Housing, Debt and Growth

Housing, Debt and Growth

Valerio Scalone∗

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December 4, 2015

Abstract

In this paper I study how debt and housing affect the trend of the economy.I build and estimate a DSGE model with endogenous growth and with hetero-geneous agents. Savers’ investments in technology determine the trend of theeconomy. Houses play the double role of durable good and of collateral pro-vided by borrowers to savers. When house prices increase, borrowers increasetheir debt. In order to finance the debt expansion, savers reduce their invest-ments in technology, thus lowering productivity growth and the trend of theeconomy. This crowding out mechanism is at play each time that house pricesraise. I estimate the model by standard Bayesian techniques and find thatproductivity growth steadily increases during the Great Moderation, mainlyexplained by positive exogenous increases in the TFP. In pre-crisis period, thehousing boom and the debt overhang crowded out investments in technology,lowering the trend. In addition, the slow recovery which followed the GreatRecession is mostly explained by a strong negative investment shock.

Keywords: DSGE estimation, Endogenous Technology, Housing, Heterogenous agents,Business Cycles;JEL: R21, R31, E3, O3.

∗LUISS Guido Carli. Email: [email protected]. I thank Salvatore Nistico and Giuseppe Ragusafor their support. I also thank Pierpaolo Benigno, Nicola Borri, Sergio de Ferra, Giorgio Di Gior-gio, Luca Fornaro, Maddalena Galardo, Anastasios Karantounias, Marco Lippi, Riccardo Masolo,Lucrezia Reichlin, Pietro Reichlin, Federica Romei, Frank Schorfheide for useful comments.

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https://www.dropbox.com/s/uyp5r98bausvojk/HousingOct2.pdf?dl=0

1 Introduction

This paper builds an empirical DSGE model with endogenous growth and het-erogeneous agents to empirically and qualitatively assess how debt dynamics andhousing affect the trend of the economy. My key finding is that the debt expansionsdecrease the trend of the economy. During debt expansions, in order to financeborrowers, savers reduce their investments in technology. This reduction lowers theproductivity and the trend of the economy. In the pre crisis period, this mechanismproduced a slowdown in productivity. Conversely, during the Great Recession, twomain forces affected productivity. First, the debt deleveraging freed resources to beinvested in technology. Second, the crisis triggered a slowdown in the accumulationof capital. Given the complementarity between capital and technology, savers de-creased investments in technology too. In absolute terms, the latter effect dominatedthe first one, causing a substantial fall of productivity.

Debt overhang and housing fluctuations have been contributing factors to theGreat Recession turmoil. Since then, the US economy did not fully recover anddid not go back to its previous balanced growth path. In order to account for theslow recovery, standard DSGE models have been complemented with endogenousgrowth mechanisms (Bianchi and Kung, 2014, Guerron-Quintana and Jinnai, 2014,Anzoategui et al. 2015). The endogenous growth mechanism allows the business cy-cle shocks to influence the trend at which economies grow. However, an explorationon the long-term consequences of debt overhang and housing fluctuations is stillmissing. What has been the evolution of productivity in the US economy in the last30 years? How did housing and debt dynamics affect productivity? In order to ad-dress these questions, I build and estimate a DSGE model encompassing endogenousgrowth, housing and heterogeneous agents. The model also features monopolisticcompetition in the wholesale sector, nominal frictions on prices and wages. In themodel, productivity is endogenously determined by the investments in technologymade by the savers of the economy. The endogenous growth mechanism allows thebusiness cycle shocks to modify the trend of the model. Savers can also buy housesor lend to borrowers. Borrowers are subject to a borrowing limit depending on thenominal value of their houses. Following an increase in the house prices, borrowersincrease their debt. In order to meet the higher demand of funds from borrowers,the savers decrease the investments in technology, lowering the TFP growth and thetrend of the economy.

First, I build the model and I estimate it using standard Bayesian techniques.Second, I estimate the historical evolution of the endogenous growth along the sam-ple and I explore the role of the different shocks. In the estimation, investments intechnology are excluded from the set of observable variables used in the estimation.The Kalman Smoother determines the evolution of productivity, hence of the trend,and which events affected it most.

According to the estimated model, when borrowers’ collateral increases, savers

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invest less in capital and in technology, in order to satisfy the larger demand of fundsfrom borrowers. This key mechanism is at play each time that a shock raises thevalue of nominal collateral and triggers an additional effect on trend. The crowdingout due to the debt expansion modifies the overall effect which the different typesof shocks have on productivity.

Concerning the evolution of productivity across the sample, I first find that thetrend of the economy has steadily increased during the Great Moderation, mainlyexplained by positive exogenous shifts in TFP. Second, productivity has been nega-tively affected during the housing boom and the debt overhang, which featured thepre-crisis period. In fact, following an exogenous increase in housing demand, bor-rowers increased their debt. Savers financed the debt expansion and afforded a largeramount of houses for themselves. Therefore, savers decreased their investments intechnology and productivity growth slowed down. Third, the Great Recession sub-stantially lowered the trend of the economy. An exogenous fall in the investments incapital strongly reduced capital accumulation. Given the complementarity betweencapital and technology, savers have been induced in investing less in technology.This effect has been delayed and partially offset by the debt deleveraging. In fact,at the beginning of the crisis, the debt deleveraging freed resources to invest in thetechnology sector. The overall effect on the trend has been substantially negative.

In standard DSGE models, macroeconomic variables grow along a balancedgrowth path. Long-term growth in the economy is explained by a constant growthof the total factor productivity. Since the TFP-enhancing growth coefficient is fixedand exogenously determined, business cycle fluctuations do not affect TFP growthand the trend of the economy, no matter what the size of the shock is. This featureof the model marks a neat separation between the business cycles fluctuations andthe long-term growth. Such limitation turned out to be compelling in the aftermathof the Great Recession, when DSGE model did not prove able to handle anaemicgrowth period or the medium-term fluctuation, which is observed in the aggregatemacroeconomic variables. The seminal works by Comin and Gertler (2006), Bianchiand Kung (2014) and Guerron-Quintana and Jinnai (2014) aim at reconciling thebusiness cycle fluctuations with the long term growth, in order to assess the ef-fects which business cycle shocks have on the evolution of the long term growth.In standard DSGE models, they incorporated a technology sector in which agentsdevote resources, determining the technological growth of the model. Therefore,business cycle shocks, in modifying agents’ investments in technology, may impacton the trend of the model. My paper contributes to this literature by studying howthe presence of debt and housing affects the evolution of the productivity. In thisway, I am able to assess how different allocations of savings can impact productivitygrowth. If savers buy houses and lend to borrowers, they are allocating their savingsin activities which do not enhance the growth potential of the economy. If saversdecide to invest in technology, this will increase the productivity of the economy.

It is worth to emphasize that in the estimation, I treat the investments in tech-

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nology as a latent variable. This marks a notable difference with respect to thethe state-of-the-art works which run empirical estimation on DSGE models withendogenous growth. This choice lies on the following reasons. First, investments intechnology determine the growth of TFP and the trend. Therefore, the inclusion oftechnology investments among the observables implicitly determines the evolution ofthe trend along the sample, letting aside shocks specifically affecting how technologyis stocked by savers. It also a priori pins down which economic events influenced thetrend more, along the sample. Second, the empirical works featuring DSGE modeland endogenous growth, did not find a consensus yet on which measure of technologyinvestments has to be adopted. Third, the long-run growth may depend on otherfactors, which are not usually included in the measure of technology investments, assuch as education and investments in human capital, to mention a few.

In Bianchi and Kung (2014),the investments in technology coincide with Researchand Development investments. They include the R&D investments series providedby the FRED dataset among the observable variables. This series exhibits largepersistence with respect to the other macroeconomic variables used in the estimation.The slowdown of the series following the IT bubble is stronger and more persistentthan the one after the Great Recession. As a result, in the estimation results, thetrend of the economy has very low sensitivity to the business cycle shocks. Also, thetrend is affected more during the IT bubble burst than during the Great Recession.

Instead, Guerron-Quintana and Jinnai use a broader measure of technology in-vestments, encompassing the R&D investments, investments in software and adver-tising. This measure dates back to the definition adopted in Nakamura (2003) andis more pro-cyclical than the series adopted by Bianchi and Kung (2014). Accordingto this definition, the inferred resilience of technology investments with respect tothe business cycle shocks is substantially smaller than in Bianchi and Kung. Andas opposed to them, Guerron and Quintana find that the Great Recession resultedin having had a substantial negative impact on the trend.

