Countercyclical policy

TheoryGuru applications

Load Economicreasoning package only if it is not already loaded

If[Length@Names["PLTools`*"]<10,
Get["http://economicreasoning.com"]]

Notes

Interpret gdp as a detrended indicator of economic activity absent policy intervention; gdp’s average is therefore the scalar denoted as trendgdp.

policy lists mean-zero additions and subtractions to gdp.  GDP with policy is therefore gdp + policy

gdp and policy are (time series) vectors: one element for each point in time.

In the Wolfram Language, x.y refers to the tensor DOT PRODUCT, NOT scalar multiplication.  For TheoryGuru purposes, tensor means vector, so that the result of x.y is a scalar.

Analysis

Setup

variance[x_]:=(x-trendgdp).(x-trendgdp)

countercyclicalpolicy=policy.(gdp-trendgdp)<0 ;
(* on average, policy adds to GDP when GDP is low and subtracts from it when GDP is high *)
(* i.e., countercyclical policy is in the right direction on average *)

Result 1: Countercyclical policy could exacerbate the business cycle

TheoryGuru[{countercyclicalpolicy,(trendgdp^2)≥0 (* clarify that trendgdp is a scalar *)},
variance[gdp+policy]≥variance[gdp](* policy exacerbates the business cycle *)]

Text interpretations of key inequalities

rtext={First@MostRecentAssumption->"Countercylical policy",
Not@First@MostRecentHypothesis->"policy to soften the business cycle."};

Result 2: Countercyclical policy is necessary but not sufficient for policy to soften the business cycle

with formulas

TheoryOverlap[(trendgdp^2)≥0,
countercyclicalpolicy,
variance[gdp+policy]<variance[gdp]]

formulas replaced with text interpretations

TheoryOverlap[(trendgdp^2)≥0,
countercyclicalpolicy,
variance[gdp+policy]<variance[gdp]]/.rtext

Variable interpretations