Chapter

IV Dynamics of Interest Rate Movements: An Empirical Study

Author(s):
Thomas Helbling, and Sena Eken
Published Date:
June 1999
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Author(s)
Taline Urné chlian, Sena Eken and Thomas Helbling 

Taline Urnéchlian with Sena Eken and Thomas Helbling

Interest rate differentials between short-term assets denominated in Lebanese pounds and comparable U.S. dollar assets have been large and positive since the 1980s. During that time, the large differentials reflected the war-related macroeconomic instability. However, they have continued to be large even after the end of 1992, when the authorities moved decisively to overcome the inflationary expectations, which had continued to prevail in the immediate postwar period, by adopting an exchange rate-based nominal anchor policy, which has been maintained since.

Positive interest rate differentials in the context of an exchange rate peg are a familiar phenomenon, reflecting inter alia the risks associated with future changes in the peg or in the exchange rate regime. They tend to be persistent. In the European Monetary System, for example, the convergence to German interest rates was gradual and occurred only together with a general convergence in macroeconomic policies. From this perspective, the persistent positive interest differential in Lebanon reflects its status as a postwar economy, overcoming a legacy of significant macroeconomic instability during the war. The phenomenon to explain is not the existence of an interest rate differential that is positive on average, but rather the speed with which it will decline, given the recent progress toward macroeconomic stability. The issue is of interest to the Lebanese authorities because the high Lebanese pound interest rates have led to a substantial burden on the budget and monetary policy.

Analytical Framework

The analytical framework of this section is based on a linear factor model designed to explain the systematic excess return on Lebanese pound treasury bills compared with U.S. dollar papers. The excess returns reflect systematic deviations from the uncovered interest parity condition, a standard benchmark in international finance.

Uncovered Interest Parity

According to the uncovered interest parity hypothesis, the nominal return differential between two assets that are identical in all respects except for the currency of denomination is equal to the expected exchange rate change over the holding period in asset-market equilibrium. In a small open economy that faces a given level of world interest rates, capital mobility should ensure the equalization of expected net yields so that the domestic interest rate, less the expected rate of depreciation, would equal the world rate. More formally, let St, be the logarithm of the spot exchange rate at time t, defined as the domestic currency price of one U.S. dollar; let E(St+n/t) be the expected value of the logarithm of the exchange rate n periods ahead, conditional on information available at time t, and let it and it* be the period t nominal interest rates on domestic and foreign assets with n periods remaining to maturity, respectively. Then, the uncovered interest parity (UIP) hypothesis can be written as:

It should be noted that E(St+n/t) is not an observable variable. To test equation (1) empirically, assumptions about the process through which financial market participants formulate expectations have to be made. Recent research has focused on the assumption of rational expectations. More specifically, the following two assumptions have to be made to obtain an empirical model with rational expectations. First, the realized spot exchange rate is equal to its expected value plus a forecast error with zero mean:

Second, the foreign exchange market is weakly efficient, in the sense that market expectations of the future spot rate are always conditional on an information set that includes past forecast errors of the exchange rate. This second assumption, taken in conjunction with the first, also implies that the stochastic process (∈t) is a white noise process, that is, the forecast errors are mutually uncorrelated at all lags:

Over the last two decades, numerous authors using a variety of data, sources, and estimation techniques have decisively rejected the uncovered interest rate parity condition, under the rational expectations hypothesis (e.g., Cumby and Obstfeld (1980, 1984) or Lewis (1994)). In particular, it has been shown that the forecast errors ∈t+n are serially correlated and, sometimes, not even stationary, thereby violating one of the basic principles of the rational expectations hypothesis.

Excess Returns

In view of the empirical evidence, ∈t+n should not be assumed to be a white noise forecast error. More appropriately, it should be considered to represent a systematic excess return, which is defined as:

The most compelling explanation for a systematic excess return is the presence of a risk premium between assets denominated in different currencies. To provide content to this argument requires a theory of the determinants of risk. Despite the theoretical advances in modeling risk (e.g., Cox, and Ingersoll, 1985), the determinants of risk are still not well understood, and recent empirical research has not yet offered consistent results.1

