On#the#Notion#of#Causality#in#Macroeconomics#
Two!Case!Studies:!The!Money!and!Prices!Debate!and!the!Phillips!
Relationship!
! ! Summer,!2015! Bachelor!thesis! Faculty!of!Economics!and!Business,!! BSc!Economics!and!Business! Words:!10,622! PREFACE."I"am"very"grateful"to"my"thesis"supervisor"Dr."Ir."M."J."Boumans"for"his"accurate" reading"suggestions"and"clear"critiques."Also"I"have"to"thank"Jet"Visser"for"listening"to"my" thoughts"with"endless"patience."ABSTRACT.!KEVIN"HOOVER’S" ANALYSIS" OF" CAUSALITY" IN" MACROECONOMICS" IS" KEY" IN" THIS" PAPER."HIS" MANY" YEARS" OF" RESEARCH" HAVE" RESULTED" IN" A" VERY" EXTENSIVE" LITERATURE" ON" THE"NOTION"OF"CAUSALITY."THIS"PAPER"IS"AIMED"AT"CLEARLY"SUMMARIZING"HIS"THOUGHTS."IT" PROVIDES" AN" EXTENSIVE" HISTORY" OF" THE" DISCUSSIONS" ABOUT" CAUSALITY."IT" EXAMINES" THE" HOOVER"METHODOLOGY"FOR"INFERRING"THE"CAUSAL"DIRECTION"BETWEEN"MONEY"AND"PRICES," AND" AN" ATTEMPT" IS" MADE" TO" APPLY" HIS" APPROACH" TO" THE" CAUSAL" DIRECTION" BETWEEN" INFLATION"AND"UNEMPLOYMENT.!
KEY! WORDS.! MACROECONOMICS," CAUSALITY," METHODOLOGY," KEVIN" HOOVER," MONEYTPRICE" DEBATE,"PHILLIPS"RELATIONSHIP.!
INTRODUCTION!
After!the!recent!financial!crisis,!the!economic!academic!society!has!been!heavily!criticized.!Even! Queen!Elizabeth!asked!LSE!scholars!why!they!did!not!see!the!crisis!coming.!It!is!an!oftenUheard! critique! that! economists! and! their! models! lost! the! connection! to! the! real! world! (consider! for! example! Caballero,! 2010).! One! of! the! reasons! for! that! might! be! the! sloppiness! with! which! economists! deal! with! causality.! Translating! real! world! issues! in! econometric! and! mathematic! models!can!conflict!with!our!perceptions!of!causality.!Consider!this!simplified!example;!if!we!say! that!A!causes!B,!we!would!not!agree!that!automatically!also!B!causes!A."Whereas!in!mathematics! that! would! not! be! a! problem;"if!! =#$%,!we!can!without!any!problems!rewrite!that!as&% =$#!.! Simon!(1953,!p.!50)!also!addresses!this!problem!and!argues!that!even!if!we!would!use!terms!as! University!of!Amsterdam! Hessel!van!Straalen! Student!Number:!10439072! Supervisor:!Dr.!Ir.!M.!J.!Boumans!
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independent" and! dependent" variables," it! often! would! not! withhold! us! from! rewriting! our!
equations!in!a!way!that!conflicts!with!the!idea!of!causality.!
! Other! problems! arise! when! correlation! is! mixed! up! with! causality.! Recently,! this! was!
ironically! illustrated! by! Höfer,! Przyrembel! and! Verleger! in! their! paper! ‘New! Evidence! for! the! Theory!of!the!Stork’,!in!which!they!find!‘prove’,!based!on!a!correlation,!that!the!number!of!storks! in! the! area! is! an! explanatory! variable! for! local! birthrates.! In! this! exaggerated! example,! the! authors!show!clearly!how!easily!mistakes!can!be!made,!and!that!we!should!not!think!to!lightly! about!causality!(Höfer,!Przyrembel,!&!Verleger,!2004).!
Discussing! causality! has! not! always! been! popular! amongst! scholars,! it! was! Milton! Friedman! who! suggested! to! put! the! discussion! to! a! rest.! He! felt! that! it! was! unsatisfactory! to! research!causality!because!the!reasoning!would!go!on!forever;!every!cause!has!a!cause,!which! has!a!cause,!that!has!a!cause,!and!so!on!(Hoover,!2001B,!p.!93).!This!paper!firmly!disagrees!with! Friedman.!It!will!be!argued!that!causality!is!a!fundamental!issue!in!economics,!that!it!should!be! researched!and!that!it!should!be!treated!with!extreme!care.!The!primary!purpose!of!this!paper!is! to! discuss! how! that! should! be! done.! Most! of! the! arguments! made! will! be! based! on! Kevin! Hoover’s! work,! professor! at! Oxford! University! and! one! of! the! leading! scholars! in! the! field! of! causality!in!economics.!Throughout!his!many!years!of!research,!he!sophisticatedly!discussed!the! various! approaches! to! causality.! He! criticizes,! for! example,! the! probabilistic! approach! for! its! failures!to!embrace!all!our!causal!intuitions,!but!does!not!fully!reject!it.!Instead,!he!uses!some!of! their!techniques,!for!example!GrangerUcausality!in!his!own!analysis!of!causality!(Boumans,!2003,! pp.!564U565).!Hoover’s!analysis!is!based!on!the!structural!approach!set!out!by!Simon!(1953).!In! Simon’s! article! ‘Causal! Ordering! and! Identifiability’,! written! in! the! tradition! of! the! Cowles! Commission,! it! is! argued! that! if! we! know! the! true! underlying! systems! explaining! the! world! around!us,!we!can!use!that!to!infer!causal!direction.!However,!that!is!problematic!when!two,!or! more,! conflicting! systems! are! consistent! with! the! same! data! (Boumans,! 2003,! p.! 565).! Hoover! suggests!solving!this!by!using!probabilistic!techniques,!such!as!Granger!causality,!to!discriminate! between! these! competing! representations.! Hoover! understands! best! how! important! and! exquisite! the! subject! of! causality! in! economics! is.! Therefor,! this! paper! is! mostly! based! on! Hoover’s!work!and!ideas.!His!book!‘Causality!in!Macroeconomics’!(2001)!is!used!as!a!foundation! for!the!historical!and!theoretical!framework!presented!in!this!paper.!!
In! order! to! get! grip! on! the! sophisticated! discussions! about! causality! and! to! see! how! contemporary!ideas!regarding!causality!came!into!being,!the!first!section!of!this!text!provides!an! historic! overview! of! these! discussions.! The! second! part! uses! Hoover’s! article! ‘The! Causal! Direction! Between! Money! and! Prices’"as! an! example! to! explain! Hoover’s! method! for! inferring!
causal! direction.! And! in! the! last! section,! an! attempt! is! made! to! use! Hoover’s! methodology! for! inferring! causal! direction! in! the! Phillips! Relation! (Phillips,! 1958).! It! should! be! clearly! emphasized!that!this!attempt!is!far!from!complete.!Due!to!a!lack!of!tools,!the!research!could!not! be!finished.!In!the!end,!suggestions!are!made!for!the!path!of!continuation.!Therefor,!it!might!be! appropriate!to!consider!this!thesis!as!a!working!paper,!which!will!be!finished!when!I!do!possess! the!tools!required.!!! 1.! A!HISTORY!OF!THE!PROBLEM!OF!CAUSALITY!IN!MACROECONOMICS! Studying!the!role!and!functioning!of!causality!is!not!new,!scholars!have!been!debating!causality! for!centuries.!To!understand!today’s!scientific!thoughts!on!causality,!it!is!important!to!consider! the! historic! work! of! the! most! influential! scientists.! The! following! paragraphs! provide! a! chronological!summary!of!the!development!of!thinking!about!cause!and!effect.!
One! of! the! first! mentioning! causality! was! Plato.! In! his! work! Pheado! he! writes! that! the! basis!for!any!‘inquiry!into!nature’!is!to!investigate!“the"cause"of"each"thing;"why"things"come"into"
existence,"why"it"goes"out"of"existence"and"why"it"exists”! (Falcon,! 2015).! Aristotle! follows! Plato’s!
tradition!in!searching!for!causes!in!the!world!around!us.!He!marks!four!categories!of!answers!to! ‘whyUquestions’:!the!material!cause,!the!formal!cause,!the!efficient!cause!and!the!final!cause.!The! material!and!formal!causes!explain!the!material!and!the!form!of!things.!The!efficient!and!final! causes!deal!with!an!entity’s!origin!and!the!result!!(Falcon,!2015).!
Hume’s! philosophical! theories! are! of! great! importance! for! today’s! debates! about! causality! in! economics.! He! made! a! clear! distinction! between! ‘is’! and! ‘ought! be’.! In! order! to! identify!the!way!it!‘ought!be’,!e.g.!to!give!policy!advice,!we!need!to!know!how!the!world!around! ‘is’,!e.g.!how!the!economy!works.!He!describes!this!in!his!essays!“Of!money”,!“Of!Interest”!and!“Of! the!Balance!of!Trade”!(Hoover,!2001,!pp.!3U5).!!
Hoover! (2001,! pp.! 3U4)! pays! special! attention! to! five! of! Hume’s! world! describing! mechanisms.!The!first!one!is!the"Quantity"Theory"of"Money"in!which!the!influences!of!the!quantity! of!goods!manufactured!and!the!level!of!money!stock!on!price!levels!are!described.!The!second!is!
the"SpecieTflow"Mechanism:! changes! in! relative! prices! cause! changes! in! the! money! stock.! The" Loanable"Funds"Doctrine"describes!that!interest!rates!are!caused!by!the!demand!for!and!supply!
of! loans.! The! Arbitrage"Doctrine"is! the! fourth! mechanism;! it! describes! simultaneous! causality! between!interest!rates!and!profits.!The!fifth!is!called!the!Sociological"Doctrine;!profits,!loans!and! goods!manufactured!are!caused!by!the!‘manners!and!customs!of!people’.!!
