Liquidity, jurisdictional uncertaintyand high interest rates in Brazil

Felipe Monteiro de SallesLSE

Abstract

Brazilian domestic real interest rates have remained extremellyhigh since in�ation was stabilized in 1994. In this paper, wepresent a model based on Woodford [1990] and Holmström andTirole [1998] to propose a reinterpretation of the Arida, Bachaand Lara-Resende [2004] jurisdictional uncertainty hypothesis.Our view is that jurisdictional uncertainty a¤ects �nancial mar-kets e¢ ciency, which has an impact on the demand for outsideliquidity and thus on the price of public bonds. We use the Sys-tem GMM methodology developed by Blundel and Bond [1998]on data from 43 countries over 15 years to test and con�rm thepredictions of the model.

1 Introduction

Brazilian real interest rates have remained extremely high since in�ationwas stabilized in 1994. The consequences of this problem are deeplyconcerning. In a country characterized by large income inequality, gov-ernment interest payments drain much needed and scarce resources fromareas such as public health and education. For the same reason, publicinvestment in infrastructure has been drastically cut, lowering the coun-try�s capacity to grow. Not surprisingly, understanding the causes ofthis phenomenon has become one of the main challenges of academicsand policymakers in the country and abroad (see Favero and Giavazzi,[2002] and Blanchard [2004]).It is usually thought that such high interest rates re�ect some sort

of �scal distortion. The government has defaulted on it�s obligationsseveral times in the past (see Rogo¤ [2005]). Many reforms needed tomaintain the �scal balance in the future, such as tax and pension re-forms, require changes in the constitution, which are politically costly

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and very di¢ cult to be implemented. This situation creates, accordingto some economists, some uncertainty regarding the sustainability of thefuture path of government debt. Interest rates would re�ect a risk of de-fault: agents charge high interest rates to compensate the risk that thegovernment will not honor it�s obligations in the future.However, a brief comparison between the domestic and foreign debt

interest rates presents an interesting contrast: the government is able toissue foreign debt at (relatively) low rates. By the moment this paperis being written, ex-ante real interest rates are around 10%, one of thelowest levels in the last ten years, while the country risk premia (mea-sured by the spread over treasury) is around 2% only. This contrast isparticularly striking because it would be expected that, in case of de-fault or renegotiation of public debt, foreigners should be more a¤ectedthan domestic citizens. It should be also reminded that the ratio ofpublic debt to GDP is only moderate and the country has been runninghigh primary surpluses in a sustained way for several years, despite theelection of a left wing party in 2002.The private sector is also plagued by similar anomalies. It mirrors the

public sector in a number of ways. For instance, the banking spread inthe country is also among the highest in the world. This problem is alsoperceived as structural and is one of the main reasons behind domestic�nancial underdevelopment in the country. Long term credit markets arealmost inexistent in the country. Domestic credit, like the maturity ofdomestic debt, is basically short run. In contrast, large �rms and bankshave access to foreign �nancial markets at reasonable low cost, just likethe public sector.The relation between the collapse of credit markets and high interest

rates paid by the government in the country has been identi�ed by Arida,Bacha and Lara-Resende [2004]. According to the authors, the �nancialunderdevelopment and high domestic interest rates result from the sameorigin: jurisdictional uncertainty. The authors present evidence thatborrowers raise funds more easily abroad then domestically. The reasonis not scarcity of domestic savings, but absence of credibility of �nancialcontracts written under Brazilian jurisdiction.The authors demonstrate the link between jurisdictional uncertainty

and real interest rates in a context of an open economy that follows anin�ation targeting regime. They claim that an amelioration of the juris-diction uncertainty problem in the country would a¤ect capital in�owsto the country, creating conditions for the central bank to lower the realrate of interest without while keeping in�ation in the target.In this paper, we propose a reinterpretation of the jurisdictional un-

certainty hypothesis. In our theoretical framework - this is a crucial point

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- we recognize that public bonds are a special type of asset, in the sensethat claims on private assets alone do not generate su¢ cient liquidity(that is, means for wealth storage) for an e¢ cient functioning of theeconomy (see Holmstrom and Tirole, [1998]). The idea that outside liq-uidity (that is, assets not issued by the private sector) may lead theeconomy to a Pareto improving equilibrium has, up to my knowledge,been �rst proposed by Samuelson [1958]. The relation between liquidityand �nancial markets imperfections has been suggested by Woodford[1990], and has been developed further in Holmstrom and Tirole [1998].Our claim is that �nancial underdevelopment leads to a lower demandfor liquidity, reducing the price of public bonds.We use the system GMM methodology proposed by Blundel and

Bond [1998] to test our hypothesis. It is shown that higher enforceabil-ity of contracts increase the e¢ ciency of the �nancial sector, which inturn a¤ects equilibrium interest rates. We then control for monetaryand �scal variables and show that results remain unchanged. Contraryto the �ndings of Gonçalves et al [2005], we �nd that �scal and monetaryvariables are unable to predict interest rates, while �nancial ine¢ ciencyarising from jurisdictional uncertainty is. We use our estimations topredict equilibrium interest rates in the country and show that actualinterest rates are in fact very close to predicted. We conclude that aninstitutional reform in domestic credit markets is a necessary conditionfor the reduction of the real rate of interest in the country.The rest of this paper is organized as follows: in the next section,

we provide a brief summary of the most important stylized facts aboutthe Brazilian economy in the recent past. In section 3, a brief summaryon the literature on �nancial markets imperfections, liquidity and equi-librium interest rates is presented. We detail our theoretical model insection 4. Section 5 describes a summary of the system GMMmethodol-ogy developed by Blundel and Bond [1998]. The results of our regressionsare presented in section 6, and section 7 concludes.

2 The Brazilian economy in the recent past

After years of hyperin�ation, the Real Plan, adopted in July 1994, wasthe �rst (out of many former attempts) stabilization plan capable ofbringing domestic in�ation down to international levels in a permanentbasis. The monetary stability has been one of the greatest achievementsof the Brazilian economy in the recent past. However, following the im-plementation of the Real Plan, a new problem has emerged: real interestrates have remained extremely high since then.Before 1999 this problem could be attributed mainly to some incon-

sistencies of the macroeconomic policy adopted in the period right after

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the stabilization of the currency (see Arida et al [2004]): the �scal policywas remarked by an absence of primary budget surplus, while monetarypolicy was oriented to defend a pegged currency. The stock of govern-ment debt raised sharply, and the sustainability of it has become one ofthe main concerns of academics and policymakers. Large trade de�citsre�ected an appreciated exchange rate. After the currency meltdown inAsia and Russia, the peg was perceived as unsustainable by domesticand foreign investors (see Goldfajn [2002]).In 1999, the situation changed drastically, mainly due a sharp rever-

sal in the macroeconomic policy adopted. In January of that year, thepeg was abandoned, and the currency was let free to �oat. In contrastwith even the most optimistic forecasts, a �nancial crisis didn�t follow(perhaps because the government o¤ered hedge against a devaluationto the private sector, see Goldfajn [2002]) and the economy even expe-rienced a small positive rate of growth. In July of the same year, thecentral bank adopted formally an in�ation targeting regime. Finally, aresponsible �scal policy became one of the most important pillar of thenew macroeconomic policy: since 1999 the country has been runningsustained primary surpluses.The macroeconomic variables reacted vigorously to the changes in

the monetary and �scal policies. The level of public debt to GDP wasstabilized and has even started to decline in the recent past. A boomin exports has followed the real exchange rate depreciation. The econ-omy has been experiencing record high trade balance surplus, and theprevious current account de�cit has been reversed to a small surplus.One should expect that a reduction on interest rates would follow.

This was indeed the case: interest rates have fallen in a signi�cant andpermanent way. However, they are still extremely high when comparedwith other emerging markets, being unable to fall below a 10% thresholdon a sustained manner.Why didn�t interest rates converge to international levels? Initially,

it was thought that the unusual sequence of a large adverse shocks (theblowing up of the NASDAQ bubble, the rationing of domestic energysupply in early 2001, September 11th, the default on Argentinian publicbonds following the collapse in the currency board in late 2001, and,�nally, the fear of an electoral victory of the worker�s party in late 2002)that hit the Brazilian economy in the period following the change inmacroeconomic policy has prevented interest rates to fall towards it�snew long term equilibrium level. It would just be a matter of time forBrazilian interest rates to converge to international levels.However, growing consensus is that the problem is in fact structural.

