Part III. International Liquidity, and the Cost of Currency Crises - Mateusz Szczurek
3.4. Empirical Application
sis much). The second equilibrium is in the point where downward sloping marginal benefit and marginal cost curves cross. The second equilibrium is a global minimum only if L(lt-1)<0. In the example above, it is clearly the optimal level of liquidity: the total gain (which is the surface below the marginal benefit curve) exceeds the total cost.
The model has several advantages:
1. It takes into account not only the obvious costs of liq-uidity, but also the dynamic effects – the costs of postponing the crisis.
2. It is relatively straightforward to estimate. The bene-fit function (logit analysis of the reserves' impact on the probability of the crisis) is deeply rooted in the existing lit-erature on leading crisis indicators. Similarly, data for the depth-of-crisis function, and interest rate premium relation-ship is widely available for a wide range of countries.
3. The model allows for an estimation of the reputation cost of the foreign exchange crisis (which is the only missing data in the whole structure).
probability of a crisis is also (implicitly) reflected in higher yield spreads of the countries involved.
What is the right level of international liquidity to hold? The answer depends very much on the cost of the crisis – on how much the policymakers risk. While the GDP cost of the crisis
may be similar in all exchange rate regimes – capital outflow, real depreciation costs, etc. are also dangerous in a float (yet one could argue that some sort of FX risk illusion keeps the real economy's exposure to the foreign exchange risk larger in fixed exchange rate countries), the reputation cost should be Table 3-2. Probability of currency crisis function
Logit Maximum Likelihood Estimation. The estimation method converged after 6 iterations Dependent variable is Y
80 observations used for estimation from 1 to 80
Regressor Coefficient Standard Error T-Ratio[Prob]
CONST -1.1402 .57917 -1.9687[.053]
LLBIS -.80637 .38436 -2.0979[.039]
REER 3.3720 1.8849 1.7889[.078]
G 8.6119 6.4455 -1.3361[.185]
Factor for the calculation of marginal effects = .10755 Maximized value of the log-likelihood function = -31.3216 Akaike Information Criterion = -35.3216
Schwarz Bayesian Criterion = -40.0857 Hannan-Quinn Criterion = -37.2317 Mean of Y = .17500
Mean of fitted Y = .025000 Goodness of fit = .85000
Pesaran-Timmermann test statistic = -59.4574[.000]
Pseudo-R-Squared = .15571 Table 3-3. Depth of the crisis function
Dependent variable is DEPR
13 observations used for estimation from 1 to 13
Regressor Coefficient Standard Error T-Ratio[Prob]
CONST -.20678.064084 -3.2267[.010]
LLBIS .14495 .051945 2.7904[.021]
REER -.66769 .13472 -4.9560[.001]
G -.14869 .28864 -.51513[.619]
R-Squared .77827 R-Bar-Squared .70436 S.E. of Regression .10170 F-stat. F( 3, 9) 10.5297[.003]
Mean of Dependent Variable -.14778 S.D. of Dependent Variable .18704 Residual Sum of Squares .093085 Equation Log-likelihood 13.6585 Akaike Info. Criterion 9.6585 Schwarz Bayesian Criterion 8.5286 DW-statistic 1.4847
Table 3-4. Domestic-foreign interest rate spread as a function of crisis probability Ordinary Least Squares Estimation
Dependent variable is SPREADS
60 observations used for estimation from 1 to 60
Regressor Coefficient Standard Error T-Ratio[Prob]
CONST 166.4071 227.7070 .73079[.468]
MODEL 2840.6 947.1194 2.9992[.004]
R-Squared .13427 R-Bar-Squared .11934 S.E. of Regression 1124.7 F-stat. F( 1, 58) 8.9954[.004]
Mean of Dependent Variable 692.5000 S.D. of Dependent Variable 1198.5 Residual Sum of Squares 7.34E+07 Equation Log-likelihood -505.6353 Akaike Info. Criterion -507.6353 Schwarz Bayesian Criterion -509.7296
different. In the extreme float case, the central bank ignores the foreign exchange fluctuations, however rapid and large they are, the reputation cost should thus be set to zero.
Another complication arises due to the fact that the govern-ment's loss function is something completely different to the
"economy's loss function". One could argue that what really matters in influencing the policymakers' liquidity preferences are expected fiscal and quasi-fiscal costs of a currency crisis.
Surprisingly, the results of the next section do not sup-port expectations of the strong influence of currency regime on the policymakers' aversion to the currency crises.
The results for the average (from the pool) country are shown in Figure 6. Vertical scale represents optimal liquidi-ty (as a reserves/short-term debt ratio) corresponding to the assumed cost of the currency crisis (as a percentage of GDP).
The results indicate that the IMF's recommendation of keeping foreign exchange reserves stock equal to the
short-term foreign debt is insufficient. Assuming the cost of the crisis at just 1% of GDP, optimal international liquidity is 1.6 times the short term foreign debt. If we believe the crises are more costly than 1% of GDP, the reserves held be a multiple of the short-term foreign debt. It is important to stress that this prescription is applicable to the average country from the sample, and may be sub-optimal for some of the analysed economies (which, for example, suffer from excessively high budget deficit, or exchange rate overvalua-tion).