Figure! 1.! gives! a! visual! representation! of! the! mechanisms! described! above.! Several! properties!are!worth!noting!here.!Hume’s!notion!of!cause!is!either!symmetric!or!asymmetric.!For! example,! the! relationship! between! the! manners! and! customs! of! people! and! the! production! of! goods!is!asymmetric.!But!he!speaks!of!mutual!causation!in!the!relation!between!prices!and!the! stock! of! money.! Another! thing! worthy! of! noting! is! that! the! presence! of! any! cohesion! between! two! factors! does! not! necessarily! imply! a! causal! relation.! For! example,! although! loans! and! the! production!of!goods!might!move!together,!it!is!not!due!to!any!causal!relationship!between!the! two,! instead! the! correlation! is! explained! by! a! third! common! factor,! manners! and! customs! of! people!(Hoover,!2001,!pp.!4U5).!!
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Figure! 1.! Note." From! Causality! in! Macroeconomics,! p.! 4,! by! K.! Hoover,! 2001,! Cambridge:! Cambridge! University!Press!
In! Plato’s! terminology,! these! mechanisms! describe! the! results! of! Hume’s! ‘inquiry! into! nature’.!In!his!search!for!economic!explanations!Hume!asked!himself!what!caused!what,!and!how! strong! these! causal! relations! were.! To! understand! causality,! Hume! came! up! with! a! thought! experiment!about!cause!and!effect.!The!cause!is!a!red!billiard!ball!striking!a!white!one,!which!is! followed! by! the! effect:! the! movement! of! the! white! ball.! Hume! distinguishes! three! elements:! causes!are!spatially!contiguous!with!their!effects,!causes!must!precede!their!effects!and!causes! must! be! necessarily! connected! to! their! effects! (Hume,! 1739,! pp.! 77,! 90U91).! But! how! do! we! observe! this! necessary! connection?! Because! there! is! always! a! possibility! that! future! observations! do! not! follow! past! ‘laws’,! conclusions! about! a! necessary! connection! can! only! be!
drawn!about!that!particular!experiment!at!that!moment!and!under!the!specific!circumstances!at! which!the!experiment!took!place!(Boumans!&!Davis,!2010,!pp.!18U19).!This!is!known!as!Hume’s! Problem"of"Induction.! Hume!concluded!that!observing!the!necessary!condition!is!not!possible,!but!that!the!idea! of!constant!conjunction!is!an!appropriate!substitute!for!the!necessary!connection!between!cause! and!effect!(Hoover,!2001,!p.!8).!We!should!be!very!careful!in!trying!to!understand!Hume!here.!He! does! not! dismiss! the! idea! of! constant! conjunction;! rather! he! tries! to! explain! that! it! cannot! be! found!in!the!objects!themselves,!but!in!the!human!mind.!The!constant!relationship!between!two! factors!is!a!starting!point!for!constant!conjunction!(Hoover,!2001B,!p.!94). But!as!Mackie!(1980,! pp.!6U9)!notices!correctly,!Hume!also!acknowledges!that!constant!conjunction!in!itself!does!not! provide!any!proof!for!the!necessary!connection,!but!that!it!is!only!the!place!where!we!get!the! idea!of!necessary!connection.!!! 1.1! THE!PROBABILISTIC!APPROACH!! !For!Hume,!causality!does!not!involve!chance.!His!account!is!deterministic;!effects!must! always!follow!their!cause!in!the!same!way.!Suppes!(1970,!p.!10)!agrees!with!Hume!but!he!looses! the! requirement! of! constant! conjunction! a! little.! He! argues! that! causal! analysis! does! involve! chance!when!one!fails!to!capture!all!determining!factors!in!a!relationship.!Hence,!in!essence!an! effect!must!always!follow!its!cause,!but!sometimes!it!does!not,!because!there!is!an!omitted!factor! in!the!analysis.!!
This!idea!of!Suppes!is!the!basis!for!modern!probabilistic!theories.!In!its!simplest!form,! the!theory!states!that:!A!is!said!to!cause!B!if!and!only!if!P(B|A)>P(B).!In!words,!A!causes!B,!if!the! probability! that! B! occurs! given! A,! is! higher! than! the! probability! that! B! occurs,! without! the! occurrence!of!A.!At!first!sight,!this!might!seem!legit,!but!the!history!of!the!probabilistic!approach! is! marked! by! the! many! adjustments! required! by! several! disproving! counterexamples! showing! how!the!theory!conflicts!with!our!intuitions.!!Hoover!(2001,!pp.!14U22)!discusses!several!of!these! attacks.!Four!of!these!counterexamples!will!be!discussed!here.!
Firstly,! Hoover! (2001,! p.! 15)! notes! properly! that! this! basic! idea! faces! the! problem! of!
observational"equivalence:! if! P(B|A)! !! P(B),! than! following! logics,! automatically! P(A|B)!P(A)!
also!holds.!The!arrows!mean!‘cause’,!so!in!words,!if!A!causes,!B,!automatically!B!causes!A.!To!see! why!this!is!problematic,!consider!the!following!example;!because!the!probability!of!getting!lung! cancer!(B)!for!smokers!(A)!is!higher!than!for!nonUsmokers,!P(B|A)!!!P(B),!A!is!said!to!cause!B.! But!by!following!logics,!this!would!also!imply!that!getting!lung!cancer!(B)!would!cause!one!to! start!smoking!(A),!P(A|B)!P(A),!which,!of!course,!is!not!intuitive.!!
! To! solve! this! problem,! Suppes! (1970)! argues! that! we! must! respect! Hume’s! second! condition;! causes! must! precede! their! effects.! When! we! implement! a! time! sequence,! the! above! reasoning! changes! to" “A! causes! B! if! and! only! if!P(B*|A*-.) > P(B*)”,! where! the! subscripts! indicate!time.!By!implementing!this!sequence!in!time,!we!are!able!to!rule!out!the!consequence! that!getting!lung!cancer!causes!one!to!smoke!(Hoover,!2001B,!pp.!101U!102).!
! GrangerUcausality!(Granger,!1980)!is!largely!in!line!with!this!argumentation!provided!by!
Suppes.! Granger’s! idea! is! that! A! is! said! to! cause! B,! if! knowing! previous! values! of! A! helps! predicting!future!values!of!B.!So!in!fact,!Granger!causality!excludes!the!possibility!of!causes!and! effects!to!occur!simultaneously.! Secondly,!the!implementation!of!time!sequence!might!solve!the!problem!of!observational! equivalence,!but!other!problems!arise!when!A!and!B!have!a!third!common!factor!(Hoover,!2001,! p.!22).!!Suppes!(1970,!p.!12)!introduces!the!term!prima"facie"cause;"that!is!A!is!a!prima"facie"cause" of!B,!if!there!are!also!cases!in!which!the!happening!of!A!is!not!followed!by!B.!!When!considering! the! previous! smoking! example,! this! would! imply! that! smoking! is! a! prima"facie"cause" of! lung! cancer,! because! smoking! can! cause! lung! cancer,! but! it! will! not! be! necessarily! the! case.! ! See! Hoover!(2001,!p.!15)!for!other!illustrative!examples.!!Smoking!being!a!prima"facie"cause"of!lung! cancer!does!not!necessarily!imply!that!smoking!is!the!true!cause!of!getting!lung!cancer.!Possibly! the!high!correlation!between!smoking!and!lung!cancer!is!the!result!of!a!common!third!factor.!For! example,! one! can! argue! that! nowadays,! most! smokers! come! from! lower! social! classes.! If! a! substantial! part! of! these! smokers! have! jobs! in! construction! work,! working! with! harmful! materials,!such!as!asbestos!or!toxic!paint,!might!genuinely!cause!the!lung!cancer.!So:!!
•! Being!a!construction!worker,!working!with!harmful!materials:!!!Smoking.! •! Being!a!construction!worker,!working!with!harmful!materials:!!!Lung!cancer,!
The!third!common!factor,!being!a!construction!worker!working!with!harmful!materials,!causes! lung!cancer,!not!smoking.!Reichenbach!(1956,!p.!158)!calls!this!the!common"cause"principle;!“If"
an" improbable" coincidence" has" occurred," there" must" exist" a" common" cause.”" In! other! words,! if!
there! is! a! correlation! between! two! factors,! there! are! three! possibilities,! either! de! first! factor! causes! the! second,! or! the! other! way! around,! or! there! is! a! common! third! factor.! Figure! 2! graphically!shows!the!smoking!example,!as!was!done!first!by!Reichenbach!(1956,!pp.!158U160).!
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Figure! 2.! Graphical! representation! showing! the! common! third! cause! principle! Note.! Representation! is! inspired!on!Reichenbachs!work!(1956,!pp.!158U160).!
! Another! famous! counterexample! is! given! by! G.! Hesslow! (1976).! His! claim! is! about! the!
relation! between! birth! control! pills,! pregancy! and! thrombosis.! Birth! control! pills! contain! chemicals! that! clot! blood,! but! the! percentage! of! people! taking! birth! control! pills! and! having! thrombosis,!is!lower!than!the!percentage!of!people!that!do!not!take!any!birth!control!pills!at!all.! The! probabilistic! approach! would! suggest! that! taking! the! pills! would! reduce! rather! than! increase! the! chance! of! getting! thrombosis.! This! paradox! is! shown! in! figure! 3.! It! is! solved! by! looking! at! pregnancy.! Pregnancy! increases! the! the! probability! of! thrombosis,! so! reducing! chances!of!pregnancy!by!taking!the!birth!control!pills,!reduces!the!chances!of!getting!thrombosis.!!
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Figure! 3.! Note." From! Causality! in! Macroeconomics,! p.! 18,! by! K.! Hoover,! 2001,! Cambridge:! Cambridge! University!Press!
