Devaluation expectations and interest rates in Mexico : the role of domestic debt management

THE WORLD BANK t - Internal Discussion Paper LATIN AMERICA AND THE CARIBBEAN REGION Report No. IDP-098 Devaluation Expectations and Interest Rates in Mexico: the Role of Domestic Debt Management Daniel F. Oks May 1991 Country Operations Division I Country Department II POS -1 Discussion Papers are not formal publications of the World Bank. They present preliminary and unpolished results of country analysis or research that is circulated to encourage discussion and comment; citation and the use of such a paper should take account of its provisional character. Thi findings, interpretations, and conclusions expressed in this paper are entirely those of the author(s) and should nqt be attributed in any manner to the World Bank, to its affiliated organizations, or to members of its Board of Executive Directors or the countries they reXesent. 1AC DISOUSSO PAPIR SEIOES IDP.12 'Argen~na: Probems for Achieving Macr by by F. Desmond McCarthy and Alfredo E. Thome, Januay 1988 DP-13 'Argen~n: Towards the Year 2000' by F. Desmond McCarthy, June 1987 IDP-14 Trade Uheraiatlon: The Lessons ol Expedence*, Paper presented In the conference "Toward a New Trade Polloy for Brauir, S~o Paulo, Apil 11 and 12, 198 IDP-16 *Aspee f Privatation: The Case ol Argenna 1976-81* by R. Luders, April 1988 IDP-17 *Aspets ol Privatation: The Case of Chile 1974-85, by D. Hachette, April 1988 IDP-18 OPivatation In Argenna and Chile: Lssons from a Comparison* D. Hachette and R. Luderm, April 19%8 IDP-19 *Prnciples ol Water Supply Pricing In Developing Countries' by Mohan Munasinghe, June 1988 IDP-20 The Status ol Energy Economics: Theory and App~*ation* by Mohan Munasinghe, June 1988 IDP-21 'What are the Prospects for Land Reform?' by Hans Binswanger and Miranda Elgin, August 1988 IDE-24 'Managing Argenina's Extømal Debt The Conttibution ol Debt Swap , Carlos Alfredo Rodrguez, January 1989 IDP-29 'Managing Mexico's Extemal Debt The Contribution of Debt Reduction Schemes, Allen Sanginés, Januay 1989 IDP-30 sDbt Reducon Schemes and the Management øf Chlean Debt, Fepe Larra in, March 1989 IDP-31 Managing BrazIs External Debt The Contributon of Debt Reductin Schemes*, D. Camelro and Rogero LF. W ~meck, IDP-32 'Leading Economic indicatr for Brazil: At Attempt at Forecastng Tuning Points, Antonio Estache, February 1989 IDP-33 -Rsa~eilng Growth with Equty, Worid Bank Poverty Aeviation Actiles In Latin America', George Psacharopoulos, April 1989 IDP-34 Brazil- Edernal D~bt Dveiopment and Prospects', Sina Vatnick, December 1988 IDP-40 'Cash D~bt Buy Backs and the Insurance Value ol Reserves, Sweder van Wijnbergen, June 1989 IDP-41 ~Growth, External D~bt and the Real Exchange Rate In Mexico, Sweder van Wijnbergen, May 1989 IDP-43 'The Macroeconomlcs of Social Security In B'azil: Flecal and Financial issues', D. Pullert and E. Y. Jfmenez, June 1989 IDP-49 wFeeding Latin America's Children*, Human Resouroes DMslon, Technical Department, October 1989 IDP-80 'Marginal Effe~e Tex Fates on Capal ncome In Argenina', Luca Baibone and Michael McKee, August 1989 IDP-SS *ABIbllogry on P~verty and hicome Distribuion In Lan Arnerca', Human Resoures Divlson, Technical Department, IDP-54 'Ecuador: Development Issues and Options for the Amazon Region', Cour~y Depuitment IV. December, 1989 IDP-55 *Fiscal Defcits, Infagon and Inter t Rates', Ru Coutnho, June 1989 IDP-56 -Regulang industrial PoBlon In Developing Countries: Some Possibe Frameworks*, Paul R. Portney, December 1989 IDP40 -Strategy for the Promodon øl Non-Tradi~onal Agricultural Exports', Martin F. Ralne, December 1989 IDP-61 'A Pøutfolio Model for Brazi', Rul Coutinho, June 1989 IDP-4 'Why Tax Incentives Do Not Promote investment In Bra~', A. Estache and V. Gaspar, February 1990 DP46 'Publc Sector 'Debt D Istres'*In Argenna's Recent Stablizaton Efforts, Paul Beckerman, July 1990 1DP-9 'Alocating Credit: How to Direct, Prie or Auction*, S. Rumachandran. June 1990 IDP-70 *LAC Economic and Sector Wort A Cdtical Revew øl Selected Issues', L Auemhelmer, June 1990 IDP-71 'Agricultural Trade In the Caubbean Community , John Nash, July 1990 IDP-72 'Poerty A~lviadon In Bra, 197087', M. Louise Fox, July 1990 IDP-73 'Fisca~ Deicits, Exchange Rate Cdsis and In~aon', $weder van Wjnbergen, Jmnuay 1990 IDP-78 'Measutng Pric Distortions from Commodty Taxation In BraD', k Estache and A. Femandes and I. Roy, July 1990 IDP-79 -Chid Care In Metropoltan Brazi', Debah Levison, August 1989 IDP-81 -Ecuador: Quiss Fiscal Dellcts, Wa~dng Through the Maze of Subeidies', Luca Barbone and Mario Vicens, August 15, 1990 IDP-82 'Social Secuty in Latin Amedc: Issues and Optlons for the Wodd Bank', Wiliam McGreevey, October 1990 OP-89 ~Braz: lasues in the Design øf Intehedual Property Rights', Antonio Estache, September 1990 IDP-90 Mas Cos, EM~ , and Quaity in Publi Hospitals: a Dominican Case', Maureen A Lewis, Margaret B. Sulvtta and GW~ m , Frgi, Auust1990 IDP-91 *Antitrust in a Developing Economy The Case of Venezuela', Lawrence J. White, August, 1990 IDP-92 Fting Nutrition Status In Adjusent Programs. Recent World Bank ActMes and Projects In Latin America', Marcelo Selk~. Fe~na, 1991 IDP-94 'Investment Portfo~o ø Social Insurance/Pension Funds in Latin Amedca and the Caribbean: Significance, Composition and Performance', Carmelo Mesa-Lago, December 1990 IDP-95 *Economic and Financial As~ of Social Secuty in Latin America and the Cadbbean: Tendencies, Problems and Aftematives for the year 2000*, Carmeo Mesa-Lago, May 1990 Dealuation .xectatione.and Interest Rates in Mexico the Role of Domestic Debt Management by Daniel F. Oka World Bank May 1991 bstract A key factor behind high real interest rates during the recent Mexicki stabilization plan was the initially low credibility about the fixed, and later on preannounced, exchange rate. While it is difficult to assess what establishes credibility, we can hypothetize which factors may hamper it. Crucial among them is the macroconsistency of the policy framework where fiscal policy plays a key role. Domestic debt management also mattered as the probability of a succesful run on the peso increased with the amount of government liabilities which could, in a given period, be exchanged for foreign reserves. For example, if the average maturity of domestic debt is low, as it was in Mexico at the beginning of the stabilization plan, this probability is high and, thus, also shows in high interest premia between peso-denominated and dollar-denominated debt. Another relevant area of debt management is debt indexation. Debt indexation may lower debt service by reducing inflation/exchange rate uncertainty premia demanded by investors and/or by reducing the ex-post cost of debt when there is a credibility gap, i.e, devaluation expetations systematically overpredict the preannounced devaluation. But there are costs associated both with lengthening the maturity of debt, as long term debt carries a liquidity premium, and with debt indexation, as it lowers the flexibility of debt management, thus, raising the Interest rate on indexed-debt. The paper concludes with an empirical evaluation of these tradeoffs and, hence, of the discrepancy between actual and optimal debt maturity and indexation in Mexico. I thank Sweder van Wijnbergen for his comments and encouragement to write this paper. I also thank Joaquin Cottani for discussions at earlier stages of preparation and Rebecca Brideau for research assistance. I am, of course, fully responsible for the contents of this paper. The views expressed are the writer's, not necessarily the World Bank's. 2 1. Introduction and SuT?ary* During the 1980s Mexico underwent a dramatic transformation from a heavily protected, interventionist and public sector-led growth economy into an open, liberal and private sector-led growth economy. This transformation was a response to changes in the world environment, particularly, the 1981-82 world recession and the external debt crisis, but also to domestic policies which were no longer regarded as viable and/or efficient. While