Michał Rubaszek - Mortgage down-payment and welfare in a life-cycle model

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Mortgage down-payment and welfare

in a life-cycle model

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Abstract

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1. Introduction

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{'7A'2$-'8A-'$%A3I'%A'"A2983)#2"8A'8C'%'B"1"2'} 8A' 2$-' B8%AD28DH%B)-' 9%2"8' 9-3)#-+' 2$-' 9"+.' 2$%2' 3)9"AF' %' *)+2' %' B%9F-' A)1*-9' 8C' $81-8EA-9+' E8)B3'C"A3'2$-1+-BH-+'R)A3-9'2$-'E%2-9SI'"<-<'"A'2$-'+"2)%2"8A'"A'E$"#$'2$-"9'$8)+-+'%9-'E892$?' B-++' 2$%A' 1892F%F-+<' 7A' 2$-' 82$-9I' "2' E8)B3' *-' E-BC%9-' 3-29"1-A2%B' 28' 2$-' -V2-A2' 2$%2' +81-' $8)+-$8B3+' E8)B3' C"A3' 2$-1+-BH-+' 9%2"8A-3' 8)2' 8C' 2$-' #9-3"2' 1%9.-2I' %A3' E"BB' A82' *-' %*B-' 28' >)9#$%+-'%'$8)+-<

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1892F%F-' 1%9.-2' "AA8H%2"8A+' %##8)A2' C89' 2$-' 8*+-9H-3' "A#9-%+-' "A' 2$-' $81-8EA-9+$">' 9%2-' "A' 2$-'TA"2-3'02%2-+<'U"A%BB?I'N%X%9"'-2h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c' >98H"3-+'' %'3"+#)++"8A'8A'2$-'#$8"#-'8C'>%9%1-2-9+<'0-#2"8A'LI'E$"#$'"+'2$-'1%"A'>%92'8C'2$-'%92"#B-I'>9-+-A2+' 2$-'9-+)B2+<'@$-'B%+2'+-#2"8A'#8A#B)3-+'%A3'3"+#)++-+'>82-A2"%B'3"9-#2"8A+'C89'C)92$-9'9-+-%9#$<

2. The model

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2.1. International capital markets

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2.2. Firms

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2.3. Demographics and preferences

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(5)

2.4. Individual income process

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(6)

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(8)

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(10)

4.3. Preferences

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(11)

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(12)

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5.2. Comparison of the benchmark and alternative economy

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References

="?%F%9"' 0<(<' [5\\c^I' TA"A+)9-3' "3"8+?A#9%2"#' 9"+.' %A3' %FF9-F%2-' +%H"AFI' The Quarterly Journal

of EconomicsI'5;\[6^I'bL\pb`c<

=!(7M'[:;55^I'Ogólnopolski raport o kredytach mieszkaniowych 2/2011I'$22>4nnEEE<%198A<>B< N%X%9"'G<I'Z$%A'G<I'e9)-F-9'a<I'!"BB-9'a<'[:;5;^I'A dynamic model of housing demand: Estimation and

policy implicationsI'O89."AF'G%>-9+I'5L\LLI'M%2"8A%B'N)9-%)'8C'K#8A81"#'(-+-%9#$<

Z%ih_89,"'!<I'()*%+,-.'!<'[:;5:^I'7A'2$-'-1>"9"#%B'-H"3-A#-'8C'2$-'"A2-92-1>89%B'#)99-A2'%##8)A2'' ' 183-B'C89'2$-'-)98'%9-%'#8)A29"-+I'Review of Development EconomicsI'5b[5^I'\Lq5;b<

Z%F-22"' !<' [:;;6^I' O-%B2$' %##)1)B%2"8A' 8H-9' 2$-' B"C-' #?#B-' %A3' >9-#%)2"8A%9?' +%H"AF+I' Journal

of Business & Economic StatisticsI':5[6^I'66\p6L6<

(16)

