MARCH by Caterina Mendicino

1 WORKING PAPER SERIES NO 743 / MARCH 27 CREDIT MARKET AND MACROECONOMIC VOLATILITY by Caterina Mendicino2 WORKING PAPER SERIES NO 743 / MARCH 27 CRED...

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WO R K I N G PA P E R S E R I E S NO 743 / MARCH 2007

CREDIT MARKET AND MACROECONOMIC VOLATILITY

ISSN 1561081-0

9 771561 081005

by Caterina Mendicino

WO R K I N G PA P E R S E R I E S NO 743 / MARCH 2007

CREDIT MARKET AND MACROECONOMIC VOLATILITY 1 by Caterina Mendicino 2

In 2007 all ECB publications feature a motif taken from the €20 banknote.

This paper can be downloaded without charge from http://www.ecb.int or from the Social Science Research Network electronic library at http://ssrn.com/abstract_id=975681.

1 Part of this work was completed during the summer 2005 under the Graduate Research Programme of the Research Directorate of the European Central Bank, which I wish to thank for hospitality. 2 Monetary and Financial Analysis Department, Bank of Canada, 234 Wellington St., Ottawa, K1A 0G9, Ontario, Canada; e-mail: [email protected]; Homepage: http://www.bankofcanada.ca/ec/cmendicino/.

© European Central Bank, 2007 Address Kaiserstrasse 29 60311 Frankfurt am Main, Germany Postal address Postfach 16 03 19 60066 Frankfurt am Main, Germany Telephone +49 69 1344 0 Internet http://www.ecb.int Fax +49 69 1344 6000 Telex 411 144 ecb d All rights reserved. Any reproduction, publication and reprint in the form of a different publication, whether printed or produced electronically, in whole or in part, is permitted only with the explicit written authorisation of the ECB or the author(s). The views expressed in this paper do not necessarily reflect those of the European Central Bank. The statement of purpose for the ECB Working Paper Series is available from the ECB website, http://www.ecb.int. ISSN 1561-0810 (print) ISSN 1725-2806 (online)

CONTENTS Abstract

4

Non-technical summary

5

1 Introduction

6

2 Related literature and empirical facts

8

3 The model 3.1 Agents’ optimal choices

11 13

4 Model solution 4.1 Benchmark parameter values 4.2 Dynamics

16 16 16

5 Credit market size and the deterministic steady state

17

6 Model dynamics 6.1 Credit market size and business cycle

18 20

7 Credit market size and output volatility: comparing model predictions with the data

21

8 One vs two-sector model: amplification and volatility

22

9 Concluding remarks

24

10 References

25

Tables and figures

31

European Central Bank Working Paper Series

45

ECB Working Paper Series No 743 March 2007

3

Abstract This paper investigates the role of credit market size as a determinant of business cycle ‡uctuations. First, using OECD data I document that credit market depth mitigates the impact of variations in productivity to output volatility. Then, I use a business cycle model with borrowing limits a la Kiyotaki and Moore (1997) to replicate this empirical regularity. The relative price of capital and the reallocation of capital are the key variables in explaining the relation between credit market size and output volatility. The model matches resonably well the reduction in productivity-driven output volatility implied by the established size of the credit market observed in OECD data. Keywords: credit frictions, reallocation of capital, asset prices. JEL codes:E21-E22- E44- G20

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ECB Working Paper Series No 743 March 2007

Non-Technical Summary

Studying the determinants of business cycle ‡uctuations is crucial for understanding the dynamics of modern economies. The aim of this paper is to examine how the degree of credit market development is related to business cycle ‡uctuations in industrialized countries. The paper presents some empirical facts and a model economy whose aim is to replicate the relation between credit market size and the volatility of output. First, OECD data are used to show that a negative and signi…cant relation exists between credit market size – as a proxy for the degree of credit market depth – and the propagation to output of variation in productivity. Credit market size substantially reduces the volatility of output driven by variations in productivity. Second, I present a model economy in which di¤erent degrees of credit market development, ceteris paribus, a¤ect the sensitivity of output to productivity shocks and thus its volatility over the business cycle. I use a stochastic dynamic general equilibrium model with collateral constraints a la Kiyotaki and Moore (1997) in which higher liquidation costs characterizes less developed credit systems. Existing literature dealing with credit markets has shown that credit frictions may be a powerful transmission mechanism that propagates and ampli…es shocks. This paper demonstrates that in a model with collateral constraints, movements in the relative price of capital and thus the reallocation of capital, substantially a¤ect the sensitivity of output to shocks. In accordance with the empirical …ndings, the model asserts that the propagation of variations in productivity to output is greater in economies with tighter credit markets. The reduction in productivity-driven output volatility implied by the model is closely related to the data.

ECB Working Paper Series No 743 March 2007

5

1

Introduction

As a result of macroeconomic, political and legal factors, credit markets signi…cantly di¤er among OECD countries1 . At the same time the volatility of the cyclical component of output shows a noticeable degree of variation across countries and time (Figure 1.a). Table 1 reports that credit market size is negatively and signi…cantly correlated with the volatility of output, consumption, investment, investment in residential properties and housing prices2 . Preliminary analysis on OECD data, indicating that smoother ‡uctuations are associated with greater sizes of the credit market, provide a reasonable ground to investigate the relation between credit market development and business cycle ‡uctuations in industrialized countries. The analysis is conducted in three steps. First, OECD data are used to document the relation between the degree of credit market development and macroeconomic ‡uctuations. Speci…cally, a greater size of the credit market, as a proxy for credit market depth, reduces the propagation of variations in productivity to output volatility. Second, I develop a two-sector business cycle model that links the degree of credit market development to the sensitivity of output to productivity shocks, and thus its volatility over the business cycle. Last, I compare the predictions of the model with the empirical …ndings. The model predicts a reduction in productivity-driven output volatility of about 20% that closely corresponds to the data evidence. Despite the stylized nature of the model, it mimics the data reasonably well both qualitatively and quantitatively. Model. The model is based on Kiyotaki and Moore (1997). To generate a reason for the existence of credit ‡ows, two types of agents are assumed, both of whom produce and consume the same type of goods using a physical asset. They di¤er in terms of discount factors, and consequently, impatient agents become borrowers. Credit constraints arise because lenders cannot force borrowers to repay. Thus, physical assets, are used not only as factors of production but also as loan collateral. My setup di¤ers from Kiyotaki and Moore (1997) framework, in that I use more standard assumptions as to preferences and 1 See e.g. La Porta, Lopes-de Silanes, Shleifer, Vishny (1997) and Djankov, Hart, McLiesh and Shleifer(2006), 2 See also …gures 1.a and 1.b. Correlations are computed for quarterly variables averaged over rolling three-year periods during the 1983-2004 a sample of 20 OECD countries.Volatility is measured as the standard deviation of the log detrended real variables. Hodrick-Prescott …lter are used to remove the estimated trend of the series.

