (Song, Storesletten and Zilibotti, 2011), size-dependent policies (Guner, Ventura and Xu, 2008; Garc ́ıa-Santana and Pijoan-Mas, 2014), labor market regulations (Garicano, Lelarge and Reenen, 2016), tariffs (Berthou, Chung, Manova and Sandoz, 2019), or capital markets regulation (Bau and Matray, 2023). However, one of the most important roles that governments play in modern economies, i.e., their role as buyers of goods and services from private sector firms, has been overlooked. We focus on this by analyzing specific size-dependent procurement policies aimed at helping small firms.

Our focus on firm-level financial frictions as a channel through which public procurement can

> 6See Trybus (2014) for details.

4
affect the macroeconomy builds on the literature that quantifies the effects of financial constraints on aggregate output and productivity. Some examples are Buera, Kaboski and Shin (2011), Midrigan and Xu (2014), Gopinath, Kalemli-Ozcan,<sup> ̈</sup> Karabarbounis and Villegas-Sanchez (2017), Leibovici (2021), David and Venkateswaran (2019), David, Schmid and Zeke (2022), and Catherine, Chaney, Huang, Sraer and Thesmar (2022).<sup>7</sup> A few papers in this literature have studied the interplay of financial frictions with different forms of taxation (Erosa and Gonz ́alez, 2019; Itskhoki and Moll, 2019; Guvenen, Kuru ̧s ̧cu, Kambourov, Ocampo and Chen, 2019) but none has focused on the expenditure side of government policies. Our finding that the type of financial frictions matters in understanding the effects of procurement on the macroeconomy is also related to recent papers that show that the type of financial frictions, i.e., earnings- vs. asset-based, and not only their severity, plays a crucial role in explaining important economic outcomes: the gains from trade liberalization (Brooks and Dovis, 2020), aggregate productivity (Li, 2022), macroeconomic fluctuations (Drechsel, 2023; Drechsel and Kim, 2022), and the transmission of monetary policy (Caglio, Darst and Kalemli ̈Ozcan, 2021).

Our results on the treatment effects of winning procurement contracts on firms are related to the recent literature analyzing the relationship between public procurement and firm dynamics. Ferraz, Finan and Szerman (2016) and Lee (2021) use quasi-experimental designs for Brazil and South Korea, respectively, to show that firms winning procurement contracts have a positive and permanent effect on firms’ performance. Hebous and Zimmermann (2021) document for the U.S. a positive relationship between winning a procurement contract and firm investment, and show that the effect disappears when looking at firms that are less likely to be financially constrained.<sup>8</sup> Our results are consistent with this body of research. We further provide novel evidence on loan acceptances and on the fact that only non-collateralized credit increases, which along with the other empirical facts that we document, can be taken as direct evidence of earnings-based financial constraints that are alleviated with procurement projects. Additionally, our results on the short-run crowding out of sales to the private sector by procurement sales are related to recent papers that investigate within-firm spillover effects across markets, like Almunia, Antr`as, L ́opez-Rodr ́ıguez and Morales (2021) and Kohn, Leibovici and Szkup (2016) with domestic versus foreign markets and Alfaro-Ure ̃na, Manelici and Vasquez (2022) with multinational corporations versus other buyers.

The rest of the paper is structured as follows. Section 2 describes the construction of the dataset and provides summary statistics. Section 3 provides our empirical evidence organized in three main stylized facts. Section 4 presents the model of firm dynamics with procurement. Section 5 discusses how we parameterize the model. Section 6 describes our benchmark economy. Section 7 provides the main quantitative results and Section 8 presents different robustness exercises. Section 9 concludes.

> 7See Buera, Kaboski and Shin (2015) for a survey of this literature.

> 8Cappelletti and Giuffrida (2021) use data for Italy to show that firms that receive public procurement contracts survive longer, a dimension of the data that we do not explore.

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After concluding, we provide an extensive Appendix with additional details on the data and the model.

# **2 Data and Summary Statistics**

Our empirical work is based on merging three large datasets at the firm level. First, we construct a novel dataset on Spanish public procurement contracts published by the official bulletin of the Spanish Central Government ( _Bolet ́ın Oficial del Estado_ , BOE) over the 2000-2013 period. We have information on the type of good or service provided, the institution awarding the contract, the initial bidding and final price of the contract, the type of procedure used to allocate the contract, and the firm(s) that won the contract. Second, we use more standard firm-level data on balance sheets and income statements of the quasi-universe of Spanish companies between 2000 and 2016, a dataset that is maintained by the Banco de Espa ̃na and taken from the Spanish Commercial Registry. And third, we use credit register data for Spain, which contain detailed information on all outstanding loans over 6,000 euros to non-financial firms granted by all banks operating in Spain (including whether or not a non-personal collateral was posted on a particular loan). Additionally, the credit register data set contains rich information on loan applications. Appendix A provides details about the different data sources and samples that we use.

**Main sample.** We merge the three data sets to build a panel of firms at the annual frequency (which is the frequency of observation of our firm-level data) with detailed information on credit and procurement activity. For our sample we only keep those firms that get at least one procurement project over the sample period.<sup>9</sup> This leaves 12,000 unique firms observed for an average of 12 years. Alternatively, in the Appendix, we also build a sample at a quarterly frequency (that delivers a tighter identification of the effects of procurement on credit growth but cannot be used to examine the effects of procurement on firm sales) and a smaller sample for those projects that have data on the full ranking of bidders.

**Procurement vs. non-procurement firms.** We find that firms participating in procurement are significantly larger and older on average, but there is considerable overlap in the support of the size and age distribution for procurement and non-procurement firms (see Table A.3 in the Appendix). For example, the average number of employees of a procurement firm is around 6 times larger than for the rest of the firms (73.56 vs. 12.75), total sales are 7 times larger (8.9 millions of euro vs. around 1.2 million), and procurement firms are 9 years older (20 vs 11 years). Yet, around 25% of procurement firms have less than 16 employees, have revenues that are lower than 1.1 million euro, and are 12 or fewer years old. We also find that conditional on having at least one procurement project, there is a lot of variation on the importance of these projects as a fraction

> 9Note that because all our empirical work uses firm-level fixed effects, the relevant variation is within-firm variation for those firms that get at least one procurement project in the sample period.

6
of firms’ total revenue. The ratio of procurement value to total revenues is 0.20 on average, with the 25th, 50th, and 75th percentiles being 0.01, 0.03 and 0.10 respectively. Finally, we observe large differences between procurement and non-procurement firms in terms of their composition of credit. In particular, procurement firms seem to rely more on non-collateralized credit (86% vs 71% on average) despite holding higher levels of assets.<sup>10</sup>

# **3 Motivating Empirical Evidence**

We begin by documenting three key facts related to the effects of procurement on firms’ outcomes. First, we show a positive relationship between obtaining a procurement contract and firms’ credit growth, which in the short run is entirely coming from credit for which no tangible collateral is posted. Second, we show that obtaining a procurement contract is related to a persistent increase in firm revenues. Interestingly, this increase in firm revenues happens alongside a short-run decline in sales to the private sector (crowding-out) followed by an increase in private sector sales above the level before the procurement shock (crowding-in). Third, the initial crowding out is particularly stronger for firms that are more likely to be financially constrained.

To study the relationship between participation in procurement and firms’ dynamics, we estimate local projection panel regressions (Jord`a, 2005). In particular, we regress the cumulative difference of variable _x_ , ∆ _h_ log( _xit_ + _h_ ) ≡ log( _xit_ + _h_ ) − log( _xit_ −1) on the regressor PROC _it_ , firm fixed effects _αi_ , sector×year fixed effects _αst_ , and lagged _x_ : where _i_ denotes firm and _h_ = 0 _,_ 1 _,...,H_ denotes the horizon at which the impact of procurement is estimated. The regressor PROC _it_ is a dummy variable that takes value 1 if the firm obtained a procurement contract in year _t_ . The inclusion of firm fixed effects implies that we are comparing the differential within-firm growth of credit across periods with and without procurement. Next, we focus on how procurement affects the evolution of several variables at the firm level.

## **3.1 Fact 1. Credit growth**

We show the results from running the regressions given by equation (1) with our sample at an annual frequency in Figure 1, where we plot the estimated _β_ 1<sup>_h_coefficientsandtheirassociated</sup> confidence intervals. Our main result is that winning a procurement contract is associated with a persistent effect on firms’ credit. On impact ( _h_ = 0), winning a procurement contract is associated with an increase in firms’ total credit of around 5.5 percentage points (see panel (a) of Figure 1).

> 10In Appendix A.5 and A.6, we provide further details about the types of projects and presence of procurement across sectors.

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We find that this effect is persistent, which implies that firms increase their credit beyond the duration of the procurement contract <!-- Start of picture text --> −1 0 1 2 3 4 −1 0 1 2 3 4 −1 0 1 2 3 4<br>years since procurement shock years since procurement shock years since procurement shock<br>(a) total credit (b) non-collateral credit (c) collateral credit<br>.1 .1 .1<br>.08 .08 .08<br>.06 .06 .06<br>.04 .04 .04<br>.02 .02 .02<br>cumulative growth rate cumulative growth rate cumulative growth rate<br>0 0 0<br>−.02 −.02 −.02<br><!-- End of picture text -->

**Notes:** This figure shows the cumulative impact of the estimate of _β_ 2<sup>_h_fromregression(1)fordifferenttimehorizons</sup> _h_ = 0 _,_ 1 _,_ 2 _,_ 3 _,_ 4, as well as its 5% confidence intervals. Panel (a) shows the results for the case of _x_ being firms’ total credit. Panel (b) shows the results for the case of _x_ being firms’ non-collateralized credit. Panel (c) shows the results for the case of _x_ being firms’ collateralized credit. As mentioned above, we have run these regressions with around 12,000 firms that have at least one contract during the sample period. Standard errors clustered at the firm level.

**Figure 1.** Procurement effect on credit

We also find that the effect on impact is entirely driven by non-collateralized credit: the effect on non-collateralized and collateralized credit is around 8 and 0 percentage points, respectively, when _h_ = 0 (see panels (b) and (c) of Figure 1). Finally, we find that, although absent on impact, the effect of procurement on collateralized credit gets bigger over time. For example, the 5 years ( _h_ = 4) cumulative effect is around 6 percentage points. This final result is consistent with the idea that firms use their extra profits earned in procurement to increase their net worth and therefore increase their borrowing capacity in the future.

An alternative explanation for the estimated “persistent” effect of procurement on credit is that obtaining a contract in a given year may increase the probability of obtaining more contracts in the subsequent periods. While it is true that there is persistence in procurement, in Appendix B.1 we show that the persistent effect of procurement on credit in credit is very similar for a subsample of firms that only obtain one contract during our sample period. Finally, a limitation of our procurement data is that it does not contain information about the duration of each contract. One potential concern is that the estimated “persistent” effect of procurement on credit results from long contracts. To have a sense of the duration of contracts in Spain, we use a different dataset, Tenders Electronic Daily (TED), which provides information on the estimated length of contracts.<sup>11</sup> For the years 2018-2019, for example, around 75% of the contracts have a duration of one year or less, 89% have a duration of two years or less, and 93% have a duration of three years or less (see Appendix B.5 for details). These numbers likely represent an upper bound, given that

> 11TED is the online version of the supplement to the Official Journal of the EU dedicated to European public procurement. See Garc ́ıa-Santana and Santamar ́ıa (2022) for details.

8
very large contracts, which tend to last longer, are over-represented in TED. As a reference for a different country, Cox et al. (2021) find that the median contract in the U.S. has a duration of 31 days and 90% of contracts last less than one year.

# **3.2 Fact 2. Sales composition and sales growth**

We next look at the evolution of firms’ total sales and their composition. In particular, we run regression (1) for the case of _x_ = firms’ total sales (see panel (a) of Figure 3) and _x_ = firms’ sales to the private sector (see panel (b) of Figure 3). Several important results emerge from running these regressions. First, as expected, we find that firms’ total sales increase after winning a procurement contract. In particular, we find that firms’ total sales increase by around 8 percentage points.