The excess return compensates investors for the risk in cross-border asset holdings. Two specific not necessarily uncorrelated risk factors can be distinguished. First, the country risk factor encompasses factors such as political risks that can hamper the cross-border transfers of both returns and principals. Second, the macroeconomic risk includes factors that cause future exchange rate changes. The nature of the macroeconomic risk premium depends on the exchange rate regime. Under a floating exchange rate regime, exchange rate changes occur frequently and tend to have a time-varying distribution; it is not surprising that many authors have found a time-varying distribution for excess returns defined according to equation (4).2 Under any regime of pegged exchange rates, the issue of the expected exchange rate changes becomes more delicate, because the peg might either be abolished or be changed in the future. This possibility raises the issue of the “peso problem.” 3

The peso problem reflects expectations of regime changes in an unstable environment. In many circumstances, countries pursue macroeconomic policies that are inconsistent with the exchange rate peg in the long run. Investors, therefore, expect the peg to be abandoned or changed in the future, but might be uncertain about the timing of these events. They base their expectations on a subjective probability distribution that differs from the empirical distribution that can be deduced from past realizations. Strictly speaking, the term “peso problem” is typically used when a regime change has not yet been observed. It is therefore impossible to detect the probability distribution underlying investors’ expectations.4

The “peso problem” has two implications. First, the uncovered interest parity hypothesis is rejected even if the two assets under consideration are perfect substitutes otherwise. Second, a tricky identification problem arises. As long as there is a probability of a regime change or an exchange rate devaluation, and without sufficient observed realizations of such events, it is impossible to distinguish empirically between rational expectations influenced by a peso problem and irrational expectations. Rogoff (1980) pointed out that when the market expects a discrete change in policy, exchange rate expectations will induce serially correlated forecast errors, with a mean that can be different from zero.5

Recent research has gone one step further by identifying the factors that affect this excess return or the probability of a regime change, or both. Many authors have linked the time-varying risk premium to macroeconomic fundamentals and indicator variables.6 In some studies, linear factor models are used to explain excess returns:

where the vector of explanatory variables Xit represents fundamentals and indicators available at time t, and where ut+n is a stationary process with zero mean.7 These variables are different for each country, and depend on the country-specific economic structure. Therefore, they will be determined later in the discussion, after reviewing some of Lebanon’s economic features.

Macroeconomic and Financial Developments, 1985–97

During the last part of the civil war (1985–89), a significant degree of macroeconomic (and political) instability prevailed.8 Large budget deficits were monetized, and inflation was accelerating. Moreover, the destruction and loss of capital, both human and physical, were particularly severe during the period, and real GDP declined. All these developments were reflected in a rapid decline of the external value of the Lebanese pound against the major currencies, a sharp increase in dollarization, and capital outflows (Figure 4.1).

Figure 4.1.Lebanese Pound–U.S, Dollar Exchange Rate and Interest Differential

Sources: Data provided by the Lebanese authorities; and IMF, International Financial Statistics

One year after the conclusion of the Taef agreement at the end of 1989, a government of national unity was reinstated, and a period of economic normalization and recovery started. Progress was nevertheless slow, and political uncertainty and macroeconomic fragility remained significant. Inflation rates remained high, and the Lebanese pound depreciated further, particularly in the first three quarters of 1992. It was only in October 1992, after the appointment of Prime Minister Hariri, that reconstruction and stabilization began.

An exchange-rate-based nominal anchor policy—targeting a slight nominal appreciation of the Lebanese pound against the U.S. dollar—has been at the core of the government’s stabilization efforts. The policy has been successful in stabilizing expectations, and inflation rates have been rapidly reduced to single-digit levels. The overall macroeconomic situation, however, remains difficult with large budget deficits, associated growing public debt, large current account deficit, and occasional episodes of domestic and regional political uncertainties. Under the circumstances, and given the virtual absence of restrictions on capital account transactions, monetary policy has born a heavy burden, as high and flexible interest rates have been necessary to ensure the exchange rate peg and to allow for a comfortable cushion of foreign exchange reserves. The high interest rates are reflected both in the excess return differential and the UIP Lebanese pound-U.S. dollar exchange rate—the exchange rate that would prevail if the uncovered interest parity between Lebanese pound and U.S. dollar assets applied. For the period December 1992 to December 1996, the UIP exchange rate has constantly been more depreciated than the actual exchange rate, confirming the bias in its capacity as a predictor of future exchange rate changes found elsewhere (Figure 4.2).