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ECB Working Paper Series No 743 March 2007

technologies3 . Aggregate uncertainty is introduced into the model, so asset prices are not perfectly predicted by the agents. To be able to investigate the behavior of economies that di¤er in terms of access to credit …nancing, I allow for the existence of liquidation costs in modeling the collateral constraint4 . According to the Schumpeterian view, aggregate shocks generate an inter-…rm reallocation of resources, and evidence of this is well established as pertains to job ‡ows. Rampini and Eisfeldt (2005) have recently demonstrated the relevance of physical capital reallocation over the business cycle5 . In fact, in the USA the amount of capital reallocation represents approximately one quarter of total investment, and that depending on how capital reallocation is measured, between 1.4 and 5.5 of the capital stock turns over each year. Furthermore, the reallocation of existing productive assets among …rms (sales and acquisitions of property, plant, and equipment) is procyclical. The model presented in this paper generates a negative relationship between the degree of credit market development and output volatility giving a primary role to variations in relative prices and thus the reallocation of capital across …rms. When the economy is hit by a positive neutral productivity shock agents increase their capital expenditure, the relative price of capital rises and existing capital is thus reallocated to the production of the capital good. In economies with a greater access to the credit market, the productivity gap between the two groups of agents is smaller. Thus, following a productivity shock, less capital is redistributed to the more productive agents. The sensitivity of asset prices to the shock is reduced and consequently less capital is reallocated to the capital good production. As a result total production reacts by less to the shock. The magnitude of the e¤ect of credit market size on the reduction in the volatility of output induced by variations in productivity is in accordance with the empirical …ndings. 3 Kiyotaki and Moore assume that the agents are risk neutral and apart from using di¤erent discount factors, they also di¤er in their production technology. In my model, both groups of agents have a concave utility function and are generally identical, except that they have di¤erent subjective discount factors. 4 As in Aghion et al. (2005) collateral requirements serve as a proxy for the degree of credit market development. Tighter collateral constraints result in a smaller size of the credit market and thus, characterize economies with a less-developed credit market. 5 See also Maksimovic and Phillips (2001), Andreade, Mitchell, and Sta¤ord (2001), Schoar (2002), Jovanovic and Rousseau (2002). A few papers also examine the behavior of capital reallocation from a microeconomic point of view. Among the main results are that capital ‡ows from less productive to more productive …rms (Maksimovic and Phillips (2001)) and that gains derived from reallocation appear larger when productivity di¤erences are greater (Lang, Stulz, and Walkling (1989) and Servaes(1990)).

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This results contribute signi…cantly to the debate concerning the ampli…cation role of collateral constraints. Cordoba and Ripoll (2004) show that adopting standard assumptions about preferences and technologies makes Kiyotaki and Moore’s model unable to generate persistent or ampli…ed shocks. Thus, their results call into question the quantitative relevance of credit frictions as a transmission mechanism. I document that in the model presented here, the magnitude of ampli…cation is related to the degree of credit rationing. The results of Cordoba and Ripoll hold only for economies with the least possible degree of credit rationing allowed by the model. Layout. The paper proceeds as follows. Section 2 discusses some empirical evidence. Section 3 presents the model, while section 4 discusses the solution method and calibration. Section 5 shows the steady-state implications of di¤erent degrees of credit rationing. Section 6 presents the dynamics of the model, and Section7 the relationship between credit market size and business cycle volatility. Section 8 investigates the importance of having two sectors of production in the model by comparing the results in terms of volatility with the one sector model version. Section 9 presents the conclusions of the study.

2

Related Literature and Empirical Facts

Literature. This paper is related to the large literature about …nancial frictions and business cycle. Most of the theoretical research focuses on credit frictions as a transmission mechanism that propagates and ampli…es shocks. Bernanke and Gertler (1989), Calstrom and Fuerst (1997), Bernanke, Gertler and Gilchrist (1999) among others, study the relevance of …nancial factors on …rm’s investment decisions, emphasizing the role of agency-costs. Kiyotaki and Moore (1997) and Kiyotaki (1998) show that if debt needs to be fully secured by collateral, small shocks can have large and persistent e¤ects on economic activity. Iacoviello (2005) documents the relevance of housing prices and collateralized debt for the transmission and ampli…cation of shocks. These papers have been very in‡uential and a big strand of the literature has used collateral constraints as an ampli…cation mechanism of shocks. Nevertheless, only few papers have analyzed the role of the degree of credit market development on business cycle ‡uctuations. Examining access to the in-

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ECB Working Paper Series No 743 March 2007

ternational credit market, Aghion, Baccheta, and Banerjee (2003) demonstrate that small open economies at an intermediate level of …nancial development are more vulnerable to shocks. Aghion, Angeletos, Banerjee, and Manova (2005) document that the degree of credit market development makes growth less sensitive to commodity price shocks. Recent papers on the U.S. Great moderation also provide some insights on the relation between …nancial factors and business cycle ‡uctuations. Justiniano and Primiceri (2006) report that the decline in the volatility of shocks speci…c to the equilibrium condition of investment accounts for most of the decline in the macro volatility. Further more they also document evidence of the fact that the reduction in the volatility of the relative price of investment corresponds remarkably well with the timing of the …nancial deregulation. Campell and Hercowitz (2005) demonstrate that indeed the …nancial reforms of the mortgage market that took place in the early 1980s., coincided with a decline in the volatility of output, consumption, and hours worked. Similarly, Guerron (2007) shows that the great moderation can be partially attributed to the decreased portfolio adjustment costs resulting by the same process of …nancial deregulation. Jermann and Quadrini (2005) attribute a primary role to a more ‡exible use of equity …nancing in accounting for a substantial reduction in macroeconomic volatility. This paper is in the same spirit of Aghion et al. (2003) and Aghion et al. (2005), but it focuses on the role of credit market depth in the transmission of variations in productivity to the volatility of output in industrialized countries. In doing so, I do not limit the analysis to the comparison of two di¤erent degrees of …nancial development –i.e. calibrated pre- and post-Great-Moderation – but I explore the theoretical nexus by analysing a full range of levels of development in the domestic credit market including all possible state of development across OECD countries in the last two decades. Cross-country analysis also suggest a link between credit market development and economic ‡uctuation. Using large samples of countries, most of which developing countries, Beck et al. (2000), Denizer, Iyigun, and Owen (2002) and Da Silva (2002) demonstrate that well-developed credit markets induce smoother output ‡uctuations. More recent papers document the e¤ects of bank …nancing and …nancial deregulation on the volatility of output growth, risk sharing and e¢ ciency. Among others, Morgan, Rime and Strahan (2006), Larrain (2006) and Acharya, Imbs and Sturgess (2006) using state-level US data suggest a

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link between …nancial modernization, industrial production volatility and specialization of investments. Empirical Evidence. In the following I test the e¤ects of the degree of credit market development on output volatility in OECD countries. In particular I examine the e¤ect of credit market size on the propagation of variation in productivity to output. Following Aghion et al (2005), I measure credit market depth, Crediti;t ; by the size of the credit market, i.e. the credit extended to the domestic private sector by banks and other …nancial institutions as a share of GDP. To test for causality I estimate a panel speci…cation: Y i;t

=

i

+

t

+

1 Crediti;t

+

control 2 Xi;t

+ ui;t

where the time index refers to non-overlapping three-year periods,

(1) Y i;t

is the standard

deviation of the business cycle component of GDP in real terms for country i, country-speci…c e¤ect,

t

i

is a

is a time-speci…c e¤ect, and ui;t is the variability in output not

explained by the regressors. All the variables refer to non-overlapping three-year periods. The dataset includes quarterly time-series data from 1983 to 2004 for 20 OECD economies6 . The volatility of the cyclical component of the Solow residuals is often used as a proxy for technology shocks. As in Backus et al.(1992), Karras and Song (1996), and Ferreira da Silva (2002), I de…ne this as the change in the log of real GDP minus 1- times the change in the log of employment. To reduce concerns about potentially omitted variables I include country …xed-e¤ects. I also allow for time …xed e¤ects to capture time trends a¤ecting all countries in the sample. However, I also control for other potential determinants of business cycle ‡uctuations, such as the variability of the short-term interest rate, terms of trade and consumption prices. Since I am interested in the volatility of the cyclical component of GDP, Solow residuals, and interest rates, the HP …lter method is used. Table 2 summarizes the results. As in Aghion et al. (2005) credit market size does not appear to be directly related to output volatility. However, private credit mitigates the impact of variations in productivity to output. Although the …xed-e¤ect speci…cation reduces concern about potentially omitted variables, in column 2 and 3 I introduce into the 6

All OECD data used are obtained from the OECD database, while the data regarding private credit come from the IFS.