<!-- Start of picture text --> −1 0 1 2 3 4 −1 0 1 2 3 4<br>years since procurement shock years since procurement shock<br>(a) total sales (b) sales to the private sector<br>.12 .12<br>.08 .08<br>.04 .04<br>0 0<br>−.04 −.04<br>−.08 −.08<br>cumulative growth rate cumulative growth rate<br>−.12 −.12<br>−.16 −.16<br><!-- End of picture text -->

**Notes:** This figure shows the cumulative impact of the estimate of _β_ 2<sup>_h_fromregression(1)fordifferenttimehorizons</sup> _h_ = 0 _,_ 1 _,_ 2 _,_ 3 _,_ 4, as well as its 5% confidence intervals. Panel (a) shows the results for the case of _x_ being firms’ total sales. Panel (b) shows the results for the case of _x_ being firms’ sales to the private sector. Standard errors clustered at the level.

**Figure 2.** Procurement effect on credit

Second, we find that this effect is persistent, which is consistent with the previous result on credit. Third, we find that sales to the private sector fall right after a firm wins a procurement contract, which means that procurement generates a short-run crowding out of sales to the private sector. In the model we will present below, this crowding out will happen because financial constraints limit firms’ production capacity, and hence firms decrease the amount of output sold to the private sector in order to deliver their procurement contracts. Finally, we find that this crowdingout effect disappears and actually gets reversed over time, meaning that procurement crowds in sales to the private sector in the long run. One interpretation of this fact is that the extra revenues of the procurement contract can be used for the financially constrained firms to accumulate wealth and finance larger operations in the future.

9
<!-- Start of picture text --> −.01<br>−.01<br>−.04<br>−.04<br>−.07<br>−.07<br>−.1<br>−.1<br>−.13<br>−.13<br>−.16 −.16<br>−.19 −.19<br>−.22 −.22<br>−.25 −.25<br>< pct 50 > pct 50, < pct 75 > pct 75, < pct 95 > pct 95 < pct 50 > pct 50, < pct 75 > pct 75, < pct 95 > pct 95<br>(a) distribution of fixed assets (b) distribution of leverage<br>% effect on impact (private sales) % effect on impact (private sales)<br><!-- End of picture text -->

**Notes:** This figure shows the effect on impact, i.e., _h_ = 0 (as well as its 5% confidence intervals), of public procurement on sales to the private sector for different percentiles of the distribution of assets (panel a), and leverage (panel b). Standard errors clustered at the firm level.

**Figure 3.** Heterogeneous effects on sales to the private sector

# **3.3 Fact 3. Heterogeneous effects of crowding-out to private sales**

The initial crowding-out of sales to the private sector may arise due to firms’ lack of borrowing capacity to serve the private and public sectors at the same time, which the extra credit obtained with the procurement contract only partially offsets. However, it could also arise due to capacity constraints or decreasing returns to scale at the firm level. If the effect is at least partly explained by financial frictions, we should find that firms more likely to be financially constrained exhibit a larger crowding out. Indeed, our simple static production problem in Section 4.6 shows this to be the case (see Appendix D.4). In the data, it is hard to identify which firms are more financially constrained. However, two conventional proxies for how financially constrained a firm is, are size (e.g., measured by assets) and leverage. We test the hypothesis that the crowding-out effect of private-sector sales is greater for more financially constrained firms by interacting the effect of procurement on dummy variables for several percentiles of the leverage and assets distribution. We present these results in Figure 3. In terms of assets, we find a negative monotonic relationship between firms’ fixed assets and the extent of the crowding out effect to private sales. In terms of leverage, we find that the crowding out effect is particularly strong for firms whose leverage is above the 95th percentile.

# **3.4 Discussion and additional evidence**

There are two possible interpretations of the observed credit growth upon procurement. The first one is that the arrival of a procurement project represents a _credit demand shock_ at the firm level, without financial frictions playing any relevant role. This will be the case if firms need to 10
borrow to increase production to satisfy the procurement demand. Such an interpretation may also be consistent with the initial crowding-out of sales to the private sector (if firms faced shortrun capacity constraints or decreasing returns to scale in production) and with the medium-run crowding-in of sales to the private sector (if firms invest in production capacity to serve the extra demand for the public sector that can be later used for the private sector operations). The second interpretation is that procurement represents a _credit supply shock_ at the firm level. This will be the case if procurement contracts can be pledged for extra borrowing and a sizeable fraction of firms doing procurement are credit-constrained. This would explain why the increase of credit at impact does not require collateral to be posted. The existence of credit constrains for firms participating in procurement is consistent with the short-run crowding-out of sales to the private sector (as financially constrained firms do not have the financial capacity to completely serve both demands) and with the crowding-out being stronger for firms more likely to be financially constrained. The medium-run crowding-in of sales to the private sector is also consistent with binding credit constraints (procurement gives firms extra profits, which can be saved and used to expand production capacity in the future).

While both interpretations are plausible, our results point to the _credit supply shock_ interpretation playing a relevant role because (i) the short-run increase in credit is limited to non-collateral credit, (ii) we provide additional evidence on the acceptance of loan applications below, and (iii) the short-run crowding out of private sales being larger for firms more likely to be constrained indicates that financial frictions affect procurement firms.<sup>12</sup> However, to gauge the relative importance of the credit _demand_ and _supply_ interpretations, we need a formal model structure as that presented in Section 4.

Appendix B provides further evidence on the relationship between firms’ participation in procurement and credit growth. We summarize the evidence here.

**Procurement and credit using quarterly frequency.** To provide tighter identification of the effect of procurement on credit, in Appendix B.2 we exploit higher frequency credit data and estimate the procurement effect on credit using quarterly data. Importantly, these specifications allow us to control for _firm_ × _year_ fixed effects, which absorb all firm characteristics, observable or unobservable, varying at the yearly frequency. First, we find that winning a procurement contract is associated with an annualized increase in credit of around 5.5 pct, which is similar in terms of magnitude to the effects on impact, i.e., _h_ = 0, estimated above in Section 3.1. And second, we also find that the effect is entirely driven by non-collateral credit.

**Winners vs. the rest.** In Appendix B.3, we use the sub-sample of procurement projects where we have information on all bidders as well as the final ranking (see Appendix A.2 for details on this

> 12Also, indirect inference motivated by our structural model, as seen in Section 5, provides evidence for procurement earnings relaxing firms’ credit constraints.

11
information). Doing so allows us to run regressions where we can identify the association between a firm’s ranking in a given auction and its ensuing credit growth. First, we find that winning firms experience significantly larger growth in credit relative to losing firms within the same auction. Second, we find that, again, all the effect is explained by non-collateral credit. Third, we find that the ranking itself does not seem to matter in explaining the evolution of credit. In particular, when excluding winners, we find no differential effect on credit growth between the firms that were ranked second vs. firms that were ranked third and fourth within the same auction. And fourth, we show all the previous results are not driven by the presence of pre-trends in the evolution of credit for winners vs. the rest.

**Loan applications.** Finally, in Appendix B.4, we exploit data on loan applications to see whether the acceptance probability of a credit application increases when firms get a procurement contract. In particular, we can see whether a firm has applied to a given bank and whether the loan application has been accepted or rejected throughout our sample period. We use this information to help identify an increase in firms’ borrowing capacity. To do so, we run regressions at the firmbank level and relate the probability of firms obtaining a loan to whether they have received a procurement contract. We find that the probability of receiving a bank loan conditional on having applied for it increases by approximately 2 percentage points in the quarter that a firm wins a procurement project, which is consistent with the idea that procurement represents a credit supply shock for the

# **4 The Model**

We set up a model of privately held heterogeneous firms. We build on standard models of firm dynamics with collateral constraints —as Midrigan and Xu (2014), Moll (2014), or Buera and Moll (2015)— and extend this setting to allow for (a) a public sector demanding goods from private firms, (b) earnings-based borrowing constraints with different degrees of pleadgeability for procurement and private sector sales, (c) downward-sloping demands in both the private and public sectors, and (d) a choice to compete for procurement projects. In the model, financial frictions distort the economy through different channels. First, for a given selection of firms into procurement, financial frictions lead to lower aggregate capital, misallocation of capital across firms, and misallocation of capital within firms across sectors. And second, financial frictions also distort the selection of firms into procurement, giving more value to firm net worth at the expense of firm productivity.

## **4.1 Technology**

Time is discrete and we omit the subscript _t_ unless it is strictly needed. The economy is populated by a continuum of size 1 of heterogeneous infinitely-lived households indexed by _i_ . Each household is also an entrepreneur running a firm that produces a differentiated intermediate good _yi_ . There 12
are two final goods in the economy: the “private sector” good, _Yp_ , used by households to consume, invest in productive capital, or prepare applications for procurement projects, and the “public sector” good _Yg_ , purchased by the government to produce (useless) public consumption.

**Final goods.** The two final goods are assembled by two final good producers combining the differentiated intermediate goods _yi_ through the following CES aggregators:

where _Ig_ is the subset of goods purchased by the public sector and _mg_ is the measure of this set. Note that _Yg_ is adjusted by _mg_ to prevent a love-for-variety effect.<sup>13</sup> We also note that _Ig_ (and the implied _mg_ ) is a policy variable and the identity of firms in this set is discussed below. The final goods producers are perfectly competitive and choose the optimal demand of intermediate goods _yip_ and _yig_ , respectively, to maximize profits taking intermediate good prices _pip_ and _pig_ , final good prices _Pp_ and _Pg_ , and the set _Ig_ as given. We assume that firms compete independently in each sector and face the following downward-sloping demands, where for convenience we define _Bp_ ≡ _PpYp_<sup>1/</sup><sup>_σp_</sup> and _Bg_ ≡ _m_<sup>−</sup> _g_<sup>1/</sup><sup>_σg_</sup> _PgYg_<sup>1/</sup><sup>_σg_</sup> . The prices _pip_ and _pig_ faced by the private and public sector producers in the purchase of the same intermediate good _i_ may differ because intermediate good _i_ producer has monopoly power over its variety and may be selling different quantities to each market. _Yg_ is the demand of the public good from the government and is a policy variable in the model, while _Yp_ is the demand of the private good from the households and it is determined in equilibrium. The aggregate prices _Pp_ and _Pg_ of the private and public goods are given by the usual aggregators: We will use the final private good as the numeraire, so we set _Pp_ = 1 in what follows.

**Intermediate inputs.** The intermediate inputs are produced by heterogeneous firms. At any period in time, these firms are characterized by their idiosyncratic stochastic productivity _si_ , their capital stock _ki_ (which depreciates at rate _δ_ ), their debt level _li_ (when _li_ > 0 the firm is a net borrower), and whether they currently hold a procurement project _di_ = 1 or not _di_ = 0. Output _yi_ is given by a simple CRS production function, _yi_ = _f_ ( _si,ki_ ) = _siki_ , that depends on capital _ki_ and managerial productivity _si_ .<sup>14</sup> The firm-specific _si_ follows a first order Markov process, specified in

> 13 Governments purchase only a fraction of goods and services provided by the private economy mainly because their needs are different than the needs of private households and firms. By removing ‘love-for-variety’ we want to eliminate this trivial effect from the analysis of the effects of the number of contracts offered.

> 14In Section 8.2 we explore a version of our model with decreasing returns to scale in production.

13
more detail below. If a procurement project is active ( _di_ = 1) a fraction of output _ui_ , chosen by the firm, is sold to the private sector and a fraction 1 − _ui_ is sold to the public sector, otherwise all output is sold to the private sector. Our simple production function implies that _ui_ is also the fraction of capital used for the production of the private sector variety, that is, _kip_ = _uiki_ .

