Each term can then be modelled using specific and tailored formulations. For instance, inflows are typically provided using assumptions from the budget plan. On the other side, outflows may be derived using hazard rate models, and increases and decreases using classical time series methods. In the process, it is still possible to separate the core balances which are likely to be unaffected by change in rates. It is also advised to perform the modelling at product level, since transactional and non-transactional accounts will have a very different behaviour. The set of explanatory variables may be extended to include customer information (e.g. age, behaviour), macro-economic factors such as the inflation, and even features of agent-like models (such as the difference in return between different investment opportunities). The models are nevertheless likely to differ significantly from one institution to the other, because the amount of deposits is largely driven by behavioural factors.
Finally, it should be noted that the distinction between the different components in the deposit flows depends on two hidden assumptions:
- The level at which the accounts are aggregated. If the aggregation (the parameter k) is performed at the customer level, transfers between different accounts of the same customer will not appear in increases and decreases.
- The frequency at which the balances are recorded. For retail sight deposits, a daily frequency is likely to provide a totally different split than a monthly frequency.
Different model formulations are also possible. For instance, using ECM has the advantage of introducing a target deposit level that each customer will try to achieve. This feature is interesting for transactional accounts and savings account, since clients tend to keep a fixed safety buffer on their overnight accounts and to invest the excess money in more lucrative financial instruments (e.g. stocks, bonds, funds, etc.). Otherwise, a seasonally adjusted ARIMA model may provide a more general framework.
In order to illustrate the type of problems one can face in volume modelling, we designed a model for the total amount of overnight and time deposits in Hungary, retrieved from the statistical data warehouse of the MNB1. A key feature of these time series is the apparent outflow from time deposits to overnight deposits taking place from 2013 onwards. In order to capture it, the following explanatory variables were included in the model:
- Principal components of the market swap and government curves
- Consumer Price Index, in order to work with constant prices. The drawback of including inflation is that it now needs to be forecasted conditional on the market interest rate scenario, which requires another econometric model.
- The difference between the client rate paid on time deposits and overnight deposits. Indeed, the outflow of time deposit is strongly correlated to a tightening of the spread between these two rates. When the premium paid on time deposits drops below 2%, volumes begin to decrease. The effect is non-linear, so the variable is transformed using a stepwise linear transformation.
- A dummy variable for the month of December, to account for year-end premiums.
1. Hungarian Central Bank
A vector error correction model was retained, whose results are reported in Figure 10 (dotted lines are out of sample predictions starting from 2005 onwards). The model perfectly captures the increase in in time deposits in end 2008, and the flows between the different type of deposits from 2013 onwards.