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ECB Working Paper Series No 743 March 2007

regression a set of control variables for other potential sources of business cycle volatility. A larger credit market does dampen the propagation of Solow residual volatility to output of about 13-18% depending on the control variables introduced in the regression. In table 2, I measure credit market size as a moving average over the three years. However, table 3 show that the result is robust independently of how credit market size is measured. In column 2, I measure credit market size as the beginning of the period value to emphasize how the established credit-to-GDP ratio a¤ects volatility in the following period. I also check the robustness of the relation, using the average over the all period sample, as a measure of credit market development that varies only in the cross-section and not over time (column 3). In all speci…cation the interaction between credit market size and the standard deviation of Solow residuals has a negative and signi…cant sign. Thus, across OECD countries, in the last twenty years, credit market size reduces the volatility of output induced by variations in productivity.

3

The Model

Consider a stochastic discrete-time economy populated by two types of households that trade two kinds of goods, a durable asset and a non-durable commodity. The durable asset, k, is reproducible and depreciates at the rate of . The commodity good, c, is produced using the durable asset and cannot be stored. At time t there are two competitive markets in the economy: the asset market in which one unit of the durable asset can be exchanged for qt units of the consumption good, and the credit market. I assume a continuum of ex ante heterogeneous households of unit mass n1 , patient entrepreneurs (denoted by 1), and n2 , impatient entrepreneurs (denoted by 2). To impose the existence of credit ‡ows in this economy, I assume that the ex ante heterogeneity is based on di¤erent subjective discount factors. Agents of type i, i = 1; 2; maximize their expected lifetime utility as given by: max

fcit ;kit ;bit g

with

1

>

2

s.t. a budget constraint cit + qt (kit

(1

Et

1 X

t iU

(cit )

t=0

) kit

1)

= Fit +

bit Rt

bit

1

(2)

ECB Working Paper Series No 743 March 2007

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and a borrowing constraint Et [qt+1 kit ]

bit+1

(3)

Real production is given by Fit = yit + qt hit where yit represents the technology for producing consumption goods and hit is the production for capital goods c yit = Zt kit j with kit

1

1

y i

h hit = Zt kit

1

h i

(4)

– j = c; h – being the stock of capital used as an input of production in the

two sectors. Unlike Kiyotaki and Moore (1997), I assume that agents have access to the same concave production technology7 . Kiyotaki and Moore take the two groups of agents to represent two di¤erent sectors of the economy; on the contrary, I assume technology to be the same for both groups of agents (

y 1

=

h 1

=

y 2

=

h ). 2

Moreover, I also allow

for reproducible capital and assume that each agent is able to produce both consumption and investment goods8 . For simplicity, I will assume that both types of production are identical9 . However, I do follow Kiyotaki and Moore (1997) in assuming that the technology is speci…c to each producer and that only the household that initiated a particular type of production has the skills necessary to complete it. Thus, if agent i decides not to put e¤ort into production between t and t + 1, there would be no production outcome at t + 1, but only the asset kit . The agents cannot precommit to produce; moreover, they are free to walk away from the production and debt contracts between t and t + 1. This results in a default problem that prompts creditors to protect themselves by collateralizing the household’s assets. Creditors know that if the household abandons its production and debt obligations, they will still get his asset. However, I assume that the lenders can repossess the borrower’s assets only after paying a proportional transaction cost, [(1 7

)Et qt+1 kit ]. Thus,

See Cordoba and Ripoll (2004) for a discussion of how di¤erent assumptions about production technology a¤ect the impact of technology shocks in the modeled economy. 8 In this way I avoid creating a rental market for capital, and make the model directly comparable to those of Kiyotaki and Moore (1997) and Cordoba and Ripoll (2004). 9 The assumption of decreasing returns in the production of invetment goods is equivalent to assume convex adjustment costs for investments.

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ECB Working Paper Series No 743 March 2007

agents cannot borrow more than a certain amount such that what they have to reimburse in Et [qt+1 kit ] ;

the next period cannot exceed the expected value of next period assets bit where

< 1; and (1

) represents the cost lenders must pay to repossess the asset. As in

Aghion, Baccheta, and Banerjee (2003) and Campbell and Hercowitz (2004), limiting the borrowing to a fraction of the expected liquidation value of the capital takes into account di¤erent degrees of credit market development. In fact, a high

represents a lower degree

of credit rationing and thus a more developed …nancial sector while a low

represents an

underdeveloped system10 . As I will show below, the model displays a one to one mapping between

3.1

and the size of the credit market.

Agents ’optimal choices

Step 1: Optimal allocation of capital I divide the agents’ problem into two steps. First, in any given period each agent allocates the existing capital to produce either consumption or investment goods by solving c kit

Zt max c kit

+ qt kit

1

1

c kit

c kit

1

1

1

This leads to the …rst-order condition, c kit

1 1

= qt kit

1

1

(5)

The relative price of capital equals the ratio of the marginal productivity of capital in the two sectors. It is possible to express the amount of capital allocated to each type of production as a fraction of the total capital owned by each agent, as follows: c kit 1

where (q) =

qt 1+qt

1

= kit

(6)

1

1 1

: Thus, the allocation of existing capital between the two productions 1

depends on the current relative price of capital. The total production of each individual can be expressed as Fit = kit

1 Zt [

+ qt (1

) ]

(7)

10 In an economy in which the legal system is very e¢ cient the commitment problem vanishes and the borrowing constraint is not necessary any more.

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Step 2: Utility maximization Now it is possible to simplify the maximization problem, obtaining max

fcit ;kit ;bit g

Et

1 X

t iU

(cit )

t=0

s.t. the budget constraint cit + qt (kit

(1

) kit

1)

= kit

1 [Zt

+ qt (1

) ]+

bit Rt

bit

1

and the borrowing constraint bit+1

Et [qt+1 kit ]

The agents’optimal choices are then characterized by uci;t Rt and qt

i Et

i Et uci;t+1

uci;t+1 qt+1 (1 uci;t

)

(8)

i Et

uci;t+1 Fki;t+1 uci;t

(9)

where Fki;t+1 is the marginal product of capital. The …rst equation relates the marginal bene…t of borrowing to its marginal cost, while h Uci;t+1 the second shows that the opportunity cost of holding one unit of capital, qt qt+1 (1 i Et Uc i;t

is greater than or equal to the expected discounted marginal product of capital.