# **4.2 Participation in public procurement**

The government has control over the subset _Ig_ of goods purchased by the public sector, and a choice of the subset _Ig_ naturally implies its measure _mg_ . In order to introduce structure in this choice, we consider that the government follows a simple stochastic rule for the allocation of procurement contracts based on the quality of the proposals. In particular, we assume that firms who wish to sell to the government next period ( _dit_ +1 = 1) must invest an amount of private sector good _bit_ > 0 today. This quantity may reflect the costs of learning how the process works, the actual costs of preparing a proposal, or the costs of establishing connections with government officials. There is always uncertainty in the outcome of the application, which reflects the fact that “equally capable” firms usually compete in the same auction with only one winner.<sup>15</sup> The probability of being able to sell to the government next period depends on the amount invested, with _η_ 0 > 0 and 1 > _η_ 1 > 0 to ensure positive and diminishing returns. Also notice that lim _b_ →0 _∂g∂b_ <u>(</u> _b_ <u>)</u> → ∞, so there will always be an interior solution in the optimal choice of _bit_ . This probability function captures in reduced form the competition for procurement projects. The slope parameter _η_ 1 controls the extent of decreasing returns to investment _bit_ , and it hence regulates firm selection into procurement. With higher _η_ 1, larger investments generate larger probabilities of wining a procurement project compared to smaller investments, thereby making firms that value a procurement project more (and hence invest a larger amount _bit_ ) more likely to win the contract. The level parameter _η_ 0 is an equilibrium object that ensures that the fraction of firms obtaining a procurement project equals the measure _mg_ of goods purchased by the public sector. Hence, the probability of procurement depends on firms’ own actions through _bit_ as well as on the actions of all other firms through the equilibrium object _η_ 0.<sup>16</sup> The winners of the competition for procurement form the set _Ig_ in that period.

> 15In practice, each government agency has its own criterion to decide the final ranking of firms, which may be based on a number of attributes as price, quality, and technical requirements. Therefore, firms always face uncertainty about how the public entity awarding the contract will perceive them and their competitors fulfilling these attributes.

> 16Alternatively, we could have followed a more structural approach in modelling the competition for public contracts. For instance, in a different setting, Michelacci and Pijoan-Mas (2012) model competition for jobs with a job finding probability depending on individual human capital relative to the average human capital of the economy. Yet, our formulation is flexible and does not require taking a stand on the complex procurement competition process.

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# **4.3 Entry and exit**

A fraction 1 − _θ_ of households die every period and are replaced by the same number of new households running new firms. To avoid changing the composition of the goods produced in the economy, the entrant households produce the varieties left vacant by the exiting households. Dying households leave accidental bequests that for simplicity are taken by the government. Entrant households start with a joint distribution of financial wealth and productivity Γ0 and with no procurement project. The wealth of the entrants is provided by the government. Alternatively, we could have assumed that all accidental bequests go to the newborns, but we want to break this link in order to have the flexibility to choose the amount of financial wealth for entrants.

# **4.4 Preferences and constraints**

Firms are owned by entrepreneurs. Entrepreneurs have CRRA preferences over consumption with curvature _μ_ , and their objective is to maximize the discounted sum of utilities.<sup>17</sup> They obtain income only from their firm so their budget constraint is given by: where tax _it_ = _τ_ [ _piptyipt_ + _pigtyigt_ −( _rt_ + _δ_ ) _kit_ ] denotes the proportional taxes on profits paid by entrepreneur _i_ at time _t_ . The tax function is purposely simple because we focus on expenditure neutral counterfactuals.<sup>18</sup> As it is standard in the literature, we only allow for one-period debt contracts _lt_ that pay a risk-free interest rate _rt_ . The amount of debt is limited by the repayment capacity of the firm through a combination of earnings-based and asset-based collateral constraint. In particular, the amount of debt of a firm coming into _t_ + 1 is limited by: If _φa_ = 0, _φp_ = 0, and _φg_ = 0 no external finance is available and all production needs to be selffinanced. With _φa_ > 0 the firm can leverage up against fixed capital. With _φp_ > 0 and _φg_ > 0 firms can borrow against the earnings generated in the private and the public sector respectively.<sup>19</sup>

> 17Modeling firms as being run by entrepreneurs with curvature in preferences over consumption could also be justified by firms’ dividend-smoothing motives, as empirically documented, e.g. Leary and Michaely (2011).

> 18Note that this simple tax function allows for tax deductibility of depreciation _δkit_ and of the (interest) opportunity cost of capital _rtkit_ . Since _lit_ ≤ _kit_ whenever the firm’s net worth is non-negative, we are implicitly allowing the firm to deduct more than just the interest payments on debt _rtlit_ .

> 19An alternative and more structural borrowing constraint would limit repayment (1 + _rt_ +1) _lit_ +1 explicitly by a fraction of undepreciated capital (1 − _δ_ ) _kit_ +1 plus earnings,

> (1 + _rt_ +1) _lit_ +1 ≤ _φ_  ̃ _a_ (1 − _δ_ ) _kit_ +1 + _φ_  ̃ _p pipt_ +1 _yipt_ +1 + _φ_  ̃ _g pigt_ +1 _yigt_ +1

> andIn steady _φg_ ≡ state1 _<u>φ</u>_  ̃+ _<u>gr</u>_<sup>.</sup> withIn counterfactualconstant _r_ thisexercises,specificationincreaseswould (decreases)be equal to (7)in thewithequilibriumthe redefinitions: _r_ would _φa_ tighten≡<sup><u>(1−</u></sup> 1<sup>_δ_</sup> +<sup><u>)</u></sup> _r_<sup> ̃</sup> _<u>φ</u>_ (loosen) _<u>a</u>_ , _φp_ ≡ 1 _<u>φ</u>_  ̃the+ _<u>pr</u>_<sup>,</sup> borrowing constraints. Our formulation ignores this second order effect.

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**Figure 4.** Timing in the Model

# **4.5 Timing and state space**

We illustrate the timing in the model in Figure 4. Regarding the non-procurement part of the model, we follow the timing convention commonly used in the firm dynamics literature. First, we assume that resources devoted to consumption are spent at the beginning of each period _t_ . Second, we assume that production in _t_ + 1 is carried out using capital installed at the end of period _t_ . Third, we assume that the household survival shock and the firms’ productivity in _t_ + 1 are revealed (in this order) before firms decide how much capital to install for next period, _kit_ +1, and how much debt to issue for next period, _lit_ +1. Regarding the variables related to procurement, we follow a similar logic. The amount of resources devoted to increase the probability of being active in procurement in _t_ + 1, i.e., _bit_ , is spent at the beginning of each period _t_ . Whether or not the firm is successful and becomes active in procurement in _t_ + 1, i.e, _dit_ +1 = 1, is revealed at the same time as productivity in _t_ + 1 and right after the survival shock. This means that procurement applications of dying households are ignored by the government and hence dying households are not awarded a procurement project that cannot be delivered.

**Alternative specification.** These assumptions on timing simplify the state-space dimensionality of the problem. In particular, let _ait_ +1 ≡ _kit_ +1 − _lit_ +1 be the firm’s net worth to be carried to next period in units of private good today. Then we can redefine the budget constraint as

The collateral constraint becomes where the parameters in the borrowing constraint are re-defined as: Hence, the production decisions (capital and sales composition) are intratemporal, while the accumulation of net worth and the investment in procurement are intertemporal. This allows to split the firm’s problem in two: a _static production_ problem and a _dynamic consumption-saving_ problem. Next, we describe them in turn.

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# **4.6 The static production problem**

The intratemporal production problem is characterized by firm productivity _s_ , firm net worth _a_ , and the availability of a procurement project _d_ . For simplicity we drop the firm subindex _i_ . Firms with _d_ = 0 only have to choose their optimal size _k_ subject to the borrowing constraint, while firms with _d_ = 1 also decide on the fraction of output _u_ ∈[0 _,_ 1] sold to the private sector. We can write the formal maximization problem for the firm of type ( _s,a,d_ = 1) as: while for the firm of type ( _s,a,d_ = 0) all the terms _pgyg_ trivially disappear and _u_ becomes equal to 1. Let _λ_ be the multiplier of the intratemporal borrowing constraint and let’s consider the general case with _d_ = 1. The optimal choices are described by the following FOC: These optimality conditions show how financial frictions distort the two decisions faced by firms: production composition and firm size. Equation (11) characterizes the composition of sales. Let _kp_ = _uk_ and _kg_ = (1 − _u_ ) _k_ . A more intuitive way of writing equation (11) is as follows: where MRPK _p_ ≡ _∂ppyp_ / _∂kp_ and MRPK _g_ ≡ _∂pgyg_ / _∂kg_ are the marginal revenue products of each firm in each sector, see Appendix D for details. With _λ_ = 0, the optimal choice requires the equalization of the marginal revenues obtained from each sector. Because of the concave revenue functions in both sectors, there is always an interior solution to this problem. With binding financial constraints ( _λ_ > 0), production is shifted towards the sector whose output can be better collateralized. For instance, if procurement contracts offer better collateral value than sales to the private sector ( _φg_ > _φp_ ) the optimal choice requires lower marginal revenues from public procurement relative to the marginal revenues from the private sector, which happens when production is shifted towards the public sector and away from the private sector. This generates misallocation of capital _within firms_ and sectoral misallocation in the aggregate.

Equation (12) determines optimal firm size, which can be rewritten as 17
**Notes:** This figure shows the solution to the firm’s problem. Panel (a) shows the size of the firm represented by the amount of capital _k_ ( _s, a, d_ ); Panel (b) shows the multiplier of the financial constraint _λ_ ( _s, a, d_ ); Panel (c) shows the profits _π_ ( _s, a, d_ ). All of them are plotted against firm’s productivity _s_ , for two different levels of net worth, and for the cases _d_ = 0 and _d_ = 1.

**Figure 5.** Solution of the static profit maximization problem

where MRPK ≡ _∂_ ( _ppyp_ + _pgyg_ )/ _∂k_ is the marginal revenue product of each firm. With _λ_ = 0 the optimal choice requires to equalize the marginal revenue product of capital to its cost, which is just _r_ + _δ_ . With binding financial constraints ( _λ_ > 0), the effective cost of capital is 1<sup>_<u>r</u>_</sup> +<sup><u>+</u></sup> _λφ_<sup>_<u>δ</u>_</sup><sup><u>+</u></sup><sup>_<u>λ</u>_</sup> _p_<sup>forsalesto</sup> the private sector and 1<sup>_<u>r</u>_</sup> +<sup><u>+</u></sup> _λφ_<sup>_<u>δ</u>_</sup><sup><u>+</u></sup><sup>_<u>λ</u>_</sup> _g_<sup>for sales to the public sector.The multiplier of the financial constraint</sup> _λ_ has two opposite effects on the cost of capital: on the one hand it increases the cost of capital as in standard asset-based financial constraints, but on the other hand, it decreases the cost of capital because a fraction of the generated output can also be collateralized. We will restrict _φp_ and _φg_ as indicated in Assumption 1 below to ensure that the earnings-based constraints cannot self-finance the optimal capital of the unconstrained problem, that is, to ensure that the financial constraints are binding for at least the entrepreneurs with zero net worth. Otherwise, all firms would be unconstrained, see Lemma 2 and Proposition 2 in Appendix D.

**Assumption 1** _The model parameters satisfy the following boundary constraints: φp_ <<sup>_σ_</sup> _σ_<sup>_<u>p</u>_−</sup> _p_<sup>1(</sup><sup>_r_+</sup><sup>_δ_)−1</sup> _and φg_ <<sup>_σ_</sup> _σ_<sup>_<u>g</u>_−</sup> _g_<sup>1(</sup><sup>_r_+</sup><sup>_δ_)−1</sup><sup>_,_</sup>

Because _σp,σg_ > 1, Assumption 1 imposes that the values of _φp_ and _φg_ are also below ( _r_ + _δ_ )<sup>−1</sup> . This implies that the effective costs of capital for the private and public sector, 1<sup>_<u>r</u>_</sup> +<sup><u>+</u></sup> _λφ_<sup>_<u>δ</u>_</sup><sup><u>+</u></sup><sup>_<u>λ</u>_</sup> _p_<sup>and</sup> 1<sup>_<u>r</u>_</sup> +<sup><u>+</u></sup> _λφ_<sup>_<u>δ</u>_</sup><sup><u>+</u></sup><sup>_<u>λ</u>_</sup> _p_<sup>,</sup> are monotonically increasing in _λ_ , reflecting the fact that financially constrained firms operate with less capital, see Lemma 1 and Proposition 1 in Appendix D. This has two consequences. First, to the extent that a significant fraction of firms are financially constrained, aggregate capital will be inefficiently low. Second, because _λ_ depends on the firm state variables ( _s,a,d_ ), there will be 18
heterogeneity in the cost of capital across firms, which will generate misallocation of capital _across firms_ and lower aggregate TFP in both the private sector and the procurement sector.

