Thesis Working Paper n°3
In his March 1968 Presidential address, Milton Friedman summarized the broad aims of every mainstream economic policy: ‘high employment, stable prices, and rapid growth’. He was also quick to point out that these goals are not always easy to bring together, and while these aims seem to be the consensus among economists, instrument policies designed to implement these objectives do not elicit the same agreement.
Monetary Policy is one of these instruments that were the subject of much debate; The global economy moved from a decade-long era of low inflation and robust growth –both of which were considered to be partly the result of sound monetary policy- to that of an economy hurled into financial turmoil, and ultimately, into persistent depression. Central bankers, just like government, put together policies and instruments to deal these economies out of recession in ways that were unimaginable a couple of years ago (ironically, Friedman finds the tight FED policy in the 1920’s as a factor in the Great Contraction. It seems Central bankers today did not make the same mistake). Although there is much debate about the efficiency of monetary policies –especially on the long run-, the fact remains, the historically low levels of interest rates are contributing to sustain world growth and OECD growth in particular. In contrast with other policy instruments, monetary policy moved to be a subtle tool, one that is not as interventionist as, say a fiscal stimulus or tax cuts, but proves to be, at least in the short run, a very powerful and effective instrument.
Just as Friedman underlined, monetary policy is there to avoid mistakes. And it seems that this negative proposition somewhat overshadows the other assigned objective to the Central Bank, namely ‘to provide a stable back-ground for the economy’ (Friedman does acknowledge the monetary policy’s ability to balance off non-monetary shocks, though). Later on, empirical research by Taylor (1993) provides policy makers with both a theoretical and practical tool to engage in a more active (but not necessarily activist) policy scope in setting interest rates.
We deal with the following: In a game theory setting, the central bank has to assign levels of interest rates and output as targets for the economy (i.e. other players) to factor-in their own computations. These targets are not computed ex-nihilo; they are the outcome of preferences over two main variables, i.e. the levels of inflation and unemployment, both of which are considered to be the main, if not the only parameters the monetary policy-makers care about. We shall prove that, if a certain set of conditions is met, the monetary policy can deliver systematically optimal welfare for the economy. We shall also verify that this optimal welfare is a Nash and strategy-proof equilibrium as per a social choice function designed by the Central Bank. As a policy-maker, the first step is to delineate the Central Bank’s preferences over levels of inflation and unemployment, levels that can be proxy for setting interest rates and output gap targets, these targets are in turn set so as to reach a certain common welfare (whose existence and salient properties are to be proven and verified in the process)
Barro & Gordon (1981) provided a simple but accurate model of Unemployment and Inflation, which will be adapted to fit in some game theory axioms used in this paper. The Barro-Gordon model can then be used to describe the Central Bank’s preferences and thus provide insight of the way of it computes both interest rates and output gap. This preliminary study of the Central Bank’s own preferences is crucial to the other players in the economy, as it conditions, up to a point, their own expectations and ultimately, their response to the Central Bank’s decisions. We shall also verify whether pre-commitment and other institutional arrangements (such as independence from the Government or ‘special interest’ groups) can help to reach a Pareto-optimal social welfare. Once conditions of rationality and Pareto-optimality are verified, The game theory setting will provide us with elements defining the equilibriums –if there are any-, first in a simple bargaining process between the Central Bank, and a Private Firm. We shall then move to a multi-players game, and verify again that earlier predictions about the Central bank’s preferences can yield an optimal welfare to the economy. Finally, we shall consider the conditions whereby the ‘Lucas Critique’ effect is either minimized, or precluded altogether.
We shall consider the improved version of Kydland & Prescott (1977) model, by Gordon (1980):
Where Ut and Utn are respectively the unemployment rate and the ‘natural’ rate of unemployment, πt and πte respectively the inflation rate and the equilibrium, ‘anticipated’ inflation rate. As a policy-maker, the central bank values these parameters, but does also take into account a ‘social cost’ function defined by the deviation of both variables from respective anchor values:
We shall however use an altered version of the said model, namely by introducing different axioms/assumptions, mainly about the use of the information set and the inflationary expectations. The rational expectation equilibrium πt is computed on the assumption that “Because there are many private agents, they [the agents] neglect any effect of their methods for formulating πte on the policymaker’s choice of πt”. We will not however retain such assumption;
Indeed, in the first very simplified instance, Central Bank faces only one private agent – and so inflationary expectations are going to be part of a strategic game, the information set will have a different use to both players. Then, in a more generalized setting, the Central Bank faces n non atomistic players, which means that their own inflationary expectations cannot be treated as given by the Central bank. Quite the opposite, the social function it devises has to be strategy proof with respect to each player’s anticipations.
This non-atomicity assumption is essential in computing the Central Bank’s desired level of inflation (and thus, the target levels of interest rates and output gap). It goes without saying that the proposed equilibrium in the Barro & Gordon model does not fit in this particular instance. The equilibrium can no longer be computed directly as a rule, but becomes a strategic game whereby each player has a certain type preference over unemployment and inflation (and react accordingly when recording signals of interest rates and output gap), and it is up to the Central Bank to devise a social function that completes the objectives assigned above.
 Robert Barro & David Gordon, ‘A Positive Theory of Monetary Policy in a Natural-rate Model’ Working Paper n°807, NBER November 1981
 Tesfatsion, Leigh ‘Notes on the Lucas Critique’ Iowa State University (2010)
 Robert Barro & David Gordon, p.34