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Predicting the quantity of LDC debt rescheduling
Economics Letters North-Holland
32 (1990) 67-73
PREDICTING
THE QUANTITY
H. LLOYD-ELLIS, Unwersity Received Accepted
67
OF LDC DEBT RESCHEDULING
G.W. MCKENZIE
of Southampton,
Southampton,
and S.H. THOMAS
SO9 5NH,
UK
16 May 1989 27 June 1989
In this paper we estimate a Type 2 Tobit model to explain both the timing nnd quantity of developing country debt rescheduling using an annual data set for 27 countries from 1977-1981 and six-monthly data for 59 countries from 1977-1985. We obtain a satisfactory model for both the timing and quantity of rescheduling which will be more useful for country risk analysis than models which predict the timing alone.
1. Introduction There is a growing literature on the use of limited dependent variable models to predict the timing of developing country debt rescheduling [e.g. Feder, Just and Ross (1981) Cline (1984) and Saini and Bates (1984)]. However, no studies have attempted to explain both the quantity and timing of a rescheduling. Such information would be very useful for practical country risk analysis. In this paper we have two aims (i) We use a Type 2 Tobit model [e.g. see Amemiya (1985)] to represent the relationship between both the timing and quantity of LDC debt rescheduling and a set of economic variables. This involves a probit model to fit probabilities and a censored linear regression model to explain quantities. We estimate an annual model for 27 larger debtor countries from 1977-1981 [similar to Cline (1984)] and a six-monthly model from 1977 (II) to 1985 (II) for 59 countries. (ii) Secondly, in the Tobit model we use a set of financial variables to capture the balance sheet structure of developing countries rather than the more traditional ‘ratio’ variables such as the debt service to exports and foreign exchange reserves to imports ratios [Avramovic (1958) Feder, Just and Ross (1981)]. In a previous paper we defend the use of financial variables such as the ratio of short-term to total bank debt for a country on both empirical and theoretical grounds [Lloyd-Ellis, McKenzie and Thomas (1989)].
2. Model specification We assume that the probability represented by a probit equation:
of country
i rescheduling
in a given time-period
can be
Y,,=X;,B+u,. * We would like to thank Singapore for comments.
016%1765/90/$3.50
(1) Peat Marwick
for financial
0 1990, Elsevier Science Publishers
support
and
seminar
B.V. (North-Holland)
participants
at the National
University
of
H. Lloyd-Ellis et al. / Predicting the quantity of LDC debt rescheduling
68
Y,, is either zero or unity depending on whether or not a rescheduling vector of variables which influence the rescheduling decision. The quantity of rescheduling is given by a linear regression equation: y
X1+ + e, if Y,,>O
= 21 i
0
otherwise.
takes place, and X,‘, is the
(2)
Here Xi, is a vector of variables which influence the quantity rescheduled, Yz,. Of course this is only non-zero if a rescheduling occurs. These two equations may be thought of as characterising the outcomes of a two-step bargaining process. First, the parties agree to reschedule (eq. 1). Then the actual amount of rescheduling is negotiated (eq. 2). B and + are vectors of parameters, e, and U, are jointly normally distributed random variables with variances u2 and unity (for normalisation) and a correlation coefficient p. Equations (1) and (2) can either be estimated jointly by maximisation of the full likelihood function or separately by using Heckman’s two-step estimator for eq. (2). The latter method involves the introduction of an extra variable, the so-called Mills ratio, to allow for the sample selection bias introduced through only using non-zero quantities [Heckman (1979)]. Both estimation methods yield similar results. We now turn to the choice of variables for Xi’, and Xi,. We have argued elsewhere (1989) that variables which capture a country’s balance-sheet position may be both empirically and theoretically superior to the more traditional macro-indicators. These variables capture changes in a country’s asset and liability position which may be associated with the onset of a financial crises [Kindleberger (1978) Minsky (1982)]. They are available with a short time lag from the Bank for International Settlements and the IMF. In addition we introduced a set of variables to capture the changing global attitudes to rescheduling and the opportunity cost of not rescheduling. Such variables included the number and value of reschedulings (NOR and VOR), the average grace and maturity of new rescheduling (WAGP and WAM) and an average mark-up on current reschedulings (WAIR). The balance-sheet variables include the ratio of short-term debt to total bank debt (ST), the ratio of foreign exchange reserves to IMF quota (RESQUOT), the ratio of long-term borrowing to total bank debt (AT), and the ratio of a country’s total bank borrowing to its bank deposits (TLA). A full description of the variables considered is given in our earlier paper (1989).