' O89."AF'G%>-9+I'6;\;I'M%2"8A%B'N)9-%)'8C'K#8A81"#'(-+-%9#$<

Z%998BB' Z<a<' [5\\]^I' N)CC-9D+28#.' +%H"AF' %A3' 2$-' B"C-' #?#B-n>-91%A-A2' "A#81-' $?>82$-+"+I' The

Quarterly Journal of EconomicsI'55:[5^I'5pLL<

Z$%1*-9+'!<I'g%99"F%'Z<I'0#$B%F-A$%)C'a<K<'[:;;\^I'=##8)A2"AF'C89'#$%AF-+'"A'2$-'$81-8EA-9+$">'' ' 9%2-I'International Economic ReviewI'L;[6^I'b]]p]:b<

Z$-A'e<'[:;5;^I'='B"C-D#?#B-'%A%B?+"+'8C'+8#"%B'+-#)9"2?'E"2$'$8)+"AFI'Review of Economic DynamicsI'' ' 56[6^I'L\]pb5L<

Z07' [:;;\^I' Structure of Wages and Salaries by Occupations in October 2008I' Z-A2%B' 02%2"+2"#%B'' ' 7CC"#-I'O%9+%E<

Z07'[:;5;%^I'Demographic Yearbook of PolandI'Z-A29%B'02%2"+2"#%B'7CC"#-I'O%9+%E< Z07'[:;5;*^I'Household Budget Surveys for 2009I'Z-A29%B'02%2"+2"#%B'7CC"#-I'O%9+%E<

Z07'[:;55Î'Labor Force Survey in Poland, IV Quarter 2010I'Z-A29%B'02%2"+2"#%B'7CC"#-I'O%9+%E< a-%28A'=<'[5\\5Î'0%H"AF'%A3'B"W)"3"2?'#8A+29%"A2+I'EconometricaI'L\[LÎ'5::5p'5:c`<

U-9A%A3-,Dd"BB%H-93-' r<I' e9)-F-9' a<' [:;55^I' Z8A+)1>2"8A' %A3' +%H"AF' 8H-9' 2$-' B"C-' #?#B-4' J8E' ' "1>892%A2'%9-'#8A+)1-9'3)9%*B-+sI'Macroeconomic DynamicsI'5L[L^I']:Lp]];<

UB83-A'!<I'j"A3m'r<'[:;;5^I'Y3"8+?A#9%2"#'9"+.'"A'2$-'TA"2-3'02%2-+'%A3'0E-3-A4'Y+'2$-9-'%'98B-'C89'' ' F8H-9A1-A2'"A+)9%A#-sI'Review of Economic DynamicsI'c[:^I'c;bpc6]<

g8)9"A#$%+'G<D7<I'G%9.-9'r<=<'[:;;:Î'Z8A+)1>2"8A'8H-9'2$-'B"C-'#?#B-I'EconometricaI'];[5Î'c]p`\< J-%2$#82-' r<I' 0289-+B-22-A' e<I' d"8B%A2-' g<j<' [:;;LÎ' @E8' H"-E+' 8C' "A-W)%B"2?' 8H-9' 2$-' B"C-' #?#B-I'

' Journal of the European Economic AssociationI'6[:p6^I']bLp]]L<

J-A3-9+8A' r<d<I' Y8%AA"3-+' f<!<' [5\`6^I' =' 183-B' 8C' $8)+"AF' 2-A)9-' #$8"#-I' American Economic

ReviewI']6[5^I'\`p556<

J)FF-22' !<' [5\\6^I' @$-' 9"+.DC9--' 9%2-' "A' $-2-98F-A-8)+D%F-A2' "A#81>B-2-D"A+)9%A#-' -#8A81"-+I'

' Journal of Economic Dynamics and ControlI'5][Lpb^I'\L6p\b\<

J)FF-22' !<' [5\\b^I' O-%B2$' 3"+29"*)2"8A' "A' B"C-D#?#B-' -#8A81"-+I' Journal of Monetary EconomicsI'' ' 6`[6^I'cb\pc\c<