In this framework, impatient agents borrow up to the maximum possible amount in a neighborhood of the deterministic steady state. In fact, if we consider the Euler equation for the impatient household in the steady state, 2 2t

=(

2 ) Uc2

1

>0

(10)

is the Lagrange multiplier associated with the borrowing constraint. Thus, if the

economy ‡uctuates around the deterministic steady state, the borrowing constraint holds with equality b2;t = Et [qt+1 k2t ]

(11)

and k2t = h

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ECB Working Paper Series No 743 March 2007

W2;t qt

c2;t t+1 Et qR t

i

(12)

i ) ,

where W2;t = F2;t + qt (1

) k2;t h ning of the period and dt = qt

1

b2;t 1 is the impatient agent’s i qt+1 Et Rt represents the di¤erence

wealth at the beginbetween the price of

capital and the amount this agent can borrow against a unit of capital, i.e., the down payment required to buy a unit of capital. Thus, in the neighborhood of the steady state for constrained agents, the marginal bene…t is always greater than the marginal cost of borrowing

Uci;t (9.a) 2;t = i Et Uci;t+1 Rt Moreover, borrowers internalize the e¤ects of their capital stock on their …nancial constraints. Thus, the marginal bene…t of holding one unit of capital is given not only by its marginal product but also by the marginal bene…t of being allowed to borrow more: qt

2 Et

Uc2;t+1 qt+1 (1 Uc2;t

)=

2 Et

Uc2;t+1 2;t Fk2;t+1 + Et qt+1 Uc2;t Uc2;t

(10.a)

Collateral constraints alter the future revenue from an additional unit of capital for the borrowers. Holding an extra unit of capital relaxes the credit constraint and thus increases their shadow price of capital. Thus, this additional return encourages borrowers to accumulate capital even though they discount the revenues more heavily that lenders. As long as the marginal product of capital di¤ers from its market price, borrowers have an incentive to change capital stock11 . In contrast, patient households are creditors in the neighborhood of the steady state. Thus, the lender’s capital decision is determined by the point at which the opportunity cost of holding capital equals its marginal product: qt

1 Et

Uc1;t+1 qt+1 (1 Uc1;t

)=

1 Et

Uc1;t+1 Fk1;t+1 Uc1;t

(10.b)

Agents’capital stock evolves according to kit = (1

) kit

1

+ hit

(13)

The total stock of capital kt is given by kt = k1t + k2t

(14)

yt = y1t + y2t = c1t + c2t

(15)

The following conditions also hold

b1t =

11

b2t

(16)

The price of capital is higher than the frictionless marginal tobin’s q for the borrowers.

ECB Working Paper Series No 743 March 2007

15

4

Model Solution

4.1

Benchmark parameter values

I calibrate the model at quarterly intervals, setting the patient households’discount factor to 0.99, such that the average annual rate of return is approximately 4%;while the impatient households’discount factor12 is 0.95. I assume the following utility function: c1it ' U (cit ) = 1 ' and set ' to equal 2.2. The productivity parameter,

(17) is 0.36, as in the tradition of the

real business cycle literature13 . The capital depreciation rate equals 0.03. The baseline choice for the fraction of borrowing-constrained population is set to 50. The parameter representing the degree of credit rationing,

, is in the [0,1] range. Finally, I calibrate

the technology shocks according to standard values in the real business cycle literature14 . Table 4 summarizes the parameter values.

4.2

Dynamics

The agents’optimal choices of borrowing and capital, together with the equilibrium conditions, represent a non-linear dynamic stochastic system of equations. Since the equations are assumed to be well-behaved functions, the solution of the system is found by using standard local approximation techniques. All the methods commonly used for such systems rely on the use of log-linear approximations around the steady state to obtain a solvable stochastic system of di¤erence equations. By …nding a solution, I mean to express all variables as linear functions of a vector of variables, both endogenous state, xt

1,

and exogenous state, zt , variables, i.e., I am seeking

the recursive equilibrium law of motion: xt = P xt

1

+ Qzt

yt = Rxt

1

+ Szt

where yt is the vector of endogenous (or jump) variables. 12

Lawrance (1991) estimates that the discount factors of poor households are in the 0.95 to 0.98 range, while according to Carroll and Samwick (1997), the empirical distribution of discount factors lies in the 0.91 to 0.99 interval. 13 See Cooley and Prescott (1995) or Prescott (1986). 14 For technology shock, see chapter 1 in Cooley and Prescott (1995) or Prescott 1986.

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ECB Working Paper Series No 743 March 2007

To solve for the recursive law of motion, I need to …nd the matrices P; Q; R; andS, so that the equilibrium described by these rules is stable. I solve this system using the undetermined coe¢ cients method of, for example, McCallum (1983), King, Plosser, and Rebelo (1987), Campbell (1994), and Uhlig (1995).15 .

5

Credit Market Size and the Deterministic Steady State

Now, I analyze how the degree of credit rationing, , a¤ects the deterministic steady state of the model. Since total output is maximized when the marginal productivity of the two groups is identical, I examine how the allocation of capital between the two groups varies with . Using households’optimal choice of capital –equations (10.a) and (10.b) – evaluated at the steady state, it is possible to show that as long as K1 = K2

1 2

1

2 (1

1

) ( 1 ) 1 (1

2)

<

1 1

,

1 1

>1

(18)

The steady-state allocation of capital depends on the subjective discount factors, 2,

1 and

the fraction of the two groups of agents, n, the depreciation rate, , and the degree of

credit market development, . Thus, the allocation under credit constraints reduces the level of capital held by the borrowers. In fact, as long as

<

1 1

= 1:0101; equation (19)

implies a di¤erence in the marginal productivity of the two groups: Figure 2a shows the steady-state productivity gap with respect to . Less credit rationing, allowing for a more e¢ cient allocation of capital between the two groups, implies a smaller productivity gap, and thus smaller losses in terms of total production. In the presence of credit frictions it is not possible to reach the e¢ cient equilibrium, but a higher

does reduce the output loss.

Figure 2b shows the deterministic steady-state values of the model’s variables with respect to the degree of credit market development, . Increased access to the credit market implies credit expansion, b ss , and thus a rise in the level of investment by borrowers, k 2ss . With more capital allocated to the most productive group of agents, there is an increase 15

See Uhlig (1995), A Toolkit for Analyzing Nonlinear Dynamic Stochastic Models Easily, for a description of the solution method.

ECB Working Paper Series No 743 March 2007

17

in the production share of constrained agents, and consequently in total production, y ss . Hence, the amount of total capital, K ss , and consumption, C ss , are higher as well16 . In the steady state, asset price depends on the marginal productivity of capital and increases with 17 .

and

The model delivers also a mapping between the ratio of private credit to total output =

b2 qk2 :

Figure 2.c shows that by varying

between zero and unity, it is possible to

reproduce the same private credit-to-GDP as found in the data and thus, directly relate the theoretical results to the empirical …ndings.

6

Model Dynamics

I now consider the response of the model economy to a productivity shock. I assume that the economy is at the steady-state level at time zero and then is hit by an unexpected 1% increase in aggregate productivity. I assume that the productivity shock follows an AR(1) process given by ln(Zt ) =

Z

ln(Zt

1)

+ "Zt ; "Zt viid N (0;

)

(19)

Figure 3.a shows the response of total aggregate output to the productivity shock. As we see, after a 1% increase in aggregate productivity, total output increases by approximately 1.2% in the …rst period and further more in the second. In what follows I will show that variations in the relative price of capital generated by the redistribution of capital between the two groups of agents, strongly contribute to the ampli…cation of the shock. In fact, variation in qt determine the reallocation of existing capital between di¤erent sectors of production (reallocation of capital in terms of use) and thus generate ampli…cation of the shock already in the period in which the shock hits the economy. As a response to a neutral technology shock, the model displays co-movement between the consumption and capital good production. However, the production of the capital good 16

Up to a certain value of , borrowers’consumption increases. This is due to both a credit channel e¤ect and a wealth e¤ect. Agents bene…t from both greater access to debt …nancing and the increasing value of their assets. However, as expected, borrowers’ steady-state consumption decreases as approaches unity. In an environment with relaxed credit restrictions, impatient agents prefer to consume more today than in the future, thus reducing the steady-state consumption level. 17 1 2 The steady state value of qss = 1 F = 1 Fk2 is always less than unity for any (1 ) k1 (1 ) 1

2

U c2

value of < 1: Thus, the model can never the equivalent to the standard one-sector real business cycle model with a one-to-one trasformation rate between consumption and capital.

