Macroeconomic E ects of Firms’ Underspending in Times of ... · Macroeconomic E ects of Firms’ Underspending in Times of Abundant Liquidity Issam Samiri PhD Economics ... My thanks

Macroeconomic Effects of Firms’ Underspending in Times of Abundant

Liquidity∗

Issam Samiri

PhD Economics

Birkbeck - University of London

November 16, 2019

Abstract

Firms typically decide their financing before starting the implementation of a new project. The time

separating the financing stage from the implementation stage can be long enough for the management of the

firm to change its views about the project’s profitability and adjust spending on its implementation accordingly.

This means that following an unpredicted negative aggregate productivity shock, the productive sector can enter

a low spending mode, thus depressing output further. When productivity is unchanged or improving, the firms

remain constrained by the previously raised financing. I study this mechanism in a standard RBC set-up and

show that it only functions when productivity drops below a critical level that depends on past interest rates.

The generated business cycle is asymmetric: downturns can be violent and brief while recoveries are moderate

and slow. When firms enter a low spending mode following an unexpected drop in productivity, the unspent

cash can be used to pay equity holders through dividend or share buybacks. I use this to provide an empirical

validation of the model’s mechanism by linking low firm productivity to higher shareholder payouts.

JEL classifications: E30; E32; E40; G35; C67; C63

Keywords: RBC; Firms’ spending; Asymmetric Cycles; Financial Frictions; Productivity ; Oc-

casionally Binding Constraints; Dividends; Share buybacks; Networks; Great Recession; ZLB

∗I would like to thank my PhD supervisor, Prof. Yunus Aksoy, for the patient encouragement, comments and advice hehas provided throughout my time as his student and Prof. Ron Smith for commenting and guiding many aspects of thiswork. My thanks also go to Dr Pedro Gomes and Dr Arupratan Daripa of the Birkbeck economics department for the manydiscussions and comments. All remaining errors are mine.

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1 Introduction

The 2008 Great Recession is associated with the bursting of the American housing bubble.The drop in house prices, combined with leverage effects, wiped out a large proportion of thewealth of households in the United States, leading to a decrease in consumer demand. Thebanking sector was also heavily exposed to the housing market through asset backed securities.The deterioration in banks’ balance sheet that followed the collapse in the value of mortgagebacked securities dented the confidence in the banking sector in a process that culminatedwith the bankruptcy of Lehman Brothers in September 2008. This led to a rationing of bankcredit available to non-financial firms and increased their financing costs. The drop of aggregateoutput that followed was both rapid and significant. The Federal Reserve as well as other majorcentral banks reacted swiftly to this chain of events. Short term interest rates were set to zeroand central banks’ balance sheets were used to engage in large scale purchase programs aimedat replenishing and stabilising the balance sheet of banks and restoring the flow of credit. Byspring 2009, the Federal Reserve stress tests concluded that commercial banks had adequatelevels of capital relative to assets, signalling the end of the financial crisis. The trough of thecycle occurred shortly after, but the recovery that followed was slow. Indeed, as confirmed bythe European Investment Bank report [EIB (2016)], ”the slowness of the recovery in investmentby firms [was] disturbing, particularly given the extraordinary monetary stimulus”. This is thestory of a particularly asymmetric cycle. The downturn was violent and brief and the recoverylong and slow. Gertler and Gilchrist (2018) provide a more detailed timeline of the GreatRecession as well as survey of the main prevailing theories explaining it in the literature.Thesurveyed theories share the common feature that net worth of borrowers affects their access tocredit and thus their ability to spend.

In this paper, however, I study a mechanism based on the way firms consider their financingand spending problems when credit is not constrained. Within the studied framework, firmsdecide their level of financing first. Following unexpected drops in productivity between thefinancing stage and the time of spending, the firm can decide to spend less than the previouslyset financing. This does not happen when productivity matches or beats expectations. Thestudied mechanism affects the business cycle in an asymmetric fashion: it worsens the slumpsof the cycle and does not operate following shocks that improve productivity. The reason forconsidering situations where credit is not rationed is two-fold. First, it has been documentedthat larger corporates with direct access to credit took advantage of this access and tappedthe bond market to counteract the decline in bank lending in the early stages of the GreatRecession. As a result, these firms could maintain stable overall debt levels throughout thecredit cycle (Adrian, Colla, and Shin (2012)). In addition, as mentioned above, liquidity wasreadily available after the early stages of the Great Recession with no significant recovery interms of output growth. The studied mechanism can therefore contribute to understanding thecollapse in output by firms that maintained access to credit markets in the early stages of theGreat Recession while providing a potential explanation to the slow recovery that followed the

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financial crisis.I also show that for the mechanism to function, negative shocks of a certain magnitude are

required. The unanticipated productivity drop necessary for firms to enter an underspendingmode is smaller in a low interest rate environment. Near the zero lower bound (ZLB), firmstake into account the higher likelihood to enter a low spending mode at a later stage. Thischanges the reaction of firms towards lower interest rates in the steady state. The firms’ steadystate financing demand is higher for lower steady state interest rates. This in turn implieshigher steady state output when steady state interest rates are low. However, this relationshipbetween steady state rates and steady state output becomes weaker when interest rates arelow. Closer to the ZLB, firms take into account the higher likelihood to enter a low spendingmode at a later stage and increase their financing demand by smaller amounts following dropsin steady state interest rates. The mechanism is studied in the context of a simple RBC modelwith money and no monetary policy channel. Nevertheless, the steady state implications ofthe firms’ underspending mechanism shed an interesting light on the behaviour of the economynear the zero lower bound. This model can be used to describe the behaviour of parts of thecorporate sector that were not constrained by a lack of credit supply during the early stages ofthe Great Recession. It also provides a potential explanation to the slow recovery that followedthe trough of the Great Recession, despite abundant credit and low costs of financing.

I assume that the perfectly competitive firms may decide to spend less than the financingraised if their productivity is affected by large unpredicted shocks in the elapsed time betweenthe financing stage and the time spending is decided. At the financing stage, the firm takes intoaccount current financing costs and expectations of future productivity and production coststo set the level of financing. This is set such that the marginal impact of financing on expectedprofit matches the cost of financing as proxied by interest rates. After executing its financingoperations and gaining more knowledge about its own productivity and the production costsit faces, the firm reviews its expenditure problem and is usually constrained by its level offinancing. How much the firm is going to spend is decided by weighing two options: eitherspending all the cash available on production, or returning a portion of it to investors. Returningcash to investors implies no gain and no loss, or equivalently a return on investment equal toone. On the other hand, the return on spending targeted at the financing stage was supposedto be large enough to cover the cost of financing - the targeted return was higher than one.As long as no unexpected negative shocks hit the firm’s productivity, the marginal profit toshareholders from spending on production would remain positive at the financing constraint andthe profit maximizing firm would spend all the cash available to finance production. However,if productivity unexpectedly drops low enough between the financing stage and the spendingstage, the firm might find it more advantageous not to make use of all the available financing.This is simply because returning some cash to investors becomes more profitable than investingall the available financing in the production process. The firm based financial mechanismstudied here only functions following unexpected deteriorations in supply side profitability andthus provides a potential explanation for the asymmetry of the business cycle.

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When interest rates are very low, the return on spending targeted at the financing stagebecomes closer to the return on holding cash (i.e. 1) and smaller drops in productivity cause thefirms to enter an unconstrained spending mode. Additionally, if productivity is more volatile,large drops in productivity become more likely. The model’s mechanism is therefore morepotent in high volatility, low rates environments. Close to the interest rates zero lower bound,the likelihood of spending being unconstrained is too large for firms to ignore at the financingstage. In the presence of the model’s mechanism, firms still increase financing when reactingto lower steady state interest rates but the increase is moderated by the higher likelihood ofentering an unconstrained spending mode at a later stage. As a result, the studied RBC modelimplies that steady state financing and output reactions to changes in steady state interestrates become muted near the ZLB. While the model is kept simple and does not include amonetary policy channel, its steady state implications provide a potential explanation to theineffectiveness of conventional monetary policy in a low interest rates environment.

In order to help explain the large drop in output during the Great Recession, the modelpresented here requires a sizeable unexpected drop in productivity. Fernald (2014) has docu-mented an important decline in total factor productivity (TFP) growth between 2005 and 2008.More recent productivity data published by the Bureau of Labour Statistics indicate a declinein utilisation-adjusted TFP growth after the end of the recession. Other factors contributingto an unexpected deterioration in firms’ profits can achieve a similar effect and push firms tospend less than the previously raised financing. For example, a collapse of consumer demandfollowing deterioration in the households’ net worth as in Mian and Sufi (2012) can play asimilar role to unexpected drops in productivity. The model also suggests that when firms areless productive or face less attractive investment opportunities, they tend to distribute part ofthe excess cash to shareholders. In order to present some empirical validation of this claim, Ibuild on the work of Fama and French (2001), Grullon and Michaely (2004) and others andstudy the relationship between the firm’s productivity and the level of cash it diverts towardsshareholders in the form of dividends and share buybacks. It has been widely documented bycorporate finance literature that firms that invest in their production process through researchand development, capital expenditure or hirings tend to distribute less cash to shareholders.The empirical work in this paper provides further confirmation of this while focusing on theimpact of total factor productivity. I find that firms with low productivity are more likely todistribute cash to shareholders and that they tend to distribute more cash relative to their size,as measured by market capitalisation.

The rest of the paper is organized as follows. Section 2 gives a brief and selective summaryof the main strands of literature related to this work and highlights this paper’s contributionsin this context. Section 3 studies the empirical evidence provided by dividends and sharebuybacks. The RBC model is set out in section 4. This section also provides a numberof theoretical results related to the model’s main mechanism and deals with technical issuesrelated to the occasionally binding financing constraints. Section 5 presents the simulationresults. Section 6 extends the model to a multiple industry set-up where firms are linked

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through input-output relationships and discusses the impact of the production network on themodel’s main mechanism. Technical proofs and further empirical and simulation results arepresented in the appendix.

2 Contributions and Related Literature

This work is related to many strands of economic literature. First, there is the empiricalliterature studying the recent slump in private investment. Even though the model I studyassumes no capital and focuses more on production spending, capital expenditure is generallya good indicator of firms’ behaviour towards total expenditure, as firms tend to cut capitalspending early when they are entering a low spending period. Because I empirically study therelationship between firm level productivity and the shareholder rewards through dividends andshare buybacks, this paper is related to the finance literature concerned with explaining therelationships between dividends and share buybacks on the one hand and corporate investmentactivities on the other. In addition, my model’s main mechanism only functions during theslumps of the business cycle, so it is related to the empirical literature concerned with businesscycle asymmetries. Then there is the ”financial acceleration” literature that highlights therelationship between finance and the real economy and shows the ”accelerating” effect of financerelated mechanisms on the business cycle. Finally, because this work also studies the effect ofthe firm financial behaviour as industry disaggregation increases, it is related to the literatureconcerned with aggregation of idiosyncratic productivity shocks.

The sluggish recovery that followed the financial crisis has been linked to weak corporateinvestment. IMF (2015) shows that private business is responsible for most of the slump inglobal investment and argues that this is caused by weak demand and, in some countries,by financial frictions and political uncertainty. EIB (2016) explains that real investment inEurope fell sharply between 2008 and 2013 before starting a recovery that led to it being backto pre-crisis levels in core European countries by 2016 while it remained substantially lowerthan pre-2008 levels in Europe’s peripheral countries. In their study of private investment inthe American economy, Gutierrez and Philippon (2016) show that investment in the UnitedStates is low relative to measures of profitability and valuation (particularly Tobin’s Q). Onthe other hand, the authors argue in another paper that investment has been low in Europe inthe post-crisis period, but in line with the relatively low levels of Tobin’s Q.1 My assumptionis that productivity affects firms’ spending in an asymmetric fashion throughout the businesscycle: productivity does impact the firms’ demand for financing throughout the cycle but theeffect on spending is only immediate following unexpected and large negative shocks. In otherwords, I assume that financial investment is consistent with Q-theory while real investment isdetermined by financial investment unless there are large unforeseen drops in productivity. Ialso show that when real interest rates are very low, the mechanism of the model is more likely

1Dottling, Gutierrez Gallardo, and Philippon (2017).

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to operate and this leads to a relative lowering of the appetite of firms towards financing anincrease in production.

Another related empirical topic is the asymmetry of the business cycle, a fact that has beenargued by economists as early as the work of Burns and Mitchell (1946). The seminal work ofNeftci (1984) provided a statistical test that proved that ”the behaviour of unemployment ischaracterized by sudden jumps and slow drops” using a finite state Markov process framework.Other authors continued to focus on this topic, for instance Ramsey and Rothman (1996)linked business cycle asymmetry to the notion of ”time irreversibility”. The latter conceptis intuitively related to the mechanism I study in this paper where predetermined financinglevels constrain firm expenditure only when productivity is higher than a minimum level thatis mainly determined by past interest rates.

This work builds on the existing finance literature concerned with explaining the levels ofcash distributed by firms towards shareholders. These cash distributions take two importantforms: dividends and share buybacks. Jensen (1986) argues that, when the firm is facingless attractive investment opportunities, a conflict of interest arises between shareholders andmanagers, with the latter having an incentive to keep more resources under their control andthus not distributing free cash flows. Share repurchases in this context can work as a way toreassure markets about this potential conflict of interests. Grullon and Michaely (2004) findthat repurchasing firms reduce their current levels of capital expenditures and research anddevelopment expenses and that their cash balances significantly decline. This corroborates thedeterioration of the investment opportunities hypothesis. They also find that, contrary to whatis suggested by the signalling hypothesis, the markets do not always react positively to theannouncement of share repurchases, as market participants are not always aware of the reduc-tion of investments opportunities available to the firm before the share buyback programme isannounced. Hribar, Jenkins, and Johnson (2006) show that there is a strong discontinuity inthe probability of accretive share repurchases around the consensus earnings per share (EPS)expected by financial analysts. Firms that would have narrowly missed the analysts’ consensusEPS are much more likely to increase their share repurchase activity in order to positively affecttheir EPS and meet the consensus than those who narrowly beat the consensus EPS. Almeida,Fos, and Kronlund (2016) exploit this discontinuity to show that EPS-motivated share buy-backs are associated with reductions in employment and investments. Fama and French (2001)focus on a the more usual way chosen by firms to divert cash towards shareholders: dividends.They study the decline in the distribution of dividends by publicly traded firms in the last20 years of the twentieth century and relate the said decline to a number of contributing fac-tors including a change in the characteristics of public firms (firms go public earlier in theirdevelopment process) and the emergence of competing ways to pay shareholders (e.g. sharebuybacks). The authors also document an empirical inverse relationship between the firms’propensity to pay dividends and the investment opportunity it faces. Since the early 80s, sharerepurchases make a significant part of the cash flows directed by firms towards investors. Itherefore construct an index combining both dividends and cash repurchases to account for all

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cash flows directed towards equity investors as opposed to those being invested in the produc-tion processes. This follows a literature that is concerned with total cash flow distributed byfirms to equity investors. Bagwell and Shoven (1989) give an early account of the increasingroles of share redistribution and take-overs as ways to distribute cash from firms towards equityinvestors and suggest that yields of return on equity investments should account for these waysof cash distribution. Robertson and Wright (2006) use a total cash flow index that takes intoaccount dividends, share repurchases and net share issues and use the constructed index in or-der to predict stock returns. Imrohoroglu and Tuzel (2014) use total factor productivity (TFP)to predict equity returns and show that while TFP underperforms other indicators such asthe market to book ratio in predicting equity returns, low productivity firms earn a significantpremium over high productivity firms in the following year. In this paper, I use various firmindicators to explain the propensity of firms to divert cash towards shareholders. Followingexisting literature, these indicators include investments in capital, research and developmentand employment. In this regard, my results provide further validation of the idea that firmsreact to lower investment opportunities by diverting cash towards shareholders. In order toprovide an empirical foundation to the mechanism presented in this paper, I show that besidethe investment indicators, total factor productivity helps predict the levels of cash diverted toequity investors. To this effect, I present evidence from repeated cross-sectional logit regres-sions documenting the propensity of firms to pay shareholders. Additionally, I present dynamicpanel data regressions explaining the size of the payout when the firm makes the decision topay.