Y%#8H"-BB8' !<I' G%H%A' !<' [:;;\^I' Housing and debt over the life cycle and over the business cycleI' ' O89."AF'G%>-9+I';\D5:I'U-3-9%B'(-+-9H-'N%A.'8C'N8+28A<

e"?82%."'M<I'!"#$%-B"3-+'=<I'M".8B8H'e<'[:;;]^<'Winners and losers in housing marketsI'Z8AC-9-A#-'' ' G%>-9'0-9"-+I';];LI'Z-A29-'C89'a?A%1"#'!%#98-#8A81"#'=A%B?+"+<

j"' O<I' j")' J<I' f%8' (<' [:;;\^I' Housing over time and over the life cycle: a structural estimationI'' ' O89."AF'G%>-9+I';\D]I'U-3-9%B'(-+-9H-'N%A.'8C'G$"B%3-B>$"%<

j"' O<I' f%8' (<' [:;;]^I' @$-' B"C-D#?#B-' -CC-#2+' 8C' $8)+-' >9"#-' #$%AF-+I' Journal of Money, Credit and

BankingI'6\[b^I'56]Lp5c;\<

MNG'[:;5;Î'Report on the Polish residential market in 2002–2009I'M%2"8A%B'N%A.'8C'G8B%A3I'O%9+%E< 7KZa'[:;;\Î'Pensions at a glance 2009: retirement-income systems in OECD countriesI'7KZaI'G%9"+< 792%B8D!%FA-'U<I'(%3?'0<'[:;;bÎ'J8)+"AF'1%9.-2'3?A%1"#+4'8A'2$-'#8A29"*)2"8A'8C'"A#81-'+$8#.+'' ' %A3'#9-3"2'#8A+29%"A2+I'Review of Economic StudiesI']6[:Î'cL\pc`L<

(%*%A%B'G<I'Z98E-'Z<O<I'YF%A'a<I'a-BBi=9"##"%'g<'[:;55^I'How to deal with real estate booms: lessons

from country experiencesI'O89."AF'G%>-9+I'55n\5I'YA2-9A%2"8A%B'!8A-2%9?'U)A3<

0289-+B-22-A' e<I' @-B1-9' Z<Y<I' f%98A' =<' [:;;c%^I' Z8A+)1>2"8A' %A3' 9"+.' +$%9"AF' 8H-9' 2$-' B"C-' #?#B-I'

' Journal of Monetary EconomicsI'L5[6^I'b;\pb66<

0289-+B-22-A'e<I'@-B1-9'Z<Y<I'f%98A'=<'[:;;c*^I'Z?#B"#%B'3?A%1"#+'"A'"3"8+?A#9%2"#'B%*89'1%9.-2'9"+.I'

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@%)#$-A' g<' [5\`b^I' U"A"2-' +2%2-' !%9.8HD#$%"A' %>>98V"1%2"8A+' 28' )A"H%9"%2-' %A3' H-#289'' ' %)289-F9-++"8A+I'Economics LettersI':;[:^I'5]]p5`5<

T9*%A"-#'=<'[:;5:^I'Life cycle income and consumption patterns in transitionI')A>)*B"+$-3'9->892< f%AF' U<' [:;;\^I' Z8A+)1>2"8A' 8H-9' 2$-' B"C-' #?#B-4' J8E' 3"CC-9-A2' "+' $8)+"AFsI' Review of Economic

DynamicsI'5:[6^I'c:6pcc6<

f%8' (<I' _$%AF' J<J<' [:;;L^I' 7>2"1%B' #8A+)1>2"8A' %A3' >892C8B"8' #$8"#-+' E"2$' 9"+.?' $8)+"AF' %A3'' ' *8998E"AF'#8A+29%"A2+I'Review of Financial StudiesI'5`[5^I'5\]p:6\<

_-B3-+' 0<G<' [5\`\^I' 7>2"1%B' #8A+)1>2"8A' E"2$' +28#$%+2"#' "A#81-4' 3-H"%2"8A+' C981' #-92%"A2?'' ' -W)"H%B-A#-I'The Quarterly Journal of EconomicsI'5;c[:^I':]Lp\`<