Gonçalves et al [2005] argue that real interest rates have remained above

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the 10% per year threshold even during a period of good shocks: recently,industrial economies have substantially decreased interest rates, creatingan environment of abundant liquidity to emerging markets and reducinginterest rates throughout the world.A number of hypothesis has been raised to explain the high and

persistent short term real interest rates in Brazil (see Arida et al [2004]).Among them, two have received most attention from the literature andpolicymakers. The �rst one identi�es unsolved �scal problems at thecore of the problem. The second one brings the discussion away fromstandard macroeconomic mechanisms and focus instead on the country�sinstitutions. This latter view is known as jurisdictional uncertainty (aconcept due Arida et al [2004]) hypothesis.The insu¢ cient �scal adjustment view states that the government

must credibly commit with even higher primary surpluses in order toreduce the stock of debt and convince investors that he is able to honorhis obligations. Public debt has increased sharply between 1995 and1999, due the recognition of old debts (�scal skeletons), loose �scal policybefore 1999 and contractionary monetary policy, creating an impressionof �scal disadjustment. Besides, since the government has defaulted onit�s obligations several times in the past (see Reinhart and Rogo¤ [2004])and has a past of very high in�ation, doubts regarding the sustainabilityof public debt are constantly a concern. In this sense, high interest rateswould re�ect a high default risk from the government.But is risk of default a plausible explanation? Consider this: dollar

denominated debt (foreign debt), usually held by foreigners, has muchhigher maturity and much lower rates than domestic debt. If risk ofdefault were really at the core of the problem, why would we observe this?In fact, the opposite would be much more likely: foreign debt shouldpresent lower maturity and higher interest rates, since the governmentwould be more willing to default on foreigners than in domestics (seeRogo¤, [1989]). Besides, most of the historical problems cited in theformer paragraph are also present in other Latin American countries,many of them receiving much worse ratings than Brazil according tospecialized agencies, and they don�t present interest rates as high as inBrazil.The jurisdictional uncertainty hypothesis states that high interest

rates arise not as a result of macroeconomic imbalances, but due thepresence of more resilient institutional distortions. Arida et al [2004]start from noticing that �nancial contracts written within Brazilian ju-risdiction are not enforceable, leading to a collapse in the long termdomestic credit market. The response of policymakers to this problemwas the imposition of a set of state interventions that has in fact aggra-

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vated the jurisdictional uncertainty problem itself. The authors claimthat the nature of the distorting policies implemented to deal with theadverse consequences on savings and investment of that uncertainty area Brazilian peculiarity, and is at the root of high interest rates in thecountry.Arida, Bacha and Lara-Resende explain the chain of causalities from

jurisdictional uncertainty to high interest rates in context of an in�ationtargeting regime model. The mechanism can be summarized as follows:a decrease in jurisdictional uncertainty increases the return of domesticassets, resulting on higher capital in�ows, which induce a real exchangerate appreciation. This situation creates a condition in which the centralbank can decrease the rate of interest without risking an increase inin�ation.The jurisdictional uncertainty hypothesis is very original in the sense

that it focus on microeconomic distortions as the core of the problem ofhigh interest rates. In our opinion, the greatest contribution of Aridaet al [2004] is to show that the link between underdeveloped domesticcredit markets and short term interest rates has been ignored by theliterature so far.However, we believe that the formalization of that hypothesis, the

way it is proposed by the authors is not satisfactory. In this paper, weprovide an alternative interpretation of the jurisdictional uncertainty hy-pothesis, that is, a di¤erent explanation why jurisdictional uncertaintya¤ects real interest rates. The model presented here is inspired by Holm-ström and Tirole [1998], and recognizes that public bonds provide theprivate sector some outside liquidity. More concretely, we will show that�nancial underdevelopment (arising from the bad quality of the coun-try�s institutions) leads to lower demand for liquid assets (public bonds),lowering the price of government bonds and thus leading to higher do-mestic interest rates.

3 Liquidity, �nancial market imperfections and realinterest rates

The term liquidity may be interpreted in many di¤erent ways. A veryusual way of measuring the liquidity of an asset is the likelihood that itwill be quickly sold without any price discount. Another way of under-standing liquidity regards the availability of �nancial instruments thatcan be used to transfer wealth across periods. In this section, we focuson this last de�nition. Henceforth, we say that an asset is liquid if itprovides a medium for wealth storage.It is also useful to distinguish between inside and outside liquidity.

The former refers to assets issued by the private sector. The latter may

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be supplied by the government (e.g. public bonds) or may also refer tounbacked assets with exogenous �nite supply, such as �at money.The idea that outside liquidity may improve welfare has, up to my

knowledge, been �rst proposed by Samuelson [1958]. The author showsthat if the economy lacks an e¢ cient storage technology, the introductionof �at money allows agents to transfer wealth across periods in a lesscostly way.The context in which money is valued in the Samuelson�s model is

one of an overlapping generations (OLG) setting: money allows intergen-erational trade. The young are willing to exchange goods against outsidemoney with the old because they know it will be possible to exchangemoney against goods when they become old themselves. If the stock ofoutside money were zero, such trade would not be possible.The relation between public liquidity and �nancial markets imperfec-

tions has been suggested by Woodford (1990). In his model, individualsreceive no endowments when they have access to investment opportu-nities. In principle they could exploit their investment opportunities byborrowing from other agents. However, if future income is not pledge-able, lending and borrowing never take place and investment must be�nanced by the individual�s own funds. To be able to invest, agentsmust transfer wealth across periods. If there is no storage technology,the only way of doing so is through purchases of public bonds.An interesting contribution of the Woodford model is to show that

the return on public bonds is lower than the one on other assets. Thisresult arrises from the fact that public bonds provide liquidity to theeconomy, and individuals are willing to pay a price to use such liquidityservices.Holmström and Tirole (1998), also in a context of �nancial markets

imperfections, investigate the productive sector demand and the privateand public supply of liquidity. Contrary to the Woodford model, Holm-ström and Tirole derive �nancial market imperfections from more basicmicrofoundations (Moral Hazard). This allows a more detailed analysisof the conditions under which public bonds can increase the stock ofliquidity of the economy.According to the authors, �rms can meet future individual liquid-

ity needs in three ways (besides purchases of public bonds): by issuingnew claims, through a credit line from a �nancial intermediary and byholding claims in other �rms. It is shown that if shocks are purely idio-syncratic, those instruments su¢ ce for the private sector to make insti-tutional arrangements to achieve the second best. However, if shocks areaggregate, the government can improve welfare by issuing public bonds.As in Woodford [1990], return on public bonds is, on average, lower

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than the return on private assets, and the authors label this di¤erenceas "liquidity premia".In the next section, we will present a model based onWoodford [1990]

and Holmström and Tirole [1998] contributions. It will be shown thatequilibrium interest rates depend not only on the stock of public bondsbut also on the development of �nancial markets.

4 The model

Time is discrete, there are three periods (1, 2 and 3) and only one good.There is no storage technology, a crucial assumption to motivate demandfor liquidity.There are two types of individuals: entrepreneurs and investors. For

simplicity, we assume that there is a continuum of measure 1 of eachtype. Both are risk neutral and derive utility from consumption in allthree periods. Therefore, the utility function of the economic agents isgiven by:

U = u(c1; c2; c3) = c1 + c2 + c3 (1)

Investors are "deep pockets", in the sense that they receive a largeendowment of goods in all three periods ( �N), but have access to no in-vestment opportunities. Besides, they cannot pledge their future endow-ment, which means that they cannot borrow. Those are very standardassumptions in the literature (see Holmström and Tirole [1998]).Entrepreneurs receive as endowment a plant of size �I, which yields a

stochastic amount of goods in period 3 in the following sense: in period2, the entrepreneur may receive a liquidity shock, which happens withprobability 1=2. In case of no shock, the plant will produce A�I goodsin period 3 (A > 1), out of which ��I (� < 1) can be used as collateral.In case of a liquidity shock, the entrepreneur must invest some goods inperiod 2 in order to keep the plant productive. More precisely, if theentrepreneur invest I � �I goods in that period, the plant will produceaI goods, 1 < a < A, in period 3. We assume that production fromperiod 2 investment is not pledgeable, which implies that in case of aliquidity shock the collateral drops to zero. We follow Holmström andTirole [1998] and assume that the liquidity shock is an aggregate shock:or all entrepreneurs are hit by the shock or none of them are.There are several ways of motivating the hypothesis above. Consider

what happens when the economy is not hit by a liquidity shock �rst.Why only a fraction � of the plant �I is available as collateral?One possibility is that production is subject to moral hazard. This

is the justi�cation present in Holmström and Tirole [1998]. For the sake

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of illustration, assume that, in period 3, the entrepreneur may choosebetween working and shirking. If he works, total production is equal toA�I goods. If he shirks, production is zero, but he enjoys a private bene�tof b�I, where b < 1. In this situation, the entrepreneur must be givenan incentive to be diligent, that is, his return from working must behigher or equal then b�I: This implies that outside investors can recoverup to (A� b) goods (assume A�b < 1), since if investors were promiseda higher amount the entrepreneur would be better of by shirking. Byletting � � A� b, we get that pledgeable income is equal to ��I.Alternatively, assume that when economy is not hit by the liquidity