fiscal adjustmeat started immediately after the debt crisis unfolded, trade and financial reforms took place mainly from 1985 onwards. Nevertheless, inflation remained high and the economy was still stagnant. Following the 1986 oil crisis, Mexico tightened its fiscal policy further, the non-oil prim::y fiscal surplus rose more than 5 percentage points of GDP in the following 2-3 years, and strongly devalued its currency. This prompted further inflation and a deeper recession. In late 1987 Mexico implemented a heterodox stabilization program aimed at reducing inflation and restoring economic growth. At the core of the stabilization strategy was an agreement (called "Pacto") between labor, government and business to freeze wages and the exchange rate, control prices, and tighten monetary and fiscal policy. The Pacto was renewed/extended (and renamed PECE) thereafter with several important changes: wages (with the exception of minimum wages) were liberalized, price controls were significantly flexibilized, and the exchange rate freeze was replaced by a preannounced rate of devaluation which came down from 1 peso a day in 1989 to 80 cents and then 40 cents a day in 1990. The program was on the whole a success: inflation was brought down to 20% by 1989, from 160% in 1987, while avoiding a recession. In fact, the economy recovered strongly after 1988 with output growing at rates of 3.1% and 3.9% in 1989 and 1990. Despite the rapid success in bringing down inflation, domestic real interest rates during the first two years of the Pacto were extremely high: on average in excess of 30%. High real interest rates threatened the stabilization program in two ways: i) by increasing the cost of servicing domestic debt; and ii) by hindering investment and, hence, the economic recovery. An important conclusion of this paper is that the deepening of fiscal adjustment and adequate public debt management were key factors in the eventual decline in real interest rates and, hence, the success of the stabilization program and subsequent recovery. High real interest rates could have led to explosive debt growth and, thus, to implicit debt repudiation through debt monetization. Behind high real interest rates was the initially low credibility about the government's ability to sustain the new program and, in particular, to maintain the fixed/preannounced exchange ra-*e. This lack of credibility led the public to systematically overestimate the exchange rate devaluation, i.e., Mexico in the late 1980's provided a fresh example of the "peso problem" (Krasker (1980)). In other countries undergoing similar stabilization strategies, e.g., Brazil and Argentina, but without the same ability to tighten fiscal policy and/or manage domestic debt, high real interest rates led to explosive domestic debt growth eventually destroying the credibility of the stabilization strategy (Beckerman (1991)). While it is difficult to assess what establishes credibility, we can hypothetize which factors erode it. Lack of credibility is crucial since it 3 could easily necessitate interest rates so high that, over time, a fiscal program that was sustainable initially becomes unsustainable as the debt burden grows. At a minimum, policy credibility requires consistency between inflation and exchange rate targets, interest rates and the fiscal stance. A deficit which cannot be financea abroad or with the inflation tax leads to a :igher debt stock. As the debt stock grows and the debt service gets burdensome the risk of monetization increases, thus turning inflation and exchange rate targets unrealistic. Thus, assessing the credibility of the Government's program entails, at the very least, determining whether inflation/exchange rate targets and debt service obligations are consistent with fiscal instruments. One important objective of this paper is, therefore, to explore the impact of fiscal policy on the interest premia carried by domestic public debt due to exchange rate devaluation expectations/uncertainty and government's solvency considerations. But the extreme volatility of real interest rates strongly suggests that fiscal consistency may not be enough. Credibility could clearly suffer if a program, sustainable at current expected values of real interest rates, inflation and the primary fiscal surplus, is vulnerable to the type of shocks that do in fact occur frequently. For example, in the case of Mexico an unexpected drop in oil prices could impair public finances immediately since oil revenue accounts for roughly the same amount of public revenue, and often more, as all taxes combined. As this reduces the macro-consistency prospects, overall policy credibility is hampered implying higher interest rates which compound the adverse impact of lower oil prices on public finances. Shocks could also be of a purely speculative nature, i.e., not based on objective risks such as terms of trade fluctuations. A loss in confidence could as well prompt higher interest rates. The subsequent impact on debt service could then turn what was initially an irrational fear into an objective problem as debt starts accummulating. Vulnerability to unexpected shocks, whether originating from private misperceptions or not, increases if the government has frequent and high funding requirements, i.e., if there is a large stock of domestic debt maturing in a short period. Vulnerability stems from the fact that the magnitude of a run on the peso derived from the shock is proportional to the level of government liabilities that mature in a given period. If these liabilities are large relative to the stock of foreign exchange reserves, the probability that the government will have to devalue in response to an attack on the peso is also large. And this, in turn, is reflected in high domestic interest rates and, in particular, in a high premium of peso denominated over dollar denominated domestic debt. One important conclusion reached in this paper is that Mexico's policy of extending the average maturity of internal debt has lowered Mexico's vulnerability to shocks, hence, contributing to lower interest rates. Giavazzi-Pagano (1989) have provided a theoretical justification for lengthening debt maturity as a means for ruling out equilibria witb positive probability of devaluation. Their framework, though, differs from ours in the sense that what prompts the collapse of the exchange rate regime is the growing debt service that results from having to refinance debt at high interest rates when a confidence crisis arises. On the other hand, lengthening the maturity of debt is not without costs. Long-term debt carries a liquidity premium over short-term debt. In Mexico, however, we 4 found that the gains derived from lengthening debt maturity exceeded the additional cost implied by the higher liquidity premium -f long-term debt. In fact, Mexico's average debt maturity was not far off from the estimated optimal debt maturity, derived from the tradeoff. Another element of domestic debt management influencing real interest rates in Mexico has been indexation. Indexation can reduce the cost of debt service when lack of policy credibility leads the pAblic to systematically overestimate inflation/devaluation and when there is high inflation/exchange rate uncertainty. Since indexed-debt service is linked to actual inflation/devaluation, its cost is not affected by high inflation/devaluation expectations (in excess of actual inClation/devaluation) and carries no inflation/devaluation uncertainty premia. The role of indexation has recently been examined by Calvo, who argues that indexation can be used to rule out "bad" equilibria that imply monetization or debt repudiation. In his framework, indexation reduces the likelihood of self-fulfilling inflationary expectations. For example, high inflation expectations lead to high nominal interest rates which, in turn, lead to explosive debt growth and, eventually, debt monetization, i.e., higher inflation. Calvo's argument applies well to Mexico where inflationary expectations were resiliently high (systematically above actual inflation) despite