Modelling Sudden Stops: The role of preferences

Suparna ChakrabortyDept. of Economics and Finance, Baruch College, CUNY�

November 11, 2006

Abstract

Empirical literature overwhelmingly suggests that Sudden Stops leadto drops in real macro variables. Can general equilibrium model predictthis link? In this paper we contend that the answer depends on the typeof preference speci�cation used. To this end, we use a small open economymodel where agents face a constraint on foreign borrowing and a SuddenStop occurs due to an abrupt tightening of the borrowing constraint. We�nd that under Cobb-Douglas preferences, the dominant wealth e¤ect ofa Sudden Stop leads to labor increases which in turn generates an outputincrease as opposed to a drop! In contrast, under GHH preferences, laboris not vulnerable to any wealth e¤ects and is determined solely by thebeginning of the period capital stock. As a result, a Sudden Stop doesnot a¤ect output on impact but leads to drops in investment. This inturn results in a drop in future labor supply which coupled with reducedcapital stock generates an output drop, albeit with a one period lag.

Keywords: Sudden Stops, General Equilibrium, Borrowing Constraints,Preference Speci�cations, Real Macro Aggregates

(JEL Classi�cation Code: F41; F32; E44; D52)

1 Introduction

Recent emerging market crises are commonly characterized by the twin phenom-enon of a sudden, sharp reversal of capital in�ow, or a Sudden Stop, followedby a large drop in output and real asset prices. While empirical analysis acrosscountries have shown these two phenomenon to be closely related with capitalaccount reversals leading to signi�cant drops in investment and output1 , theo-retically establishing this link has been more of a challenge. As noted by EnriqueMendoza (2006) "Sudden Stops are a puzzle for a large class of macroeconomic

�Contact email: suparna_chakraborty@baruch.cuny.edu1For details, see Calvo and Reinhart (2000), Milesi-Ferreti and Razin (2000) and Calvo,

Izquierdo and Loo-Kung (2006)

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models in which current account is an e¢ cient vehicle for consumption smooth-ing and investment �nancing, and countries enjoy unlimited access to creditmarkets... In contrast, the recent literature on Sudden Stops emphasizes therole of frictions in the world capital market".

Consequently, current literature on Sudden Stops have moved away from theassumption of frictionless credit markets and embraced an environment in whichan emerging economy faces a sudden loss of access to international credit. Thepopular model used in this framework is that of a small, open economy generalequilibrium model with collateral constraints on foreign borrowing. In this envi-ronment, Sudden Stops occur as a result of a sudden tightening of the collateralconstraint triggered by policy shocks (policy-uncertainty) or shocks to worldinterest rates (involuntary contagion). Studies that have used �nancial frictionsmodels to quantitatively study Sudden Stops include Guillermo Calvo (1998),Guillermo Calvo and Carmen Reinhart (2000), Guillermo Calvo and EnriqueMendoza (2000), Enrique Mendoza (2002), Enrique Mendoza and KatherineSmith (2006), Mendoza (2006) and Pablo Neumeyer and Fabrizio Perri (2005)amongst others.

However, in recent years, the success of the �nancial frictions model tostudy Sudden Stops had been questioned by V.V. Chari, Ellen MacGrattan andPatrick Kehoe (2005), henceforth CKM (2005). Using a small, open economymodel with collateral constraints on foreign borrowings to study the Mexicancrisis, CKM (2005) �nds that sudden stops by themselves are not enough togenerate an output drop, and in fact leads to an increase in output.

What explains this di¤erence in outcome? Under what conditions can stan-dard neoclassical models of Sudden Stops yield outcomes consistent with data?In this paper we investigate these questions and argue that preference speci�-cations play a key role in determining the success or failure of a standard openeconomy neoclassical model of Sudden Stops to reproduce facts from emergingmarkets.

Our study is motivated by the observation that though most studies thatattempt to link Sudden Stops with output drops rely on the basic structure of asmall, open economy general equilibrium model with collateral constraints, theyoften vary in two important aspects: (1) presence or absence of other frictions inaddition to �nancial frictions in the form of collateral constraints and (2) pref-erence speci�cations used. More speci�cally, the studies that have successfullypredicted drops in output as a result of a Sudden Stop have introduced frictionslike advance payments constraints on labor or working capital in addition tocollateral constraints . In addition, they use the Greenwood, Hercowitz andHu¤man(1988) preference speci�cations (commonly referred to as GHH) whichhas the unique property that by construction, the marginal rate of substitutionbetween consumption and leisure is independent of consumption and hence la-bor supply is not subject to any wealth e¤ects. For example, Mendoza (2006)

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introduces a collateral constraint on working capital which is a modi�ed formof the advance-payments constraint on working capital used by Neumeyer andPerri (2005). Mendoza and Smith (2006) introduce asset trading costs in addi-tion to usual collateral constraint and Lawrence Christiano, Christopher Gustand Jorge Roldos (2004) introduce advance payments constraints on intermedi-ate inputs. As far as preference speci�cations are concerned, all of these studiesuse the GHH preference speci�cations.

As opposed to this, the only friction in the model used by CKM (2005)is the collateral constraint on foreign borrowing. In addition, CKM (2005)uses Cobb-Douglas preference speci�cation which is a standard one used inreal business cycle literature. The Cobb-Douglas preference speci�cation di¤ersfrom the GHH speci�cation in that the marginal rate of substitution betweenconsumption and leisure depends on consumption and thus equilibrium laboris vulnerable to wealth e¤ects. Calibrating their model to the Mexican case,CKM �nds that Sudden Stops by themselves infact lead to output increases.Comparing their results with that of previous models, CKM suggests that theintroduction of other frictions like advance-payments constraints can in somesituations (namely when the fund towards advance payments is kept in a non-interest bearing escrow account) overturn the positive impact of a Sudden Stopand lead to declines in output.

In this paper, we concentrate on the second di¤erence: namely the di¤erencein preference speci�cations. It is our contention that the di¤erence in preferencespeci�cations is a nontrivial one and at the heart of the di¤erence in modeloutcomes. In other words, the success of real business cycle small, open economy(RBC-SOE) models to predict an output drop due to a sudden stop hinges onthe choice of preference speci�cations alone.

To test our conjecture, we take a model of a small, open economy embed-ded in the world economy populated by agents who face a consumption-leisurechoice every period and production takes a labor-augmenting Cobb-Douglasform. The only �nancial friction in our model is a collateral constraint on for-eign borrowing which re�ects �uctuations in the economy�s access to funds in theinternational market. We consider two alternative preference speci�cations: aGHH speci�cation and a Cobb-Douglas preference speci�cation (non-separablein consumption and leisure). For reasonable parameterization, we �nd that asudden stop in our model leads to an output drop if preferences are of the GHHform and leads to output increases when preferences are Cobb-Douglas. Thusour model prediction di¤ers based on what type of preference speci�cation isused.