Figure 4.2.Uncovered Interest Parity and Excess Returns

Sources: Data provided by the Lebanese authorities; and IMF, International Financial Statistics

1 Exchange rate given by the requirement that the lagged three-month interest rate differential is equal to the actual three-month exchange rate change.

2 On a quarterly basis in comparison with three-month U.S. dollar treasury bills.

To ensure the exchange rate peg, monetary policy and public debt management have been closely coordinated (see Section V). The authorities have set monetary policy parameters, particularly the interest rates in the primary sales of treasury bills, such that official foreign exchange reserves cover a significant share of the domestic currency debt, which is largely short-term and therefore constitutes a potential quasi-monetary liability. In times of favorable financial market sentiments, treasury bills above and beyond the financing needs of the treasury’s budget needs have been issued—to sterilize foreign exchange inflows through matching increases in the accounts of the treasury with the central bank. This cushion has allowed the authorities some temporary interest rate smoothing during times of financial market turbulence. In this sense, both treasury bill interest rates and official foreign exchange reserves are not only reflecting the preferences and expectations of investors, but also the monetary policy reaction function of the authorities. The negative relationship between changes in the interest differential on Lebanese pound and U.S. dollar treasury bills and changes in the ratio of gross official foreign exchange reserves to treasury bills shown in Figure 4.3 could be a reflection of the monetary authorities’ policy to ensure a sufficient coverage of short-term Lebanese pound debt by reserves. Moreover, the positive correlation between the change in the yield spread (between 24-month treasury bonds and 3-month treasury bills) and changes in the share of short-term treasury bills in the total treasury bills and bonds outstanding provides evidence of the authorities’ attempt to offset the impact of market pressures on the maturity structure of the domestic currency debt.

Figure 4.3.Interest Rate Dynamics and Monetary Policy

Sources: Data provided by the Lebanese authorities; and IMF, International Financial Statistic

1 Gross official foreign exchange reserves as percent of total treasury bills outstanding.

2 Spread between return on 24-month treasury bonds and on 3-month treasury bills.

3 Share of short-term treasury bills(3, 6, and 12 months) in total treasury bills and bonds outstanding.

An Empirical Examination of the Interest Rate Differential Between the Lebanese Pound and the U.S. Dollar

In this subsection, the interest rate dynamics in Lebanon during the period 1993–96 is examined empirically from three different angles. First, the basic time series statistics for the deviations from the uncovered interest parity condition are analyzed to determine whether they have been significant. Second, the interaction between monetary policy and the interest dynamics is investigated. Finally, an empirical model that relates the excess return to macro-economic fundamentals is estimated.

Testing for the Uncovered Interest Rate Parity

The tests of the uncovered interest rate parity hypothesis are based on the analysis of the time series properties of the quarterly excess return t+3 on three-month Lebanese pound treasury bills relative to three-month U.S. dollar treasury bills.9 The analysis was conducted using monthly data, with the sample covering the period 1993–97. The sample was chosen because it encompasses a period during which the authorities were implementing an exchange-rate-based nominal anchor policy, and during which treasury bills sold in auctions were the most important Lebanese pound assets.

The basic statistics presented in Table 4.1 indicate that, during the period 1993–97, the mean excess return was equal 13.9 percent (on an annual basis) and was significantly different from zero, and that the interest rate differential between three-month Lebanese pound and U.S. dollar treasury bills systematically overstated the change in the Lebanese pound-U.S. dollar exchange rate over the subsequent three months. Moreover, the excess return series displays serial correlation, which indicates that the risk premium and exchange rate expectations reflected in this variable were changing only gradually over time. The hypothesis is supported by the sample mean of the first difference of the excess return (significantly different from zero at a 5.3 percent level), which suggests that the excess return was declining by 0.4 percent a year during 1993–97.

Table 4.1.Analysis of Excess Returns1
t∈ ε t
Sample1993M1–97M121993M1–96M12
Mean0.033-0.0009
Standard deviation0.0090.004
RHO(l)2
QP(12)30.7460.209
122.995.036
[0.000][0.984]
PPF(2)4-4.437-5.475
ADF(1)5-4.526-5.316
Normality611.30898.952
[0.043][0.000]
Source: IMF staff calculations, based on data provided by the authorities.

Marginal significance levels in brackets.

First-order autocorrelation coefficient.

Portmanteau test statistics, follow χ2 distribution.