Finally, Anzoategui et al. (2015) adopt the R&D investments exclusively usedby the firms, in explicit contrast with the choice made by Bianchi and Kung. Thisdifferent series is more pro-cyclical with respect to the NIPA R&D series.

In this paper, since technology investments are a latent variable, the Kalmanfilter delivers the most likely path which the productivity growth follows. After theestimation, I reconstruct the evolution of the productivity growth and the trend byusing the the Kalman Smoother. Second, I analyse to which extent the differentshocks impacted on the trend of the economy along the sample.

In addition, I use this framework to analyse how the presence of debt (andheterogeneity among households) affect shocks propagation through the economy. Ifocus on the final effects on long-term productivity growth. In fact, with respect tothe models without debt (Bianchi and Kung (2014), Guerron-Quintana and Jinnai2015, Anzoategui et al. (2015)), this model features an additional propagationmechanism of the shocks. Each time that a shock affects the nominal value of

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collateral, debt dynamics modify how much savers invest in technology, ultimatelyinfluencing the trend. Therefore, I first compare the benchmark estimation impulseresponses with the ones obtained in two different cases:

• The fraction of borrowers and the net debt of the economy are set to zero (zerodebt scenario);

• The fraction of borrowers equals half of the population (large debt scenario);

Second, I compare the counterfactual productivity growth obtained in the two dif-ferent scenarios with respect to the benchmark exercise. I obtain the counterfactualsimulations of the productivity by feeding the model with the sequence of shockssmoothed in the benchmark estimation exercise.

I first find that the housing demand shock, a temporal but very persistent in-crease of the demand of houses, has a negative impact on the productivity growth.Initially, an increase in housing demand positively affects the value of nominal col-lateral of borrowers. The debt expansion induces savers to decrease investments intechnology. After few quarters, savers increase their share of houses and furtherreduce investments in technology.

Second, according to the results, during the 90’s and the 00’s, the productiv-ity looks steadily growing along the sample mainly pushed by positive exogenousincreases in the TFP. Since 2003, a strong positive housing shock partially crowdsout the technological investment, lowering the productivity and the trend. Finally,during the Great Recession, a negative Investment shock strongly decreases theproductivity growth. As shown by Justiniano, Primiceri, Tambalotti, (2011), theInvestment shock can be interpreted as the premium shock, mimicking how thecredit conditions for firms evolve.

Third, the response of technology to a negative Investment shock is severelyinfluenced by the presence of debt in the economy. In a model without heterogeneousagents, the response of productivity to a negative Investment shock is unambiguouslynegative, because of the complementarity relation between capital and technology.Instead, in a model with debt, productivity growth overshoots: the initial effect ispositive and only after some quarters the effect turns negative. Since a negativeInvestment shock decreases the value of the nominal collateral, borrowers are forcedto reduce their debt, freeing resources that can be invested in technology. Oncethe deleveraging phase is over and debt goes back to its steady state level, saversstrongly decrease technology investments. The final effect on technology is larger(and postponed) than in the case of no inequality. In a model with no heterogeneitythis additional propagation mechanism does not exist. The net debts remains fixedat zero and fluctuations of the nominal value of housing do not impact on technologyinvestments. Conversely, the weight of this new propagation mechanism increaseswith the size of the debt.

From the comparison of the productivity growth obtained in the counterfactualsimulations, it turns out that debt and heterogeneity among households are crucial

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to provoking the slowdown in the productivity growth found during the housingboom. Also, the presence of debt in the economy postpones the negative effects onthe trends which the Investment shock had on the trend in the aftermath of theGreat Recession.

The remainder of the paper is organized as follows. Section 2 presents a reviewof the existing literature. Section 3 presents the model. Section 4 presents theestimation strategy. Section 5 presents the results. Section 6 presents the counter-factual exercises. Section 7 concludes.

2 Literature

The attempt to reconcile business cycle and growth dates back to Comin andGertler (2006), where the authors detect medium-term fluctuations of output, pro-ductivity and technology adoption featured by a pro-cyclicality relation. They inte-grate a RBC model with a technology sector with horizontal innovations a la Romer(1990). Horizontal innovations expand the variety of intermediate goods. Theirmodel is able to generate fluctuations similar to the ones detected in the empiricalpart of their paper.

The works by Anzoategui et al.(2015), Bianchi and Kung (2014) and Guerron-Quintana and Jinnai (2014) tackle endogenous growth from an empirical perspective,in order to assess the effects which business cycle shocks have on the evolution ofthe long term growth.

Bianchi and Kung (2014) build a standard DSGE model with nominal frictionsand monopolistic competition of the intermediate sector adding a technology sectorwith vertical innovation and utilization rate. In vertical innovation, endogenousgrowth has a Schumpeterian nature and the technology is created on the top of aprevious technology (Aghion and Howitt, 1992). In the estimation, as a measure fortechnology investment, Bianchi and Kung use R&D investments according to theNIPA definition. In Bianchi and Kung’s results, the Marginal efficiency investmentshock (MEI) is found to have the main role in leading both the business cycle andgrowth. The MEI shock already identified by Justiniano Primiceri and Tambalotti(2011) as one of the major sources of fluctuations, is positively correlated with theCredit spread, measured as the difference between the high yield and the AAAcorporate bond. Two main events are analysed through the lens of the model:the 00’s Great Recession and the 70’s Great Inflation. In the first, the technologyinvestment, i.e the trend, is not as affected as in the IT bubble burst period. In the70’s, high inflation is explained also by shocks lowering the technology investments.

Guerron-Quintana and Jinnai (2014) implement a RBC model with Kyotaki-Moore constraints on the entrepreneurs. Their model incorporates a technology sec-tor with horizontal innovations. Liquidity shocks hitting entrepreneur’s constraintlimit her investments in innovation and lower the technology trend. Estimation isperformed on the set of dynamic parameters. They use the Nakamura (2003) se-

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ries as technology investments. According to Nakamura’s definition, the measure forthe investments in technology encompasses software investments, R&D investments,and advertising. According to their analysis, liquidity shocks limiting the borrowingcapacity of entrepreneurs had a crucial role in determining the 2008-2009 economicslowdown.

Anzotegui et al. (2015) build and estimate a DSGE model along the lines ofComin and Gertler (2006). As technology investments, they use business R&Dinvestments. This series takes out public investments in R&D from the NIPA seriesused in Bianchi and Kung (2014).1

I contribute to this stream of literature by studying the role which debt andhousing have in affecting the endogenous growth. This is important to analyse howsavers’ decisions affect the trend of the economy, when they allocate their wealthamong different activities. In order to do so I add the housing sector and het-erogeneous agents in a DSGE model with endogenous growth. Since a consensusfeaturing the measure to use as technology investments is missing, I chose to esti-mate the model excluding the technology investments from the set of the observablevariables.

The recent financial crisis sparkled new interest for the role of financial frictions.Concerning this topic, Guerrieri and Iacoviello 2014 build a model with heteroge-neous agents with occasionally binding borrowing constraints for the borrowers. Anexogenous reduction in collateral demand lowers the borrowing limit for borrowers,forcing them to reduce consumption and borrowing. The increase of consumption ofsavers does not compensate for the reduction by the borrowers bringing a slowdownin overall consumption. Interestingly, the presence of the occasionally binding bor-rowing constraint and a non-linear solution method deliver an asymmetric effect ofcollateral nominal value variation, where an increase does not have the same effectsin absolute terms than does a decrease.

Mendoza (2010) builds a SOE-DSGE model with occasionally binding constrainton borrowing to model the sudden stop and their asymmetric behaviour on theemerging markets’ economies. Christiano, Eichnebaum and Trabandt (2014) incor-porate financial frictions into a standard DSGE model with nominal frictions andendogenous labour force supply. They estimate the model using pre-2008 data. Ac-cording to their model a financial wedge and a preference shock represent the bulkof the causes determining the Great Recession. 2

1In macrofinance, Kung and Schmidt (2013) adopt a DSGE model with long-term endogenousgrowth. Recursive Epstein-Zin preferences make the agents care for the long-term prospects ofgrowth. This key assumption is crucial to explain the high equity premium and the low and stablerisk-free rate. Kung (2014) explains the term structure adopting a model in which wage markup shocks generate a negative relation between inflation and output movement. An interactionwith the monetary policy contributes to explain the term structure dynamics and its interactionin periods of weak versus sustained growth.