The intuition behind our result is straight forward and follows from the equi-librium �rst order conditions. Under Cobb-Douglas preferences, the marginalrate of substitution between consumption and leisure depends on consumptionand consequently is not immune to the wealth e¤ects. Thus a Sudden Stop which

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can be interpreted as a sudden decline in the wealth of the economy causes asharp decline in consumption and leisure (which are both normal goods) whichin turn implies an increase in labor hours. Under standard Cobb-Douglas pro-duction functions, an increase in labor hours (given the predetermined capitalstock) leads to an increase in output, thus generating the result that SuddenStops lead to output increases on impact. In addition, an increase in laborincreases the expected returns on capital and for su¢ ciently persistent shocks,triggers an increase in investment.

As opposed to this, under GHH preference speci�cations the marginal rateof substitution between consumption and leisure is independent of consumption.Thus labor in any period is uniquely determined by the beginning of the periodcapital stock which is predetermined. Given this structure, a Sudden Stop hasno e¤ect on current labor hours and consequently on current output. However,the wealth e¤ect of a sudden stop leads to a decline of private consumption thatraises the marginal utility of consumption in the current period. At the sametime, unchanged labor results in unchanged real wages and marginal produc-tivity of capital remains the same, so there is no incentive to invest. Given theintertemporal substitution condition, increases in marginal utility of consump-tion in the current period coupled with unchanged real wage rate leads to areduction in investment which leads to declines in future capital stock. Giventhat labor hours is a function of capital stock, declines in future stock of capitalreduces labor supply at future dates which leads to declines in future output,setting in motion the phenomenon of output drops due to sudden stops.

The rest of the paper is organized as follows. In Section Two, we presentsome stylized facts from emerging markets before and after a �nancial crisis. InSection Three, we present the model. In Section Four, we present the theoret-ical propositions that we use to solve our model. In Section Five, we discussthe transmission mechanism of a Sudden Stop using both theory and empiricalanalysis. We begin by theoretically establishing our result. Next we provide theresults of calibration and the impulse responses of our model under alternativepreference speci�cations before moving on to sensitivity analysis in Section Six.We perform two robustness tests: in the �rst experiment, we test the robust-ness of our results under alternative speci�cations of persistence parameters ofthe exogenous shocks a¤ecting our economy and in the second experiment, wetest the robustness of our results to alternative speci�cations of the collateralconstraints. Section Seven concludes the paper.

2 Stylized Facts from Emerging Economies fac-ing a Sudden Stop

We �rst document some stylized facts from a sample of emerging economies thatexperienced a "Sudden Stop". We look at the experiences of Argentina, Brazil,

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Mexico and South Korea for which we could �nd the most complete data set.The data that we collect is from Neumeyer and Perri (2005). For a detaileddescription of the data source one can look at the Data Appendix by Neumeyerand Perri (2005) which is available at :http://pages.stern.nyu.edu/~fperri/data/neuperri.pdf.As Calvo and Reinhart(2000) points out, the two regions which have been

most prone to a �nancial crisis brought about by a Sudden Stop is Latin Americaand East Asia. In Latin America, we currently have two periods of crisis, onein the early eighties and the second one during the last quarter of 1994 to the�rst quarter of 1995. As opposed to this, the �nancial crisis in East Asia startswith the Thai crisis in 1997. In our analysis, we concentrate on the nineties anddocument the shifts in real private consumption, real investment and real GDPalong with shifts in employment and labor hours in the periods immediatelypreceding and immediately after the �nancial crisis.

Argentina

In Figure 1-a we plot the percentage change in real GDP, real private con-sumption and real investment in Argentina during three sub-periods 1994:3-1994:4, 1994:4-1995:1 and 1995:1-1995:2. We �nd that between the third andlast quarter of 1994, consumption increased by 1.84% before dropping by 7.5%during 1994:4-1995:1. It then recovered by 1.37% during 1995:1 to 1995:2. Cor-responding numbers for real investment and output show an increase by 2.74%and 1.53% respectively during 1994:3 to 1994:4 before registering a decline by15.6% and 7.5% during 1994:4 to 1995:1. Subsequently, real investment and realoutput improved (or declined less) and the rate of decline of real investment fellto 5.9% while real output registered a growth rate of 4.25% during 1995:1 to1995:2

The data for employment and labor hours from Argentina is only availablesemi-annually so we go back to the last half of 1993 for our analysis. As Figure 1-b shows, the rate of growth of employment during the last half of 1993 was .26%and the rate of growth in labor hours was-.49%. During the �rst half of 1994employment decreased by 1.47% though labor hours increased by .05%. Duringthe last half of 1994, both employment and labor hours registered signi�cantdeclines by 2.12% and 1.02% respectively. Following this, employment recoveredand grew by .4% during the �rst half of 1995 though labor hours still registereda decline by 2.3%.

Brazil

In Figures 2-a and 2-b, we plot the experience of Brazil during 1994-1995. AsFigure 2-a shows, during 1994:3 to 1994:4, real consumption in Brazil increasedby 9.38% before declining by 2.53% during 1994:4 to 1995:1. Between the �rstand second quarters of 1995, real consumption still declined but by a smaller

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magnitude of .63%. The experience of real investment and output also mimicsthe experience of real consumption. During 1994:3 to 1994:4, real investmentgrew by 13.7% and real output grew by 1.11% . However, during 1994:4 to1995:1, real investment fell by 2.12% and real GDP fell by 4.06%. Real invest-ment and real GDP subsequently grew and in 1995:1 to 1995:2, real investmentincreased by 3.19% and real GDP increased by 2.61%.

As for employment and labor hours, during 1994:3 to 1994:4, employmentgrew by 1.56% though labor hours registered a decline by 1%. During 1994:4to 1995:1, employment declined at the rate of .67% and labor hours fell by .2%before subsequent recovery during 1995:1 to 1995:2 when employment grew by1.11% and labor hours grew by 1.43%.

Mexico

The experience of Mexico during a "Sudden Stop" is demonstrated in Figures3-a and 3-b. During the quarter 1994:3 to 1994:4, real private consumptionregistered a growth rate of 4.9%. Real investment and real GDP grew by 5.2%and 8.3% respectively. However, the next quarter saw a signi�cant decline inreal macro aggregates. Real private consumption fell by 12%. Real investmentand Real GDP fell by 27.2% and 7.28% respectively. During the next quarter,Mexico recovered somewhat with real aggregates still registering a fall, butby a smaller magnitude. For example, during 1995:1 to 1995:2, real privateconsumption fell by 2.98%, real investment fell by 12.7% and real output fell by4.97%.