**Static policy functions.** In Appendix D we characterize analytically the solution to for both non-procurement ( _d_ = 0) and procurement firms ( _d_ = 1) whenever _σg_ = _σp_ . In Figure 5, we illustrate the numerical solution for both cases with the parameterization discussed in Section 5. Panels (a) and (d) show the optimal choices _k_ ( _s,a,d_ ) and _u_ ( _s,a,d_ ), respectively. Panels (b) and (c) show the associated shadow value of the financial constraint _λ_ ( _s,a,d_ ) and a profit function _π_ ( _s,a,d_ ), respectively.

First, as is common in standard models of firm dynamics with collateral constraints, constrained firms with no procurement see their capital and profits increase with net worth (while the shadow value of the borrowing constraints declines) until the point in which the financial constraints stop binding and net worth plays no role. Second, different from models with only asset-based collateral constraints, financially constrained firms without procurement increase capital and profits when productivity increases. This happens through the earnings-based constraint, which allows more productive firms to generate more revenues at the same level of net worth and hence expand production. Note also that more productive firms are more financially constrained at any level of net worth (their shadow value of the borrowing constraint is larger) because the expansion of borrowing possibilities with _s_ is lower than the increase in the optimal size. Third, looking at firms with procurement, the fraction of output sold by constrained firms to the private sector is decreasing in productivity _s_ and increasing in net worth _a_ , which simply says that more financially constrained firms, conditional on participating, have a higher fraction of their capital allocated to the production of goods sold to the government. This last result is true under _φg_ > _φp_ and it would be the opposite if _φg_ < _φp_ . Finally, note also that capital, profits, and the shadow value of the borrowing constraint for firms with procurement evolve with _s_ and _a_ as in the case without procurement.

# **4.7 A procurement shock**

We can also analyze the static effect of a procurement shock by comparing the solutions of the _d_ = 1 and _d_ = 0 cases at any value of the state variables _s_ and _a_ , details are in Appendix D.4. For unconstrained firms, a procurement shock leaves operations in the private sector unchanged, _yp_ ( _s,a,_ 1) = _yp_ ( _s,a,_ 0), increases firm size to serve the public demand, _k_ ( _s,a,_ 1)− _k_ ( _s,a,_ 0) > 0, and increases profits, _π_ ( _s,a,_ 1) − _π_ ( _s,a,_ 0) > 0. This is due to the constant returns to scale production assumption and the absence of adjustment costs. The value of procurement _π_ ( _s,a,_ 1) − _π_ ( _s,a,_ 0) is independent from _a_ and increases with _s_ as more productive firms can deliver larger projects.

For constrained firms things are more complex. A procurement shock tightens the financial constraint whenever _φg_ ≤ _φp_ . With _φg_ = _φp_ this is because the firm with _d_ = 1 has two demands 19
to serve, which are equally pledgeable, and has the same net worth to finance capital in the two different markets. As a result the firm scales down the operations in the private sector to free up collateral for the production in the public sector, which generates a negative within-firm private sector spillover of the procurement contract, that is, _yp_ ( _s,a,_ 1) < _yp_ ( _s,a,_ 0). When _φg_ < _φp_ the financial situation is aggravated because the public sector demand can be self-financed to a lesser extent than the private sector one and the negative private sector spillover is larger. Instead, when _φg_ > _φp_ public procurement may alleviate the firm financial situation because the public sector demand can be self-financed to a larger extent. However, this will only be relevant for firms with little or no wealth, which will be less constrained when obtaining a procurement project than they were originally and will use the extra financing capacity coming from the public sector to scale up operations in the private sector, generating a positive spillover. This is precisely stated in Proposition 13 in Appendix D.4. In our numerical exercises with _φg_ > _φp_ , with a realistic calibration, and endogenously accumulated net worth distributions, however, a procurement shock always increases firm size, makes the firm more constrained, and always generates a _negative_ spillover on the private sector sales for constrained firms that obtain procurement. Finally, a procurement shock also increases profits among constrained firms. For the empirically relevant case _φg_ > _φp_ , this is more so for the more productive and the wealthier firms, because these two variables determine the capacity to deliver large projects. The only exception is for the firms with little or no wealth discussed above, in which case the increase of profits with procurement actually falls with net worth, see Proposition 15 in Appendix D.4.

# **4.8 The dynamic problem**

The _dynamic consumption-saving_ problem can be written in recursive form: The first constraint says that the expected firm’s value for tomorrow is an average of the firm’s value under procurement, i.e., _d_<sup>′</sup> = 1, and no procurement, i.e., _d_<sup>′</sup> = 0, weighted by the endogenous probability of procurement _g_ ( _b_ ). This probability is why the expectations operator E depends on _b_ in addition to _s_ . The FOC for the choices of _a_<sup>′</sup> and _b_ are: 20
**Notes:** The first and second panels show the net saving rules _ga_ ( _s, a, d_ )) for firms of different levels of productivity and net worth, both for non-procurement and procurement firms respectively. The third and fourth panels show the endogenous probability of obtaining procurement contracts evaluated at the optimal rules _gb_ ( _s, a, d_ ) for firms with different levels of productivity and net worth, both for non-procurement and procurement firms respectively.

**Figure 6.** Decision rules

The first equation is the standard Euler equation that emerges in models of heterogeneous firms with financial constraints. In future states where the firm is not constrained in the static production problem _∂π_ ( _s_<sup>′</sup> _,a_<sup>′</sup> _,d_<sup>′</sup> )/ _∂a_<sup>′</sup> = 0 and the return to accumulate wealth is just _r_ . Instead, in states where the firm is financially constrained in the static production problem there is an extra return _∂π_ ( _s_<sup>′</sup> _,a_<sup>′</sup> _,d_<sup>′</sup> )/ _∂a_<sup>′</sup> = _φaλ_ ( _s_<sup>′</sup> _,a_<sup>′</sup> _,d_<sup>′</sup> ) > 0 above _r_ to accumulating net worth, which is given by the increase in (after tax) profits due to relaxing the firm’s collateral constraint, see Appendix D. The second equation determines the optimal spending in _b_ : the entrepreneur will equalize its marginal utility of consumption to the marginal return of _b_ , which is given by the expected increase of the firm’s value coming from the possibility of selling to the government. Because of the properties of _g_ ( _b_ ) and because _Es_ ′∣ _s_ [ _V_ ( _s_<sup>′</sup> _,a_<sup>′</sup> _,_ 1) − _V_ ( _s_<sup>′</sup> _,a_<sup>′</sup> _,_ 0)] > 0) the right hand side declines with _b_ .<sup>20</sup>

**Decision rules.** Figure 6 illustrates the net saving decision _a_<sup>′</sup> − _a_ of firms without and with procurement (first and second panel respectively). At low levels of net worth there is a hump-shaped relationship between net savings and net worth that is driven by the tradeoff between smoothing consumption vs. relaxing future borrowing constraints, a feature present in similar models like Midrigan and Xu (2014). At larger levels of wealth, the saving behavior follows the logic in Aiyagari (1994): net savings decrease monotonically with net worth and there is a target level of wealth that is larger for larger productivity _s_ . This figure also shows large differences between procurement and non-procurement firms in terms of saving decisions. In particular, procurement firms save more conditional on their current net worth _a_ and productivity shock _s_ . This difference is driven by the fact that profits are higher for firms that are active in procurement, which relaxes their budget constraint and hence allow them to save more without sacrificing too much consumption.

Figure 6 also shows the function _g_ ( _b_ ) evaluated at the actual choice of _b_ for firms with different levels of net worth and productivity, both for non-procurement (third panel) and procurement

> 20Proposition 15 in Appendix D shows that _π_ ( _s, a,_ 1)− _π_ ( _s, a,_ 0) > 0, and _V_ ( _s, a,_ 1)− _V_ ( _s, a,_ 0) inherits this property as _d_ plays no other role than increasing profits _π_ in the value function.

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firms (fourth panel). The first thing to notice is that high-net worth firms invest more resources in increasing their probability of being able to sell to the government. This emerges as a result of an interesting trade-off: in the dynamic problem there are two competing options for saving and increasing future wealth. On the one hand, households can accumulate wealth _a_<sup>′</sup> , which also relaxes the asset-based constraint and increases profits next period (right hand side of Equation (14)). On the other hand, they can alternatively invest in applications for procurement projects that will increase expected future earnings, and potentially also relax the earnings-based constraint if _φg_ > _φb_ (right hand side of (15)). Appendix D shows that<sup>_∂_2</sup><sup>_π_</sup> _∂a_<sup><u>(</u></sup><sup>_s,_2</sup><sup>_a,d_</sup><sup><u>)</u></sup> < 0, which means that the return of accumulating net worth is lower for firms with more net worth (see Corollaries 3, 6, and 7). The profit premium of a procurement project _π_ ( _s,a,_ 1)− _π_ ( _s,a,_ 0) increases with net worth for constrained firms, see Proposition 15 in Appendix D.4, and so does _V_ ( _s,a,_ 1) − _V_ ( _s,a,_ 0), which means that the return of investment in procurement is larger for firms with more net worth. This higher profits premium for higher _a_ happens because selling to the government does not relax the borrowing constraints completely, which means that firms still rely on their own assets for determining the size of their procurement contracts. This reflects a “size effect”: the bigger the procurement projects the firm expects to be able to deliver, the higher the expected profits that participating in procurement generates. Therefore, we obtain the result that the investment in procurement projects increases with firm net worth.

The second thing to notice is that there are almost no differences in _g_ between procurement and non-procurement firms for given _s_ ad _a_ . The reason is that, conditional on _b_ , the probability of obtaining contracts tomorrow is independent from whether the firm is active in procurement today. Procurement firms spend a bit more on _b_ though for low levels of _a_ , which simply reflects the fact that these have more available resources at hand.

# **4.9 Steady state equilibrium**

Let **X** ≡ _S_ × _A_ × {0 _,_ 1} be the state space of the household problem, **X** 1 ≡ _S_ × _A_ × {1} the subset of the state space for firms with a procurement project, X a _σ_ -algebra generated by **X** , and Γ a probability measure over X . Given government policy parameters _Yg_ and _mg_ and a distribution of entrants Γ0, we define the steady state equilibrium of the model as (i) firms’ policy functions, (ii) the probability measure Γ, (iii) total amount of final private good _Yp_ , (iv) interest rate _r_ , (v) tax rate _τ_ , (vi) relative price of the final public good _Pg_ , and (vii) the procurement probability shifter _η_ 0, so that: a) Entrepreneurs solve their optimization problem b) The probability measure Γ is stationary 22
c) The market for the private good clears: d) The market for the public good clears: e) The probability of obtaining procurement projects is consistent with the measure of goods bought by the public sector: f) The budget constraint of the government holds: g) By Walras law, the credit market clears: Several comments are in order. First, the parameter _η_ 0 driving the average probability of a procurement project is an equilibrium object that ensures meeting equilibrium condition (e). It summarizes in reduced form the competition for projects. Second, the government can accumulate financial wealth _D_ , which serves as an aggregate counterpart for the loans of entrepreneurs such that loans do not need to be in zero net supply in condition (g). Indeed, _D_ will be calibrated to match an interest rate of _r_ = 5% given the total amount of debt relative to capital held by firms in the data. Third, condition (f) establishes that the government budget constraint in steady state is such that procurement is financed by taxes, plus interest revenues from the stationary amount of government wealth _D_ , plus accidental bequests left by dying entrepreneurs, minus the initial net worth provided by the government to newly born entrepreneurs (which is dictated by the exogenously fixed distribution of entrants Γ0). Finally, we note that the aggregate objects determined in general equilibrium that are relevant for the optimization problem of households are _Yp_ , _r_ , _τ_ , _Pg_ , and _η_ 0.