2More in general Del Negro et al. (2010), Piazzesi and Schneider (2007), Jerman and Quadrini(2009), and Christiano Motto and Rostagno (2010) and Liu, Wang and Zha, (2011) highlight the

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I contribute to this stream of literature by focusing on the effects which debtand housing dynamics have on the trend of the economy. I build on Guerrieri andIacoviello (2014), adding a vertical innovation sector which generates endogenousgrowth. To the best of my knowledge, this is the first paper to model the interactionbetween financial frictions and endogenous growth. This is important to shed somelight on the role which housing and debt dynamics have in affecting the long rungrowth.

The model is also related to the stream of literature that is trying to get some in-sight about the secular stagnation and the persistent period of weak growth featuredin Japan in the Euro-area and until recently in the US. Eggertson and Mehrotra(2014) build a three generation overlapping generations model. A debt-deleveragingshock can lead to a permanent or very persistent period of stagnation, essentiallydue to an overbalance of saving over demand for loans, pushing the necessary in-terest rate below the ZLB. Benigno and Fornaro (2015) build a model capable ofgenerating a permanent stagnation trap where low demand expectations push firmsto decrease technology investment, moving the economy into a lower growth equi-librium. Liquidity trap and the ZLB exacerbate the reduction in demand and theconsequent trend reduction.

I contribute to this stream of literature by providing an empirical assessment onthe effect which strong negative downturns can have on the trend of the economy.

3 The model

The model is a standard New-Keynesian DSGE model (Smets and Wouters2007), with nominal frictions, two types of agents (savers and borrowers), collat-eral in the utility function, investments in technology affecting the TFP.

The supply side is standard except for a vertical innovation sector, which is in-corporated to generate a Schumpeterian mechanism of endogenous growth. (Bianchiand Kung, 2014, Aghion and Howitt, 1992). Standard monopolistic competition forthe wholesale sector and Calvo price and wage settings are also introduced. Thecentral bank sets the interest rate. (Justiniano, Primiceri and Tambalotti, 2009).

On the demand side, there are two types of households: savers and borrowers.They both have housing in their utility function. In addition, houses play the role ofcollateral provided by borrowers to savers, as in Guerrieri and Iacoviello (2014). Bor-rowers supply labour and demand consumption goods and housing services. Saverssupply labour, demand consumption goods and housing services. Also, they lendto borrowers. Only savers accumulate capital and produce innovation in the econ-omy. Importantly, borrowers are subject to a borrowing constraint which is equal

role of financial frictions and heterogeneity as one of the main drivers of the Great Recession.Concerning the role of inequality, Ravenna and Vincent (2014) study the role of the heterogeneityto explain the divergence in debt-to-income ratios in US data. Borri and Reichlin (2015) analysethe drivers of housing wealth adopting a long-run perspective.

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to a fraction of their housing wealth. The borrowing constraint is assumed to bindin steady state. When house prices increase, borrowers can expand their debt. Inorder to meet the higher demand of borrowings, savers reduce their investments intechnology and lower productivity growth in the economy.

3.1 Households

The savers and the borrowers maximize the following utility functions:

E0

∞∑t=0

βtzt

(Γlog (Ct − εCt−1) + jtlogHt −

1

1 + ηn1+ηt

)(1)

E0

∞∑t=0

β′tzt

(Γ′log(C′

t − εC′

t−1

)+ jtlogH

′

t −1

1 + ηn′1+ηt

)(2)

where the prime symbol applies to borrowers’ variables. Ct is consumption, Ht isthe collateral, and nt are the hours worked. jt is an AR(1) process propagating ex-ogenous shocks to the demand for collateral, zt is the AR(1) propagating preferenceshocks:

log(jt) = (1− ρj)j + ρjlog(jt−1) + uj,t (3)

log(zt) = ρzlog(zt−1) + uz,t (4)

where uj,t, zt are n.i.d. shocks with variances σ2j and σ2

z .

The scaling factors Γ =(

µ−εµ−βµε

)and Γ

′=(

µ−εµ−β′µε

); imply that in steady state

the marginal utilities for consumption are equal to: 1/c and 1/c′3.The budget constraint for the saver agent is:

Ct +QtHt + It + St +Bt = Wtnt +QtHt−1 + [rK,tuK,t − aK(uK,t)]Kt−1+

[rN,tuN,t − aN(uN,t)]Nt−1 +Rt−1Bt−1

πt+DIVt

(5)

where Kt and Nt are the capital and the technology stocks owned by the saver.uK,t and uN,t are the utilization rates for capital and technology. Kt = uK,tKt−1and Nt = uN,tNt−1 are the capital and technology services rent from firms. rK,tand rN,t are the rental rates for capital and technology services. wt is the wage perhour worked, Qt is the price of collateral, It and St are the investments in capitaland technology. Bt are the loans made to the borrower, Rt is the interest rate setby the central bank. aK(uK,t) = 1

σk

(u2k,t − 1

)and aN(uN,t) = 1

σn

(u2n,t − 1

)are the

maintenance costs for capital and technology services. Dividends DIVt derive fromthe mark up applied by firms. πt = Pt

Pt−1is the inflation.

3µ is the steady state technology growth rate, i.e the steady state growth rate of the economy

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The saver cumulates capital and technology according to the following laws ofmotion:

Kt = (1− δk)Kt−1 + ξMEI,t

(It − φK

(It − It−1)2

I

)(6)

Nt = (1− δn)Nt−1 +

(St − φN

(St − St−1)2

S

)(7)

ξMEI,t is an AR(1) process capturing marginal efficiency investment shocks (MEI),identified by Justiniano et al. as one of the main shock driving the business cycle,highly correlated with the credit spreads for firms, mimicking tensions in the finan-cial sector. In the model the shock affects the efficiency through which investmentsare converted into capital.

log(ξMEI,t) = ρMEI log(ξI,t−1) + uMEI,t (8)

where uMEI,t is a n.i.d. process with variances σ2MEI .

The borrower does not accumulate capital or technology, she buys and sellscollateral, consumes, works and borrows from the saver. Her budget constraint is:

C′

t +QtH′

t +Rt−1Bt−1

πt= w

′

tn′

t +QtH′

t−1 +Bt (9)

Borrowers are subject to the occasionally binding borrowing constraint:

Bt ≤ γBt−1

πt+ (1− γ)MQtH

′

t (10)

where M is the loan to value ratio with respect to the collateral owned by theborrower, γ is the inertia of the borrowing limit.

3.2 Firms

The final good is produced in a perfectly competitive market. An homogeneousfinal good is assembled according to the CES technology function:

Y dt =

(∫ 1

0

Yλp−1

λp,t

j,t dj

) λpλp−1

. (11)

where Y dt is the final output demanded, λp is the goods elasticity of substitution.

Firms maximize their profits and obtain the following demand function:

Yj,t = Y dt

(Pt(j)

Pt

)−λp. (12)

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where Pt is the price of the final good and Pt(j) is the price of the intermediategood. The price of the final good is obtained by:

Pt =

[∫ 1

0

Pt(j)1−λpdj

] 11−λp

. (13)

The intermediate firm j produces the good according to the following productionfunction:

Y (j)t = K(j)αt

(AtN(j)ηtN

1−ηt n

(1−σ)t n

′σt

)1−α− FNt (14)

with Nt =∫ 1

0N(j)dj is the aggregate stock of technology, (1 − η) is the degree of

technological spillovers. The stationary technology evolves according to:

log(At) = (1− ρA)log(A∗) + ρAlog(At−1) + ua,t (15)

with ua,t ∼ N(0, σ2a). A

∗ is picked to matched the balanced growth evidence as inBianchi and Kung (2014) and Kung (2014).

Intermediate firms can re-optimize the price according to a Calvo rule: eachperiod 1− θP firms can optimally reset their price. The remaining part of the firmscan index their prices by past inflation. The degree of indexation is controlled bythe parameter χp ∈ [0, 1].

The maximization problem faced by intermediate firms is the following:

maxEt

∞∑τ=0

(βθp)τ uc,t+τuc,t

{(τ∏s=1

Πχ pi,tpt+τ

−mct+τ

)Yi,t+τ

}(16)

s.t.

Yi,t+τ =

(τ∏s=1

Πχt+s−1

pi,tpt+τ

)−λp,tY dt+τ (17)

The solution of the maximization problem delivers a standard New-Keynesian PhillipsCurve.

3.3 Labour market

Households supply homogeneous labour hours to an intermediate union sector.The union differentiates labour and resells it to the labour packers. The labourpackers resell it to the firms.

Importantly, markets for savers and borrowers are segregated. The labour unionhave market power and can set the wages taking into account the labour demandfunction of the labour packers for both households independently.