The! fourth! example! in! which! causal! intuitions! are! contradicted! is! when! nonhomogeneous! reference! classes! are! used! to! calculate! probabilities.! This! problem! is! also! known! as! “Simpson’s! paradox”.! See! Hoover! (2001,! pp.! 19U21)! for! an! example! of! the! paradox!
regarding! sex! discrimination! in! faculty! salaries.! In! this! paper! the! paradox! is! explained! by! a! fictional! example! regarding! two! rival! Universities! in! Amsterdam;! Amsterdam! University! (AU),! and! Leisure! University! (LU).! Both! universities! offer! similar! programs! in! Business! Administration.! Recent! research! has! shown! that! more! and! more! students! prefer! studying! Business! Administration! at! AU! than! at! LU.! Therefor,! LU’s! management! asked! on! of! their! wellU respected!marketing!professors!to!come!up!with!a!campaign!to!boost!the!number!of!applications! again.!The!professor!did!his!research!and!found!the!following!tenUyear!average!numbers:! University# Number#of# applications# Number#of#students# that#graduate# within#three#years# Number#of#students# that#do#not#graduate# within#three#years# Amsterdam!University! 800! 600! 200! Leisure!University! 600! 500! 100! Based!on!these!facts,!the!professor!argued!that!LU!should!start!a!campaign!which!states!that!LU! offers!better!guidance!to!students.!After!all,!at!LU!4/5th!of!the!students!is!able!to!graduate!within! three!years,!whereas!this!number!is!only!2/3rd!at!AU.!As!soon!as!AU’s!management!was!informed!
about! this! campaign,! they! were! shocked! for! a! moment.! But! soon! they! realized! that! the! LU’s! marketing! professor! made! a! mistake.! As! AU! underlines! the! importance! of! performing! well,! it! argues! that! it! is! important! to! make! a! distinction! between! between! ‘highUleveled! students’! (average!grade!7!or!higher,!on!a!scale!0U10),!and!‘moderate!students’!(average!grade!lower!than! 7)!when!looking!at!study!delays.!AU’s!management!found!the!following!tenUyear!average!facts:! University# ‘High>leveled# students’# per#year# Number#of#‘high> leveled#students’#that# graduate#within#three# years# Number#of#‘high> leveled#students’# that#do#not# graduate#within# three#years# Amsterdam!University! 575! 405! 170! Leisure!University! 102! 69! 33! University# ‘Moderate# students’# per#year# Number#of# ‘moderate# students’#that# graduate#within# three#years# Number#of#‘moderate# students’#that#do#not# graduate#within#three# years# Amsterdam!University! 225! 195! 30! Leisure!University! 498! 431! 67!
AU’s!management!calculated!the!percentages!of!good!and!moderate!students!that!were!able!to! graduate! within! three! years,! and! concluded! that! AU! outperforms! LU! in! all! classes,! contrary! to! LU’s!marketing!professor.!Consider!the!following!table:! ! Amsterdam# University# Leisure# University# ‘HighUleveled!students’!graduating!within!3!years!(%)! 70.43%! 67.64%! ‘Moderate!students’!graduating!within!3!years!(%)! 86.67%! 86.55%! !
This! is! a! typical! example! of! Simpson’s! (1951)! paradox.! It! exposes! a! mistake! that! can! be! made! when!the!probabilistic!approach!is!used!for!causality!matters.!If!we!would!have!to!believe!the! marketing! professor! at! LU,! studying! at! his! university! would! less! likely! result! in! a! study! delay.! Whereas! AU’s! management! proofs! that! is! nonsense.! Not! only! do! they! have! more! students! graduating!with!an!average!grade!7!or!higher,!also!the!percentages!highUleveled,!as!well!as!the! moderate!students,!graduating!in!three!years!is!higher.!!
The!above!critiques!on!the!probabilistic!approach!are!only!a!selection!of!a!much!longer! list!of!critiques.!Hoover!(2001B,!p.!106)!argues!that!the!sophisticating!adjustments!required!by! these!critiques!suggest!that!the!accuracy!of!the!probabilistic!account!is!strongly!connected!with! the! descriptions! of! the! hypothetically! true! causal! mechanisms,! represented! in! path! diagrams! such! as! figures! 1,! 2! and! 3.! Because! of! the! implicit! use! of! these! causal! mechanisms,! the! probabilistic! approach! is! the! appropriate! one! only! if! the! causal! paths! are! the! correct! ones.! He! argues! that! “causal" structures" are" fundamental”,! so! instead! of! the! implicit! use! of! these! mechanisms!we!should!explicitly!look!into!them.!
1.2! THE!STRUCTURAL!APPROACH!
The! structural! approach! is! about! describing! the! world,! economy! in! our! case,! around! us.! It! is! about!what!makes!what!happen.!Hume!argues!that!causes!make!effects!happen!as!a!necessary! connection!(Hoover,!2001B,!p.!107).!But!as!Hoover!(2001B,!p.!107)!notes,!this!idea!of!necessary! connection! does! not! always! fit! well! with! our! intuitions! of! causality.! He! explains! this! with! an! example!of!an!explosion!caused!by!dry!air,!gas!and!a!match.!The!match!is!causing!the!explosion,! but!it!is!not!a!necessary!condition!for!the!explosion!to!happen,!because!it!can!be!caused!by!many! other! factors.! Also,! the! match! alone! is! not! sufficient! for! the! explosion! to! happen,! because! the! other!two!factors!are!also!needed.!But,!the!factors!together!are!sufficient!to!cause!an!explosion! (Hoover,!2001B,!p.!108).!!
! Hoover’s! idea! is! in! line! with! Mackie’s! INUS! condition.! Mackie! (1965)! made! a! great! contribution! to! the! idea! of! how! causes! and! effects! are! related.! Mackie’s! INUS! condition! is! an!
“insufficient,"but"necessary,"part"of"a"condition"which"is"in"itself"unnecessary"but"sufficient"for"the" result.”!(Mackie,!1965,!p.!245).!To!see!what!this!means,!consider!the!explosion!again.!The!match,!
gas!and!dry!air!are!INUS!conditions!for!the!explosion!because!they!are!insufficient,!as!none!of!the! individuals! alone! can! cause! an! explosion,! though! they! are! necessary,! as! they! all! have! to! be! present! for! the! explosion! to! happen.! The! set! of! conditions! is! sufficient" for! an! explosion! to! happen,!although!not!necessary,!because!we!can!think!of!many!other!sets!of!other!conditions!that! can!cause!an!explosion.! How!does!this!INUS!condition!relate!to!causality!in!macroeconomics?!Although!somewhat! earlier!in!time,!Simon!defined!causality!in!a!way!that!resembles!the!then!not!yet!existing!INUS! conditions!of!Mackie.!Consider!Simon’s!(1953)!definition:! “Definition"3.7:"Let"1"designate"the"set"of"variables"endogenous"to"a"complete"subset"B," and"let"2"designate"the"set"endogenous"to"a"complete"subset"C."Then"the"variables"of"2" are"directly"causally"dependent"on"the"variables"of"1"(1 → 2)"if"at"least"one"member"of" 1"appears"as"an"exogenous"variable"in"C."We"can"say"also"that"the"subset"of"equations"B" has"direct"precedence"over"the"subset"C.”"(p. 57)" In!Simon’s!definition!the!variables!of!1,!are!in!fact!INUS!conditions!of!2,!and!not!vice!versa.!His! idea!is!to!represent!mechanisms!as!a!set!of!equations,!which!one!needs!to!solve!to!infer!causal! direction.!Consider!the!following!example!Simon!(1953)!gives:! “(1.1)" " 4..5." " " " = 4.6" ""(1.2)" " 47.5.& + & 47757" " = 476" " " ""(1.3)" " """"""" &&&&&4$757& + & 4$$5$"""""""= 4$6”"(p.!58)!
In!this!example!the!variables!are!denoted!as!5,!and!49:!are!parameters.!Equation!(1.1)!he!calls!a!
minimal"complete"subset"of"zero"order"because! it! contains! one! variable! only.!Equation! (1.1)! can!
be! used! to! calculate! the! endogenous! variable!x.!(x.= &<<=>
==).!5.!Can! be! used! to! solve! for!x7,! and!
x7′s!value!can!be!used!to!calculate!x$.!Therefor,!for!Simon!finds!that,!“5."is"the"direct"cause"of"57," and"57"of"5$”!(1953,!p.!58).!!
The!idea!here!is!to!make!statements!about!the!world’s!structure,!equations!(1.1),!(1.2)! and! (1.3),! independent! of! any! models.! It,! can! be! problematic! to! determine! whether! the! represented!structure!is!correct,!and!if!not,!how!to!obtain!it.!But!assuming!it!is!possible!to!set!out! the! economy’s! structure! correctly,! and! by! making! a! clear! distinction! between! the! role! of!
variables!and!coefficients,!Simon!is!able!to!infer!the!system’s!causal!direction!(Hoover,!2001,!pp.! 39U40!&!59).!!
Hoover! (2001,! p.! 38)! notes! that! the! Simon’s! method! as! described! above,! suffers! from! observational!equivalence.!To!illustrate!this,!he!uses!the!following!mechanism!constisting!of!the! following!equations:!
(1.4)! a..x.+ a.7x7= a.6,!
(1.5)" B7.5. = 476."
In!this!system!5.!causes!57.!However,!what!if!we!could!reorder!this!system!into:!
(1.6)!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!a..x.+ a.7x7= a.6,!
(1.7)" B7.57= 476."