shock, the plant produces a random quantity ~A�I goods, where ~A � 0 andE( ~A) = A� 1. Assume further that ~A is observable by the entrepreneuronly and that the plant itself can be also consumed after production isrealized. This implies that total amount of goods available for consump-tion is �Ia + �I; so the expected value of overall production (goods plusplant) is A�I. However, outside investors can in principle claim only �Iof that amount, since the entrepreneur will always have the incentive tosay that ~A = 0. If we assume further that recovering collateral involvessome costs equal to (1��) the amount of the debt, the total income theentrepreneur can commit to pay is ��I. In this sense, � would measurethe e¢ ciency of the �nancial sector.Let�s now consider the case in which the economy is hit by a liquidity

shock. Why don�t period 2 investment create any pledgeable income?There are at least three possibilities:First, one could simply assume that in case of a liquidity shock the

project collapses completely. However, a new idea may arise, and theentrepreneur may have access to a new productive investment opportu-nity. Thus, we can interpret period 2 investment as the expenses to setup a new plant and the term a could be interpreted as the return on thisnew project.Alternatively, one can assume that, instead of goods (as stated above),

period 2 investment yields only a private bene�t to the entrepreneur.Although the project is not productive, he would enjoy utility by con-tinuing it. By investing I goods in that period, �nal production remainsequal to zero, but he enjoys aI of private bene�t which is not sharedwith outside investors.Finally, one can assume that in case of a liquidity shock the plant can

still produce ~AI goods if period 2 investment is I. However, if investmentand production are non observable, the entrepreneur can always claim,as argued above, that ~A = 0, so that the proceeds of investment are notpledgeable.Let�s now come back to our basic assumptions. We assume there is

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a government that issues public bonds in period 1. One public bondis an asset that provides the owner one good in period 2, paid by thegovernment. Bonds are backed by period 2 taxes on investors, and theproceeds from selling them are distributed, in period 1, to investors in alump-sum way.We may now proceed and study the optimal decisions of economic

agents and the resulting equilibrium. Since the model is dynamic, westart by solving it �rst in period 3 and use the results to solve for theformer periods.

4.1 Period 3In period 3, no decision is taken. The entrepreneur simply gets the pro-duction of the plant, pays his debt (in case he has available collateral)and consume the di¤erence. The investor obtains his endowment, re-ceives what is owned by his debtors (as long as the latter have availablecollateral) and consume.

4.1.1 No liquidity shock

Denote by Une;3 the period 3 utility of the entrepreneur in case of no period2 liquidity shock, where the subscript e; 3 stands for the entrepreneur inthe third period and the superscript n for the state of nature (no period2 liquidity shock):

Une;3 = A�I � (d1 + d2) (2)

In equation (2), term dt stands for the amount of goods promisedto be paid by the entrepreneur, in period 3, in a debt contract signedwith a creditor in period t. In other words, dt is the amount of goodsborrowed by the entrepreneur in period t 2 f1; 2g times the gross rateof interest between periods t and 3. We use the notation dt instead ofdne;t because only entrepreneurs can borrow, so we can drop the term e inthis case. Besides, the entrepreneur cannot borrow in case of a liquidityshock, so we can also drop the superscript n.Using a similar notation, the period 3 utility of the investor in case

of no period 2 liquidity shock is given by:

Uni;3 =�N + (l1 + l2) (3)

where lt stands for the amount of goods to be received by the investor,in period 3, according to a debt contract signed with a debtor in period t.That is, lt is the amount of goods lent by the investor in period t 2 f1; 2gtimes the gross rate of interest between periods t and 3. It should beclear that in equilibrium dt = lt, but we will come back to this last pointlatter.

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4.1.2 Liquidity shock

In case of a liquidity shock in period 2, the aggregate supply of collateraldrops to zero in the economy. Debtors default on their �nancial contracts,and creditors receive nothing. The utility of the entrepreneur is givensimply by:

U se;3 = aI (4)

where, as explained above, I 2�0; �I�is the investment made by the

entrepreneur in the second period. The superscript s stands for period2 liquidity shock.The utility of the investors in case of a period 2 shock is given by:

U si;3 =�N (5)

4.2 Period 2Once the state contingent period 3 equilibrium has been determined, wecan use the results to investigate the second period decisions of economicagents.

4.2.1 No liquidity shock

Assume �rst there is no period 2 liquidity shock. We will solve sepa-rately the investor�s and entrepreneur�s maximization problem and thencompute the equilibrium.

Investors problem The decisions of the investor consist on how muchto lend to entrepreneurs and how much to consume to maximize period2 onwards utility:

Problem 1

maxcni;2;l2

Uni;2 = cni;2 + U

ni;3 = c

ni;2 + �N + l1 + l2 (6)

subject tocni;2 + l2S

�12 = �N � � 2 +Bi (7)

cni;2 � 0 (8)

l2 � 0 (9)

The second equality in equation (6) makes use of equation (3). Equa-tion (7) is the budget constraint: period 2 consumption plus the amountof goods lent (l2S�12 ), where S2 is the gross interest rate between periods2 and 3, is equal to the investor�s endowment ( �N) minus taxes (� 2) plusthe amount of public bonds purchased in period 1, Bi. We do not use the

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subscript i in � 2 because only investors pay taxes. Equation (8) statesthat consumption cannot be negative. Equation (9) is the investor�sborrowing constraint, and says that investors cannot borrow (that is,investors cannot lend a negative amount). This last statement followsdirectly from the fact that the future endowment from the investors isnonpledgeable.We don�t need to solve the maximization problems of the economic

agents entirely. It su¢ ces to present some results that follows from thesolutions. It is easy to see that the solution of problem 1 implies thefollowing conditions: 8<:

S2 > 1) cni;2 = 0S2 = 1) any

�cni;2; l2

S2 < 1) l2 = 0

(10)

Throughout this paper, the term "any fx1; :::; xng" means that anycombination of x1; :::; xn that satis�es the constraints of the problem isa solution. For instance, the second row of (10) tells us that if S1 = 2then

�cni;2; l2

can take any value as long as (7) to (9) are satis�ed.

Remember that �N is a large number, so it is sometimes useful tothink of it as "in�nite". It is particularly useful to think of �N as anumber when solving the investors�maximization problem and make�N tend to in�nite in market clearing conditions. Thus, the conditionsstated in 10 plus the constraints (7) to (9) make clear that investors arewilling to supply "any" amount of funds at zero (net) interest rate incase of no liquidity shock in period 2. That is, the supply of funds frominvestors is in�nitely elastic at S2 = 1.

Entrepreneur�s problem In case of no liquidity shock, the entrepre-neur chooses howmuch to borrow (from investors or other entrepreneurs)or lend (to other entrepreneurs only, since investors have no pledgeableincome) and to consume in that period in order to maximize lifetimeutility:

Problem 2

maxcne;2;d2

Une;2 = cne;2 + U

ne;2 = c

ne;2 + A

�I � (d1 + d2) (11)

subject tocne;2 = Be + d2S

�12 (12)

d2 � ��I � d1 (13)

cne;2 � 0 (14)

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Equation (11) makes use of equation (2). Equation (12) is the en-trepreneur period 2 budget constraint: he uses his proceeds from publicbonds purchased in the former period (Be) and borrows from investorsor other entrepreneurs (d2) in order to consume (cne;2). Equation (13) isthe entrepreneur borrowing constraint: the overall borrowing (d1 + d2)cannot exceed the available collateral, ��I. Equation (14) states thatconsumption cannot be negative.The solution of problem 2 is given by the following set of conditions:8<:

S2 > 1) d2 = �BeS2S2 = 1) any

�cne;2; d2

S2 < 1) d2 = ��I � d1

(15)

Market clearing condition Throughout this paper, we will considerthe symmetric equilibrium, for the ease of explanation. Equilibrium in�nancial markets implies that the total amount lent by investors is equalto the total amount borrowed by entrepreneurs:

l2 = d2 (16)

From (10),(15) and (16), it is clear that S2 > 1 cannot be an equi-librium. There are two possibilities:If ��I � d1 = 0, then there is no pledgeable income in the economy

and the �nancial market collapse. From equations (9), (13) and (16), wehave:

l2 = d2 = 0 (17)

If ��I � d1 < 0, then a period 2 �nancial market exists. Equations(10), (15) and (16) imply:

S2 = 1 (18)

0 � l2 = d2 � ��I � d1 (19)

Using the market clearing conditions (17) or (18) plus equations (6)and (7), it is easy to show that

Uni;2 = 2 �N � � 2 + l1 +Bi (20)

Similarly, from (17) or (18) plus (11) and (12), we have that

Une;2 = Be + A�I � d1 (21)

4.2.2 Liquidity shock

Let�s now investigate the economic agents�decisions when the economyis hit by a liquidity shock.