The labour packers operate in perfect competition, reassemble labour to be usedby the intermediate firms according to the following functions:

ndt =

(∫ σ

0

n(l)λw−1λw

t dl

) λw,tλw−1

, (18)

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n′dt =

(∫ 1

σ

n(l)′ λw−1λw

t dl

) λwλw−1

, (19)

where ndt and n′dt are the hours supplied by savers and borrowers, λw is the labour

elasticity.The labour packers buy differentiated labour and resell it to the firms. Maxi-

mizing their profits, the following demand function for labour is obtained:

n(l)t =

(W (l)tWt

)−λwndt . (20)

n′(l)t =

(W′(l)t

W′t

)−λwn′dt . (21)

Labour packers operate in perfect competition. Combining the zero profit conditionwith this demand functions, the following wages are obtained:

Wt =

(∫ σ

0

Wt(l)1−λwdl

) 11−λw

(22)

W′dt =

(∫ 1

σ

Wt(l)′1−λwdl

) 11−λw

. (23)

Labour unions differentiate the labour and set the wages taking into account thelabour demand function of the labour packers. Their presence allows the householdsto obtain a mark up for both types of agents, over their desired wages W h

t and W′ht ,

where:W ht =

un,tuc,t

, (24)

W′ht =

u′n,t

u′c,t

, (25)

where uc,t and un,t are the marginal utilities for consumption and labour.Labour unions are subject to Calvo frictions when setting the wages: θw can

optimally reset wages and 1− θw can partially index their wage by past indexation.The parameter χw ∈ [0, 1] controls the degree of indexation.

Labour unions will maximize the following objective function for the savers:

maxEt

∞∑τ=0

(βθw)τ{(

τ∏s=1

Πχwt+s−1

Πt+s

Wj,t −W hj,t+τ

)nj,t+τ

}(26)

s.t.

nj,t+τ =

(Πχwt+s−1

Πt+s

Wj,t

Wt+τ

)−λf,tndt+τ (27)

An isomorphic maximization holds for the borrowers. The maximization problemsfor the maximization of the wage mark up delivers standard New-Keynesian WagePhillips curve for the two type of agents.

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3.4 Monetary policy

The central bank sets the policy rate according to the rule:

Rt = max

[1, R1−ρRRρR

t−1

(Πt

Π∗

)φπ(1−ρR)(∆Yt∆Y

)φy(1−ρR)χM,t

], (28)

where χM,t is the AR(1) monetary policy process:

χM,t = ρMχM,t−1 + uM,t. (29)

uM,t is an n.i.d. monetary policy shock with variance σ2M . R is the steady state

interest rate and ∆Yt is the percentage variation of output, π∗ is the inflation target.

3.5 Market clearing

The market clearing condition for the product is the following:

Y dt = ak(uk,t)Kt−1 + an(un,t)Nt−1 + Ct + It + St; (30)

Y st =

(Atun,tNt−1n

d1−σn′dσ)1−α (

uk,t ¯Kt−1)α

; (31)

For the collateral:Ht +H

′

t = 1. (32)

3.6 Endogenous growth and the trend

In DSGE models, the macroeconomic variables grow around a trend, determinedby the the productivity growth of the economy. Therefore, in order to get thesolution, each trending variable is usually detrended by productivity.

In the DSGE models with exogenous technological growth, the productivityin the economy quarterly grows by a fixed growth coefficient parameter γ, whichsteadily increases the productivity in the economy. The TFP process is:

log(TFPt) = log(γ) + log(TFPt−1) + ua. (33)

The growth coefficient γ usually assumes a positive value around 1.005. Hence, thelog-variables will have a linear trend with a slope equal to log(γ), ensuring an annualgrowth close to 2% per year for all the aggregate macroeconomic variables as suchas Income, Consumption, Investments and so forth.

In this model, the productivity growth is endogenous and depends on how house-holds accumulate technology (i.e. savers’ technology investments decisions):

Nt = (1− δn)Nt−1 +

(St − ψn

(St − St−1)2

S

), (34)

13

and the total factor productivity of the model is going to be determined by:

TFPt = AtuN,tNt−1, (35)

where At is the stationary productivity subject to n.i.d. TFP shocks, uN,t is theutilization rate of technology, also stationary. Thus, the trend associated to theproductivity growth is exclusively determined by the accumulation of technologystock Nt. Therefore, the growth coefficient of technology µt will be time varyingand endogenous:

µt =Nt

Nt−1. (36)

Moreover, the trend of the economy featuring the macroeconomic variables will beobtained by:

Trendt =T∏t=t0

µt. (37)

3.7 Solution

Once the equilibrium conditions are derived, the model is detrended by Nt. Lowercases variables represent the stationary variables.

ct =CtNt

(38)

In steady state, the borrowing constraint (10) is binding and I assume that theborrowing constraint remains binding through the sample. The model is solved bylinearization.

4 Estimation

The linearised model is estimated using standard Bayesian techniques (An andSchorfheide, 2007). To compute the likelihood, I chose the following set of observ-able variables: the log-differences of Consumption, Investments, Housing prices andthe level of Interest rates and Inflation.4 Each observable variation is the com-posite effect of two sources of variations: the stationary component and the trendcomponent:

OBSt = log(obst)− log(obst−1) + log(µt), (39)

4The main goal of the estimation is to make inference on the evolution of the trend. Since thetrend of wages during the last 30 years has been influenced by structural changes not related tothe productivity evolution, wages are excluded from the set of observables. For the same typeof reason, the trend of government spending is related to changes which are not explained bytechnological growth. Government spending is excluded from the model.

14

where OBSt is the quarterly observed variation; log(obst)−log(obst−1) is the (model)stationary component of the variation, and log(µt) is the trend component. Dataare obtained by the FRED dataset. Further details on observation equations anddata are housed in the Appendix. The sample spans form 1983Q1 to 2009Q2,encompassing the Great Moderation period and the Great Recession. Only fewobservations are in the period of Zero Lower Bound.

The structural shocks hitting the economy are: the TFP shock, the MarginalEfficiency Investment (MEI) shock, the Preference shock, the Monetary policy shockand the Housing shock.

4.1 Trend and R&D series

The model is estimated without using the technology investments among theobservable variables. This choice marks an important difference with respect to thestate-of-the-art empirical works dealing with endogenous growth and business cycles(Bianchi and Kung (2014) and Guerron-Quintana and Jinnai (2014).

When the technology investments series are used in the estimation, the estima-tion process is not free to pin down the technological growth implied by the model,letting aside shocks hitting the law of motion for technology.

OBSt = log(obst)− log(obst−1) + log(µt); (40)

TECHt = log(st)− log(st−1) + log(µt); (41)

1 =(1− δn)

µt+

(st − ψn

(st − st−1

µt)2

s

). (42)

where OBSt is the quarterly variation of an observed macroeconomic variable,TECHt is the quarterly variation of the observed technology investments. Equations(40) is one of the observation equations; (41) is also an observable equation, whentechnology investments are considered in the set of observables. Equation (42) isone of the equilibrium conditions of the model and links the technology growth (µt)to the investments in technology made by savers (st). When technology investmentsare in the set of observables, the sequence of µt is pinned down by the joint presenceof Eq. (41) and Eq. (42). This choice affects the estimation of the trend along twomain dimensions. First, it affects the persistence of the technology accumulationprocess. Depending on the definition given to the productivity enhancing invest-ments, a different persistence will be pinned down in the estimation of the model.If the technology investments definition encompasses only R&D investments, as inBianchi and Kung (2014), the time series used is very persistent, the business cycleshocks will marginally affect the trend of the economy. If a broader definition oftechnology is adopted, technology investments can encompass software and adver-tising spendings too, as it is the case for Nakamura (2003) and Guerron-Quintanaand Jinnai (2014) or Anzoategui et al (2015). These alternative choices cause a

15

smaller persistence of the process. As a consequence, the business cycle shocks willhave a stronger impact on technology investments and on the time varying growthcoefficient (the trend).

Bianchi and Kung (2014) consider a technology which is mainly explained bythe R&D investments, according to the NIPA definition. Since the series is verypersistent, they find that the technology process is extremely persistent too. In theirestimation exercise, the adjustment cost of technology investments is φN = 100.03).According to their estimate exercise, most of the variation in the total TFP of themodel is explained by TFP shocks and technology utilization rate decisions, whilethe accumulation of technology stock (i.e. the trend of the model) is only marginallyperturbed by the business cycle shocks.

