Dynamic forecasting of banking crises with a Qual VAR

Figures & data

Table 1. Crisis dates.

IFS Code	Country	Crisis Dates
112	United Kingdom	1974–1976 1984 1991 1995 2007–2014
128	Denmark	1987–1992 2008–2014
132	France	1994–1995 2008–2014
134	Germany	2008–2010
136	Italy	1990–1995 2008–2014
144	Sweden	1991–1994 2008–2010
158	Japan	1992–2001
172	Finland	1991–1994
184	Spain	1977–1985 2008–2014
193	Australia	1989–1992
199	South Africa	1977–1978 1985 1989
233	Colombia	1982–1987 1998–2000
238	Costa Rica	1987–1991 1994–1996
273	Mexico	1981–1982 1993–1997
542	Korea Republic	1985–1988 1997–2000
566	Philippines	1981–1987 1997–2001
578	Thailand	1979 1983–1987 1996–2000
964	Poland	1991–1995

Figure 1. Posterior mean of latent banking crisis indicator with end-of sample forecasts and 68 percent probability interval.

Figure 3. Forecast error variance decomposition by sector for each country.

Figure 4. Out-of-sample forecasts: ROC curves.

Figure 2. Posterior mean of latent banking crisis indicator with end-of sample forecasts and 68 percent (95 percent where specified) probability interval: Robustness check.

Table 2. Out-of-sample forecasts of banking crisis probabilities.

	South Africa 1989		United Kingdom 1991		Colombia 1998-2000		Philippines 1997-2000
Date	Probability	Crisis	Probability	Crisis	Probability	Crisis	Probability	Crisis
t - 3	0.239	0	0.127	0	0.370	0	0.453	0
t - 2	0.338	0	0.230	0	0.697	0	0.718	0
t - 1	0.423	0	0.318	0	0.785	0	0.669	0
t	0.527	1	0.398	1	0.818	1	0.702	1
t + 1	0.576	1	0.455	1	0.833	1	0.685	1
t + 2	0.568	1	0.480	1	0.817	1	0.703	1
t + 3	0.560	1	0.515	1	0.794	1	0.722	1
t + 4	0.564	0	0.540	0	0.766	1	0.717	1
t + 5	0.551	0	0.547	0	0.752	1	0.720	1
t + 6	0.530	0	0.575	0	0.737	1	0.718	1
t + 7	0.517	0	0.586	0	0.710	1	0.721	1
t + 8	0.486	0	0.604	0	0.691	1	0.712	1
	Korea 1997–2000		Costa Rica 1994–1996		France 2008–2014		Spain 2008–2014
Date	Probability	Crisis	Probability	Crisis	Probability	Crisis	Probability	Crisis
t - 3	0.043	0	0.000	0	0.495	0	0.042	0
t - 2	0.050	0	0.242	0	0.702	0	0.188	0
t - 1	0.043	0	0.335	0	0.726	0	0.218	0
t	0.083	1	0.370	1	0.756	1	0.287	1
t + 1	0.142	1	0.392	1	0.800	1	0.302	1
t + 2	0.189	1	0.387	1	0.802	1	0.347	1
t + 3	0.238	1	0.393	1	0.797	1	0.396	1
t + 4	0.278	1	0.397	1	0.814	1	0.418	1
t + 5	0.321	1	0.404	1	0.822	1	0.445	1
t + 6	0.352	1	0.382	1	0.827	1	0.454	1
t + 7	0.385	1	0.380	1	0.823	1	0.458	1
t + 8	0.407	1	0.399	1	0.818	1	0.471	1
	Sweden 2008–2010		Italy 2008–2014		Denmark 2008–2010		Japan control, 2008–2010
Date	Probability	Crisis	Probability	Crisis	Probability	Crisis	Probability	Crisis
t - 3	0.152	0	0.087	0	0.177	0	0.000	0
t - 2	0.432	0	0.393	0	0.197	0	0.113	0
t - 1	0.414	0	0.459	0	0.237	0	0.115	0
t	0.471	1	0.469	1	0.256	1	0.162	0
t + 1	0.404	1	0.443	1	0.273	1	0.165	0
t + 2	0.422	1	0.437	1	0.281	1	0.171	0
t + 3	0.378	1	0.439	1	0.299	1	0.173	0
t + 4	0.383	1	0.445	1	0.309	1	0.191	0
t + 5	0.331	1	0.434	1	0.318	1	0.186	0
t + 6	0.343	1	0.438	1	0.332	1	0.187	0
t + 7	0.302	1	0.435	1	0.354	1	0.184	0
t + 8	0.313	1	0.428	1	0.357	1	0.178	0
	Mexico control, 2008–2010		Thailand control, 2008–2010		Poland control, 2008–2010		Australia control, 2008–2010
Date	Probability	Crisis	Probability	Crisis	Probability	Crisis	Probability	Crisis
t - 3	0.002	0	0.000	0	0.000	0	0.000	0
t - 2	0.077	0	0.000	0	0.117	0	0.000	0
t - 1	0.113	0	0.000	0	0.168	0	0.000	0
t	0.153	0	0.000	0	0.122	0	0.000	0
t + 1	0.160	0	0.000	0	0.142	0	0.000	0
t + 2	0.157	0	0.000	0	0.142	0	0.000	0
t + 3	0.181	0	0.000	0	0.148	0	0.000	0
t + 4	0.189	0	0.000	0	0.134	0	0.000	0
	Mexico control, 2008–2010		Thailand control, 2008–2010		Poland control, 2008–2010		Australia control, 2008–2010
Date	Probability	Crisis	Probability	Crisis	Probability	Crisis	Probability	Crisis
t + 5	0.203	0	0.000	0	0.152	0	0.000	0
t + 6	0.205	0	0.001	0	0.145	0	0.002	0
t + 7	0.218	0	0.002	0	0.153	0	0.006	0
t + 8	0.225	0	0.003	0	0.159	0	0.015	0