The term ”financial acceleration” was first coined in a 1996 paper by Bernanke, Gertler andGilchrist, in which the authors focused on the agency costs of lending and their endogenouschanges over the business cycle. The seminal paper of Kiyotaki and Moore (1997) linked thefirms’ ability to borrow to the value of the collateral they own and thus to the fluctuation ofthe business cycle, providing a new motivation for the financial acceleration mechanism. Alater paper by Bernanke, Gertler, and Gilchrist (1998) builds on Kiyotaki and Moore’s ideaand develops a New Keynesian model where the cost of external funding of firms depends ontheir net worth. In this paper, I focus on the firm’s decision making process regarding itsown financing and spending when credit is abundant. By separating the financing problemfrom the spending problem, one gives the firm more realistic economic agency as it actuallycontrols the use of the funds raised in the financing stage. The firm exerts its control on realinvestment and can choose to invest less under low productivity conditions even if credit isreadily available. This can deepen and lengthen economic downturns and unlike many otherfinancial accelerators studied in the literature, influences the business cycle in an asymmetricfashion. I also show that when real interest rates are low enough, the model’s main mechanismstart impacting the firms’ financing decision in the steady state. Assuming decreasing returns toscale, lower interest rates lead to a higher raised financing levels. This behaviour is moderatedby the model’s mechanism when rates are near the zero lower bound. When faced with very lowrates, firms anticipate the likelihood of entering an unconstrained spending mode as early as

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the financing stage and lower financing relative to an economy where the financing constraintalways hold. This can slow the improvements in output following positive shocks so that dropsin outputs are severe and immediate while recoveries are slow and more moderate. Unlike theusual financial accelerator mechanisms that are more concerned with credit availability, themechanism I present is rooted in the firm level financing/spending process; it functions even ifcredit is readily available and affects the business cycle in an asymmetric fashion.

There is a vast literature dealing with the idiosyncratic origins of aggregate fluctuations. Theseminal work of Leontief (1941) has pioneered the use of input-output tables to study the effectof industry-specific shocks on aggregate output. In a more recent work, Gabaix (2011) arguesthat idiosyncratic firm-level shocks can explain an important part of the aggregate movement ifthe firm size distribution presents a fat tail towards large firms. In the same article, the authorexplains that the fat tailed firm size distribution has strong empirical justification and thatas a result, ”the idiosyncratic movements of the largest 100 firms in the United States appearto justify about one third of variations in output growth”. Acemoglu, Carvalho, Ozdaglar,and Tahbaz-Salehi (2012) argue that even in the case of a very disaggregated economy, i.e.an economy with a large number of industries, the properties of the input-output matrix canguarantee that industry-specific shocks carry on to affect the aggregate quantities and do notvanish due to the law of large numbers. According to the authors, this is the case when somesectors play an asymmetric role as a supplier to other sectors as it is the case in a ”star”production network. The nature of the production network linking industries plays a similarrole in this paper as I find that a star network makes the asymmetries generated by the model’smain mechanism subsist even when the economy contains of a very large number of industries.

3 Empirical Evidence

In this section, I present an empirical foundation for the main mechanism of the model. Themodel’s mechanism assumes that firms finance production before using the funds raised to payfor production costs. If the firm’s productivity unexpectedly drops between the financing stageand the spending stage, the management of the firm can choose to cancel some of its spendingplans made at the financing stage and return a portion of the cash raised to investors withoutinvesting it in the production process. To provide an empirical foundation for such mechanism,one would ideally need a way to measure changes in the spending intentions of firms, associatethese changes of intention with an increase of the cash diverted towards shareholders and linkthis process to a worsening in the firm’s productivity. The data available to me does not providea way to measure such change in the firm’s spending intentions. I therefore focus on the cashdiverted towards investors instead. I construct a measure of the overall cash diverted towardsshareholders that includes both dividends and share buybacks (”Distributed Cash”). I thendocument the marginal effect of productivity and other growth indicators on the propensity todivert cash towards shareholders using cross-sectional logit regressions repeated for every year

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of the studied sample period. I assume that an increase in shareholder payout beyond what canbe explained by the relevant firm’s characteristics and cash flow figures signals a reduction in thefirm appetite towards spending. Thus, an inverse marginal relationship between productivityand ”Distributed Cash” is an indication of a positive marginal relationship between productivityand production spending. To confirm and strengthen the results from the cross-sectional logitregressions, I run a fixed effect panel data regression explaining the size of the payout made byfirms choosing to distribute some cash towards shareholders.

3.1 Cash Distributed to Equity Holders

Firms can divert cash towards shareholders in different manners. The method chosen depends,among other things, on the intended recipients, the aim behind the distribution and its fiscalimplications. Namely, firms distribute cash to ordinary equity holders through three importantchannels:

• Dividends are the most common way for a firm to distribute cash to shareholders. Theyare subject to corporate taxation and to taxes on revenue. Dividends are typically paid ina periodic fashion. This implies that starting to pay dividends or increasing their amountcreates an expectation of such behaviour continuing in the future.

• Firms can decide to buy back their own shares (Share Buybacks). This can happenthrough fixed price tender offers and since 1982 mostly through open market operations.2

After selling all or part of their shares, ordinary equity holders are subject to taxes oncapital gains. Capital gains tax rates are typically lower than revenue tax rates, theyexclude the cost at which the shares were bought and can be netted against capital lossesfrom other investments by the seller. Share repurchases are therefore at a significantadvantage relative to dividends from a tax perspective.

• Firms can also distribute cash towards equity holders through cash financed mergersand acquisitions. I will not focus on this particular channel for two reasons. First, whenfirms buy shares of other companies during a merger and acquisition process, they aretypically paying the shareholders of other companies. More importantly, using cash tofinance the acquisition of another company can be considered as a form of investment inthe physical, human and intangible capital of the acquired company.

Following the more lenient 1982 regulations, share buybacks have emerged in the mid 1980s asa major way to compensate equity holders beside dividend payments. The left panel of figure1 illustrates this trend and shows the evolution of the average yearly share repurchases versus

2The 10b-18 rule of 1982 provides guarantees to the firms willing to repurchased their own stock that they would not bein breach of stock manipulation rules if they adhere to certain conditions (Safe Harbor conditions) regarding the manner,timing, price and size of the repurchase. This regulation and others implemented around the same time period simplified theexecution of share buybacks and limited the legal liability facing the repurchasing firm.

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the annual dividends over time in the sample provided by Compustat for firms based in theUnited States. The right panel of figure 1 also shows that from the early 1970s a significantnumber of firms choose to buy their own stock back while not distributing dividends. Takinginto consideration both dividends and share buybacks is therefore important when studyinghow firms decide to divert cash towards shareholders.

Figure 1: Evolution over time of the average amount distributed through dividends and share buybacks in log format byU.S. firms covered by Compustat (left). Proportion of Compustat U.S. firms with positive cash return to equity holdersthrough: dividends only, share buybacks only and a combination of the dividend and share buybacks (right). Grey areasindicate NBER recession periods. Appendix A.1 explains how share buybacks are derived and other data treatments.

3.2 Data

In the remainder of this section, I try to explain three figures representing the cash divertedby the firm to the ordinary shareholders: dividends, share repurchases and ”Distributed Cash”defined as the sum of both. The ”Distributed Cash” is a measure of the overall cash diverted tocommon shareholders. The cost to the company is different and depends on the tax treatmentof dividends and share buybacks. A number of firm’s characteristics and financial indicatorsare used in order to explain the flow of funds towards ordinary shareholders. Three stand outas reflecting the firm’s appetite for growth. These are productivity, investment expenses andthe market to book ratio. High investment expenses are a direct indication that the firm is in agrowth mode while a high market to book ratio can reflect a view by market participants thatthe firm has a high potential for growth. Total Factor Productivity (TFP) is used as a proxyfor the firm’s efficiency of production and is typically high for growth firms.3 TFP is obtained

3See Imrohoroglu and Tuzel (2014).

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following Imrohoroglu and Tuzel (2014)

TFP =g

k0.75 × l0.22, (3.1)

where g is value added by the firm, the firm-level capital stock k is given by gross plant, propertyand equipment (PPEGT) and the stock of labour l is given by the number of employees.Investment expenses include investment in capital (CAPEX) and in research and development(R&D). The market to book ratio is defined as the market value of ordinary equity divided bythe previous period’s assets’ value.

I control for a number of firm level characteristics and cash-flow figures. These include sizerelated controls, namely, the firm’s asset value and market capitalisation. I also control fornet income as an indicator of the firm’s profitability. High levels of cash and cash equivalentassets may indicate the presence of idle financial resources, providing a motivation for the firmto reward shareholders. I therefore include a measure of cash and cash equivalent assets tothe set of control variables. The number of employees is also included as it both serves as sizeindicator and an indicator of the firm’s wiliness to hire.

I use Compustat US data to get or derive all the firm level variables of interest.4 Followingexisting corporate finance literature, utilities and financial industry firms are removed from thesample as these companies are subject to specific regulations that impact dividends’ distribu-tion. To avoid outliers, firms with no assets are also excluded. Share repurchases are defined,following Fama and French (2001), as the increase in Treasury stock if the Treasury stock isnot missing. Following Almeida, Fos, and Kronlund (2016), if the Treasury stock is missing inthe current or prior year, share repurchases are measured as the difference between stock pur-chases and stock issuances using the cash flow statements. If either measures is negative, sharerepurchases are set to zero for the corresponding period. This data treatment is maintained forthe rest of this section.

Many of the studied firm characteristics and financial data vary in magnitude for a singlefirm throughout the firm’s life cycle and between firms of different sizes at the same timeperiod. Without any scaling, big firms would influence the regressions’ results more than smallfirms and later periods of the sample would influence the results more than earlier periods dueto the combined effects of inflation and capital accumulation. In order to correct for theseeffects, I scale all of the variables, except for the market to book ratio that does not requirescaling and the assets’ value that I keep as an unscaled measure of the size of the firm. Debt,cash holdings, net income, CAPEX, R&D investments, the number of employees and TFP aredivided by the value of the previous period’s assets.5 The market capitalisation, is replaced byits percentile equivalent.6 Dividends, share buybacks and the distributed cash are divided by

4The cost of labour data is obtained by multiplying the Compustat number of employees by the average wages from theSocial Security Administration. As explained in appendix A.1, the cost of labour is useful in the derivation of the firm levelvalue added.

5These scaling choices are, to a large extent, inspired by Fama and French (2001).6By percentile form of a variable Xt, I mean the transformation PercentileXt (x) = 100× number of observations satisfying Xt<x

number of observations at time t .

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the previous market capitalisation. All variables, except for the market capitalisation percentile,are Winsorised at the 1% level to correct for the outliers’ effect. Appendix A.1 provides moredetails about the definition of the derived variables as well as a summary of the transformationapplied to the data.

3.3 Firm’s Propensity to Pay: evidence from repeated cross-sectionallogit regressions

In order to explain the decision of the firm’s management to payback investors, I run a seriesof cross-section logit regressions repeated for every fiscal year between 1980 and 2013, wherethe dependent variable is the ”Distributed Cash” and the main explanatory variables are thelagged indicators for the firm’s appetite to grow: TFP, market to book ratio and the investmentexpenses (CAPEX and R&D).7 In order to avoid competing effects between these growth indi-cators, separate regressions are run to get the respective marginal effect of TFP, market to bookratio and the combined effects of CAPEX and R&D expenditures. The market capitalisationpercentile, assets, cash and cash equivalents, net income, debt and number of employees areused as lagged controls in all the regressions. Two digit industry dummies are also includedin the regressions to account for industry related effects. The repeated logit regressions can bedescribed by the following equation:

yt = βx,txt−1 + βz,tzt−1 + industry dummies, (3.2)

where yt is the ”distributed cash” variable, xt−1 denotes the lagged growth indicators of interest,and zt−1 are the lagged controls

xt−1 := TFP or Market/Book or [CAPEX, R&D] or [TFP, Market/Book, CAPEX, R&D],

zt−1 = [Market Capitalisation, Assets, Cash, Net Income, Debt, Employees].

Figure 2 reports the estimated coefficients βx,t of the growth indicators and the corresponding95% confidence intervals. Firms with high growth indicators are less likely to divert cashtowards investors, the effects being both economically and statistically significant. This isconsistent with Fama and French (2001) who find that firms with high investment opportunitiesas reflected by high asset growth rates and high market to book ratios are less likely to paydividends. The results presented here confirm these findings when including share buybacks inthe measure of cash diverted towards equity holders. Although TFP has a statistically weakermarginal effect when compared to other growth indicators, its effect remains both statisticallyand economically significant for most of the studied period. This provides the main empiricaljustification to the model in section 4. When simultaneously including all the growth indicatorsinto the regressions, the effects of the market to book ratio and R&D dominate the effects of

7The appendix shows regressions’ results when the dependent variable is dividends and share buybacks.

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other growth indicators. The marginal effects of CAPEX and TFP remain negative for most ofthe studied period but lose their statistical significance in most years. This is consistent withImrohoroglu and Tuzel (2014) who find that firms with low TFP have significantly higher equityreturns in the following year but that the TFP effect is not significant when other predictors,such as the market to book ratio, are used alongside TFP to predict equity returns.

The marginal effects of the used controls are presented in appendix A.3. The results confirmthe literature findings with regard to the relationship between some of the firm’s characteristicsand the propensity to pay shareholders. Large firms i.e. those with large assets and highmarket capitalisation tend to distribute more cash towards equity holders. Furthermore, asone may expect, firms that are burdened by relatively high debt levels are less likely to payequity investors, the debt effect being significant for almost every year of the studied timeperiod. Finally, the evidence from the logit regressions shows no significant impact of cash onthe propensity to pay. This is not an intuitive result. It is legitimate to suspect that highlevels of cash holdings may indicate a low investment opportunity and therefore incite the firmto pay equity holders. I propose two possible justifications for this non intuitive cash effect.First, the static nature of the regressions does not allow for taking into account the firm’sidiosyncratic need of holding cash. For example, firms may keep hold of relatively high cashamounts because of a lack of access to capital markets, thus a high cash holding relative toassets might reflect that the firm is still in an early development stage and has not reachedthe size where it can rely on capital markets to help manage its cash flows. Firms that arestill in the early stages of their development are less likely to reward shareholders through cashdistributions.8 Additionally, the absence of dynamic effects of cash holdings makes it harderto interpret the results. In order to correct for these issues, I run a number of panel data fixedeffects regressions explaining the size of the cash diverted towards shareholders.

3.4 Size of Payout: evidence from dynamic fixed effects regressions

After considering the propensity of firms to divert any cash at all towards shareholders, I nowturn to the size of the payout, expressed as a fraction of the previous period’s market capitali-sation. In order to capture the strong persistence of cash distributions and to control for nontime varying firm level characteristics, I exclude observations where no cash has been returnedand run a two-way fixed effect dynamic panel data regression to explain the size of the cashreturned to ordinary equity holders during the period between 1980 and 2013. Similarly to thestatic regressions case, each of the main growth indicators are included in a separate regressionto assess its effect in absence of other indicators. I also present the results of a regressionincluding all the growth indicators to show which ones maintain a significant effect in presenceof the others. The size of the overall cash distributed to shareholders is a strongly persistent

8The negative correlation between the cash to asset ratio and the value of the firm’s assets seem to give some credit tothis explanation (table 6 of appendix A.2).