Philips-Perron unit root test, 2 lags.

Augmented Dickey-Fuller unit root test, 2 lags.

Test statistics follows χ2 distribution.

Source: IMF staff calculations, based on data provided by the authorities.

Marginal significance levels in brackets.

First-order autocorrelation coefficient.

Portmanteau test statistics, follow χ2 distribution.

Philips-Perron unit root test, 2 lags.

Augmented Dickey-Fuller unit root test, 2 lags.

Test statistics follows χ2 distribution.

Monetary Policy, Lebanese Pound–U.S. Dollar Interest Rate Differential, and Yield Spread

As argued earlier, the interest rate differential between three-month Lebanese pound and U.S. dollar treasury bills and the yield spread between 24-month Lebanese pound treasury bonds and three-month treasury bills may not only reflect the expectations and preferences of investors, but also the reaction function of the monetary authorities. To study the interaction between monetary policy and the interest differential and the yield spread, respectively, two bivariate vector autoregressive models (VARs) were estimated. The results will be helpful for the subsequent specification of an empirical model for the excess returns t+3 because they determine whether the role of monetary policy in the determination of this variable needs to be taken into account in the empirical analysis.

The first bivariate VAR involves the changes in the interest differential on three-month Lebanese pound and U.S. dollar treasury bills,it-It10 and changes in the ratio of gross foreign exchange reserves Rt to treasury bills T,. If the monetary authorities target a range for the ratio of reserves to treasury bills by using the interest differential as an instrument, then past realizations of the instrument have some predictive power for the current value of the target variable while past realizations of the target should not have any predictive power for the current value of the instrument. The Granger causality tests reported in Table 4.2 do not confirm the hypothesis that there has been a target-instrument relationship between the ratio of gross foreign exchange reserves to treasury bills and the interest rate differential during the period 1993–97. For the period 1993–96, however, such a target-instrument relationship could be found. It is noteworthy that a VAR analysis for the period 1993–96 involving the levels of the interest differential and the ratio of reserves to treasury bills does not indicate any clear-cut directions of Granger causality. These results suggest that the monetary authorities tried to avoid sharp changes in the ratio of foreign exchange reserves to treasury bills during 1993–96 rather than targeting a specific value for the variable.

Table 4.2.Monetary Policy, the Lebanese Pound–U.S. Dollar Interest Differential, and Yield Spread: Granger Causality Tests1
A.VAR l: Lebanese Pound-US. Dollar Interest Differential and the Ratio of Reserve to Treasury Bills2
1993M1–97M12
Δ(it1/t1*)Δ(Rt1/Tt1)
Δ(it/t*)1.583.12
(0.21)(0.08)
Δ(Rt/Tt)0.008.08
(0.99)(0.01)
1993M1–96M12
Δ(it1/t1*)Δ(Rt1/Tt1)
Δ(it/t*)5.670.09
(0.02)(0.76)
Δ(Rt/Tt)48.500.92
(0.00)(0.34)
B.VAR II:Yield Spread and the Ratio of Short-Term to Total Treasury Bills3 1993M1–97M12
Δ(it124it1)Δ(STt1/Tt1)
Δ(it24it)2.132.45
(0.13)(0.10)
Δ(STt/Tt)0.7222.34
(0.49)(0.00)
Source: IMF staff calculations based on data provided by the authorities.

F-test of the null hypothesis that the explanatory variables in the columns can be excluded from the equation with the variable in the row as dependent variable (marginal significance level in parentheses). For example, the F-test statistic of the null hypothesis that lagged values of the ratio of reserves to treasury bills have no impact on the current period interest differential is 0.09.

Based on first-order VARs.

Based on a second-order VAR.

Source: IMF staff calculations based on data provided by the authorities.

F-test of the null hypothesis that the explanatory variables in the columns can be excluded from the equation with the variable in the row as dependent variable (marginal significance level in parentheses). For example, the F-test statistic of the null hypothesis that lagged values of the ratio of reserves to treasury bills have no impact on the current period interest differential is 0.09.

Based on first-order VARs.

Based on a second-order VAR.

