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Minimizing the political/economic time lag for economic recovery.

I. Introduction

The purpose of this brief analysis is to determine how to minimize the time it takes recession-combatting policies to lead to economic recovery. We assume that political (inside) lags are slower than economic (outside) ones and that the transmission lag is a barrier between the political and economic mediums through which the policy moves. The objective is to minimize the time lag from recession to boom.

To proceed, we tell the following plausible story about the United States economy. The United States economy is in a recession and the White House only grudgingly admits it and the Congress insists the recession is not abating. The White House wishes to do nothing to get the economy out of this slump. Meanwhile, both the Congress and White House have been urging the Fed to cut interest rates further.(1) The Fed, however, has been very Scrooge-like in using monetary policy because it is worried about inflation in the long run. But under some pressure from the White House, the Fed has been forced to cut interest rates by 35 percent from their peak prior to the recession.(2) Yet, this effort has not triggered an increase in aggregate demand for goods and services in the economy.

As politicians wrangle over the state of the U.S. economy, consumers are suffering from declining purchasing power and their confidence is flagging. The President says a tax cut will not help the economy because of its long time lag. By the time a tax cut works its way through the economy, the recession will be over.

The impotence of fiscal and monetary policy reflects the problems of lags in policy. Lags can be classified as those having to do with politics only, inside lags, and those having to do with economics only, outside lags. These lags are described on a time continuum below.(3)

The media--politics and economics--through which policy is transmitted, do not respond equally to policy because on the political side, policy-makers have imperfect information and don't know when and to what degree a given policy is appropriate in a given situation. For example, cut taxes. Whose? When? By how much? On the economic side, a tax cut will work quickly because it raises disposable income when it goes into effect. That doesn't mean that spending will increase--consumers may be uncertain about the economy and may refuse to spend, or they may be more disposed to reduce their outstanding debt.

Nevertheless, we can say with some confidence that the inside lags are slower than the outside lags. The transmission lag serves as a barrier (constraint) between them. What then can be done to minimize the time it takes for a policy to have an impact on the recovery?

II. Model

The present analysis is a purely theoretical approach to the dilemma facing policymakers. The dilemma can be depicted by Figure 1.

The policy that moves the economy from recession to boom must operate in two mediums--the political medium and the economic medium. The total time from |t.sub.0~ to |t.sub.5~ will be minimized if the policy takes advantage of the faster medium. We assume the path of the policy takes it through point C. The total time spent (distance divided by velocity) in the political medium is

|T.sub.p~ = RC/|v.sub.p~ = |(|a.sup.2~ + |x.sup.2~).sup.1/2~/|v.sub.p~ (1)

where |v.sub.p~ represents the velocity of the political process.

The time that the policy takes in the economic medium is

|T.sub.e~ = RC/|v.sub.e~ = |(|a.sup.2~ + |y.sup.2~).sup.1/2~/|v.sub.e~ (2)

where |v.sub.e~ is the velocity of the economic process.

The sum of the time spent in both mediums is

T = |(|a.sup.2~ + |x.sup.2~).sup.1/2~/|v.sub.p~ + |(|a.sup.2~ + |(|a.sup.2~ + |y.sup.2)~.sup.1/2~/|v.sub.p~ (3)

The problem is to choose a point on the constraint such as C which will minimize the total time of the policy, subject to the constraint

c = x + y (4)

The solution can be found through a Langrange process

L = |(|a.sup.2~ + |x.sup.2~).sup.1/2~/|v.sub.p~ + |(|a.sup.2~ + |y.sup.2~).sup.1/2~/|v.sub.e~ + |Mu~(c - x - y) (5)

Differentiating (5) with respect to x and y, we obtain

(sin ||Phi~.sub.p~)|v.sub.p~ - |Mu~ = 0 (6)

(sin ||Phi~.sub.e~)|v.sub.e~ - |Mu~ = 0 (7)

where sin ||Phi~.sub.p~ = x/|(|a.sup.2~ + |x.sup.2~).sup.1/2~ and sin ||phi~.sub.e~ = y/|(|a.sup.2~ + |y.sup.2~).sup.1/2~.

Equations (6) and (7) may be written as

|v.sub.p~/|v.sub.e~ = sin |0.sub.p~/sin |0.sub.e~ = x/y (8)

Equation (8) states that the total time it takes from recession to boom (or recognition lag to consumption lag) is minimized if a point such as C is chosen in Figure 1 so that the ratio of the velocity of the political process (inside lag) to the economic process (outside lag) is equal to the ratio of the proportion of the political variable x to the economic variable y.

From Equation (8), we know that x/y = |v.sub.p~/|v.sub.e~. Substitute y = (|v.sub.e~/|v.sub.p~) |center dot~ x into the budget constraint x + y = C and solve for x to get the optimal choice for x. That is,

x = C/|1 + (|v.sub.e~/|v.sub.p~)~ (9)

and similarly,

y = C |center dot~/|1 + (|v.sub.p~/|v.sub.e~)~ (10)

Equations (9) and (10) show that when |v.sub.p~/|v.sub.e~ (which may be called the relative efficiency of the political process) is higher, y decreases and x increases.

III. Conclusion

The conclusion is that if the political process becomes more efficient, its velocity will increase. This gives rise to a paradox. Since the political process is slower in the political medium than in the economic medium, more time is spent in that medium--i.e., the political medium, which increases the time from recession to boom. But if political process becomes more efficient, more time should be spent in that medium because that would reduce the time from recession to boom. The paradox is resolved when it is understood that we want to maximize the duration of time in the medium in which the policy moves faster (i.e., the more efficient medium) and minimize the duration of time in the one in which it moves more slowly. That strategy would minimize the time from recession to boom.


1. See The Economist (1, p. 28).

2. Newsweek (2, p. 46).

3. Scott and Nigro (3, ch. 29) discuss these lags at some length.


The Economist, "Bad Tidings," (November 23, 1991).

Newsweek, "Greenspan's Dilemma: How Low can You go?" (Oct. 7, 1991)

Scott, Robert Hanes and Nic Nigro. Principles of Economics (New York: Macmillan Publishing Co., Inc., 1982).
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Author:Patterson, Seymour
Publication:American Economist
Date:Sep 22, 1993
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