13

-150

-100

-50

050

1980 1990 2000 2010 2020year

TFP estimate 95% lower limit95% upper limit

-1.5

-1-.5

0

1980 1990 2000 2010 2020year

Market/Book estimate 95% lower limit95% upper limit

-10

-50

1980 1990 2000 2010 2020year

CAPEX estimate 95% lower limit95% upper limit

-25

-20

-15

-10

-50

1980 1990 2000 2010 2020year

RD estimate 95% lower limit95% upper limit

Figure 2: Repeated logit cross-section regressions estimates with 95% confidence boundaries corresponding to the effectsof TFP, Market/Book and investment variables (CAPEX and R&D) on the firm’s propensity to pay shareholders. Thelogit regressions are repeated for every year from 1980 to 2013. The TFP marginal effect is estimated without controllingfor Market/Book, CAPEX and R&D, The Market/Book marginal effect is estimated without controlling for TFP, CAPEXand R&D and the CAPEX and R&D effects are estimated in the same repeated regressions that exclude both TFP andMarket/Book. Controls common to all regressions include: market capitalisation, assets, cash, net income, debt and thenumber of employees. Grey areas indicate NBER recession periods.

process. This requires the inclusion of multiple lagged dependent variables in the regressions.To deal with the issue of estimating the coefficients of the lagged dependent variables, I excludefirms with less than 15 observations within the sample period, this guarantees that the averagenumber of time observations per firm is higher than 20 in all regressions.9 The latter conditionrestricts the size of the sample substantially. In order to increase the sample size, I exclude

9See Nickell (1981) and Bruno (2005) for more on the issue of estimating dynamic panel data regressions with a largenumber of units and a small number of observations per unit.

14

the sparsely populated R&D variable from all regressions.10 The model can be summarised asfollows

yt =3∑i=1

βiyt−i + βxxt−1 + βzzt−1 + fixed effects + time dummies, (3.3)

where yt is the distributed cash expressed as a fraction of the previous period’s market capital-isation, xt−1 denotes the growth indicators of interest

xt−1 := TFP or Market/Book or CAPEX or [TFP, Market/Book, CAPEX],

and zt−1 are the same controls as in the logit regressions presented in subsection 3.3.The results in table 1 confirm the strong persistence of the size of the payout. Furthermore,

all growth indicators have economically and statistically significant effects when other growthindicators are excluded. The Akaike information criteria show that the market to book ratiooutperforms TFP and CAPEX as a growth indicator. This is confirmed by the results of themodel that uses all growth indicators as explanatory variables (Full Model). In this model, themarket to book ratio is the only growth indicator with a statistically significant coefficient atthe 0.001 confidence level. The dynamic regressions’ results confirm that large firms by assets’value tend to pay more relative to their market capitalisation with the estimated coefficientbeing statistically and economically significant and stable in value in all regressions. In thepresence of the market to book ratio in the regression, the latter result is extended to largefirms by market capitalisation. The presence of the book to market ratio as an explanatoryvariable is also required for net income to have a positive and statistically significant effect.As predicted above, when controlling for the firm’s idiosyncratic effects and taking dynamicaspects into account, firms with relatively high cash holding tend to pay shareholders more.This is consistent with the agency theory presented by Jensen (1986), stipulating that firmsholding large sums of idle cash have an incentive to distribute more through dividends and sharebuybacks in order to reassure shareholders on the potential conflict of interest where corporatemanagers keep large cash amounts on the firm’s balance sheet as a way to increase resourcesunder their control. Finally, the size of the distributed cash decreases with the number ofemployees. When controlling for the firm’s fixed effects, changes in the number of employeesrepresent a proxy for investment in the labour force.

3.5 Summary of the empirical results

After considering empirical evidence linking the firm’s appetite to grow to its propensity topay shareholders and the size of the payouts, it appears that firms with an ability and appetitefor growth divert less cash towards shareholders. I measure the appetite/ability to grow usingthe market to book ratio, investment expenses and TFP. While the market to book ratio

10Excluding R&D expenses for the repeated logit regressions does not affect the estimation results in a way that underminesthe conclusion made in subsection 3.3.

15

performs better than other growth indicators in predicting distributions to shareholders, theTFP’s marginal effect on the propensity to pay and size of the payouts is significant both ineconomic and statistic terms in the absence of other growth indicators.11 As predicted by thetheory, firms holding large sums of cash are more likely to divert cash towards shareholders.This relationship fails to appear in the repeated static logit regressions that fail to control forthe changes in cash levels and for the firm idiosyncratic effects, but is shown in the fixed effectdynamic regression explaining the size of shareholders payout.

The model developed in section 4 assumes that profit maximising firms can choose to dis-tribute some of the cash at their disposal to shareholders instead of spending to produce, follow-ing unpredicted drops in productivity. The evidence presented above can serve as an empiricaljustification to model’s mechanism linking the firm’s productivity to the firm’s spending.

Full Model TFP Effect Market/Book Effect Investment Effect

L.Cash Dist. 0.165∗∗∗ 0.179∗∗∗ 0.166∗∗∗ 0.178∗∗∗

L2.Cash Dist. 0.0466∗∗∗ 0.0517∗∗∗ 0.0475∗∗∗ 0.0502∗∗∗

L3.Cash Dist. 0.0437∗∗∗ 0.0473∗∗∗ 0.0446∗∗∗ 0.0462∗∗∗

L.TFP -0.310 -0.851∗∗

L.Market/Book -0.00441∗∗∗ -0.00458∗∗∗

L.CAPEX -0.0144∗∗ -0.0232∗∗∗

L.Market Cap. Percentile 0.000161∗∗ -0.0000132 0.000172∗∗ 0.0000219L.Assets 0.000000448∗∗∗ 0.000000573∗∗∗ 0.000000450∗∗∗ 0.000000522∗∗∗

L.Cash 0.0283∗∗∗ 0.0241∗∗∗ 0.0287∗∗∗ 0.0227∗∗∗

L.Net Income 0.0158∗ -0.00895 0.0127∗ -0.00744L.Debt -0.0172∗∗∗ -0.0180∗∗∗ -0.0183∗∗∗ -0.0166∗∗∗

L.Employees -0.227∗∗∗ -0.271∗∗∗ -0.234∗∗∗ -0.257∗∗∗

Constant 0.0267∗∗∗ 0.0323∗∗∗ 0.0254∗∗∗ 0.0315∗∗∗

AIC -103710.2 -103486.7 -103702.9 -103503.7∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

Table 1: Two-way fixed effects dynamic model for the size of the cash distributed.

4 The model

In the previous section, I showed that firms with lower productivity tend to divert more cashtowards shareholders instead of investing in the production process. In this section, I build

11The market to book ratio is derived using the share price. It is reasonable to assume that market participants take intoaccount information regarding the firm’s productivity and investment expenses when setting their beliefs about the shareprice. Additionally, TFP is a noisy measure of the firm’s production efficiency. It is therefore not surprising that market tobook ratio is a superior measure of the firm’s ability/wiliness to grow.

16

t

Firm decides its

t

financing level ιt

borrows ιt at rate rt

realizes new productivity

eut+1 and wages ht+1

t+ 1

Constrained Case: high ut+1

uses all financing ιt to fundexpenditure ζt+1 = ιt

t+ 1Unconstrained Case: low ut+1

firm gives back some cash to shareholdersζt+1 < ιt

Figure 3: Timeline of the firm financing and spending process.

a general equilibrium model that replicates this relationship between firm productivity andspending. To that end, I separate the firm’s financing problem from its spending problem. Thefirm first sets its financing based on its assessment of productivity at the financing stage. Pro-duction spending is decided some time after the financing stage and the previously set financingacts as an upper limit for potential spending. Following some unpredicted deterioration in pro-ductivity between the financing stage and spending stage, the firm can set spending at a lowerlevel than the financing constraint.

In the set-up I consider, households maximize their utility to decide consumption and leisuresubject to a budget constraint. The single consumption good is produced by firms that areconstrained by a Cobb-Douglas production function. Production is financed by householdsthrough bond issuance. In the absence of credit risk, all firms face the same interest rate: rt. Thediagram in figure 3 explains the firm’s financing/spending decision process: the representativefirm decides its financing level ιt at time t and raises the required amount using bonds beforediscovering the new productivity eut+1 between time t and time t+ 1. At time t+ 1, the profit-maximizing firm assesses its own productivity and the prevailing wages then chooses whetherto spend all the raised financing ιt (constrained spending case) or to spend less than the raisedfinancing level ζt+1 < ιt (unconstrained spending case).

Apart from the financing/spending time friction explained above, the model is fairly stan-dard and builds on the early RBC framework in Long and Plosser (1983). The remaining ofthis section details the behaviours of households and firms before commenting on the level of

17

productivity drop required for firms to enter an underspending mode.

4.1 Households

Households derive utility from leisure and consumption. Their utility function takes the form

ut = ln (ct) + χ ln (1− lt) , (4.1)

where lt denotes the household’s labour, ct consumption, and χ is a parameter that controls forhouseholds’ dislike of labour. Consumers maximize their expected lifetime utility discountedat rate β under their budget constraint in order to set their consumption, their leisure time1− lt and how much they save through corporate bonds bt

maxct,lt,bt

Et∞∑t=1

βtut. (4.2)

Consumers own production firms that provide them with a cash flow πt and are subject to thebudget constraint12

bt + ct = rt−1bt−1 + htlt + πt, (4.3)

with ht denoting wages and rt the bond’s interest rate satisfying the Euler equation

1

ct= βrtEt

1

ct+1

. (4.4)

Finally households are indifferent between consumption and leisure as long as

χct = ht(1− lt). (4.5)

4.2 Firms

The representative firm is constrained by the technology

f(t, lt) = eutlγt , (4.6)

where lt denotes labour, γ the production elasticity of labour and eut a stochastic productivityprocess. Within the studied framework, increasing returns to scale would imply infinite financ-ing demand and constant return to scale would lead to undetermined levels of firm financing.Empirically, many studies could not reject the constant return to scale hypothesis on the the

12Equity investors cover the debt payment shortfall in the case where the firms proceeds do not cover its debt obligations.This means that equity related cash-flows from the firm to households can be negative.

18

industry level while others point towards a slightly decreasing returns to scale.13 Decreasingreturns to scale are therefore used as a source of curvature in the profit function that guaranteesa unique solution to the financing problem (γ < 1).14

The log-productivity ut is assumed to follow an AR(1) process with the volatility parameterσ and the mean-reversion ρ,

ut = ρut−1 + σet.

The firm finances production by issuing bond contracts that are held by the households andthat pay an interest rate rt. At time t, the firm decides the amount ιt that will potentially beinvested in next period’s production process. To do so, the firm maximizes its expected profitthat is function of the future sales proceeds f(t+ 1, lt+1) and the present cost of rising debt rt

maxιt

Etf(t+ 1, lt+1)− rtιt. (4.7)

At period t + 1, the representative firm chooses labour lt+1 to maximize profit given thepredetermined level of financing ιt

maxlt+1

f(t+ 1, lt+1)− ht+1lt+1, (4.8)

s.a. ht+1lt+1 ≤ ιt. (4.9)

Increasing returns to scale being excluded (γ < 1), it is not obvious whether the constraint 4.9holds or not. Let’s define ζt as the level of wage spending at time t

ζt+1 := ht+1lt+1. (4.10)

One can rewrite production as a function of the actual expenditure level ζt+1, wages and thestochastic productivity15

f(t+ 1, lt+1) = eut+1ζγt+1

hγt+1

. (4.11)

If the financing constraint is not binding, the firm sets labour such as the marginal returnon labour equals the market wages. The latter condition is equivalent to setting the marginalreturn on expenditure to one, the same as the marginal return on cash. In other words, when

13Syverson (2004), Olley and Pakes (1996) and others could not statistically reject the constant return to scale hypothesis.Other studies find slight to moderate decreasing return to scale, for example, Gao and Kehrig (2017).

14This is consistent with the literature concerned with heterogeneous firms as for or example in Restuccia and Rogerson(2008) and Bartelsman, Haltiwanger, and Scarpetta (2013).

15This formulation of production justifies the decreasing returns to scale assumption. The firm profit is πt+1 = eut+1ζγt+1

hγt+1−

ζt+1. Clearly, if γ = 1 spending is undetermined and if γ > 1, firms would prefer to spend an infinite amount and so the loandemand would be infinite.

19

unconstrained by financing, firms set their expenditure at a level where they are indifferentbetween holding cash and producing

γeut+1

hγt+1

ζγ−1t+1 = 1. (4.12)

Combining the consumption/leisure indifference equation 4.5 with the goods’ clearance condi-tion enables to rewrite the latter unconstrained spending condition as follows16

ζt+1 =γ

(1 + χ/γ)γeut+1 . (4.13)

On the other hand, if the constraint is binding then the value of spending ζt+1 is obviouslysame as the previously set financing ιt. In all cases, one can write

ζt+1 = minιt,γ

(1 + χ/γ)γeut+1. (4.14)

Using the solution of the spending problem, the first order condition characterising thefinancing problem 4.7 can be rewritten in a way that accounts for both the binding and non-binding constraint situations

rtι1−γt =Et

[1ιt< γ

(1+χ/γ)γeut+1γ

eut+1

hγt+1

]. (4.15)

Equation 4.15 provides an intuitive behaviour for the level of financing ιt as a function ofproductivity shocks and wages: as long as technology exhibits decreasing returns to scale(γ < 1), investments are negatively impacted by higher costs of financing rt and by higherwages ht+1, while they increase with log productivity ut+1. The financing equation also reflectsthe fact that the financing constraint becomes irrelevant to the firm’s profit when spendingis unconstrained, i.e when γ

(1+χ/γ)γeut+1 ≤ ιt. Finally, it is worth noting that the model’s

mechanism reduces financing compared to a model where the financing constraint always binds.

4.3 Critical Productivity Level

When productivity is low enough, the expected marginal product of spending equals that ofcash (i.e. 1). The level of log productivity at which this happens is given by condition 4.12, orequivalently u(t) ≤ u∗(t) where the critical log-productivity u∗t is given by

u∗t = −γ + γ ln [1 + χ/γ] + ιt−1, (4.16)

where the superscript notation . is used for logarithmic values. Clearly low previous periodfinancing ιt−1 implies a lower critical productivity level u∗t and makes it less likely for the

16Appendix B.1 provides a detailed proof of the formula for unconstrained spending.

20

mechanism of the model to operate as it would be more likely for the financing constraint tobe binding. If one assumes that the economy is previously in the steady state and that ratesare not close enough to zero such as the steady state financing approximation in appendix B.3holds, equation 4.16 simplifies to

u∗t ≈ −r − γ ln

[1 + (χ/γ)r

1 + χ/γ

]. (4.17)

The economy being assumed to be previously in the steady state, u∗t in the latter formula canbe interpreted as a change in log-productivity. The latter expression also shows the crucialeffects played by interest rates in this model. Low interest rates levels imply that firms takeon less profitable projects, a smaller drop of productivity is therefore sufficient to make theseprojects less profitable than holding cash: everything else being equal, a low interest rate, lowproductivity growth environment is favourable to firms raising debt before diverting some ofthe cash raised towards equity holders instead of using it to fund production.

The effect of the labour supply parameter χ is worth commenting on. For a given financingconstraint ιt−1, high values of the parameter χ reflect more dislike to work by households. Thisin turn implies that wages have to remain relatively high after a negative productivity shockto maintain enough workforce in work. As a result, the marginal return of spending at thespending constraint is lower and this makes it more likely for spending to be unconstrainedby financing.17 This reasoning is confirmed by equation 4.16. On the other hand, the wageelasticity of labour supply has a greater negative effect on the steady state financing constraintι.18 Overall, as shown by equation 4.17, high values of χ increase the level of productivity droprequired for firms to enter an unconstrained spending mode from the steady state. This in turnmakes it less likely for the model’s main mechanism to operate.