18

ECB Working Paper Series No 743 March 2007

displays evidence of signi…cant ampli…cation, while the production of the consumption good reacts much less markedly (Figure 3.b). As a positive shock hits the economy, borrowers – limited in their capital holding before the occurrence of the shock by the existence of borrowing constraints –increase their demand for productive assets. Thus the user cost of holding capital rises as shown in Figure 3.b. The increase in the relative price of capital implies a more pro…table use of the input of production in the capital good sector and thus a reallocation of capital towards this production. This allows for the agents to more easily smooth the e¤ect of the shock through investment. The change of use of the existing productive asset a¤ects the impact of the shock on the two productions. As indicated by ; capital is reallocated towards the production of investment goods in coincidence of the two major peaks of ampli…cation18 ^=

q^t (1

)

This explains the stronger e¤ect of the shock on the production of the capital good. With asset prices increasing and the production of investment goods strongly reacting to the shock, the response of aggregate real output to a productivity shock is greatly ampli…ed. The rise in borrowers’current investment expenditures propagates the positive e¤ect of the shock to their production over time. Since the marginal productivity of capital is higher for borrowers, this also generates a second period ampli…cation on aggregate production19 . Figure 3b also shows that the rise in asset prices coupled with the increase in borrowers’ capital expenditure, implies a credit boom20 . For the patient agents to be willing to increase the amount of funds o¤ered for borrowing, the interest rate must increase in the …rst period. Figure 3.c presents the dynamics of the two groups’production in more detail. Since in the …rst period the agents decide to reallocate their own capital towards the production of capital goods, all agents’ productions behave identically. In the second period, given the redistribution of capital towards patient agents, the productions speci…c to constrained 18

Variables are in log devation from their steady state values. In fact, when the capital used by the most productive agents increases — as well as their share of production (F2;t =Ft ) – the e¤ect of the shock is ampli…ed even more. 19

20

^t+1 ^bt+1 = q^t+1 + k

ECB Working Paper Series No 743 March 2007

19

agents are more strongly a¤ected by the shock and display a signi…cant degree of ampli…cation. In contrast, the ampli…cation on lenders’productions is minimal. The reallocation of capital between the two sectors still a¤ects the production behavior of both groups in the second period. However, what generates di¤erences in the impact of the shock is the fact that the capital held by constrained agents increases substantially. Thus, while in the …rst period the only source of ampli…cation is the reallocation of capital in terms of use, in the second period both sectorial and ownership reallocation take place.

6.1

Credit Market Size and Business Cycle

In what follows, I consider how the sensitivity of output to productivity shocks is a¤ected by

and consequently the size of the credit market. Figure 4.a, shows the initial impact

of productivity shocks – i.e., the intensity of reaction for any given value of

. As a

result, more-developed credit markets display reduced ampli…cation of productivity shocks on output21 . Looking at the decomposition of output, a larger credit market magni…es the reaction of consumption goods production while weakening the response of investment goods production. The di¤erence between the reactions of the two sectors is explained by the dynamics of the relative price of capital and thus the capital reallocation between the two sector. As shown in Figure 4.b (top panel), reducing credit market frictions lowers the sensitivity of asset prices to productivity shocks and consistently reduces the magnitude of capital reallocation. Given that in economies with a lower degree of credit rationing the productivity gap between lenders and borrowers is smaller, less capital is redistributed to the borrowers to …ll the gap. Thus, borrowers’demand for capital rises by less reducing the increase in the relative price of capital. So, it becomes less pro…table to reallocate capital to the production of investment goods. In economies with greater access to credit, ceteris paribus, less capital (as collateral) is needed to be able to borrow the same amount, so less capital is reallocated to the production of investment goods. This e¤ect contributes to the same shock having a weaker impact on total aggregate production. Since the decreased reaction of the capital production sector is greater than the ampli…cation of the shock in the consumption goods production, a larger credit market dampens the propagation of productivity shocks to output.

21

This …nding is in accordance with Calstrom and Fuerst’s (1997) results of a stronger impact of neutral technology shocks on output when a lower value or the monitoring cost in the …nancial contract is assumed.

20

ECB Working Paper Series No 743 March 2007

Cordoba and Ripoll (2004), assuming

= 1 in the standard Kiyotaki and Moore

setup, show that collateral constraints are unable to generate ampli…cation of productivity shocks. This …nding still holds in the model presented here. However, if we allow for di¤erent degrees of credit market development the magnitude of the initial ampli…cation impact varies with the credit market size. Thus, the ampli…cation of productivity shocks to output is greater in economies with tighter collateral constraints. Once we allow for to be lower than unity, the ampli…cation generated in the model is no longer negligible.

7

Credit market size and output volatility: comparing model predictions with the data

Finally, I examine the relationship between the volatility of the cyclical component of output and the size of the credit market delivered by the model. The aim is to document that the model can reproduce the fact that credit market size reduces the volatility of output induced by variations in productivity by the same magnitude as observed across time and countries. I simulate the model economy for three di¤erent values of ; f0:2; 0:5; 0:9g : The

productivity shock follows an AR(1) process, i.e., ln(Zt ) = N (0;

Z

ln(Zt

1)

+ "Zt ; "Zt viid

): The standard deviation of the productivity process is calibrated to match the

average standard deviation of the cyclical component of the Solow residual for all sampled countries during the 1983:1-2004:4 period. Thus, I set the standard deviation of the productivity equal to the average value (

z

= 0.9875,

z

= 0), and generate arti…cial series for

asset prices, output, and investment and consumption goods, for any given credit market size. Table 5 reports the results. The volatility of output implied by =0.5 is 3% lower than the volatility obtained with =0.2. A more substantial di¤erence occurs when we compare output volatility for higher values of . Output is 17% less volatile when =0.9 than when =0.5. Since

determines the steady state credit market size of the model, estimations

in table 3 column 2, in which I measure credit size as the beginning of the period value, are directly comparable with the results of the model. According to the estimations a well developed credit market reduces the volatility of output due to variations in productivity of about 18%. The size of the credit market in the sample corresponds to values of

in

ECB Working Paper Series No 743 March 2007

21

the theoretical model above 0.5 (see …gure 2.c). Thus a reduction of output volatility of about 17% is in accordance with the empirical estimates. Despite its stylized nature, the model is quite successful in matching the data. For completeness, I simulate the model for 1000 values of

in the [0,1] range. The

number of simulated series for the calculation of moments is 5000 for any given . Figure 5 shows that, the standard deviation of total output decreases with the size of the credit market. The model display also a lower volatility of asset prices22 (see Figure 5, middle panel). The volatility of investment relative to consumption goods decreases with the degree of credit friction as well. The impact of variations in productivity to output volatility is reduced by about 26% for

between 0.0001 and unity and around 20% for

between

0.5 and unity. In both the model and the data there is a clear evidence that well developed credit markets induce smoother business cycle ‡uctuations. The reduction in productivitydriven output volatility implied by the established size of the credit market in the model is of the same magnitude as documented by the empirical …ndings reported in section 2. Thus, the model mimics the data very closely both qualitatively and quantitatively.