3. Results Two sets of results are presented: the first involves annual data for 27 large debtor countries from 197771981, while the second uses six-monthly data for 59 countries from 1977-1985. For the annual data we include a wide range of conventional variables as well as our balance-sheet variables. For the six-monthly model many of the traditional variables are unavailable and so we concentrate on our balance-sheet variables and those representing global attitudes to rescheduling. All economic and balance-sheet variables are lagged one period. Tables la and lb contain our estimates of the Type 2 Tobit model. Note that the rescheduling variable refers to both bank and official debt restructuring as identified in the IMF Capital Markets Reports. 3.1. Annual results
The specifications presented in tables la and lb contain similar variables to those estimated in our logit model of debt rescheduling (1989), albeit with very different coefficients. We began with a wide
H. Lloyd-Ellis Table
et al. / Predicting the quantity of LDC debt rescheduling
69
la
Annual
results (t-values
in parentheses).
Parameter
Type 2 Tobit FIML
Heckman method
Selection equation CONSTANT
-9.616
- 10.114 (-
( - 2.534)
PEXP
TLA
ST
AT
0.798
0.719
(2.912)
(1.215)
0.520
0.514
(3.459)
(2.815)
9.366
9.998
(2.035)
(1.187)
10.191
10.792
(1.952)
(1.140)
- 0.379
RESQUOT
- 0.370
( - 2.464)
(-1.468)
0.426
R2 Regression equation CONSTANT
0.426
- 0.430 ( - 1.4630
ST
1.464)
- 0.426 (-1.018) 1.636 (1.754)
1.593 (2.721) - 0.077
Mills ratio
( - 0.728) _
Sigma (a)
0.194 (1.535)
_
Rho(p)
-0.535 (-4.138)
R2
Critical level
0.670
0.507
Type 1
Type 2
Type 1
Type 2
0.1
1
18
1
16
0.2
3
11
3
12
0.3
4
5
4
6
0.4
5
4
5
4
0.5
7
3
7
2
0.6
7
2
7
2
0.7
8
1
9
1
0.8
8
0
9
0
0.9
11
0
11
0
Total number of rescheduling:
11
H. Lloyd-Ellis
70
et al. / Predicting the quantity of LDC debt rescheduling
Table lb Semi-annual
results (t-values
Parameters
in parentheses).
Type 2 Tobit Heckman
FIML
method
Selection equation CONSTANT
- 2.526 (-6.118)
TLA
MT
UT
UA
0.065
0.063
(2.527)
(2.097)
2.082
2.015
(3.655)
(3.464)
2.896
2.869
(3.877)
(3.911)
- 2.510 ( - 4.084)
RESQUOT
- 0.052 (-
1.825)
NOR
VOR
WA GP
1.455)
DUM
R2 Regression equation CONSTANT
1.739)
-0.018 (-
1.251)
0.010
0.009
(1.568)
(1.327)
0.805
0.817
(4.891)
(4.916)
0.197
0.199
- 0.090
- 0.091 ( - 0.467)
RESQUOT
WAM
0.645
0.639
(2.724)
(2.184)
0.025
0.025
(1.691)
(1.785)
0.002
0.002
(2.112)
(1.897)
- 0.083 (-
1.206)
Sigma ((T)
0.249 (3.118) - 0.325 (- 11.513)
Rho(P) R2
- 0.017 (-
( - 0.550)
ST
Mills ratio
0.081 (2.338)
-0.019
WAM
- 0.051 ( - 1.277)
0.084
1.946)
(-
- 2.529 (-4.585)
(2.501) -0.018 (-
- 2.490 (-5.177)
0.752
0.721
H. Lloyd-Ellis
11
et al. / Predicting the quantity of LDC debt rescheduling
Table lb (continued) Critical level
Type 1
Type 2
Type 1
Type 2
0.1
12
152
13 29 42 50 58 68 69 69 69
156 65 42 16 9 6 0 0 0
28 0.2 43 0.3 50 0.4 58 0.5 68 0.6 69 0.7 69 0.8 69 0.9 Total number of reschedulings: 69
68 43 16 9 3 1 0 0
set of both conventional macro-variables and balance-sheet variables and sequentially eliminated the insignificant variables. Our preferred probit equation (see Table la) contains the rate of growth of export volume (PEXP), together with the balance-sheet variables ST, AT, TLA, and RESQUOT. The coefficients accord with our interpretation regarding financial crises, with a deteriorating cash flow position (falling RESQUOT) leading to a build-up of short-term debt (ST) and an increase in bank borrowing relative to deposits (TIA). However, of the many variables considered for the equation explaining the quantity of rescheduling, only the ratio of short-term to total bank debt was important. It may be thought that we are effectively estimating an identity if only short-term debt is rescheduled; however, note that the right-hand side variable is lagged one period and that in practice it is not necessarily the short-term component of debt which is rescheduled, but rather the medium and longer-term debt of any country. The Mills ratio is not significant but in the joint estimation p is very important with a t-value of over 4. In the only similar study of which we are aware, Dudley and Montmarquette (1976) investigate US foreign aid policy assuming the independence of e, and u,. This is clearly unlikely