the success of price stabilization. However, debt indexation reduces the flexibility of debt management as it prevents the government from implicitly repudiating debt through higher inflation/ devaluation in response to shocks. The reduced flexibility implies a higher real interest rate on indexed debt, the higher premium capturing a higher risk of explicit debt repudiation, e.g., through an unscheduled tax or sheer repudiation. The Pacto experience in Mexico shows that the impact of indexation on real interest rates on indexed debt was in fact larger than interest savings derived from the credibility gap. The fact that the share of indexed debt averaged less than 5% over the period suggests that the government may have been aware of this. In Section 2 we describe fiscal policy and debt management in the context of the changing external environment during the 1980s. In Section 3 we assess the impact of fiscal policy and debt management on domestic interest rates. In Section 4 we assess factors behind devaluation expectations and in Section 5 we assess factors behind explicit debt repudiation risks. In Sections 6 and 7 we evaluate empirically the tradeoffs on which we base our measures of optimal debt maturity and optimal debt indexation. Technical and methodological issues are in Annexes 1 to 7. 2. External Shocks, Fiscal Adjustment and Debt Management in the 1980s. In the 1970s fast economic growth, abundant foreign finance, and low or negative domestic real interest rates moderated the impact of growing fiscal deficits on the domestic public debt-GDP ratio. The picture changed drastically in the 1980s as the drying up of foreign finance, lower oil prices and the ensuing output stagnation forced the government to rely more heavily on domestic sources of finance such as debt issue and inflation tax. This became necessary even though there was an unprecedented improvement in the primary fiscal balance which was turned around from an 8% of GDP deficit into an 8% surplus. S In this context, the increase in the domestic public debt-GDP ratio in 1983 and 1986-87 (Figure 1 and Annex 1) were a rational response to the impact of lower oil prices and the cut back of foreign credit ou public sector finances (Figure 2). Debt financing allowed the government to smooth out the necessary fiscal adjustment over time. Fiscal austerity was characterized by a drastic reduction in capital expenses, about 7 percentage points of GDP between 1981 and 1986, as well as a large increase in public sector prices which raised public firms sales by 6 rercentage points of GDP between 1981 and 1985. Fiscal adjustment deepened after 1986 (Figure 3): the primary fiscal surplus averaged a record 8% of GDP in 1988-90 and the operational fiscal deficit became a surplus in 1987 and in 1990. Important reforms in the tax system (reductions in marginal corporate tax rates, elimination of tax exemptions and indexation of tax bases) and tax administration (VAT collection, more audits and severe penalties to evaders) increased the tax-GDP ratio 30% between 1985-87 and 1990. And non-financial public expenditure was cut by a further 7 percentage points of GDP between 1986 and 1990. Fiscal tightening in 1988-1989 was also a planned response to the substantial decline in inflation revenue due to the succesful 1988 stabilization program. However, negative foreign finance and high domestic real interest rates led to a new increase in the domestic debt-GDP ratio in 1989. Negative net foreign finance stemmed partly from the implementation of the foreign debt agreement under the Brady Initiative which finally took effect in March 1990. The sharp rise in real interest rates (Figure 4) and, to a lesser extent, the higher debt stock and the larger share of more expensive bond (compared to bank) financing (Figure 1), implied that in 1989 servicing domestic debt was in real terms three times more burdensome than servicing foreign debt (even though foreign public debt was more than twice larger in size than domestic debt). While Mexico's consolidated domestic public debt is not large relative to GDP, on average 17% at its peak in 198V (excluding debt of development banks), the high level of real interest rates has turned it into the single largest and potentially more explosive component of public expenditure. In 1990 Mexico implemented a foreign debt agreement with commercial bank creditors involving the restructuring of US$48.9 billion of Mexico's external debt. The debt relief package has reduced the net transfer Mexico needs to make to its creditors by slightly less than 2% of GDP over the 1989-1994 period on average; half of this amount was due to the lengthening of maturity implied by the deal, and about 0.5% of GDP was due to interest savings (van Wijnbergen (1990)). Domestic debt service also benefitted from the 1989-90 foreign debt agreement: in July 1989, following its announcement, domestic interest rates dropped by more than 20 percentage points. They recovered partially afterwards, to decline again after the final implementation of the foreign debt deal in March 1990, to record low levels for the decade. Domestic and foreign interest savings led to an inflation-adjusted (operational) fiscal surplus of around 2% in 1990 and, as a consequence, domestic public debt started to drop. 3. Policy Credibility and Interest Rates. 6 At the core of the Pacto were a fixed exchange rate and, later on, a preannounced declining rate of slide of the peso against the dollar. The exchange rate provided a nominal anchor for prices and thus contributed to lower inflation. However, at least initially financial markets did not fully believe that the exchange rate rule, and for that matter the stabilization strategy itself, was sustainable. This lack of policy credibility was reflected in high devaluation expectations and exchange rate uncertainty, as the high differential between interest rates on peso-denominated public debt (Cates) and interest rates on dollar-indexed domestic debt (Pagates) plus the rate of preannounced devaluation (Figure 5) illustrates. Khor-Ro4as Suares (1990) showed that the Cetes-Pagafes interest differential was in fact explained by the forward premium on foreign exchange (the interest parity theorem) which, in turn, captures devaluation expectations (the Fisher Hypothesis). A survey of inflation and exchange rate devaluation expectations conducted by INEGI also illustrates the issue of poor policy credibility: according to this survey, since the Pacto began firms have systematically overpredicted inflation and the rate of devaluation (Figures 7 and 8). The initial lack of policy credibility was not only reflected in high devaluation/inflation expectations and or exchange rate/inflation uncertainty. Dollar-indexed domestic public debt (Pagafes) also carried a substantial premium over comparable foreign interest rates such as US Treasury Bills (Figure 6). This premium reflects explicit debt repudiation risks, e.g., repudiation through an unscheduled tax on debt rather than through devaluation/inflation. Explicit debt repudiation fears in Mexico are probably rooted in the 1982 forced conversion of dollar bank deposits at an artificially low exchange rate. However, both the Cetes-Pagafes and the Pagafes-US Treasury Bill interest differentials dropped sharply during the period, particularly, in 1990 (Figures 5 and 6). In the next two sections we assess the roles played by fiscal policy and debt.management in the evolution of these interest differentials. 