8

One vs Two- Sector Model: Ampli…cation and Volatility

In what follows I show that the two-sector model displays greater ampli…cation and persistence of productivity shocks than the standard Kiyotaki and Moore model. Figure 6.a compares the reaction of total aggregate production in the present model with the response in the one-sector model. In the one-sector version of the model aggregate capital is …xed in supply and only one consumption good is produced. The only source of ampli…cation is the redistribution of capital in favor of the borrowers. Thus, there is ampli…cation of the shock only in the second period. In contrast, in the two-sector model, even in the …rst period the reallocation of capital towards investment goods production and the increase in the price of these goods already generated signi…cant ampli…cation. In the second period still greater ampli…cation is generated, not only by this mechanism, but also by the redis22 This result is in accordance with the …ndings of Justiniano and Primiceri (2005). In fact, they demonstrate that the volatility of the relative price of investment in terms of consumption goods decreased following …nancial deregulation in the U.S. in the early 1980s. Moreover, the decline in the volatility of the relative price of investment was simultaneous with the timing of the “Great Moderation.”

22

ECB Working Paper Series No 743 March 2007

tribution of capital. Thus, the existence of collateral constraints in the two-sector version of the model generates more ampli…cation and persistence of productivity shocks than does the standard Kiyotaki and Moore setup. Figure 6.b shows how the size of the credit market a¤ects the transmission of productivity shocks in the standard one-sector model. An inverted U-shaped relationship is delivered by the model. As pointed out by Cordoba and Ripoll (2004), in the one-sector model, the elasticity of total output to technology shocks can be written as follows23 : yz

=

yk2 k2 z

=

Fk 2 Fk 1 y 2 Fk 2 y

k2 z

The …rst term is the productivity gap between constrained and unconstrained agents, is the share of collateral in production, k2 z

y2 y

is the production share of constrained agents, and

is the redistribution of capital. In the one-sector model, the fraction of total output

produced by constrained agents increases with increasing values of

because more capital

is held by the constrained population. However, for the same reason, the productivity gap decreases with . Thus, the second impact of productivity shocks on total output depends on these two opposing forces24 . As a result, the degree of credit market development a¤ects the reaction of output to productivity shocks di¤erently in the two models. Also in the 1-sector model, the magnitude of the initial ampli…cation impact varies with credit market size. Once we allow for is no longer

negligible25 .

to be lower than unity, the ampli…cation generated in the model However, the ampli…cation of productivity shocks to output is

greater in economies at an intermediate level of credit market development. Figure 6.c compare the relationship between output volatility and degree of credit market development predicted by the two-sector and one-sector framework. Only the twosector model displays a negative relation between the implied standard deviation of output and the assumed credit market size at the beginning of the period. 23

Since the initial impact of the shock would always be equal to the shock itself, we are now looking at the second-period e¤ect of the shock. 24 Regardless as to the shape of the capital reaction to technology shocks, the relationship between and the second impact of zt on yt assumes an inverted U shape; this is, of course, more pronounced when k2 z is not monotonic. 25 For further discussion on the ampli…cation role of collateral constraints refer to Mendicino (2006).

ECB Working Paper Series No 743 March 2007

23

9

Concluding Remarks

In this paper I revisit the relationship between the degree of credit market development and business cycle volatility. I present some evidence concerning the fact that industrialized countries with better-developed credit markets experience smoother business cycle ‡uctuations. I develop a two-sector business cycle model, built on that of Kiyotaki and Moore (1997), to investigate the contribution of credit market development to the decrease in macroeconomic volatility. To explain the behavior of economies that di¤er in terms of access to credit …nancing, I also allow for the existence of liquidation costs in modeling the collateral constraint. Relying on a business cycle model that takes into account di¤erent degrees of credit frictions, I demonstrate that tighter credit markets greatly amplify the propagation to output of variations in productivity. As a result, the reduction in productivity-driven output volatility implied by the model is closely related to the data.

Acknowledgments: I am indebted to Giancarlo Corsetti, Martin Floden, Zvi Hercowitz and Lars Ljungqvist for useful feedback on this project. I am also grateful to Francisco Covas, Ferre de Graeve, Nicola Gennaioli, Jesper Linde, Pietro Reichlin, Guido Rey and seminar participants at the SSE, Sverige Riksbank, EUI, ECB, Banco de Portugal, Magyar Nemzeti Bank, CEU, Bank of Canada, Federal Reserve Board, SUNY at Albany and HEC Montreal, 4th Macro Dynamics workshop, 2006 SED meeting and 7th conference Bank of Finland/CEPR for valuable discussions. I acknowledge …nancial support from the research grant of the Bankforkinstitute Foundation. This paper is built on the …rst chapter of my dissertation. The view expressed are my own and do not necessarly re‡ect the view of neither the European Central Bank nor the Bank of Canada. All errors are mine. First Draft: December 2004. This Draft: March 2007.

24

ECB Working Paper Series No 743 March 2007

10

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Table 1: Correlation with Credit Market Size Countries 20, Period 1983-2004

credit

(y) -0.2992**

(c) -0.2089**

(I) -0.2498**

(Ih) -0.2575**

(q) -0.1052*

(y), (c), (I), (ih), standard deviation of respectively detrended log real output, consumption, investment andinvestment in residential properties. (q) standard deviation of detrended log housing prices, credit stands for credit to the private sector as a share of gdp, is the ratio during the same period. Three years avagages Data on 20 OECD countries. Source: OECD. 1 and 5 per cent signi…cant coe¢ cients respectively one and two stars.

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Table 2: Credit and Output Volatility. Fixed E¤ects -0.137519 -0.132813 -0.179567 credit*solow (solow) credit

(0.079350)

(0.077951)

0.626929 (0.144504) 0.229395

0.630919

0.702902

(0.110335)

(0.143700)

(0.175903)

0.293451

0.287628

(0.369062) (0.408291) (0.460433) 0.570027 0.589365 0.583302 Countries 20 20 20 obs 140 140 140 Period 1983-04 1983-04 1983-04 Dependent Variable, (y), standard deviation of detrended log real output. Credit is the credit market size averaged over the 3 year period. Col 2. controls: volatility of interest rate, terms of trade, cpi Col 3. controls: property rights, volatility of interest rate, terms of trade, cpi Panel regressions based on 3-year non-overlapping averages. Country and time-…xed e¤ects included. White-type robust standard errors in parenthesis, 5 and 10 per cent signi…cant coe¢ cients respectively in bold and italics

R2

Table 3: Credit and Output Volatility. Fixed E¤ects -0.179567 -0.182865 credit*solow (0.110335)

(solow) credit

(0.049198)

-0.302671 (0.085678)

0.702902

0.686364

1.020229

(0.175903)

(0.166009)

(0.205955)

0.287628

0.293451

(0.502297) (0.426280) 2 R 0.583302 0.595468 0.586303 Countries 20 20 20 obs 140 140 140 Period 1983-04 1983-04 1983-04 Dependent Variable, (y), standard deviation of detrended log real output. Col. 1: Credit is the credit market size averaged over the 3 year period. Col. 2: Credit is the credit market size at the beginning of the period Col. 3: Credit is the credit market size averaged over the all period Controls: property rights, volatility of interest rate, terms of trade, cpi. Panel based on 3-year non-overlapping averages. Country and time-…xed e¤ects included. White-type robust standard errors in parenthesis, 5 and 10 per cent signi…cant coe¢ cients respectively in bold and italics.