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Appendix

@%*B-'5 N-A#$1%9.'>%9%1-2-9",%2"8A Demographics M)1*-9'8C'#8$892+' J bb M)1*-9'8C'E89."AF'#8$892+' J~ cL 0)9H"H"AF'>98*%*"B"2"-+' s_j Z07'[:;5;%^

Individual income process

=F-'>98tB-'8C'>983)#2"H"2?' z_j Z07'[:;;\P':;55^ G-9+"+2-A#-'8C'"3"8+?A#9%2"#'>983)#2"H"2?' * ;<\b d%9"%A#-'8C'"3"8+?A#9%2"#'>983)#2"H"2?' 1_e2 ;<;:L G-A+"8A'9->B%#-1-A2'9%2-' # ;<c Preferences a"+#8)A2'C%#289' ) ;<\` ("+.'%H-9+"8A' $ 5<L; 0$%9-'8C'A8AD$8)+"AF'#8A+)1>2"8A'"A')2"B"2?' 9 ;<]L T2"B"2?'B8++'C981'9-A2"AF' + ;<\; N-W)-+2'>9-C-9-A#-' % 5;

Technology and housing market

7>-AA-++'8C'2$-'-#8A81?' ! ;<;5 Z%>"2%B'+$%9-'"A'>983)#2"8A'C)A#2"8A' 2 ;<6; a->9-#"%2"8A'9%2-' # ;<5; J8)+"AF'1%"A2-A%A#-'#8+2' , ;<;6 @9%A+%#2"8A'#8+2'8C'+-BB"AF' '1 ;<;: @9%A+%#2"8A'#8+2'8C'*)?"AF' '2 ;<;6 !"A"1)1'38EAD>%?1-A2'9%2"8' ( ;<5; '

(19)

@%*B-':

Z81>%9"+8A'8C'*-A#$1%9.'%A3'%B2-9A%2"H-'-#8A81"-+'

!'u';<5 !'u';<6 !'u';<L !'u';<]

YA2-9-+2'9%2-'"A'l' :<6b\ :<6]c :<6`` :<6`: Z%>"2%B'28'gaG'9%2"8' :<c:b :<c:L :<c:: :<c:6 YAH-+21-A2'%+'l'8C'gaG' :;<L :;<L :;<c :;<c J8)+"AF'"AH-+21-A2'%+'l'8C'gaG' 55<c 55<c 55<L 55<L Z8A+)1>2"8A'%+'l'8C'gaG' b6<; b6<; b:<\ b:<\ 'U9%#2"8A'8C'$8)+-$8B3+'E"2$'3-*2' :\<: :5<6 5L<6 5;<] J8)+-$8B3'3-*2'%+'l'8C'gaG' c6<; :6<: 55<` L<: J81-8EA-9+$">'9%2"8' `]<b ]\<b ]6<: b`<b =H<'%F-'8C't9+2'$8)+-'>)9#$%+-' :b<` 65<] 6c<\ 6]<b 0$%9-'8C'9-A2-3'$8)+-+'"A'282%B'$8)+"AF'+28#.' ]<; 56<L 5\<5 :6<5 ' @%*B-'6 O-BC%9-'B8++'3)-'28'"A#9-%+-'"A'38EAD>%?1-A2'9-W)"9-1-A2+ e

Share PLN –v_(e) _{% of lifespan consumption –}_"(e)

#₀(e) !/'u';<6 !/'u';<L !/'u';<] !/'u';<6 !/'u';<L !/'u';<]

;<:] :<5 :5` c:5 cc\ ;<56: ;<:L: ;<:b` ;<c; \<; :L` 6cc 6cb ;<5c: ;<:b6 ;<:`L ;<L` :6<5 :c] cb` L;` ;<5cb ;<:]: ;<:\6 ;<`c 65<b :`5 Lc5 L\] ;<5:] ;<:c; ;<:b6 5<:6 :6<5 :\; L`c bL] ;<;\b ;<5\5 ;<:5c 5<]\ \<; 6;] bL; ]LL ;<;]6 ;<5L: ;<5]] :<b5 :<5 cb6 \Lb 55cL ;<;]L ;<5L6 ;<5`6 =FF9-F%2- ;<5:; ;<::\ ;<:L5 M82-+4'E-BC%9-'B8++'"A'#81>%9"+8A'28'2$-'*-A#$1%9.'-#8A81?'E"2$'("= 0.1<'