The second bivariate VAR involves the changes in the secondary market yield spread between Lebanese pound 24-month treasury bonds and 3-month treasury bills,i24t -it,11 and changes in the share of short-term treasury bills STt(up to 12 months) in total treasury bills and bonds T, outstanding. If the monetary authorities target a range for the share of short-term treasury bills in total treasury bills using the yield spread as an instrument, then past realizations of the instrument should again have some predictive power for the current value of the target variable. The Granger causality tests reported in Table 4.2 do not confirm the hypothesis that there has been a target-instrument relationship between the share of short-term treasury bills in total treasury bills and bonds outstanding during the period 1993–97.12 In fact, the direction of causality is the reverse. Changes in ratio of short-term to total treasury bills precede changes in the yield spread. One reason for this result could be that the monetary authorities react to changes in investors’ preferences regarding the maturity structure with a lag. In particular, it could be that changes in the maturity structure of the flows rather than the composition of the stock are targeted. These results suggest that changes in the maturity structure were not of the same immediate importance to the monetary authorities as changes in the ratio of gross official foreign exchange reserves to treasury bills.

A Linear Factor Model Explaining Excess Returns

Explaining the excess return t+3 with a linear factor model aims at relating the risk premium captured in this variable to macroeconomic fundamentals and to political factors, which are captured by a dummy variable. As shown above, the recent empirical evidence does not suggest that monetary policy actions had a strong direct impact on the dependent variable. In the empirical analysis, the following explanatory variables were included: the growth rate of the domestic public debt, the growth rate of M2, the growth rate of domestic credit, the growth rate of the real exchange rate, the first lag of the dependent variable, and a dummy variable. With the exception of the last two variables, all were lagged by one period to avoid simultaneity problems.

The model is based on the following rationale:

  • Expectations about future events, particularly regime changes that are unrelated to current macroeconomic fundamentals, are captured by the first lag of the endogenous variable. As shown by the literature on peso problems, expectations about future regime changes tend to be persistent, suggesting a positive relationship between the current excess return and its lagged value.

  • The variation of the gross foreign reserves of the central bank is a measure for the exchange rate risk in Lebanon perceived by investors. Since the central bank is pursuing an exchange-rate-based nominal anchor policy, changes in the perceived exchange risk and therefore demand for Lebanese pound assets would be reflected as a variation in gross reserves. However, there is also feedback from the level of gross foreign exchange reserves to the perceived exchange rate risk. Accordingly, an increase in the growth of foreign exchange reserves would ceteris paribus lower the risk of an exchange rate regime change and then lower the excess return.

  • The fiscal deficit, which can be approximated by the percentage variation of the domestic debt, is a good indicator for the country’s creditworthiness. This variable can be expected to be positively correlated with interest rates because investors require larger returns to increase the share of treasury bills in their portfolio.13

  • Similarly, the ratio of M2 to M3 is an indicator for investors’ expectations, because it reflects the demand for Lebanese pound assets by residents.14 An increase in this ratio would, ceteris paribus, lead to a decrease in the excess return.

  • The growth rate of domestic credit to the private sector is used as an indicator for real sector growth. Given the lack of sufficiently long time series for summary measures of real sector activity, the domestic credit variable serves as a proxy variable. An increase in private sector credit growth, being interpreted as an increase in GDP growth, would, ceteris paribus, reduce the fiscal deficit as a percent of GDP and reduce the supply of domestic assets, but increase the demand for domestic assets, thereby reducing the excess return.

  • The real effective exchange rate is an indicator for the external sector viability. An increase in the growth rate of this variable would reduce the competitiveness of the economy and, ceteris paribus, reduce the external current account balance and increase the need for capital inflows. This would require an increase in the excess return.

  • The 0–1 dummy variable takes the value 1 during periods of heightened political uncertainty. These periods are related to the uncertainty about the presidential elections in 1995, the cabinet crisis following Prime Minister Hariri’s resignation threat in early 1995, and the bombings in April 1996, The impact of political uncertainty on the excess return can be expected to be positive.

The estimation results, which are presented in the appendix, imply that current macroeconomic fundamentals explain only a small fraction of the movement in the excess return on treasury bills during the period of January 1993–December 1997. Only the ratio of M2 to M3 turned out to be significant, with the expected negative sign. All other variables, except for the first lag of the dependent variable and the dummy variable, were insignificant. These results suggest that the demand for Lebanese pound assets by resident investors is important in determining the excess return and that expectations about future exchange rate changes are not tightly linked to other current macroeconomic fundamentals. This is consistent with a hypothesis that is often stated in Lebanon, namely, that expectation-linked, sociopolitical conditions are the dominant determinants of local financial market conditions.