In!this!system!57!causes!5..!When!we!lack!information!to!distinguish!between!the!two!systems,!
we! face! the! problem! of! observational" equivalence.! This! system! written! down! in! these! forms,! cannot!be!used!to!infer!causal!direction.!To!solve!this,!Hoover!(2001B,!p.!110U111)!suggests!that! one! set! of! parameters! must! be! regarded! as! true.! So! to! make! Simon’s! account! useful,! we! must! have! some! causal! knowledge! as! a! starting! point.! Hoover! (2001,! p.! 191U192)! suggests! that! we! should!combine!probabilistic!approaches!such!as!Granger!causality,!with!historical!knowledge!to! solve!the!problem!of!observational!equivalence.!To!understand!how,!consider!Hoover’s!view!on! the!causal!direction!between!money!and!prices.!
2.! CASE!STUDY!1:!CAUSAL!DEBATE:!MONEY!AND!PRICES!
The!Money"Price"Debate"questions!the!causal!direction!between!money!growth!and!price!levels.! On! one! hand,! monetary! business! cyclists! state! that! changes! in! money! stock! causes! prices! to! change.!On!the!other!hand,!business!cycle!theorists!argue!that!money!is!neutral!and!that!changes! in! real! economic! factors,! such! as! investments! or! government! expenditures,! causes! prices! to! change.!This!very!extensively!conducted!debate!can!be!used!to!expose!the!importance!and!the! role!of!causality!in!macroeconomics.!!
Searching!for!the!answer!to!which!approach!is!the!correct!one,!a!whole!new!discussion! arose.!What!techniques!are!appropriate!to!identify!the!causal!direction!between!output!growth! and!money!growth?!In!this!section,!the!methodology!suggested!by!Hoover!(e.g.!1990,!1991,!p.! 382)! will! be! discussed.! As! said! earlier,! he! argues! that! structures! should! be! explicitly! investigated.!So!he!adapts!Simon’s!structural!approach.!Hoover!(1991,!p.!382)!argues!that!“once"
institutions" and" the" economic" environment" must" be" combined" with" (available)" statistical" techniques"to"gather"evidence"about"the"actual"causal"direction"in"the"economy”.""
! Hoover!(1991,!p.!383)!starts!by!supposing!that!the!observable!data!on!prices!and!money!
come! from! an! unobservable! dataUgenerating! process.! He! describes! this! process! by! their! joint! distribution.!This!joint!distribution!can!be!split!up!in!two:!
(2.1.)! &C D, F = C D F C F = C F D C(D).!
Each! partition! represents! another! causal! direction.!C D F C F !states! that! P! causes! M,! and! C F D C(D)!that! M! causes! P.! If! all! the! data! comes! from! one! policy! regime! only,! the! joint! probability! distribution! will! be! invariant! as! well! as! the! two! partitions.! If! there! were! no! interventions!in!the!regimes!described!by!the!data,!the!two!partitions!would!be!observationally! equivalent.! In! other! words,! there! would! be! insufficient! proof! to! discriminate! between! the! two! causal!directions!(Hoover,!1991,!P!384).!!Hoover!argues!that:!
!“[…]! if" there" are" interventions" in" the" dataTgenerating" process" (i.e.," changes" of"
regime)," and" crucially" if" we" can" attribute" the" interventions" either" to" the" moneyT determination" or" to" the" priceTdetermination" process," then" the" patterns" of" stability" and" instability" of" the" conditional" and" marginal" distributions" in" the" alternative" partitions"give"important"information"about"the"underlying"causal"order"in"the"dataT generating"process.”"(1991,!p.!384)!
Hence,! he! argues! that! we! can! use! changes! in! the! underlying! dataUgenerating! process,! such! as! interventions!in!the!money!or!price!determining!policies,!to!identify!the!true!causal!direction.!To! discover! distinct! interventions! Hoover! (1991,! 387U388)! starts! by! collecting! information! about! the!institutions!and!economic!environment.!He!constructs!a!chronologic!history!of!interventions! in! the! moneyU! and! priceUdeterminations! processes! to! identify! baseline! periods! in! which! no! important! changes! to! these! processes! have! occurred.! Using! statistical! techniques! that! confirm! structural!breaks!in!the!data!and!recursive!regression!techniques,!Hoover!is!able!to!discriminate! between!the!two!observationally!equivalent!distributions.!To!see!how!this!works,!consider!the! following!theoretical!framework.!
Suppose! that! the! unobservable! true! data! generating! process! in! which! money! causes! prices!can!be!written!as!follows!(Hoover,!1991,!p.!385):!
(2.2.)! “F = 4D + G,&&&&G~I(0, KL7),!
In! this! system:!OPM G, M = 0,!Q GRGR-: = 0,!Q MRMR-: = 0,!S = 1, 2, … , ∞.!Hoover! uses! the! reduced!forms!of!equation!(2.2)!and!(2.3),! (2.4.)! “F = 4B + 4M + G!and! (2.5.)! D = B + M,”& to!describe!probability!distributions:! (2.6.)! “C(F|D) = I(4D, KL7),! (2.7.)! C D = I B, KN7 ,& (2.8.)! C D F = I( 4KN7F + BKL7 47KN7+ KL7 , KL7KN7 47KN7+ KL7 ),& (2.9.)! C F = I(4B, 47K N7+ KL7)”!(Hoover,!1991,!p.!385).! In!periods!where!the!moneyU!and!price!determination!processes!are!unaltered,!the!coefficients! 4,!KL7,&B!and!KN7!will!not!change,!so!the!probability!distributions!will!not!change.!But,!suppose!that! the!money!determination!process!changes!because,!for!example,!the!Federal!Reserve!changes!its! monetary!policy,!either!B!or!KN7!will!change.!!That!would!affect!equation!(2.7),!(2.8)!and!(2.9),!but! not!equation!(2.6).!On!the!other!hand,!if!there!is!a!change!in!the!price!determination!system,!4!or! KL7!will!change.!This!will!alter!equations!(2.6),!(2.8)!and!(2.9),!but!not!(2.7).!Clearly,!the!partition!
C F D C(D)!is! more! stable! than!C D F C F !in! this! system.! Which! suggests! that! money! causes!prices.!The!opposite!would!be!true!if!prices!would!have!caused!money!in!the!underlying! data! generating! process! (Hoover! 1991,! p.! 386).! When! equations! (2.6)! U! (2.9)! are! seen! as! regression! equations,! we! can! check! the! invariance! of! their! coefficients! by! using! regression! estimation!techniques.!!
! Hoover’s! strategy! has! some! complications.! The! first! difficulty! Hoover! (1991,! p.! 386)!
describes! is! when! prices! are! caused! by! money! in! a! system! with! a! feedforward"mechanism."In! such!mechanisms,!agents!anticipate!rationally!on!the!conducted!policies.!If!they!do!so,!equation! (2.6)! will! no! longer! be! invariant! and! causal! inference! can! only! be! based! on! the! invariance! of!
equation!(2.7)!when!looking!at!changes!in!the!price!determination!system.!Secondly,!OPM G, M =
0!might! not! be! true! as! a! consequence! of! an! omitted! third! factor.! If! that! factor! is! observable,! Hoover! (1991,! p.! 386)! suggests! to! condition! on! it.! If! it! is! not! observable! and! cannot! be! conditioned,! then! a! change! in! the! money! determination! process! will! no! longer! result! in! an! unchanged! equation! (2.6).! Still,! causality! can! be! inferred! by! looking! at! price! regime! changes,! because,!as!with!rational!expectations,!equation!(2.7)!will!remain!invariant.!!
2.1!!MONEY!AND!PRICE!DEBATE:!HISTORICAL!AND!INSTITUTIONAL!KNOWLEDGE!
Hoover!(1991,!p.!387)!applies!his!strategy!to!the!debate!on!causal!direction!between!money!and! prices! by! constructing! a! historical! overview! of! the! interventions! in! the! money! and! price! determining!processes.!Periods!without!interventions!in!the!money!and!price!regimes!he!calls!
baseline" periods." In! these! periods! the! regressions! should! result! in! stable! coefficients.! And! if!
interventions!in!the!price!and!money!determination!processes!can!be!identified,!that!can!be!used! to!check!the!relative!stability!of!the!distributions.!These!interventions!are!summarized!in!table! A:! Table#A## 1950:IIIU1952:II! Credit!controls,!controls!peak!around!1951:I! 1951:I! Fed/Treasury!Accord! 1951:IU1953:I! Wage!and!price!controls! 1966:III! Credit!crunch!and!associated!policy!measures! 1968:III! Implementation!of!reserve!accounting! 1984:I! Reintroduction!of!contemporaneous!reserve!accounting! 1971:IIIU1974:II! Nixon's!wage/price!controls! 1972:I! Implementation!of!explicit!monetary!targets! 1972:IIU1980:I! Implementation!of!interestUbearing!checking!accounts! 1979:IVU!1982:III! Experiment!with!reserve!base!control! 1974:I! Oil!price!shock! 1979:IV! Oil!price!shock! 1980:!I! Credit!controls.!
Note." From! The! causal! direction! between! money! and! prices,! p.! 389,! by! K.! Hoover,! 1991," Journal"of"Monetary"Economics."Table"is"selfTconstructed."
Table!A!suggests!that!there!are!no!significant!changes!in!neither!of!the!processes!in!the!period! 1954:IU1966:II.! Hence! we! expect! the! coefficients! of! the! regressions! belonging! to! the! various! distributions!to!be!stable.!Hoover!tests!this!in!the!empirical!part!of!his!method.!!!
2.2! ! !MONEY! AND!PRICE!DEBATE:!THE!‘HENDRY!APPROACH’!FOR!ESTIMATING! THE!REGRESSION!
EQUATIONS!
