Dynamic Macroeconomics

15.3.1 The Tinbergen-Theil Theory of Discretionary Aggregate Demand Policies
To introduce the Tinbergen-Theil theory of discretionary macroeconomic
policy, we shall consider the following simplified stochastic log-linear
version of the AD-AS Keynesian macro model:

---

where y denotes the logarithm of aggregate real output, which is determined
by the equality of aggregate demand y
d
with aggregate supply y
s
; g is the
logarithm of real government expenditure; i is the nominal interest rate; m is
the logarithm of the money supply; p is the logarithm of the price level; v
d
is
an exogenous stochastic shock to aggregate demand; v
m
is an exogenous
stochastic shock to money demand; v
s
is an exogenous stochastic shock to
aggregate supply; w is the log of the nominal wage, assumed exogenous; and
a
0
, a
1
, a
2
, b, and c are exogenous fixed parameters. Equation 
(15.24)
 is a log-
linear IS curve, 
(15.25)
 a log-linear LM curve, and 
(15.26)
 a log-linear AS
curve (the aggregate supply function). Equation 
(15.27)
is the equilibrium
condition in the output market.
In the Tinbergen terminology, the (potential) policy targets are y and p,
and the policy instruments are g, m, and i. Because m and i are linearly
related through the money demand function, only one of the two can be used
as an independent instrument of monetary policy, and the other will be
determined endogenously.
Let us initially assume that the monetary policy instrument of the
government is the money supply. Then the model determines three
endogenous variables, y, p, and i, as functions of the exogenous policy
instruments g and m, the exogenous shocks, and the exogenous parameters.
Using the money demand function to substitute for the nominal interest rate in
the IS curve 
(15.24)
, we get the following aggregate demand function:
Thus, the model consisting of the aggregate demand function 
(15.28)
, the
aggregate supply function 
(15.26)
, and the equilibrium condition 
(15.27)
determines output and the price level as functions of the exogenous shocks
and the policy instruments m and g.

---