As for employment and labor hours, during 1994:3 to 1994:4, employmentfell by 1.15% while labor hours registered an increase by 3.2%. During the nextquarter, employment fell by 1.1% and labor hours fell by .85%. Employment andlabor hours both recovered during 1995:1 to 1995:2, with employment growingat the rate of .54% and labor hours growing at the rate of 2.2%.Thus for the Latin American countries, we do �nd evidence of decline in

employment and labor hours along with real output, investment and real privateconsumption in the aftermath of a Sudden Stop.Does the Asian crisis show a similar pattern?

Though the Asian crisis started mainly in Thailand and spread to otherregions, we look at the experience of South Korea as data is most complete forSouth Korea.

South Korea

The experience of South Korea is summarized in Figures 4-a and 4-b. Weplot quarterly changes in real private consumption, real investment and realGDP along with changes in employment and labor hours for the years 1997 and

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1998. Between 1997:2 to 1997:3, we �nd private consumption increases by .86%and real GDP increases by 1% though there is a decline in real investment by2.75%. However during 1997:3 to 1997:4, real consumption falls by 1.6% alongwith investment and output that declines by 3.3% and .27% respectively.The situation in much worse during 1997:4 to 1998:1 when real private con-

sumption registers a decline by 12.5%. Real investment also continues to declinewith the rate of decline being 15.7% and real output registers a decline by 7.2%.The situation marginally improves in 1998:1 to 1998:2 when real consumptionincreases by .06%. Real investment and real output still registers a decline butthe rate of decline reduces to 3.7% and 1.5% respectively.

As for employment and labor hours, during 1997:2 to 1997:3, employmentfalls by .06% along with a .4% decline in labor hours. However the trend changesin 1997:3 to 1997:4 when employment falls by .64% but labor hours registersa marginal increase by .5%. The situation is reversed during 1997:4 to 1998:1when both employment and labor hours decline by 2.61% and 3% respectively.During the following quarter employment continues to decline though at a lowerrate of 2% but labor hours instead grows at a rate of 1.4%

Given our stylized facts, we �nd that the experience of both Latin Americaand East Asia in the throes of the �nancial crisis was similar. Real macro-aggregates along with employment and labor hours register a signi�cant declinein the aftermath of a Sudden Stop. As for the magnitude of the decline, Mex-ico and South Korea experienced larger declines as compared to Argentina andBrazil. The rate of recovery in Mexico and South Korea is also slower as com-pared to Argentina and Brazil.

The success or the failure of an RBC-SOE model of "Sudden Stops" dependson the ability of the model to quantitatively replicate these observations both interms of direction of change (i.e. a decline of real macro aggregates and labor)as well as magnitude.

In this paper, we show that the ability of RBC-SOE models to correctly pre-dict the "direction" of change depends on the choice of preference speci�cations.

3 Model

Our model can be summarized as a general equilibrium model of a small openeconomy that is embedded in the world economy. We assume that there is asingle homogeneous good in each period. The small open economy is populatedby measure one of identical and in�nitely lived agents, whom we shall henceforthrefer to as households, and a large number of identical �rms that produce thehomogeneous good. The households are risk averse and can borrow from the

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rest of the world. However, the households face collateral constraints that limitstheir ability to borrow. The borrowing limit can be exogenously �xed by thelender or endogenously determined by the wealth of the household. In ouranalysis, a "Sudden Stop" is modelled as a sudden tightening of the collateralconstraint which limits the small open economy�s ability to borrow from theinternational market.

3.1 Firms and Technology

At every time period t, the representative �rm hires labor l(t), and capital k(t)from the households to produce the �nal good y(t): The good y(t) is produced us-ing a constant-returns-to-scale labor augmenting technology, F (k(t); l(t); z(t))where z(t) represents the productivity shock at time t:Thus the problem of the representative �rm every period t is to choose labor

l(t) and capital k(t) to maximize pro�ts:

F (k(t); l(t); z(t))� w(t)l(t)� rk(t)k(t) (1)

where w(t) is the wage rate and rk(t) is the rental rate of capital. Note thatin our representation of the �rms�problem, the �rm does not trade in bondswith the rest of the world. This speci�cation is di¤erent from that of Neumeyerand Perri(2005) where �rms need to borrow working capital from the rest of theworld in advance "due to a friction in the technology for transferring resourcesto the households that provide labor services", or that of Christiano, Gust andRoldos (2004) where �rms borrow in advance to pay for intermediate inputs.Thus in our model, the �rms are not subject to any �nancial frictions.Given the above speci�cation of the �rms problem, the equilibrium labor

demand and demand for capital by the �rm is determined by the standardmarginal productivity conditions that equate returns to labor and capital withtheir marginal productivity:

w(t) = Fl(k(t); l(t); z(t)) (2)

rk(t) = Fk(k(t); l(t); z(t)) (3)

3.2 Households

A household begins period t with a stock of capital k(t) and a stock of borrow-ings b(t): During the period, the households make consumption and investmentdecisions denoted by c(t) and x(t) that is �nanced by income from two sources:wage income w(t)l(t) and rental income from capital rk(t)k(t) received from

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�rms in lieu of labor and capital supply. In addition, the households make in-terest payments R(t)b(t) to the rest of the world where R(t) is the gross worldinterest rate at time t. In addition, the households can borrow b(t+1) from theinternational capital market. The preferences of the household are representedby:

1Xt=0

�tu(c(t); l(t)) (4)

where � 2 (0; 1) determines the rate of time preference. The period utilityfunction u is a standard continuously di¤erentiable concave function.Households maximize present discounted value of lifetime utility (Equation

4) subject to the period budget constraint:

c(t) + x(t) � w(t)l(t) + rk(t)k(t) + b(t+ 1)�R(t)b(t)� Tt (5)

where Tt are the lumpsum taxes paid to the government.Capital stock at time t evolves according to the following:

k(t) � x(t� 1) + (1� �) k(t� 1) (6)

In addition to the budget constraint, households face a collateral constraintwhich restricts their borrowing such that:

b(t) � B(t) (7)

where B(t) denotes the maximum amount that a household can borrow inperiod t:

B(t) can be set exogenously by the lender or be determined endogenouslyby the wealth of the households. Thus :

B(t) = B(t) when exogenously determined (8)

B(t) = v(k(t+ 1)), when endogenously determined, (9)

where v(k(t + 1)) is an increasing function of the capital stock such thatvk(k(t+ 1)) > 0:

If the collateral constraint is endogenous, it can be determined ex-post suchthat:

v(k(t+ 1)) = Et�(t+ 1)k(t+ 1)

R(t+ 1); 0 � �(t+ 1) � 1 (10)

in which the debt is limited by the discounted one-period-ahead liquidationvalue of the collateral similar to Nobuhiro Kiyotaki and John Moore (1997)where �(t+1) is the fraction of collateral that can be liquidated by the lender attime t+1 in case of non-repayment of the loan . Under this speci�cation, �Sudden

