Download Rational Expectations and Monetary Policy

Andrew Dahlem
Game Theory
April 15, 2008
Examining the Rational Expectations and Monetary Policy Game
In the realm of game theory, many applications may be made to the world of
Economics. Several types of auctions and bargaining procedures can be analyzed in this
way. One type of game that can be analyzed in an Economic context is the one played
by The Federal Reserve’s Federal Open Market Committee and the Labor Markets
(workers and firms) of the Economy. This game determines the course of Economic
growth each time it is played. Thus it is vital to understand the underpinnings of this
game in order to begin to understand its consequences.
The Federal Reserve System (Fed) is the central bank of the United States;
responsible to some degree for managing the macro-economy. The purpose of the Fed
is to control the rates of inflation and unemployment in a way that the economy
continues along a steady growth path. In order to accomplish this goal, the Fed targets
real interest rates through the buying and selling of government securities. The purpose
of this study will be to examine the role and effects of monetary policy in the framework
of a game between the Fed and labor markets in the macro-economy.
When determining the actions of monetary policy, the Fed cannot just arbitrarily
pick an interest rate that magically produces the desired rates of inflation and
unemployment. By targeting a rate of interest and controlling the growth of the money
supply, the Fed can direct inflation. It cannot control supply shocks to the economy,
thus it does not have full control over the inflation rate. According to Phillips’ theory,
there is an inverse relationship between inflation and unemployment. From this
relationship, the Fed derives its target inflation / unemployment tradeoff. For example,
if the Fed wanted to stimulate the economy, it would target a lower interest rate which
would result in a higher target inflation rate and lower target unemployment. To
accomplish this end, the Fed would buy Government Securities on the open market,
giving banks larger sums of money to lend, and lowering real interest rates.
Even before the Fed determines the actions of monetary policy, workers set
wage contracts in the labor market. Workers determine the value of their time and
make long term contracts (usually a set term of 3 to 5 years) based on the wage they are
willing to work for and their expectations of future inflation. These contracts are dealt
in the form of nominal dollars, thus if workers do not anticipate inflation, any raises
bargained for could be inflated away. If the workers believe that the Fed will allow
inflation to occur, they will set a higher wage to account for the loss due to inflation. If
the workers believe that inflation will remain low or constant, they will choose a lower
contract rate. This is where rational and static expectations come into play. Static
expectations occur in the economy when there is a pervasive feeling throughout the
economy that the growth rate will stay the same as it has been in the past, or change
very little in the future. In this scenario, the workers are complacent and do not worry
about accounting for future inflation or recession. The theory of rational expectations is
the belief that people make decisions based on the maximum amount of knowledge
that they can reasonably access. Economists like Robert Lucas, Thomas Sargent, and
Edward Prescott hypothesized rational individuals would gather knowledge and form
expectations regarding the economy and anticipated policy changes affecting it. Under
rational expectations, the Phillips curve adjusts as fast as or faster than anticipated
policy changes, thus policy changes have zero effect on the level of production or
unemployment. Unanticipated policy changes still have some affect on the economy
under rational expectations but not as large as the Fed would wish them to be.
After both the workers and the Fed make their decisions, the firms must decide
whether or not to increase output. They do this in the form of hiring or laying off
workers. The firms’ actions are determined by the wage price and inflation also,
however they measure worth in terms of real wage dollars in terms of price. If the
workers choose a high wage, and the Fed plays low inflation, the cost per worker to the
firms rises and firms will lay off workers or not higher. The result is then a higher
unemployment rate and low inflation for the economy. The firms cannot reduce wages
across the board to deflate real wage prices due to wage price rigidity.
Firms whose nominal wages are raised by constraints pass on
their increased costs in higher prices. The markup is constant,
because of constant elasticity of demand, and so the average real
wage will be unchanged by the impact of wage constraints. The
real average wage has two components. The first component is
the unconstrained real wage that results from labor supply and
demand or bargaining, and is a function of the unemployment
rate. The other component of real wages is due to downward
wage rigidity. When this component increases, unemployment
must increase by enough to lower the unconstrained component
equally, to keep average real wages constant. The increase in the
component due to downward rigidity can be thought of as a
permanent cost shock. Typically, it takes a 2 percent increase in
un- employment to offset such a 1 percent cost shock. (Akerlof,
Mankiw 1996)
Now that some background of the players has been established, it is important
to set up the game and further examine the interactions therein. The model I have
chosen is taken from the book Game Theory with Economic Applications (Bierman and
Fernandez, 1993), and a model developed by Kydland and Prescott as described here:
A game suggested by Finn Kydland and Edward Prescott (1977)
has received con- siderable attention.2 In this game, wage setters
have to specify the nominal wage in a labor contract before the
Fed sets the money supply. The Fed wants a higher level of
employment than the wage setters, but it is also inflation
conscious. The wage setters know that the Fed will be tempted to
inflate away some of their real wage, to achieve a higher level of
employment, so they pur- posely set the wage high. The Fed
weights its employment and inflation objectives, and only finds it
optimal to inflate the real wage down to the level wanted by the
wage setters. The noncooperative solution has an ineffi- cient
inflation bias, simply because the Fed has no credible way of
precommitting itself to a noninflationary policy. Adding a stabilization role for monetary policy, and private information, the
Kydland-Prescott game can be used to model the scenario
outlined above. (Canzoneri, 1985)
As has already been discussed, the game consists of three players: Workers, The
Fed, and Firms. It is played over two periods sequentially. Each of the players’ strategy
sets are as follows:
Strategy Set Workers: Low Wage, High Wage
Strategy Set Fed: Low Inflation, High Inflation
Strategy Set Firms: Low Output, High Output
Now that the game has been set up, we must take into consideration certain
assumptions that must be made before actions occur. First, it must be assumed that all
inflation stems from growth in the money supply. While this is an extreme monetarist
assumption, it is essential to the simplicity of the game. The second assumption is that
the Fed chooses the target rate of inflation directly. Although I have previously stated
that the best the Fed can do is influence the rate of inflation, this assumption must be
made for the game function properly. Thirdly, due to wage price rigidity, it must be
assumed that firms may only hire and lay off workers, rather than attempting to cut
costs through wage price reduction. Finally, assume that the Fed signals its move to the
Workers and Firms prior to the beginning of the game, but is not bound to move in
accordance with that signal.