As opposed to Bianchi and Kung, Anzoategui et al (2015) use business R&Dinvestments, which exclude public expenditure on R&D and include investmentson software. Therefore the measure is more pro-cyclical with respect to the NIPAdefinition.

Instead, Guerron-Quintana and Jinnay (2014) use a broader definition of tech-nology investments, in line with the series reported in Nakamura (2003). Technologyinvestments corresponds twice the measure of software, plus twice R&D investmentsplus a measure for advertising. Using this series as observable in the estimation pro-cess, they find that the role of business cycle shocks in affecting investments intechnology (hence the trend) is much stronger, due to the smaller persistence of thetechnology process used as observable (φN = 2.73).

Second, when the technology series is imposed as an observable, the observationof technology investments pins down the peaks and the troughs of the growth co-efficient, the periods of low growth and periods of sustained growth. As a result,Bianchi and Kung find that the the trend has been negatively affected more by theIT bubble burst than by the Great Recession. This results lies on the definitionof technology on which their estimation is based. Instead, Guerron-Quintana andJinnay find that the Great Recession substantially lowered the trend.

In the estimation exercise of this paper, the technology is a latent variable andthe Kalman filter delivers the estimate for the path of the technology investments.This choice is also coherent with the vision for which long-run growth of the economycan depend on factors which are not included in the traditional measures of R&Dand software expenditures. Nakamura’s inclusion of advertising in the measureof technology investments goes in this direction. Nonetheless, other soft factorscan explain the long-run TFP growth, as such as education and human capitalaccumulation to mention a few.

4.2 Calibrated parameters

The parameters affecting the steady steady are calibrated in order to match thelong-term conditions of the economy (See Table 1). The parameter α is equal to

16

Par Value Sourceβ 0.995 Interest rateβ′

0.9895 Debt ratioα 0.33 Capital income ratioδK 0.025 Investment to capital ratioδN 0.03 Balanced Growth pathM 0.90 LTV ratioj 0.01 Housing Wealthγ 0.4547 Autocorrelation of debtη 0.05 Balanced Growth pathA 1 Balanced Growth pathϕ 1 Frisch elasticityλp 1.2 Price Mark upλw 1.2 Wage Mark up

Table 1: Calibrated parameters: values and their source.

0.33, δK equals 0.0025, as standard in literature. The subjective discount factor ofsavers is equal to 0.995, to get a annual steady state real interest rate of 4.03%.The subjective discount factor of borrowers is equal to 0.9895, in order to matchthe ratio of private debt in the economy, equal to 0.6. The parameters for theelasticity of substitution among different goods (λp) ad among labour (λw) are bothequal to 1.2, in order to obtain 20% steady state mark-ups. Concerning the debtequation, the steady state Loan to Value parameter is equal to 0.9, whereas theautocorrelation of the debt γ is .4548, the elasticity of labour supply ϕ is equal to1. These values are standard in literature and are not jointly estimated with themodel to avoid identification issues. The stationary TFP growth parameter (A) isset equal to 1 and the technology sector parameter (η) of the economy is .05, δNequals 0.030, in order to match the balanced growth path of the economy. Theparameter j determines the relative importance of housing with respect to non-durable consumption goods in the utility function and is set equal to 0.01, in orderto match the relative size of housing wealth with respect to the income wealth to1.5. These values are in line with the estimated values by Guerrieri and Iacoviello(2014). Concerning the structural parameters, priors are chosen starting by Smetsand Wouters (2007) and by Guerrieri and Iacoviello (see Table 2). Concerning theAR(1) stochastic processes, the autocorrelation parameters have prior mean equalto 0.5 and standard deviation equal to 0.2. Priors for the standard deviations of theshocks are very diffuse, with a mean equal to 0.01 and standard deviation equal to4.

17

5 Results

Results are reported in Table 2. The standard deviations of the marginal effi-ciency investment shocks and the housing shocks are σMEI = 0.046 and σJ = 0.097.Standard deviation for the TFP shock is 0.013, while for the monetary policy andthe preference shocks, σZ = 0.014 and σM = 0.002. Autocorrelations for the TFPshock is 0.865. Housing process autocorrelation is large and equal to 0.971. Thepreference process and the MEI process exhibit large persistence (ρZ = 0.843 andρMEI = 0.800). The autocorrelation for the monetary policy shock ρM equals 0.585.

Results for the monetary policy coefficients are very standard: the inflation policyresponse parameter φP is 1.852, while φY for output is 0.105. Autocorrelation of thepolicy rate ρR is 0.612. The price stickiness θP is 0.637, whereas the wage stickinessθW is 0.567. Price indexation ξP is 0.282 and wage indexation ξW is 0.428.The fraction of borrowers is equal to 0.227, a result in line with the literature butsmaller than the one found by Guerrieri and Iacoviello (2014). The consumptionhabit parameter is equal to 0.510. The inflation target is 1.005, equal to an yearlysteady state inflation of 2%.

The adjustment cost for capital investments is equal to 4.213 and the one fortechnology investments is equal to 11.122.

5.1 Impulse Responses: the housing shock

The first goal of the paper is to qualitatively assess how debt and housing dy-namics affect the trend of the economy. A positive housing shock is a temporarybut very persistent increase in the demand for houses, for both households. Impulseresponses following a positive housing shocks are reported in Fig. 1. On the top-leftpanel, the percentage variation of technology from its steady state is reported.5 Apositive housing demand shock lowers the trend of the model. The negative effecton productivity is explained by two main elements. First, the shock hits the econ-omy and increases housing prices. This increase of the collateral allows borrowers toexpand their debt. In order to meet the higher demand of debt, savers invest less intechnology. Second, after few quarters, savers increase their share of houses. whileborrowers are forced to deleverage. In order to buy more houses, savers will keep in-vestments in technology below their steady state. This reduction lowers productivitygrowth and temporarily reduces the trend of the economy.

5.2 Impulse Responses: TFP and MEI shocks

The presence of debt adds an additional propagation channel in the model, trig-gered by debt expansion. The crowding out mechanism, associated to debt expan-

5In this model, the investments in technology are the unique determinant of the technologystocks. Therefore, the top-left panel represents also the percentage variation of technology invest-ments, of the growth coefficient.

18

Prior PosteriorParam Type Mean St.dev Mean Mode 5% 95%ρA Beta 0.500 0.200 0.865 0.883 0.813 0.920ρMEI Beta 0.500 0.200 0.800 0.836 0.729 0.876ρJ Beta 0.500 0.200 0.971 0.993 0.948 0.996ρZ Beta 0.500 0.200 0.843 0.859 0.762 0.919ρM Beta 0.500 0.200 0.585 0.537 0.501 0.671φP Beta 1.500 0.250 1.852 1.454 1.444 2.255ρR Beta 0.750 0.100 0.612 0.580 0.532 0.687φY Normal 0.100 0.050 0.105 0.124 0.063 0.145θP Beta 0.500 0.075 0.637 0.655 0.543 0.733θW Beta 0.500 0.075 0.567 0.643 0.428 0.718χP Beta 0.500 0.100 0.282 0.255 0.155 0.405χW Beta 0.500 0.100 0.428 0.442 0.271 0.587σ Beta 0.500 0.200 0.227 0.138 0.103 0.351φK Gamma 5.000 2.000 4.213 1.834 1.474 7.031φN Gamma 5.000 2.000 11.122 10.047 6.825 15.421ε Beta 0.500 0.100 0.510 0.429 0.399 0.625π Normal 1.005 0.001 1.005 1.005 1.004 1.006σA InvGamma 0.010 4.000 0.013 0.012 0.009 0.017σMEI InvGamma 0.010 4.000 0.046 0.021 0.017 0.077σJ InvGamma 0.010 4.000 0.097 0.033 0.027 0.164σZ InvGamma 0.010 2.000 0.014 0.010 0.008 0.019σM InvGamma 0.010 4.000 0.002 0.002 0.002 0.002

Table 2: Estimated parameters: Prior distribution: Type, Mean and StandardDeviation, Posterior distribution: Mean, Mode, 90% error bounds.

19

0 20 40−4

−2

0

2x 10

−3

Productivity 0 20 40

0

0.5

1

1.5

House Price 0 20 40

−4

−2

0

2

4

Debt

0 20 40−1

0

1

2

Savers Houses0 20 40

−4

−2

0

2

Borr Houses 0 20 40

−0.1

0

0.1

0.2

0.3

Interest Rate

0 20 40−0.15

−0.1

−0.05

0

0.05

Savers Cons 0 20 40

−0.5

0

0.5

1

Borr Cons 0 20 40

−0.05

0

0.05

0.1

0.15

Inflation

Figure 1: Impulse responses to an housing demand shock. The y-axis measurespercentage deviation from the steady state.