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Investor�s problem When there is a liquidity shock, overall supplyof collateral drops to zero and the credit market collapses. The investorsimply consume his income, which is given by his endowment, minustaxes plus public bonds purchased in the former period:

csi;2 = �N � � 2 +Bi (22)

Entrepreneur�s problem In case of a liquidity shock, the entrepre-neur must choose not only how much to consume but also it�s optimalinvestment to keep the plant productive:

Problem 3maxcse;2;I

U se;2 = cse;2 + U

se;3 = c

se;2 + aI (23)

subject tocse;2 + I = Be (24)

cse;2 � 0 (25)

0 � I � �I (26)

Equation (23) makes use of (4). Equation (24) is the entrepreneurperiod 2 budget constraint: he uses his proceeds from public bondspurchased in the former period (Be) in order to consume (cse;2) and invest(I). Notice that the entrepreneur neither borrows not lends becausethe availability of collateral in the economy drops to zero. As before,equation (25) states that consumption cannot be negative. Equation (26)says that reinvestment cannot be neither negative nor exceed the size ofthe plant, �I.The solution of problem 3 is given by:�

I = min�Be; �I

cse;2 = Be �min

�Be; �I

(27)

Equilibrium From (5) and (22), it is easy to check that the utility ofthe investors in case of a liquidity shock is given by:

U si;2 = csi;2 + U

si;3 = 2

�N � � 2 +Bi (28)

From (23) and (27), the utility of entrepreneurs in case of a liquidityshock is:

U se;2 = Be + (a� 1)min�Be; �I

(29)

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4.3 Period 1 decisionsWe may now use the results of the previous section to study the period 1decisions of the investor and entrepreneur. Let Vi(Bi; l1) is the expected(from period 1 point of view) intertemporal utility from period 2 onwardsof the investor given Bi and l1:

V (Bi; l1) � E1(Ui;2jBi; l1) =Uni;2 + U

si;2

2(30)

Similarly, de�ne the expected period 2 utility of the entrepreneur as

V (Be; d1) � E1(Ue;2jBe; d1) =Une;2 + U

se;2

2(31)

From (20), (28) and (30), we have:

V (Bi; l1) =l12+ 2 �N � � 2 +Bi (32)

Similarly, from (21), (29) and (31), we have:

V (Be; d1) = Be +A�I � d1 + (a� 1)min

�Be; �I

2

(33)

4.3.1 Investor�s decisions

In period 1, investors choose how much to consume, how much to lendto entrepreneurs and how much to purchase of public bonds:

Problem 4

maxci;1;Bi;l1

Ui;1 = ci;1 + V (Bi; l1) = ci;1 +l12+ 2 �N � � 2 +Bi (34)

subject to

ci;1 = �N � � 1 � S�11l12� PBi (35)

l1 � 0 (36)

ci;1 � 0 (37)

Bi � 0 (38)

Equation (34) makes use of (33). Equation (35) is the budget con-straint: the investor consumes it�s endowment ( �N) minus taxes (� 1)minus what he lends to entrepreneurs (S�11

l12) minus the cost of pur-

chasing public debt (PBi), where S1 is the gross interest rate betweenperiod 1 and 3 and P is the price of the public bond. Throughput thispaper, we will refer to S1 simply as "banking spread". Equation (36) is

15

the borrowing constraint: investors cannot borrow. Equation (37) and(38) says that consumption and the demand of public bonds cannot benegative.The solution of problem depends on P and S1. In what follows, it is

easy to show that:8>>>><>>>>:P � 1; S1 > 2) l1 =

��N � � 1

�S1

P � 1; S1 < 2) l1 = 0P > 1; S1 = 2) Bi = 0; any fci;1; l1gP = 1; S1 = 2) any fci;1; Bi; l1g

P < 1) ci;1 = 0

(39)

The linear structure of the problem makes our interpretations veryeasy to explain: the supply of funds is in�nitely elastic at S1 = 2 and thedemand for public bonds of investors is also in�nitely elastic at P = 1.

4.3.2 Entrepreneur�s decision

In period 1, the entrepreneur must chose how much to borrow (d1), toconsume (ce;1) and to purchase of public goods (Be) in order to maximizelifetime utility:

Problem 5

maxce;1;Be;d1

Ue;1 = ce;1 +Be + A�I � d1 +max

�Be � �I; 0

+ amin

�Be; �I

2

(40)subject to

PBe + ce;1 = S�11 d1 (41)

d1 � ��I (42)

Be � 0 (43)

ce;1 � 0 (44)

Equation (41) is the period 1 budget constraint. The entrepreneurborrows S�11 d1 and uses the funds to consume and to purchase publicbonds. Equation (42) is the borrowing constraint: the entrepreneurcannot promise to pay more than it�s available collateral when there isno liquidity shock. Equation (43) says that the entrepreneur cannot sellpublic bonds, and (44) that consumption cannot be negative.The following conditions arise directly from the solution of problem

5:

16

8>>>><>>>>:S1 = 2; P >

a+12) Be = 0; any fce;1; d1g

S1 = 2; P =a+12) 0 � Be � �

a+1�I; any fce;1; d1g

S1 = 2; 1 � P < a+12) Be =

�2P�I; d1 =

�2�I

P < 1) ce;1 = 0S1 < 2) d1 =

�2�I

(45)

4.3.3 Equilibrium

The market clearing condition in the �nancial, public bonds and goodmarket are given by:

l1 = d1 (46)

Bi +Be = �B (47)

ci;1 + ce;1 = �N (48)

where �B is the aggregate supply of public bonds, which we take asgiven.Equation (46) states that total lending from investors must equal

total borrowing from entrepreneurs. Equation (47) says that aggregatedemand for public bonds, Bi+Be, must equal aggregate supply of pub-lic bonds, �B. Finally, from equation (48) we have that in equilibriumaggregate consumption is equal to the investor�s endowment.We will now prove that, in equilibrium, the following pair of condi-

tions hold: �P � 1S1 = 2

(49)

The proof is as follows: assume P < 1: From (39) and (45), we haveci;1 = ce;1 = 0. Using (48), we have 0 = �N , which is an absurd. ThusP � 1.Since P � 1, we have from equations (39) that S1 > 2 implies l1 =

S1��N � � 1

�. Using (42) and (46), we have d1 � ��I < S1

��N � � 1

�= l1,

which is an absurd (the last inequality comes from the fact that �N islarge). If S1 < 2, from (45) we have that (42) binds. Since P � 1,from (39), (45) and (46), we have l1 = 0 < ��I = d1;which is an absurd.Therefore, we have that S1 = 2.For the sake of completeness, the government budget constraint is

given by the following equations:

P �B = �� 1 (50)

17

�B = � 2 (51)

That is, as explained before, the proceeds from selling public bondsare distributed to investors and taxes to back such bonds are also paidby them.

4.4 Aggregate demand for public bondsTo write the aggregate demand in a more convenient way, de�ne

Bl ���I

a+ 1;Bu �

��I

2;Pu �

a+ 1

2(52)

where the subscript l (u) stands for lower (upper) cuto¤.From equations (39), (45), (47) and (49), we can write the aggregate

the equilibrium in the public bond market as:8<:�B < Bl ) P = Pu

Bl � �B � Bu ) P = ��I=2 �B�B > Bu ) P = 1

(53)

The conditions (53) show that, given the other parameters of theeconomy, the price of public bonds is a negative function of �B. The factthat P falls with �B is not new in the literature, as many models ariseat similar conclusions. In the next section, we will investigate in detailhow �nancial development also a¤ects the demand for public bonds.The Brazilian economy presents a moderate level of public debt when

compared with other countries, but very high interest rates. Why is thatso? In the next section, we follow the hypothesis of Arida, Bacha andLara-Resende that jurisdictional uncertainty may be at the root of theproblem.

4.5 Interest rates and �nancial underdevelopmentThe law and �nance literature has presented strong empirical evidencethat a legal system that gives strong rights to creditors increases theamount of income borrowers can fully pledge (see Beck and Levine [2005]for a survey on the topic), boosting �nancial development. Since a goodlaw is of no use if not enforceable, we interpret � as a measure of thequality not only of the legal but also of the juridical system. The higherthe value of �, the higher is the availability of collateral, or, equivalently,more e¢ cient the legal and juridical system are (see also Caballero andKrishnamurthy [2001]).De�ne

18

Ll �2 �B�I;Lu �

(a+ 1) �B�I

(54)

Using (53) and (54), it is easy to see that, given the level of publicdebt, equilibrium interest rates depend on the level of �nancial develop-ment: 8<:

� < Ll ) P = 1Ll � � � Lu ) P = ��I=2 �B

� > Bu ) P = Pu

(55)

Even countries with small or moderate �B may present low price ofpublic bonds if �nancial ine¢ ciency is high enough (that is, if � issu¢ ciently low). We believe this is a crucial result to understand highinterest rates in Brazil. This interpretation is quite useful in the sensethat it provides a di¤erent view for the jurisdictional uncertainty theoryof Arida, Bacha and Lara-Resende [2004]. Here, developed �nancialmarkets increase the demand for public bonds, leading to higher pricesor, equivalently, lower rate of interest on public bonds.