These results may also reflect other factors. The sample period is short, covering a period of recovery, reconstruction, and stabilization, during which the excess return has, on average, been declining. Current and past realizations of macroeconomic fundamentals might therefore contain little information for future macroeconomic developments since their behavioral pattern is changing during such a period of transition. Signaling future policy actions could be much more important under these circumstances. Furthermore, lagged values of the growth rates of domestic public debt and the foreign exchange reserves are likely to have weak leading indicator properties with respect to the excess return as a result of the conduct of monetary policy discussed above.

Conclusions

Domestic interest rates in Lebanon have exceeded world market rates by a large margin in the context of an exchange-rate-based nominal anchor policy that targeted a slight nominal appreciation of the Lebanese pound against the U.S. dollar. The average interest rate differential between three-month treasury bills denominated in Lebanese pounds and U.S. dollars has amounted to about 12 percent during 1993–96, implying an average annualized excess return of about 16 percent.

The main conclusions from the empirical analysis of this interest differential may be summarized as follows:

  • The uncovered interest rate parity relationship does not hold in Lebanon. As a result, interest rate differentials between the Lebanese pound and the U.S. dollar denominated similar assets are not good predictors for the future exchange rate.

  • Deviations from uncovered interest rate parity suggest the existence of a risk premium, possibly related to a peso problem.

  • A model that incorporates macroeconomic fundamentals, such as changes in money supply, helps explain the excess return on domestic assets, albeit to a limited degree only. The empirical model also provides evidence that shocks and expectations about future events that are not captured by current fundamentals have a long-lasting effect on excess returns, which indicates that credibility and reputation effects are important.

These findings suggest that interest rates are responsive to policy developments as well as to external shocks in Lebanon. Therefore, the authorities should reduce the vulnerability of the economy to exogenous shocks and implement policies that enhance credibility and reduce the risk premium in interest rates. With regard to the latter, a front-loaded fiscal adjustment and a sustainable macroeconomic policy mix are crucial.

Appendix. Explaining Excess Returns in Lebanon, 1993–97

This appendix, based on the linear factor model discussed at the beginning of the section, tries to set up an empirical model that relates the excess return ∈t+3 to macroeconomic fundamentals, to its own lagged value, and to a dummy variable, denoted with It, that captures periods of heightened political uncertainty.

The set of currently observed macroeconomic fundamentals includes the growth rate of gross official foreign exchange reserves (converted into Lebanese pounds), denoted with R, the growth rate of the domestic public debt, D, the ratio of M2 to M3. the growth rate of domestic credit. DC and the percentage change of the real exchange rate, RER,

All explanatory variables except for the dummy variable (and the lagged value of the dependent variable) are lagged by one period to avoid problems related to the simultaneity between the dependent and the current period explanatory variables. These problems arise because the excess return during the period 1993–97 is largely determined by the interest differential given the steady and predictable Lebanese pound appreciation. The lagged explanatory variables therefore have the character of leading indicator variables. Moreover, the model is also specified using natural logarithms for the excess return and other variables in levels to reduce the volatility of the estimation error.15

The empirical model for the excess return can therefore be written as:

where η t denotes a residual.

Equation (5) was estimated with ordinary least squares for the period January 1993 to December 1997.16 The results, which are reported in Table 4.3, show that many variables were insignificant, including the growth rate of gross official foreign exchange reserves, the growth rate of the domestic public debt, the growth rate of domestic credit, and the growth rate of the real exchange rate.

Table 4.3.Explaining Excess Returns, 1993M1–1997M121
Dependent variablelnε(εt+3)lnε(εt+3)
Estimation methodOLSOLS
Explanatory variables
lnε(εt+2)0.6580.700
(0.126)(0.082)
ΔlnRt10.602
(0.645)
ΔlnDt1-0.257
(0.358)
ΔlnDCt1-0.101
(6.354)
ΔlnRERt1-0.936
(0.921)
Δln(M2t1/M3t1)-0.565-0.435
(0.209)(0.113)
/t0.0570.060
(0.029)(0.025)
R20.9020.904
σ0.0830.082
D.W.1.7421.761
AR(1-2)20.904 [0.411]0.683 [0.509]
ARCH(1)30.725 [0.399]0.417 [0.521]
DF4-6.864-6.913
Source: IMF staff calculations, based on data provided by the authorities.