0 20 40−0.01

0

0.01

0.02


−0.5

0

0.5

1

House Price 0 20 40

−1

0

1

2

3

Debt

0 20 40−1

−0.5

0

0.5


−1

0

1

2

Borr Houses 0 20 40

−0.5

0

0.5

Interest Rate

0 20 40−0.5

0

0.5

1

Savers Cons 0 20 40

−0.5

0

0.5

1

Borr Cons 0 20 40

−1

−0.5

0

0.5

Inflation

Figure 2: Impulse responses with respect to: TFP shock (solid blue lines), MEIshock (red lines). The y-axis measures percentage deviation from the steady state.

20

sion, affects also the final effects which the different type of shocks have on theeconomy. The TFP shock has a positive effect on the profitability of investments incapital and in technology (Fig. 2, solid lines). Therefore, savers invest in capital andtechnology, dismissing houses. However, the relative price of housing with respectto non-durable increases, allowing borrowers to expand their debt. This crowdingout partially offsets the positive effect of the shock in investments in technology.Overall, the final effect remains substantially positive.

The crowding out mechanism importantly affects the effect which MEI shockshave on productivity growth. A positive marginal efficiency investments shockstemporarily increases the demand for investments in capital. The overall effect of apositive shock on the trend is positive, given the complementarity relation betweencapital and technology. However, the presence of debt makes the technology invest-ments overshoot (Fig. 2, dashed lines). The initial effect of the shock on technologyis negative for two reasons. First, when the shock hits the economy, investing incapital becomes relatively more convenient than investing in technology. Therefore,more resources are used for the capital accumulation rather than for the technologyaccumulation. Second, since the positive MEI expands income, the relative priceof houses with respect to non-durable goods increases, triggering a debt expansion.This debt expansion reduces the investments in technology, because of the crowdingout mechanism. After few quarters, investments in technology overshoot and theoverall effect becomes strongly positive. First, when the marginal efficiency of theinvestments go back to its steady state, savers increase investments in technologybecause of the complementarity relation between capital and technology. Second,when borrowers start to deleverage, they free resources which can be invested intechnology investments.

5.3 The trend variation

The estimation allows us to study the evolution of productivity and of the trendalong the sample. The Kalman smoother delvers the best estimate for the evolutionof the technology investments (hence of the trend). Figure 3 shows the evolutionof the smoothed growth coefficient µt. The steady state growth trend is matchedat µss = 1.0045, which makes the steady state annual growth close to 2%. Thesolid line represents the smoothed estimate for the growth coefficient. The dashedline represents the projection of the growth coefficient during the years of the slowrecovery6.

6Since the model solution is linear, the sample ends at the beginning of the Great Recession.The strong negative downturn in demand moved the policy rate to its minimum (the Zero LowerBound, ZLB). The ZLB introduces a non-linearity which cannot be address with the linearizationmethods and the standard Bayesian techniques (the Kalman filter). In future extension of thepaper, I will solve the model using non-linear methods to take into account for the role of the ZLB.Estimation will be performed using the Approximate Bayesian Computation techniques (Scalone,2015)

21

1985 1990 1995 2000 2005 2010 2015 20201.002

1.003

1.004

1.005

1.006

1.007

1.008

1.009

Time varying trend

ProjectionSmoothed

Figure 3: Smoothed time varying growth coefficient µt (solid line). The dashed lineis its projected path.

1985 1990 1995 2000 2005 2010 2015 20200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Time varying trend

ProjectionSmoothed

Figure 4: Smoothed time varying growth trend (cumulated). (solid line). Thedashed line is its projected path.

22

The evolution of the growth coefficient can be divided in three phases. In thefirst part of the sample, during the Great Moderation, the growth coefficient steadilyincreased. In the second part of the sample, during the housing boom and the debtoverhang, the growth coefficient started to decrease. In the final part of the sample,during the Great Recession, the growth coefficient substantially decreased. A peak(µt = 1.0079) is reached around the years 2004-2005. The blue dashed line showsthe projection for the growth coefficient for the following 50 quarters after the endof the sample, with a trough around the year 2015.

In order to check the role of the different types of shocks on technology accu-mulation, I simulate the estimated model by using the sequence of the smoothedshocks and excluding one type of shock at time. I compare this simulation withsmoothed sequence coming out of the estimation exercise. The difference betweenthe two series evidences the role of the shock which is excluded in the simulation.In Figure 5, the smoothed series of technology investments (solid lines) is comparedwith the counter-factual technology investments, obtained by excluding the housingshocks from the simulation (dashed lines). In the years between 1990 and 1995, inthe counter factual without the housing shocks, the investments are lower. Instead,in the years of the housing boom between 2004-2007, the housing shock lowers theinvestments in technology. During this period, the expansion of debt and the in-crease in housing demand crowded out technology, negatively affecting productivity.Figure 6 reports the evolution of the growth coefficient µt. in the first half of the

90′s and in the last part of the sample (the fall in housing demand and the delever-aging), the counter-factual without the housing shock is lower than the benchmarksmoothed series (solid lines). In the aftermath of the crisis, the deleveraging par-tially offset the negative slowdown in productivity. This mechanism is evidencedby the series reported in Figure 7. The solid lines represent the smoothed variablesfor debt, the housing share of savers, the house prices and the time varying trend.The dashed lines are the simulated series, obtained by excluding the housing shock.From the counterfactual simulation we can infer that, without the housing shock,

the strong increase in housing prices, the debt overhang and the increase of housesdetained by borrowers would have not been observed. Also, the growth coefficientwould have kept increasing during the period 2003-2007, since debt overhang wouldhave not crowded out investments in housing.

Figures 8 and 10 report the smoothed estimates for the technology investments(solid line) and their counterfactuals when, respectively, TFP shocks and MEI shocksare set to zero. The TFP shock has an important role in increasing the trend ofthe economy since 1995 to 2007 (Figure 8). Since the Great Recession, negativeTFP shocks are responsible for reducing the investments in technology. Figure9 confirms that the TFP shock is the main driver of the increase in the growthtrend of the economy, especially in the years around the 2000. The MEI shockhas a crucial role in determining the dynamics of the endogenous growth trend inthe final part of the sample. The initial effect of a negative MEI shock on the

23

1985 1990 1995 2000 2005 20104.45

4.5

4.55

4.6

4.65

4.7

4.75

4.8

4.85

4.9

4.95x 10

−3

R&D Investments

BenchmarkNo Housing shocks

Figure 5: Smoothed Technology investments (levels). The solid lines are thesmoothed values, the dashed lines are the smoothed Technology investments withoutthe housing shocks.

1985 1990 1995 2000 2005 2010 2015 20201.002

1.003

1.004

1.005

1.006

1.007

1.008

1.009

Time varying Trend


Figure 6: Smoothed time varying growth coefficient µt (levels). The solid line is thesmoothed value, the dashed line is the smoothed growth trend without the housingshocks.

24

1985 1990 1995 2000 2005

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Debt


1985 1990 1995 2000 20050.5

0.55

0.6

0.65

0.7

0.75

0.8

Savers Houses

1985 1990 1995 2000 2005

−0.1

0

0.1

0.2

0.3

House prices1985 1990 1995 2000 2005

1.003

1.004

1.005

1.006

1.007

1.008

Time Varying Trend

Figure 7: Smoothed variables (solid lines) and their counterfactual without housingshocks (dashed lines): Debt, Savers houses, House prices, Time varying growthtrend.

1985 1990 1995 2000 2005 20104.5

4.55

4.6

4.65

4.7

4.75

4.8

4.85

4.9

4.95x 10

−3

R&D Investments

BenchmarkNo TFP shocks

Figure 8: Smoothed technology investments (levels). The solid lines are thesmoothed values, the dashed lines are the smoothed technology investments withoutthe TFP shocks.

25

1985 1990 1995 2000 2005 2010 2015 20201.002

1.003

1.004

1.005

1.006

1.007

1.008

1.009

Time varying Trend

BenchmarkNo TFP shocks

Figure 9: Smoothed time varying growth coefficient µt (levels). The solid line isthe smoothed value, the dashed line is the smoothed growth trend without the TFPshocks.