# **5 Calibration**

The model period is one year. We classify the model parameters into four different blocks. The first block contains parameters related to preferences, technology, and productivity that we set to predetermined values. We calibrate the parameters in the other three blocks such that in equilibrium 23
the model matches several moments measured in the Spanish economy. Our model matches well all the targeted moments. Panel A in Table 1 shows the definition of the parameters as well as their inferred values. Panel B shows the description of moments and their value in the data and in the model. In the remaining of this section we discuss our calibration choices and identification.

# **5.1 Block #1: preferences and technology**

We set the relative risk aversion coefficient _μ_ equal to 2, the CES elasticities _σp_ and _σg_ both equal to 3, the discount factor _β_ equal to 0.94, and the annual depreciation rate _δ_ equal to 0.10, which are all within the range of standard values in the literature. Finally, in this block we also include the parameters governing firms’ idiosyncratic productivity. We assume that the log of a firm’s productivity process _s_ evolves over time according to an AR(1) process with Gaussian shocks and unconditional mean _s_ ̄ ≡ E[log( _s_ )]. We set the autocorrelation coefficient _ρs_ equal to 0.80 and the standard deviation of the innovations _σs_ equal to 0.30, as estimated by Ruiz-Garc ́ıa (2020) using the same dataset of firms. We discretize the process following the Rouwenhorst method, allowing for _Ns_ = 5 different states. Our model matches quite well the moments that are usually used in the literature to pin down these two parameters. In our sample the one-year autocorrelation of firms’ log sales is 0.89 (which compares to 0.82 implied by our model) and the standard deviation of firms’ sales growth is 0.57 (which compares to 0.49 implied by our model).

# **5.2 Block #2: financial constraints**

Our model contains three parameters governing firms’ financial constraints: _φa_ , _φp_ , and _φg_ . We choose a value of _φa_ so that the model matches the credit-to-capital ratio observed in our microlevel data, 0.55. Regarding parameterizing _φp_ and _φg_ , we proceed as follows. Given the credit constraint in equation (7), and after dividing by _k_ and taking first differences, changes in firms’ leverage for constrained firms are given by: where _lit_ / _kit_ is the firms’ leverage, i.e., total credit divided by fixed assets; _pityit_ / _kit_ is the firms’ total average product of capital, measured as total value added (minus wages) divided by total fixed assets; _pigtyigt_ / _kit_ is the firms’ value added (minus wages) coming from selling to the government divided by the firm’s total stock of capital. We can therefore recover _φg_ and _φp_ using indirect inference by setting the coefficients _β_ 1 and _β_ 2 from an OLS regression of equation (16) to be equal in the data and the model.<sup>21</sup> Table 2 presents the results from running the empirical counterpart of

> 21The construction of “output”, i.e., _pityit_ in the data requires some explanation. Following the recent literature on earnings-based constraints (e.g., Drechsel (2023)), we assume that the flow variable that firms can collateralize is EBITDA: sales net of overhead and labor costs, without subtracting investment, interest payments or taxes. Because

24
<u>Panel B: Moments</u> Panel A: <u>parameters</u>

|Block 1||(1)<br>Value||||
|---|---|---|---|---|---|
|_μ_|CRRA coefcient|2.00||||
|_σp_|CES private sector|3.00||||
|_σp_|CES government|3.00|predetermined|||
|_β_|Discount factor|0.94||||
|_δ_|Depreciation rate|0.10||||
|_ρs_|AR(1) correlation|0.80||||
|_σs_|AR(1) variance|0.30||||
|Block 2||||Data|Model|
|_φa_|borrowing const. (_a_)|2.81|Credit/K|0.55|0.55|
|_φp_|borrowing const. (_ppyp_)<br>|0.27|reg. coefcient (_φp_)<br>|0.30|0.30|
|_φg_|borrowing const. (_pgyg_)|0.41|reg. coefcient (_φg_)|0.22|0.22|
|Block 3||||||
|_η_0|probability function (level)|0.78|Consistency of _g_(_b_) with _mg_|–||
|_η_1|probability function (slope)|0.62|Procurement premium|0.72|0.71|
|_Yg_|demand shifter|0.83|Share of procurement in GDP|0.12|0.12|
|_mg_|measure of procurement goods|0.12|Percentage of procurement frms|12%|12%|
|Block 4||||||
|D|Government lending|0.86|Interest rate|5%|5%|
| ̄_s_|Productivity shifter|-6.51|K/Y (aggregate)|3.88|3.84|
|_θ_|Survival probability|0.95|Exit rate|5%|5%|

**Notes:** This table summarizes our baseline calibration. Government wealth _D_ is expressed as a fraction of total credit in the model economy. In column (1), we show the parameter values in our baseline calibration.

**Table 1.** Calibration

equation (16) for firms with at least one procurement contract in our sample, using the same sample that we use in Section 3. Columns (1) and (2) show the estimated coefficients when including and not including firm FEs, respectively. Because equation (16) should hold with equality only for firms whose financial constraint is binding, in columns (3) and (4), we run the same regression using a sample of firms that are likely to be financially constrained. In particular, we run the regressions for firms with leverage ratios above the median, which, through the lens of our model, is a strong proxy for whether the firm is financially constrained. We find the same two results across all the specifications. First, the estimated coefficient _β_ 1 is positive, which is evidence of earnings-based borrowing constraints ( _φp_ > 0). Second, the estimated coefficient _β_ 2 is also positive, which is evidence that revenues from the public sector can be pledged to a higher extend than earnings from the privare sector ( _φg_ > _φp_ ).

We take column (4) as our preferred specification. This delivers estimates _β_ 1 = 0 _._ 292 and we do not have labor in our model, that variable is equal to the firm’s value added _piptyipt_ + _pigtyigt_ . However, in the data, we compute the counterpart of that variable as: Because we do not observe the use of factors separately for what is used to deliver sales to the private vs. the government sector. To compute value added generated by selling to the government, we assume that the intermediate goods and the labor share in total expenditure is constant within the firm, i.e., it does not change depending on whether the firm sells to the private sector or the government.

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||**All **|**frms**|> **Med**|**ian leverage**|
|---|---|---|---|---|
||(1)|(2)|(3)|(4)|
|∆_pityit_/_kit_|0.208<sup>_a_</sup>|0.211<sup>_a_</sup>|0.303<sup>_a_</sup>|0.292<sup>_a_</sup>|
||(0.001)|(0.001)|(0.001)<br>|(0.001)<br>|
|∆_pigtyigt_/_kit_|0.182<sup>_a_</sup>|0.161<sup>_a_</sup>|0.229<sup>_b_</sup>|0.191<sup>_b_</sup>|
||(0.055)|(0.052)|(0.100)|(0.089)|
|Observations|61,445|62,442|29,528|30,037|
|R-squared|0.238|0.084|0.296|0.118|
|Sector×year FE|Yes|Yes|Yes|Yes|
|Firm FE|Yes|No|Yes|No|

**Notes:** This table presents results from estimating the relationship between the change in firm’s leverage and the change in its average product of capital and change in its earnings coming from selling to the government divided by the firm’s total stock of capital. Regression (16) is estimated with firms obtaining at least one procurement project over 2000-13 using annual data. Standard errors are clustered at the firm level;<sup>_a_</sup> indicates significance at the 1% level,<sup>_b_</sup> at the 5% level, and<sup>_c_</sup> at the 10% level.

## **Table 2.** Change in Leverage and Procurement

_β_ 2 = 0 _._ 191. For the model to generate these regression coefficients and a credit-to-capital ratio of 0.55 we need _φp_ = 0 _._ 10, _φg_ = 0 _._ 15, and _φa_ = 0 _._ 64. Hence, firms can pledge 10% of their annual earnings from selling to the private sector, 15% of their annual earnings from selling to the government, and 64% of their capital stock. Using equation (10), these numbers translate into _φp_ = 0 _._ 27, _φg_ = 0 _._ 41, and _φa_ = 2 _._ 81, which mean that firms can increase their capital by 27% of their annual earnings in the private sector and by 41% of their annual earnings from selling to the government.<sup>22</sup> This is the result of a multiplier effect: firms can borrow against their revenues, allowing them to buy more capital, which can be partly collateralized to obtain further credit. This is an important interaction and captures how earnings-based constraints affect a firm’s ability to grow also depends on the value of _φa_ .

# **5.3 Block #3: participation and size of procurement**

There are four parameters driving the size and composition of procurement: _Yg_ , _mg_ , _η_ 0, and _η_ 1. The parameters _Yg_ and _mg_ are policy parameters governing the relative size of procurement in the economy and the fraction of goods bought by the government. To capture the size of procurement in the aggregate economy, we set _Yg_ to match the share of procurement in GDP equal to 12.1%, which is the value we measure in the Spanish national accounts in the year 2006. To capture the number of firms that sell to the government, we proceed as follows. In our micro data, when looking across all sectors, only 0.5% percent of firms participate in procurement in a given year. However, whereas our balance sheet and income statement data covers the quasi-universe of Spanish companies, our procurement data only captures around 13% of the total procurement value measured in national

> 22We note that both _φp_ and _φg_ satisfy Assumption 1, which means that capital cannot be self-financed through the earnings-based constraints, see Lemma 2 in Appendix D.

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accounts. If we assume that the number of procurement firms relative to the value of procurement is the same in our sample as in the whole population, we can scale up the share of procurement firms to 3.8% (0.005 / 0.13 = 0.038). However, this is probably a lower bound for the number of firms active in procurement because our procurement dataset is biased towards contracts awarded by the central government, which are bigger than the contracts awarded by other governments layers (e.g., local governments), and hence are probably more concentrated to a few firms.

To have a more credible estimate of the actual number of firms active in procurement, we make use of a recently available dataset provided by Spanish Government, _Plataforma de Contrataci ́on del Sector P ́ublico (PLACSP)_ , where all types of public agencies in Spain are required to upload their procurement activity. Although the platform includes information since 2013, compliance was only strong starting in March 2018, when introducing information on all contracts became compulsory by law.<sup>23</sup> Using information for the year 2019 (when the coverage is already high and before COVID), we measure around 75,000 firms with at least one procurement contract in the platform, which represents around 12% of the total number of active firms in the data. In our baseline calibration, we therefore set _mg_ equal to 12% and use the 3.8% as a robustness exercise.

We calibrate the level parameter _η_ 0 to ensure that the fraction of firms doing procurement equals the fraction of goods bought by the government, _mg_ , which is the equilibrium condition (e) (see section 4.9). Regarding the curvature parameter _η_ 1, we identify it by matching the selection pattern of firms into procurement observed in the data. We proceed as follows. In the data, we select firms with no procurement contracts between 1999 and 2005. Then, we classify as procurement firms those firms that obtain at least one contract in 2006. We define the “procurement premium” as the relative difference in size (measured by value added) between procurement and non-procurement firms in 2005 (only exploiting variation across firms within the same 4-digit industry). That is, we want the model to match the ex-ante difference in size between procurement and non-procurement firms. We measure this procurement premium to be 72%.

The intuition why the parameter _η_ 1 affects the selection of firms into procurement is as follows. When _η_ 1 approaches zero, the probability function _g_ ( _b_ ) exhibits strong diminishing marginal returns in _b_ : the marginal increase in probability falls quickly as firms invest more. This makes differences in _b_ across firms inconsequential for their probability of selling to the government, and hence generates very little selection, with complete randomness in allocation when _η_ 1 = 0. Conversely, when _η_ 1 approaches 1, the diminishing marginal returns are small: the marginal increase in probability falls slowly with _b_ as firms invest more. This implies that differences in _b_ translate into big differences in the probability of participating in procurement, which generates a strong selection pattern.