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Stops�can occur when lenders expect �(t+1) to decrease or R(t+1) to increase.This speci�cation is di¤erent from the usual ex-ante collateral constraint usedin literature so far (Mendoza and Smith (2006), Mendoza (2006)) which takesthe form of a margin clause summarized by:

v(k(t+ 1)) = �(t)k(t+ 1), 0 � �(t) � 1 (11)

where the custody of the collateral is surrendered to the lender at the timethe debt contract is negotiated and the borrowing limit does not depend onexpectations about the future, but rather on the current value of wealth. Underthis speci�cation, �Sudden Stops�occur due to a sudden decline in �(t):Mendoza and Smith (2006) suggests that due to a variety of reasons related

to international lending, collateral constraints of the margin-call form should beused in analyzing Sudden Stops.As opposed to the endogenous speci�cation, a "Sudden Stop" under exoge-

nous collateral constraint occurs due to a sudden drop in the upper limit onborrowing B(t):

3.3 Government and Resource Constraints

Government in this economy collects lumpsum taxes from the consumers to�nance government consumption g(t) such that the budget constraint everyperiod is balanced where:

g(t) = T (t) (12)

The resource constraint in this economy takes the form:

c(t) + x(t) + g(t)� b(t+ 1) +R(t)b(t) � y(t) (13)

3.4 Timing of the economy

The consumers begin period t with capital stock k(t) and stock of foreign borrow-ings b(t): At the beginning of period t; shocks to productivity z(t); world interestrates R(t); government spending g(t) and external borrowing limit B(t+1) arerealized. Given these realizations, the consumers and �rms make their consump-tion, labor and investment decisions to maximize the present discounted value ofutility (in case of consumers) and pro�ts (in case of �rms) and prices are deter-mined such that the goods and the factor markets clear. Thus, in any period t;the equilibrium allocations fc(t); l(t); k(t+ 1); b(t+ 1)g and prices fw(t); rk(t)gare functions of the exogenous state variables fz(t); g(t); R(t); B(t+ 1)g and theendogenous state variables fk(t); b(t)g:The time-line of events is depicted graphically in Chart One.

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3.5 Equilibrium and Balanced Growth

Given initial conditions k(0) and b(0), a sequence of exogenous variables fB(t);R(t); z(t); g(t)g1t=0, an equilibrium in this economy is given by a set of prices

fw(t); rk(t)g1t=0 and a set of allocationsfc(t); l(t); k(t+1); b(t+1); y(t)g1t=0 suchthat (i) at the equilibrium prices the goods and factor markets clear and (ii)given the equilibrium prices , the allocations solve the �rm�s and household�sproblem.A balanced growth path for this economy is one in which R(t); rk(t) and l(t)

are constant and all other variables grow at a constant rate that is the averagelong term rate of technical progress.

4 Analysis

The objective of this section is to compare the macroeconomic implication ofa "Sudden Stop" in a model with GHH preferences with that of a model withCobb-Douglas preferences. Our baseline case is a small, open economy with ex-ogenous borrowing constraint. We calibrate our model to the Mexican economyand compare the impulse responses under alternative preference speci�cations.In latter sections, we also plot the impulse responses of models with endogenousborrowing constraints to show that our results are not sensitive to alternativespeci�cations of the borrowing constraint.

4.1 Theoretical Propositions

To solve our model, we use the following two propositions:(1) Proposition one establishes that a small open economy with exogenous

borrowing constraint is numerically equivalent to a prototype growth model ofa closed economy with exogenous government consumption, referred to as a�government consumption wedge�. A Sudden Stop in the small open economyis equivalent to an increase in government consumption in the closed economy.Given this proposition, it is enough for our analysis to look at the closed econ-omy model outcomes when the economy faces a sudden increase in governmentconsumption. This way of analyzing the impact of a Sudden Stop is similar toCKM (2005).(2) In Proposition two, we state the necessary and su¢ cient condition re-

quired in our model for borrowing constraints to bind with equality.

4.1.1 Proposition One: Equivalence results

To prove our equivalence result, let us �rst state the �rst order conditions of ourbaseline economy. Solving the household�s and the �rm�s optimization problems,we can summarize the �rst order conditions by:

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ul(c(t); l(t))

uc(c(t); l(t))= w(t) (14)

�Etuc(c(t+ 1); l(t+ 1))

uc(c(t); l(t))(rk(t+ 1) + 1� �) = 1 (15)

Fl(k(t); l(t); z(t)) = w(t) (16)

Fk(k(t); l(t); z(t)) = rk(t) (17)

k(t+ 1)� (1� �)k(t) = x(t) (18)

F (k(t); l(t); z(t)) = y(t) (19)

c(t) + x(t) + g(t)� b(t+ 1) +R(t)b(t) = y(t) (20)

Equation (14) and(15) follows from the consumer�s problem. Equation (14)shows that in equilibrium, the marginal rate of substitution between consump-tion and leisure is equal to the real wage rate and Equation (15) is the intertem-poral condition that equates the marginal utility of consumption in period twith the marginal utility of consumption in period t + 1. Equation (16) and(17) follows from the �rm�s problem and denotes that in equilibrium, the wagerate and the rental rate on capital is equal to their marginal productivities.Equation (18) denotes the evolution of capital stock over time. Equations (19)and (20) summarizes the production and resource constraints.Next, consider a closed economy with an exogenous stochastic variable bg(t)

which we call "government consumption wedge" that is �nanced by lumpsumtaxes bt(t)Then the economic problem facing the consumers in this closed economy can

be summarized by:

MaxE0

1Xt=0

�tu(c(t); l(t))

s:t:

1:c(t) + x(t) � w(t)l(t) + rk(t)k(t)� btt2:k(t+ 1) � (1� �)k(t) + x(t)3:Non� negativity constraints

The economic problem facing the �rms is given by:

Max y(t)� w(t)l(t) � rk(t)k(t)s:t:

y(t) � F (k(t); l(t); z(t))

The government balances budget such that bg(t) = bt(t)12

Thus the �rst-order conditions of the prototype economy can be summarizedby the set of equations:

ul(c(t); l(t))

uc(c(t); l(t))= w(t) (21)

�Etuc(c(t+ 1); l(t+ 1))

uc(c(t); l(t))(rk(t+ 1) + 1� �) = 1 (22)

Fl(k(t); l(t); z(t)) = w(t) (23)

Fk(k(t); l(t); z(t)) = rk(t) (24)

k(t+ 1)� (1� �)k(t) = x(t) (25)

F (k(t); l(t); z(t)) = y(t) (26)

c(t) + x(t) + bg(t) = y(t) (27)

Thus given initial condition k(0), and a sequence of productivity shocksand government expenditure fz(t); bg(t)g1t=0, an equilibrium in this economy isgiven by a set of prices fw(t); rk(t)g1t=0 and a set of allocationsfc(t); l(t); k(t+1); y(t)g1t=0 such that the �rst order conditions are satis�ed.