When steady state rates are close to zero, the steady state approximations used to establishthe relationship 4.17 are not valid any more. Indeed, when costs of borrowing are very low,it becomes more likely for the model’s mechanism to operate. Firms take this into accountand reduce their steady state financing accordingly as per the investment equation 4.15. Thismeans that financing is lower than the approximation value used to derive equation 4.17. Whichimplies that the exact critical productivity u∗ is lower than the one suggested by equation 4.17.The point concerning the steady state financing when rates are low will be made clearer whenconsidering the effect of the model mechanism on steady state variables in section 5.

4.4 Equilibrium and Market Clearing

The equilibrium is realized when prices (ht, rt) and the quantities ct, bt, ιt, kt, and lt are suchthat firms maximize expected profit at the financing stage subject to the technology constraint

17Note that, at the constraint, the consumption/leisure indifference equation for households can be written ht+1 = ιt+χct+1

and that the marginal return on ons spending is γeut+1ιγ−1t /hγt+1.

18See equation B.11 of appendix B.3.

21

and maximize profit at the spending stage subject to the technology and financing constraints,households maximize utility subject to their budget constraint and the various markets withinthe economy clear. These markets are:

• The labour market where households labour supply must meet firms’ labour demand.

• The good’s market where all the production is consumed by households

ct = xt, (4.18)

where xt is the overall production of good i at time t

xt =ζγthγteut . (4.19)

• The bond market where households’ supply must meet the production sector financingdemands

bt = ιt. (4.20)

Finally, it is worth noting that the results of this section and those in the appendix B enablethe simulation of the model with no recourse to some perturbation technique. The detailedsimulation routine is presented in appendix D.2.

5 Simulation Results

5.1 Calibration and Steady State Results

The utility discount factor β determines the equilibrium rates of financing and is therefore keyto the main mechanism of the model. Mehra and Prescott (1985) report that between 1889 and1978 the average annual real return on equity was 7%, while the average annual real return onshort term debt was 1%. In the current set-up, I assume an investment horizon of one year, Ithen target an equilibrium interest rate closer to the return on short term debt at 2%, which ismore in line with the low real interest rates experienced since 2008. This pins down preferencediscounting β = 0.98. Following Atkeson and Kehoe (2005), I assume that the firm returnto scale parameter takes the value γ = 0.85.19 The volatility parameter σ = 2% is chosento match a quarterly productivity fluctuation around 1% and the mean reversion parameteris set at ρ = 0.7. The calibration is performed in the steady state to match a steady statelevel of employment of l = 0.33. This determines the value of the labour provision parameterχ = 1.69.20 Table 2 shows the steady state variables corresponding to the calibrated model.

19See also Atkenson, Khan, and Ohanian (1996). Importantly, the assumed value of γ does not impact the effects discussedin this section as long as some decreasing return to scale is maintained γ < 1.

20For more details regarding the steady state equations and the calibration process, please refer to appendix B.3 and D.1.

22

r 1.02 h 0.983 l 0.33x 0.390 c 0.390 ζ 0.324

Table 2: Assumed and calibrated model SS variables

Importantly, when the steady state rates are close enough to the zero lower bound (β > 0.98),the steady state is impacted by the model’s main mechanism. The calibration and steady statevariables would differ if one assumes that the financing constraint always holds. In order toassess the impact of the model mechanism on the steady state variables, I show the steadystate results in the presence and absence of the model’s main mechanism for different values ofutility discounting β in figure 4. Away from the zero lower bound, lower steady state interestrates increase the steady state financing levels. This implies higher steady state wages, labourand consumption. When steady state rates are below 2%, firms target a lower profitability atthe financing stage. This in turn makes it more likely that the profitability will not exceed thatof holding cash at the spending stage. Firms take this into account and reduce their financinglevels when compared to the benchmark model where firms always spend all the cash raisedat the financing stage. Close to the interest rates zero lower bound, the model’s mechanismstarts impacting the steady state financing such as higher discounting of households’ preferences(or lower steady states rates) has less effect on steady state output. While there is no directmonetary policy channel in the model, the last observation provides a potential reason formonetary policy to be less effective near the zero lower bound.

The drop in log productivity required for the model’s mechanism to operate as a functionof the steady state interest rates is shown in figure 5. The figure shows both the exact resultfollowing from formula 4.16 and the one derived from approximation 4.17. Clearly the approx-imation fails for low interest rates; independently of steady state interest rates, a minimumof a −1.5× standard deviation negative productivity drop is required for firms to enter anunderspending mode. As explained above, this is due to firms reacting to the low steady stateinterest rate by updating their financing behaviour to account for the higher likelihood of thefinancing raised being beyond what will be needed. Even when steady state rates are nearthe zero lower bound, the event of entering an unconstrained spending mode remains unlikely:under the assumption of normal productivity shocks the probability of underspending is alwayslower than 7% if the economy was previously in the steady state. Near the zero lower bound,the mechanism’s operates indirectly through lowering steady state financing, which moderatesthe likelihood of unconstrained spending.

23

Figure 4: Effect of changing utility discounting β on steady state variables. The benchmark model assumes thatfirms never underspend. The figures show the steady state variables as a function of the steady state rate 1/β− 1.

24

5.2 The Dynamic Effects of the Model’s Mechanism

The results in section 4 provide the foundation of a routine that enables the simulation of themodel without having to rely on some perturbation technique based on approximations aroundthe steady state. This is crucial as large shocks are required for the model’s mechanism tofunction. The used routine is detailed in appendix D.2.

I present impulse response functions illustrating the dynamic effects of the model’s mainmechanism. Figure 6 compares impulse responses of the model with the firm’s underspend-ing mechanism to a version of the model where the financing constraints are always binding(benchmark). The figure shows the impulse responses of the main model variables to a largenegative shock to productivity (−4× standard deviations).21 When the model’s main mecha-nism is functioning, the impact of the large negative shock is felt sooner as firms adapt aftergaining knowledge of the new lower levels of productivity by reducing expenditure before thelower financing levels affect the economy. On the other hand, when the firms cannot adjustexpenditure, their previous level of financing, that was based on a more optimistic view of pro-ductivity, helps dampen the severity of the current negative shock. The drop in spending bythe unconstrained firms lowers nominal labour demand and implies that wages do not increaseas much as they do when spending is always constrained. This dampens the reaction of labourprovision to the drop in productivity when spending is not constrained and, in turn, implies amore severe output drop. The effect on deposit rates is interesting, they are immediately lowerafter a negative shock hits the economy when firms cannot adjust expenditure. Consumersrealise that when firms are always constrained, part of the effects of the negative shocks arefelt in the period following the shock as firms adjust financing. Consumption is therefore ex-pected to be lower in the period immediately following the shock. The consumption smoothinghouseholds react by increasing demand for bonds. This in turn causes rates to drop lower thanthe steady state level. When firms can adjust spending, the consumption is at its lowest levelimmediately following shock and is expected to increase afterwards, interest rates are thereforehigher than in the steady state.

Beside the direct impact consisting of pushing firms towards an unconstrained spendingmode following large negative shocks, the model mechanism also has indirect effects that aremore visible following positive shocks to productivity. To illustrate these effects, figure 7reports the responses of the model and the benchmark model to moderate positive and negativeshocks (1× standard deviation). Given the moderate size of the shock, firms do not enter anunconstrained spending mode whether the model’s mechanism is present or not. This impliesthat, in the period when the shock happens, the reaction is similar in the presence and absenceof the model’s mechanism.22 Interest rates drop following a positive shock. This is expectedas households increase savings in order to smooth consumption. Lower interest rates imply

21As shown in figure 5, assuming 1/β − 1 = 2%, a negative log-productivity shock of more than 2× standard deviations isrequired for the mechanism to operate.

22The slight difference is caused by the models converging to different steady states.

25

Figure 5: Effect of changing utility discounting β on steady state variables on the critical log productivity droprequired for the model’s mechanism to operate. The figure shows the critical log productivity u∗, expressed as amultiple of the shocks standard deviation, as a function of the steady state rate 1/β − 1.

26

that the main mechanism is more likely to function, hence the greater difference between themodel and the benchmark financing levels in the periods following a positive shock to theeconomy. The greater difference in financing implies a greater difference in wages, hours andoutput following positive shocks. On the other hand, following a moderate negative shock,interest rates increase to counter the lower credit supply. This dampens the effect of themodel’s mechanism on financing and, in turn, reduces the difference between the model andthe benchmark in terms of wages, hours and output.

To summarise, the model’s main mechanism worsens the extreme lows of the business cycleby pushing firms into an underspending mode. In addition, the studied mechanism can slowdown the recoveries because of the reaction of interest rates to improving economic conditions.Both of these effects are exacerbated by a low interest rates and high volatility environment.

Figure 6: Impulse response functions following a large negative drop in productivity (−4× standard deviations).The graph shows relative deviations from the steady states for all variables but interest rates that are shownwithout any transformation.

27

Figure 7: Impulse response functions following a moderate positive and negative drop in productivity(1× standard deviation). The graph shows relative deviations from the steady states for all variables butinterest rates that are shown without any transformation.

6 Extension: Firms’ Underspending in a Network of

Multiple Industries

In this section, I extend the model to a multiple industry set-up where firms are linked throughinput-output relationships. In this set-up, n different consumption goods are produced byindustries indexed i = 1, ..., n. These industries are constrained by a Cobb-Douglas productionfunction and use each other’s output as intermediary input. The use by each industry of inputsprovided by other industries is given by the use input-output matrix W := (wij)i,j=1...n where∑n

j=1wij = 1. The input-output structure as summarised by the input-output matrix W iskey to the propagation of shocks among industries. This propagation happens through theproduction cost channel: shocks in one industry impact the price of the good it produces andcan impact the cost of production facing other industries as a result. The subsection below

28

provides the details underlying the model extension.

6.1 Extending the Model to a Multiple Industry Set-Up

Households

Households maximize their utility to decide over labour provision and the consumption of ndifferent goods subject to a budget constraint. The utility is extended to allow the consumptionof multiple goods as follows

U(l(t);C(t)) = χ ln (1− l(t)) +n∑i=1

θi ln(ci(t)), (6.1)

where ci(t) the good i consumption and θi the utility elasticity associated with consuming goodi, with

∑ni=1 θi = 1. A portion ψi of the production cost is financed through the issuance

of bonds that are held by households and that pay an interest r(t). The remaining financingneeds are secured through households’ equity investments. Consumers decide their consumptionbundle C(t) := (c1(t), ..., cn(t))′, bond holdings b(t) and labour provision l(t) by maximizinglifelong expected utility

maxC(t),l(t),b(t)

Et∞∑t=1

βtU(l(t);C(t)), (6.2)

while being subject to the budget constraint

b(t) +n∑i=1

pi(t)ci(t) = r(t− 1)b(t− 1) + h(t)l(t) + π(t), (6.3)

where pi(t) is the price of good i and, as in the single industry case, h(t) are wages and π(t)are the equity related cash flows. Consumers are therefore indifferent between goods as long as

pi(t)ci(t) = θics(t), (6.4)

where cs(t) :=∑n

i=1 pi(t)ci(t) denotes the overall consumption spending. On the other hand,bond rates must satisfy the Euler equation below for i = 1, ..., n,

1

cs(t)= βr(t)Et

1

cs(t+ 1). (6.5)

Finally, as in the single industry case, labour provision is governed by equation 4.5.

29

Firms

The consumption goods are produced by industries indexed i = 1, ..., n that are constrained bya Cobb-Douglas production function and that use each other’s output as intermediary input

fi(t;Xi(t); li(t)) = zi(t)li(t)γ

n∏j=1

xi,j(t)αwi,j , (6.6)

where li is the labour employed by industry i and Xi(t) := (xi,1(t), ..., xi,n(t))′ denotes the vectorof the outputs xi,j(t) of industries j = 1, .., n used as intermediary inputs by industry i. The useby each industry of intermediary inputs provided by other industries is determined by the useinput-output matrix W = (wij)i,j=1...n where

∑nj=1wij = 1 and the overall use of intermediary

inputs is governed by the elasticity parameter α. A firm’s productivity zi is determined by theindustry to which it belongs and is assumed to be log-normal

zi(t) = exp (ui(t)) , (6.7)

where ui(t) i = 1, ..., n are industry-specific shocks that are assumed to be AR(1)

ui(t) = ρiui(t− 1) + σiei(t),

where σi is an industry-specific volatility parameter and ρi denotes the industry-specific mean-reversion. The productivity processes are therefore driven by the iid normal innovations ei thatare also assumed to be independent across industries.

Firms finance a portion ψi of the potential production cost through bond contracts held byhouseholds and paying an interest rate r(t). The rest of the required financing is also providedby the households in the form of equity investments. They decide at time t the amount ιi(t) thatwill potentially be invested in next period’s production process. To do so, the firm maximizesits expected profit that is function of the expected sales proceed pi(t + 1)fi(.), the level offinancing ιi, the cost of rising debt r(t) and the opportunity cost as seen by the equity investorand represented by a rate of return on equity λi

maxιi(t)

Etpi(t+ 1)fi(t+ 1;Xi(t+ 1); li(t+ 1))− ιi(t) (ψir(t) + (1− ψi)λi) . (6.8)

Similarly to the single industry case, assuming decreasing returns to scale (α + γ < 1), onecan derive an industry-specific equation linking the level of financing within industry i to theexpected productivity within the same industry, expected sale prices and expected productioncosts

Et[1ιi(t)1−α−γ<(α+γ)eui(t+1) pi(t+1)

κi(P (t+1);h(t+1)) (α+ γ) eui(t+1) pi(t+ 1)

κi (P (t+ 1);h(t+ 1))

]= (ψir(t) + (1− ψi)λi) ιi(t)1−α−γ ,

(6.9)

30

where κi is an index representing the cost of production facing firms within industry i. theindex κi is a function of the good prices P (t + 1) := (p1(t + 1), ..., pn(t + 1))′, wages h(t + 1)and the input-out matrix W = (wi,j)

κi(P (t+ 1);h(t+ 1)) :=(α + γ)α+γ

ααγγh(t+ 1)γ

n∏j=1

(pj(t+ 1)

wi,j

)αwi,j. (6.10)

The financing equation 6.9 confirms the importance of the decreasing returns to scale assump-tion in guaranteeing finite levels of financing demands. Additionally, Under the decreasingreturns to scale assumption, financing levels increase with expected sale prices and productiv-ity while being inversely related to the expected production costs κi. The production cost indexκi is key in propagating shocks originating in a single industry to the rest of the productionnetwork: a negative shock impacting industry j reduces good j supply and increases the priceof the same good as a result. This in turn increases the production cost κi facing all industriesi where the good j is used (these are the industries i such as wi,j 6= 0).

The main mechanism of the model functions in a similar way to the single industry case assummarised in the diagram in figure 3. A firm belonging to an industry i decides its financinglevel ιi(t) at time t, raises equity and debt financing before discovering the new productivityeui(t+1), new sale prices pt+1 and the new production cost it faces κi(t+ 1). At time t+ 1, thefirm assesses its own productivity as well as the prevailing wages and prices then decides itsoverall spending ζi(t+ 1) := h(t+ 1)li(t+ 1) +

∑nj=1 pj(t+ 1)xij(t+ 1) in order to maximize its

profit subject the previously determined spending constraint ιi

maxXi(t+1),li(t+1)

pi(t+ 1)fi(Xi(t+ 1); li(t+ 1))−Xi(t+ 1)′.P (t+ 1)− h(t+ 1)li(t+ 1), (6.11)

s.a. Xi(t+ 1)′.P (t+ 1) + h(t+ 1)li(t+ 1) ≤ ιi(t). (6.12)

The firm chooses whether to spend all the raised financing ιi(t) (constrained case) or to spendless than the raised financing level ζi(t + 1) < ιi(t) (unconstrained case) as per the followingequation

ζi(t+ 1)1−α−γ = minιi(t)1−α−γ, (α + γ)eui(t+1) pi(t+ 1)

κi(P (t+ 1); l(t+ 1)). (6.13)

The firm’s spending is then allocated to the various inputs taking into account the price of eachinput and the prevailing input-output structure

pj(t+ 1)xij(t+ 1) =α

α + γwijζi(t+ 1), (6.14)

h(t+ 1)li(t+ 1) =γ

α + γζi(t+ 1). (6.15)

31

The intuitions from the single-industry model are maintained, with firms entering unconstrainedspending when their industry’s log productivity is a lower than a critical value determined byprevious financing, sale prices pi and production costs κi. The input-output relations influencesthe model’s main mechanism through the production cost channel: a negative shock originatingin a subset of industries can propagate to other industries by increasing their production costs,thus making spending unconstrained even in industries where productivity is improving. Theeffect the production network has on the underspending mechanism is discussed in more detailsin subsection 6.2.