in practice, as our results indicate. Further we find that both quantity equations explain over 50% of the variation in the rescheduled quantities despite the fact that only one economic variable is present. These compare favourably with the fit achieved for the study of US aid policy mentioned above, and must be considered very satisfactory for a mixed cross-section/ time-series model without fixed effects. An evaluation of the predictive capability of models involving qualitative variables depends crucially on (i) an examination of the type I and type II errors that occur at different probability levels, and (ii) a subjective evaluation of the relative costs of the two types of error. Note that in this context a type I error involves not predicting a rescheduling which occurs, while a type II error involves predicting a rescheduling when one actually did not take place. Previous studies have implicitly ignored the relative costs by choosing a critical value which minimises the sum of the two errors. For the FIML results shown in table la this occurs at critical levels 0.4, 0.5, 0.6 and 0.8, yielding error rates similar to those presented in the survey paper by Saini and Bates (1984). However, this procedure is misleading as it is unlikely to reflect the relative valuations of the two types of errors either by policy makers or by private sector risk analysts. Consider the opportunity costs associated with the two errors: if funds are not lent to a country which is predicted to restructure but, in fact, does not, the opportunity cost will be the interest differential over the next best alternative investment (which may be only a couple of percentage points over the risk-free Treasury rate). This is the opportunity cost of a type II error. On the other hand, the opportunity cost of making a type I error is clearly much greater: at one extreme the borrower could actually
12
H. Lloyd-Ellis
et al. / Predicting the quantity of LDC debt rescheduling
default, though as yet restructuring usually involves deferment of interest and/or amortisation payments. Hence selecting models by minimising the sum of the type I and type II errors [as in Feder and Just (1977) and others] may be quite misleading. 3.2. Semi-annual
results
From the annual results it would appear that the traditional variables do not add greatly to the model once the balance-sheet variables are present, In any case many of the traditional economic variables are not available on a six-monthly basis. For the semi-annual model we include variables to capture global attitudes to rescheduling together with our balance-sheet variables. Again we begin from a general model containing a wide range of balance-sheet and ‘global’ variables and simplify sequentially to obtain a sensible and data consistent significant relationship. Table lb contains both the FIML and Heckman two-step estimates of our model: the selection equation includes total bank borrowing relative to total deposits (TM); foreign exchange reserves relative to the IMF quota (RESQUOT); the proportion of medium-term to total bank debt (MT); undisbursed credit commitments divided by total bank lending to that country (UT); and unallocated credit divided by total lending to a country (UA); together with the four ‘global’ or ‘herd’ variables NOR, VOR, WAGP and WAM. A dummy variable (DUM), consisting of ones in the two periods following a rescheduling, captures the changed financial position of a country immediately after a rescheduling. The regression equation to explain the quantity of rescheduling now includes the short-term to total debt ratio (ST), the reserves to IMF quota ratio (RESQUOT), and the weighted average of maturity periods on new rescheduling, WAM. The Mills ratio is once more not significant but again we have a highly significant negative value for p from the FIML estimates. The quantity equations now explain over 70% of the variations in rescheduled quantities which is rather startling given the heterogeneous nature of the countries involved in the exercise and the fact that the data is mixed cross-section/time-series. If we wish to minim&e the sum of type I and type II errors we again find our error rates compare favourably with the literature [see Saini and Bates (1984)].