5 Empirical investigation

5.1 Sample descriptionThe time dimension of our sample is given by 7 periods. Each periodconsists on two years. Thus, period 1 relates to the years of 1991-92,period 2 to the years of 1993-94 and so on. This choice re�ects thefact that our measure of jurisdictional uncertainty is available on a twoyear base starting from 1996 (see section 5.1.1 below). The inclusion ofthe periods 1991-92 and 1993-94 in our sample is to increase the setof available instruments in our estimations (see section 5.2, where wedescribe our econometric methodology).The choice of countries in our sample also given by data availability.

We have selected the 43 emerging and industrial countries for which thereis data available, for at least one period, on all the variables used in ourregressions (see section 5.1.1 for a formal de�nition of the variables),which consist of: real interest rates, in�ation, net interest margin, ruleof law, foreign direct investment and domestic public debt.

5.1.1 Data description

In�ation and real interest rates To construct our series of realinterest rates and in�ation, we have used monthly data (quarterly whenmonthly data is not available) from the IFS.The monthly in�ation rate is de�ned as

19

�̂s =�P̂s=P̂s�1 � 1

�� 100 (56)

where P̂s is the consumer price index (code 64...ZF) of month s.Monthly data on nominal interest rates come on an yearly basis. Our

�rst step was to transform the data to a monthly basis:

{̂ms = [(1 + {̂ys=100) ^ (1=12)� 1] � 100 (57)

where {̂ys is the money market rate (code 60B..ZF) of month s. Thesuperscripts m and y indicate monthly and yearly basis. If {̂ys=100 issmall, it makes little di¤erence if we calculate the nominal interest rateson a monthly basis according to the formula {̂ms = {̂

ys=12. However, some

countries present high in�ation levels, so we prefer to use equation (57).Notice also that although {̂ys=100 is sometimes high, in our sample thevalue of {̂ms =100 and �̂s are always small. Using this result, once we havethe monthly nominal interest rate and the in�ation rate on a monthlybasis, we calculate the real interest rate as follows:

r̂s = 12 � (̂{ms � �̂s) (58)

The real interest rate r̂t on period t 2 f1; 7g is the median of realinterest rates, given by equation, in the 24 months that form the biannualperiod of the years 1989 + 2t and 1990 + 2t. For instance, real interestrates in period t = 1 is given by the median of real interest rates r̂sbetween January of 1991 and December of 1992. If the series r̂s is notavailable for all months that form period t, we do not calculate r̂t. Forexample, if the series r̂s is not available for all months between januaryof 1991 and december of 1992, the series r̂t will not be available for t = 1.We calculate the in�ation rate �̂t in a similar way.We have also calculated the real interest rate series (r̂t) using treasury

bill rate (code 60C..ZF) as our measure of nominal interest rate, usingthe same methodology described above. Besides, we have done the samecalculations based on quarterly data as well. Therefore, we are left with4 series of real interest rates, depending on the series we use as a measureof nominal interest rates (money market or treasury bill rate) and thefrequency used (monthly or quarterly data).The real interest rate series ~rt used in the regressions and throughout

the paper is constructed as follows: �rst, we use the real interest rate(r̂t) calculated using the money market rate and a monthly frequency asour measure of real interest rates. Whenever such series is not availablefor a given period, we use the "monthly frequency / treasury bill rate"series instead. If neither are available, we use the "quarterly frequency

20

/ money market rate" series. If this last series is not available neither,we use the "quarterly frequency / treasury bill" series.Similarly, as our measure of in�ation we use the series �̂t based on

monthly data (quarterly if not available).Why have we decided to use such complicated methodology instead

of simply subtracting in�ation from nominal interest rate with data onan yearly frequency, as is frequently done in the literature? The reason isthat the "standard" methodology predicts extremely unrealistic real in-terest rates in countries with unpredictable in�ation rates. For instance,our methodology predicts interest rates of 38% and 26% for the Brazil-ian economy in periods 1 and 2 respectively (that is, for years 1991-92and 1993-94), which were remarked by extremely high in�ation. In con-trast, the values using the "standard" methodology are 69% and 96%respectively. In our sample, there are other countries that presentedquite unpredictable in�ation, notably Russia, Turkey and Argentina.Our methodology predicts much less volatile interest rates than the onespredicted by the standard methods.

Other variables The other variables used in this paper come fromvarious sources and most of them are available in an yearly frequency.When this is the case, the value a variable xt assumes on a period t 2f1; 7g is the average between the years 1989 + 2t and 1990 + 2t.Financial market ine¢ ciency We follow the suggestion of Beck,

Demirguç-Kunt and Levine [1999] and use net interest margin as ourmeasure of �nancial market ine¢ ciency. This variable is de�ned as thevalue of the bank�s net interest revenue as a share of it�s total assets.Clearly this variable is an imperfect measure of the ine¢ ciency of

the �nancial markets. One particular drawback is that it depends on thevalue of real interest rates itself: higher interest rates can lead to highernet interest margins, so a typical endogeneity problem arrises.As will be explained shortly, the econometric methodology used in

this paper deals directly with this problem, though the use of suitableinstruments.

Domestic public debt As a measure of the size of (domestic)public debt, we use public bond market capitalization to GDP in Beck,Demirguç-Kunt and Levine [1999]. This variable is de�ned as the totalamount of outstanding domestic debt securities issued by the publicsector over GDP.We have decided to use only domestic debt (instead of total debt)

because the model presented in section 4 predicts that only public debtissued domestically a¤ect equilibrium interest rates. For instance, ifthere is no default risk, foreign debt should a¤ect equilibrium interna-

21

tional real interest rates, but not domestic.This variable is also subject to endogeneity. An increase in the real

rate of interest may reduce the prices of bonds, leading to a lower publicbond market capitalization. Once again, the econometric methodologyshould control for this fact.

Capital �ows The foreign direct investment (henceforth FDI) se-ries can be obtained directly from the World Bank WDI. The series usedis Foreign direct investment, net in�ows (% of GDP). We have chosenthis variable as our measure of capital �ows due it�s wide availability andfor the fact that it re�ects changes in the long term environment (suchas institutional changes) better than other measures of capital �ow.

Jurisdictional uncertainty We follow Gonçalves et al [2005] anduse as measure of jurisdictional uncertainty the Rule of Law series inKaufman et al [2003]. This variable measures "the quality of contractenforcement, the police, and the courts, as well as the likelihood of crimeand violence".This variable is available for the years 1996, 1998, 2000, 2002 and

2004. The value the variable "jurisdictional uncertainty" assumes in pe-riod t 2 f1; :::; 7g is equal to the value the variable "rule of law" assumeson year 1990 + 2t. Therefore, we have available data on jurisdictionaluncertainty only for periods t 2 f3; :::; 7g.

5.2 Econometric methodology: GMM approachIn this section, we will brie�y expose the theory of generalized method ofmoments (GMM) estimation of dynamic panel data. This econometricmethod is interesting in the context of this paper because, as mentionedabove, it allows for endogeneity of explanatory variables.Consider the following AR(1) model with unobserved individual ef-

fects:

yit = �yit�1 + �i + vit (59)

for i = 1; :::; N and t = 2; :::; T .We make the following standard assumptions (see Blundell and Bond

[1998]):Assumption 1 (error components structure)

E(�i) = E(vit) = E(�ivit) = 0 (60)

Assumption 2 (serially uncorrelated shocks)

E(visvit) = 0 for s 6= t (61)

22

Assumption 3 (predetermined initial conditions)

E(yi1vit) = 0 for i = 1; :::; N and t = 2; :::; T (62)

Pooled OLS estimates of equation (59) are inconsistent, since the ex-planatory variable yit�1 is positively correlated with the �i component ofthe error term, (�i + vit). Within groups estimations solve this problem,but introduces a new type of inconsistency, due the correlation betweenthe (transformed) dependent variable, yi;t�1 � 1

T�1PT�1

j=1 yi;j, and the

(transformed) error term, vi;t � 1T�1

PTj=2 vi;j (see Bond, [2002]).