Model Closing and Market Clearing Conditions

Due to price indeterminacy, an additional constraint is required to close the model, I choose azero-inflation constraint

n∏i=1

pi(t)θi = 1. (6.16)

Note that this assumption is not as conspicuous as it might seem, for instance it impliesthat cash is inflation protected. In real life situations cash depreciates with inflation and theequivalent of the set-up I am assuming here would require the existence of some inflationprotected investment or very low inflation. Inflation protected investments do exit. Moreover,this model has been designed with the post 2008 low inflation period in mind. However, it isimportant to note that while this model can be adapted for the use of financial assets otherthan cash, a careful reconsideration of the firm problem would then be needed. Indeed, in orderfor financial asset returns to be compared to the returns of production projects, one need tocarefully consider issues related to the investment horizon corresponding to each alternative.23

These considerations are beyond the scope of this paper.For clarity, I extend the clearing conditions corresponding to all markets as follows:

• The labour market

l(t) =n∑i

li(t). (6.17)

• The markets for goods i = 1, ..., n

ci(t) +n∑j=1

xj,i(t) = xi(t), (6.18)

23This can be done, for example, by assuming that the firm has a two periods timeline where it makes its financing decisionat the beginning of its life cycle then gains knowledge about productivity after one time period and decides whether toinvest in a financial asset or produce before entering a production process that takes one time period or holding a financialinvestment for the same time period.

32

where xi(t) is the overall production of good i at time t

xi(t) =ζi(t)

α+γ

κi(P (t);h(t))eui(t). (6.19)

• The bond market where households’ supply must meet the production sector demand

b(t) =n∑i=1

ψiιi(t). (6.20)

In what remains of this section, I study the effect of the input-output relationships andthe effect of households consumption preferences on the model’s mechanism and present someindustry aggregation results. A careful study of the model in the multi-industry set-up isprovided by appendix C.1. The said appendix provides a number of theoretical results thatare used to derive the main result of subsection 6.2. These results enable the simulation of themultiple-industry model without having to rely on some perturbation based technique.24

6.2 Effect of Input-Output Relationships and Consumers’ Prefer-ences

In order to study the behaviour of the model’s main mechanism when the number of industriesmaking the productive sector becomes large, I focus on the situation where all industries enteran unconstrained spending mode. The proposition below provides a sufficient and necessarycondition for every industry to spend less then the financing constraint.25

Proposition 1. All industries are facing relaxed financing constraints if and only if

cs(t) ≤ 1

α + γminτi 6=0

ιi(t− 1)

τi, (6.21)

where cs(t) :=∑n

i=1 pi(t)ci(t) is the household’s consumption spending and the constants τiare non negative and are defined as: (τ1, ..., τn)′ := LΘ, with L being the Leontief matrixL := (In,n − αW ′)−1 and Θ := (θ1, ..., θn)′ a vector representing consumption preferences. Ifthe steady state financing rates si := ψi

1β

+ (1− ψi)λi are all positive and far enough from thezero lower bound and the economy is previously in the steady state, then all the industries wouldrelax their financing constraints if and only if consumer spending cs(t) verifies

cs(t)− cs ≤ − 1

α + γ[n∑j=1

(sj − 1)ιj)] maxτi 6=0

φiτi, (6.22)

24The routine is presented in appendix D.325The proof of the proposition is in Appendix C.4. It also follows immediately from proposition 7.

33

where ιi is the industry i steady state financing and (φ1, ..., φn)′ := LF , with F := (f1, ..., fn)being a vector representing the fraction of the steady state cost of financing of each industry tothe overall cost of financing: fi = (si−1)ιi∑n

j=1(sj−1)ιj.

Proposition 1 links the event where the whole economy enters an underspending mode to thelevels of raised financing and to the constants τi that are explicitly determined by consumptionpreferences as summarised by the vector Θ := (θ1, ..., θn)′ and the matrix αW := α(wi,j)i,j=1,...,n

summarising the input output relationships. As one might expect, higher financing levelsιi(t − 1) make it more likely for all industries to enter an underspending mode. On the otherhand, one can prove that in the absence of the model’s main mechanism, industry i produces afraction (1−α)τi of the overall output in the steady state. This means that the ratio ιi(t−1)/τi,key to condition 6.21, can be interpreted as relating the financing allocated to industry i tothe proportion of steady state output produced by the same industry in absence of the model’smechanism.

Condition 6.22 shows more explicitly the effect of overall cost of financing∑n

j=1(sj − 1)ιj.The lower the overall cost of financing the more likely it is for all industries to be unconstrainedby their financing levels. In the case where the cost of financing ratios F match preferences Θ,the Leontief matrix matters less to condition 6.22 as φi

τi= 1 for all industries. It is important

to note that condition 6.22 fails to describe the model’s main mechanism when real financingrates are too close to the zero lower bound. One can therefore not use this condition to studythe model’s behaviour close to the ZLB. The reason for this is that the steady state financingapproximation used to derive 6.22 from 6.21 depends on the firms ignoring the likelihood of theunconstrained spending at financing stage. As documented in the single industry case, whenfinancing rates are close to the ZLB, unconstrained spending becomes likely enough for the firmto start taking it into consideration at the financing stage and lowering its financing demandas a result.

When no industry is constrained, consumer spending is log-normally distributed with thelog-normal volatility:

σ∗cs :=√

Θ′L′V LΘ, (6.23)

where V is the variance/covariance matrix of the industry shocks ei. This formulation enablesto see that potential industry shocks correlations would increase the volatility σ∗cs and thereforemake the model mechanism more likely to operate. In the current set-up V has zero off diagonalelements. To simplify further, assume that: σi = σ for i = 1, ..., n. Then the formula for σ∗cssimplifies as follows:

σ∗cs = σ

√√√√ n∑i=1

τ 2i , (6.24)

with the constants τi being the element of the vector T := (τi)i=1,...,n := LΘ.

34

The vector T comprises the effect of both preferences Θ and the input-output matrix W onthe volatility σ∗cs. To fix ideas, lets first study the effect of preferences. To that effect assumethat all industries are disconnected: W = In,n. Then the value of σ∗cs would be

σ∗cs =σ

1− α

√√√√ n∑i=1

θ2i . (6.25)

In the case where households preferences restrict consumption to single good: θ1 = 1 andθi = 0 for i > 1, the volatility of consumer spending is maximal σ∗cs = σ

1−α while it is minimal

σ∗cs = σ1−α

1√n, when consumers like all goods equally θi = 1/n for i = 1, .., n. Everything else

being equal, an economy where consumers preferences are spread across many goods wouldhave a lower aggregate fluctuations and the mechanism of the model would be less likely tooperate.26

To isolate the impact of the input-output network on aggregation, one can assume thathouseholds do not prefer some goods to others (θi = 1/n). This puts us in the set-up presentedin Acemoglu, Carvalho, Ozdaglar, and Tahbaz-Salehi (2012) and leads to the same conclusion,namely that fluctuations are higher for networks characterised by dominant industries that playan asymmetric role as a supplier to other sectors. An example of such networks is the ”star”production network (figure 9). I refer the reader to the aforementioned paper for more detailson the network effects on aggregation of industry-specific shocks and turn to network effects inthe context of the main mechanism studied in this paper. The following proposition provides acharacterisation of the critical aggregate industry productivity below which all industries enteran unconstrained spending mode assuming the economy was previously at the steady state.27

Proposition 2. Assuming the economy is previously in the steady state, that labour provisionis inelastic (l(t) = l), that the return expected by equity investors is the same across industries(λi = λ, for i = 1, ..., n) and that the resulting common steady state financing rate is positiveand far enough from the zero lower bound, then all industries would enter an unconstrainedspending mode if and only if the aggregate shock is lower than a critical value u∗:

T ′.U ≤ u∗, (6.26)

where, as before, T := (τ1, ..., τn)′ := LΘ and U := (u1, ..., un)′ is the vector of industry shocksand. The critical value u∗ is given by

u∗ = − s

1− α+

γ

1− αln

(s− α1− α

)+ (1− α− γ)T ′.

[T − E

]+ ln

(min

i=1,...,n

εiτi

), (6.27)

where s = ψ 1β

+ (1 − ψ)λ is the common steady state financing rate across industries, E :=

(ε1, ..., εn)′ := (1/s) (In,n − (α/s)W ′)−1 Θ and the log values are noted using the . upper script.

26Appendix C.1 explains further the centrality of consumption spending to output fluctuations in this model.27Proof in appendix C.4.

35

1

2

3

4

Figure 8: Fully connected network in an economy with 4 industries. Arrows show the sense of inputprovision: they depart from the industry providing the intermediary input and arrive to the industry usingthe good as an input.

Proposition 2 shows that both the nature of the input-output relatioships and the level ofsteady state financing rate matter to the aggregation of the model’s mechanism. To assess theeffect of the input-output matrix, I assume that θi = 1/n for i = 1, ..., n and study the model’saggregation under two notable networks: the fully connected network and the star network.

Fully connected network: In the case where all industries play a symmetric role in theeconomy and are all equally interconnected (wij = 1/n, θi = 1/n), the consumer spendingvolatility would be minimal: σ∗cs = σ

1−α1√n. The critical value of the aggregate shock in this

case is given byu∗ = − ln(s). (6.28)

The portability of all the industries entering an unconstrained spending mode from the steadystate converges to zero for large n: Φ(−1−α

σln(s)

√n) ≈ 0 for n >> 1. Under the fully connected

network, the model’s mechanism will not operate for very disaggregated economies (large n) aslong as the industry-specific shocks remain independent of each other.

Star network: On the other hand, if one assumes that one industry (let’s say industry 1) isthe only provider of intermediary input and that no good is preferred to others by consumers(wij = 1 if j = 1 and wij = 0 otherwise, θi = 1/n for all i), one finds a higher value of consumer

36

1

2 3

4

Figure 9: Star network in an economy with 4 industries. Arrows show the sense of input provision: theydepart from the industry providing the intermediary input and arrive to the industry using the good as aninput.

spending volatility

σ∗cs = σ

√(n− 1)

1

n2+

(1

n+

α

1− α

)2

≈ ασ

1− αfor n >> 1. (6.29)

The critical aggregate shock value converges to the following constant for a large number ofindustries n

u∗star ≈ −1 + γ

1− αln(s)− (1− α− γ) ln

(s− α1− α

). (6.30)

So that the probability of all the industries entering an unconstrained spending mode from thesteady state remains stable for large number of industries around the positive constant value:Φ(−u∗star

σ1−αα

). Under a star network, the mechanism of the model can operate, independentlyof the number industries populating the supply side of the economy.

The results point towards the fact that input-output production networks where a smallnumber of industries play an important role in providing intermediary inputs would imply thatthe mechanism of the model is more likely to operate and does not cease to function when thenumber of independent industries is large. These results are consistent with and guided byexisting literature, for instance Acemoglu, Carvalho, Ozdaglar, and Tahbaz-Salehi (2012) andextend a literature mainly concerned with the network origins of aggregate output volatility ina direction where part of the asymmetries affecting the distribution of aggregate variables canalso be attributed to the nature of the production networks prevailing in the economy.

37

7 Conclusion

I presented a financial mechanism rooted in the way firms change their behaviour towardssetting current expenditure as a reaction to unexpected large negative shocks to productivity.When affected by large drops in productivity, firms can react by reducing spending to lowerlevels than those permitted by the financial resources at their disposal. The change of spendingbehaviour can worsen and lengthen the trough of the business cycle, as firms adjust theirexpenditure before the effects of lower corporate financing hit the economy. This mechanismhas important implications in terms of business cycle asymmetry. Firms would only adjustexpenditures following large negative shocks to productivity while they remain constrained bypreviously determined levels of financing if productivity is improving.

I also showed that the model’s main mechanism is more likely to operate when interest ratesare low. This has two main implications. First, if improving productivity and output causelower interest rates, the likelihood of the mechanism functioning increases. In order to accountfor the higher likelihood to enter an underspending mode, firms would respond by targetinglower financing levels relative to a model where the financing constraint always holds. Thisimplies that the presence of the model’s mechanism can slow the improvements in output duringperiods of improving productivity by indirectly operating through the interest rates channel.Secondly, the effect of interest rates levels on the model’s mechanism has some monetary policyimplications. An expansionary monetary policy that pushes interest rates close to the zerolower bound is expected to make it possible for firms to take on less profitable projects. Theseprojects being barely profitable at the financing stage, they are less likely to be profitable atall later on if the firm’s productivity deteriorates or if the macroeconomic conditions are worse.The firm’s take this into account and while it still increases its financing demand to respond tolower financing rates, this response is muted by its fear to raise more money than what will berequired at a later stage. This dampens the firms’ reaction to lower interest rates and makesmonetary policy less potent.

To provide an empirical validation of the model, I study the effect of productivity on thepropensity of firms to pay shareholders back and on the size of these payouts. I show thathigher firm level productivity lowers both the likelihood and the levels of the payouts. Iassume that part of the cash diverted towards investors would have been spent on improvingor increasing production had the firm decided against rewarding shareholders in the shortterm. The latter assumption and the negative empirical relationship between productivityand investor payouts indicate that firms decrease spending to respond to negative productivityshocks. By considering the financing and spending problems facing the firm separately, themodel I present gives firms a greater and more realistic economic agency and helps illustratethe relationship between productivity, firm spending and the levels of cash diverted towardsshareholders.

The model is then extended to a multi-industry set-up where firms are linked trough input-output relationships and where industry-specific shocks drive aggregate fluctuations and are

38

assumed to be independent of each other. I showed that a negative productivity shock origi-nating in a subset of industries can propagate through intermediary input channels and makeother industries enter a low spending mode where they spend less than the cash previouslyearmarked for production. These intermediary input channels are key to the functioning ofthe multi-industry version of the model and provide an additional explanation to how crisespropagate across industries.

Importantly, the model’s mechanism does not necessarily become irrelevant as the numberof industries in the economy increases. To the contrary, I showed that under some assumptionson the nature of the input-output relationships, the likelihood of the mechanism operating isless affected by the level of disaggregation of the supply side of the economy. The nature ofthe input-output production network is key to the aggregation of the model’s mechanism: aproduction network where a small number of industries provide most of the intermediary inputin the economy will maintain the model’s mechanism irrespective of the degree of industrialdiversification. This is in line with the literature on the effects of production networks on theaggregation of idiosyncratic volatilities.

The model could be extended to allow for capital accumulation. In the presence of persistentcapital, current spending cuts by the corporate sector would imply lower future capital andwould affect output for longer as a result. This would strengthen the main mechanism ofthe model and make its effects more persistent. Enriching the model with persistent capitalconsiderably complicates the firm’s spending decision and will be the subject of future research.Another area for extending the model concerns its use to analyse monetary policy near theinterest rates zero lower bound. This is of particular interest, given that the model’s mainmechanism is particularly potent when real interest rates are low.