4. Conclusion We have estimated a Type 2 Tobit model to explain the timing and quantity of LDC debt rescheduling using both Heckman’s two-step method and FIML. We are able to explain up to 75% of the variation in the quantity rescheduled using a simple parsimonious model. This information can add greatly to that provided by simple predictions of the probability of rescheduling given by logit or probit models.
References Amemiya, T., 1985, Advanced econometrics (Harvard University Press, Cambridge, MA). Avramovic, D. et al., 1958, Economic growth and external debt (Johns Hopkins Press, Baltimore, MD). Bank for International Settlements, Various issues, Maturity distribution of international bank lending (BIS, Basle). Cline, W.R., 1984, International debt: Systemic risk and policy response (MIT Press, Cambridge, MA). Dudley, L. and C. Montmarquette, 1976, A model of the supply of bilateral foreign aid, American Economic Review 66, 132-142. Feder, G. and R.E. Just, 1977, A study of debt servicing capacity applying logit analysis, Journal of Development Economics 4, 25-38. Feder, G., R.E. Just and K. Ross, 1981, Projecting debt servicing capacity of developing countries, Journal of Financial and Quantitative Analysis XVI, no. 5, 651-669.
H. Lloyd-Ellis
et al. / Predicting the quantity oJLDC
debt rescheduhng
13
Heckman, J.J., 1979, Sample selection bias as a specification error, Econometrics 47, 153-162. International Monetary Fund, Various issues, Capital markets reports, various issues (IMF, Washington, DC). Kindleberger, C.P., 1978. Manias, panics and crashes (Basic Books, New York). Lloyd-Ellis, H., G.W. McKenzie and S.H. Thomas, 1989, Using country balance sheet data to predict debt rescheduling. Economics Letters 31, no. 2, 173-177. Minsky, H.P., 1982, Inflation, recession and economic policy (M.E. Sharpe, New York). Saini, K.G. and P.S. Bates, 1984, A survey of quantitative approaches to country risk analysis, Journal of Banking and Finance 8. 357-370.
32 (1990) 67-73
PREDICTING
THE QUANTITY
H. LLOYD-ELLIS, Unwersity Received Accepted
67
OF LDC DEBT RESCHEDULING
G.W. MCKENZIE
of Southampton,
Southampton,
and S.H. THOMAS
SO9 5NH,
UK
16 May 1989 27 June 1989
In this paper we estimate a Type 2 Tobit model to explain both the timing nnd quantity of developing country debt rescheduling using an annual data set for 27 countries from 1977-1981 and six-monthly data for 59 countries from 1977-1985. We obtain a satisfactory model for both the timing and quantity of rescheduling which will be more useful for country risk analysis than models which predict the timing alone.
1. Introduction There is a growing literature on the use of limited dependent variable models to predict the timing of developing country debt rescheduling [e.g. Feder, Just and Ross (1981) Cline (1984) and Saini and Bates (1984)]. However, no studies have attempted to explain both the quantity and timing of a rescheduling. Such information would be very useful for practical country risk analysis. In this paper we have two aims (i) We use a Type 2 Tobit model [e.g. see Amemiya (1985)] to represent the relationship between both the timing and quantity of LDC debt rescheduling and a set of economic variables. This involves a probit model to fit probabilities and a censored linear regression model to explain quantities. We estimate an annual model for 27 larger debtor countries from 1977-1981 [similar to Cline (1984)] and a six-monthly model from 1977 (II) to 1985 (II) for 59 countries. (ii) Secondly, in the Tobit model we use a set of financial variables to capture the balance sheet structure of developing countries rather than the more traditional ‘ratio’ variables such as the debt service to exports and foreign exchange reserves to imports ratios [Avramovic (1958) Feder, Just and Ross (1981)]. In a previous paper we defend the use of financial variables such as the ratio of short-term to total bank debt for a country on both empirical and theoretical grounds [Lloyd-Ellis, McKenzie and Thomas (1989)].