4. Factors Behind Devaluation ExPectations/Exchange Rate Uncertainty. While it is clear that the Cetes-Pagafe interest differential measures devaluation expectations/exchange rate uncertainty it 1s difficult to know which factors underlie devaluation expectations/exchante rate uncertainty. Here we focus on debt management factors. More specifically, we hypothetize a positive impact on devaluation expectations/exchange rate uncertainty of the difference between public debt maturing in the month plus base money and foreign exchange reserves (other variables such as the primary fiscal surplus were explored but found not to carry explanatory power). The larger the stocks of base money and debt that matures in a given period, the less likely that a given stock of reserves will resist a speculative attack and, hence, the more likely that a devaluation will take place. In order to assess empirically this hypothesis we postulate a process to describe the formation of devaluation expectations. Devaluation expectations are assumed to follow a stochastic binary process where agents either expect 7 no devaluation (on top of the preannounced one) or a fixed devaluation. The size of the devaluation can either be treated as exogenous or as a function of other variables (we tried the degree of exchange rate appreciation but found it statistically insignificant)l here we assumed an exogenously given 30% devaluation. The probability of devaluation is assumed to depend on the difference between public debt maturing in the month plus base money and foreign exchange reserves. The Cetes-Pagafes interest differential can then be decomposed into the sum of devaluation expectations, the product of the endogenous probability of devaluation and the exogenously fixed size of the devaluation, and the exchange rate uncertainty premium, the product of the proxy for exchange rate uncertainty (the variance of devaluation expectations) and the risk-aversion coefficient. The model is fully described in Annexes 2 and 3. The resulting expression was estimated econometrically using non-linear least squares for the October 1988-December 1990 period. Although the Pacto was first announced in late 1987, the period prior to the July 1988 elections was characterized by political uncertainty and, in any case, the third phase of the Pacto, or PECE, was only announced a few months afterwards. The regression analysis includes a dummy for the foreign debt agreement which takes value one from July onwards, i.e., after the debt deal was first announceO. The econometric methodology and results are in Annex 4. The econometric analysis confirmed the hypothesis that an increase (reduction) in the difference between public debt maturing in the month plus base money and foreign exchange reserves raised (lowered) unscheduled devaluation expectations, as measured by the Cetes-Pagafes interest differential (adjusted by the preannounced rate of devaluation). The fact that debt maturity, the principal variable affecting the explanatory variable during the period, was lengthened significantly may, thus, have been the main factor behind the sharp decline of interest rates. Instead, there was no evidence, under the present model, of agents demanding a premium for exchange rate uncertainty (as measured by the variance of the postulated process for deva.uation expectations), i.e., agents were not risk-averse. The dummy for the foreign debt agreement had the expected sign but was only significant at an 80% level of confidence. Other explanatory variables of the probability of devaluation, e.g., the primary fiscal surplus, or of the size of the expected devaluation, e.g., the level of real exchange rate appreciation, were not found to be statistically significant. 5. Explicit Debt Repudiation Risks. The other important factor behind high real interest rates were fears of explicit debt repudiation, captured by the interest differential between dollar-indexed domestic debt (Pagafes) and US Treasury Bills. What lies behind explicit debt repudiation fears? Likelihood of debt repudiation depends on the ability as well as the willingness of the government to service its debt. A government's willingness to service debt stems from a variety of factors, e.g., economic and political factors that affect costs and benefits of default. However, these factors are difficult to assess and measure. It is easier instead to assess the ability to service public debt, i.e., the 8 solvency of the government. The latter can be assessed through a comparison of the net present value of primary (non-interest) fiscal surpluses and a given public debt stock. This is actually the criterium we employ here. Though future surpluses are unknown, a good proxy for our analysis (we need not know more than private investors do in any case), is the current primary surplus. To test this hypothesis we run a simple linear regression with the PLgafes-US Treasury Bill interest differential as dependent variable. The explanatory variables were the constant term, the primary fiscal surplus lagged up to two months, the degree of debt indexation (see Section 7 for a discussion on its inclusion) and the same dummy for the foreign debt deal as in Section 4. The actual regression and econometric results are reported in Annex 5. The results confirm that increases in the lagged real primary fiscal surplus have reduced fears of explicit debt repudiation. There is also evidence that debt indexation tended to increase the Pagafee-US Treasury Bill interest differential and that the foreign debt deal lowered the in,srest differential. We now turn back to debt management. A longer maturity of debt can reduce devaluation expectations but may also raise average interest rates due to the liquidity premium on long-term debt. Similarly, debt ind4 ation can reduce uncertainty premia but can also raise explicit debt repudi tion risks. These tradeoffs are examined next. 6. Lenothening the Maturity of Domestic _ebt. In recent years Mexico has lengthened the maturity of its domestic debt (Figure 9). The lengthening of debt maturity followed the introduction of medium-term floating rate bonds, called "Bondes", in mid-1988 (Figure 10) after which maturity followed an upward trend, only temporarily interrupted. More recently the upward trend was prompted by an improvement in private sector confidence reflected both in a sharp decline of the long-term liquidity premium and an investor's shift from 28 days Cetes to 90, 180 and 365 days Cetes. The 180 and 365 days Cetes were introduced in 1990 along with long- term inflation-indexed bonds, called Ajustabonos (introduced 4-n late 1989), with up to a S year maturity. 9 Table.2: Main Characteristice of Government Bonds IOUX AA81A Maturity Service 1. Ajusta- 15% real 3 to 5 years quarterly bonos CPI indexed sold at discount 2. Bondes Cetes 28 days 1 to 2 years quarterly sold at discount 3. Cetes sold at 28 days according discount to 365 days to term 4. Pagafes dollar rate 28 days monthly indexed to controlled dollar rate S. Tesobonos dollar rate, 30-90 days indexed to free dollar rate At first glance, the switch to longer maturities has been costly: the premium of Bondes, the most important (in size) medium/long-term bond, over Cetes, referred to as "sobretasa", was positive throughout the period; it has dropped, though, from about 2.7 percentage points in 1988 to less than 1 percentage point in 1990. Moreover, the increase in the share of Bondes has probably exerted a positive impact on the liquidity premium. And long-term debt usually also carries a higher uncertainty premium, particularly, when the government cannot credibly precommit to its anti-inflation stance. However, since most medium/long-term debt is at a floating short-term rate only the liquidity premium is rilevant in the case of Mexico. The Bondes interest rate is adjusted every 28 days with the short-term Cetes interest rate (so uncertainty derived from, say, inflation one year from now does not affect the premium). Lengthening debt maturity may still be beneficial, though. A longer debt maturity reduces the uncertainty surrounding frequent and high funding debt renewrls and, in particular, it may lower the probability that a speculative run against the peso would lead to a devaluation. The more debt that on average has to be renewed, i.e., the shorter the maturity, the less likely that the government will be able to resist foreign exchange demands from investors switching from debt to foreign assets without promptng a devaluation. In short, the net effect of lengthening debt maturity on debt service in 10 Mexico has three componentes i) the higher interest cost on swapped debt due to the