(20)

U"F)9-'5 0)9H"H%B'>98*%*"B"2?'%A3'1-3"%A'>983)#2"H"2? 20 30 40 50 60 70 80 0.88 0.90 0.92 0.94 0.96 0.98 1.00 Survival probability 20 30 40 50 60 70 80 0 0.5 1.0 1.5

(21)

U"F)9-': j"C-'#?#B-'>%2$ ' M82-+4'2$-'tF)9-'>9-+-A2+'2$-'%H-9%F-'H%B)-+'C89'%BB'%F-'#8$892+'%+'E-BB'%+'2$-'"A3"H"3)%B'H%B)-+'C89'2$9--'9%A381B?' +-B-#2-3'$8)+-$8B3+I'%++)1"AF'2$%2'2$-?'+)9H"H-'2"BB'2$-'B%+2'>-9"83<'=BB'H%B)-+'%9-'-V>9-++-3'"A'2$<'GjM<' 20 30 40 50 60 70 80 0 20 40 60 80 100 Non-housing consumption 20 30 40 50 60 70 80 -500 0 500 1000 1500 Financial assets 20 30 40 50 60 70 80 0 100 200 300 400 500

Owned house value

20 30 40 50 60 70 80

0 50 100 150

Annual after-tax labor income

Household 1 Household 2 Household 3 Population average

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U"F)9-'6 Z81>%9"+8A'8C'*-A#$1%9.'%A3'%B2-9A%2"H-'-#8A81"-+ M82-+4'%H-9%F-'H%B)-+'C89'-%#$'%F-'#8$892<'=BB'H%B)-+I'*)2'2$-'$81-8EA-9+$">'9%2"8I'%9-'-V>9-++-3'"A'2$<'GjM<' 20 30 40 50 60 70 80 0 50 100 150 200 Debt 20 30 40 50 60 70 80 -200 0 200 400 600 Financial assets 20 30 40 50 60 70 80 0 0.2 0.4 0.6 0.8 1.0 Homeownership ratio 20 30 40 50 60 70 80 0 100 200 300

400 Owned house value

20 30 40 50 60 70 80 10 20 30 40 50 60 Non-housing consumption 20 30 40 50 60 70 80 50 100 150 200 250 300 350

400 Used house value

γ = 0.1 γ = 0.3 γ = 0.5 γ = 0.7

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Acknowledgments

Y' E8)B3' B".-' 28' 2$%A.' !"#$%&' N9,8,%DN9,-,"A%I' !"#$-B-' Z%i' _89,"I' (?+,%93' e8.8+,#,?v+."I' r%#-.' w%+,-.I' e9,?+,28C' 7B+,-E+."I' !%9F%9"2%' ()*"8I' =B-.+%A39%' T9*%A"-#I' 2E8' %A8A?18)+' 9-C-9--+' %A3'2$-'>%92"#">%A2+'8C'2$-'C8BB8E"AF'#8AC-9-A#-+4'0!fK:;5:'[!%AA$-"1I':;5:^I'MNG'K#8A81"#' 0-1"A%9' [O%9+%EI' :;55^' %A3' 0gJ' K#8A81"#' 0-1"A%9' [O%9+%EI' :;55^' C89' $-B>C)B' #811-A2+<' =BB' 9-1%"A"AF' -9989+' %9-' 1?' 8EA<' @$-' H"-E+' -V>9-++-3' "A' 2$"+' >%>-9' %9-' 8C' 2$-' %)2$89' %A3' 38' A82' 9->9-+-A2'2$-'8CC"#"%B'+2%A#-'8C'2$-'M%2"8A%B'N%A.'8C'G8B%A3<

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