2. Model specification We assume that the probability represented by a probit equation:
of country
i rescheduling
in a given time-period
can be
Y,,=X;,B+u,. * We would like to thank Singapore for comments.
016%1765/90/$3.50
(1) Peat Marwick
for financial
0 1990, Elsevier Science Publishers
support
and
seminar
B.V. (North-Holland)
participants
at the National
University
of
H. Lloyd-Ellis et al. / Predicting the quantity of LDC debt rescheduling
68
Y,, is either zero or unity depending on whether or not a rescheduling vector of variables which influence the rescheduling decision. The quantity of rescheduling is given by a linear regression equation: y
X1+ + e, if Y,,>O
= 21 i
0
otherwise.
takes place, and X,‘, is the
(2)
Here Xi, is a vector of variables which influence the quantity rescheduled, Yz,. Of course this is only non-zero if a rescheduling occurs. These two equations may be thought of as characterising the outcomes of a two-step bargaining process. First, the parties agree to reschedule (eq. 1). Then the actual amount of rescheduling is negotiated (eq. 2). B and + are vectors of parameters, e, and U, are jointly normally distributed random variables with variances u2 and unity (for normalisation) and a correlation coefficient p. Equations (1) and (2) can either be estimated jointly by maximisation of the full likelihood function or separately by using Heckman’s two-step estimator for eq. (2). The latter method involves the introduction of an extra variable, the so-called Mills ratio, to allow for the sample selection bias introduced through only using non-zero quantities [Heckman (1979)]. Both estimation methods yield similar results. We now turn to the choice of variables for Xi’, and Xi,. We have argued elsewhere (1989) that variables which capture a country’s balance-sheet position may be both empirically and theoretically superior to the more traditional macro-indicators. These variables capture changes in a country’s asset and liability position which may be associated with the onset of a financial crises [Kindleberger (1978) Minsky (1982)]. They are available with a short time lag from the Bank for International Settlements and the IMF. In addition we introduced a set of variables to capture the changing global attitudes to rescheduling and the opportunity cost of not rescheduling. Such variables included the number and value of reschedulings (NOR and VOR), the average grace and maturity of new rescheduling (WAGP and WAM) and an average mark-up on current reschedulings (WAIR). The balance-sheet variables include the ratio of short-term debt to total bank debt (ST), the ratio of foreign exchange reserves to IMF quota (RESQUOT), the ratio of long-term borrowing to total bank debt (AT), and the ratio of a country’s total bank borrowing to its bank deposits (TLA). A full description of the variables considered is given in our earlier paper (1989).
3. Results Two sets of results are presented: the first involves annual data for 27 large debtor countries from 197771981, while the second uses six-monthly data for 59 countries from 1977-1985. For the annual data we include a wide range of conventional variables as well as our balance-sheet variables. For the six-monthly model many of the traditional variables are unavailable and so we concentrate on our balance-sheet variables and those representing global attitudes to rescheduling. All economic and balance-sheet variables are lagged one period. Tables la and lb contain our estimates of the Type 2 Tobit model. Note that the rescheduling variable refers to both bank and official debt restructuring as identified in the IMF Capital Markets Reports. 3.1. Annual results
The specifications presented in tables la and lb contain similar variables to those estimated in our logit model of debt rescheduling (1989), albeit with very different coefficients. We began with a wide
H. Lloyd-Ellis Table
et al. / Predicting the quantity of LDC debt rescheduling
69
la
Annual
results (t-values
in parentheses).