1985 1990 1995 2000 2005 20104.45

4.5

4.55

4.6

4.65

4.7

4.75

4.8

4.85

4.9

4.95x 10

−3

R&D Investments

BenchmarkNo MEI shocks

Figure 10: Smoothed technology investments (levels). The solid lines are thesmoothed values, the dashed lines are the smoothed technology investments withoutthe MEI shocks.

26

trend is positive, and after 20 quarters becomes strongly negative. In Figure 10the dashed line represents the counterfactual technology investments without theMEI shock, while the solid lines is the benchmark smoothed sequence. The 2001and the 2008 downturns are mainly featured by negative MEI shocks. On impact,investments in technology increase. As shown in the impulse responses, after fewquarters, technology investments overshoot and strongly decrease the trend. Rightafter the Great Recession, the counterfactual growth coefficient remains higher thanin the smoothed benchmark case (Figure 11). In the projected path, the benchmarkgrowth coefficient falls below the counterfactual, because of the long-term negativeeffect which the negative MEI shock has on the technology investments.

6 Debt and growth

The following experiment aims at shedding some light on the role which debthas in the propagation of shocks. The focus will be on the effects on productivitygrowth.In this model, heterogeneity derives from two elements. One is the difference inpreferences, where a fraction of households is more patient than another. A secondsource of inequality between the two types of agents comes from the limited accessto capital and technology market: only savers accumulate capital and technologyand rent them to firms.

The experiment consists in producing impulse responses and counterfactuals intwo different extreme cases:

• Zero debt economy: the fraction of borrowers σ is set to 0, bt is constantlyequal to zero, and housing loses its role of collateral.

• Larger debt: half of the agents are borrowers (σ = 0.5). In this case thequantity of total debt in the economy is larger. This case is not that far fromsome of the estimate results obtained in literature (i.e. Guerrieri and Iacoviello(2014) find σ = 0.42).

The impulse responses of the models are analysed, focusing on the cases where debtaffects the dynamics of technology investments.

As already anticipated, debt dynamics affect the way in which the MEI shockpropagates through the economy and impacts on productivity growth. In Figure12, impulse responses to a positive MEI shock are reported: the solid lines for thebenchmark case, the dashed lines for the model with no debt and the dash-dottedlines for the large debt case.

The response of technology to the shock is strongly affected by the presence ofdebt. In particular, when the model has zero net debt, the model converges to theBianchi and Kung’s model, except for the presence of a fixed endowment durablegood in the utility function. In that case, impulse responses are very similar to the

27

1985 1990 1995 2000 2005 2010 2015 20201.002

1.003

1.004

1.005

1.006

1.007

1.008

1.009

Time varying Trend

BenchmarkNo MEI shocks

Figure 11: Smoothed time varying growth coefficient µt (levels). The solid line isthe smoothed value, the dashed line is the smoothed growth trend without the MEIshocks.

0 20 40−2

−1

0

1

2x 10

−3


−0.1

−0.05

0

0.05

0.1

House Price 0 20 40

−0.1

0

0.1

0.2

0.3

Debt

0 20 40−0.1

−0.05

0

0.05

0.1


−0.05

0

0.05

0.1

0.15

Borr Houses 0 20 40

−5

0

5

10x 10

−3

Interest Rate

0 20 40−0.02

0

0.02

0.04

Savers Cons 0 20 40

−5

0

5

10

15x 10

−3

Borr Cons 0 20 40

−2

0

2

4

6x 10

−3

Inflation

Figure 12: Impulse responses to a MEI shock when the fraction of borrowers is:σ = 0.22 (solid lines), σ = 0 (dashed lines), σ = 0.5 (dash-dotted lines). The y-axismeasures absolute deviation from the steady state.

28

ones found by Bianchi and Kung. When a positive MEI shock hits the economy,technology investments slowly and monotonically increase over time. This resultstands on the complementarity between technology and capital, and on the largeadjustment costs in the technology accumulation law of motion. Instead, when themodel features a role fro debt and housing, the technology investments overshoot(solid lines). Also, the larger the fraction of borrowers, the larger is the overshootingof technology investments (dash-dotted line). The difference lies on the fact thatwhen a positive MEI shock hits the economy, the housing prices increase because ofthe higher relative scarcity of housing with respect to the non-durable goods. Thisgenerates debt expansion and crowds out investments in technology.

Concerning the propagation of the TFP shock, debt slightly reduces the positiveeffects on growth, following an increase in housing prices. The larger the fraction ofborrowers, the larger the crowding out effect deriving by the debt expansion will be(Figure 13).

Debt has an important role in affecting the effect of the preference shock onthe technology investments too. A positive preference shock decreases the degreeof patience of agents, Therefore households increase their demand of houses andnon-durable goods. If the fraction of borrowers in the economy is equal to 0, theeffect of a positive preference shock on technology accumulation is negative, sincehouseholds consume more and invest less in technology. Instead, when the economyencompasses a fraction of borrowers, a preference shock pushes savers to increase theshare of houses, forcing borrowers to reduce their debt. Thanks to this deleveraging,resources are freed and are invested by savers in technology. When σ = 0.5, thelatter effect dominates the reduction associated to an increase in consumption. Inthe benchmark case, the two effects almost offset each other, causing an ambiguouseffect on technology.

The presence of borrowers in the economy affects the overall effect which mone-tary policy shocks have too (Figure 15). In a model without borrowers, a negativemonetary policy shock depresses demand, lowering investments in technology (solidlines). In the case of a large debt (dash-dotted lines), a negative monetary policyshock has a positive effect on technology because of two channels. First, the mone-tary policy shock causes a reduction of house prices. Second, the cost of borrowingincreases, due to the increase of the real interest rate. These two events force thedeleveraging and free resources to invest in technology. In a large debt scenario, thepositive effects overcome the direct negative effect which the monetary policy shockhas on the investments. In the benchmark case (solid lines), the two effects balanceeach other, provoking an ambiguous effect on technology.

Finally, the housing shock does not have any effect in case of σ = 0 (Figure16). In this case, the housing shock and the increase in house prices do not crowdout investments in technology, whereas net debt constantly remains at zero (dashedlines).

In order to assess to which extent inequality affected the growth coefficient path,

29

0 20 400

1

2

3x 10

−3


0

0.05

0.1

0.15

0.2

House Price 0 20 40

0

0.05

0.1

0.15

0.2

Debt

0 20 40−0.06

−0.04

−0.02

0

0.02


−0.02

0

0.02

0.04

0.06

Borr Houses 0 20 40

−15

−10

−5

0

5x 10

−3

Interest Rate

0 20 400

0.02

0.04

0.06

Savers Cons 0 20 40

−0.01

0

0.01

0.02

0.03

Borr Cons 0 20 40

−0.02

−0.01

0

0.01

Inflation

Figure 13: Impulse responses to a TFP shock when the fraction of borrowers is:σ = 0.22 (solid lines), σ = 0 (dashed lines), σ = 0.5 (dash-dotted lines). The y-axismeasures absolute deviation from the steady state.

0 20 40−2

−1

0

1

2x 10

−4


−0.04

−0.02

0

0.02

House Price 0 20 40

−0.1

−0.05

0

0.05

0.1

Debt

0 20 40−0.02

0

0.02

0.04

0.06


−0.06

−0.04

−0.02

0

0.02

Borr Houses 0 20 40

−5

0

5

10x 10

−3

Interest Rate

0 20 400

0.02

0.04

0.06

Savers Cons 0 20 40

0

0.005

0.01

0.015

0.02

Borr Cons 0 20 40

−1

0

1

2

3x 10

−3

Inflation

Figure 14: Impulse responses to a Preference shock when the fraction of borrowersis: σ = 0.22 (solid lines), σ = 0 (dashed lines), σ = 0.5 (dash-dotted lines). They-axis measures absolute deviation from the steady state.

30

0 20 40−4

−2

0

2

4x 10

−4


−0.15

−0.1

−0.05

0

0.05

House Price 0 20 40

−0.3

−0.2

−0.1

0

0.1

Debt

0 20 40−0.05

0

0.05

0.1

0.15


−0.15

−0.1

−0.05

0

0.05

Borr Houses 0 20 40

−0.01

−0.005

0

0.005

0.01

Interest Rate

0 20 40−0.03

−0.02

−0.01

0

0.01

Savers Cons 0 20 40

−0.02

−0.01

0

0.01

Borr Cons 0 20 40

−0.02

−0.01

0

0.01

Inflation

Figure 15: Impulse responses to a Monetary shock when the fraction of borrowersis: σ = 0.22 (solid lines), σ = 0 (dashed lines), σ = 0.5 (dash-dotted lines). They-axis measures absolute deviation from the steady state.