39

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A Empirical Appendix

A.1 Data and derived variables

These variables are reported directly by the data: assets’ value, cash and cash equivalent, net income,CAPEX spending, R&D spending and the number of employees. Other variables are derived as follows.

Market Capitalisation = ”Common Shares Outstanding” × ”Price Close - Annual - Calendar”;

Debt = ”Debt in Current Liabilities - Total” + ”Long-Term Debt - Total”;

Market to Book = ”Market Capitalisation” / ”Assets - Total”;

Value Added = ”Operating Income Before Depreciation” + ”Employees” x ”Average Wage fromthe Social Security Administration”;

Share Buybacks = 1 year change in ”Treasury Stock - Common”, if the above is negative or missinguse: ”Purchase of Common and Preferred Stock” minus ”Sale of Common and Preferred Stock”. Ifboth figures are negative or missing, Share Buybacks are set to zero for the corresponding period.

Except for the assets value, all the variables are scaled either using the percentile form of thevariable or through division by the previous time period’s assets or the previous market capitalisation.All the variables but those in percentile form are 1% Winsorised to deal with outlier values. Thesedata transformations are summarised in table 3.

Divided by previous assets Percentile form Divided by previous market cap. Winsorised (1%)

Assets XCash Distributed X XDividends X XShare Buybacks X XProductivity X XMarket to Book XMarket Capitalisation XCash X XNet Income X XDebt X XCAPEX X XR&D X XEmployees X X

Table 3: Summary of transformation applied to the models’ variables.

A.2 Descriptive Statistics

I present the summary statistics of the indicators used to construct the regressions variable in table4, the summary statistics of the transformed variables are in table 5. The correlation matrix of thevariables as used in the regressions are in table 6.

43

mean sd min p1 p25 p50 p75 p99 maxCash Distributed 73.888 601.318 0.000 0.000 0.000 0.000 5.140 1503.000 67643.805Dividends 47.022 389.746 0.000 0.000 0.000 0.000 2.037 982.000 67643.805Shares Buyback 23.639 313.908 0.000 0.000 0.000 0.000 0.000 461.587 34420.000TFP 0.108 0.565 -19.817 -0.612 0.063 0.096 0.143 0.865 62.818Market Cap. 2256.373 13201.111 0.000 0.673 21.739 107.184 619.620 43294.660 1819781.875CAPEX 148.673 977.177 -401.609 0.000 0.765 5.202 34.439 2760.000 65028.000RD 85.499 487.317 -0.546 0.000 0.187 2.724 17.110 2015.000 14035.289Market Cap. 2256.373 13201.111 0.000 0.673 21.739 107.184 619.620 43294.660 1819781.875Assets 2200.237 13328.365 0.500 0.976 20.940 106.471 601.955 39042.000 797769.000Cash 212.667 1406.270 -40.000 0.000 1.248 8.535 52.369 4007.000 91052.000Net Income 91.633 1056.326 -98696.000 -353.714 -2.317 1.387 18.784 2285.294 125000.000Debt 668.750 5355.187 0.000 0.000 1.671 16.847 168.752 11122.700 523762.000Employees 9.213 37.640 0.000 0.002 0.163 0.849 4.350 144.785 2200.000

Table 4: Summary statistics of the unscaled data used to construct the dependent and independent variables used in thevarious regressions: all cash variables are in millions of U.S. dollars, the number of employees is in thousands, data for the1980-2013 period.

mean sd min p1 p25 p50 p75 p99 maxCash Dist. 0.019 0.040 0.000 0.000 0.000 0.000 0.023 0.244 0.244dividend 0.010 0.021 0.000 0.000 0.000 0.000 0.011 0.117 0.117shares Buybacks 0.008 0.026 0.000 0.000 0.000 0.000 0.000 0.171 0.171TFP 0.002 0.009 -0.043 -0.043 0.000 0.000 0.002 0.045 0.045Market/Book 1.784 2.748 0.047 0.047 0.448 0.901 1.841 17.174 17.174CAPEX 0.091 0.125 0.000 0.000 0.023 0.050 0.104 0.760 0.760RD 0.083 0.131 0.000 0.000 0.004 0.032 0.106 0.723 0.723Cash 0.191 0.308 0.000 0.000 0.022 0.077 0.223 1.812 1.812Net Income -0.039 0.283 -1.497 -1.497 -0.056 0.031 0.084 0.430 0.430Debt 0.286 0.264 0.000 0.000 0.080 0.237 0.408 1.369 1.369Employees 0.013 0.020 0.000 0.000 0.003 0.007 0.016 0.100 0.187

Table 5: Summary statistics of the scaled variables used in the regression models, data for the 1980-2013 period.

Cash Dist. Div. Shares Buy. TFP Mkt/Book CAPEX R&D Mkt Cap. Assets Cash Net Inc. Debt Empl.Cash Dist. 1.00 0.65 0.75 -0.02 -0.15 -0.07 -0.18 0.15 0.13 -0.12 0.13 -0.00 -0.03Div. 0.65 1.00 0.05 -0.03 -0.14 -0.05 -0.21 0.24 0.19 -0.15 0.15 0.01 -0.02Shares Buy. 0.75 0.05 1.00 -0.01 -0.10 -0.07 -0.10 0.05 0.05 -0.06 0.07 -0.02 -0.02TFP -0.02 -0.03 -0.01 1.00 -0.03 0.07 -0.22 -0.16 -0.07 -0.05 0.48 0.05 0.21Mkt/Book -0.15 -0.14 -0.10 -0.03 1.00 0.25 0.50 0.15 -0.07 0.63 -0.21 -0.06 0.10CAPEX -0.07 -0.05 -0.07 0.07 0.25 1.00 0.09 0.08 -0.04 0.13 -0.01 0.26 0.17R&D -0.18 -0.21 -0.10 -0.22 0.50 0.09 1.00 -0.08 -0.12 0.58 -0.50 -0.16 -0.08Mkt. Cap. 0.15 0.24 0.05 -0.16 0.15 0.08 -0.08 1.00 0.46 0.02 0.27 0.02 -0.12Assets 0.13 0.19 0.05 -0.07 -0.07 -0.04 -0.12 0.46 1.00 -0.09 0.10 0.03 -0.15Cash -0.12 -0.15 -0.06 -0.05 0.63 0.13 0.58 0.02 -0.09 1.00 -0.24 -0.14 0.04Net Inc. 0.13 0.15 0.07 0.48 -0.21 -0.01 -0.50 0.27 0.10 -0.24 1.00 -0.02 0.06Debt -0.00 0.01 -0.02 0.05 -0.06 0.26 -0.16 0.02 0.03 -0.14 -0.02 1.00 0.09Empl. -0.03 -0.02 -0.02 0.21 0.10 0.17 -0.08 -0.12 -0.15 0.04 0.06 0.09 1.00

Table 6: Correlation matrix of regressions’ variables (1980-2013).

A.3 More Empirical Results

Further empirical results are presented in this subsection. First, I show in figures 10 and 11 theresults of the static logit regressions explaining the propensity to pay dividends and to buy sharesback using a single growth indicator: TFP, market/book or investment expenses (CAPEX and R&D).The results suggest that TFP is better able to predict the propensity of firms to pay shareholdersthrough dividends than the propensity to pay through share buybacks. I also present the completeresults of the logit regressions including all growth indicators results and explaining, respectively, thepropensity to return cash, to pay dividends and to buy shares back in figures 12 to 14.

The dynamic fixed effect regression results for the size of dividends and share buybacks are in

44

tables 7 and 8. The results show that both dividends and share buybacks sizes are persistent processeswith dividends’ size showing stronger persistence. When explaining the size of dividends and sharebuybacks separately from each other, TFP fails to have a statistically significant effect even whenother growth indicators are excluded from the regression. This provides extra motivation to considerthe combined ”returned cash” variable. Firms investing in capital expenditure tend to execute smallershare buybacks operation, while CAPEX investments do not appear to affect the size of dividends.Large firms by market capitalisation tend to pay large dividends relative to their market capitalisationwith assets’ size having little impact on the size of dividends. On the other hand, large firms by assetsare more likely to complete larger share buyback operations with little effect attributed to the marketcapitalisation percentile. Higher net income increases the size of dividends while not impacting thesize of share buybacks operations. The results also suggest that firms use share buybacks more thandividends to manage relatively high cash balances. Finally, hiring reduces the size of both dividendsand share buybacks relative to market capitalisation.

Full Model TFP Effect Market/Book Effect Investment EffectL.dividend 0.476∗∗∗ 0.485∗∗∗ 0.476∗∗∗ 0.486∗∗∗

L2.dividend 0.0807∗∗∗ 0.0815∗∗∗ 0.0803∗∗∗ 0.0814∗∗∗

L3.dividend 0.0484∗∗∗ 0.0489∗∗∗ 0.0481∗∗∗ 0.0489∗∗∗

L.TFP -0.122 -0.245L.Market/Book -0.00131∗∗∗ -0.00130∗∗∗

L.CAPEX 0.00198 -0.000475L.Market Cap. Percentile 0.000111∗∗∗ 0.0000628∗∗ 0.000115∗∗∗ 0.0000706∗∗

L.Assets 5.68e-08∗ 7.98e-08∗∗ 5.13e-08 7.24e-08∗

L.Cash 0.00409∗∗ 0.00304∗ 0.00397∗∗ 0.00295∗

L.Net Income 0.00682∗ 0.000652 0.00680∗∗ -0.0000160L.Debt -0.00106 -0.000881 -0.000940 -0.000868L.Employees -0.0345∗ -0.0449∗∗ -0.0334∗ -0.0445∗∗

Constant 0.00423∗∗ 0.00600∗∗∗ 0.00406∗∗ 0.00551∗∗∗

AIC -149110.5 -148992.1 -149112.0 -148987.9

∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

Table 7: Dynamic two way fixed effect model FE model explaining the size of dividends.

Full Model TFP Effect Market/Book Effect Investment EffectL.shares Buybacks 0.106∗∗∗ 0.119∗∗∗ 0.108∗∗∗ 0.116∗∗∗

L2.shares Buybacks 0.000624 0.00365 0.00164 0.00227L3.shares Buybacks 0.0304∗ 0.0331∗ 0.0312∗ 0.0319∗

L.TFP 0.302 -0.275L.Market/Book -0.00324∗∗∗ -0.00336∗∗∗

L.CAPEX -0.0217∗∗ -0.0283∗∗∗

L.Market Cap. Percentile 0.0000603 -0.0000875 0.0000481 -0.0000693L.Assets 0.000000401∗∗∗ 0.000000534∗∗∗ 0.000000425∗∗∗ 0.000000501∗∗∗

L.Cash 0.0286∗∗∗ 0.0246∗∗∗ 0.0293∗∗∗ 0.0239∗∗∗

L.Net Income 0.00735 -0.0117 0.00541 -0.00786L.Debt -0.0192∗∗∗ -0.0203∗∗∗ -0.0206∗∗∗ -0.0184∗∗∗

L.Employees -0.270∗∗∗ -0.316∗∗∗ -0.285∗∗∗ -0.295∗∗∗

Constant 0.0293∗∗∗ 0.0345∗∗∗ 0.0292∗∗∗ 0.0346∗∗∗

AIC -50282.3 -50209.9 -50276.7 -50225.6

∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

Table 8: Dynamic two way fixed effect model FE model explaining the size of share buybacks.

45

-150

-100

-50

050

1980 1990 2000 2010 2020year

TFP estimate 95% lower limit95% upper limit

-1.5

-1-.5

0

1980 1990 2000 2010 2020year

Market/Book estimate 95% lower limit95% upper limit

-15

-10

-50

1980 1990 2000 2010 2020year

CAPEX estimate 95% lower limit95% upper limit

-25

-20

-15

-10

-50

1980 1990 2000 2010 2020year

RD estimate 95% lower limit95% upper limit

Figure 10: Repeated logit cross-section regressions estimates with 95% confidence boundaries corresponding to the effectsof TFP, Market/Book and investment variables (CAPEX and R&D) on the firm’s propensity to pay shareholders throughdividends. The logit regressions are repeated for every year from 1980 to 2013. The TFP marginal effect is estimated withoutcontrolling for Market/Book, CAPEX and R&D, The Market/Book marginal effect is estimated without controlling for TFP,CAPEX and R&D and the CAPEX and R&D effects are estimated in the same repeated regressions that exclude both TFPand Market/Book. Controls common to all regressions include: market capitalisation, assets, cash, net income, debt and thenumber of employees. Grey areas indicate NBER recession periods.

A.4 Tests

The studied dependent variables follow strongly persistent processes. Failing to correct for suchpersistence can cause serial correlation tests to fail. I present the serial correlation test in table 10.The tests show that serial correlation is either statistically insignificant or too low to seriously affectthe result of the regressions.

Running dynamic panel data models for a large number of units and a small number of observationsper unit comes with the issue of a biased estimate of the coefficient of the lagged dependent variables.

46

-100

-50

050

1980 1990 2000 2010 2020year

TFP estimate 95% lower limit95% upper limit

-1-.5

0

1980 1990 2000 2010 2020year

Market/Book estimate 95% lower limit95% upper limit

-10

-50

5

1980 1990 2000 2010 2020year

CAPEX estimate 95% lower limit95% upper limit

-15

-10

-50

1980 1990 2000 2010 2020year

RD estimate 95% lower limit95% upper limit

Figure 11: Repeated logit cross-section regressions estimates with 95% confidence boundaries correspondingto the effects of TFP, Market/Book and investment variables (CAPEX and R&D) on the firm’s propensityto pay shareholders through share buybacks. The logit regressions are repeated for every year from 1980 to2013. The TFP marginal effect is estimated without controlling for Market/Book, CAPEX and R&D, TheMarket/Book marginal effect is estimated without controlling for TFP, CAPEX and R&D and the CAPEXand R&D effects are estimated in the same repeated regressions that exclude both TFP and Market/Book.Controls common to all regressions include: market capitalisation, assets, cash, net income, debt and thenumber of employees. Grey areas indicate NBER recession periods.

The absence of an important serial correlation in the error terms provides an indication that thereis little underestimation of the lagged variables coefficient if any. To gain more confidence aroundthis issue, regressions are run where the number of observations per firm is unrestricted, is requiredto be higher than 30 (T ≥ 30) (table 11) . The results show that, as expected by the theory, alow number of observation per unit leads to underestimating the autoregressive coefficients. The

47

Full Model TFP Effect Market/Book Effect Investment EffectL.Cash Dist. 0.0848∗∗∗ 0.0948∗∗∗ 0.0856∗∗∗ 0.0942∗∗∗

L2.Cash Dist. 0.0104 0.0137∗ 0.0111 0.0123L3.Cash Dist. 0.00137 0.00307 0.00210 0.00240L.TFP -0.279∗ -0.511∗∗∗

L.Market/Book -0.00418∗∗∗ -0.00438∗∗∗

L.CAPEX -0.0136∗∗∗ -0.0237∗∗∗

L.Market Cap. Percentile 0.000202∗∗∗ -0.0000396 0.000212∗∗∗ 0.00000660L.Assets 0.000000472∗∗∗ 0.000000628∗∗∗ 0.000000473∗∗∗ 0.000000573∗∗∗

L.Cash 0.0300∗∗∗ 0.0200∗∗∗ 0.0305∗∗∗ 0.0197∗∗∗

L.Net Income 0.0194∗∗∗ 0.00882∗ 0.0161∗∗∗ 0.00755∗

L.Debt -0.0162∗∗∗ -0.0177∗∗∗ -0.0174∗∗∗ -0.0157∗∗∗

L.Employees -0.226∗∗∗ -0.288∗∗∗ -0.239∗∗∗ -0.279∗∗∗

Constant 0.0333∗∗∗ 0.0418∗∗∗ 0.0321∗∗∗ 0.0404∗∗∗

AIC -222850.4 -222349.5 -222825.2 -222379.2

∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

Table 9: Dynamic two way fixed effect model FE model explaining the size of distributed cash, no exclusion of firms basedon the number of observations.

