29 October 2007

Credible threats, moral hazard and Northern Rock

Continuing last week's post on game theory

Entry deterrence

'Entry deterrence' is an example of trying to manipulate a rival player's moves. In this case, it involves an incumbent firm trying to prevent the entry of potential rivals into a market.

Successful entry deterrence depends on avoiding the non-credible threat problem. If you want to make things too difficult for a potential entrant to bother entering, you have to do so in a way which binds you, i.e. you have to commit to a particular strategy. This has to involve ex ante (i.e. prior to the other player’s move) and irreversible action which prima facie is suboptimal for player 1 (and therefore is said to be ‘strategic’, i.e. undertaken only for the purposes of affecting the other player’s behaviour) but which ultimately pays because it succeeds in deterring entry.

Excess (in the sense of surplus) capacity is not an effective way of deterring entry; in fact it represents a non-credible-threat. An incumbent would never expand capacity in response to entry, he would always contract. (Unless there is imperfect information, in which case he may try to convince the other player he is irrational.) However, over-investment in capacity may succeed in deterring entry. This is the Dixit* model in which the incumbent invests irreversibly to expand the capacity at which he can produce at low marginal cost, beyond what he would do left to himself. The point is that this results in a post-entry equilibrium in which his output is higher than what it would have been, and the entrant’s lower — indeed, so low that the latter can’t cover its fixed cost.

Moral Hazard

'Moral hazard' arises when player A wishes to contract with player B for the performance of a variable task by B, the outcome of which will depend partly on (i) B's effort and partly on (ii) random factors, and where it is impossible to ascertain how much the outcome is due to (i) versus (ii). The problem is that B does not have as much incentive to perform as would be optimal. In the case of theft insurance, for example, the insured does not have the ideal level of incentive to protect his property because the insurer cannot monitor what he does, and he will therefore tend to under-protect it.

There is a connection between credible threats and moral hazard. To avoid moral hazard, A wants B to believe there will be penalties for indulging in 'immoral' behaviour. However, the threat to penalise errant behaviour has to be credible. Either the penalty has to be unavoidable, e.g. criminal legal sanctions, or it has to be somehow in A's interests to apply it. The problem is that the application of a punishment is not usually intrinsically beneficial for the punisher. One possible way out is through reputation: if A's reputation for truth-telling and toughness is valuable to A, then A announcing publicly that a penalty will be imposed could lead to a cost for A if he then fails to implement. In this way, the threat to punish would become credible.

Applying this to the Bank of England, a threat not to bail out a bank in trouble except in very limited circumstances is at risk of not being credible and therefore of not being effectual, unless reneging on the threat can be regarded as somehow costly for the Bank. However, it is not clear how the Bank, or any of its agents, could suffer from the failure to penalise an errant lender. Possibly when the Bank was still relatively controlled by the government (pre-1997), the desire of the ruling party to be re-elected could have provided such an incentive.

When there is imperfect information about whether the failure to carry out a threat is costly for the threatener, it is possible for the threat to be credible by exploiting uncertainty. However, once a player has reneged on his threat without obvious negative repercussions, the possibility of future credible threats is more or less eliminated.

* Dixit, A. (1980) 'The Role of Investment in Entry Deterrence', Economic Journal 90, 95-106.

22 October 2007

A short introduction to game theory

In game theory, we are usually looking for one or more equilibria (ideally only one), which we regard as representing the likely outcome of a particular situation. The principal criteria which an equilibrium is expected to satisfy are the Nash equilibrium condition and 'subgame perfection'.

Dominant strategies

We can write the strategy of player i as si. By strategy we mean a particular move or policy, e.g. “produce low output” (collude), or “cooperate if and only if the other player did so the previous round” (trigger).

We can write the payoff to player 1
if player 1 plays s1 and player 2 plays s2
as u1(s1,s2).

If u1(s1A,s2) < u1(s1B, s2) for all possible s2 and some s1B
(i.e. whatever player 2 does, it is possible for player 1 to do better than s1A)
then s1A is a dominated strategy.

If a strategy remains after iterative removal of all dominated strategies, it is a rationalisable strategy.

If there is only one rationalisable strategy, it is the dominant strategy (e.g. “defect” in the Prisoner's Dilemma game).

Nash Equilibrium

For n players, (s1*,s2*,…,sn*) is a Nash equilibrium (NE) if and only if:
ui(s1*,s2*,…,si*,…,sn*) ³ ui(s1*,s2*,…,si,…,sn*) for all si and all i.

All NEs consist of rationalisable strategies, but not all combinations of rationalisable strategies are NEs.

All combinations of dominant strategies are NEs, but not all NEs consist of dominant strategies.