Table 3. In-sample probit forecasts.

	Predicted Condition
True Condition		Positive	Negative
	Positive	74%	26%
	Negative	46%	54%

Table 4. Out-of-sample Qual VAR forecasts.

	Predicted Condition
True Condition		Positive	Negative
	Positive	93%	7%
	Negative	25%	75%

Table 5. Out-of-sample probit forecasts.

	Predicted Condition
True Condition		Positive	Negative
	Positive	52%	48%
	Negative	34%	66%

Table 6. Out-of-sample forecasts: AUROC results.

	Qual VAR			Binomial
	Full Sample	Emerging Markets	Developed Economies	Probit Model
Mean	0.850	0.887	0.827	0.666
CI Lower Bound	0.797	0.813	0.746	0.591
CI Upper Bound	0.904	0.962	0.907	0.741
Standard Error	0.027	0.038	0.041	0.038

Upper and lower bounds are based on 95 percent confidence intervals. Variance of AUC is defined by DeLong, DeLong, and Clarke-Pearson (1988) and estimated with algorithm specified by Sun and Weichao (2014).

Table A1. Variables and transformations.

Variable	Definition	Category	Source
LRGDP	Annualized real gross domestic product growth, in logs	Real	IFS
LRPCE	Annualized real consumption expenditure growth, in logs	Real	IFS
LRFCF	Annualized real fixed capital formation growth, in logs	Real	IFS
BD	Ratio of bank deposits relative to gross domestic product	Banking	IFS
BC	Ratio of bank credit to private sector to gross domestic product	Banking	IFS
BR	Reserves as ratio to gross domestic product	Banking	IFS
LCPI	Annualized consumer inflation growth, in logs	Banking	IFS
RIR	Real interest rates	Banking	IFS
LRER	Annualized real exchange rate growth, in logs	External	IFS
TOT	Imports to exports as proxy for terms of trade	External	IFS
LRE	Annualized real exports growth, in logs	External	IFS

Table A2. Unit-root tests.

ADF – Fisher Test (Levels)
Variable	Specification	Inverse chi-squared	Inverse normal	Inverse logit t	Modified inv. chi-squared
LRDGP	c,4	91.655***	−5.606***	−5.924***	7.456***
LRPCE	c,4	176.912***	−9.811***	−12.146***	18.114***
LRFCF	c,4	130.472***	−7.895***	−8.849***	12.309***
BD	c,4	24.184	1.623	1.511	−0.976
BC	c,4	23.066	3.212	3.742	−1.116
BR	c,4	62.092***	−1.634**	−2.212**	3.761***
LCPI	c,4	64.881***	−3.750***	−3.790***	4.110***
RIR	c,4	42.918*	−1.745**	−1.684**	1.364*
LRER	c,4	191.417***	−10.186***	−13.111***	19.927***
TOT	c,4	46.622**	−1.439*	−1.306*	1.827**
LRE	c,4	188.645***	−10.605***	−13.024***	19.580***
Phillips-Perron – Fischer Test (Levels)
LRDGP	c,4	984.373***	−29.573***	−68.251***	119.046***
LRPCE	c,4	1046.933***	−30.706***	−72.589***	126.866***
LRFCF	c,4	787.818***	−25.543***	−54.623***	94.477***
BD	c,4	25.729	1.790	1.640	−0.783
BC	c,4	85.513***	0.313	−2.104**	6.689***
BR	c,4	42.572*	−0.592	−0.574	1.321*
LCPI	c,4	498.250***	−19.005***	−34.536***	58.281***
RIR	c,4	62.686***	−3.687***	−3.591***	3.835***
LRER	c,4	676.290***	−23.315***	−46.867***	80.536***
TOT	c,4	152.946***	−7.071***	−9.457***	15.118***
LRE	c,4	1041.946***	−30.667***	−72.243***	126.243***

Unit root tests are constructed using Augmented Dicky-Fuller (see Hamilton, 1994) and Phillips and Perron (see Phillips & Perron, 1988) procedures. Based on Choi (2001), four different methods are assessed to test the null hypothesis of a unit root across all panels, through an inverse, inverse-normal, inverse-logit transformation and a modification of the inverse transformation of the p-values. The latter is appropriate for N → ∞.