First di¤erentiating allows us to eliminate both sources of inconsis-tency. Taking �rst di¤erences of equation (59), we �nd

�yit = ��yit�1 +�vit (63)

The term �i is absent from equation (63), but the terms �yit�1 and�vit are correlated (due the presence of the term yi;t�1 in the formerand vi;t�1 in the latter). This problem can be solved easily by the use ofinstruments, since �yi;t�2 or yi;t�2 are valid instrumental variables for�yit�1 in equation (63). Two-stage least squares estimations of equation(63) have been proposed by Anderson and Hsiao [1981].Arellano and Bond [1991] apply the GMM technique developed by

Hansen [1982]. They notice that former lags of the dependent variable(yi;t�2; yi;t�3; :::) are also valid instruments for �yit�1; and propose theestimation of the model (63) by GMM.Formally, assumptions (60)-(62) imply the following m = 0:5(T �

1)(T � 2) moment restrictions

E [yi;t�s�vit] = 0 for t = 3; :::; T and s � 2 (64)

which can be written as

E [Z 0i�vi] = 0 (65)

where Zi is the following (T � 2)�m instrument matrix:

Zi =

2664yi1 0 0 ::: 0 ::: 00 yi1 yi2 ::: 0 ::: 0: : : ::: : : :0 0 0 ::: yi1 ::: yi;T�2

3775 (66)

and the (T � 2) vector �vi is given by

�vi = (�vi3;�vi4; :::;�viT )0 (67)

23

The asymptotically e¢ cient GMM estimator (see Wooldridge 2002)based on moments (64) minimizes

JN =

1

N

NXi=1

�v0iZi

!WN

1

N

NXi=1

Z 0i�vi

!(68)

where WN is the weighting matrix de�ned as

WN =

1

N

NXi=1

Z 0i�v̂i�v̂0iZi

!(69)

where �v̂i are (consistent) estimates of the �rst-di¤erenced residualsobtained by a preliminary consistent estimator. The �rst step weightmatrix is generally given by

W1N =

1

N

NXi=1

Z 0iHZi

!(70)

where H is a (T � 2) square matrix with 2�s on the main diagonal,-1�s on the �rst o¤-diagonals and 0�s elsewhere (under homoskedasticdisturbances, the one step GMM estimator using W1N instead of WN

in equation (68) also yields an asymptotically e¢ cient GMM estimator,that�s why H is a good choice for the weight matrix of the �rst-stepcomputations). General results for GMM estimators (see Wooldridge,2002) indicate that the estimator is consistent and asymptotically normal(as N tends to in�nity and for �xed T ).Despite it�s good asymptotic properties, the two step GMM estima-

tor presents unreliable asymptotic standard errors and t-ratios in �nitesamples (see Bond [2002]). Windmeijer [2005] proposes a correction thatprovides more precise estimates of the variance of two step GMM esti-mators, and the �nite sample properties are shown to be as good asgood as the one step estimator (t-tests based on the corrected two stepstandard errors are found to be as reliable as the one step estimator).The GMM approach has a further advantage with respect to the two

stage least squares estimators: for T > 3, the model is overidenti�ed,and the validity of assumptions (60)-(62), used to derive (64) as validmoments, can be tested (as a group) by the standard Sargan test (seeBond, [2002]).Besides, the important assumption of serially uncorrelated shocks

(61) can (and should!) be veri�ed by the test of no second-order ser-ial correlation in the �rst-di¤erenced residuals (see Arellano and Bond[1991]). If hypothesis (61) is valid, then the series�vit will present a neg-ative �rst-order autocorrelation and zero second-order autocorrelation,

24

since cov(�vit;�vi;t�1) = cov(vit�vi;t�1; vi;t�1�vi;t�2) = �var(vi;t�1) <0 and cov(�vit;�vi;t�2) = cov(vit � vi;t�1; vi;t�2 � vi;t�3) = 0.The GMM procedure (one or two steps) may present serious �nite

sample bias when the instruments are weak (see Blundell and Bond[1998]). In the next section, we will see that a further (mild and testable)assumption allows us to derive an estimator with superior �nite sampleproperties.

5.3 System GMMUnder a more restrictive set of assumptions, we can derive a furtherset of moment conditions to be used in a GMM setting. We keep thehypothesis that (60)-(62) hold, and consider the additional assumptionthat

E (�i�yi2) = 0 for i = 1; :::; N (71)

Assumption (71), when combined with (60)-(62), implies the follow-ing linear moment conditions:

E (uit�yi;t�1) = 0 for i = 1; :::; N and t = 3; :::; T (72)

We can use the moment conditions (64) and (72) to construct a GMMestimator that makes use of this new information. Formally, the momentconditions can be written as

E�Z+0i u

+i

�= 0 (73)

where new instrument matrix is given by

Z+i =

266664Zi 0 0 ::: 00 �yi2 0 ::: 00 0 �yi3 ::: 0: : : ::: :0 0 0 :::�yi;T�1

377775 (74)

and

u+i = (�vi3;�vi4; :::;�viT ; ui3; :::; uiT )0 (75)

The validity of (71) can be tested using standard Sargan tests ofoveridenti�cation (which tests (60)-(62) and (71) as a group) or usingDi¤erence Sargan between the �rst-di¤erenced GMM and the systemGMM (which tests (71) separately).The system GMM is particularly useful in small samples when the

series is very persistent (see Bond [2002]).

25

Another important property of the system GMM method is thatit allows for additional explanatory variables in (59). More precisely,this method provides consistent estimates even when those variables areendogenous with respect to the shocks uit. The formal derivation ofthe extension of the system GMM to additional explanatory variables isstraightforward and will be presented in the next section.

5.4 Endogenous variablesConsider an additional explanatory variable xit

yit = �yit�1 + �xit + �i + vit (76)

for i = 1; :::; N and t = 2; :::; T . An important point is that weallow xit to be correlated with �i and to vit. Formally, our assumptionregarding the additional explanatory variable is that it is endogenous isthe sense that

E [xitvis] 6= 0 for i = 1; :::; N and s � t (77)

Proceeding in an analogous way as done in section, we can get rid o¤the correlation between the endogenous variable and the residual by �rstdi¤erentiating equation (76) and making use of lags of the endogenousvariables as instruments. Formally, we are interested in estimating

�yit = ��yit�1 + ��xit +�vit (78)

Assumption (77) implies that the following moment conditions areavailable:

E [xi;t�s�vit] 6= 0 for t = 3; :::; N and s � 2 (79)

The moments derived in (79) can be used together with (64) and, if(71) also holds, (72), in the GMM estimation of (78). Assumption (77)can be tested, together with the other assumptions of the model, by astandard Sargan overidenti�cation test.As in the former section, further assumptions about the correlation

between individual e¤ects and �rst di¤erences of the explanatory vari-ables allows us to derive further moment conditions. In this sense, anassumption analogous to (71) in the context of an endogenous explana-tory variable is

E [�i�xit] = 0 for i = 1; :::; N and t = 2; :::; T (80)

which implies moment conditions also similar to the ones derived in(72):

26

E [�xit�1uit] = 0 for i = 1; :::; N and t = 3; :::; T (81)

As before, the validity of (80) can be tested using Sargan tests ofoveridenti�cation or Di¤erence Sargan tests.

5.5 Measurement errorsAssume the variable yit is not directly observable. Instead, we observe

~yit = yit +mit (82)

where mit is a serially uncorrelated measurement error.

E [mitmis] = 0 for all i and t 6= s (83)

Besides, assume that this term is with all but the current disturbancevit:

E [mitvis] = 0 for all i and t 6= s (84)

If equations (82)-(84) hold, the model can be written as:

~yit = �~yit�1 + �i + �it (85)

�it = vit +mit � �mit�1 (86)

Taking �rst di¤erence of (85)-(86), we �nd:

�~yit = ��~yit�1 +��it (87)

��it = �vit +�mit � ��mit�1 (88)

The model is very similar with the one presented in sections 5.2and 5.3. The di¤erence is that term ��it presents now a positive secondorder correlation, due the presence of the term mit�2 in both ��it and��it�2. This problem is easy to solve: it implies that only variables ~yit�3(instead of ~yit�2, see equation 64) and earlier are valid instruments forthe equations in �rst di¤erences:

E [~yi;t�s�vit] = 0 for t = 3; :::; T and s � 3 (89)

Additional moments for equations in levels may be available in thepresence of measurement errors. If

E [�i�mit] = 0 for all i and all t (90)

27

then the following conditions are available:

E [�~yi;t�2 (�i + �it)] = 0 for i = 1; :::; N and t = 4; :::; T (91)

In sum: if the necessary assumptions for the estimation of the systemGMM model hold but the dependent variable is observed with a mea-surement error satisfying the assumptions, moments (89) and (91) areavailable for the estimation of the parameters of the model in a GMMsetting as explained in sections 5.2 and 5.3.