Autocorrelation-heteroskedasticity constant standard errors in parentheses. Marginal significance levels in square brackets.

Lagrange multiplier test for second-order autocorrelation in the residuals; the test statistics follows an F-distribution.

Test statistics follows an F-distribution.

Dickey-Fuller unit root tests applied to residuals (no constant included); test statistics denotes t-statistics.

Source: IMF staff calculations, based on data provided by the authorities.

Autocorrelation-heteroskedasticity constant standard errors in parentheses. Marginal significance levels in square brackets.

Lagrange multiplier test for second-order autocorrelation in the residuals; the test statistics follows an F-distribution.

Test statistics follows an F-distribution.

Dickey-Fuller unit root tests applied to residuals (no constant included); test statistics denotes t-statistics.

The final empirical model that was estimated after using Wald tests to reduce the number of explanatory variables is reported in the last column of Table 4.3. Three variables turned out to be significant: the ratio of Ml to M3, the dummy variable, and the lagged value of the dependent variable.

Equation (5) was also estimated for different sample periods. Overall, the results are qualitatively similar, although the quantitative impact of the various explanatory variables on the excess return depends on the sample period.

Note: The initial draft of this section was prepared by Taline Urné chlian of the Banque du Liban while she was a summer intern in the IMF’s Middle Eastern Department.

See, among many others, Cochrane and Hansen (1992), Lewis (1994), and Kocherlakota (1996).

The first use of the term “peso problem” is attributed to Milton Friedman in his examination of the Mexican peso market during the early 1970s, where deposit rates remained substantially above U.S. dollar interest rates, even though the exchange rate was fixed. Friedman argued that this interest differential reflected themarket’s expectations of a devaluation of the peso. Subsequently, in 1976, the peso was devalued by 46 percent and was allowed to float thereafter.

In empirical studies, however, the problem often remains relevant because only a few regime changes are typically observed during a given time period, so that standard distributions used in empirical research provide bad approximations.

Recent empirical work showed that peso problems can have significant effects on the forecast errors. For example, Lewis (1990) found that the presence of a peso problem during the period of interest rates targeting in the United States induced sizable effects upon excess returns on longer-term bonds and allowed interest rates to fluctuate widely.

See Caramazza (1993), Chen and Giovannini (1993), and Holden and Vick∅ ren (1996) for recent studies.

By specifying equation (5), it is assumed that the excess returns t as well as the explanatory variables Xit are stationary, that is, integrated of order zero I(0). If, however, the excess returns t were I(1), then the factor model would have to be formulated as an error correction model (Engle and Granger (1987)).

See Eken and others (1995) for a more detailed description of macroeconomic developments during the war years.

Quarterly excess returns are calculated according to equation (4).

The interest rate differential on these three-month treasury bills is referred to as interest differential in the remainder of the paper.

The yield spread between Lebanese pound 24-month treasury bonds and three-month treasury bills is referred to as yield spread in the remainder of the paper.

Estimating the same VAR for the period 1993–96 yields similar results.

In principle, the growth rate of the domestic public debt in excess of the growth rate of wealth should be used. However, due to data limitations and difficulties in defining the relevant wealth variables with capital mobility, the simple model growth rate of domestic debt is used.

M2 is the sum of currency in circulation and of Lebanese pouond sight and demand deposits. Given the very limited Lebanese pound lending to the private sector, bank holdings of treasury bills are the major counterpart of M2 in the balance sheet of the monetary sector. It should be noted, however, that the domestic public debt is also held directly by the nonbank public, including nonresident investors. The latter are not allowed to hold Lebanese pound deposits with the banking system. The indicator properties of M2 are therefore different from those of the growth rate of the domestic public debt, since the latter variable captures changes in the asset holding by both resident and nonresident investors.

The estimation of the model in levels yields results, that are qualitatively similar to those reported. The residuals, however, have the natural characteristics of a time series process with autoregressive condition heteroskedasticity (ARCH). Estimating an ARCH model would not provide any additional insight, however, and the log specification allows one to avoid the problem.

In a first stage, unit root tests were applied to all the explanatory variables for the period January 1993–December 1996. All of them turned out to be stationary.

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