After having selected the boom and bust periods the three different phases demand the use of ordered probit or logit model. Since the logit approach has advantages to detect extreme cases we use ordered logit models which are a limited dependent variable model to predict these different phases of financial development. The explanatory variables are not transformed into dummy variables but are included in a linear fashion. The probability that extreme situations (booms or busts) occur is assumed to be a function of a vector of explanatory variables.

Where yt is the financial development dummy series and xt a set of explanatory variables, b is a vector of free parameters to be estimated and F is the logistic distribution function which ensures that the predicted outcome of the model always lies between 0 and 1. The direction of the effect of a change in xt depends on the sign of the b coefficient. The coefficients estimated by these models cannot be interpreted as the marginal effect of the independent variable on the dependent variable as b is weighted by the factorf the logistic density function that depends on all regressors.

Thus the sign of b shows the direction of the change in the probability of falling in the bust phase, when xt changes. Pr(yt =1) changes in the opposite direction of the sign of b, while Pr(yt =3) (boom phase) changes in the same direction as that of the sign of b. Hence a positive coefficient in the model may be interpreted that the corresponding variable has potential in raising the predictive probability of booms.

The empirical analysis in this paper will be based on the second approach and make use of pooled ordered logit techniques. As already mentioned, the fundamental variables are grouped into monetary, real and financial variables categories, and specified in form of either annual or quarterly growth rates and/or as deviations from a trend and/or as ratios to GDP.

Applying logit techniques for our unbalanced data set enables us to estimate the probability of occurrence of a composite indicator development in the next quarter. In order to compare the performance across the several ordered logit models, we are looking at the significance of the coefficients and the pseudo R2 As for the next step regarding the ordered logit estimations, we start off from the models selected in Gerdesmeier, Reimers and Roffia and test different lags for all the explanatory variables. In a subsequent step, we tested the inclusion of several measures of interest rates (spread, short and long-term interest rates) and finally we tested the significant of other variables, such as real GDP and stock prices. Table 1 presents the results of the preferred specification which includes credit growth gap, house price growth gap, house price changes, inflation rate, the interest rates spread and the stock price growth.10 Concentrating on the boom phases to explain the sign of the coefficients the estimate confirm that an increase of the lending-gap positively influence the occurrence of a boom period. This is in line with results of Borio et al and Gerdesmeier et al. Moreover, raises in house price gaps, in house prices and stock prices positively affect the probability of booms. To some extent it presents persistence in the markets and confirms results of Candelon et al. The positive coefficient of the spread variable may be explained by link of the financial market to the real economy. A positive difference between the short term rate and the long term rate shows the expansive stance of monetary policy. This affects the aggregate demand of the economy. Economic agents may increase the investment in the house markets and the increase in aggregate demand expands the profits of companies, which both influence our financial indicator. The coefficient of the inflation rate is negative and do not fuel the boom periods. It is worth noting that the growth rate of GDP or the investment-output-ratio have no significant coefficient. These variables are deleted. This notwithstanding, the coefficient values are not as intuitive to interpret. In fact, eq.(9) shows that the coefficients are not constant marginal effects of the variable on boom probability since the variable’s effect is conditional on the values of all other explanatory variables. Rather, the slope-coefficients represent the effects of Xt the respective right-hand variables when all other variables are held at their sample means. The pseudo R2 is 0.16.

As regards the threshold value of the probability, designing a good forecasting model requires balancing the number of false alarms and the number of failures. In general, the value depends on the costs related to the two different types of errors and their assessment by the policy maker. In this section, we use the maximum of predicted probability to determine the existence of a category. Using this decision rule the number of correct calls is 3.9% of busts, 98.7% of normal and 14.3% of booms, respectively. It is apparent that this decision rule prefers the normal situation. It will be helpful if the decision maker gives all situations the same weight. In section 4.3 the issue will be discussed more deeply.

**Table 1. Results of the preferred specification**

Variable | Coefficient | Standard error | z-Statistic |

D4 ncl gap 1 | 0.404 | (0.074) | 5.447 |

D4 ncl gap 2 | -0.320 | (0.072) | 4.396 |

D4 nhp gap 1 | 0.087 | (0.014) | 6.077 |

D1 nhp 1 | 0.200 | (0.029) | 7.000 |

D1 nhp 4 | -0.059 | (0.030) | 1.985 |

D4 n sto 1 | 0.034 | (0.004) | 7.744 |

D4 n sto 2 | -0.019 | (0.004) | 4.482 |

Spread 1 | 0.084 | (0.025) | 3.298 |

D1 hicp 1 | -0.340 | (0.051) | 6.627 |

Limit 2 | -2.986 | ||

Limit 3 | 2.646 | ||

Pseudo R2 | 0.162 |