Cash Dist. Resid. Div. Resid. Shares Buy. Resid.L.residuals -0.0157 -0.0151 0.0271∗∗

L2.residuals -0.0198∗ -0.00164 0.0174∗

L3.residuals -0.0122 0.00187 -0.000427L4.residuals -0.0126 -0.00202 -0.0117L5.residuals -0.0203∗ -0.0133 -0.0215∗∗

L6.residuals -0.0145 0.00523 -0.00812L7.residuals -0.0175∗ 0.0107 -0.0294∗∗∗

Constant 0.000289∗∗∗ -0.000513∗∗∗ -0.0129∗∗∗

Observations 21834 21834 21930

∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

Table 10: Autocorrelation tests (Full Models).

differences in the lagged dependent variables estimates remain small when increasing the minimumnumber of observations per firm from 15 to 30.

48

Cash Dist. T ≥ 15 T ≥ 30 Div. T≥ 15 T ≥ 30 Shares Buy. ≥ 15 T ≥ 30L.Cash Dist. 0.0848∗∗∗ 0.165∗∗∗ 0.187∗∗∗

(0.00767) (0.0102) (0.0169)

L2.Cash Dist. 0.0104 0.0466∗∗∗ 0.0523∗∗∗

(0.00651) (0.00798) (0.0122)

L3.Cash Dist. 0.00137 0.0437∗∗∗ 0.0588∗∗∗

(0.00667) (0.00843) (0.0145)

L.dividend 0.363∗∗∗ 0.476∗∗∗ 0.472∗∗∗

(0.0123) (0.0167) (0.0323)

L2.dividend 0.0618∗∗∗ 0.0807∗∗∗ 0.134∗∗∗

(0.00987) (0.0134) (0.0258)

L3.dividend 0.0278∗∗∗ 0.0484∗∗∗ 0.0603∗∗

(0.00780) (0.00962) (0.0205)

L.shares Buybacks 0.0267∗∗ 0.106∗∗∗ 0.106∗∗∗

(0.00985) (0.0143) (0.0225)

L2.shares Buybacks -0.0358∗∗∗ 0.000624 0.0133(0.00937) (0.0132) (0.0191)

L3.shares Buybacks -0.0286∗∗ 0.0304∗ 0.0131(0.01000) (0.0134) (0.0191)

Observations 58812 26029 9329 43338 24287 9255 32775 12526 4660

Standard errors in parentheses∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

Table 11: Lagged dependent variables tests. The lagged variables coefficients from the model including allfirms are shown next to estimates of the same coefficients from a models excluding firms with less than 15observations and 30 observations respectively.

49

-100

-50

050

1980 1990 2000 2010 2020year

TFP estimate 95% lower limit95% upper limit

-1-.8

-.6-.4

-.20

1980 1990 2000 2010 2020year

Market/Book estimate 95% lower limit95% upper limit

-10

-50

5

1980 1990 2000 2010 2020year

CAPEX estimate 95% lower limit95% upper limit

0.0

2.0

4.0

6.0

8

1980 1990 2000 2010 2020year

Market Cap. Percentile estimate 95% lower limit95% upper limit

-.000

50

.000

5.0

01.0

015

1980 1990 2000 2010 2020year

Assets estimate 95% lower limit95% upper limit

-3-2

-10

1

1980 1990 2000 2010 2020year

Cash estimate 95% lower limit95% upper limit

Figure 12: Repeated logit cross-section regressions estimates with 95% confidence boundaries for the full model explainingthe distributed cash (continued below).

50

05

1015

1980 1990 2000 2010 2020year

Net Income estimate 95% lower limit95% upper limit

-4-3

-2-1

0

1980 1990 2000 2010 2020year

Debt estimate 95% lower limit95% upper limit

-40

-20

020

1980 1990 2000 2010 2020year

Employees estimate 95% lower limit95% upper limit

Figure 12: Repeated logit cross-section regressions estimates with 95% confidence boundaries for the full model explainingthe distributed cash.

51

-100

-50

050

1980 1990 2000 2010 2020year

TFP estimate 95% lower limit95% upper limit

-1.5

-1-.5

0

1980 1990 2000 2010 2020year

Market/Book estimate 95% lower limit95% upper limit

-10

-50

5

1980 1990 2000 2010 2020year

CAPEX estimate 95% lower limit95% upper limit

0.0

2.0

4.0

6.0

8.1

1980 1990 2000 2010 2020year

Market Cap. Percentile estimate 95% lower limit95% upper limit

-.000

20

.000

2.0

004

.000

6

1980 1990 2000 2010 2020year

Assets estimate 95% lower limit95% upper limit

-6-4

-20

2

1980 1990 2000 2010 2020year

Cash estimate 95% lower limit95% upper limit

Figure 13: Repeated logit cross-section regressions estimates with 95% confidence boundaries for the full model explainingthe propensity to pay dividends (continued below).

52

05

1015

1980 1990 2000 2010 2020year

Net Income estimate 95% lower limit95% upper limit

-4-3

-2-1

0

1980 1990 2000 2010 2020year

Debt estimate 95% lower limit95% upper limit

-20

-10

010

2030

1980 1990 2000 2010 2020year

Employees estimate 95% lower limit95% upper limit

Figure 13: Repeated logit cross-section regressions estimates with 95% confidence boundaries for the full model explainingthe propensity to pay dividends.

53

-100

-50

050

1980 1990 2000 2010 2020year

TFP estimate 95% lower limit95% upper limit

-1-.8

-.6-.4

-.20

1980 1990 2000 2010 2020year

Market/Book estimate 95% lower limit95% upper limit

-10

-50

5

1980 1990 2000 2010 2020year

CAPEX estimate 95% lower limit95% upper limit

-.02

0.0

2.0

4.0

6

1980 1990 2000 2010 2020year

Market Cap. Percentile estimate 95% lower limit95% upper limit

-.000

1-.0

0005

0.0

0005

.000

1

1980 1990 2000 2010 2020year

Assets estimate 95% lower limit95% upper limit

-2-1

01

23

1980 1990 2000 2010 2020year

Cash estimate 95% lower limit95% upper limit

Figure 14: Repeated logit cross-section regressions estimates with 95% confidence boundaries for the full model explainingshare buybacks (continued below).

54

02

46

8

1980 1990 2000 2010 2020year

Net Income estimate 95% lower limit95% upper limit

-3-2

-10

1

1980 1990 2000 2010 2020year

Debt estimate 95% lower limit95% upper limit

-40

-20

020

1980 1990 2000 2010 2020year

Employees estimate 95% lower limit95% upper limit

Figure 14: Repeated logit cross-section regressions estimates with 95% confidence boundaries for the full model explainingshare buybacks.

55

B Technical Appendix

B.1 Unconstrained Spending

Another way to write the condition 4.12 for unconstrained spending is:

f(t, lt) =1

γζt (B.1)

using B.1 and the goods clearance equation 4.18 yields an expression of consumption when spendingis not constrained

ct =1

γζt (B.2)

plugging B.2 into the household’s leisure/consumption equation 4.5 yields

ht = (1 + χ/γ)ζt (B.3)

The latter wages formulation and condition 4.12 yield the level of unconstrained spending as a functionof log productivity

ζt =γ

(1 + χ/γ)γeut (B.4)

or in log formζt = γ − γ ln(1 + χ/γ) + ut (B.5)

B.2 Wages in the Constrained Spending Case

In the constrained spending case, spending is predetermined

htlt = ιt−1 (B.6)

Plugging the last equation into the labour provision condition 4.5 yields

χct = ht − ιt−1 (B.7)

On the other hand, production in the constrained case is

xt =ιγthγteut (B.8)

Plugging B.8 into B.7 yields an equation determining wages as a function of productivity eut , thepreviously set financing ιt−1 and the model’s parameters when spending is constrained

χιγt−1

hγteut = ht − ιt−1 (B.9)

56

B.3 Steady State

The following proposition gives the steady state (SS) equations determining the model equilibrium,when rates are high enough such as the model’s mechanism remains unlikely to operate.

Proposition 3. Assuming that 1β > 1 + σ in the steady state, the SS equilibrium of the model exists,

is unique and the SS variables are determined by the following approximations

r ≈ 1

β(B.10)

ζ = i ≈ γβ

(1 + χγβ )γ

(B.11)

c = x ≈ 1

(1 + χγβ )γ

(B.12)

h ≈ γβ(1 +χ

γβ)1−γ (B.13)

l ≈ 1

1 + χγβ

(B.14)

Proof. The steady state version of the Euler equation where a first order approximation of the expec-tation is used yields the SS rates as in equation B.10.28 Assuming that 1

β > 1 + σ makes it unlikelyfor the model’s mechanism to function when the system is at the steady state. This simplifies theinvestment equation to

rι ≈ γx (B.15)

Using the latter equation and the consumption/leisure indifference equation 4.5 while noticing that thegood market clears (x = c) gives the following relationship between steady state wages and financing

h ≈ (1 +χ

γβ)ι (B.16)

Plugging the last relationship into the technology equation yields

c = x ≈ 1

(1 + χγβ )γ

(B.17)

Then, from the above, expression B.16 yields the SS wages expression B.13, expression B.15 yieldsB.11 and B.14 is derived from the definition of spending ι = ζ = hl.

In the case where steady state are too low to assume that the model’s mechanism is unlikely tooperate when the system is previously in the steady state, a numerical solution is required to solve theinvestment equation for steady state spending ι. I present an algorithm for determining the steadystate in the general case in appendix D.1.

28Note that the steady state approximation of the Euler equation requires small variance of the shocks to be valid.

57

C Technical Appendix: Multiple Industries’ Model

C.1 Model Theoretical Results

I present below a number of results that enable the numerical simulation of the model without recourseto a perturbation type method similar to what is performed by numerical suits such as ”Dynare”. Asit will be shown below, all contemporaneous nominal model variables but investments ιi(t) can beexpressed as a function of current consumption spending and previously determined state variables(namely the previous period industry financing).29 Consumption spending, on the other hand, isdetermined as a function of previously determined state variables and current industry shocks. Thismodel structure proves crucial in simplifying the simulation procedure. To simplify the expositionof the model results, I assume that if there are m industries where the financing constraints are notbinding, then these industries have indices 1, ...,m. This notational assumption can be made withoutany loss of generality and will be adopted for the remainder of this section.30 Otherwise, the modelassumptions are the same as above and are assumed throughout this section with the exception of themodel closure assumption that is introduced only when needed.

The following lemma is derived from the goods clearing equations and the model first order equa-tions and shows that firm revenues are only function of current expenditure and current consumptionspending.31

Lemma 1. The firms revenues are determined by the current levels of firms’ expenditure and currentconsumption spending

REV (t) =α

α+ γW ′Z(t) + cs(t)Θ (C.1)

where REV (t) := (p1(t)x1(t), ..., pn(t)xn(t))′ is the vector of industry revenues, Z(t) := (ζ1(t), ..., ζn(t))′

is the expenditure vector, Θ := (θ1, ..., θn)′, W the input-output matrix and cs(t) :=∑n

i=1 pi(t)ci(t)the overall consumption spending.

In the case where all industries are constrained by their previous period financing, their expenditureis predetermined and so is their nominal demand of various intermediary inputs. This means that,when all financing constraints are holding, consumption spending plays a central role in this model asthe only contemporaneous variable determining overall nominal demand. The following propositionextends the centrality of consumption spending to the case where some industries’ spending is notconstrained, as it expresses the expenditure of non constrained industries as a function of currentconsumption spending and predetermined model state variables.

Proposition 4. The firms’ expenditure is a function of the firm financing raised in the previous periodand consumption spending. Either the level of expenditure is equal to the previously raised financing(binding constraint industries) or, for industries where the constraint is not binding, it is determined

29Although inflation is absent from the model, some quantities are expressed in money terms and some are not.30The notational assumption would imply that notations might change from one time period t to the other but we will be

focusing on solving the model one time step at a time.31The proof of this Lemma as well as the other results presented in this subsection are detailed in appendix C.2.

58

by current consumption spending and previous period financing.

Z1:m(t) = LmαW ′1:m,m+1:nIm+1:n(t− 1) + (α+ γ)cs(t)Θ1:m

(C.2)

where Lm := (Im,m − αW ′1:m,1:m)−1 is the Leontief matrix corresponding to the subset of un-

constrained industries i = 1, ...,m, Im,m denotes the identity matrix of size m × m and ifM := (mi,j) is a matrix, then Mp:q,r:s denotes the sub-matrix Mp:q,r:s := (mi,j)i∈p,...,q,j∈r,...,s.

Combining proposition 4 and lemma 1 shows that revenues revi(t) := pi(t)xi(t) are also determinedby consumption spending and previous period financing. Using the first order equations and the marketclearing conditions, it follows from proposition 4, that other nominal variables are also determined bycurrent consumption spending and previous period investment levels. In other words, the full currentshocks impact on most nominal variables is reflected through the current consumption spending. Thevariables that depend directly on specific industry shocks are prices pi(t), the interest rate r(t) and thefinancing levels ιi(t). Prices pi(t) adjust to reflect the varying levels of production across industries,while the financing levels and interest rates are forward looking variables that depend on the agentsexpectations of the next period realization of industry-specific shocks.

Proposition 5. Revenues revi(t) := pi(t)xi(t), cost of intermediary inputs pi(t)xij(t), industry labourcosts h(t)li(t), households labour revenues h(t)l(t) and households consumption costs pi(t)ci(t) aredetermined by current consumption spending and state variables, namely the previously determinedindustry financing.

As explained above, prices depend both on consumption spending (through revenues) and onindustry-specific shocks as per the proposition below.

Proposition 6. The matrix In,n − αW is invertible and prices are a function of the level of firmsexpenditure, consumption spending, household labour supply and industry shocks as per the equationbelow

P (t) = L′A+ γ(ζ(t)− l(t))1n,1 + ˜REV (t)− (α+ γ)Z(t)− U(t)

(C.3)

where the superscript . is used for logarithmic values, U := (u1(t), ..., un(t))′ is the industries’ logproductivity vector, Z(t) := (ζ1(t), ..., ζn(t))′ the industries’ spending vector, ζ(t) :=

∑ni=1 ζi(t) the

overall firms’ spending and A := (ai)i=1,...,n is a constant vector with ai := α ln(α + γ) − αα −α∑n

j=1wijwij.

In order to close the model, an assumption regarding prices is needed. I make the assumption thatthe price index p(t) :=

∏ni=1 pi(t)

θi is constant and equal to one. Or equivalently:

Assumption 1.n∑i=1

θipi(t) = 0 (C.4)

The no-inflation model closing assumption provides a way to determine the current consumptionspending level as a function of state variables and current shocks. Indeed, combining the assumption

59

1 and proposition 6 provides a relationship between consumption spending and aggregate labour whilehouseholds preferences relates labour to consumption as per equation 4.5. These two relationshipsprovide a way to numerically solve for consumption spending cs(t) as a function of previously setindustry financing and current productivity shocks. In the case where no financing constraint isbinding, previous period financing is irrelevant and wages are only function of current shocks andmodel parameters; Under assumption 1 and in the case where none of the financing constraints arebinding, one can derive a closed-from solution for consumption spending as a function of industryshocks and parameters of the model.

cs∗(t) =γ

1− αl(t) + Θ′L′(D + U) (C.5)

where D := (d1, ..., dn)′ is a constant vector that is a function of the model parameters

D := −A+ [α ln(α+ γ) + γ ln(1− α)]1n,1 − (1− α− γ) ln(LΘ) (C.6)

and L is the Leontief Inverse.The finance related forward-looking variables that are the interest rater(t) and the current financing levels ι(t) depend on agents’ expectations. They are respectivelydetermined by the Euler equation and the industry financing problems.