Now we are ready to begin examining the game. Prior to the initial move, the
Fed signals the other players as to the nature of its move. It does this through its
primary directive of maintaining growth through non-inflationary low unemployment.
The key to this statement is that the Fed usually places more emphasis on maintaining
low or no inflation than it does about causing growth. If this is the case then the Fed will
signal that it will play low inflation to the Workers and Firms. The Workers will then
make the first play.
Game
Workers
Low Wages
High Wages
Fed
Low Inflation
Low Inflation
Low
Output
High
Output
High
Inflation
Low
Output High
Output
High
Inflation
Low
Output High
Output
Firms
Low
Output High
Output
If the Workers believe the Fed’s signal, they will choose to play Low Wages
believing that their nominal wage rate is safe from future inflation. They will be happy
to work at the lower contracted rate due to the fact that it will still purchase as much in
the future as it did in the past.
The Fed gets to make the next move, where the Fed will be tempted to cheat on
its earlier intention of low inflation. The rationale behind this cheating is that at a cost
of a small amount of inflation, it can obtain extra output from the firms. This is done by
inflating the workers wages away. The Fed will then play high inflation to induce the
Firms to increase output.
The Firms will always choose high output when the Fed plays high inflation. This
is due to the fact that the real wage will be much less than the nominal wage because of
the inflation caused by the Fed. The only time that the Firms should play Low Output is
when the Workers choose High Wages and the Fed chooses Low Inflation.
This game can be solved through backwards induction. The optimal path occurs
Game
Workers
Low Wages
High Wages
Fed
Low Inflation
Low
Output
High
Output
Low Inflation
High
Inflation
Low
Output High
Output
High
Inflation
Low
Output High
Output
Firms
Low
Output High
Output
when the firms play high output. In this game the Fed will always increase inflation to
encourage this response from the firms. Thus the best scenario for the workers is to
anticipate the Fed cheating on their promise and choose High Wage contracts. The
question remains, what does this mean to the economy?
The Fed, in signaling that it will choose low inflation and then cheating shows
that its’ actions are time inconsistent. While it wishes to uphold the low inflation goals
it has set for itself, the expected outcome of higher output (in the form of lower
unemployment) is simply too inviting not to cheat the workers.
Thus the Workers will
use rational expectations to see that though the Fed is signaling low inflation, there is
reason to believe that the Fed will cheat on its signal to the Workers and Firms, and they
will always play high wages in effort to recoup some of the losses to inflation. When
this occurs, the Fed will in effect lose its play, as the only credible thing that it can do is
to increase inflation to keep the unemployment status quo.
An example: Suppose that the Fed signals to the Workers and Firms that it
wishes to target an inflation rate of 2 percent. The Workers set a three year contract
wage of $45,000 per year with a built in raise of 2 percent per year to offset the
inflation. The Fed sees this and in an attempt to raise output, grows the money supply
at a rate of 4 percent inflation. The Workers’ nominal wage at the end of the third year
has risen to $46,818, but in real terms, that amount can only purchase $43,147 worth of
goods. While the overall output has risen due to the firms decreasing unemployment by
hiring, the standard of living and willingness to work for the Workers has decreased
substantially. (This amounts to a net loss of $3,671 in the last year alone.)
While my analysis of this model lacks mathematical technicality, I believe that I
have accurately expressed the theory behind the monetary policy – rational
expectations game. This model exemplifies the conclusion that workers will use rational
expectations when determining wage contracts, and the Fed and firms will be forced to
move accordingly.
Works Cited
Akerlof, George A., William T. Dickens, George L. Perry, Robert J. Gordon, N. Gregory
Mankiw. The Macroeconomics of Low Inflation Brookings Papers on Economic Activity,
Vol. 1996, No. 1, (1996), pp. 1-76, (The Brookings Institution),
http://www.jstor.org/stable/2534646 (20/04/2008).
Barro, Robert J. and David B. Gordon. A Positive Theory of Monetary Policy in a Natural
Rate Model The Journal of Political Economy, Vol. 91, No. 4, (Aug., 1983), pp. 589-610.
(The University of Chicago Press). http://www.jstor.org/stable/1831069 (20/04/2008).
Bierman, H. Scott and Luis Hernandez. “Game Theory with Economic Applications.”
(1993) pp.167 – 183. (Addison-Wesley Publishing Company, Inc.)
Canzoneri, Matthew B. Monetary Policy Games and the Role of Private Information.
The American Economic Review, Vol. 75, No. 5, (Dec., 1985), pp. 1056-1070. (American
Economic Association). http://www.jstor.org/stable/1818645 (20/04/2008).
Kydland, Finn E. and Edward C. Prescott. Rules Rather than Discretion: The Inconsistency
of Optimal Source Plans. The Journal of Political Economy, Vol. 85, No. 3, (Jun., 1977),
pp. 473-492. (The University of Chicago Press) http://www.jstor.org/stable/1830193
(20/04/2008).