Summarizing the result in our �rst proposition we get the following:

Proposition 1 Given a set of initial allocations k(0) and b(0) and a set ofexogenous variables fB(t); R(t); z(t); g(t)g consider an equilibrium of the smallopen economy with exogenous borrowing constraint given by a set of allocationsfc(t); l(t); k(t+ 1); b(t+ 1); y(t)g and a set of prices fw(t); rk(t)g. Let us de�nethe government consumption in the prototype economy as bg(t) = g(t)�b(t+1)+R(t)b(t): Then the allocations fc(t); l(t); k(t + 1); y(t)g and prices fw(t); rk(t)gare an equilibrium of the prototype closed economy

Proof. The proof follows by comparing the �rst order conditions of the originaleconomy summarized by equations (14) to (20) with that of the associatedprototype economy summarized by equations (21) to (27).Note that equations (14) to (19) are same as equations (21) to (26). Further,

given the speci�cation of government consumption wedge bg(t) in the statementof Proposition One, equation (20) is equal to equation (27), thus proving propo-sition one. Q.E.D.

Note that a decline in b(t+1) in the small open economy would be equivalentto an increase in bg(t) in the prototype closed economy.4.1.2 Proposition Two: Necessary and su¢ cient condition for bind-

ing borrowing constraint

Analytically, we can prove the necessary and su¢ cient condition for bindingborrowing constraint only for the deterministic steady state. Proposition Twosummarizes the result.

13

Proposition 2 In the small open economy speci�ed in Section 2, borrowingconstraint of the consumer binds in the deterministic steady state as long as�R < 1 where R denotes the steady state world interest rate and � is the constantrate of time preference.

Proof. The proof follows from the deterministic steady state conditions of themodel. For details, refer to Appendix AGiven this proposition, we assume that borrowing constraint binds in the

neighborhood of the steady state which allows us to solve the model using theusual log-linearization techniques pioneered by Robert King, Charles Plosserand Sergio Rebelo (1988)..

4.2 Functional form and baseline calibrations

We begin with a speci�cation of the functional forms:

The production function is of the labor-augmenting Cobb-Doulgas form:

y(t) = F (k(t); l(t); z(t)) = (k(t))� �z(t)l(t)(1 + )t

�1��(28)

For GHH preferences:

u(c(t); l(t)) =

�c(t)� (l(t))v(1+ )t

v

�1��� 1

1� � ; � > 1 (29)

= log

�c(t)� (l(t))

v(1 + )t

v

�; � = 0 (30)

For Non-separable (Cobb-Douglas) preferences:

u(c(t); l(t)) =

�c(t)� (1� l(t))1��

�1��� 1

1� � ; � > 1 (31)

= � log c(t) + (1� �) log(1� l(t)); � = 0

The GHH preferences are similar to the one used by Perri and Neumeyer(2005) and is di¤erent from the ones used by Mendoza (2006) who uses LarryEpstein�s (1983) Stationary Cardinal Utility function with endogenous subjec-tive rate of time preference. In our GHH speci�cation, rate of time preferenceis assumed to be a constant and is independent of consumer�s choices at time

14

t: Note that in our GHH speci�cation, utility of leisure increases with techno-logical progress. This speci�cation helps us to maintain consistency with longrun growth. As shown by Jess Benhabib et. all (1991), this speci�cation can beinterpreted as a reduced form speci�cation of an economy with home productionwhere the long run rate of technical progress in the home production sector isgiven by (1 + ): The Cobb-Douglas preferences of the non-separable type iscommon to business cycle literature and has been advocated by Finn Kydlandand Edward Prescott(1982) and Thomas Cooley and Edward Prescott(1995)amongst others.The solution algorithm requires speci�cation of values of preference and tech-

nology parameters (�; �; v; ; ; �) : For specifying the parameters we follow thestandard calibration technique used in Real Business Cycle (RBC) literaturesuch that the deterministic steady state moments of the model economy matchthe moments of the Mexican data.We begin by setting the growth rate to be (:04):25 to match the long-term

quarterly growth rate of the Mexican economy. The quarterly rate of deprecia-tion � is set to match the average GDP shares of investment and capital wherethe ratios are :217 and 2:5 where the investment to GDP ratio is taken fromWorld Development Indicators (also used in Mendoza (2006)) and the capital-output ratio is from Mendoza(2006). As in Mendoza (2006) and Mendoza andSmith (2006), we assume that � = 2 and v = 2 that yields the value of la-bor to :65: This results in a labor supply function with elasticity = 1:54.Our measure is slightly di¤erent from Perri and Neumeyer (2005) who arguethat for emerging economies � is close to 5 and v is closer to 1:6: In case ofCobb-Douglas preferences, � the weight of consumption in utility is calculatedas :6434 There is a lot of controversy surrounding the labor share in Mexicoas discussed in Timothy Kehoe et. al.(2002) who takes the value closer to :7 assuggested by Douglas Gollin (2002). We consider 1� � to be :65, a value usedby Mendoza (2006) and close to Gollin�s estimate. The steady state gross worldrate of interest is 1:065 which yields a per quarter �gure of 1:0159:The external debt to GDP ratio is taken as :2425. This is set to match

the market value of debt to capital of 9:7% which is closer to the estimates inliterature and has been used by Mendoza and Smith (2006) amongst others.Mendoza (2006) argues that debt-otuput ratio is 215% when domestic agentsown all capital but that is deemed too high by Phillip Lane and Gian MariaMilesi-Ferretti (2001).We further assume that log deviations of productivity and government ex-

penditure from their respective steady states (where log deviation of variablem(t) from its steady state is represented by em(t)) follows a vector autoregres-sive process of order one. For estimating the parameters of the VAR process,we consider the TFP series as measured by Solow residuals. The parametersgoverning the VAR process for government wedge is measured from the govern-ment expenditure and the external debt series where government consumptionwedge bg(t) is measured by2 :

2CKM (2005) takes the sum of the net export series and government expenditure to rep-

15

bg(t) = g(t)� b(t+ 1) +R(t)b(t)The results of our calibration are summarized in Table One.

5 Transmission process of a Sudden Stop: The-ory and Impulse Responses

In Proposition One we have established the numerical equivalence of a smallopen economy model with collateral constraints and a closed economy modelwith exogenous government consumption called "government consumption wedge".Further, it was established that a sudden stop in a small open economy is equiv-alent to an exogenous increase in government consumption wedge in the closedeconomy. To understand the impact of a Sudden Stop, it therefore su¢ ces to un-derstand how an increase in government consumption a¤ects the closed economywhen preferences are GHH as compared to when preferences are Cobb-Douglas.In this section, we provide the results of our theoretical and empirical analysis.