The! second! step! Hoover! takes! is! estimating! the! regression! equations! belonging! to! the! four! distributions!(Hoover,!1991,!pp.!389U401).!To!make!sure!that!the!invariance!of!the!coefficients! explain! the! causal! direction! and! that! they! are! not! due! to! misspecification! of! the! regression!
equations! Hoover! (1991,! p.! 389)! uses! the! generalUtoUspecific! modeling! method! of! Hendry! and! Richard! (1982).! Hoover! (1991,! p.! 391)! prefers! the! Hendry! method! to! the! use! of! vector! autoregressions! as! was! suggested! by! Sims! (1980).! He! argues! that! when! using! vector! autoregression!techniques,!there!would!be!dramatically!few!degrees!of!freedom!because!of!the! large!quantity!of!coefficients!to!be!estimated.!That!would!result!in!!inaccurate!estimations,!which! would!reduce!the!reliability!of!the!structural!change!tests!in!the!third!step!of!his!methodology.! Pagan!(1987,!p.!4)!summarizes!Hendry’s!method!in!four!steps.!The!first!step!is!to!design! a!general!model!that!includes!the!variables!from!the!equilibrium!relationship!based!on!economic! theory,!such!that!the!dynamics!of!the!process!are!minimally!limited.!Typically,!these!variables! are!lags!of!the!dependent!variable!and!other!variables!suggested!by!the!relevant!theory.!In!the! second! step,! the! model! is! reUparameterized! to! make! sure! that! the! independent! variables! are! interpretable.!The!third!step!is!to!reduce!the!model!to!a!minimum!form!that!still!fits!the!data.! And! in! the! final! step! Pagan! mentions,! looking! at! the! residuals! and! predicting! power,! the! weaknesses!of!the!model!are!tested.!
! We! can! use! Pagan’s! (1987)! review! of! Hendry’s! method! to! understand! the! underlying!
theoretical! idea.! Consider! the! following! example! Pagan! (1987,! pp.! 4U5)! gives! concerning! the! determinants! of! the! velocity! of! circulation! of! money.! He! argues! that! theory! suggests! that! the! logarithm!of!money!supply!(m)!should!be!defined!by!the!logarithms!of!prices!(p),!real!income!(y)! and!the!nominal!interest!rate!(i).!Step!one!should!be!to!define!a!dynamic!equation!as!follows:!
“YR = Z:[.4:YR-:+ ]:[6B:\R-:+ ^:[6O:_R-:+ b:[6`:aR-:”! (Pagan,!1987,!p.!5),!
where!e,!f,!g!and!h!are!set!as!high!as!reasonable.!Usually!they!are!set!5!for!quarterly!data.!When! the! model! is! estimated,! it! serves! as! a! benchmark! to! which! other! competitive! models! are! compared!(Pagan,!1987,!p.!5).!This!model!can!be!written!in!many!different!forms!that!result!in! the!same!estimated!unknown!variables,!but!that!treat!the!information!in!the!data!differently,!and! therefore! might! be! more! understandable! and! easier! to! interpret! (Pagan,! 1987,! p.! 5).! Investigation! of! possible! restrictions! must! then! lead! to! the! most! compendious! specification! (Hoover,!2005,!p.!27).!Pagan!(1987,!p.!87)!argues!that!Hendry!usually!rewrites!the!dynamics!in! the!model!as!an!‘error!correction!mechanism’.!!For!the!velocity!of!circulation!of!money!example! Hendry!and!Mizon!(1978,!as!cited!in!Pagan,!1987,!p.!6)!came!up!with!this!model:!
! “ ∆(Y − \)R = 1.61 + 0.21∆_R− 0.81∆aR+ 0.26∆(Y − \)R-.− 0.4∆\R− 0.23(Y − \ −
! For! Pagan! (1987,! p.! 6)! this! process! of! specification! is! “more"of"an"art"than"a"science”." Hoover! (2005,! p.! 27)! argues! that! the! reUparameterization! process! must! be! based! on! common! sense! and! the! availability! and! quality! of! the! data,! but! since! the! true! dataUgenerating! process! cannot! be! observed,! it! is! not! possible! to! prove! that! the! general! model! nor! its! reductions! represent! the! true! dataUgenerating! process.! However,! thoroughly! investigating! the! space! of! alternative! specification,! the! generalUtoUspecific! method! protects! against! the! probability! that! alternative!(better)!specifications!are!being!ignored,!and!it!therefore!secures!the!model!against! missing!information!(Hoover,!2005,!p.!28).! ! If!the!Hendry!method!is!performed!correctly,! (a)! “the"model"is"coherent"with"the"data"(i.e.,"fits"the"data"up"to"an"innovation" that"is"white"noise"and,"further,"a"martingale"difference"sequence"relative"to" the"selected"database);" (b)! It"validly"conditions"on"variables"that"are"weakly"exogenous"with"respect"to" the"parameter"of"interest;" (c)! It"encompasses"rival"models;" (d)! Its"formulation"is"consistent"with"economic"theory;" (e)! It"has"a"parsimoniously"chosen"and"orthogonal"decision"variables”"(Phillips,! 1988,!pp.!352U353)." Property!(a)!implies!that!the!model!fits!the!data!up!to!innovations!that!cause!the!model!to!not!be! autocorrelated.!Hence,!until!the!moment!that!looking!at!previous!values!of!the!model’s!estimates! will! not! help! predicting! current/future! values! anymore.! Whereas! property! (b)! states! that! the! model! must! condition! on! weakly! exogenous! variables! such! that! the! estimated! unknown! coefficients!will!not!be!biased.!Property!(c),!(d)!and!(e)!imply!that!the!resulting!model!is!the!best! one! compared! to! its! rivals,! that! it! correctly! describes! economic! theory! and! that! it! is! written! down!in!its!most!simplified!version!respectively.!!
! So!how!does!Hoover!put!this!to!practice?!He!starts!with!the!general!unrestricted!models.!
For!the!price!probability!distribution!that!is!a!regression!based!on!five!lags!of!money!(measured! by!the!main!monetary!aggregate!M1)!and!prices!(Consumer!Price!Index)!themselves!and!on!the! lagged! values! of! other! independent! variables,! which! he! chose! based! on! relevant! economic! theory.!For!the!price!regression,!as!suggested!by!theory,!he!includes!wages!(W),!longUrun!(LR)! and! shortUrun! (SR)! interest! rates.! He! considered! many! additional! regressors,! such! as! labor! productivity,!time!deposits,!unit!labor!costs!and!the!unemployment!rate,!but!these!factors!where! omitted!later!because!their!(lagged)!values!had!no!influence!on!prices!at!5%!significance!level!
(Hoover,!1991,!pp.!394U395).!Using!the!PCUGIVE!(5th!version)!software,!programmed!by!Hendry! and!Doornik,!for!the!reUparameterization!process,!Hoover!finds!that:!! “The"complete"price"regression"is:" ∆iFj =0.18∆[0.039] −#k-. 0.0033∆op0.0014 +0.0022∆0.000677op-#−0.0046∆0.00277rp-#− 0.066(iFj−k)-s 0.013 − 0.071iFj-s 0.023 + 0.016∆7D-. 0.057 + 0.56 0.015 + &3&uv4uPw4x&`yYYavu”!(1991,!p.!394)! For!the!money!determinations!process,!Hoover!(1991,!pp.!398U399)!does!not!use!M1!to!measure! money!because!it!would!be!awkward!to!act!as!if!M1!reacts!freely!to!all!sorts!of!regressors,!when! in!reality!it!is!fully!controlled!by!the!Federal!Reserve!System.!Instead,!he!uses!demand!deposits! (DD)! to! measure! money.! Applying! the! Hendry! method! as! described! above! and! satisfying! all! desirable!properties,!he!finds!that:!
“The"complete"money"regression"is:"
∆# CC − iFj = 0.91∆0.0033 &&&&&&&&&&&&&&&&&&&&&&&&&&#(CC − iFj)-. −0.26∆0.075 &&&&&&&#iFj +1.56∆iFj0.21 &&&&&&&&&&&&-#"
−0.012∆0.0018 &&&&&&&&&&&#op-. − 0.018∆ rp − op0.0034 &&&&&&&&&&&&&&&&&&− 0.010∆(rp−op)-$+0.078∆0.015 &&&&&&&&&&&&&&&&&7∆zIF-7 − 0.0079(CC − zIF − iFj)0.0060 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&-s."
" " " (Hoover,!1991,!p.!398)! !
Neither!regression!model!is!autocorrelated!or!has!autoregressive!conditional!heteroskedasticity! up!to!the!fourth!order,!also!the!estimated!residuals!are!normally!distributed,!all!at!a!significance! level!of!5!percent!(Hoover,!1991,!p.!398).!Hoover!(1991,!398)!therefore!concludes!that!we!can! accept! the! complete! price! regression! as! a! minimal! form! of! the! distribution! belonging! to! the! distribution!function.!
The!longUrun!solutions!for!money!and!prices!are!respectively:!! (2.10)!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!CC = zIF + iFj.!(Hoover,!1991,!p.!398),!and! (2.11)!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!iFj = 0.48k + 4.1.!(Hoover,!1991,!p.!395).!
These! forms! seemed! to! encompass! every! other! model! including! more! regressors! than! these.! Assuming!that!wages!(W)!are!exogenous,!we!can!use!Simon’s!definition!of!causality!to!get!a!first! impression!of!the!causal!direction:!CPI!must!be!solved!before!DD!can!be!solved.!So!in!Simon’s! view!that!would!mean!that!prices!cause!money.!! ! By!leaving!out!the!variables!to!which!the!distributions!are!marginalized!and!applying!the! general!to!specific!method!again,!Hoover!(1991,!p.!399)!obtains!the!regressions!of!the!marginal! distributions.!See!Hoover’s!(1991,!p.!392!and!396)!results!for!the!price!and!money!regressions!in! the!following!two!tables!respectively:! !
Figure! 4."Note."From! The! causal! direction! between! money! and! prices,! p.! 392,! by! K.! Hoover,! 1991,"
!