32

ECB Working Paper Series No 743 March 2007

Table 4: Parameter Values preferences discount rate

1 = 0:99 2 = 0:95 ' = 2:2

shock process autocorrelation variance

z

= 0=0:95

technology depreciation rate

= 0:36 = 0:03

borrowing limit population

2 [0; 1] n = 0:5

Table 5: Volatility Simulated Series

0.2 0.5 0.9

(y) 1.3462 1.3096 1.1155

(I) (C)

2.1377 1.7570 1.2514

(q) 1.4915 1.3398 1.0374

ECB Working Paper Series No 743 March 2007

33

Output Volatility and Credit Market Size 4 3.5 3

s.d. output

2.5 2 1.5 1 0.5 0

1

1.5

2

2.5

3 3.5 credit market size

4

4.5

5

5.5

Figure 1a plots the measure of credit market development against the measure of business cycle volatility. Output's standard deviations as well as the average of private credit as a share of Gdp are calculated on quarterly data for 3 nonoverlapping year

Asset Prices Volatility and Credit Market Size 0.14

0.12

s.d. asset prices

0.1

0.08

0.06

0.04

0.02

0

1

1.5

2

2.5

3 3.5 credit market size

4

4.5

5

5.5

Figure 1b plots the measure of credit market development against the measure of business cycle volatility. Asset Prices ' standard deviations as well as the average of private credit as a share of Gdp are on quarterly data for 3 non-overlapping year

34

ECB Working Paper Series No 743 March 2007

MP as a function of γ

0.04

MP2 0.035

0.03 output losses 0.025 MP1 0.02

0.015

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

γ Figure 2.a shows how the steady state productivity gap in total production between the two groups of agents varies with respect to γ.

ECB Working Paper Series No 743 March 2007

35

Yss

Steady State w.r.t. γ Y1ss

Y2ss

10

5.5

5

9.5

5

4

9

0

0.5 C1ss

1

6

4.5

0

0.5 C2ss

3

1

4.5

0

0.5 K1ss

1

0

0.5

1

4

0

0.5 K2ss

0

1

200

0.8

100

0.6

0

0

γ

0

0.5 qss

1

0.5

0.4

1

0

0.5

1

γ

γ

Steady State w.r.t. γ

k ss

hss

230

7

220

Fss

13.5 13

6.5

210

12.5 6

200 190

1

50

150

100

0.5 bss

100

5.5 5

0

0

0.5

1

5.5

12 0

F1ss

0.5

1

11.5

F2ss

7

7

6.9

6

0

0.5 -3

1.9

x 10

1

µ

1.8 1.7

6.8 6.7

5

0

0.5

γ

1

4

1.6 0

0.5

γ

1

1.5

0

0.5

1

γ

Figure 2.b shows how the steady state values of the model's variables change with respect to the degree of credit market development γ.

36

ECB Working Paper Series No 743 March 2007

credit/gdp 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

γ Figure 2.c shows how the steady state values of the size of the credit market change with respect to the degree of credit market development γ.

Total Output F 1.2

% deviation from SS

1

0.8

0.6

0.4

0.2

0

0

0.5

1

1.5

2

2.5

Years

Figure 3.a shows the response of total aggregate output to a 1% increase in productivity.

ECB Working Paper Series No 743 March 2007

37

Response to Z

Response to Z 1

1.5

1

% deviation from SS

% deviation from SS

0.8

h

0.5

y

0.6 0.4

0.2

0

0

0.5

1

1.5

2

0

2.5

0

0.5

Years

1

1.5

2

2.5

2

2.5

2

2.5

2

2.5

Years

Response to Z

Response to Z

0.1

1.5

% deviation from SS

% deviation from SS

0 -0.1 -0.2

th

-0.3

1

F 0.5

-0.4 0

0.5

1

1.5

2

0

2.5

0

0.5

Years

1

1.5

Years

Response to Z

Response to Z

1.5

1

% deviation from SS

% deviation from SS

0

k2

0.5

0

-0.2

k1 -0.4

-0.6

-0.8 0

0.5

1

1.5

2

2.5

0

0.5

Years

1

1.5

Years

Response to Z

Response to Z

0.8

% deviation from SS

% deviation from SS

1

q

0.6 0.4

0.1

R

0.05

0.2 0 0

0

0.5

1 Years

1.5

2

2.5

0

0.5

1

1.5

Years

Figure 3.b shows the responses to a 1% increase in productivity.

38

ECB Working Paper Series No 743 March 2007

ECB Working Paper Series No 743 March 2007

39

% deviation from SS

% deviation from SS

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0

0.2

0.4

0.6

0.8

1

1.2

0

0

0

0.5

F1

0.5

F2

0.5

F

Years

1

Response to Z

Years

1

Response to Z

Years

1

Response to Z

1.5

1.5

1.5

2

2

2

2.5

2.5

2.5

0

0.5

1

1.5

0

0.5

1

1.5

2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0

0

0

0.5

h1

0.5

h2

0.5

h

Years

1

Response to Z

Years

1

Response to Z

Years

1

Response to Z

1.5

1.5

1.5

2

2

2

2.5

2.5

2.5

0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

1.2

0

0.2

0.4

0.6

0.8

1

0

0

0

0.5

y1

0.5

y2

0.5

y

Years

1

Response to Z

Years

1

Response to Z

Years

1

Response to Z

1.5

1.5

1.5

2

2

2

2.5

2.5

2.5

Figure 3.c: responses of the model economy to an unexpected 1% increase in aggregate productivity. The units on the vertical axes are percentage deviations from the steady state, while on the horizontal axes are years.

% deviation from SS

% deviation from SS % deviation from SS % deviation from SS

% deviation from SS % deviation from SS % deviation from SS

Sensitivity of Total Production to Productivity Shocks 1.35

1.3

1.25

1.2

1.15

1.1

1.05

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

γ Figure 4.a: first impact of the shock on production -- i.e. the intensity of reaction for any given γ

capital good

consumption good

total production

1

1.8

1.35

0.98

1.7

1.3

0.96

1.6

1.25

0.94 1.5 1.2

0.92 1.4 0.9

1.15 1.3

0.88 0.86

1.05

1.1

0.84 0.82

1.1

1.2

0

0.5

γ

1

1

0

0.5

γ

1

1

0

0.5

1

γ

Figure 4.b: first impact of the shock on production -- i.e. the intensity of reaction for any given γ

40

ECB Working Paper Series No 743 March 2007

ECB Working Paper Series No 743 March 2007

41

0

0.5

1

1.5

-0.8

-0.6

-0.4

-0.2

0

0

0

0.2

0.2

0.3

0.3

γ

0.5

0.6

0.4

γ

0.5

0.6

Asset Prices

0.4

0.7

0.7

0.8

0.8

0.9

0.9

Figure 4.c: first impact of the shock capital reallocation and asset prices.

0.1

0.1

Capital Reallocation

1

1

42

ECB Working Paper Series No 743 March 2007

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

0

0.2

0.4

γ

0.6

S.D. Total Output

1

0 0

0.2

0.4

γ

0.6

S.D. Asset Prices

0.8

1

1

1.2

1.4

1.6

1.8

2

2.2

2.4

0

Figure 5: standard deviations given a particular value for γ.

