RDP 8713: Estimating the Inflationary Effects of Depreciation 3. The Model of Price Determination

(a) Domestic Prices

A commonly-used approach in many studies of inflation is the mark-up model in which price movements simply reflect movements in costs. The approach has the advantage of simplicity in estimation and interpretation.

The mark-up model is obtained as follows. Let the aggregate price of consumer goods (PC_d) be a weighted average of the prices of domestically-produced consumer goods (P_d) and the price in domestic currency of foreign-produced consumer goods (P_f).

P_d can be thought of as a mark-up on costs of production. Let the production function for domestic consumer goods be represented by

where K and L represent capital and labour, respectively, and E represents energy input, along the lines proposed by Helliwell et al. (1982). If F is homogeneous of degree one, then competitive equilibrium requires that

where W is the wage rate, R the rental cost per unit of capital and P_E the price per unit of energy.

This then implies that the unit price is the sum of the unit costs for labour, capital and energy. That is

If several simplifying assumptions are made, as is shown in Appendix 1, the following estimating equation is obtained:

where P_d is the domestic price index, w is average earnings, z the trend growth in labour productivity, p_e a measure of energy prices, p_m import prices and D_t a “demand pressure” variable, as a proxy for short-term fluctuations in returns to capital. All variables are quarterly percentage changes. ε_t is an error term with the usual properties.

The major assumptions implicit in the estimation equation are as follows:

• the mix of inputs in the productive process does not change;
• changes in unit capital costs are only cyclical (and are captured by D), or trend (and are thus picked up by a); and
• the import penetration ratio is constant, when in fact it may, and almost certainly will, vary over time.

The single-equation model employed in this paper treats wages and exchange rates as exogenous. There are, of course, good reasons for endogenising these variables. One reason is that there may be feedback effects from prices to wages. There is some evidence that the dominant causation in the wage-price framework in Australia is from wages to prices and not vice-versa, though this issue is not beyond dispute.^[7]

In the event, a single-equation specification has been used, though the authors remain aware of its shortcomings.

(b) Import Prices

For the purposes of the paper, import prices are assumed to be determined by world prices and exchange rates.^[8] With variables defined in percentage change form,

where p_w is the world price and e the exchange rate measured as units of domestic currency per unit of foreign currency and ε_t is a white noise error term.

Footnotes

See, for example, Boehm and Martin (1986) who investigate the issue using a VAR analysis of six variables (prices, wages, money, import prices, government current expenditure and the rate of employment). They concluded that “…during periods when the Arbitration Commission applied either full or partial wage indexation, wages generally led prices” (p.19). On the other hand, Alston and Chalfant (1987), who included only three variables find evidence of bi-directional causation between prices and wages, and of causation from money to both prices and wages. Interestingly, Boehm and Martin found no direct effect from money to either prices of wages. [7]

An alternative hypothesis is that domestic influences also affect import prices. One hypothesis would be that there is a second class of imports whose prices are determined by the domestic inflation rate. Another hypothesis would be that the speed of adjustment to exchange rate changes is influenced by domestic factors. These hypotheses were tested but there was little evidence of any such effects. In particular, if there is permanent “absorption” from exchange rate changes the hypothesis of full pass-through from world prices and exchange rates should be rejected, but it is not. [8]