3.4.3. How Much the Policy Makers Fear the Crisis?
The final empirical application of the model involves find-ing the cost of the crisis as seen (or expected) by the poli-cymaker. Assuming that the amount of international liquidi-ty held by the central banks is rational (in the model sense),
we can find out how much the policymakers fear the cur-rency crisis. The process involves finding out the value of χ (implicit estimation of crisis cost by the policymaker) for which marginal cost curve of the liquidity crosses marginal benefit curve of the liquidity at the level of actually held international reserves.
In the following analysis it sometimes happens that the cost curve has such a shape that it is impossible to find a χ, which would minimise the loss function at the desired level of the international liquidity. In such cases to gain some insight of the possible range of reputation cost χ, we assumed the largest χfor which the total benefit exceeds total cost (both integrated between 0 and the actual inter-national liquidity held).
Table 3-5 shows the summary of the results, cost of the currency crises expected by the governments and central banks of the countries listed, as of end-99. Figure 3-6 shows graphs of the 4Q99 liquidity's marginal cost and benefits curves of the countries in the sample, as well as implicit expected crisis cost – χ(in US$m).
The results show quite a wide disparity of implicit cur-rency crisis cost to the policy makers. Discarding the
Moldova's outlier (which, most probably results from extremely low amount of short term BIS reported debt), the implicit cost estimation by the policymakers varies from 5% of GDP (Malaysia) down to 0.3% (Dominican Republic).
The results seem to have little to do with the exchange rate arrangements, which is somewhat disturbing: apart from Malaysia, the first nine countries on the list have a floating or managed floating exchange rate.
Figure 3-5. Optimal liquidity holding versus cost of the crisis
2 4 6 8 10
% GDP 1
2 3 4 5 LLBIS
Table 3-5. Crisis cost to the policy maker, as of end-99
Country % of GDP US$m
MOLDOVA 43.1% 500
MALAYSIA 12.1% 9500
CZECH REPUBLIC 5.0% 2650
POLAND 3.3% 5220
CHILE 2.7% 1800
SLOVAK REPUBLIC 2.1% 420
KOREA 2.0% 7950
PHILIPPINES 1.8% 1370
SOUTH AFRICA 1.5% 2000
RUSSIA 1.4% 2650
ARGENTINA 1.3% 3730
COSTA RICA 1.2% 175
ECUADOR 0.9% 180
CHINA,P.R.: MAINLAND 0.9% 8600
COLOMBIA 0.8% 710
BRAZIL 0.8% 4150
ROMANIA 0.4% 150
PAKISTAN 0.4% 250
DOMINICAN REPUBLIC 0.3% 50
Argentina χ= 3730
1 2 3 4 5 LLBIS
100 200 300 400 500 600 US$m
Brazil, χ=4150
2 4 6 8Reserves LLBIS
200 400 600 800 1000 US$m
Chile, χ= 1800
1 2 3 4 5 LLBIS
100 200 300 400 500 600 US$m
China (Mainland), χ= 8600
2 4 6 8 LLBIS
-4000 -2000 2000 4000 6000 US$m
Colombia, χ= 710
2 4 6 8 LLBIS
50 100 150 200 US$m
Costa Rica, χ= 175
2 4 6 8 LLBIS
5 10 15 20 25 30 US$m
Czech Republic, χ= 2650
2 4 6 8 LLBIS
25 50 75 100 125 150 175 US$m
Dominican Republic, χ= 50
2 4 6 8 LLBIS
2 4 6 8 10 12 14
US$m Ecuador, χ= 180
2 4 6 8 LLBIS
5 10 15 20 25 30 US$m
Korea (South), χ= 7950
2 4 6 8 LLBIS
200 400 600 800 1000 1200 1400 US$m
Malaysia, χ= 9500
2 4 6 8 LLBIS
200 400 600 800 1000 1200 1400 US$m
Moldova, χ= 500
2 4 6 8 LLBIS
1 2 3 4 5
US$m Pakistan, χ= 250
2 4 6 8 LLBIS
10 20 30 40 50
US$m Philippines, χ= 1370
2 4 6 8 LLBIS
50 100 150 200 250 US$m
Poland, χ= 5220
2 4 6 8 LLBIS
50 100 150 200 US$m
Romania, χ= 150
2 4 6 8 LLBIS
10 20 30 40 50 60 US$m
Russia, χ= 2650
2 4 6 8 LLBIS
50 100 150 200 250 US$m
Slovak Republic, χ= 420
2 4 6 8 LLBIS
10 20 30 40 50 60 70
US$m South Africa, χ= 2000
1 2 3 4 5 LLBIS
50 100 150 200 250 300 US$m
Sample mean, χ= 3200
2 4 6 8 LLBIS
50 100 150 200 250 300 US$m