6 Results

6.1 Equilibrium interest ratesIn this section, we are interested in estimating the parameters of thefollowing equation:

rit = �0rit�1 + �1x1;it + :::+ �nxn;it + �t + �i + vit (92)

where rit is the ex-ante real interest rate, x1;it; :::; xn;it are explanatoryvariables, �t is an unobserved individual e¤ect and vit is an error term.By de�nition, the ex-ante real interest rate is given by:

rit = iit � Et�1�it (93)

Where iit is the nominal interest rate and �it the in�ation rate.Clearly, the term Et�1�it is not observable. However, if we assume thateconomic agents use all available information to predict in�ation (thatis, if we assume rational expectations), then we have that:

�it = Et�1�it �mit (94)

where mit is the di¤erence between expected and actual in�ation.Rational expectations imply that conditions (83)-(84) and (90) hold.Let ~rit denote the ex-post real interest rate:

~rit = iit � �it (95)

Substituting (94) and (95) into (93), we �nd that:

~rit = rit +mit (96)

The methodology described in section 5.5 can be applied to the esti-mation of the parameters of equation (92).The �rst version of (92) we want to estimate is:

~rit = �0~rit�1 + �1nit + �2fit + �t + �i + vit (97)

28

where nit and fit stand for net interest margin and foreign directinvestment.Our goal is to compare the predictions of the model presented in

section 4 with the original Arida, Bacha and Lara-Resende hypothesis.The former predicts a positive �1, while the latter predicts a positive�2. Besides, we are interested in investigating whether our institutionalvariables (rule of law and regulatory quality) are good instruments inthe estimation of (97).Table 1 shows the results for the estimation of (97) using di¤erent

econometric techniques. The �rst two columns present OLS and WithinGroups (henceforth WG) estimations of (97), while the last two columnsuse the system GMM method presented before. As explained in section,OLS and WG provide inconsistent estimations under the presence ofan individual e¤ect �i. However, Bond [1998] argues that in practicesuch estimators may be useful, since the estimator of the parameter�0 is known to be positively biased in OLS and negatively biased inWG estimations. Therefore, if individual e¤ects is an issue, consistentestimators should predict a value for �0 between the ones estimated byOLS and WG:

Let�s analyze the third column of table 1 �rst. We have used asinstruments in the estimation of (97) lags of real interest rates. Noticethat we haven�t used lagged values of net interest margin as instruments.The reason, as mentioned above, is that we want to investigate how ourestimations of �1 and �2 change according to our choice of instruments.

29

The estimated coe¢ cient for �0, 0.369, lies between OLS (0.386) andFE (0.227) estimators, and is signi�cant at 10%. Both the Sargan (p-value 0.552) and the di¤erence Sargan (p-value 0.615) tests accept thevalidity of the instruments at usual levels. As predicted, the AB tests for(�rst di¤erence) residual serial correlation indicate negative �rst orderand positive second order correlation, but both are not signi�cative atusual levels. However, for our estimators to be consistent, we need to testwhether there is no third order (�rst di¤erence) residual autocorrelation.The hypothesis of no such correlation is easily accepted by the AB tests(p-value 0.807). All tests indicate the the estimators presented on thethird column of table 1 are consistent.Our estimations of �1 and �2, which are our main interest here, are

close to zero and are not statistically signi�cant. There are two possibil-ities, that will be investigated shortly. The �rst one is simply that thetrue value of �1 and �2 is zero. The second one is that the true valueof the parameters is positive but lagged values of real interest rates areweak instruments for net interest margin and foreign direct investment.If this last explanation is correct, then the use better instruments shouldprovide a positive and statistically signi�cative value for the parameters.In this sense, the sole di¤erence between columns 3 and 4 is that in

the latter we a measure of jurisdictional uncertainty (that is, the variablerule of law) and quality of regulation (regulatory quality) as instrumentsfor the estimation of (97). Column 4 shows that the coe¢ cient on netinterest margin has the predicted sign and is now signi�cative at 1%,and the coe¢ cient on lagged interest rates is now signi�cative at 1%.Comparing the results presented on columns 3 and 4, it is clear thatjurisdictional uncertainty and regulatory quality are good instrumentsfor net interest rate margin and that the e¢ ciency of �nancial marketsa¤ects real interest rates.The coe¢ cient �0 is slightly higher than our OLS estimates, thus our

results should be interpreted with care. Anyway, the results presentedon table 1 con�rm the predictions of the model presented on section 4.It remains to be investigated whether there are other channels through

which jurisdictional uncertainty a¤ects real interest rates. That is, giventhe net interest rate margin, does our measure of jurisdictional uncer-tainty provide further information for the determination of the real rateof interest? To shed some light on this issue, we estimate the followingequation:

~rit = �0~rit�1 + �1nit + �2jit + �3qit + �t + �i + vit (98)

where jit stands for rule of law and qit for regulatory quality. As be-fore, we don�t use lagged variables of net interest margin as instruments.

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Instead, we use lagged values of real interest rate plus rule of law andregulatory quality as instruments.Table 2 shows that the estimated coe¢ cient on the institutional qual-

ity (rule of law and regulatory quality) variables are statistically equalto zero, but the coe¢ cient on netinterest margin remains signi�cativeat 1%. This result strongly suggests that institutional quality a¤ectsequilibrium interest rates through the e¢ ciency of �nancial markets.

Finally, we control for monetary and �scal variables that may alsoa¤ect real interest rates. As Gonçalves et al [2005] observe, jurisdictionaluncertainty (and net interest rate margin) may be correlated with thereal rate of interest because both may be correlated with in�ation orgovernment debt.Since we do not observe expected in�ation, we use actual in�ation

instead and treat the measurement error in a similar way as we havedone so far (see Bond [2002]). Our goal is to estimate the followingspeci�cation:

~rit = �0~rit�1 + �1nit + �2�it + �3bit + �t + �i + vit (99)

In our estimations of (99), we use as instruments lagged values of allvariables plus rule of law and regulatory quality, but we don�t use �veand further lags as instruments in our system GMM estimation to avoidthe over¢ ting problem (see Bond):

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The third column of table 4 shows that the inclusion of �scal and mon-etary controls do not a¤ect our basic results. The standard errors ofpublic bond are extremely large, and the coe¢ cient has the wrong sign.The coe¢ cient on in�ation is negative and statistically signi�cant at

10%. Why is that so? In general, one should expect a positive relation, ashigher expected in�ation lead the central bank to raise interest rates. Webelieve that this comes from the fact that some countries have followeda �xed exchange rate regime during a considerable part of the periodstudied. Periods of scarce capital �ows for developing economies are oftenassociated with higher real domestic interest rates and real exchange ratedepreciation. In a �xed exchange rate regime, the latter is equivalent tode�ation, so we have that in those countries higher interest rates areusually associated with low in�ation.In this sense, the coe¢ cient �2 in equation (99) seems to capture the

relative incidence of di¤erent exchange rate regimes among the countriesin our sample.

6.2 Brazilian interest rates in the recent pastIn this section, we use the results found in the former section to studyin more detail the behavior of the Brazilian economy in the recent past.Our chosen econometric speci�cation chosen is:

~rit = �0~rit�1 + �1nit + �t + �i + vit (100)

since among the variables selected only the net interest margins hasbeen able to predict the real rate of interest on a satisfactory manner.

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Our �rst step will be estimate equation (100). Results are presentedin table 4. In the results shown in the third column, we use all availableinstruments. In other words, lags of real interest rate and net interestmargin plus rule of law and regulatory quality are used as valid instru-ments.