A good way to summarise this section’s results is to note that they provide a way to numericallysimulate the model. Indeed, assuming a particular set of industries where the financing constraintis relaxed, the no inflation assumption provides a way to determine current consumption. Then nonconstrained expenditures can be calculate as in proposition 4. Using the new productivity levels,the calculated firms’ expenditures and consumer spending, prices are obtained from proposition 6.Consumption and production factors follow from first order conditions while the interest rate andfinancing levels are solved through numerical integration of the Euler and the investment equationsrespectively. Appendix D.3 provides more details on the simulation methodology (Semi-AnalyticalMethod).

The proposition below provides a criteria to determine which set of industries, if any, is facingbinding constraints.

Proposition 7. There are exactly m unconstrained industries i = 1, ...,m if and only if

1

α+ γmax

i=m+1,...,n

δmi (Im+1:n)

ηmi< cs(t) ≤ 1

α+ γmin

i=1,...,m

νi(Im+1:n)

τmi(C.7)

whereTm := (τm1 , ..., τ

mm )′ := LmΘ1:m

(ηmm+1, ..., ηmn )′ = αW ′m+1:n,1:mTm + Θm+1:n

(δmm+1, ..., δmn )′ = Im+1,n(t− 1)− (α2W ′m+1:n,1:mLmW ′1:m,m+1:n + αWm+1:n,m+1:n)Im+1:n(t− 1)

(νm1 , ..., νmm)′ = Im+1:n(t− 1)− αLmW ′1:m,m+1:nIm+1:n(t− 1)

Note that the constants τmi , ..., τmm and ηm+1, ..., ηn depend on the input-output structure and

households preferences while the variables δmi and νmi also depend on the previous period financingwithin the set of constrained industries Im+1:n(t− 1). Independently of the level of shocks and theirinfluence on consumption spending, a feasible set of unconstrained industries i = 1, ...,m needs to

verify maxi=m+1,...,nδmi (Im+1:n)

ηi< mini=1,...,m

νi(Im+1:n)τmi

.

60

C.2 Model Theoretical Results: Proofs

Assume that the first m industries have non binding investment constraints, while the investmentconstraint binds in the remaining n−m industries. Then the invested capital can be written as:

ζi(t)1−α−γ = (α+ γ)eui(t)

pi(t)

κi(t)for i = 1, ...,m (C.8)

ζi(t) = ιi(t− 1) for i = m+ 1, ..., n (C.9)

The clearing equation of good i combined with the first order condition of the productive sector andthe consumer indifference between consumption and leisure yield the equation of lemma 1

pi(t)xi(t) =1

α+ γ

n∑j=1

αwjiζj(t) + cs(t)θi (C.10)

The technology function combined with the production sector first order conditions yield32

pi(t)xi(t) = eui(t)pi(t)

κi(t)ζi(t)

α+γ (C.11)

Combining C.8 and C.11 yields a linear relationship between firm revenues and expenditure for indus-tries that are not constrained by their financing levels

pi(t)xi(t) =1

α+ γζi(t) for i = 1, ...,m (C.12)

Now combine C.12 with C.10 to get an equation implying the levels of invested capital in the industrieswhere the investment constraints are not binding (i ≤ m)

ζi(t)−m∑j=1

αwjiζj(t) = (α+ γ)cs(t)θi +n∑

j=m+1

αwjiιj(t) (C.13)

Equations C.13 can be inverted as follows

Z1:m = LmαW ′1:m,m+1:nIm+1:n + (α+ γ)cs(t)Θ1:m

(C.14)

where, if X := (xi,j), we define Xp:q,r:s := (xi,j)p≤i≤q,r≤j≤s, Lm :=Im,m − αW ′1:m,1:m

−1and the

remaining matrix notations are as above. At this stage, one needs to justify the matrix inversion inthe above formulae. The matrix αW ′1:m,1:m is non-negative and the sum of its columns is lower thanone, the Perron-Frobenius theorem guarantees that all its left eigenvalues are less than 1 in modulus.This implies that Im,m−αW ′1:m,1:m is invertible. The inverse of the latter matrix is also non-negative.This follows from

Lm =

∞∑i=0

(αW ′1:m,1:m)n (C.15)

32Note that this is equivalent to equation 4.11.

61

Once the expenditure within each industry is determined, one can use equation C.10 to determinethe industries revenues revi(t) := pi(t)xi(t)

REV (t) =α

α+ γW ′Z(t) + cs(t)Θ (C.16)

and then use equation C.11 to determine the ratios pi(t)κi(t)

in a logarithmic form

pi(t)− κi(t) = ˜revi(t)− ui(t)− (α+ γ)ζi(t) (C.17)

Using the the firm’s first order condition for labour, one can solve the log-linear system above asfollows

P (t) = L′A+ γ(ζ(t)− l(t))1n,1 + ˜REV (t)− (α+ γ)Z(t)− U(t)

(C.18)

Where A := (ai) is a constant vector and ai := α ln(α+γ)−αα−α∑n

j=1wijwij as per proposition 6.Prices are a direct function of consumption spending cs(t) and labour l(t) and an indirect function

of cs(t) through invested capital ζi(t) and revenues revi(t), one can therefore use the model closingconvention to determine wages.

Θ′L′.A+ γ(ζ(t)− l(t))1n,1 + ˜REV (t)− (α+ γ)Z(t)− U(t)

= 0 (C.19)

The latter equation is not easy to solve analytically but can be easily inverted numerically, given somelabour provision equation emanating from households preferences, so that consumption spending cs(t)is determined as a function of industry shocks ui(t) and previous level of financial investments ιi(t).For instance, in the case where industries are not constrained, equation C.19 can be rewritten as

cs(t) =γ

1− αl(t) + Θ′L′(D + U) (C.20)

where the vector D is defined as above D := −A+[α ln(α+ γ) + γ ln(1− α)]1n,1−(1−α−γ) ln(LΘ).Equations C.20 follows from C.19 through remarking that when no industry is constrained revenuesare simply linked to firms’ spending as per equation C.12 and that we have the identity: 11,n.LΘ =1/(1− α).33

Writing lemma 1 for the set of constrained industries and using C.14 yields

REVm+1:n = cs(t)(αW ′m+1:n,1:mLmΘ1:m + Θm+1:n

)+

α

α+ γ

(αW ′m+1:n,1:mLmW ′1:m,m+1:n +W ′m+1:n,m+1:n

)Im+1:n

writing the binding and non binding constraints conditions in the form below yields the resultof proposition 7.

REVm+1:n >1

α + γIm+1:n (C.21)

Z1:m ≤ I1:m (C.22)

33The identity follows from C.15, that∑mj=1 wij = 1 and that

∑ni=1 θi = 1.

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C.3 Steady State

The following proposition gives the steady state (SS) equations determining the model equilibrium inthe case where interest rates are not near the zero lower bound. As explained in more details below,the model is calibrated in the steady state, hence the choice of using an exogenous SS employment lto express other SS model variables.

Proposition 8. Under the model closing assumption 1 and assuming non negative financing rates inthe steady state, the SS equilibrium of the model exists, is unique and the SS variables are determinedby the following system of equations

• The steady state interest rate is given by

r =1

β(C.23)

• SS expenditures are equal to SS investments and are a function of wages

I = Z = (α+ γ)cs (In,n − αΓ)−1 Ω (C.24)

where In,n is the square identity matrix with n rows and n columns, Γ = diag(1/s1, ..., 1/sn)W ′,Ω = (θ1/s1, ..., θn/sn)′ and si is the overall industry SS financing rate si := ψir + (1− ψi)λi.

• The logarithm of SS good prices are expressed as a function of SS wages and expenditure asfollows

P = L′(A+ (γζ − γl − ln(α+ γ))1n,1 + S + (1− α− γ)Z

)(C.25)

where the superscript . is used for logarithmic values, S := (s1, ..., sn)′ and as before

A := (ai)i=1...n with ai := α ln(α + γ)− αα− α∑n

j=1wijwij.

• SS industry inputs are

xij =α

α + γwij

ζipj

(C.26)

• the SS consumption levels are

ci =siζi

(α + γ)pi−

n∑j=1

xji (C.27)

• finally, assumption 1 implies that SS consumer spending is expressed using the modelparameters as follows

cs =γ

1− αl + Θ′L′D (C.28)

where D := −S−A+[α ln(α+γ)−γ ln(11,n.(In,n−αΓ)−1Ω)]1n,1−(1−α−γ) ln ((In,n − αΓ)−1Ω).

63

Clearly, the above proposition provides closed-form expressions for all steady state variables as afunction of the model parameters. This is explicit for steady state consumer spending, while steadystate expenditures are expressed as a function of steady-state consumer spending and the modelparameters. Once steady state consumption spending and expenditures are known, one can easilyobtain the remaining steady state variables.

Proof. The SS version of the Euler equation

R = 1/β (C.29)

In the absence of unforeseen negative productivity shocks, the financing constraints hold in thesteady state. Combining the goods clearing equation 4.18 and the first order conditions for labourprovision, the firm’s first order equations for goods and labour and the investment equation 4.15

siα+ γ

ζi =α

α+ γ

n∑j=1

wjiζj + csΘ (C.30)

where si := ψiβ +(1−ψi)λi is the steady state overall cost of financing within industry i. Alternatively,

in matrix format, one can write(In,n − αΓ) Z = (α+ γ)csΩ (C.31)

where In,n is the square identity matrix with n rows and n columns, Γ = diag(1/s1, ..., 1/sn)W ′ andΩ = (θ1/s1, ..., θn/sn)′. Because αΓ is a non negative matrix with column sums less than one, thePerron-Frobenius theorem guarantees that all its left eigenvalues are less than 1 in modulus. Thisimplies that In,n − αΓ is invertible so that one can solve for the steady state investment levels asfollows

Z = (α+ γ)cs (In,n − αΓ)−1 Ω (C.32)

Note here that θ ≥ 0 and (In,n − αΓ)−1 > 0 guarantee that Z ≥ 0. More precisely, as long as θi > 0or there exist j and q ∈ N∗ such as θj > 0 and the (i, j) element of the matrix W q is non nil, thenζi > 0. In other terms, capital is dedicated to an industry as long as its produce is directly consumedby households or if its produce is used directly or indirectly by another industry which produce isconsumed by households.

Writing proposition 6 in the SS yields the SS good prices. Replacing for the steady state expen-diture in the latter equation and using the zero-inflation closing equation leads to an expression forsteady state consumer spending as a function of the model parameters. Finally, The formulae for thesteady state production inputs follow from the firm’s first order conditions and the formulae for thesteady state consumptions and overall labour follow from the clearing conditions.

C.4 The Effect of Input/Output Relationships: Proofs

I call Z∗ is the expenditures when no constraint is binding and cs∗(t) the corresponding consumptionspending and rewrite equation C.14 as for m = n:

Z∗(t) = (α+ γ)cs∗(t)T (C.33)

64

where as defined above T := LΘ. All industry constraints would be non binding if Z∗(t) ≤ I(t − 1),where the inequality is meant in the element by element sense. This is equivalent to:

cs(t) ≤ 1

(α+ γ)minτi 6=0

ιi(t− 1)

τi(C.34)

where the constants τi are defined as (τ1, ..., τn)′ := T . These constants are non negative because theLeontief matrix is positive and the vector Θ is non negative.

Now let’s assume that the economy is previously in the steady state. First, I write the steady stateexpenditures in a more adequate form using equation C.30:

I = (α+ γ)csLΘ− n∑j=1

(sj − 1)ιjLF (C.35)

where F := (f1, ..., fn) and fi := (si−1)ιi∑nj=1(sj−1)ιj

represents the fraction of industry i nominal financing

cost to the overall nominal financing cost. One can then rewrite equation C.34 as follows:

cs(t)− cs ≤ − 1

α+ γmaxτi 6=0

n∑j=1

(sj − 1)ιjφiτi

(C.36)

where (φ1, ..., φn)′ := LF .Now assume that the economy is previously in the steady state, the previous financing is therefore

given by equation C.32 so that condition C.34 can be rewritten:

cs∗(t)

cs≤ min

τi 6=0

εiτi

(C.37)

where εi is defined as in proposition 2. Combining the last condition with equations C.5 and C.28yield the result of proposition 2.34

D Numerical Procedures

D.1 Steady State Determination Routine

I present an algorithm that enables to solve for the steady state variables for all values of β.

1. SS rates r are approximated by B.10.

2. solve the investment equation numerically for the SS spending ι

rι1−γ = γEt[1ιt< γ

(1+χ/γ)γeut+1γ

eut+1

hγt+1

](D.1)

where ht+1 is in turn solved for numerically using B.9.

34Note that when all industry face the same financing rates in the SS:∑ni=1 εi = 1/(s− α).

65

3. Use the SS version of equation B.9 to solve for the SS wages

χιγ

hγ= h− ι (D.2)

4. use the consumption/leisure indifference equation to calculate SS consumption/production

x = c =h− ιχ

(D.3)

5. finally SS labour is given by l = ι/h.

D.2 Simulation: Semi-Analytical method

In this appendix, I provide a numerical method for solving the model without the need for someperturbation based technique. Using the results established in the appendix and those established insection 4, one can simulate the model following the following steps.

1. compute the critical log productivity u∗t using equation 4.16.

2. compare the log productivity ut to the critical level u∗t

(a) if ut >= u∗t : spending is constrained ζt = ιt−1 and wages ht are given by B.3.

(b) if ut < u∗t : compute spending ζt using equation 4.13 and solve for wages ht using B.9.

3. compute the current period production f(t, lt) using equation 4.19.

4. compute consumption ct using the good’s clearing equation 4.18.

5. compute labour lt using the labour provision condition 4.5.

6. calculate interest rates rt and financing ιt through numerical integration of equations 4.4 and4.14 where the steps 1 to 5 can be used to compute the next periods variables conditional on thelevel of the next period’s log productivity ut+1.

D.3 Simulation: Semi-Analytical method in the multiple-industryset-up

The results of subsection C.1 can be used to provide a semi-analytical simulation procedure as detailedbelow.

Algorithm 1. (Semi-Analytical Method) In order to numerically simulate the model variables ata given time t+ 1 given the state variables ι1(t), ..., ι1(t) and the current shocks u1(t+ 1), ..., u1(t+ 1),follow the steps:

1. assume a certain set of non biding constraint industries.

2. numerically solve for the wages using: the model zero-inflation model closure assumption, propo-sitions 6 and 4 and lemma 1. If the problem has no solutions, assume a different set of bindingconstraint industries. Otherwise go to the next step.

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3. calculate the industry expenditures using proposition 4 and prices using proposition 6.

4. deduce all other variables but r(t) and ιi(t) using the first order conditions.

5. check that the marginal return on expenditure is strictly greater than one in all industries wherethe constraint is assumed to be binding. If not, assume another set of binding-constraint indus-tries and start again from step 2.

6. calculate the interest rate r(t) using the Euler equation, current period investments ιi(t) usingthe investment identities 6.9 and steps 1 to 4 to determine the next step non forward-lookingvariables conditional on the next period shocks.

D.4 More IRFs

The impulse responses to a large positive shock are presented in figure 15. In the immediate aftermathof the shock, the model and benchmark model react similarly as spending in both models remainconstrained by financing. This changes in the time periods following the shock. Interest rates drop tosignificantly lower levels following large positive shocks. This implies that when firms are allowed toadjust spending, their likelihood of entering an unconstrained spending mode becomes much higher.The firms set financing at a lower level relatively to the benchmark model. This implies a lower outputin the presence of the model’s main mechanism.

Figure 15: Impulse response functions following a large positive shock (4× standard deviations). Thegraph shows relative deiviations from the steady states for all variables but interest rates that are shownwithout any transformation.

67