> 23In particular, that law (“Ley 9/2017, de 8 de noviembre, de Contratos del Sector P ́ublico”) was aimed to adopt the European Parliament directives 2014/23/UE and 2014/24/UE.

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<!-- Start of picture text --> 02 Perc. proc. firms Proc. premium<br>0.15sr ae<br>0.8<br><!-- End of picture text --> <!-- Start of picture text --> Reg. coef. (Yp) O4 Reg. coef. (%,)<br>eee Le<br>0.3 0.2<br><!-- End of picture text --> <!-- Start of picture text --> 0.1 0.6<br>0.7 0.8 0.9 0.56 0.6 0.64<br>No TM<br><!-- End of picture text --> <!-- Start of picture text --> 0.2 ;<br>01 02 03 O04 0.2 0.4 0.6<br>dp dg<br><!-- End of picture text -->
The figure shows that the fraction of firms selling to the government, the procurement premium, and the two estimated coefficients in the leverage regression, Equation (16), are very informative about their associated parameters. In Appendix C, we show these relationships for all possible combinations of moments and parameters.

# **6 The Benchmark Economy**

This section describes three relevant dimensions of our benchmark economy: the selection pattern of firms into procurement, the treatment effect of a procurement shock on firm dynamics, and the macroeconomic consequences of procurement.

## **6.1 Selection**

In our calibration, we use _η_ 1 to target one moment related to selection: the “procurement premium” in value added of 72% (the relative value added of procurement vs. non-procurement firms before they obtain a procurement project). As discussed in Section 4.6, the value of procurement, _V_ ( _s,a,d_ = 1) − _V_ ( _s,a,d_ = 0), is increasing in firms’ ability to deliver large projects, which is determined by productivity _s_ for unconstrained firms and also by net worth _a_ for constrained firms. Hence, in the model firms self-select into procurement based on their productivity _s_ and their net worth _a_ . When we compute the “procurement premium” for _s_ and _a_ we find that procurement firms are ex-ante 35% more productive and hold ex ante 44% more net wealth. These premia will be affected in our counterfactuals, which will be important to understand the aggregate consequences of changing the allocation of procurement to firms.

## **6.2 Treatment and other un-targeted moments**

In our calibration, we use _φg_ to target one moment related to the treatment effect of procurement: the change in leverage resulting from increasing sales to the government for firms likely to be financially constrained. What we do next is to examine the model predicted dynamic responses of credit and sales after a procurement shock, and compare them to the evidence presented in Section 3. To do so, we use model-simulated data to estimate the same local projection regressions that we run in the data. Importantly, none of this evidence was targeted in our calibration.

**Credit.** In Panel (a) of Figure 8, we show the estimated cumulative effects on credit of a procurement shock for different time horizons, both in the model and in the data. The first thing to note is that, when using “all firms” to run the regression in the model, the implied effect on impact is distinctly higher compared to its counterpart in the data (∼ 39% vs. ∼ 5%). Starting in the first year after the procurement shock, however, the cumulative effects in the model and the data become similar, converging at somewhere around 5% in the year 3 after the shock. In that

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<!-- Start of picture text --> .13<br>.4 model (all firms) .09<br>.37<br>.34 .05<br>.31 .01<br>.28 −.03<br>.25<br>−.07<br>.22<br>.19 −.11<br>.16 −.15 data<br>.13 model (rest. sample) −.19<br>.1<br>−.23<br>.07<br>−.27<br>.04<br>data model (all firms)<br>.01 −.31<br>−.02 −.35<br>−1 0 1 2 3 4 −1 0 1 2 3 4<br>years since procurement shock years since procurement shock<br>(a) credit (b) sales to the private sector<br>cumulative growth rate cumulative growth rate<br><!-- End of picture text -->

**Notes:** This figure shows the cumulative impact of the estimate of _β_ 2<sup>_h_(anditsassociated10%confidencebands)</sup> from regression (1) for different time horizons _h_ = 0 _,_ 1 _,_ 2 _,_ 3 _,_ 4 _._ Panel (a) shows the results for the case of _x_ being firms’ total sales. Panel (b) shows the results for the case of _x_ being firms’ sales to the private sector. The line “data” shows the estimated coefficients using the real data, i.e., same results as in panel (a) of Figure 1. The line “model (all firms)” shows the results when using all firms in our simulated sample. The line “model (rest. sample)” shows the results when restricting the simulated sample to observations where credit growth is below the top 10 % and above the bottom 10%.

**Figure 8.** Procurement effect on credit and private sales

respect, both in the model and in the data, we observe a similar long-lasting effect of procurement on credit.

We note that the sharp peak observed at _h_ = 0 is mostly driven by a set of very few unconstrained firms that dramatically increase credit to expand their operations at the time of the shock, and decrease it afterwards. That is, procurement represents a large demand shock for these firms, and by the timing assumptions in our model, the only source to finance the firm’s capital expansion is debt. For example, within the set of firms that are unconstrained throughout the simulated sample, 25% of them have their credit increased by 4 times after receiving a procurement shock. These unconstrained firms operate with a capital stock which is very similar to their net worth (with credit being close to zero). When they get a procurement contract, their optimal capital stock increase at impact leads to very large percentage changes in credit. On the other hand, for constrained firms, the highest increase in credit observed in our model-simulated sample is around 85%. Our model performs significantly better once we remove the extremely responsive firms from our simulated sample. For example, the increase in credit at _h_ = 0 becomes around 9.5% once we remove the bottom and top 10% observations in terms of the change in credit. In reality, the unconstrained firms have access to other sources of funds, such as drawing down their cash positions or retaining more earnings (paying fewer dividends), so one should not expect to see such a large unconditional spike in the data. Given that the focus of our study is on the interplay between financial frictions 30
**Notes:** This figure shows the share of government purchases accounted for by procurement firms, i.e., firms with at least one procurement contract, falling into different parts of the distribution of _k_ . In the data, we have used data for the year 2006. Very similar patterns are observed in different years.

**Figure 9.** Distribution of government purchases across procurement firms

(and thus, financially constrained firms) and public procurement, most importantly the dynamic “crowding-in” benefits of winning public procurement contracts, we take the results in Panel (a) at horizons _h_ ≥ 1 as evidence that the model performs remarkably well in this regard.

**Sales to the private sector.** We next look at the evolution of firms’ sales to the private sector in Panel (b) of Figure 8. Similar to the data, our model predicts a “crowding-out” effect on impact and a “crowding-in” effect from _h_ = 1 onwards. As discussed in Section 4.6, this is because at impact constrained firms have to split their scarce collateral between the two sectors (a financial problem that is only partially alleviated by the extra credit generated by selling to the government). However, the new profits generated from procurement allow the firm to accumulate more net worth over time. This higher level of net worth will ease the firm’s financial constraint (lowering _λ_ ) and hence allow it to increase output in the private sector in the subsequent periods. Similarly to the effect of procurement on credit, our model over predicts the “crowding-out” effect at impact (∼35% in the model vs. ∼13% in the data) but does a better job in replicating the “crowding-in” effect from _h_ = 1 onwards (firms increase sales to the private sector by around 8% at _h_ = 1 and around 2-3% at _h_ = 4 both in the model and the data).

**Endogenous persistence in sales to the government.** We also find that the procurement contract has a persistent positive effect on _b_ , which is the result of an increase in the firm’s net worth. In particular, we find an increase of around 8, 6, and 3% estimated for one, two, and three years, respectively, after the firm obtains a contract (see Figure F.1). This result identifies a channel through which the model endogenously generates some persistence in firms’ participation in procurement. To have a sense of how strong this channel is as compared to the data, we compute the probability of obtaining a contract over the next three years, i.e., _t_ + 1, _t_ + 2, or _t_ + 3, conditional on a firm having a contract in _t_ . In the data, this number is quite high, 75%, which compares to its model counterpart of 42%. That is, our model generates more than one-half of the persistence observed in the data.

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**Distribution of government purchases across firms.** Finally, we also show how the model distribution of procurement sales across firms compares to its counterpart in the data. As explained above, firms with higher _s_ and _a_ will self-select into procurement. Although we control this selection pattern by calibrating _η_ 1 to the observed procurement premium, we do not explicitly target any moment of the distribution of firms’ sales to the government. To see how well the model does along this dimension, we look at the share of government purchases accounted for firms of different size as measured by their levels of assets _k_ . In Figure 9, we compute the share of procurement sales accounted for by firms in different size-groups, based on _k_ . First, the model captures well the fact that bigger firms account for higher shares of government purchases, which is a combination of these firms selecting more into procurement and getting bigger contracts. Second, the model does an overall good job in generating the shares that we observe in the data, especially so given our admittedly simple procurement allocation system. That being said, the model falls somewhat short of the large concentration of procurement by the biggest firms. In the data, procurement firms above the 75th percentile in the _k_ distribution account for 74% of total government purchases, which compares to 53% in the model.

# **6.3 The macroeconomy**

Aggregating output over firms we get that _Yp_ = TFP _pKp_ and _Yg_ = TFP _gKg_ , where TFP _p_ and TFP _g_ are weighted averages of firm-level productities _s_ and distortions _λ_ , see Appendix E for details. We can define GDP in units of the private sector good as _Y_ ≡ _Yp_ + _PgYg_ , which leads to _Y_ = TFP _K_ , where aggregate capital is _K_ ≡ _Kp_ + _Kg_ and aggregate productivity is TFP ≡<sup>_K_</sup> _K_<sup>_<u>p</u>_TFP</sup><sup>_p_+</sup><sup>_K_</sup> _K_<sup>_<u>g</u>Pg_TFP</sup><sup>_g_.</sup> In column (1) of Table 3 we report all these objects for our benchmark economy.

**Productivity.** We find significant differences in aggregate productivity across the two sectors: TFP in the procurement sector is 18.6% higher than in the private sector (0.306 vs. 0.258). The difference in sectoral TFP can arise for two reasons: (a) selection of firms into procurement based on _s_ and (b) different misallocation of capital across firms in the production of goods in each sector (see Appendix E for details). In our economy the main reason for the higher productivity in the public sector is the selection of more productive firms into procurement, which more than offsets the slightly higher misallocation of capital in the production of procurement goods. Indeed, absent misallocation, TFP in the procurement sector would be 19.6% higher than in the private sector.

The selection of more productive firms into procurement is due to their ability to deliver larger projects. In particular, the average _s_ is almost 30% higher in procurement. The higher misallocation in procurement arises due to the fact that firms producing for both the government and the public sector are _ex post_ more financially constrained (the average _λ_ is twice as high for procurement firms). This is the result of procurement firms facing a much larger demand, which is harder to finance despite the selection of wealthier firms into procurement (the average _a_ is around 80% larger 32
for procurement firms) and despite _φg_ > _φp_ . A way to quantify the extent of misallocation in each sector is by looking at the variance in the log MRPK across firms, which is around 40% higher in the procurement sector (0.045 vs. 0.033). As a result, the aggregate TFP gains of equalizing MRPK across firms are 6.6% in procurement and 5.7% in the private sector.

**Relative prices.** We next look at the price of public goods relative to private goods, which will be important to understand some of the results from the policy counterfactuals. The relative price can be written as:

where MRPK _g_ , MRPK _p_ , TFP _g_ , and TFP _p_ are the weighted average marginal revenue products and sectorial TFP’s (see Appendix E for derivations). As in standard multi-sector models, the ratio of relative prices is inversely related to sectorial TFPs. However, equation (18) also implies that the relative price is positively related to the ratio of average marginal revenue products in each sector. That is, a relatively high sectorial “wedge” —arising from a suboptimal allocation of capital into the sector— is associated with a higher relative price. Because firms active in procurement are on average more financially constrained, i.e., have a higher _λ_ , the average wedge in the procurement sector is higher. In particular, in our benchmark economy, MRPK _g_ is around 7% higher than MRPK _p_ . However, as mentioned above, TFP _g_ is 21% higher than TFP _p_ . All together the relative price of public goods is _Pg_ / _Pp_ = 0 _._ 901.