Figure! 5."Note."From! The! causal! direction! between! money! and! prices,! p.! 396,! by! K.! Hoover,! 1991,"
Journal"of"Monetary"Economics"
!
! ! ! !2.3! ! ! MONEY! AND! PRICE! DEBATE:! RELATIVE! STABILITY! OF! THE!CONDITIONAL! AND! MARGINAL! DISTRIBUTIONS:!
As! mentioned! earlier,! Hoover’s! third! step! is! to! check! the! relative! stability! of! the! regression! coefficients! belonging! to! the! different! marginal! and! conditional! regression! equations.! In! this! paragraph!a!brief!summary!is!given!of!his!method,!results!and!interpretations.!
To! identify! structural! breaks,! he! suggests! to! answer! two! questions:! “Does"a"structural"
break"occur"at"all?"And"given"that"it"occurs,"exactly"when?”"(Hoover,! 1992,! p.! 238).! So! in! other!
words,!Hoover!(1991,!p.!401)!wishes!to!prove!that!the!institutional!interventions!he!found!in!the! chronology! from! step! one! genuinely! cause! a! break! in! the! data.! And! secondly,! he! checks! the! relative!firmness!of!the!regressions!coefficients!of!the!various!distributions.!To!see!the!structural! breaks,! their! timing! and! their! effects! on! the! stability! of! the! coefficients,! he! tests! every! specification! with! the! next! four! tests:! “a"constantTbase"sequential"Chow"test,"a"constantThorizon"
sequential" Chow" test," one" stepTahead" sequential" Chow" test" and" plots" of" recursively" estimated" regression"coefficient"against"their"standard"errors"(projected"forward"and"backward).”"(Hoover,!
1991,!pp.!402U403).!!
a)!
The"constantTbase"Chow"test:"For!the!constantUbase!Chow!test!the!data!is!split!in!two!parts;!the!baseline!period!and!a!period! running! from! the! last! quarter! of! the! baseline! period! to! the! last! quarter! of! the! recursive! regression.!This!Chow!test!localizes!breakpoints.!The!constantUbase!Chow!test’s!results,!‘break! point’!as!reported!by!Hoover,!reflect!the!first!period!in!which!the!null!of!no!break!is!rejected!at!a! 5%!percent!significance!level!(Hoover,!1991,!p.!405).!!
b)!
The"constantThorizon"Chow"test:"This!test!splits!the!data!at!each!observation!between!the!end!of!the!baseline!period!and!the!last! observation! of! the! sample.! The! maximum! statistics! found! are! reported! here,! they! indicate! the! most!significant!single!break!point!in!the!sample!(Hoover,!1991,!p.!402).!It!should!be!carefully! noticed! that! besides! the! maximum! reported! here,! there! might! also! be! other! (local)! maxima! (Hoover,!1991,!p.!403).!
c)!
The"one"stepTahead"sequential"Chow"test:"In! the! oneUstepUahead! sequential! Chow! test,! coefficient! stability! is! tested! by! comparing! the! recursive!estimates!of!each!regression!with!a!new!regression!that!is!using!one!more!observation.! All!of!these!estimates!are!independent!of!each!other.!Therefor,!in!sufficiently!large!samples!and!a! fiveUpercent!significance!level,!we!would!expect!at!least!five!percent!of!the!statistics!to!exceed! the!critical!value!(Harvey,!1981,!pp.!55U56,!as!cited!in!Hoover,!1991,!p.!403).!!That!is!why!Hoover!
(1991,!pp.!403U410)!reports!the!ratios!of!the!number!of!statistics!that!trespass!the!critical!value! to!the!total!number!of!observations.!!
d)!
Visual"inquiry"of"the"recursive"estimates"of"the"coefficients:"Hoover! (1991,! p.! 403)! emphasizes! the! important! complementary! role! of! visual! inquiry! of! the! coefficient! stability,! and! therefor! reports! numerous! plots! representing! the! coefficients’! evaluation!over!time.!
Hoover! argues! that! it! is! important! to! examine! more! than! one! test,! because! the! type,! moment! and! possible! multiplicity! of! interventions! in! the! price! and! money! determining! processes! cannot! be! known! beforehand.! According! to! him,! combining! information! of! multiple! origins! will! help! constructing! a! persuasive! argument! (Hoover,! 1991,! pp.! 403U404).! Hoover’s! sample!runs!from!1950:I!to!1985:IV.!According!to!table!A,!the!baseline!period!runs!from!1954:I! to! 1966:II.! He! separately! performs! the! four! tests! to! the! periods! before! and! after! this! baseline! period:!
2.3.1!!!BEFORE!THE!BASELINE!PERIOD!(PROJECTED!BACKWARD):!
The!period!before!the!baseline!period!runs!from!1953:IV!(which!is!the!last!observation! before! the! baseline! period)! back! until! 1950:I! (which! is! the! first! observation! in! the! data! set).! Hoover!performs!the!Chow!tests!projected!backward.!The!most!important!results!from!the!Chow! tests!are!shown!in!the!following!figure:!
! Figure! 6.""Note."From! The! causal! direction! between! money! and! prices,! p.! 405,! by! K.! Hoover,! 1991,"
2.3.1.1!!!PRICE!REGRESSIONS:!
So! how! should! we! interpret! these! results?! Figure! 6! shows! interventions! in! the! price! determination! process,! as! we! expected! from! the! historic! chronology.! The! oneUstepUahead! sequential!Chow!test!reports!break!points!at!1951:I!and!1952:II!that!correspond!exactly!with!the! implementation!and!shut!down!of!the!wage!and!price!controls!(see!table!A)!(Hoover,!1991,!p.! 406).!The!constantUbase!Chow!test!reports!1952:III!as!a!breaking!point!for!all!price!regression,! this! corresponds! with! the! elimination! of! the! credit! controls.! Notable! is! that! the! dates! corresponding!to!the!maximum!oneUstepUahead!Chow!statistics!(1951:I)!exactly!match!the!peaks! of!the!credit!controls.!! ! Figure!7.!Note."From!The!causal!direction!between!money!and!prices,!p.!406,!by!K.!Hoover,! 1991,"Journal"of"Monetary"Economics" ! The!plot!of!the!recursively!estimated!regression!coefficients!and!their!standard!errors!is! shown!by!Hoover!in!figure!7.!It!illustrates!the!instability!of!the!constant!of!the!complete!price! regressions! in! the! period! 1950:IU1953:II.! He! does! not! show! the! figures! corresponding! to! the! other!coefficients,!but!ensures!us!that!they!‘tell"the"same"story’!(Hoover,!1991,!p.!406).!The!plots! confirm!the!evidence!provided!by!Figure!6;!after!the!introduction!of!the!credit!controls!in!1950:I! the! constant! steeply! decreases,! this! fall! ends! with! the! Fed/Treasury! Accord! in! 1951:I,! also! instability!caused!by!the!peaking!of!the!credit!controls!(1951:1)!can!clearly!be!seen!in!Figure!7.!! 2.3.1.2!MONEY!REGRESSIONS:!
In!the!money!regression!statistics!in!Figure!6,!projection!4.7!(corresponding!to!regression!2.3)! stands!out.!The!constantUbase!Chow!test!does!not!find!statistics!that!would!reject!the!null!of!no!
coefficient!values!of!the!money!regression!marginal!on!interest!rates!to!be!more!or!less!straight! lines.!Hoover!(1991,!pp.!408U409)!reports!the!coefficient!on!iFj-s,!‘the"most"unstable"coefficient"
from"projection"(4.7)’,"in!figure!8.!So!although!Hoover!does!not!show!stability!plots!of!the!other!
coefficients! from! projection! 4.7,! he! ensures! us! that! they! would! show! even! more! stable! lines.! Figure!8!indeed!shows!stability!of!the!coefficient.!!
! Figure!8."Note:"From!The!causal!direction!between!money!and!prices,!p.!408,!by!K.!Hoover,! 1991,"Journal"of"Monetary"Economics"
! These!results!are!well!suited!for!indicating!the!causal!direction.!We!should!keep!in!mind!
that! credit! controls! were! implemented! in! 1950:III,! that! these! were! most! heavily! controlled! around! 1951:I,! and! were! slowly! ended! in! the! period! from! 1951:IV! to! 1952:II! (See! table! A).! Combining!that!institutional!knowledge!with!the!money!regression!marginalized!on!the!interest! rate! that! does! not! show! significant! breaks! in! the! stability! of! the! regression! coefficients,! that! however,!does!show!a!break!when!the!regression!is!also!marginalized!on!prices,!gives!exactly! the!kind!of!evidence!what!Hoover!was!hoping!to!gather.!Hoover!uses!the!information!about!the! difference! between! projection! 4.7! and! 4.8! to! infer! causal! direction! (Hoover,! 1991,! p.! 408).! Because! the! money! regression! is! stable! when! interest! rates! are! omitted! and! unstable! when! omitting!prices,!Hoover!(1991,!p.!409)!argues!that!it!must!be!that!prices!cause!money,!and!that! interest!rates!do!not.!"
2.3.2!!!AFTER!THE!BASELINE!PERIOD!(PROJECTED!FORWARD):!
! Figure!9."Note."From!The!causal!direction!between!money!and!prices,!p.!410,!by!K.!Hoover,! 1991,"Journal"of"Monetary"Economics" ! Figure!10."Note:"From!The!causal!direction!between!money!and!prices,!p.!412,!by!K.!Hoover,! 1991,"Journal"of"Monetary"Economics" " Hoover!(1991,!p.!412)!is!able!to!identify!distinct!changes!in!the!price!regime.!He!reports!the!FU
Although!he!does!not!report!graphs!of!the!other!price!regressions,!he!argues!that!they!look!very! similar.! If! that! is! truly! the! case,! one! might! argue! that! the! problematic! fits,! especially! around! 1973U1975!and!1979U1984,!are!the!result!of!changes!in!the!price!generating!process!caused!by! the! Nixon’s! price! controls! (see! table! A).! However,! Hoover! (1991,! p.! 411)! argues! that! that! is! unlikely! because! there! are! no! structural! breaks! to! be! found! at! 1971:I! and! 1971:IV,! which! we! should! have! found! if! the! breaks! were! caused! by! Nixon’s! price! controls.! More! realistically! the! shocks!in!the!price!generating!process!are!the!result!of!sudden!increases!in!oil!prices!in!1974:I,! 1979:II!and!1981:III!(Hoover,!1991,!p.!411).!!
