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Rotterdam Model

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IV.I.2 The Rotterdam model

For each element i, equation (IV.I.1-26) can be written as (on dropping *)

Rotterdam Model

(IV.I.2-1)

Now we define

(IV.I.2-2)

and

(IV.I.2-3)

The elasticity of marginal consumption can thereby be found by combining (IV.I.2-2) and (IV.I.2-3) as

(IV.I.2-4)

Furthermore, let

(IV.I.2-5)

The definitions in (IV.I.2-3) and (IV.I.2-5) will be used as parameters that have to be estimated. This is possible due to the fact that both sets of parameters are dimensionless invariants over time.

Using (IV.I.1-20), the following vector equation can be easily found

(IV.I.2-6)

and on using (IV.I.1-19), (IV.I.2-3), and (IV.I.1-9) it follows that

(IV.I.2-7)

and consequently, using (IV.I.2-7) and (IV.I.2-3), this yields

(IV.I.2-8)

Equation (IV.I.2-7) is a very important restriction implying that the number of parameters to be estimated can be reduced! This gain in degrees of freedom is considered one of the desired properties of the Rotterdam model.
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