# **7 Policy Experiments**

Our empirical evidence in Section 3 and the quantitative results in Section 6 show that procurement contracts help firms grow out of their financial constraints. At the same time, in Section 5 we have seen that smaller firms, typically the most constrained, participate less in procurement. This suggest that making procurement contracts available to smaller firms may lead to aggregate output gains. For this reason, in this section we quantify the aggregate effects of reforming the public procurement allocation system through _expenditure-neutral_ changes that favor small firms. Recall that aggregate GDP (in units of the private good) is _Y_ ≡ _Yp_ + _PgYg_ . As mentioned above, the counterfactuals we run are _expenditure-neutral_ , meaning that _PgYg_ will remain constant by construction. That is, changes in _Yp_ will drive all the changes in GDP. However, although _PgYg_ remains constant, _Yg_ and _Pg_ are allowed to change. Because we also want to study the impact of the reform on the “real” provision of public goods, we use an alternative definition of GDP where we keep _Pg_ constant at its level in the benchmark calibration. We refer to this alternative measure as “real” GDP, indicating that we measure it at relative prices from the baseline economy.

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# **7.1 Counterfactual 1: Targeting the selection pattern**

We first run an experiment that encourages the participation of smaller firms in procurement. This counterfactual aims to reproduce the type of “set-aside” policies for small businesses implemented, for example, by the U.S. Small Business Administration. Policies of this type could be those that facilitate access to the competition for procurement contracts —like better publicity or direct assistance to prepare the application— or measures to provide more transparency of the whole process.

To evaluate this type of policies, we reduce the parameter _η_ 1 so that the model generates a procurement size premium of 50%, as opposed to the 72% in the baseline calibration. That is, we solve for a new economy in which the procurement system gives relatively lower weight to firms’ investment in _b_ , making it easier for small firms to participate. We also change _η_ 0 and _Yg_ so that the fraction of procurement firms _mg_ and total government expenditure _PgYg_ remain unchanged.

We present the main results from this exercise in column (2) of Table 3, which shows the relative change of some relevant variables compared to their counterparts in the benchmark economy.<sup>25</sup> As mentioned before, we report the two measures of GDP: “nominal” GDP, which uses the relative price of procurement _Pg_ in the reformed economy, and “real” GDP, which keeps the price _Pg_ of the benchmark economy. We also report changes in the levels of capital in the two sectors and the aggregate, together with changes in variables related to misallocation and aggregate TFP.

**Aggregate output.** We find that the reform increases nominal GDP by around 1.07%.<sup>26</sup> Since we keep _PgYg_ constant in our experiment, this increase comes entirely from a 1.21% increase in _Yp_ . Importantly, we find only a tiny increase in “real” GDP of 0.05%. The reason is that, due to the policy experiment, the relative price of procurement _Pg_ increases (making the provision of public goods more costly), and hence the total amount of public sector goods _Yg_ falls. The fall in _Yg_ is apparent in the real measure of GDP growth but not in the nominal (as nominal expenditure remains constant). We will come back to the increase in _Pg_ below.

**TFP vs. K.** We can decompose the increase in “nominal” GDP into that coming from capital accumulation vs. TFP. We find that most of the increase in GDP (around 75%) is accounted for by an increase in the aggregate stock of capital _K_ , which increases by 0.78%. In Section 7.3 below, we will provide more details that will help understand the evolution of the stock of capital. The rest is explained by an increase of 0.28% in aggregate “nominal” TFP, which is the result of a slight increase in TFP _p_ (0.09%), a large reduction in TFP _g_ (6.85%), and the above-mentioned increase in _Pg_ . When keeping constant _Pg_ to its value in the benchmark economy, our model predicts a

> 25We report the difference, not the relative change, for variables that are already in shares, i.e., the percentage of procurement firms and the share of procurement in GDP, as well as for the interest rate _r_ , the tax _τ_ , and the parameters _η_ 0 and _η_ 1.

> 26 This compares to a 12% increase in GDP of eliminating financial frictions in our economy (setting _φa_ →∞).

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decrease in “real” TFP (3.49%) due to the large fall in TFP _g_ .<sup>27</sup>

**Why do TFP** _p_ **and TFP** _g_ **change?** The increase in TFP _p_ is the result of the beneficial effects of procurement on wealth accumulation of small firms. In the new steady state, firms that had a relatively high MRPK _ip_ in the benchmark economy are more likely to be active in procurement, which allows them to accumulate more assets and hence operate with a higher level of capital in the private sector (see Section 6). This reallocation of procurement contracts towards relatively high MRPK _ip_ firms implies a reduction in the dispersion of MRPK _ip_ and hence in misallocation.

The decrease in TFP _g_ is explained by a change in the selection of firms into procurement and hence by the change in the composition of procurement firms. In particular, procurement firms in this counterfactual economy have lower relative productivity _s_ (7.98% less) and lower relative net worth _a_ (14.78% less). As a result, procurement firms are relatively less productive and relatively more constrained (as reflected by a larger _λ_ ). This leads to the decline in TFP _g_ due to both lower _s_ (lower first-best productivity) and lower _a_ (more misallocation).

**A reduction in the efficiency of public goods provision: Why does** _Pg_ **increase?** As explained above, the relative price of public goods depends on the ratio of sectorial wedges times the inverse of relative sectorial TFPs, see equation (18). We have just seen that the ratio TFP _p_ /TFP _g_ increases substantially, first and foremost because selection along productivity _s_ into procurement worsens. Moreover, because the counterfactual procurement system also selects firms that have relatively lower net worth _a_ , and are thus more financially constrained, all else equal, it leads to a relative increase in the procurement sectorial wedge, as captured by MRPK _g_ . Both of these forces raise _Pg_ . This is an important result that highlights an interesting tradeoff for the government: by targeting small firms, governments also end up buying from firms that are small not because they are constrained but because they are fundamentally less productive. This fact compounds the force that buying from a relatively more constrained firm, even at identical productivities, implies a restricted supplied quantity and higher price. Under constant government expenditures, all of this necessarily implies an underlying lower provision of public goods.

# **7.2 Counterfactual 2: Decreasing contract size**

Our policy experiment in the previous section is only one possible way for governments to promote the participation of small firms into procurement. An alternative policy would be to decrease the size of procurement contracts, which is at the core of the European Commission’s agenda for public procurement regulation. We therefore perform a second experiment that consists in reducing the size of contracts while keeping the same level of expenditure _PgYg_ . In practice, we solve for a counterfactual economy in which the fraction of firms from which the government buys, _mg_ ,

> 27We derive aggregate TFP in Appendix E.

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||**(1)**|**(2)**|**(3)**|
|---|---|---|---|
||**Benchmark**<br>(levels)|**Count 1**<br>% change|**Count 2**<br>% change|
|Output||||
|_Yp_|6.035|1.21%|-0.97%|
|_Yg_|0.904|-8.55%|0.05%|
|GDP|6.850|1.07%|-0.85%|
|real GDP|6.850|0.05%|-0.85%|
|Capital||||
|_Kp_|23.395|1.11%|-1.07%|
|_Kg_|2.956|-1.82%|3.24%|
|_Kp_+_Kg_|26.351|0.78%|-0.59%|
|Productivity||||
|TFP_p_|0.258|0.09%|0.10%|
|TFP_g_|0.306|-6.85%|-3.09%|
|TFP|0.260|0.28%|-0.27%|
|real TFP|0.534|-3.49%|-1.55%|
|MRPK_p_|0.258|0.07%|0.05%|
|MRPK_g_|0.276|1.89%|-3.10%|
|TFP_p_ gain|0.057|-1.76%|-1.87%|
|TFP_g_ gain|0.066|9.14%|-12.09%|
|Prices/tax||||
|_Pg_/_Pp_|0.901|9.38%|-0.01%|
|_r_|0.050|0.0010|0.0001|
|_τ_|-0.079|0.103|-0.032|
|Size of procurement||||
|% frms|0.120|0.000|0.080|
|Share GDP|0.119|-0.001|0.001|
|_η_0|0.783|-0.212|0.563|
|_η_1|0.624|-0.128|0.000|
|Selection||||
|ratio mean _s_|1.289|-7.98%|-2.70%|
|ratio mean _a_|1.776|-14.78%|-8.52%|
|ratio mean _λ_|2.082|12.32%|-20.13%|

**Notes:** Column (1) shows the main results from the benchmark economy. Column (2) shows the results from running counterfactual 1, which consists in changing _η_ 0, _η_ 1, and _Yg_ so that the procurement size premium decreases from 72% to 50%, while keeping unchanged the % of procurement firms and the procurement expenditure _PgYg_ . Column (3) shows the results from running counterfactual 2, which consists in changing _η_ 0 and _Yg_ so that the model generates an increase of procurement firms from 12% to 20% while keeping unchanged the procurement expenditure _PgYg_ , which decreases the average size of contracts accordingly.

**Table 3.** Counterfactuals

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increases from 12% to 20%.<sup>28</sup> We do so by increasing _η_ 0 and adjusting _Yg_ so that _PgYg_ remains unchanged. We also keep _η_ 1 unchanged.

We show the results from running this policy experiment in column (3) of Table 3. In contrast to the previous counterfactual, we find that the reform reduces nominal GDP by around 0.85%. Out of this decline, around 70% is explained by a fall in aggregate capital and the rest by a decline in aggregate TFP. As in the previous counterfactual, we will explain the behavior of capital accumulation below (see Section 7.3).

Also different from the first counterfactual, _Pg_ remains virtually unchanged. As in the previous counterfactual, TFP _p_ /TFP _g_ goes up, which should raise _Pg_ . However, the average wedge in the procurement sector MRPK _g_ decreases by a similar amount, 3.10%. As in the previous counterfactual, the policy allocates procurement contracts to smaller firms, which leads to a pool of procurement firms that are both less productive and have less net worth. However, different from the previous counterfactual this policy also reduces the average contract size. This makes procurement firms relatively less constrained (instead of relatively more constrained as in the previous counterfactual) because they have a smaller demand to serve (the average _λ_ of procurement firms declines by 20%) and hence the wedge in the procurement sector is smaller.

# **7.3 Understanding the effects on capital accumulation**

The main factor driving changes in aggregate GDP in the two experiments is capital accumulation. In the first counterfactual, a higher _K_ explains around 73% of the rise in GDP. In the second counterfactual, a lower _K_ explains around 70% of the fall in GDP. In this section, we provide more details about the specific mechanisms driving changes in _K_ .

To do so, we solve for an intermediate version of the two counterfactual economies that aims to isolate the different channels at play. Table 4 again reports statistics of our benchmark economy in column (0), of this intermediate exercise in column (1), and of the complete counterfactual economy in column (2).

**Long-run partial equilibrium effect.** Financially constrained firms that get procurement projects increase their revenues and can accumulate net worth at a faster pace and hence increase their private sector activity in the long run. In the intermediate step (“Long-run PE”), we isolate the aggregate effects of this strengthening of the self-financing mechanism. To do so, we solve for a new steady state partial equilibrium economy under the new _η_ 0 and _η_ 1, adjusting _Yg_ so that _PgYg_ remains unchanged, keeping the same _r_ and _τ_ as in the benchmark, and imposing that the policy functions of the dynamic problem _c_ ( _s,a,d_ ), _a_<sup>′</sup> ( _s,a,d_ ) and _b_ ( _s,a,d_ ) remain unchanged (as

> 28This represents a large change in the average size of contracts. In the counterfactual economy, the average size of the contract is 60% of that in the benchmark economy. The European Commission is not explicit about by how much governments should decrease the size of the contracts: “[...] Such division could be done on a quantitative basis, making the size of the individual contracts better correspond to the capacity of SMEs [...].” (see the Public Sector Directive 2014/24/EU for details.)