All formal tests indicate that our estimates are consistent, but theresults are not entirely satisfactory. The p-value of the di¤erence Sargantest is small and the coe¢ cient on lagged interest rates is higher thanthe estimated using OLS.We then decided to estimate (101) under a less stringent set of con-

ditions, and present the results in column (4). We have used third andearlier lags on real interest rates as instruments in the equations in �rstdi¤erence, and the institutional variables (rule of law and regulatoryquality) as exogenous instruments in both equations in �rst di¤erenceand in levels. The estimates of �0 lies comfortably between our OLSand WG estimates, and the Hansen and di¤erence Sargan tests easilyaccepts the use of rule of law and regulatory quality as exogenous in-struments. The estimated �1 is close to the one presented in the thirdcolumn and is statistically signi�cant at 1%, while the estimated �0 isno longer signi�cant at usual levels. This is perhaps the cost of using asmaller set of instruments.Given our estimates of �0 and �1, we can use equation (101) to

predict the behavior of Brazilian real interest rates in the recent past:

~rpit = �0~rit�1 + �1nit + �t (101)

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where the superscript p stands for prediction and the values �0 and�1 are the ones presented in the third column of table 4.Notice that our de�nition of predicted interest rates does not include

the individual e¤ect �i. Before presenting our results, it is important thatthe reader bear in mind that the period 1991-94 corresponds roughly tothe "hyperin�ation period", the period 1995-98 to the "�xed exchangerate period" and the period 1999-2004 to the "in�ation targeting period"(see section 2).Figure 1 shows that both actual and predicted interest rates have

been falling consistently during the whole period of our sample. In arough approximation, actual real interest rates have been around 30%in the hyperin�ation period, 20% in the �xed exchange rate period and10% in the in�ation targeting regime. It is interesting to notice alsothat, re�ecting the currency collapse on Asia and Russian in the period1997-98, interest rates have been much higher than predicted in thatperiod:

These results are expected given the discussion presented in section2. We attribute the drastic reductions on the level of the real rate ofinterest to the adoption of the Real Plan in 1994 and to the adoption ofan in�ation targeting regime in 1999.This analysis seems to contradict the results presented in the former

section. We have seen that our selected �scal and monetary factors wereunable to explain the behavior of the real rate of interest. Our inter-pretation is that the relevant �scal and monetary factors are di¢ cult tomeasure and to compare internationally. For instance, what matters for

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the determination of interest rates is more the monetary policy adoptedthan the expected level of in�ation. Also, the sustainability of publicdebt seems to be a relevant �scal determination of interest rates, thoughrisk premium arguments. Both factors are di¢ cult to measure, althoughsome progress has been made recently (see Rogo¤).After the adoption of the in�ation targeting regime, observed real

interest rates have been quite close to it�s predicted level. This is con-sistent with the view that the change on �scal and monetary policy in1999 has allowed the real interest rate to converge toward it�s equilib-rium level. However, what most economists didn�t expect is that thelatter is still very high for international standards, so both rates are stillextremely high when compared with other countries.The highest level recorded of predicted interest rates for the in�ation

targeting period (that is, for t 2 f5; 6; 7g) in all countries of our sample(excluding Brazil) is 9.40% per year (Argentina in 2001-02). The valuesfor the Brazilian economy during that period were 13.82%, 11.08% and8.23%, for t = 5; 6; 7 respectively. Taking into account the whole sample,only the Brazilian economy has recorded predicted interest rates at levelshigher than 10%, with the exception of Argentina in 1991-92 and Russiain 1997-98. In fact, the only period in which predicted Brazilian interestrates were lower than 10% was the 2003-04 period.Let�s now compare our estimations with a naive AR(1) model. Our

goal is to have a feeling of how much information we loose when we don�ttake the e¢ ciency of �nancial markets into account:

~rit = �0~rit�1 + �t + �i + vit (102)

Results are presented on table 6:

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Once �0 has been estimated (see table 6), we can calculate the pre-dictions of our "naive" model, de�ned as:

~rnit = �0~rit�1 + �t (103)

Figure 1 shows very clear evidence that the naive model providesvery poor predictions for interest rates in the country for all periodsof our sample. In particular, both observed real interest rates and thepredictions based on equation (101) have been substantially higher thenour naive predictions. A lot of information is lost when we do not controlfor the net interest rate margin. The evidence presented in this paper isconsistent with the view that the Brazilian real interest rates have beenunable to converge to international levels after 1999 because �nancialmarkets are extremely ine¢ cient in the country.One word of caution is needed here: by no means we claim that

�scal and monetary factors are irrelevant to the determination of thereal rate of interest. We have informally argued in sections 2 and in thepresent one that the macroeconomic policy adopted in the period af-ter the implementation of the Real Plan have been partially responsiblefor the high observed interest rate during that period. Instead, whatthe evidence presented throughout this paper suggests is that �scal andmonetary factors are unable to explain why real interest rates have re-mained extremely high from 1999 onwards. In other words, we believethat higher �scal surpluses or changes in the monetary policy adoptedwill not have the desired e¤ects on the real rate of interest in the presentcontext.

7 Future research and policy recommendations

We have presented formal econometric evidence that the e¢ ciency of�nancial markets a¤ects the real rate of interest in a signi�cant way.Besides, the predictions of our model �t quite well the behavior of theBrazilian interest rates in the recent past.The next natural step is to answer the following question: why are

net interest margins so high in Brazil? One possibility is that the qualityof the judicial system and enforceability of contracts is particularly badin the country. Figure 2 plots the median of the variable "rule of law"against the median of the variable "net interest margin" for the wholeperiod and all the countries of our sample:

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Blaming jurisdictional uncertainty alone is not enough, as the qualityof the Brazilian juridical system is not particularly bad when comparedwith other countries: Colombia, Indonesia, Pakistan, Philippines andRussia have had worse ratings then Brazil. The country�s net interestmargin, around 12% per year, is more than two times higher than the�tted value in our (cross section) regression presented in �gure 2, whichmakes clear that rule of law is far from capable of explaining the remark-able ine¢ ciency of the �nancial market in the country. Using regulatoryquality instead of rule of law yields similar results.In other words, our results point to the direction that jurisdictional

uncertainty explains, to a large extent, the e¢ ciency of Brazilian (andother countries) �nancial markets, but the fact other countries withworse jurisdiction present more e¢ cient �nancial markets and the verypoor �t for the Brazilian economy presented in �gure 2 suggest that wewere unable to fully identify the key determinants of the net interestmargin.Before we proceed, it is important to make clear that we do not claim

that the jurisdictional uncertainty hypothesis is �awed. Arida, Bachaand Lara-Resende have stressed the point that what is peculiar to theBrazilian economy is not the quality of the judicial system itself, but thestate interventions adopted to deal with the problem of jurisdictionaluncertainty. The problem is that this is very di¢ cult to be veri�ed, duethe impossibility of performing a formal international comparison.Anyway, even if Arida, Bacha and Lara-Resende�s jurisdictional un-

certainty hypothesis is proved to be a important issue, as the results ofthe present paper strongly suggest, nothing guarantees it is the most rel-evant one. Anything that a¤ects the net interest margin will a¤ect the

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real rate of interest as well. Demirguç-Kunt and Huizinga [1999] haveused bank level data for 80 countries (including Brazil) in the periodfrom 1988 to 1995 to investigate the determinants of net interest mar-gin. The authors present evidence that net interest margins re�ect a widemyriad of determinants, such as macroeconomic conditions, the charac-teristics of the �nancial sector, taxation, institutional characteristics ofthe country, among others.If high interest rates in the country are really the outcome of an

extremely ine¢ cient �nancial market, identifying the precise factors thatlead to high net interest margins in the country would provide extremelyrelevant information for policy purposes.

8 Final remarks

In a recent contribution, Arida, Bacha and Lara-Resende [2004] haveidenti�ed the presence of particularly acute anti-creditor bias withinBrazilian institutions. They claim that jurisdictional uncertainty liesbehind the country�s high interest rates.The theoretical contributions of Woodford [1990], and specially of

Holmström and Tirole [1998] provide the perfect theoretical environmentin which the jurisdictional uncertainty hypothesis can be fully developed.Anti-creditor bias and lack of credibility of �nancial contracts a¤ect thee¢ ciency of the �nancial markets in a negative way. In it�s turn, thisproblems translates into lower demand for liquid assets, as the pledgeableincome of entrepreneurs drops as a result of low creditor protection. Theprice of government bonds re�ect the scarce demand for liquid assets.We have used the system GMM estimation methodology developed

by Blundell and Bond [1998] to perform several tests of our reinter-pretation of the jurisdictional uncertainty hypothesis. The results werequite encouraging. We have presented evidence that the quality of thecountry�s judicial system is a good instrument for the e¢ ciency of the�nancial markets, which has a relevant impact on the determination ofreal interest rates. Besides, jurisdictional uncertainty provides no furtherinformation than those contained in the e¢ ciency of �nancial markets.Our results are robust to the introduction of �scal and monetary con-trols.Using our results to investigate the dynamics of the Brazilian real rate

of interest in the recent past, we have argued that the macroeconomicpolicy adopted in 1999 has been extremely important to bring interestrates from 20% per year to a much lower 10% level. Our interpretation isthat the adoption of a responsible �scal policy and an in�ation targetingregime has allowed the real rate of interest to quickly converge to it�s newequilibrium level. However, this level is still very high when compared

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even with similar countries, given that distortions on �nancial marketsare higher in the country than elsewhere. If this argument is correct, incontrast to what usually argued by some economists, even if the countryimplements a (sometimes very costly) �scal reform and be able to runa fully credible in�ation targeting regime, interest rates will fail to falltowards international levels.Finally, we have argued that the e¢ ciency of the �nancial markets

re�ect further institutional and regulatory factors, besides jurisdictionaluncertainty. More importantly, some of those factors are measurableand allow an international comparison. Our suggested future topic forresearch and policy recommendations is to try identify such distortionsso that the problem of high rate of interest in the country can be attackedin it�s most fundamental causes.

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