long-term debt liquidity premium; ii) the increase in this premium derived from the increase in the share of long-term debt; and iii) the lower interest cost derived from lower devaluation expectations/uncertainty. A formal derivation of the impact of lengthening debt maturity on the average cost of domestic debt as well as an econometric evaluation is presented in Annex 6. The evidence presented in Annex 6 confirms the expected signs for these factors and shows that in net terms Mexico has benefitted, and could have further benefitted (at least in the margin), from lengthening debt maturity during the March 1988-October 1990 period. Despite the higher interest cost of Bondes and despite the adverse effect on the liquidity premium of a larger share of Bondes in total bonds (this effect, though, was not always statistically significant), raising the maturity further would have been beneficial due to the negative effect of a longer maturity on the Cates rate (and, hence, on the Bondes rate). However, between April 1989 and May 1990, and in October 1990 lengthening debt maturity actually increased the average cost of domestic debt. Although lengthening debt maturity in the margin was desirable we do not know to what extent (beyond the margin) it is desirable. The existence of a tradeoff implies there is an optimal (minimum cost) maturity structure. As maturity lengthens, the liquidity premium could grow faster than the Cetes rate drops and so a too-long maturity could become undesirable. Based on the procedure described in Annex 6, the optimal maturity would have been attaines if Bondes had represented, on average, 45% of domestic debt for the March 1988-October 1990 period (assuming that all relationships are linear). Actually this is close to the actual average of 43 percent. Thus, although on average debt maturity could have been lengthened, the government was not far off from what would have been optimal. It is also worth mentioning ti4at in two-thirds of the months, debt maturity moved in the right direction, i.e., lengthened when it was advisable to lengthen. 7. Indexatiop. In late 1986 Mexico introduced debt indexation. The share of indexed- debt in total debt held by the private sector and commercial banks grew steadily over the period averaging slightly less than 5% in 1988-90. The two main instruments employed by Mexico were dollar-indexed Pagafes (introduced in late 1986), which represented 4.4% of the total in December 1988 (their share later dropped), and inflation-indexed Ajustabonos (introduced in late 1989), which represented 8% of the total in late 1990. The government also issued dollar-indexed Tesobonos (linked to the free dollar exchange rate instead of the controlled rate used for Pagafes) but these bonds were never large in size. In situations where poor policy credibility leads to high (ex-post) real interest rates, (the situation in Mexico up until recently), the issue of indexed debt helps to lower the cost of debt servicing. Indexed-debt can lower the cost of debt service in at least three ways. First, indexed-debt 11 provides an insurance to investors, e.g., against an unexpected devaluation, thus, eliminating the exchange rate uncertainty premia that govezament pays on nominal debt. Second, when agents systematically overpredict inflation/ devaluation, as in Mexico, indexation reduces interest payments as the ex-post inflation component of indexed-dabt is lower than the ex-ante inflation component of nominal debt. Note that the systematic overprediction of inflation/devaluation is consistent with efficient markets (Krasker (1980)). Third, indexation can also reduce a government's incentive to inflate/devalue, as it can no longer reduce the real value of debt through inflation/devaluation. This implies lower devaluation expectations and/or uncertainty and, hence, lower interest rates on nominal debt. The recent Mexican experience provides support for at least some of these factors (see Section 3 for the second factor and Table 1 of Annex 6 for the third factor), thus, suggesting that more indexation would have allowed reduction in the ex- post cost of debt service. However, debt indexation also carries costs. In particular, it reduces the flexibility of debt management as it prevents the government from implicitly repudiating debt through higher inflation/devaluation in response to shocks. The reduced flexibility could lead to higher real interest rate on indexed-debt, the higher premium capturing a higher risk of explicit debt repudiation, e.g., through an unscheduled tax or sheer debt repudiation. For a given solvency situation, if indexation reduces prospects for implicit debt repudiation (through inflation/devaluation) it should simultaneously raise the risk of explicit debt repudiation. Casual evidence of the possible impact of indexation on the interest rate of indexed-debt is provided by the 1988 fourfold increase in the Pagafe-US Treasury Bill interest differential following the fourfold increase in the share of Pagafes in total debt. The econometric evidence is even more conclusive. Indexation exerted a statistically significant positive impact on both the Pagafe-US Treasury Bill interest differential (Table 1 of Annex 5) and on the real Pagafes interest rate (Table 1 of Annex 7). In short, indexation may either lower or increase the average cost of debt. The following factors have to be quantified to evaluate whether, and to what extent, indexation may be beneficial: i) the devaluation uncertainty premium implicit in nominal debt; ii) the discrepancy between expected and actual devaluation; iii) the favorable impact of indexation on the exchange rate uncertainty premium implicit in nominal debt; and iv) the impact of indexation on the explicit debt repudiation risk premium. A first approach to marginal gains from indexation only takes into account the first two factors i) and ii) above. The sum of these factors is, by definition, equal to the Cetes-Pagafes interest differential less the preannounced (actual) devaluation rate. If this difference is positive, as it was during most of the 1988-90 period (Figure 5), it follows that a shift to more indexed-debt would have been desirable: it was on average 27 percentage points in the period March 1988 to July 1989, declining thereafter to around 5 percentage points in the second half of 1990. A more complete evaluation of the marginal impact of an increase in the level of indexation requires also considering factors iii) and iv). From our analysis in Section 4 it becomes apparent that assessing iii) is not feasible since we were not able to 12 identify a statistically significant exchange rate uncertainty premium. This, though# may mean precisely that iii) is not relevant in any case. Instead, as mentioned in the previous paragraph, factor iv) was relevant. And as our quantitative analysis in Annex 7 shows, it more than offset the beneficial effects of indexation implied by i) and ii). To sum up, in the margin further indexation would have raised the average cost of debt throughout the 1988-90 period. However, while this approach suffices to decide if in the margin more/less indexation was desirable, it does not answer the question of how much more/les indexation was desirable, i.e., it does not suffice to determine the optimal level of indexation. For large changes in the level of indexation we need an expression for the Cetes and Pagafes interest rates as a function of the level of indexation. As we show in Annex 7, these expressions are derived from the regressions used to estimate factors ii) and iv) above. The optimal level of indexation is then the one that minimizes the average interest cost of debt which is, in turn, based on those expressions. According to these estimates the optimal share of debt indexation should have been zero. This may explain why despite the large credibility gap, as measured by the Cetes-Pagafes interest differential adjusted by the preannounced devaluation rate, average indexation did not exceed 5% during the period. The optimal indexation calculation procedure has several drawbacks: i) we imputed the Pagafes interest rate to the entire stock of indexed debt while the share of Ajustabonos was actually much larger towards the end of 1990; ii) we assumed that all functional relationships were linear; and iii) the degree of indexation is partly endogenous. The last two drawbacks also apply to our estimate of optimal debt maturity. Further research is required at the very least to tackle these issues. 