Parameter
Type 2 Tobit FIML
Heckman method
Selection equation CONSTANT
-9.616
- 10.114 (-
( - 2.534)
PEXP
TLA
ST
AT
0.798
0.719
(2.912)
(1.215)
0.520
0.514
(3.459)
(2.815)
9.366
9.998
(2.035)
(1.187)
10.191
10.792
(1.952)
(1.140)
- 0.379
RESQUOT
- 0.370
( - 2.464)
(-1.468)
0.426
R2 Regression equation CONSTANT
0.426
- 0.430 ( - 1.4630
ST
1.464)
- 0.426 (-1.018) 1.636 (1.754)
1.593 (2.721) - 0.077
Mills ratio
( - 0.728) _
Sigma (a)
0.194 (1.535)
_
Rho(p)
-0.535 (-4.138)
R2
Critical level
0.670
0.507
Type 1
Type 2
Type 1
Type 2
0.1
1
18
1
16
0.2
3
11
3
12
0.3
4
5
4
6
0.4
5
4
5
4
0.5
7
3
7
2
0.6
7
2
7
2
0.7
8
1
9
1
0.8
8
0
9
0
0.9
11
0
11
0
Total number of rescheduling:
11
H. Lloyd-Ellis
70
et al. / Predicting the quantity of LDC debt rescheduling
Table lb Semi-annual
results (t-values
Parameters
in parentheses).
Type 2 Tobit Heckman
FIML
method
Selection equation CONSTANT
- 2.526 (-6.118)
TLA
MT
UT
UA
0.065
0.063
(2.527)
(2.097)
2.082
2.015
(3.655)
(3.464)
2.896
2.869
(3.877)
(3.911)
- 2.510 ( - 4.084)
RESQUOT
- 0.052 (-
1.825)
NOR
VOR
WA GP
1.455)
DUM
R2 Regression equation CONSTANT
1.739)
-0.018 (-
1.251)
0.010
0.009
(1.568)
(1.327)
0.805
0.817
(4.891)
(4.916)
0.197
0.199
- 0.090
- 0.091 ( - 0.467)
RESQUOT
WAM
0.645
0.639
(2.724)
(2.184)
0.025
0.025
(1.691)
(1.785)
0.002
0.002
(2.112)
(1.897)
- 0.083 (-
1.206)
Sigma ((T)
0.249 (3.118) - 0.325 (- 11.513)
Rho(P) R2
- 0.017 (-
( - 0.550)
ST
Mills ratio
0.081 (2.338)
-0.019
WAM
- 0.051 ( - 1.277)
0.084
1.946)
(-
- 2.529 (-4.585)
(2.501) -0.018 (-
- 2.490 (-5.177)
0.752
0.721
H. Lloyd-Ellis
11
et al. / Predicting the quantity of LDC debt rescheduling
Table lb (continued) Critical level
Type 1
Type 2
Type 1
Type 2
0.1
12
152
13 29 42 50 58 68 69 69 69
156 65 42 16 9 6 0 0 0
28 0.2 43 0.3 50 0.4 58 0.5 68 0.6 69 0.7 69 0.8 69 0.9 Total number of reschedulings: 69
68 43 16 9 3 1 0 0
set of both conventional macro-variables and balance-sheet variables and sequentially eliminated the insignificant variables. Our preferred probit equation (see Table la) contains the rate of growth of export volume (PEXP), together with the balance-sheet variables ST, AT, TLA, and RESQUOT. The coefficients accord with our interpretation regarding financial crises, with a deteriorating cash flow position (falling RESQUOT) leading to a build-up of short-term debt (ST) and an increase in bank borrowing relative to deposits (TIA). However, of the many variables considered for the equation explaining the quantity of rescheduling, only the ratio of short-term to total bank debt was important. It may be thought that we are effectively estimating an identity if only short-term debt is rescheduled; however, note that the right-hand side variable is lagged one period and that in practice it is not necessarily the short-term component of debt which is rescheduled, but rather the medium and longer-term debt of any country. The Mills ratio is not significant but in the joint estimation p is very important with a t-value of over 4. In the only similar study of which we are aware, Dudley and Montmarquette (1976) investigate US foreign aid policy assuming the independence of e, and u,. This is clearly unlikely in practice, as our results indicate. Further we find that both quantity equations explain over 50% of the variation in the rescheduled quantities despite the fact that only one economic variable is present. These compare favourably with the fit achieved for the study of US aid policy mentioned above, and must be considered very satisfactory for a mixed cross-section/ time-series model without fixed effects. An evaluation of the predictive capability of models involving qualitative variables depends crucially on (i) an examination of the type I and type II errors that occur at different probability levels, and (ii) a subjective evaluation of the relative costs of the two types of error. Note that in this context a type I error involves not predicting a rescheduling which occurs, while a type II error involves predicting a rescheduling when one actually did not take place. Previous studies have implicitly ignored the relative costs by choosing a critical value which minimises the sum of the two errors. For the FIML results shown in table la this occurs at critical levels 0.4, 0.5, 0.6 and 0.8, yielding