0 20 40−6

−4

−2

0

2x 10

−4


0.05

0.1

0.15

0.2

0.25

House Price 0 20 40

−0.2

0

0.2

0.4

0.6

Debt

0 20 40−0.1

0

0.1

0.2

0.3


−0.2

−0.1

0

0.1

0.2

Borr Houses 0 20 40

−5

0

5

10x 10

−3

Interest Rate

0 20 40−15

−10

−5

0

5x 10

−3

Savers Cons 0 20 40

−5

0

5

10

15x 10

−3

Borr Cons 0 20 40

−5

0

5

10x 10

−3

Inflation

Figure 16: Impulse responses to a Housing shock when the fraction of borrowers is:σ = 0.22 (solid lines), σ = 0 (dashed lines), σ = 0.5 (dash-dotted lines). The y-axismeasures absolute deviation from the steady state.

31

1985 1990 1995 2000 2005 2010 2015 20201.002

1.003

1.004

1.005

1.006

1.007

1.008

1.009

σ=0.22

σ=0

σ=0.5

1985 1990 1995 2000 2005 2010 2015 2020−0.5

0

0.5

1

1.5

2

Figure 17: Smoothed endogenous growth coefficient µt and debt bt in the benchmarkcase (σ = 0.22 (solid lines)). Counterfactual simulated µt when σ = 0 (dashed lines),σ = 0.5 (dash-dotted lines).-Levels

two conterfactual simulations are produced (Figure 17). The solid lines are thesmoothed growth coefficient µt and the smoothed debt bt obtained after the esti-mation exercise. The dashed line represent the same variables simulated by thesame model without heterogeneity among agents (σ = 0). The path is obtainedby feeding the model with the sequence of the smoothed shocks obtained in thebenchmark estimation exercise. The dash-dotted lines are the counterfactual witha larger fraction of borrowers. This scenario is obtained by simulating the model byfeeding the sequence of smoothed shocks, when the fraction of borrowers σ equals0. The main difference in the dynamics of the growth coefficients is featured by twoelements:

• the size of the effect deriving from the housing shocks according to the differentweight of debt in the economy;

• the timing and the sign of the response of the growth coefficient to the MEIshock, according to the different degrees of inequality.

In the case of σ = 0, the net debt of the economy is constantly equal to 0. Thedynamics of debt do not affect the business cycle and the representative agent de-cisions. The simulated counterfactual growth coefficient (dashed line), is below thesmoothed growth coefficient (solid line) during the 90’s. Instead, the scenario withlarger debt in economy features a larger growth coefficient in the same period. Thisis mostly due to the negative demand shock found in the estimation result (see Fig-ure 18). The reduction in debt which is triggered by the negative housing shock,

32

makes savers to invest more resources in technology. The consequences of the shockpersist across all the decade. In the second half of the 00’s, the opposite happens.A positive housing demand shock fosters debt and crowds out the investments intechnology. The larger the fraction of borrowers in the economy, the larger the ef-fect of the housing shock. In the case of zero debt economy (dashed line), housingdoes not produce effects on the growth coefficient, which keeps steadily increasinguntil the Great Recession. In 2007-2008, a negative housing demand shock forcesagents to deleverage. This effect sustains the investments in technology right afterthe crisis. In the scenario without debt, this effect is missing.

Debt affects the growth coefficient also through the delayed effect of the MEIshock. In the aftermath of the Great Recession, in the zero debt scenario (dashedlines), the effect of a negative MEI shock pushes savers to slowly reduce investmentsin technology. Since the adjustment cost for technology investments is larger thanthe one for capital investments, the effect of the shock on the reduction is verypersistent. According to the model, the MEI shock of the Great Recession is stillnegatively affecting savers’ investments in technology. However, in the benchmarkscenario, the negative MEI shock pushes borrowers to deleverage. For this reason,savers invest the freed resources in technology. This partially offsets the reductionin technology. When the deleveraging ends, since the stock of capital is below itssteady state, investments in technology overshoot. This effect is amplified in thelarge debt scenario, because of the larger influence which debt dynamics have onthe economy.

7 Conclusion

This paper analyses the effects of debt on the evolution of growth and on produc-tivity through the lens of an empirical DSGE model. Particular emphasis is givento the role of housing demand shocks and debt dynamics in affecting the trend ofthe economy.

Heterogeneous agents and a technology sector are incorporated in an otherwisestandard new-Keynesian DSGE model, with nominal frictions on prices and wages.Estimation is conducted using standard Bayesian techniques.

An increase in housing demand favours a reduction of investments in technology.This is due to an initial expansion of debt and to a crowding out of investmentsin technology in favour of housing. More in general, the crowding out effect ofinvestments in technology is a propagation mechanism in the model, at play eachtime that a shock increases the value of the nominal collateral of borrowers.

The estimation exercise is conducted treating the technology investments as alatent variable. This marks a difference with state-of-the-art literature empiricallyinquiring about endogenous growth in DSGE models. The smoothed growth coeffi-cient steadily increases during the Great Moderation and sharply falls down after theGreat Recession. MEI shocks and TFP shocks are confirmed as the main drivers

33

of the growth coefficient. Interestingly, the effect of the MEI shock is postponedwith respect to the case of model with no debt in the model. This effect is relatedto the fact that a negative MEI shock triggers a decrease in nominal collateral forborrowers, which forces borrowers to deleverage and frees resources to be investedin technology.

Also, a counterfactual exercise shows that debt among households affected theevolution the growth coefficient during the sample, mainly in the second half ofthe sample. All things equal, heterogeneity and debt increase the sensitivity ofthe economy to housing shocks and postpone the effects of the MEI shocks onproductivity.

In order to take into account the role of the occasionally binding constraint on theinterest rate (Zero Lower Bound) and on borrowing, a future extension will explorethe use of the non-linear solution methods (Guerrieri and Iacoviello,2014, Maliar andMaliar, 2014). Non-linear estimation is going to be conducted though non standardBayesian technique, as such as the Approximate Bayesian Computation (Scalone,2015). This part is left for future research.

Also, as a possible extension, the model could be used to analyse the direct effectswhich housing fluctuations have on the borrowing constraints of entrepreneurs, inline with the model by Liu, Wang and Zha (2011).

34

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Appendix

Data

Data sources for the estimation are as follows.

• Consumption: Ctott = logCt+C′tC+C′

.Data (dataC): PCEC, Seasonally Adjusted, Quarterly per capita variation.Deflated by GDP deflator.

• Investments in capital : It = log ItI

.Data dataI : Private Non-residential fixed investments, PNFI, Seasonally Ad-justed, Quarterly per capita variation. Deflated by GDP deflator.

• Inflation: πt = πt − 1.Data dataP : Implicit Price Deflator, GDPDEF, Seasonally Adjusted, Quar-terly variation.

• Interest Rate:rt = Rt − 1.Data dataR: Effective Federal Funds rate, FEDFUNDS, levels.

• Houses Prices: Qt = logQtQ. Data dataQ: All-Transactions House Price Index

for the United States, USSTHPI, Quarterly, Quarterly variation.

Observation equations

The model is estimated using five observables and five structural shocks. Theobservation equations are:

dataC = log(ctott)− log(ctott−1) + log(µt);

dataI = log(invt)− log(invt−1) + log(µt);

dataQ = log(qt)− log(qt−1) + log(µt);

dataP = πt − 1;

dataR = Rt − 1.

Exogenous processes

The AR(1) processes for the structural shocks are as follows.The process for the stationary component of the TFP is:

χA,t = ρAχA,t−1 + uA,t; (43)

39

The process for the Marginal Efficiency Investment shock is:

χMEI,t = ρMEIχMEI,t−1 + uMEI,t; (44)

The process for the Housing demand shock is:

jt = (1− ρj)j + ρjjt−1 + uJ,t; (45)

The process for the preference shock is:

zt = ρZzt−1 + uZ,t; (46)

The process for the monetary policy shock is:

χM,t = ρMχM,t−1 + uM,t; (47)

1985 1990 1995 2000 2005

−0.05

0

0.05

0.1

TFP process1985 1990 1995 2000 2005

−0.4

−0.3

−0.2

−0.1

0

MEI process1985 1990 1995 2000 2005

−5

0

5

10x 10

−3

Housing process

1985 1990 1995 2000 2005−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

Preference process1985 1990 1995 2000 2005

−8

−6

−4

−2

0

2x 10

−3

Monetary process

Figure 18: Smoothed exogenously driven processes.

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Documents

Housing, Debt and Growth