Mixed strategy equilibrium

A mixed strategy is a probability distribution over strategies. I.e. a given player is playing each of his possible strategies with some probability. For example, firm A produces high output with 40% probability and low output with 60%, and firm B similarly mixes these strategies, but in the ratio 70:30. The game may be one-shot, so the point isn’t necessarily that the players alternate between strategies.

In this case the NE consists of optimal probability choices by each player given the probability choices of other players.

Once you allow for mixed strategies then every (finite) game has at least one NE.

Non-cooperative game

In a cooperative game, the rules permit binding agreements prior to play. (Hence collusion would be possible in a one-shot cooperative game.) In practice, we are usually concerned with games in which this is not possible, i.e. a non-coooperative game.

Games of complete information

• Players’ payoffs as functions of other players' moves are common knowledge.
• Each player knows that other players are 'rational' (i.e. payoff-maximising), and knows that they know that he is rational.

Static and dynamic games

In a static (or ‘one-shot’) game, players move simultaneously and only once. In a dynamic game, players either move alternately, or more than once, or both. Bertrand and Cournot models of oligopoly competition are both static games, while the Stackelberg model (firm B moves after firm A) is a dynamic game.

An equilibrium for a dynamic game must satisfy subgame perfection.

Normal and extensive forms

A game expressed in ‘normal form’ is in the form of a payoff matrix, as shown below for the Prisoner's Dilemma game.

A game expressed in ‘extensive form’ shows the ‘tree’ of the possible move paths depending on what each player does at each stage. A dynamic game can only be shown in extensive form.

Repeated games

The same agents repeatedly playing a given one-shot game (“form game”) in sequence is called a supergame. A supergame can consist of either a finite, or an infinite, repetition of a form game. Or we could have a game with a certain probability p of being repeated, i.e. a probability 1 – p of breakdown.

A strategy in this context can be contingent on what other players have done in previous moves.

Subgame perfection

For a dynamic game, some Nash equilibria are not acceptable as solutions because one or more players will want to, and be able to, avoid those outcomes. The subgame perfection criterion demands that, at each stage of the game, the strategy followed is still optimal from that point on.

Non-credible threat

A 'non-credible threat' is a strategy that one player is trying to use to manipulate the behaviour of another (usually via the second move in a sequential game), which forms part of a Nash equilibrium but one that is not subgame perfect.

The strategy is one which is being claimed in some way by the threatening player (e.g. by means of a signal that he is capable of using it) but which is not credible: although the threatened player’s optimal response to the strategy is to do what the threatening player wants, the former knows that by moving first in a different way, the latter will adopt another strategy to generate a different Nash equilibrium.

In a sense, there is no ‘credible threat’ — the term ‘threat’ implies that player 1 will do something specifically designed to harm player 2 if player 2 doesn’t comply, but such a threat would never be carried out in a finite game with perfect information because such a move would not be optimal for player 2. Player 2 will always ‘accommodate’ when it comes to it.

[Next week: applying game theory to Northern Rock & the Bank of England]

8 October 2007

Depreciation and price regulation

Price regulation, for example in the case of a monopoly supplier, often involves determining an acceptable rate of profit. Profit is normally calculated after ‘depreciation’ i.e. taking account of the wearing out of capital assets. It is sometimes suggested that, since depreciation is not a real cost, actual capital expenditure should be used instead to determine the real profit level under different output prices, and hence the acceptable output price. In this article I argue against this approach.

1. The purpose of depreciation

According to Financial Reporting Standard 15 issued by the UK’s Accounting Standards Board, the objective of depreciation is “to reflect in operating profit the cost of the use of the tangible fixed assets (i.e. the amount of economic benefits consumed by the entity)”. The Standard adds that depreciation should be allocated to accounting periods in a way that reflects “as fairly as possible the pattern in which the asset’s economic benefits are consumed by the entity.”

The purpose of depreciation is therefore not to accumulate reserves to finance the future replacement of the assets which are being depreciated. The purchase of an asset is an expense for a company. The choice of accounting treatment is between a full write-off against profits at the time of purchase, and a gradual write-off over the useful life of the asset. In neither case is a corresponding fund set up for eventual replacement.

This view of depreciation, that it represents past rather than future expenditure, is reflected in taxation law. Some form of gradual write-off of past capital expenditure is usually allowed as a deduction in calculating taxable profit. Transfers of profit to fixed asset reserves, on the other hand, are not permitted as deductions. In the UK, this is true both for corporation tax and for petroleum revenue tax. Most other countries’ tax regimes share the same view of depreciation.

2. Return on capital expenditure

The return on a company’s investment in capital expenditure is two-fold. First, the company expects to recoup the capital expenditure over the life of the relevant assets. If it does no more than that, it is simply breaking even. Second, it expects to earn revenue over and above this break-even level during the life of the assets. This additional revenue represents its profit, and is the return on the capital employed.

The first, merely neutral, element in the return on investment is taken into account by deducting depreciation in the calculation of real profit. Hence if depreciation is excluded as a cost in calculating profit, a misleading figure for return on capital is obtained.