13 Bank of Mexico "Indicadores Economicos" various numbers. Beckerman, Paul "Public Sector 'Debt Distress' in Argentina's Recent Stabilization Efforts". World Bank mimeo, May 1991. Calvo, Guillermo "Controlling Inflation: The Problem of Non-Indexed Debt", in S. Edwards and F. Larrain, eds., "Debt Adjustment and Recovery: Latin America's Prospects for Growth and Development', New York, Basil Blackwell. Giavazi, Prancesco and Marco Pagano "Confidence Crises and Public Debt Management", NBER Working Paper # 2926, April 1989. INEGI (National Institute of Statistics# Mexico), "Avances de Informacion Economica: Informe de Expectativas Empresariales" various numbers. Khor, HoL and Liliana Rojas-Suarez "Risk and Interest Rates in Mexico", mimeo IMP, September 1990. Krasker, William S. "The Peso Problem in Testing the Efficiency of Forward Exchange Markets". Journal of*Monetary Economics 6 (April 1980). Mood, Alexander M. and Franklin A. Graybill "Introduction to the Theory of Statistics". McGraw Hill. 1963. Wijnbergen, Sweder van "Mexico and the Brady Plan", Economic Policy, Volume 11, 1991. 14 AMX 1. Consolidated Domestic Public Debt, Operatonal Fiscal peficits. and Finance SourcestMethodoloa -of Calculation 1. The Domestic Public Debt Measure Domestic public sector interest bearing debt is defined as the consolidated debt of the non-financial public sector (NFPS), which includes the federal government and parastatals, and the Bank of Mexico (SM). Consolidated debt is derived as the sum of: i) net credit (credit in domestic and foreign currency less monetary and non-monetary obligations) to NFPS by commercial banks and development banks; ii) bonds issued by the NFPS held by the domestic private sector and financial intermediaries excluding BM; iii) net liabilities of BM with the domestic private sector and other banks. The data sources are: "Indicadores Economicos" (1E, published by SM) for ii), and the SIE-BANXICO database (also of SM) for i) and iii). The codes and/or names of the specific items entering the calculation and the calculation procedure is available in LOTUS (the file name is METHODOL.WK1). The debt-GDP ratio reported in Figure 1 is based on an annual average of end of period monthly debt observations and annual GDP. 2. The Consolidated Deficit Discrepancies between our public deficit measure and BM's are due to differences in coverage and the inflation correction. Differences in coverage are: i) we exclude gross domestic lending by development banks (which Bank of Mexico includes in the financial deficit) from our deficit measure; and ii) we exclude public asset sales as a revenue source in the deficit measure (since this is a finance source below the line). The difference in the inflation correction is that, unlike the BM, we subtract the inflation erosion of foreign debt from the operational measure of the deficit. 3. Public Sector Borrowing Requirement (PSBR): Finance Sources The finance mix of the PSBR shown in Figure 3 is based on BM annual reports. PSBR corresponds to the official nomina'l financial deficit concept, which consolidates the NFPS deficit with development bank's gross lending (called "financial intermediation"), but differs from it in that it is derived from sources of funds data rather than from income-expenditure data. 4. The Real Debt Service In order to estimate the consolidated operational (real) deficit we first substitute nominal interest payments by real interest payments. By definition the real interest rate is: (1) r - (1+i)/(1+w) - 1 where: r,i are the real and nominal interest rates W is the inflation rate 15 Given w and the nominal interest service B*i the real interest service B*r can be expressedt (2) B*r -*j - (w/1+w)*B*(1+1) We refer to the sebond term of the right hand side as the monetary correction. The inflation correction of the real interest service r*B*r is excluded in the BM measure. Note that since both r and w were large in Mexico this term is significant. The same procedure can be applied to estimate the real foreign debt service. The national CPI was used to measure domestic inflation and the United States producer price index was the proxy for foreign inflation. Inflation is measured December to December. Since the nominal interest service available measures interest along the year we employed average debt stocks to calculate the monetary correction of domestic and foreign debt and average exchange rates were used to convert the stock of foreign debt into domestic currency. Data is available upon request. 5. The Consolidated Nominal and Q2erational Deficit: Finance Sources The consolidated nominal deficit (CND) and its finance sources can be expressed in simplified form as: (3) -PrS + B*i + e*P*i* w 6C + 63 + e*6F where: PrS is the primary (non-financial) fiscal surplus e is the average exchange rate F is the stock of foreign consolidated public debt a is the stock of domestic consolidated public debt i* is the foreign nominal interest rate C non-interest bearing base money 6 indicates the incremental operator, e.g., 6B = B.1 - B Debt stocks B and F are beginning of period stocks. End of period stocks are indicated with a +1 subscript. The consolidated operational deficit (COD) is obtaind subtracting the monetary correction of domestic and foreign debt from B*i and e*F*i' respectively: (4) -PrS + (B*i - ( 1+w)*B*(1+i)] + [e*F*i* - ( = -PrS + B*r + e*F*r* a 00D = ) 6 6C + (68 - (w/1+w)*B*(1+i)3 + [e*67 - e*(l'/1+w')*F*(1+i')) where: a* is the foreign rate of inflation r* is the foreign real interest rate 16 ANNEX 2. Risk gremia BreakdokM Arbitrage between peso- and dollar-denominated domestic debt (respectively Cates and Pagafes) implies: (1) (1 + R,) - (1 + Rv)* (I + a)(2 + a*a) where: &., is the rate of return of asset c (Cetes) and p (Pagafes) a is a measure of exchange rate uncertainty a is the coefficient of risk aversion *1 is the expected rate of devaluation Similarly, arbitrage between domestic dollar-denominated debt (Pagafes) and the assumed riskless US Treasury Bill implies: (2) (1 + %,) -(1 + Rn) *a + z) *(l + p*r) where: P. is the rate of return on "safe" US Treasury Bills Z is the expected rate of Pagafe repudiation r is a measure of debt repudiation uncertainty Sis the coefficient of risk aversion 17 ANEX 3. A Model of the Devaluation Exeetations/UncertaintX We assume that an unscheduled (not preannounced) exchange rate devaluation xt has the binary distribution: (1) xt xt (constant) with probability pt t = 1...T = 0 with probability (1 - pt) Thus, the expected value of xt is: (2) E(x) = xt*p And its variance (Mood Graybill (1963)) ist (3) o(x) m E(xt) - [E(xt)] ) = x 2*pt - x *Ptl The total expected devaluation has a certain component, the preannounced devaluation rate x., and an uncertain component, xt: (4) e - (1 + xt)*(l + E(x,)) - 1 Thus, based on equations (3) and (4) and equation (1) of Annex 2, and taking the variance of xt as the proxy for exchange rate uncertainty, the Cetes-Pagafes interest differential adjusted for the preannounced rate of devaluation is: (5) (1 + R.)/(l + %)*(1 + xt") - (1 + E(x,))*(1 + a*Y(x)) = (1 + xt*pt)*(l + a*(x2aPt _ C 2*p 2)) We may focus on the particular case in which the probability of a devaluation of size x., pt, is described by the following linear process: (6) Pt - PI + J2*Yt + P3*Zt where: pl, p. and p3 are constant coefficients y, z are explanatory variables, e.g., domestic debt The size of the devaluation xt can be either considered exogenous or endogenous, e.g., on a measure of real exchange rate appreciation: (7) xt = TI + r2*et where: Tip T, are constant coefficients e is an explanatory variable Substituting (6) and (7) in (5): (8) (1 + Re)/(1 + PV)*(1 + xt) U (1 + (I + Tl*et)*(I, + p2*y + p*Zt)]* .. � s � д �F ~ -1 + �► Q fD '� е .