RDP 9202: Some Tests of Competition in the Australian Housing Loan Market 3. The Conjectural Variations Model

Figure 2 presents a prima facie case that the housing market is only reasonably competitive, with the equivalent of only seven equal sized banks in the market. However, conventional measures of concentration, such as the Herfindahl index, are flawed as indicators of competition because they take no account of the behaviour of the firms (banks in our case) under consideration. Substantial competition can exist in industries with only a few competitors, e.g. the Australian airline industry appears to be very competitive (at present), with only two firms. On the other hand, Ausubel (1991) finds huge monopoly profits in the United States credit card industry, where there are over 4,000 firms!

This point has been well-known for many years to economists working in applied industrial organisation, but it seems to have escaped the notice of many participants in the current debate on the state of Australian banking. The conjectural variations approach (introduced by Bowley 1924) takes into account the behaviour of firms in estimating the degree of non-competitiveness in an industry.

Specifically, consider an n firm industry where each firm chooses its output q_i to maximize its profits Π, defined as revenues less costs,

where P is the industry price (charged by all firms) and Q is industry output.

The first order conditions for this problem are

where dC_i/dq_i is the marginal cost of the i'th firm. Note that

Note that

and that

Thus the quantity produced by firm i, q_i, affects total production in the market directly and indirectly through its effect on the price, P.

The first order conditions can be re-written as

Define

This is the sum of the reactions of all of the other firms in the market to a change in the quantity produced by firm i, as perceived by that firm. With banks, the relevant quantity is the real value of loans in any specified period.^[2]

Several interesting special cases can be derived:

(i) α_i = −1, for all firms. In this case, each firm sets price equal to marginal cost, i.e. perfect competition prevails in the industry. Each firm perceives that any increase in its output will be exactly offset by its competitors, so that industry output (and therefore price) is exogenous to each firm.

(ii) α_i = −1 + 1/S_i, where s_i is the market share of the i'th firm. Here, the reactions are such that each firm tries to maintain a stable market share. This is the case of perfect collusion, or a cartel between the firms. In this case, there is effectively just one firm in the industry, which acts as a profit-maximising monopolist. Substitution of α_i = −1 + 1/S_i into (6) yields

This is the profit maximising condition for a monopolist, i.e. marginal revenue (which is greater than price) equal to marginal cost.

(iii) α_i = 0. In this case, each firm conjectures that its competitors will not (in aggregate) respond to any change in its output. This is the case of a Cournot oligopoly.

Of course, in empirical applications, none of these special cases is likely to arise exactly. The degree of competition can be measured by the adjusted Herfindahl index:

Thus, both the degree of concentration and behaviour determine the measure of competition in the industry. When there is perfect competition (α_i = −1, for all i), then , regardless of the degree of concentration. In the case of perfect collusion (α_i = −1 + 1/s_i, for all i), then , again regardless of the degree of concentration. Only in the case of Cournot oligopoly (α_i = 0, for all i) do the unadjusted and adjusted Herfindahl indices coincide.

The econometric problem is to estimate the parameters α_i. However, some specification issues need to be resolved before estimation can proceed. That is, there are factors other than conjectural variations influence the amount of lending done by banks. The most obvious of these are the return on the loan and the cost of funds, for which we use the relevant housing loan interest rate, and the 90 day bank accepted bill rate, respectively. These interest rates are lagged one period. We also include a constant, eleven seasonal dummy variables and a dummy for the new reporting forms introduced in January 1989. An additional dummy is introduced to account for ANZ's takeover of National Mutual Royal Bank in April 1990.

The theory is also entirely static.^[3] In practice, however, the response of banks to changes in lending by other banks need not occur in the same period. We specify our model so that banks respond to the loans made by their competitors in the previous period (month, in this case).

Obviously, we cannot include every bank, no matter how small, in the model, so we exclude all banks with a market share of less than ten per cent. This leaves us with five banks in the housing loan market: the Commonwealth (CBA), Westpac (WBC), National Australia Bank (NAB), ANZ, and State Bank of Victoria (SBV). Furthermore, since we are not estimating a demand function, the housing interest rate is exogenous in this model.^[4] This means that, given the interest rate, the total value of loans is pre-determined. To take account of this, we introduce a “residual bank” (RES), which is defined as the total market less the five banks above.

The housing model to be estimated is set out in equations 10–15. The subscripts 1…6 refer to CBA, WBC, NAB, ANZ, SBV and RES respectively. Thus, q_1,t is the value of housing loans made by the Commonwealth Bank in period t, q_2,t−1 refers to loans made by Westpac in the previous period etc. The coefficients of main interest are the β_ij, i≠j.

The test for competition is that the following restrictions on the model's coefficients jointly hold:

To test for collusion, −1 is replaced by −1 + 1/s_i (i=1…6), where s₁…s₆ are the shares of each of the six banks in the sample. In the test for Cournot oligopoly the restrictions are that the coefficients sum to zero. These tests involve cross equation restrictions, so we use a systems estimator, iterative seemingly unrelated regressions, to estimate the model.

Footnotes

A limitation of our approach is that the conjectural variations framework assumes that firms compete by varying quantities. In the case of housing loans by banks other forms of competition may also be relevant. Although data for housing loan rates do not appear to vary greatly between banks, they might still compete on price, e.g. by offering lower rates to new borrowers (for a limited time) or by competing on fees. They also compete, to an extent, by offering different products, e.g. fixed versus floating rate mortgages. [2]

There are many dynamic models of oligopoly in the industrial organisation literature; see Shapiro (1989) for a survey. Thus far, however, their testable implications have not been well developed. [3]

We use each bank's own interest rates for housing in their respective equations, except for SBV and RES, for which we use the CBA rate. In practice, there is very little variation in housing interest rates across banks at any point in time. [4]