THE ECONOMETRICS OF MACROECONOMIC MODELLING
An example: modelling the household sector
The complete Haavelmo distribution function—for example, the joint distribution (2.1) of all variables of the macro model—is not tractable and hence not an operational starting point for empirical econometric analysis. In practice, we have to split the system into subsystems of variables and to analyse each of them separately. Joint modelling is considered only within subsystems. But by so doing, one risks ignoring possible influences across the subsystems. This would translate into invalid conditioning (the weak exogeneity assumption is not satisfied) and invalid marginalisation (by omitting relevant explanatory variables from the analysis), which are known to imply inefficient statistical estimation and inference. The practical implementation of these principles is shown in an example drawn from the modelling of the household sector of the RIMINI model (see Chapter 1).
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The process of sequential decomposition into conditional and marginal models is done repeatedly within the subsystems of RIMINI. In the household sector subsystem, total consumer expenditure, cht, is modelled as a function of real household disposable income, yht, and real household wealth, wht. (Here and in the rest of the book, small letters denote logs of variables.) Total wealth consists of the real value of the stock of housing capital plus net financial wealth. The volume of the residential housing stock is denoted Ht and the real housing price is (PH)t/Pt, where Pt is the national accounts price deflator for total consumption expenditure. The sum of net real financial assets is equal to the difference between real gross financial assets and real loans (Mt — Lt), yielding
The joint distribution function for this subsystem can be written as (2.1) with xt = (cht, yht, wht). The conditional submodel for total real consumer expenditure cht (Brodin and Nymoen 1992—B&N hereafter), is
Dcy, w (cht I yht, wht; ^c)?
relying on the corresponding conditional density function, (2.4), to be a valid representation of the DGP. RIMINI contains submodels for yht and for all individual components in wht. For example, the conditional submodel for simultaneous determination of housing prices, pht, and real household loans, lt, is
Dwy (pht, lt I RLt, yht, ht—1; ^w ),
where RLt denotes the interest rate on loans, and conditional submodels for the net addition to housing capital stock Aht, and the price of new housing capital, phnt
Dah (Aht I pht, phnt, RLt, yht, h—i; ^Ah)
Dphn• (phnt I pht, pjt, ht-1; phn), where pjt is the deflator of gross investments in dwellings.