! By! inspecting! the! coefficient! plots! of! projections! 5.1U5.8,! Hoover! (1991,! pp.! 412U415)!
finds! evidence! that! omission! of! money! in! the! price! regression! has! a! stabilizing! effect.! Additionally,! he! finds! that! omitting! interest! rates! from! the! money! regressions! result! in! more! stable! coefficients,! as! projection! 5.7! has! the! lowest! maxUChow! (11.9)! score! of! all! money! regressions.!Especially!interesting!here!is!the!increasing!instability!when!prices!are!omitted!as! well,!a!maximum!Chow!statistic!of!18.2!instead!of!11.9.!
2.4!MONEY!AND!PRICE!DEBATE:!CONCLUSION!
Money! regressions! conditional! on! prices! appear! to! be! more! stable! than! money! regressions! marginal! of! prices,! and! price! regressions! conditional! on! money! appear! to! be! less! stable! than! price! regression! marginal! of! money! (Hoover,! 1991,! p.! 417).! Bases! upon! these! arguments,! Hoover’s!conclusion!favors!the!view!that!money!is!caused!by!prices.!
3.! CASE!STUDY!2:!THE!PHILLIPS!RELATIONSHIP!
In!his!famous!paper,!Phillips!(1958)!found!evidence!for!a!relation!between!unemployment!and! inflation! in! the! United! Kingdom! based! on! unemployment! rates! and! wage! inflation! rates! from! 1861!to!1957.!He!found!a!negative!tradeUoff!between!the!two.!Graphically,!that!would!result!in!a! downward! sloping! Phillips! curve.! However,! in! reality! this! seems! not! be! the! case.! Figure! 11! shows!the!relation!between!inflation!and!unemployment!in!the!United!States!from!1980U2015! and!illustrates!the!empirical!failure!of!the!Phillips!Curve.!!
! Figure!11.!Scatterplot!of!quarterly!inflation!and!unemployment!rates!in!the!US,!(1980:IU2015:I)!
! Although!the!relation!is!not!clearly!represented!in!the!data,!the!Phillips!Curve!is!still!used!
by! the! Federal! Reserve.! Consider! for! example! Peach,! Rich! and! Linder! (2013)! in! which! they! extensively! use! the! Phillips! relationship! to! predict! future! inflation! rates,! or! Anderson,! Barrow! and! Butcher! (2003)! who! discuss! the! implications! of! gender! for! the! usefulness! of! the! Phillips! curve.! So,! although! its! empirical! failure,! the! Phillips! curve! is! still! very! popular! amongst! policy! makers.!To!prevent!policy!makers!and!advisors!from!any!mistakes,!it!is!a!necessity!to!properly! understand!this!relation.!Is!there!a!clear!causal!direction!between!inflation!and!unemployment?! And! if! so,! what! causes! what?! Therefor,! the! aim! of! this! section! is! to! find! the! causal! direction! between!unemployment!and!inflation.!
3.1!CAUSAL!DIRECTION!BETWEEN!UNEMPLOYMENT!AND!INFLATION!
To! investigate! the! causal! direction! between! unemployment! and! inflation! this! paper! uses! Hoover’s! methodology! as! described! above.! See! Hoover! (1991,! p.! 385U418).! The! question! of! interest! here! is,! suppose! the! government! can! control! unemployment! rates,! can! it! thereby! also! control! inflation! rates?! To! answer! this! question,! we! look! at! a! 35Uyear! period,! running! from! 1980:IU2015:I.!!
Consider! the! following! theoretic! framework! to! see! how! this! will! be! investigated.! Suppose! the! true,! unobservable,! underlying! dataUgenerating! process! can! be! described! by! the! following! system!of!equations! U3 U2 U1 0 1 2 3 4 0 2 4 6 8 10 12 Inflation Unemployment
(3.1)!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!{ = 4| + G,&&&&G~I(0, KL7),!
(3.2)!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!| = |}+ M,&&&&M~I(0, K N7),!
under! the! assumption! that!OPM G, M = 0,!Q GRGR-: = 0,!Q MRMR-: = 0,!S = 1, 2, … , ∞.!Under!
Simon’s!(1953)!definition!of!causality!|!would!cause!{!in!this!system,!because!|!is!independent! of!{!and! must! be! solved! before!{!can! be! determined.! We! can! write! the! reduced! forms! of! equations!(3.1)!and!(3.2)!as:! (3.3)!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!&{ = 4|}+ 4M + G,! (3.4)!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!| = |}+ M.! The!joint!probability!distribution!can!be!written!as!follows:! (3.5)!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!C |, { = C | { C { = C { | C(|).! So!the!two!parts!of!the!joint!probability!distribution!are:! (3.6)!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!C({||) = I(4|, KL7),! (3.7)!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!C | = I |}, K N7 ,! (3.8)!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!C | { = I( 4KN7{ + |}KL7 47KN7+ KL7 , KL7KN7 47KN7+ KL7 ),! (3.9)!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!C { = I(4|}, 47K N7+ KL7).! If!a!distinct!change!in!the!unemployment!generating!process!could!be!identified,!either! |}!or!K
N7!should!be!changed.!That!would!imply!that!we!would!find!C | , C | { !and!C { !to!be!
unstable,!and!C { | !to!be!stable.!Conversely,!if!the!inflation!generating!process!is!changed,!4!or! KL7!changes.! That! would! affect!C { | , C | { !and!C { ,! but! not!C | .! So! clearly,! if! equations!
(3.1)!and!(3.2)!would!represent!the!true!causal!order,!C { | C(|)!would!be!the!stable!partition.! If! the! true,! underlying! dataUgenerating! process! had! been! reversed,! so! if! inflation! would! have! caused!unemployment,!we!would!find!aC | { C { &to!be!the!most!stable!partition.!!
Hoover’s!strategy!to!infer!causal!direction!goes!as!follows:!equations!(3.6)U(3.9)!can!be! interpreted! as! regression! equations! and! institutional! and! historical! knowledge! can! be! used! to! identify!distinct!regime!shocks.!The!estimated!coefficients!should!be!stable!in!these!periods.!And! finally,!by!checking!the!relative!stability!of!the!different!partitions,!it!can!be!shown!with!which! causal!direction!the!data!is!consistent!(Hoover,!2001,!p.!387).! 3.1.1!HISTORICAL!OVERVIEW!UNEMPLOYMENT!IN!THE!AFTER!WAR!PERIOD!IN!THE!US:! Hoover!suggests!looking!at!historical!events!to!identify!distinct!changes!in!the!underlying!data! generating!processes.!That!implies!searching!for!events!that!could!have!affected!unemployment! and! inflation! rates.! So,! historical! and! institutional! knowledge! can! be! used! to! identify! distinct!
regime!shocks,!but!this!might!be!easer!said!than!done."Where!should!the!search!for!such!‘shocks’! start?!How!should!we!determine!which!events!to!include!in!the!chronology?!Answers!to!these! questions! are! not! unambiguous.! So! this! paragraph! is! an! attempt! to! provide! a! complete! chronological!overview!of!major!interventions!in!the!inflation!and!unemployment!determining! processes.!!
To! give! direction! to! the! search! it! might! be! useful! to! look! at! the! development! of! the! unemployment! and! inflation! in! the! United! States! in! the! period! 1980:IU2015:I.! These! developments!are!plotted!in!Figures!12!and!13.!Fancy!econometrical!and!statistical!techniques! are!avoided!here,!as!they!might!give!the!impression!that!the!identified!shocks!shown!by!the!data! are! necessarily! the! result! of! a! distinct! unemployment! generating! process.! The! sole! purpose! of! these!graphs!is!to!draw!our!attentions!to!the!periods!in!time!in!which!the!unemployment!rapidly! changes.!Further!historical!and!institutional!research!is!needed!to!identify!interventions!that!can! be!clearly!attributed!to!changes!in!the!unemployment.!Whether!or!not!these!interventions!truly! cause! ‘breaks’! in! the! dataUgenerating! process,! will! be! tested! in! the! third! stage! of! this! investigation.!! ! Figure!12.!US:!Unemployment!Rates.!(1980:I–2015:I)! ! Figure!13.!US!Inflation!Rates.!(1980:IU2014:II).!
!