-. v ^ ' � �" � Р+� � � 1.в '¢' р й Ф �tвt r. "r и м � ... � � .- � + и z г� и V � и � У n '+' � У 1Е � R v � 19 AMEX 4. Devaluation 3MCtAti0n91MDCftX&aint11 120MR&K c-Est t -2 Equation (8) of Annex 3 was estimated econometrically employing non-linear least squares (NLS). All regressions were run for the period October 1988- December 1990. The dependent variab.e Is based on annualized rates for Cetes and Pagafes of 28 days. Interest rates for month t are measured at the end of month (t-1) and the preannounced devaluation for month t is equal to the actual devaluation of the controlled exchange rate between the beginning and the and of month t. The initial set of explanatory variables (discussed in Section 4) is% the difference between public debt maturing in the month plus base money and foreign exchange reserves (variable z in Annex 3); the primary fiscal surplus (variable y); and the degree -)f real peso appreciation compared to the average 1987 level (variable e). Variables z and y are real, deflated by the CPI, and variable a measures the difference between the real exchange rate of the peso against the US dollar in the period and the real exchange rate in 1987 as a percentage of the real exchange rate in 1981. A dummy was included in all regressions to account for the foreign debt agreement announced in July 1989; the dummy takes value 0 up to June 2989 and value 1 thereafter. When serial autocorrelation was detected the dependent variable was included lagged one period as a regressor. The expected signs for the coefficients are: (1) a > 0 1 P2 < 0 1 P3 > 0 1 T2 > 0 The primary fiscal surplus and real exchange rate appreciation were not found to be statistically significant factors of, respectively, the probability of a devaluation and the size of the expected devaluation. The regression was, thus, reestimated excluding these variables assuming that the size of the expected devaluation was a fixed 30% and the probability of devaluation depended only an variable z. In the resulting regression the coefficient a was statistically insignificant (it was also insignificantly different from zero in the previous regressions). So we re-ran the regression eliminating a, I.e.$ making it equal to zero. We finally re-ran the regression without p, since it was also found to be insignificantly different from zero. After sequentially eliminating all statistically insignificant coefficients, as described above, we were left with the following regression reported in Table 1: (2) [(1 + R.)/(l + Pv)*(l + x?) - 1] = 0.3*(P2*Zt) + CI*Dl + c,* 1 (1 + Rj / (I + PV_j) * (1 + x,-?) - 1 20 Table 1 NLS. October 1988-Dgcember 1990 Regression (2). Linear. Coefficient Standard Error p2 0.226 0.0752 2.998 c, -0.017 0.0174 -0.974 Ca 0.308 0.1993 1.546 R-squared 0.272 Durbin-Watson Stat. 1.686 Log likelihood 46.728 F-statistic 4.481 It follows that only variable z was a significant factor with the expected sign of the Cetes-Pagafes interest differential (adjusted for the preannounced devaluation). There is no evidence, under the present model, of agents demanding a premium for exchange rate uncertainty, i.e., agents are not risk-averse. The dummy for the foreign debt agreement has the expected sign but is only significant at an 80% level of confidence. 21 ANNEX S. Vxlicit Debt Repudiation. Econometrig.Results In order to assess the impact of fiscal policy on explicit debt repudiation expectations, we hypothetize that debt repudiation expectations is a linnar function of lagged primary fiscal surpluses and of the degree of indexation (see Section 5 for a discussion)s (1) z - 01 + 02*y + 43*1 where: Z and y are defined*as in Annexes 2 and 3 *1, 61 and 03 are constant terms I is the degree of idexation (defined in Annex 7) We then substitute (1) in equation (1) of Annex 2 to obtain an expression for the Pagafe-US Treasury Bill interest differential% (2) (1 + Pv)/(1 + R) - I * e + 02*y + ,*I Equation (2) is estimated using OLS. Up to 3 lags for variable y were Initially considered. As in Annex 4 a dummy for the foreign debt agreement is included in the regression and, since we detected first order serial autocorrelation, we also included the dependent variable lagged one period as a regressor. Since the Pagafe-US T.Bill differential is not directly affected by exchange rate policy, to the extent that both are dollar denominated assets, the period of analysis is March 1987-December 1990; Pagafes were first issued in late 1986. Results for the resulting regression, equation (3) below, are reported in Table 1. (3) (1 + )v)/(l + R,) - 1 = 01 + e2.1*yl + 02.2*y., + 03*I + cj*(1+ (I 4R-)/(l + Rn-j) - 1) + c2*D1 Table 1 OLS. March 1987-December 1990. Regression (3). Linear. gefficient Standard Error T-Statistic *1 0.108 0.036 2.976 '62. -4.464E-05 2.213E-05 -2.018 e1-. -4.114E-05 2.220E-05 -1.853 6, 0.857 0.433 1.979 cl 0.608 0.101 6.019 c2 -0.053 0.020 -2.422 R-squared 0.716 Durbin-Watson Stat. 1.821 Log likelihood 68.687 F-statistic 19.669 All variables were statistically significant and their coefficients carried the expected sign, i.e., higher indexation and lower primary fiscal surpluses raised debt repudiation fears. 22 ANNEX 6. A Model to Evaluate Debt Maturitys Econometric gesults We first consider a model to assess the marginal impact on public debt service of an exchange of medium term debt (Bondes) for short term debt (Cetes), i.e. a lengtheniAg of the maturity of debt. For simplicity we only consider two interest rates, on Cetes and on Bondes; these bonds accounted for roughly 90% of all public bonds during the period. The average cost of debt service is therefore equal tot (1) DS/B - (Bb/B)*ib + (B*/B)*ia - T*ib + (1 - T)*La (2) T - Sb/ (Bb + We) - b/ where: DS approximates total domestic debt service 8 is the total stock of bonds Bb is the stock of Bondes and Ajustabonos (long-term bonds) B is the stock of Cetes, Pagafes and Tesobonos (short-term bonds) iL. io are the nominal interest rates of Bondes (long-term) and Cetes (short-term) T is the share of long-term debt, i.e., our measure of debt maturity Differentiating (1) with respect to T: (3) d(DS/B)/dT - (ib - L,) + T*(dib/dT - di,/dT) From the discussion in Annex 2 the Cetes-Pagafes interest differential depends on devaluation expectations and, assuming no exchange rate uncertainty premium (e.g., a equal 0), 1, can be expressed: (4) i4 - iv + e" + 1,*,u where: i, is the Pagafe (dollar-indexed) interest rate times one plus the preannounced (actual) rate of devaluation e is the expected rate of an unscheduled devaluation In turn, the Bondes interest rate differs from the Cetes rate by the long- term liquidity premium: (5) i is + a + **4 where: a is the liquidity premium For reasons discussed in Sections 6 and 7 s and c are influenced by debt maturity and e is also influenced by the degree of indexation (see Annex 7 for its measurement) in the following way: (6) s is(T) ST > 0 (7) eu e"(T,I) CUT < 0, ell < 0 23 wheres the subindex indicates partial derivatives I is the degree of indexation (Annex 7) Substituting (4) to (7) in (3) we get: (8) d(DS/B)/dT - (i4 - i,) + T*(Es*(1 + i) + eu*(l + iv)*s) In order to compute (8) we need estimates for s and u,. To estimate these parameters we run simple regressions using OLS. As before we introduced a constant term, a dummy for the foreign debt agreement and the lagged dependent variable entered as a regressor to eliminate serial autocorrelation (if present). We approximate the expected unscheduled devaluation a by the Cates- Pagafe interest differential (the preannounced devaluation component of the expected devaluation was made part of i, in the actual regression), i.e., consistent with Annex 5, we assume no exchange rate uncertainty premium. The resulting regressions, (9) and (10) below, are reported in Table 1. Regressiona were run for the March 1988-October 1990 period since long-term bonds (Bondes) started to be Issued in early 1988. (9) sa c + cj*s. + c2*D1 + eT*T (10) u" ce + cj*e".z + cj*D1 + aAT*T + e*A** Table 1 a) OLS. March 1988-October 