5.1 Theoretical Analysis

In this segment, we want to theoretically establish the reasons behind the sen-sitivity of RBC-SOE model outcomes to preference speci�cations. Speci�cally,we want to theoretically establish the result that the model with Cobb-Douglaspreference speci�cations yield an increase in output when faced with a SuddenStop. As opposed to this, with GHH preferences, the model yields a drop inoutput in response to a Sudden Stop, though with a one period lag.Note that in our prototype growth model, equations (21) to (27) reduce to:

ul(c(t); l(t))

uc(c(t); l(t))= Fl(t)

(32)

�Etuc(c(t+ 1); l(t+ 1))

uc(c(t); l(t))(Fk(k(t+ 1); l(t+ 1); z(t+ 1)) + 1� �) = 1 (33)

c(t) + k(t+ 1)� (1� �)k(t) + bg(t) = y(t) (34)

F (k(t); l(t); z(t)) = y(t) (35)

where Equation (32) shows that in equilibrium, the marginal rate of sub-stitution between leisure and consumption is equal to the marginal product oflabor. Equation (33) is the intertemporal optimization condition. Equation

resent government consumption wedge where a decline in net exports due to a sudden stopcorrespond to a rise in government wedge.

16

(34) is the resource constraint and Equation (35) is the production constraint.Thus in any period t;given k(t), z(t); and g(t), Equations (32)-(35) solve for theunique equilibrium values of fy(t); c(t); l(t); k(t+ 1)g:Consider a "Sudden Stop" in a small open economy with binding collateral

constraint. This stop manifests itself as a drop inB(t+1). Under our assumptionthat borrowing constraint binds, this results in a drop in consumer borrowingb(t+1) which translates in the prototype economy to an increase in governmentexpenditure. To see this, note that we de�ne the government expenditure bybg(t) = g(t) � b(t + 1) + R(t)b(t): Thus, all other things remaining constant, adrop in b(t+ 1) implies a rise in bg(t):Let us consider GHH preferences. Then equation (32) reduces to:

ul(c(t); l(t))

uc(c(t); l(t))= � l(t)v�1 = Fl(k(t); l(t); z(t)) (36)

which implies that labor at time t or l(t) is a function of the predeterminedcapital stock k(t) only. For example, when production function is Cobb-Douglas,equation (32) reduces to:

l(t) =

�(1� �)

(k(t))�(z(t))1��

� 1v+��1

(37)

Therefore, any change in government expenditure bg(t) has no e¤ect on laborin period t; hence output remains unchanged. However according to the resourceconstraint, an increase in bg(t) causes a fall in c(t) and k(t+1)3 : Given that laborin period t+ 1 or l(t+ 1) is:

l(t+ 1) =

�(1� �)

(k(t+ 1))�(z(t+ 1))1��

� 1v+��1

(38)

A fall in k(t+1), assuming that z(t+1) has not changed, reduces labor in periodt+ 1 and given that output in period t+ 1 is:

y(t+ 1) = (k(t+ 1))�(z(t+ 1)l(t+ 1))

1�� (39)

a drop in k(t+ 1) and l(t+ 1) results in a drop in y(t+ 1) thus resulting in an"Output Drop" due to a "Sudden Stop".

The alternative is a non-separable (Cobb-Douglas) speci�cation of the formin which case:

ul(c(t); l(t))

uc(c(t); l(t))= � (1� �)

�

c(t)

(1� l(t)) < 0 (40)

Assuming Cobb-Douglas production function, Equation (32) reduces to:

3A fall in c(t) increases uc(t) thus creating an incentive for consumers to intertemporallysubstitute consumption from tomorrow(t + 1) to today(t). This results in a fall in period tinvestment x(t) hence a fall in k(t+ 1)

17

(1� �)�

c(t)

(1� l(t)) = (1� �)y(t)

l(t)(41)

Substituting the value of y(t) from the production function:

(1� �)�

c(t) = (1� �)�k(t)

l(t)

��(1� l(t)) (42)

which implicitly gives the relation between labor and consumption in periodt where:

@l(t)

@c(t)< 0; (as opposed to zero in the GHH case) (43)

As shown in business cycle literature in the works of S. Rao Aiyagari,Lawrence Christiano and Martin Eichenbaum (1992), Ellen MacGrattan andAnton Braun (1993) and others, the rise in government expenditure causes adecline in wealth of private households. Given that both consumption c(t) andleisure (1 � l(t)) is a normal good, a decline in wealth causes a decline in c(t)and (1� l(t)) which in turn implies an increase in labor l(t):Given the Cobb-Douglas production function in period t :

y(t) = (k(t))�(z(t)l(t))

1�� (44)

an increase in l(t) , given the predetermined capital stock k(t) and unchangedproductivity z(t) results in an increase in output y(t):Thus in case of non-separable Cobb-Douglas preferences, sudden stops cause

an increase in output at impact!The results so far are graphically summarized in Chart Two.

5.2 Impulse Responses

In this section we highlight the impulse responses of our model to a "SuddenStop". We use the technique of log-linearization and given our calibrationswe can solve for the decision rules. For our impulse responses, we run 500simulations, with each simulation being of length 80 which is the same as ourdata sample (for calibration we took 20 years of quarterly data from 1983 to2003 which gives a sample size of 80). This is the same length as used byNeumeyer and Perri (2005).

Figure 5-a shows the result of a 1% positive shock to government expenditurewedge in a prototype growth model with GHH preferences. In this experimentshock to government consumption is not very persistent (�g = :86). The resultscon�rm our theoretical �ndings that on impact there is no e¤ect on labor l(t)

18

and output y(t), while next period capital k(t + 1) registers a decline by .04%and current period consumption c(t) declines by :11%. In the next period, laborand output both drop and the economy goes into a decline that continues forthree periods after the initial impact of the shock before gradually recovering.

Figure 5-b plots the impulse response of a 1% positive shock to governmentexpenditure in a model with non-separable preferences where shocks are notvery persistent(�g = :86). On impact, labor and output registers an increaseby :04%and :03% respectively while future capital investment falls by :03% andcurrent period consumption fall by :1%. Thus a neoclassical growth model withnon-separable preferences generates an output increase as opposed to an outputdrop when faced with a sudden stop, which is contrary to data.

Note that in our analysis, k(t+1) registers a fall due to the sudden stop underboth preference speci�cations. However, in literature, a shock to governmentconsumption leads to a rise in investment along with output and labor undernon-separable preferences. We suspect that the response of k(t+ 1) is sensitiveto the persistence of the stochastic process of government consumption wedge.

In the next section on sensitivity analysis, we therefore begin by checkingthe model outcome when shocks to government consumption wedge are verypersistent (�g = :99):Next we experiment with a case when the shocks are very temporary (�g =

:5):Finally, we move on to check the robustness of our results when borrowing

constraint is endogenous as opposed to exogenous as in our benchmark.

