Folk Theorem

In Brazil, the dynamic of the central bank behavior is a function of inflation dynamic, which in turn is a function of government policy dynamic. In some sense, from the central bank of view, the rate decision is taking the expected government policy as given. On the other hand, the government policy in Brazil is also a function of the central bank’s policy. Given the primary budget target and public debt constraint, the government’s projection must be in line with the central bank rate decision. In some sense, both are facing a non-cooperative dilemma.

The recent program by the government suggests that government expenditure will rise in the next few years. This is feasible only if the central bank’s rate dynamic is in line with the government projection. It is particularly important for the government since its debt dynamic depends on the interest rate dynamics. As the central bank said that debt/GDP ratio will be lower in 2007 mainly because of the decline in interest rate. From the prospect of the government, if government expenditure continues to increase, together with the continuation of rate decline, economic growth will rise, while the debt dynamic will be improved. This is the objective of the government. Of course, the government also needs luck from the benign external environment. Currently, more than 30% of total debt are fixed rate fixed, with average of maturity of about 1 year. Roll over risk is a concern.

From the prospect of the central bank, it takes the government policy as given. Its objective is stable inflation. As mentioned previously, they care mostly on money supply and inflation expectation. Rising government spending will increase the credit growth, hence M2/M3. It also increases inflation expectation. Both lead the bank be more cautious in rate cut. This is the objective of the central bank.

They face a dilemma. By construction, these two institutions are independent. Their jobs are inflation and employment/growth respectively. The government prefers the central bank to be more aggressive in cutting rate. The central bank prefers the government to be less aggressive in government spending. Since this is a repeated game, we should expect some signaling between the two parties over time. One clear signal by the central bank is the last week’s 25 bp, instead of 50bp, cut. It provides a signal to the government that if the government acts irresponsibly, all the fiscal stimulus will be counter balanced by contractionary monetary policy. The net result will be worsening debt sustainability without growth. Similarly, by announcing publicly that the improving debt dynamic and economic growth requires interest rate cut. The government signals the bank that the bank will face a lot of pressures if it is too conservative.

These signals are simply to show both parties that if either one of the party deviates from the feasible strategies, the other party will trigger a “revenge”. Of course, the feasible strategies should be somewhere in the middle. The government is not too aggressive in public spending, which will not drive too much inflationary pressure. The central bank continues to cut rate, but in a gradual pace.

If you remember in your game theory 101, there is a “folk theorem” that captures the essence of the above story.

From Wikipedia, “all of the players of the game first must have a certain feasible outcome in mind. Then the players need only adhere to an almost grim trigger strategy under which any deviation from the strategy which will bring about the intended outcome is punished to a degree such that any gains made by the deviator on account of the deviation are exactly cancelled out. Thus, there is no advantage to any player for deviating from the course which will bring out the intended, and arbitrary outcome, and the game will proceed in exactly the manner to bring about that outcome.”