error rates similar to those presented in the survey paper by Saini and Bates (1984). However, this procedure is misleading as it is unlikely to reflect the relative valuations of the two types of errors either by policy makers or by private sector risk analysts. Consider the opportunity costs associated with the two errors: if funds are not lent to a country which is predicted to restructure but, in fact, does not, the opportunity cost will be the interest differential over the next best alternative investment (which may be only a couple of percentage points over the risk-free Treasury rate). This is the opportunity cost of a type II error. On the other hand, the opportunity cost of making a type I error is clearly much greater: at one extreme the borrower could actually
12
H. Lloyd-Ellis
et al. / Predicting the quantity of LDC debt rescheduling
default, though as yet restructuring usually involves deferment of interest and/or amortisation payments. Hence selecting models by minimising the sum of the type I and type II errors [as in Feder and Just (1977) and others] may be quite misleading. 3.2. Semi-annual
results
From the annual results it would appear that the traditional variables do not add greatly to the model once the balance-sheet variables are present, In any case many of the traditional economic variables are not available on a six-monthly basis. For the semi-annual model we include variables to capture global attitudes to rescheduling together with our balance-sheet variables. Again we begin from a general model containing a wide range of balance-sheet and ‘global’ variables and simplify sequentially to obtain a sensible and data consistent significant relationship. Table lb contains both the FIML and Heckman two-step estimates of our model: the selection equation includes total bank borrowing relative to total deposits (TM); foreign exchange reserves relative to the IMF quota (RESQUOT); the proportion of medium-term to total bank debt (MT); undisbursed credit commitments divided by total bank lending to that country (UT); and unallocated credit divided by total lending to a country (UA); together with the four ‘global’ or ‘herd’ variables NOR, VOR, WAGP and WAM. A dummy variable (DUM), consisting of ones in the two periods following a rescheduling, captures the changed financial position of a country immediately after a rescheduling. The regression equation to explain the quantity of rescheduling now includes the short-term to total debt ratio (ST), the reserves to IMF quota ratio (RESQUOT), and the weighted average of maturity periods on new rescheduling, WAM. The Mills ratio is once more not significant but again we have a highly significant negative value for p from the FIML estimates. The quantity equations now explain over 70% of the variations in rescheduled quantities which is rather startling given the heterogeneous nature of the countries involved in the exercise and the fact that the data is mixed cross-section/time-series. If we wish to minim&e the sum of type I and type II errors we again find our error rates compare favourably with the literature [see Saini and Bates (1984)].
4. Conclusion We have estimated a Type 2 Tobit model to explain the timing and quantity of LDC debt rescheduling using both Heckman’s two-step method and FIML. We are able to explain up to 75% of the variation in the quantity rescheduled using a simple parsimonious model. This information can add greatly to that provided by simple predictions of the probability of rescheduling given by logit or probit models.
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Heckman, J.J., 1979, Sample selection bias as a specification error, Econometrics 47, 153-162. International Monetary Fund, Various issues, Capital markets reports, various issues (IMF, Washington, DC). Kindleberger, C.P., 1978. Manias, panics and crashes (Basic Books, New York). Lloyd-Ellis, H., G.W. McKenzie and S.H. Thomas, 1989, Using country balance sheet data to predict debt rescheduling. Economics Letters 31, no. 2, 173-177. Minsky, H.P., 1982, Inflation, recession and economic policy (M.E. Sharpe, New York). Saini, K.G. and P.S. Bates, 1984, A survey of quantitative approaches to country risk analysis, Journal of Banking and Finance 8. 357-370.