Research Discussion Paper – RDP 22 Inter-related Factor Demands A Preliminary Report


This paper reports on recent experiments to derive inter-related factor demand equations for the Reserve Bank of Australia quarterly econometric model RBA2.

The arguments leading to the inter-related approach to factor demand estimation have been set out in articles by Nadiri and Rosen [6] and Coen and Hickman [1]. In both these studies it is assumed that all desired factor levels are determined by cost minimisation subject to a Cobb/Douglas production function, output demand and relative factor prices. Nadiri and Rosen introduce factor intensities separately and postulate that the production function holds at all times. Coen and Hickman require their production function to hold only for desired factor levels, but require the estimated coefficients in the adjustment equations to give logically consistent estimates of the coefficients of the underlying production function.

The models used in these studies may be modified in a number of fruitful directions. First there is a class of modifications that involves using additional structural information. Among them are:

  1. The investment process in particular involves substantial time delays between the decision, the incurring of costs and the receipt of income. These timing differences cannot be brought into the structure except by expectations over different time horizons.
  2. Prior information on the relative costs and speeds of the different factor adjustment processes can be included.
  3. Supply constraints can be allowed to influence the factor adjustment processes.
  4. Full interdependence can be achieved both for parameter estimates and for factor adjustment paths. Nadiri and Rosen have inter-related factor adjustment paths, but do not require consistent production function parameter estimates. Coen and Hickman force consistent parameter estimates, but have unrelated factor adjustment paths.

A second class of modifications involves generalising the structure. Among these are:

  1. The introduction of different ex-ante and ex-post substitutability between the factors.
  2. The introduction of an elasticity of substitution different from one.
  3. The variation of the factors in the production function, by disaggregating or by including further factors such as inventories.
  4. The introduction of richer expectations processes.

The Canadian and Australian models are attempts to introduce some of these modifications.