6 Sensitivity Analysis

6.1 Experiment One: Variations in persistence

Suppose �g = :99:In Figure 6-a we plot the impulse response under GHH preferences and in

Figure 6-b we plot the impulse responses with non-separable preferences. We�nd that under GHH preferences, even with very persistent preferences, a 1%increase in government consumption leads to a drop in k(t+1) by :01% on impactand consumption c(t) drops by :22% which then leads to drops in future outputsand labor. Furthermore, the impact of a Sudden Stop is much more persistent ascompared to our benchmark case. Compared to the GHH case, when preferencesare Cobb-Douglas, we �nd that labor and output increases by :08% and :05%respectively and consumption drops by :18%: The response of future capitalstock k(t + 1) is now di¤erent from our benchmark case. We �nd k(t + 1)increases by :01% on impact. This result is similar to Aiyagari, Christiano and

19

Eichenbaum (1992) who �nd that for su¢ ciently persistent positive shocks togovernment consumption, investment registers an increase.

Next, let us consider a case where shocks are more temporary, with �g = :5:In Figure 7-a we plot the impulse response under GHH preferences and �nd

that future capital stock k(t+ 1) registers a fall by :05% and consumption fallsby �:05%: Output and labor remains unchanged on impact but the in nextperiod drops by more than :04% and :02% respectively. The persistence of theshock is less and output and labor starts recovering immediately after it drops inperiod t+1 as opposed to our benchmark case when it took three periods beforerecovery. In Figure 7-b, we plot responses under Cobb-Douglas preferences. A1% shock to government consumption wedge at impact causes an increase inoutput by :01% and labor by :02%. Consumption on the other hand declines bylittle more than :04% and future capital stock k(t+ 1) falls by :05%: The e¤ectof the shock is not very persistent as expected.

6.2 Experiment Two: Alternative Collateral Constraints

Our second experiment tests the sensitivity of our results if collateral constraintsare endogenously determined as opposed to exogenous.We consider a margin call requirement summarized by:

b(t+ 1) � ��(t)k(t+ 1) (45)

where �(t) is the loan to value ratio and is exogenously determined by thelenders. �(t) depends on a number of factors including a country�s reputation,the �nancial and political environment. A sudden stop in this economy takesthe form of a sudden decline in �(t) which implies that borrowers get less moneyfrom the lender. In our model we take sudden stop phenomenon as given andassume that the deviation of �(t) from its steady state follow a VAR process ororder one, where

�(t) = (1� ��)�+ ���(t� 1) + ��t (46)

We calculate the steady state value � = 9:7% that matches the market valueof debt to capital. According to our estimates, �� = :86 and �(��t) = :06:In Figure 8-a and 8-b we provide the impulse responses of a 1% negative

shock to �(t) on real output assuming preferences to be of the GHH form andCobb-Douglas respectively.

Under GHH preferences, a sudden decline in �(t) has no impact on labor andoutput in period zero, but does lead to a marginal increase in c(t) and a 1:08%decline in k(t + 1) that eventually leads to declines in future labor supply andoutput such that output falls by almost :5% and labor falls by a little more than:2%: Note that the magnitude of the response of macro variables to a Sudden

20

Stop is higher under endogenous borrowing constraints as opposed to exogenousborrowing constraint as discussed in the benchmark analysis.Under Cobb-Douglas speci�cations, a 1% decline in �(t) on impact leads to

a :05% increase in labor supply which in turn increases output by :005% thusresulting in a marginal increase in y(t) as a result of a sudden stop, a �ndingsimilar to the results of an exogenous collateral in our benchmark analysis.Period t consumption c(t) and future capital k(t + 1) does fall by :2% and 1%respectively.

Thus the sensitivity analysis shows that our results are robust to both al-ternative persistence speci�cations as well as alternative collateral constraintspeci�cations.

7 Conclusion

Existing empirical studies on Sudden Stops overwhelmingly show that the phe-nomenon of Sudden Stops or a sudden, sharp withdrawal of capital in�ow intoa nation is overwhelmingly linked with a drop in real macro variables. However,theoretically establishing this link has been more of a challenge. In this con-text, current literature gives us two widely di¤erent outcomes. At one end ofthe spectrum, we have studies that quantitatively show that the phenomenonof Sudden Stops can lead to signi�cant drops in output and investment in thecontext of a small, open economy general equilibrium model. At the oppositeextreme, we have studies that show just the opposite where Sudden Stops leadsto output increases!This anomaly in existing literature looks particularly puzzling given that

both groups of studies essentially use the same model structure of a small openeconomy model with collateral constraints on foreign borrowings where SuddenStops occur due to an abrupt tightening of the borrowing constraint either dueto policy changes or due to changes in the world interest rates.

In this paper, we investigate the reasons behind this anomaly. Looking atthe two groups of studies, we �nd that though the essential structure of themodel is the same, there are two di¤erences: (1) the studies that successfullygenerate output drops as a result of Sudden Stops use GHH preferences asopposed to Cobb-Douglas preferences used by studies that �nd the oppositeand (2) the former group of studies also includes additional constraints likeadvance-payment constraints on wage payment or intermediate inputs.It is our contention that the di¤erence in preference speci�cations is a non-

trivial one and is the key element that determines the success or failure of asmall open economy model of Sudden Stops to generate outcomes consistentwith data.

We establish our result by using a standard small, open economy model withexogenous borrowing constraints. First, we theoretically show that when prefer-

21

ences are of the Cobb-douglas form, the dominant wealth e¤ect of a Sudden Stopleads to an increase in labor. As a result, given standard Cobb-Douglas produc-tion functions, an increase in labor with predetermined capital stock results inan increase in output. As opposed to this, under GHH preferences, labor is notsubject to the wealth e¤ect of a Sudden Stop and by construction is predeter-mined by the beginning of the period capital stock. In this scenario, a SuddenStop does not a¤ect current labor, hence current output but reduces investmentwhich reduces the future capital stock. Given that labor supply depends oncapital stock only, a reduction in future capital stock leads to a reduction infuture labor supply and as a result output drops. We also establish our resultsby plotting impulse responses for reasonable parameterization of our model.Sensitivity analysis shows that our result is robust to alternative speci�cationsof the collateral constraint (when collateral constraint is endogenous).

One of the shortcomings of using the GHH preferences is that output andlabor responds to a Sudden Stop with a one period lag. It has been suggested byMendoza (2006) that advance-payments constraints might help us overcome thisproblem by generating an output drop at impact instead of one period lag. Thesecond shortcoming is that though RBC-SOE models with GHH preferencesgets right the "direction" of change in macro aggregates, the magnitude ofresponse to a "Sudden Stop" is much smaller. This problem is not speci�c touse of preferences, but rather a more general problem of models with borrowingconstraints as shown by Naryana Kocherlakota (2000). Mendoza (2006) arguesthat using additional constraints like advance payments might help in increasingthe magnitude of response. In this paper we show that the magnitude of responseis higher in case of endogenous constraints as compared to exogenous constraintsas expected but it still falls far short of the data. Getting the magnitude rightin models with borrowing constraints remains a challenge for future research.