3. Financing of asset replacement

There are two principal sources of finance for companies. The more important of the two is internal finance, i.e. a company using its own reserves, represented by cash or short-term investments. Alternatively, a company may obtain external finance, either equity (typically by means of rights issues) or borrowing. Most finance, particularly for fixed asset replacement, is internal.

Typically companies replace fixed assets gradually each year as they wear out, and the asset replacement profile is relatively smooth over time. Since real cashflow exceeds accounting profit by the amount of the depreciation charge, this annual undistributable cashflow excess can be used to finance annual asset replacement. The match between depreciation and fixed asset replacement expenditure is likely to be reasonably close, especially if the current cost accounting form of depreciation is used.

Where the asset replacement profile is not smooth, e.g. where a large asset base is expected to wear out during a relatively narrow time-window (as may happen e.g. with oil or gas pipelines), there are two choices for what to do with the undistributable cashflow excess represented by depreciation.

First, it can be accumulated over a period of years in the form of cash or liquid investments for the purpose of eventual investment in fixed assets. Secondly, the accumulating funds can be invested in long-term projects or business operations in such a way that the funds are potentially ‘tied up’. In that case, external finance may have to be raised when the time comes for the programme of asset replacement. However, subject to capital market imperfections, this should be as efficient a way of financing the programme as the internal accumulation of funds.

A criticism of the first of these two possible approaches is that the purpose of the company from the point of view of its shareholders is to invest available shareholders’ funds in business activities which will earn a better return on those funds than shareholders could do for themselves.

Accumulating large cash or short-term investment reserves is not usually considered appropriate for a company. Companies with large cash reserves are often under pressure from shareholders and analysts to eliminate the reserves in order not to dilute return on capital employed, by using the funds for expansion.

4. Fixed asset reserves

The use of fixed asset reserves to accumulate funds specifically for the purpose of future fixed asset expenditure is not a common business practice in the UK, nor indeed in the rest of Europe or in the US. On the other hand, a company with good financial management will inevitably plan for future cash requirements by appropriate build-up of cash levels or by arranging borrowing facilities in advance.

The closest analogy in UK commercial practice is the use of so-called ‘captive insurance companies’, which are effectively ring-fenced funds designed to provide financial cover for the kinds of eventuality normally insured against, but without the owner of the captive insurance company losing ultimate control over the insurance monies.

5. The effect of price regulation

Where price regulation is based on a target rate of return on capital employed, it is sometimes questioned whether depreciation should be taken into account as an expense in calculating permitted revenue levels. For example, it was argued in relation to TransCo* that, to the extent that depreciation in a period is not matched by expenditure on fixed assets in the same period, allowing depreciation as a cost results in an excessive permitted revenue level.

To the extent that allowed revenue under the depreciation-based approach to setting revenue would exceed allowed revenue under a pay-as-you-go approach [i.e. including current capital expenditure among costs which revenue has to cover], revenue could be considered to be provided to TransCo in advance of its cash requirements. **

However, this argument fails to take into account the point about depreciation made above, namely that it represents a return of initial capital which must be covered by revenue, in addition to any ‘return’ on capital in the sense of profits, for the business to meet its objectives.

Saying that any excess of depreciation over fixed asset expenditure represents a kind of distortion can be used to argue that a justification must be found if the distortion is to be permitted. In the case of TransCo, one justification which has been proposed is that a build-up of such excesses is required to fund an eventual reversal of the situation, i.e. that in due course capital needs for fixed asset replacement will exceed depreciation charges. The authors cited above argue against this by claming that, in view of the difficulties in predicting future required fixed asset expenditure,

the uncertainty associated with the level of future capital spending may well mean that the case for any revenue advancement is weak.

This is an unsatisfactory argument since what is here called ‘revenue advancement’ is not an active process requiring judgments about the appropriate levels of advancement, but rather a case of passively allowing the existing excesses of depreciation charges over fixed asset expenditure to build up in anticipation of a future investment programme. Uncertainty over the precise amount of expenditure involved in this programme is not sufficient to undermine the validity of such ‘revenue advancement’.

One argument in favour of allowing depreciation rather than expected capital expenditure as a cost in calculating permitted revenue is that the resulting price cap is likely to be much less stable under the latter method. Annual depreciation typically has a much smoother profile over time than capital expenditure.

* now part of National Grid plc

** Arthur Andersen, TransCo 1997 price review, 3.6.

1 October 2007

Charts of the month

These are two charts from Marc Faber's recent lecture 'Gloom, Doom, or Boom?'. The first (source: Ned Davis Research) shows that the last time US debt grew to such stratospheric levels as now was in the 1930s.

The second chart (source: Stifel Nicolaus) suggests that we are due for an upturn in consumer inflation.