0.8

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0.2

0.4

γ

0.6

0.8

S.D. Investment wrt Consumption

1

ECB Working Paper Series No 743 March 2007

43

% deviation from SS

0

0.2

0.4

0.6

0.8

1

1.2

1

Years

1.5

2

Ft=Ztkt-1 (θ t α+qt (1-θ) t α)

0.5

2.5

0

0.2

0.4

0.6

0.8

1

0

0.5

1 Years

1.5

Yt=Ztkt-1α

y

Total Output

One-sector

Figure 6.a shows the response of total aggregate output to a 1% increase in productivity in the two-sector and one-sector model

0

F

Total Output

Two-sector

% deviation from SS

2

2.5

44

ECB Working Paper Series No 743 March 2007

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

0

0.8

0.9

1 0

0.1

0.2

0.3

0.4

γ

0.5

0.6

0.7

0.8

Sensitivity of Total Output to Productivity Shocks

0.1

0.3

0.4

γ

0.5

0.6

0.7

0.8

0.9

1

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

0.1

0.2

0.3

0.4

γ

0.5

0.6

S.D. Total Output

0.7

Figure 6.c : each point represents the standard deviations given a particular value for γ

0.2

S.D. Total Output

0.8

Figure 6.b: first impact of the shock on production -- i.e. the intensity of reaction for any given γ

0.7

-0.05

0.6

1

γ

0

1.05

0.5

0.05

1.1

0.4

0.1

1.15

0.3

0.15

1.2

0.2

0.2

1.25

0.1

0.25

1.3

0

0.3

Sensitivity of Total Production to Productivity Shocks

1.35

0.9

0.9

1

1

European Central Bank Working Paper Series For a complete list of Working Papers published by the ECB, please visit the ECB’s website (http://www.ecb.int)

699 “The behaviour of producer prices: some evidence from the French PPI micro data” by E. Gautier, December 2006. 700 “Forecasting using a large number of predictors: is Bayesian regression a valid alternative to principal components?” by C. De Mol, D. Giannone and L. Reichlin, December 2006. 701 “Is there a single frontier in a single European banking market?” by J. W. B. Bos and H. Schmiedel, December 2006. 702 “Comparing financial systems: a structural analysis” by S. Champonnois, December 2006. 703 “Comovements in volatility in the euro money market” by N. Cassola and C. Morana, December 2006. 704 “Are money and consumption additively separable in the euro area? A non-parametric approach” by B. E. Jones and L. Stracca, December 2006. 705 “What does a technology shock do? A VAR analysis with model-based sign restrictions” by L. Dedola and S. Neri, December 2006. 706 “What drives investors’ behaviour in different FX market segments? A VAR-based return decomposition analysis” by O. Castrén, C. Osbat and M. Sydow, December 2006. 707 “Ramsey monetary policy with labour market frictions” by E. Faia, January 2007. 708 “Regional housing market spillovers in the US: lessons from regional divergences in a common monetary policy setting” by I.Vansteenkiste, January 2007. 709 “Quantifying and sustaining welfare gains from monetary commitment” by P. Levine, P. McAdam and J. Pearlman, January 2007. 710 “Pricing of settlement link services and mergers of central securities depositories” by J. Tapking, January 2007. 711 “What “hides” behind sovereign debt ratings?” by A. Afonso, P. Gomes and P. Rother, January 2007. 712 “Opening the black box: structural factor models with large cross-sections” by M. Forni, D. Giannone, M. Lippi and L. Reichlin, January 2007. 713 “Balance of payment crises in emerging markets: how early were the “early” warning signals?” by M. Bussière, January 2007. 714 “The dynamics of bank spreads and financial structure” by R. Gropp, C. Kok Sørensen and J.-D. Lichtenberger, January 2007. 715 “Emerging Asia’s growth and integration: how autonomous are business cycles?” by R. Rüffer, M. Sánchez and J.-G. Shen, January 2007. ECB Working Paper Series No 743 March 2007

45

716 “Adjusting to the euro” by G. Fagan and V. Gaspar, January 2007. 717 “Discretion rather than rules? When is discretionary policy-making better than the timeless perspective?” by S. Sauer, January 2007. 718 “Drift and breaks in labor productivity” by L. Benati, January 2007. 719 “US imbalances: the role of technology and policy” by R. Bems, L. Dedola and F. Smets, January 2007. 720 “Real price wage rigidities in a model with matching frictions” by K. Kuester, February 2007. 721 “Are survey-based inflation expectations in the euro area informative?” by R. Mestre, February 2007. 722 “Shocks and frictions in US business cycles: a Bayesian DSGE approach” by F. Smets and R. Wouters, February 2007. 723 “Asset allocation by penalized least squares” by S. Manganelli, February 2007. 724 “The transmission of emerging market shocks to global equity markets” by L. Cuadro Sáez, M. Fratzscher and C. Thimann, February 2007. 725 ”Inflation forecasts, monetary policy and unemployment dynamics: evidence from the US and the euro area” by C. Altavilla and M. Ciccarelli, February 2007. 726 “Using intraday data to gauge financial market responses to Fed and ECB monetary policy decisions” by M. Andersson, February 2007. 727 “Price setting in the euro area: some stylised facts from individual producer price data” by P.Vermeulen, D. Dias, M. Dossche, E. Gautier, I. Hernando, R. Sabbatini and H. Stahl, February 2007. 728 “Price changes in Finland: some evidence from micro CPI data” by S. Kurri, February 2007. 729 “Fast micro and slow macro: can aggregation explain the persistence of inflation?” by F. Altissimo, B. Mojon and P. Zaffaroni, February 2007. 730 “What drives business cycles and international trade in emerging market economies?” by M. Sánchez, February 2007. 731 “International trade, technological shocks and spillovers in the labour market: a GVAR analysis of the US manufacturing sector” by P. Hiebert and I.Vansteenkiste, February 2007. 732 “Liquidity shocks and asset price boom/bust cycles” by R. Adalid and C. Detken, February 2007. 733 “Mortgage interest rate dispersion in the euro area” by C. Kok Sørensen and J.-D. Lichtenberger, February 2007. 734 “Inflation risk premia in the term structure of interest rates” by P. Hördahl and O. Tristani, February 2007. 735 “Market based compensation, price informativeness and short-term trading” by R. Calcagno and F. Heider, February 2007.

46

ECB Working Paper Series No 743 March 2007

736 “Transaction costs and informational cascades in financial markets: theory and experimental evidence” by M. Cipriani and A. Guarino, February 2007. 737 “Structural balances and revenue windfalls: the role of asset prices revisited” by R. Morris and L. Schuknecht, March 2007. 738 “Commodity prices, money and inflation” by F. Browne and D. Cronin, March 2007. 739 “Exchange rate pass-through in emerging markets” by M. Ca’ Zorzi, E. Hahn and M. Sánchez, March 2007. 740 “Transition economy convergence in a two-country model: implications for monetary integration” by J. Brůha and J. Podpiera, March 2007. 741 “Sectoral money demand models for the euro area based on a common set of determinants” by J. von Landesberger, March 2007. 742 “The Eurosystem, the US Federal Reserve and the Bank of Japan: similarities and differences” by D. Gerdesmeier, F. P. Mongelli and B. Roffia, March 2007. 743 “Credit market and macroeconomic volatility” by C. Mendicino, March 2007.

ECB Working Paper Series No 743 March 2007

47

ISSN 1561081-0

9 771561 081005

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