22

Table One: Baseline parameter values

Shocks

Name Process Parameter ValuesProductivity ez(t) = �zez(t� 1) + �z(t) �z = :91 s:e: (�z) = :04

Government expenditure eg(t) = �geg(t� 1) + �g(t) �z = :86 s:e: (�g) = :05

Preference parameters

Parameters Symbol GHH Cobb-DouglasDiscount factor � .96 .96Utility curvature � 2 2Labor curvature v 2Consumption weight � .64Labor weight 1.54

Technology parameters

Parameters Symbol ValuesRate of quarterly technological progress .01Labor share in GDP � .65Depreciation rate � .08

23

Figure 1-a: % change in real aggregates (Argentina)

Figure 1-b: % change in labor (Argentina)

24

Figure 2-a: % change in real aggregates (Brazil)

Figure 2-b: % change in labor (Brazil)

25

Figure 3-a: % change in real aggregates (Mexico)

Figure 3-b: % change in labor (Mexico)

26

Figure 4-a: % change in real aggregates (South Korea)

Figure 4-b: % change in labor (South Korea)

27

Period t

Period t beginswith stock of

capital k(t) andstock of

borrowings b(t)

Period t+1 beginswith stock of

capital k(t+1) andborrowings b(t+1)

Shocks toz(t), g(t), R(t)and B(t+1)

realized

Production,consumption

and investmentoccurs

Household’sdecision andfirms decisiontakes place

Period t+1

Chart 1: Time-line of events

Sudden Stops hitthe economy atthe beginning of

period t

No change in laborl(t)

Labor l(t)increases

Period t+1 capitalstock k(t+1) falls

Period tconsumption c(t)

falls

No change inoutput y(t)

Investment x(t)falls

Period t+1 laborl(t+1) falls

GHH Preferences

Period t

Period t+1

Cobb­DouglasPreferences

Period t

Output y(t)increases

Period tconsumption c(t)

falls

Investment x(t)increases for

sufficientpersistence

Period t+1 outputy(t+1) falls

Period t

Chart2: Transmission Process of a "Sudden Stop"

28

0 1 2 3 4 5 6 7 8­0.16

­0.14

­0.12

­0.1

­0.08

­0.06

­0.04

­0.02

0Impulse responses to a shock in govt

Periods after shock

Per

cent

 dev

iatio

n fro

m s

tead

y st

ate

capital

output

cons

labor

Figure 5-a: GHH preferences-Benchmark Case

0 1 2 3 4 5 6 7 8­0.1

­0.08

­0.06

­0.04

­0.02

0

0.02

0.04

0.06Impulse responses to a shock in govt

Periods after shock

Per

cent

 dev

iatio

n fro

m s

tead

y st

ate

capital

output

cons

labor

Figure 5-b: Cobb-Douglas preferences-Benchmark Case

29

0 1 2 3 4 5 6 7 8­0.25

­0.2

­0.15

­0.1

­0.05

0Impulse responses to a shock in govt

Periods after shock

Per

cent

 dev

iatio

n fro

m s

tead

y st

ate capital

output

cons

labor

Figure 6-a: GHH preferences with �g = :99

0 1 2 3 4 5 6 7 8­0.2

­0.15

­0.1

­0.05

0

0.05

0.1

0.15Impulse responses to a shock in govt

Periods after shock

Per

cent

 dev

iatio

n fro

m s

tead

y st

ate

capital

output

cons

labor

Figure 6-b: Cobb-Douglas preferences with �g = :99

30

0 1 2 3 4 5 6 7 8­0.09

­0.08

­0.07

­0.06

­0.05

­0.04

­0.03

­0.02

­0.01

0Impulse responses to a shock in govt

Periods after shock

Per

cent

 dev

iatio

n fro

m s

tead

y st

ate

capital

output

cons

labor

Figure 7-a: GHH preferences with �g = :5

0 1 2 3 4 5 6 7 8­0.07

­0.06

­0.05

­0.04

­0.03

­0.02

­0.01

0

0.01

0.02

0.03Impulse responses to a shock in govt

Periods after shock

Per

cent

 dev

iatio

n fro

m s

tead

y st

ate

capital

output

cons

labor

Figure 7-b: Cobb-Douglas preferences with �g = :5

31

0 1 2 3 4 5 6 7 8­1.2

­1

­0.8

­0.6

­0.4

­0.2

0

0.2

0.4Impulse responses to a shock in phi

Periods after shock

Per

cent

 dev

iatio

n fro

m s

tead

y st

ate

capital

output

cons

labor

Figure 8-a: GHH preferences under Margin-Call

0 1 2 3 4 5 6 7 8­1.2

­1

­0.8

­0.6

­0.4

­0.2

0

0.2Impulse responses to a shock in phi

Periods after shock

Per

cent

 dev

iatio

n fro

m s

tead

y st

ate

capital

output

cons

labor

Figure 8-b: Cobb-Douglas preferences under Margin-Call

32

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35

APPENDIX ALagrangian for the consumer�s problem:

$ =

2664 E01Pt=0

�tu(c(t); l(t))

+�(t)�t(w(t)l(t) + rk(t)k(t) + b(t+ 1)�R(t)b(t)� c(t)� k(t+ 1) + (1� �)k(t)� T (t))+�(t)(B(t+ 1)� b(t+ 1))

3775where �t�(t) is the lagrange multiplier on budget constraint and�(t) is the lagrange multiplier on the borrowing constraint.Lagrangian for the �rm�s problem:

$ = y(t)� w(t)l(t)� rk(t)k(t) + �2(t)(F (k(t); l(t); z(t))� y(t)Govt. budget constraint can be summarized by:

g(t) = T (t)

Summarizing the equations in the deterministic steady state :

uc(c(t); l(t)) = �(t) (47)ul(c(t); l(t))

uc(c(t); l(t))= �(t) (48)

�Etuc(c(t+ 1); l(t+ 1))

uc(c(t); l(t))(rk(t+ 1) + 1� �) = 1 (49)

Fl(k(t); l(t); z(t)) = w(t) (50)

Fk(k(t); l(t); z(t)) = rk(t) (51)

c(t) + x(t) + g(t)� b(t+ 1) +R(t)b(t) = y(t) (52)

k(t+ 1)� (1� �)k(t) = x(t) (53)

F (k(t); l(t); z(t)) = y(t) (54)��t�(t)�R(t+ 1)�t+1�(t+ 1)� �(t)�t

��(t)�t = 0 (55)

Given � > 0; Equation (56) reduces to:��t�(t)�R(t+ 1)�t+1�(t+ 1)� �(t)�t

��(t) = 0

which in the steady-state reduces to:

(1�R� � �)� = 0Borrowing constraint binds in the steady state if � > 0:Then 2664

� > 0) (1�R� � �) = 0) � = 1�R�) 1 > R�

3775

36