0 5 10 15 Q1 !1 98 0 Q1 !1 98 1 Q1 !1 98 2 Q1 !1 98 3 Q1 !1 98 4 Q1 !1 98 5 Q1 !1 98 6 Q1 !1 98 7 Q1 !1 98 8 Q1 !1 98 9 Q1 !1 99 0 Q1 !1 99 1 Q1 !1 99 2 Q1 !1 99 3 Q1 !1 99 4 Q1 !1 99 5 Q1 !1 99 6 Q1 !1 99 7 Q1 !1 99 8 Q1 !1 99 9 Q1 !2 00 0 Q1 !2 00 1 Q1 !2 00 2 Q1 !2 00 3 Q1 !2 00 4 Q1 !2 00 5 Q1 !2 00 6 Q1 !2 00 7 Q1 !2 00 8 Q1 !2 00 9 Q1 !2 01 0 Q1 !2 01 1 Q1 !2 01 2 Q1 !2 01 3 Q1 !2 01 4 Q1 !2 01 5 %# U n em p lo ym en t US:#Unemployment:#1980:1>2015:I U4 U2 0 2 4 Q1 !1 98 0 Q1 !1 98 1 Q1 !1 98 2 Q1 !1 98 3 Q1 !1 98 4 Q1 !1 98 5 Q1 !1 98 6 Q1 !1 98 7 Q1 !1 98 8 Q1 !1 98 9 Q1 !1 99 0 Q1 !1 99 1 Q1 !1 99 2 Q1 !1 99 3 Q1 !1 99 4 Q1 !1 99 5 Q1 !1 99 6 Q1 !1 99 7 Q1 !1 99 8 Q1 !1 99 9 Q1 !2 00 0 Q1 !2 00 1 Q1 !2 00 2 Q1 !2 00 3 Q1 !2 00 4 Q1 !2 00 5 Q1 !2 00 6 Q1 !2 00 7 Q1 !2 00 8 Q1 !2 00 9 Q1 !2 01 0 Q1 !2 01 1 Q1 !2 01 2 Q1 !2 01 3 Q1 !2 01 4 %# In fl at io n US:#Inflation:#1980:I>2014IIThese! graphs! suggest! that! the! periods! 1980U1981,! 1985U1987,! 1990U1991,! 2000U2001! and! 2006U2007! are! worth! of! investigating.! This! investigation! was! conducted! by! examining! public! data!sources!of!the!United!States!government!and!available!literature.!! The!steep!increase!in!unemployment!in!1981!and!steep!decrease!in!1982!might!be!the! result!of!the!recession!in!the!United!States!between!the!second!quarter!of!1981!until!the!third! quarter!of!1982.!Present!Reagan!reduced!income!taxes!with!25!percent!and!in!1986!the!Reagan! administration!reformed!the!tax!system!by!a!simplifying!and!reducing!tax!levels!(Hoover,!1992,! p.!233).!1986!Is!also!known!for!the!fall!of!oil!prices!(Mankiw,!2000,!p.!409).!In!1990!a!recession! hit!the!United!States!(Gardner,!1994).!Another!important!intervention!is!the!subprime!mortgage! crisis,!the!start!of!the!financial!crisis!from!2007U2009!followed!by!a!severe!worldwide!recession,! which! peaked! when! Lehman! Brothers! collapsed! in! September! 2008! (Mankiw,! 2000,! pp.! 575U 577).! To! stimulate! investments,! the! Federal! Reserve! decreased! shortUterm! interest! rates! to! nearby! zero! percent! in! early! 2009.! Also,! in! 2009! president! Obama! signed! the! American! Reinvestment!and!Recovery!Act,!which!aimed!at!creating!new!jobs,!boosting!the!economy!and! increasing! transparency! of! government! spending.! In! November! 2010,! the! Federal! Reserve! announced! its! plans! to! spur! the! economy! and! improve! employment! rates! by! implementing! quantitative!easing!program!QE2,!in!which!it!expanded!its!treasury!holding!with!600!billion!US! dollars!(Federal!Reserve!System).!
The! Great! Moderation! that! took! place! from! 1980:IIU2007! has! great! potential! to! be! the! relatively!stable!period.!It!is!known!for!its!economic!calm,!especially!after!Reagans!tax!reforms,! and! although! the! United! States! were! involved! in! numerous! wars! during! this! period,! most! of! them!did!not!cause!any!shocks!to!the!economy.!A!possible!explanation!for!the!absence!of!major! interventions!caused!by!these!wars!might!be!that!the!United!States!were!swayed!by!the!‘Vietnam! Syndrome’! (Herring,! 2002).! Such! that,! in! the! aftermath! of! the! Vietnam! War,! wars! that! were! fought,!such!as!the!Gulf!war,!were!conducted!with!great!caution!and!did!not!affect!the!economy.! One! intervention! we! cannot! leave! out! however,! is! the! terrorist! attack! in! New! York! City! in! September!2001.!Therefor,!a!tranquil!baseline!can!be!identified!between!1986U2001:IV;!this!will! be! the! starting! point! of! the! empirical! research! of! this! investigation.! A! summary! of! the! interventions!can!be!found!in!Table!B.!
! ! !
Table#B:# 1979:IVU1980:II! 1980! 1986! 2001:IV! 2007:I! 2008:IV! 2009:I! 2009:I! 2010:IV! Oil!price!shock,!followed!by!a!recession! Reagan!tax!Cuts! Tax!reforms,!fall!in!oil!prices! Terrorist!attacks!on!New!York!City! Start!of!subprime!mortgage!crisis! Collapse!of!Lehman!Brothers! Reinvestment!and!Recovery!Act! Federal!Reserve!decreases!shortUterm!interest!rates! Federal!Reserve!Announces!QE2! 3.2!ESTIMATING!THE!MARGINAL!AND!CONDITIONAL!DISTRIBUTION!FUNCTIONS! Strictly!following!Hoover’s!methodology,!the!next!step!is!to!estimate!the!regressions!belonging! to!the!marginal!and!conditional!distribution!functions!(3.6U3.9).!The!Hendry!method!appears!to! be!the!most!appropriate!modeling!method!to!avoid!misspecification!of!the!regression!equations.!! The! general! unrestricted! models! for! unemployment! and! inflation! are! based! on! the! available! relevant! theories.! For! this,! Mankiw’s! standard! work! Macroeconomics"(2000)! is! used.! He! suggests! that! inflation! is! affected! by! interest! rates,! money! growth,! exchange! rates! and! unemployment.!Therefor,!in!the!general!unrestricted!model!for!inflation,!the!natural!logarithm! of!inflation!(i)!is!explained!by!the!values!and!lagged!values!of!the!natural!logarithms!of!interest! rates!(r),!money!growth!(∆D1),!exchange!rates!(x)!and!unemployment!(U);! aR = 4: Z :[. ~R-:+ B:∆D1R-: ] :[6 + O: ^ :[6 5R-:+ `:|R-: b :[6 &
Hendry! (1982)! suggests! to! use! five! lags,! so! e,! f,! g! and! h! will! be! 5.! Theories! as! described! by! Mankiw! (2000),! suggest! that! unemployment! levels! are! determined! by! inflation! levels,! laborU force!participations,!minimum!wage!levels,!and!the!gross!national!product.!Therefor,!the!natural! rate! of! unemployment! (U)! in! the! general! unrestricted! model! is! explained! by! the! values! and! lagged!(5)!values!of!the!natural!logarithms!of!inflation!(i)"laborUforce!participation!(l),!minimum! wage!levels!(w),!gross!national!product!(y):! |R = 4: Z :[. aR-:+ B:xR-: ] :[6 + O: ^ :[6 R-:+ `:_R-: b :[6 !
Continuing! this! research! requires! the! use! of! PCUGIVES.! It! would! result! in! the! regression! equations!describing!the!various!distributions.!Unfortunately,!I!am!not!able!to!use!PCUGIVES!due! to! two! fundamental! complications.! Firstly,! PCUGIVES! is! not! provided! by! the! University! of! Amsterdam!and!currently!I!lack!funds!to!acquire!it!myself.!Secondly,!if!I!would!buy!PCUGIVES,! finishing! Hendry’s! method! would! require! computer! programming! skills! I! do! not! have! yet.! Therefor,!I!will!take!several!programming!courses!next!academic!year,!so!that!after!I!bought!the! program,!I!will!be!able!to!finish!this!research!as!my!master!thesis.!!
4.!CONCLUSION!
The!objective!of!this!paper!was!to!show!how!to!deal!with!causality!in!macroeconomics.!Several! reasons! have! been! given! why! this! should! be! researched.! Economists! have! been! criticized! for! losing!the!connection!with!reality.!It!was!argued!that!this!might!be!due!to!the!potential!sloppy! usage!of!causality!in!their!models.!For!example,!translating!the!world!around!us!to!mathematical! equations! can! cause! conflicts! with! our! causal! intuitions.! Besides,! it! should! be! realized! that! correlation! is! not! the! same! as! causality.! To! make! sure! no! mistakes! are! made! when! using! economic!models!for!policy!making,!we!should!carefully!approach!causality.!Three!approaches! have!been!discussed:!the!probabilistic!account,!structural!approach!and!Hoover’s!analysis.!
The!probabilistic!approach!states!that!A!causes!B,!if!it!is!more!likely!that!B!occurs!after! the! occurrence! of! A,! then! that! B! happens! without! A! happing! first.! It! became! clear! that! the! probabilistic!approach,!of!which!Granger!causality!is!the!most!famous!application,!does!not!meet! all! causal! intuitions.! Four! disproving! arguments! were! given.! Firstly,! opponents! of! the! probabilistic! approach! argued! that! it! suffers! from! the! problem! of! observational! equivalence.! Suppes!contradicted!this!by!implementing!a!time!sequence.!However,!the!implementation!of!a! time!sequence!did!not!solve!Hesslow’s!paradox!or!problems!arising!from!a!common!third!cause,! nor! did! it! solve! the! issues! arising! from! Simpsons’s! paradox.! These! disproving! arguments! exposed!the!shortcomings!of!the!probabilistic!approach.!Hoover!argued!that!the!reliability!of!the! probabilistic!approach!depends!on!the!ability!of!the!underlying!mechanism!to!correctly!describe! reality.!
! Hoover!suggests!that!we!should!explicitly!focus!on!the!underlying!mechanisms!used!in!
the!probabilistic!approach.!He!uses!the!structural!approach!as!was!described!by!Simon.!Simon’s! view! is! about! capturing! the! world! around! us! and! translating! it! to! a! system! of! equations! that! exactly! describes! it.! Hoover! argues! that! the! events! in! the! world! around! us! are! caused! by! an! unobservable! dataUgenerating! process.! We! can! spit! the! underlying! dataUgenerating! processes! into!its!marginal!and!conditional!distributions,!and!subsequently!we!can!use!shocks!to!this!dataU