Table A3. Out-of-sample prediction dates.

IFS Code	Country	Crisis	No-Crisis
112	United Kingdom	2007–2014
128	Denmark	2008–2014
132	France	2008–2014
134	Germany		2013–2016
136	Italy	2008–2014
144	Sweden	2008–2010
158	Japan		2008–2014
172	Finland		2013–2016
184	Spain	2008–2014
193	Australia		2008–2014
199	South Africa	1989
233	Colombia	1998–2000
238	Costa Rica	1994–1996
273	Mexico		2008–2014
542	Korea Republic	1997–2000
566	Philippines	1997–2001
578	Thailand		2008–2014
964	Poland		2008–2014

A selection of countries that did not experience banking distress during the Global Financial Crisis (GFC) serve as control group for out-of-sample testing. In the case of Germany and Finland, a more recent period is selected to test applicability of out-of-sample predictive power, particularly during the European sovereign debt crisis.

Table A4. Out-of-sample forecasts of banking crisis probabilities: robustness check.

Germany, control, 2013–2015
	Burn 300; Draw 1,200	Burn 1,000; Draw 1,200	Burn 300; Draw 2,000	Burn 1,000; Draw 2,000
Date	Probability				Crisis
t - 3	0.000	0.000	0.053	0.000	0
t - 2	0.013	0.005	0.092	0.038	0
t - 1	0.072	0.013	0.140	0.070	0
t	0.097	0.040	0.180	0.146	0
t + 1	0.134	0.054	0.207	0.145	0
t + 2	0.148	0.086	0.235	0.203	0
t + 3	0.196	0.116	0.251	0.209	0
t + 4	0.219	0.141	0.295	0.249	0
t + 5	0.263	0.165	0.305	0.240	0
t + 6	0.256	0.189	0.337	0.281	0
t + 7	0.282	0.213	0.350	0.272	0
t + 8	0.285	0.214	0.353	0.311	0
Finland, control, 2013–2015
	Burn 300 Draw 1,200	Burn 1,000; Draw 1,200	Burn 300; Draw 2,000	Burn 1,000; Draw 2,000
Date	Probability				Crisis
t - 3	0.029	0.000	0.011	0.012	0
t - 2	0.048	0.003	0.020	0.021	0
t - 1	0.122	0.009	0.040	0.066	0
t	0.116	0.013	0.051	0.071	0
t + 1	0.142	0.021	0.069	0.098	0
t + 2	0.133	0.026	0.073	0.105	0
t + 3	0.144	0.027	0.075	0.122	0
t + 4	0.147	0.030	0.075	0.128	0
t + 5	0.150	0.032	0.086	0.137	0
t + 6	0.159	0.043	0.092	0.140	0
t + 7	0.157	0.048	0.102	0.149	0
t + 8	0.144	0.052	0.100	0.148	0
	Germany, control, 2013–2016			Finland, control, 2013–2016
Date	Probability		Crisis
t - 3	0.000		0	0.053
t - 2	0.031		0	0.060
t - 1	0.053		0	0.075
t	0.119		0	0.086
t + 1	0.128		0	0.105
t + 2	0.171		0	0.108
t + 3	0.172		0	0.122
t + 4	0.217		0	0.126
t + 5	0.237		0	0.130
t + 6	0.268		0	0.139
t + 7	0.277		0	0.154
t + 8	0.279		0	0.159
t + 9	0.290		0	0.000
t + 10	0.282		0	0.000
t + 11	0.260		0	0.000
t + 12	0.259		0	0.000

Table A5. Probit model results.

Probit Results
No. of observations:	1,200
Constrained log-likelihood:	−732.187
Max. log-likelihood:	−653.420
LR-chiˆ2:	157.53***
AIC:	1.109
BIC:	−7116.170
Variable	dy/dx
LRDGP	0.440 (0.745)
LRPCE	0.175 (0.560)
LRFCF	−0.761 (0.389)***
BD	0.462 (0.071)***
BC	−0.335 (0.048)***
BR	−0.016 (0.003)***
LCPI	6.801 (2.040)***
RIR	0.027 (0.006)***
LRER	−3.636 (0.309)***
TOT	0.000 (0.000)***
LRE	−0.363 (1.072)

Margins with standard errors in brackets, *** 1% level of significance

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