1990. Regression (9). Linear. Coefficient Standard Error T-Statistic *T 0.329 0.925 0.355 eg 1.241 0.468 2.652 c 0.409 0.139 2.937 C2 -1.140 0.388 -2.941 R-squared 0.748 Durbin-Watson Stat. 1.730 Log likelihood -25.442 F-statistic 27.675 a') OLS. 1988.03-1990.10. Regression (9) excluding co. Linear. Coefficient Standard.Rrar T-Statistic BT 1.872 0.791 2.365 c, 0.693 0.098 7.097 C2 -0.962 0.420 -2.293 R-squared 0.684 Durbin-Watson Stat. 1.896 Log likelihood -29.028 F-statistic 31.451 24 (Continues Table 1) b) OLS. 1988.03-1990-10. Regression (10). Linear. Coefficient Standard Error T-StatIstic e -0.529 0.561 -0.942 aT -0.201 0.111 -1.803 Co 0.203 0.058 3.496 ca 0.262 0.044 5.953 c2 0.004 0.033 0.132 R-squared 0.820 Durbin-Watson Stat. 1.677 Log likelihood 51.150 F-statistic 30.692 b') OLS. 1988.03-1990-10. Regression (10) excluding D1. Linear. Coefficient Standatd Error TStatistic Gul -0.503 0.516 -0.973 e" -0.189 0.066 -2.856 co 0.198 0.046 4.258 ca 0.264 0.040 6.532 R-squared 0.820 Durbin-Watson Stat. 1.662 Log likelihood 51.139 F-statistic 42.405 The signs of the parameters were the expected ones. However, as Table 1 a) and a,) show, the coefficient of eT is not significantly different from zero when we include the constant term. The fact that it is signficant when the constant term is excluded suggests that it may simply be catching up on a trend factor. Substitution of the estimates of sT and IT in (8) and computation of (8) (based on the regressions of Table 1 a) and b)) indicates that lengthening debt maturity has on average for the period reduced, in the margin, the average cost of debt service. However, between April 1989 and May 1990, and in October 1990 shortening debt maturity would have reduced the average debt service in the rargin. The optimal debt maturity T, i.e., the one that minimizes (1), is obtained from the first order condition for minimization, i.e., obtained by equating (8) to zero: (11) T' - - (i - '.)/[ST*(1 + i) + CUT*(l + iv)*B] The average optimal debt maturity (T') for 1988.03-1990.10 was 0.45, whereas the actual average debt maturity was 0.42. It is also worth 25 mentioning that two-thirds of the time debt maturity moved in the right direction, e.g., lengthened when it was advisable to lengthen. Note, that we have assumed that debt maturity was policy determined. It is in fact at least in part endogenously determined: for a given interest rate structure the average maturity reflects private agent's preferences as much as the government's. The fact that maturity was not totally exogenous, though, could create an endogeneity problem in the regressions run. 26 ANNEX 7. A Model to Ealuate Indexation. Econometric Results We first propose a model to assess the marginal impact on debt service of an exchange of indexed-debt (Pagafes or Ajustabonos) for nonindexed-debt (Cetes or Bondes), i.e., an increase in indexation. The ex-post nominal interest service is: (1) DS - B'*(ij + an + i1*ff) + Bat* where: DS is the ex-post nominal interest service B, Ba are the stocks of indexed- and nonindexed-debt respectiv ely ij, L are the real and nominal interest rates on indexed- and nonindexed-debt respectively sO is the actual rate of devaluation Defining I as the share of indexed debts (2) I - Bt/(B1 + BR) We can rewrite the average cost of debt service DS/Bt (1') DS/B - I*(it + * + ij*ea) + (1 - 1aIn where: B is the total stock of bonds, i.e., the sum of B, and B, We approximate i with the Pagafes (dollar-indexed) interest rate and i, with the Cetes nominal interest rate. From Annex 2, and using the same notation as there, we can express i, as: (3) i, = i + a + a*o + il*e + a*o*ii + a*o*e + iia*a*a If for simplicity we assume no risk aversion, i.e., a equal to zero, which is consistent with the results reported in Annex 5, and we decompose the expected devaluation e into the preannounced (actual) component ea and the unscheduled devaluation component e, (3) can be rewritten: (3') i, ij + s* + ii*a + e*(l + i + * + ij*e6) Based on the discussiorn in Section 7, we hypothetise that i,, cu and a depend on I in the following way: (4) 11 - ii(I) if > 0 (5) eu c "(T,I) EUT < 0, e"x < 0 as in Annex 6 (6) a - o(I) o' < 0 The signs for the partial derivatives in (4) and (5) are consistent with the estimates for i' and for cu. (reported in Table 1 b) of Annex 6). The regression for estimating i', the coefficient c4 in (7), is reported in Table 1: 27 (7) a a + c*Py- + cI*D1 + c3*y + C4*1 where: c it Of..4 are constant coefficients Is %, y and D1 are defined in Annexes 4 to 6. Table 1 OLS. March 1988-November 1990. Regression (7). Linear. Coefficient Standard_IrX2r T-Statistic co 0.115 0.031 3.749 cl 0.492 0.077 6.383 C, -0.073 0.015 -4.778 c3 -1.787E-05 1.465E-05 -1.219 c4 0.965 0.276 3.497 R-squared 0.881 Durbin-Watson Stat. 1.106 Log likelihood 70.813 F-statistic 51.851 We can now assess the impact on the cost of debt service of an increase in indexation. From (1') and (30)-(4): (8) d(DS/B)/dI - d[i1 + c"*(l + ii) + (1 - I)*,u*(1 + ii + ea*(1 + ii))]/dI - i'*(l + 4a)*(1 + (1 - I)*CU] - 64*(1 + i, + ea*(1 + i,)) + C"s*(1 - I)*(1 + i, + **(1 + il)) The first term in (8) is positive (at least as long as eu is not negative) and reflects the adverse impact on explicit debt repudiation expectations of an increase in indexation; the second term is negative when there is lack of policy credibility (cu > 0) and captures interest savings derived from the fact that indexed debt is adjusted with actual rather than (higher) actual devaluation; the third term is also negative and reflects the additional interest savings, on non-indexed debt,due to the negative impact of indexation on unscheduled devaluation expectations. The evaluation of (8) indicates that in the margin indexation would have increased the average cost of debt service. It must be mentioned, though, that e4. was only significant at an 80% level of confidence. To determine optimal indexation I', i.e., the level of I that minimizes (1'), we equate (8) to zero, that is, the first order condition for minimization of (1'). This implies: 28 (9) 1** (1**( + c*)*(1 + 6*) + (1 + i, + 6**(1 + L))*(-6A + e2/ (ss* (1 + iS + ga*(1 + i)) + eU*i'*(1 + sa)) According to our estimates optimal indexation was zero (1* was negative throughout the period). 29 Figure 1. Consolidated Public Debt. (annual average debt as % of GDP) 18 16 I 10 6 2 014 1982 1983 1984 1985 1986 1987 1988 1989 1990 Years Bank Finance B Bonds 30 Figure 2. Consolidated Public Deficits. (as % of GDP) 10- 0 -10 -15 198219831984198519861987198819891990 Years Primary Surplus Operational Deficit Nominal Deficit 31 Figure 3. Public Sector Borrowing Requirement (as % of GDP) 18 16-- 14--- . -- ---- a12 - ---- 12 0 4 . I 0 -2 1980198119821983198419851986198719881989 Years Foreign Finance M Money Finance MDomestic Debt M..). PSSR 32 Figure 4. Real Interest Rates on Public 140 Bonds. (annual percent) 120 100- 80- C < 20 - - - -*.- - 0. -20. -40 June 1987 June 1988 June 1989 June 1990 Years .- Pagafes (dollar) +- Real Cetes 28 days 33 Figure 5. Devaluation Expectations. Cetes-Pagafes-Preannounced Devaluation. 140 120- 100 Unscheduled Devaluation Expectations 0plus Exchange Rate Uncertainty 00. Premium 20- June 19889 June 1990 Years 34 Figure 6. Domestic and Foreign Dollar Interest Rates (annual %) 40 ~30 c 20 10 June 1987 June 1988 June 1989 June 1990 Years -m- Pagofes -+- US Treasury Bill 35 Figure 7. Inflation and Inflation 250 Expectations (annual percentage) 200 Based on INEGI Survey a 150 *100 50- 87.1 87.3 88.1 88.3 89.1 89.3 90.1 quarters -n- Inflation (CPI) '+- Expected Inflation 36 Figure 8. Actual and Expected Exchan( 300' Rate Devaluation (annual ercenta ge) 200 Based on INEGI Survey C 100 50- 0* 87.1 87.3 88.1 88.3 89.1 89.3 90.1 90.3 quarters * Devaluation Rate + Expctd. Devaluation 37 Figure 9. Average Bond Maturity. (days) 250 200 150 0 5O - - - --- - - - June 1988 June 1989 June 1990 -* Bnd Maturity 38 Figure 10. Public Bond Structure. (thous. mill. pesos of 1987) 35 30 25- 20- 15-- 10 5 0 June 1987 June 1988 June 1989 June 1990 YEARS Cetes Bondes P3gafes+Ajusto [=Q "Other"