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<u>Panel A: Count. 1</u>

||(0)|(1)|(2)|
|---|---|---|---|
||**Benchmark**<br>(levels)|**Long-run PE**<br>(% change)|**Full GE**<br>(% change)|
|_Yp_|6.035|3.51%|1.21%|
|_K_|26.351|3.02%|0.78%|
|GDP|6.850|3.08%|1.07%|
|_r_|0.050|0.0000|0.0010|
|||Panel B: Count. 2||
|_Yp_|6.035|0.47%|-0.97%|
|_K_|26.351|0.77%|-0.59%|
|GDP|6.850|0.42%|-0.85%|
|_r_|0.050|0.0000|0.0001|

**Notes:** This table shows the results from running different versions of our model. Columns (0) and (2) show the value of the variables both in our benchmark economy and in the new steady state. Column (1) refers to the “Long-run partial equilibrium effect.” Importantly, in column (1), we solve the model by using the _η_ 0 and _η_ 1 that we use to compute the new steady states, and adjust _Yg_ so that _PgYg_ remains unchanged.

# **Table 4.** Channels

a ratio of the entrepreneurs’ cash on hand (1 + _r_ ) _a_ + (1 − _τ_ ) _π_ ( _s,a,d_ )). This economy delivers a joint distribution Γ of firms over the state space **X** that is different from the benchmark. Our goal is to quanitfy the mechanical accumulation effect that income from procurement generates on directly affected firms, without taking into account adjustments in dynamic decisions or GE effects. Column (1) of Table 4 shows a significant positive effect of this channel on the macroeconomy. In counterfactual 1, the implied capital stock and GDP are 3.02% and 3.08% higher than in the benchmark. In counterfactual 2, _K_ and GDP are 0.77% and 0.42% higher than in the benchmark. Hence, if we keep the policy functions of the dynamic problem and the interest rate unchanged, reforming the procurement allocation system in a way that favors small firms generates a positive aggregate effect because it allows more constrained firms to accumulate more net worth, grow out of their financial constraints, and hence produce more in the long run.

**Full effect.** We next study the aggregate effect of the changes in the policy functions of the dynamic problem and prices in general equilibrium. We find that the reforms reduce the incentives for big firms to accumulate assets over time, which shrinks (in counterfactual 1) or even turns negative (in counterfactual 2) the output gains associated to the reforms.

One of the main reasons why firms accumulate assets in our model is the fact that they expect to obtain a public procurement contract at some point. That is, obtaining a procurement contract is a big demand shock in response to which firms want to expand their capital stock, causing even relatively big firms to accumulate precautionary savings. Intuitively, productive firms want to have enough net worth so that they minimize the probability of being constrained in case the procurement shock is realized. In a context in which the average contract size is lower or in which obtaining a contract is less likely, this precautionary savings motive becomes weaker.

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**Notes:** This figure shows the “average” life cycle profile of a large number of firms, all drawing the highest productivity level _s_ in every period, simulated in our model under three different scenarios: the benchmark economy (blue solid line), counterfactual 1 (green dotted line), and counterfactual 2 (red dashed line).

**Figure 10.** Firms’ life cycle profiles

In Figure 10, we show how this reduction in firms’ incentives manifests in our model. This figure simulates the average life cycle profile of a cohort of firms in the benchmark economy (solid blue line), in counterfactual 1 (dotted green line), and in counterfactual 2 (dashed red line). In particular, we take a large number of newborn firms that draw the highest productivity shock every period and obtain procurement projects according to the probability _g_ ( _b_ ) and their choices of _b_ . We focus on firms that draw the highest productivity state in every period to capture the fact that changes in saving incentives across the different economies will be especially apparent in firms that expect to operate at large scales.

We find that the three economies exhibit common patterns. As they age, firms become larger —accumulate more net worth, operate with more capital, and sell more both in the private and procurement sector— and less financially constrained. The panels for _pgyg_ and _d_ show the differences in the procurement allocation systems across the three economies. The probability of participating in procurement, given by _d_ , is the highest in counterfactual 2 (there is a higher number of contracts) and the lowest in counterfactual 1 (the number of contracts is the same but high _s_ firms are less likely to get them). In terms of the revenues from procurement ( _pgyg_ ), the highest ones are under the benchmark economy, despite the fact that the probability of getting a contract is significantly 39
higher in the counterfactual 2. This is driven by the fact that contracts are considerably bigger in the benchmark than in counterfactual 2.

The most important finding from this figure has to do with the evolution of _a_ and _k_ over the firms’ life cycle. We find that net worth accumulation by high _s_ firms is the highest in the benchmark economy. In counterfactual 1, these firms prefer to accumulate slightly less because, although the size of contracts is still big, it is less likely for high _s_ firms to obtain them.<sup>29</sup> The big difference becomes visible in counterfactual 2, where firms’ net worth accumulation is significantly lower. This also becomes apparent when looking at the evolution of _k_ . In the counterfactual 2 economy, firms reach their optimal size at an age that is noticeably earlier than in the other two economies. To provide some intuition on this result, refer back to the Euler equation (14). The strength of the precautionary savings motive (or self-financing channel) is given by the term _∂π_ <u>(</u> _s_<sup>′</sup> _<u>,a</u>_<sup>′</sup> _<u>,d</u>_<sup>′</sup> <u>)</u> _∂a_<sup>~~′~~</sup> , which is equal to _φaλ_<sup>′</sup> (see Appendix D.2 and D.3). That is, the expected value of the financial constraint multiplier represents an extra return to asset accumulation. In other words, firms that expect to be financially constrained next period will accumulate more assets today. In counterfactual 2 contracts are smaller, and hence firms expected _λ_<sup>′</sup> in case of obtaining a contract is smaller too.

The panel _λ_ − _λBase_ in Figure 10 compares the _λ_ ’s in the two counterfactual economies with the one in the benchmark economy. We find that the _λ_ ’s tend to be smaller in the two counterfactuals for high _s_ firms, and particularly so in counterfactual 2. This is driven by the fact that, in counterfactual 2 the procurement contracts are smaller so firms do not need much financial capacity to expand in order to service them, and in counterfactual 1 the old high productivity firms become less likely to win procurement contracts as these are being reallocated to firms with lower _a_ and _s_ .

# **8 Robustness exercises**

We close the paper by looking at two important variations of our benchmark economy.

## **8.1 The importance of** _φg_ > _φp_

Our firm-level panel regressions show that leverage increases with firm earnings, and more so when earnings come from the public sector (see Table 2). Through the lens of our model, this evidence implies that earnings from the public sector can be pledged to obtain credit to a larger extent than earnings from the public sector ( _φg_ > _φp_ ). In this section we want to assess the role played by this asymmetry. To do so, we compare the macroeconomic effects of the policy reforms in a world where _φg_ = _φp_ . In particular, we decrease _φg_ such that _φg_ = _φp_ = 0 _._ 27 (the value of _φp_ in our baseline economy) and run the same counterfactuals as we did in Section 7.1 and Section 7.2.

> 29Instead, in counterfactual 1, all firms with _s_ lower than the highest state, accumulate _more_ net worth compared to the baseline.

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<!-- Start of picture text --> (a) Counterfactual 1 (b) Counterfactual 2<br><!-- End of picture text -->

**Notes:** This figure shows the % changes (y-axis) in the main aggregates as the result of conducting Counterfactual 1 and Counterfactual 2, both in our baseline economy and in an in the same economy but under _φg_ = _φp_ = 0 _._ 27. Notice that the numbers associated to the blue bars ( _φg_ > _φp_ ) are the same as reported in columns (2) and (3) in Table 3.

**Figure 11.** Policy reforms under _φp_ = _φg_

Panels (a) and (b) in Figure 11 report the % changes of the main aggregates in the _φg_ > _φp_ vs. _φg_ = _φp_ cases for Counterfactual 1 and Counterfactual 2 exercises respectively. Our main finding is that if government contracts were less pledegable, changes in the procurement system that facilitate the presence of small firms would be associated with worse macroeconomic outcomes. In the case of keeping the average size of contracts but increasing the strength of diminishing returns to _b_ , i.e., Counterfactual 1, the increase in nominal GDP would be 0.54% in the _φg_ = _φp_ case (vs. 1.07% in the _φg_ > _φp_ case). In the case of reducing the average size of contracts, i.e., Counterfactual 2, the fall in nominal GDP would be -2.00% in the _φg_ = _φp_ case (vs. -0.85% in the _φg_ > _φp_ case).

The reason for these results is as follows. When _φg_ = _φp_ , the private sector negative spillover of procurement in the short run is larger because there is no extra financing through public earnings to alleviate the problem of scarce collateral (see Proposition 13 in Appendix D). In addition, by reducing the extent to which borrowing capacity increases when participating in procurement, the long-run positive effects also weaken. Overall, procurement is less effective in helping constrained firms increase their production.

# **8.2 Decreasing returns to scale**

Our second exercise assesses the sensitivity of our main results to alternative assumptions on firms’ technology. In particular, instead of assuming a CRS production function, we consider: where _α_ = 1 would correspond to our baseline CRS economy.

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As discussed in Section 4.7, with CRS the static problem of firms that are not financially constrained can be solved independently for the private and public sectors. That is, how much an unconstrained firm sells to the government does not affect firms’ decisions in selling to the private sector and hence the crowding-out effect of procurement to private sales is absent. This result breaks under DRS. As we show in Appendix G, the elasticity of private sales to an increase in _Bg_ (a demand shock in the public sector) for unconstrained firms is given by: This elasticity is < 0 when _α_ < 1 and = 0 when _α_ = 1. Therefore, the overall short-run crowding-out effect of procurement to private sales would be bigger under DRS: in addition to the crowding-out coming from financial frictions there would be the crowding out coming from DRS, which would affect all firms (constrained and unconstrained).

There are three reasons why we use CRS as our preferred technology. First, our model already generates an average crowding out effect which is large enough compared to the data (see Figure 8). Second, we find evidence consistent with zero (or close to zero) crowding out effect for unconstrained firms (see Figure 3). And third, most of our analytical results for the intra-temporal production problem can only be obtained with CRS. In principle, it is not obvious under which of the two technology assumptions we should expect larger gains from reallocating procurement contracts towards small firms. On the one hand, in an economy without financial frictions, a bigger share of small firms in government procurement would be justified by the fact that the largest firms will be relatively less productive with DRS than in a world with CRS. On the other hand, under financial frictions, a lower share of firms will be financially constrained under DRS because the firm optimal size will be lower.

To assess the importance of CRS for our policy counterfactuals, we carry out a similar calibration strategy as the one explained in Section 5 but under the assumption that _α_ = 0 _._ 85 (Atkeson and Kehoe (2005)) and implement Counterfactual 1. We find that the aggregate gains of promoting the participation of small firms are slightly higher under DRS (see Figure G.1). For example, in terms of GDP, the gains would be 1.07% under CRS vs. 1.53% under DRS. This result is mostly explained by a larger effect on capital accumulation under DRS: 1.43 vs. 0.78%.

# **9 Conclusion**

In this paper, we quantify the macroeconomic impact of changes in the public procurement allocation system. To do so, we use a comprehensive framework that builds on three steps: selection, treatment, and the interplay between procurement and the macroeconomy. We use our framework to evaluate some of the policy reforms that are currently implemented in the US or are in the 42
industrial policy agenda of the European Commission. In particular, we quantify the long-run macroeconomic effects of a size-dependent expenditure-neutral policy reform that consists of facilitating small firms’ participation by either targeting them in the allocation process or by breaking down big projects into smaller ones.

Our results point towards the presence of long-run positive effects for directly affected firms, but also suggest the existence of important changes in large firms’ dynamic behaviors that could shrink the expansionary effects of changes in the procurement allocation system, or even make the effects negative. Our findings show that both the sign and size of these effects and hence the overall macroeconomic impact of this type of policies crucially depends on the severity and type of financial frictions in the economy. But the effects also depend on the type of reform, which determines how the change in procurement harms larger firms. These findings suggest that the optimal procurement allocation system in a country would depend on the specific institutional characteristics of the economy.

We view our contribution as part of a broader research agenda on the macroeconomic effects of government procurement, a policy that is surprisingly understudied. This paper only investigates the long-run consequences of expenditure-neutral changes in the procurement allocation system. Issues like the short-term consequences of reforms, or the potential implications for the effectiveness of fiscal policy are still unexplored. We would like to emphasize that pursuing this research agenda will deliver important policy implications.

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