Saving on a Rainy Day, Borrowing for a Rainy Day Sule Alan 12 Thomas Crossley 123 Hamish Low 23 Paper at:http://www.ifs.org.uk/wps/wp1211.pdf 1 Koc University 2 University of Cambridge 3 Institute for Fiscal Studies 25 October 2012 Alan, Crossley and Low (Cambridge) Rainy Days 25 October 2012 1 / 28
Motivation What does a recession imply for di¤erent households? I E¤ect on income only part of the story I Increased uncertainty (unemployment, asset prices) I Contractions in supply of credit How do households respond? Alan, Crossley and Low (Cambridge) Rainy Days 25 October 2012 2 / 28
Motivation: Savings Rates Over Time Spike in saving: consumption not smoothed, fall in borrowing Alan, Crossley and Low (Cambridge) Rainy Days 25 October 2012 3 / 28
Motivation PIH: consume a permanent income change and annuity value of a transitory income change: I Transitory income loss � ! saving level and rate both fall I Permanent income loss � ! no change in savings level; denominator e¤ect leads to rate rise Alan, Crossley and Low (Cambridge) Rainy Days 25 October 2012 4 / 28
Motivation PIH: consume a permanent income change and annuity value of a transitory income change: I Transitory income loss � ! saving level and rate both fall I Permanent income loss � ! no change in savings level; denominator e¤ect leads to rate rise Model saving during booms and recessions in a life-cycle model with stable preferences Distinguish e¤ects of di¤erent types of recession Alan, Crossley and Low (Cambridge) Rainy Days 25 October 2012 4 / 28
Motivation: What is a Recession? Aggregate shock to income (permanent or transitory) 1 Rise in uncertainty 2 I idiosyncratic risk rises in recessions (Carroll, 1992) I variance of highly persistent shocks rises (Blundell, Low and Preston, 2011) Credit crisis 3 I rationing credit raises aggregate saving? Guerrieri and Lorenzoni (2011) I Mian and Su… (2009, 2010): over-indebtedness Wealth destruction 4 I sharp falls in asset prices - rebuilding balance sheets? I Moore and Palumbo (2011); de Nardi et al (2011) Alan, Crossley and Low (Cambridge) Rainy Days 25 October 2012 5 / 28
Outline Life-cycle Model of Saving in Recessions 1 Data: E¤ect of Recessions on Savings Rates 2 Model Inputs and Calibration 3 Simulated Responses to di¤erent types of Recession 4 Alan, Crossley and Low (Cambridge) Rainy Days 25 October 2012 6 / 28
Life-cycle Model of Saving Standard life-cycle dynamic portfolio allocation model Possibility of recession: 2 state Markov process Aggregate income shock 1 Aggregate income shock and idiosyncratic uncertainty higher 2 Aggregate income shock and credit market tightening. 3 Possibility of asset crash (whether in a recession or not) Alan, Crossley and Low (Cambridge) Rainy Days 25 October 2012 7 / 28
Life-cycle Model of Saving Standard life-cycle dynamic portfolio allocation model Possibility of recession: 2 state Markov process Aggregate income shock 1 Aggregate income shock and idiosyncratic uncertainty higher 2 Aggregate income shock and credit market tightening. 3 Possibility of asset crash (whether in a recession or not) Realisation of a recession can occur with or without a crash Explicit aggregation from micro to macro Alan, Crossley and Low (Cambridge) Rainy Days 25 October 2012 7 / 28
Life-cycle Model of Saving " # T � t β j ( c t + j ) 1 � γ ∑ V t = max c , q , d E t 1 � γ j = 0 c t + q t � d t � x t x t + 1 = ( 1 + r q t + 1 ) q t � ( 1 + r ) d t + y t + 1 x t : cash-on-hand at the start of period q t : holding of a risky asset at end of the period d t : debt owed at end of the period ( d t < 0 indicates saving in the safe asset) Alan, Crossley and Low (Cambridge) Rainy Days 25 October 2012 8 / 28
Life-cycle Model Recession 2 state Markov process: Boom t + 1 Recession t + 1 Boom t π 1 � π 1 � ρ ρ Recession t Asymmetric process Alan, Crossley and Low (Cambridge) Rainy Days 25 October 2012 9 / 28
Life-cycle Model Stochastic Return Process Composite Risky Asset Excess returns are iid Possibility of a crash in the asset price: a return of � φ Probability of a crash is p R in a recession, p B in a boom, p R > p B . Alan, Crossley and Low (Cambridge) Rainy Days 25 October 2012 10 / 28
Life-cycle Model Income Process Y iat : stochastic labour income for individual i age a in period t : ln Y iat = ln Y P u iat � N ( 0 , σ 2 iat + λ D t + u iat , u ) ln Y P iat = ln Y P η iat � N ( 0 , σ 2 iat � 1 + f ( age ) + θ D t + η iat η , t ) λ transitory e¤ect of a recession : θ permanent e¤ect of a recession : ∆ ln Y iat = f ( age ) + θ D t + λ ∆ D t + η iat + ∆ u iat Alan, Crossley and Low (Cambridge) Rainy Days 25 October 2012 11 / 28
Life-cycle Model Variance Shock Recession How does the variance of permanent and transitory idiosyncratic shocks ( η iat and u iat ) evolve over the business cycle? N ( 0 , σ 2 η it � η , B ) in boom N ( 0 , σ 2 η it � η , R ) in recession Focus on increase in permanent variance in recessions (Blundell, Low, Preston, 2011) Alan, Crossley and Low (Cambridge) Rainy Days 25 October 2012 12 / 28
Life-cycle Model Alternative Credit Constraints Implicit constraint: cannot borrow more than repay with certainty 1 Explicit quantity constraint: cannot borrow more than a certain level 2 d it � ¯ d Alan, Crossley and Low (Cambridge) Rainy Days 25 October 2012 13 / 28
Life-cycle Model Alternative Credit Constraints Implicit constraint: cannot borrow more than repay with certainty 1 Explicit quantity constraint: cannot borrow more than a certain level 2 d it � ¯ d Explicit quantity constraint dependent on income: 3 d it < 3 Y it Flow constraint: cannot increase the stock of debt (have to repay 4 interest) : d it � d it � 1 if d it > 0 Alan, Crossley and Low (Cambridge) Rainy Days 25 October 2012 13 / 28
Life-cycle Model Alternative Credit Constraints Implicit constraint: cannot borrow more than repay with certainty 1 Explicit quantity constraint: cannot borrow more than a certain level 2 d it � ¯ d Explicit quantity constraint dependent on income: 3 d it < 3 Y it Flow constraint: cannot increase the stock of debt (have to repay 4 interest) : d it � d it � 1 if d it > 0 Credit Supply Shock Recession : ‡ow constraint comes into place. Alan, Crossley and Low (Cambridge) Rainy Days 25 October 2012 13 / 28
Precautionary Borrowing First-order condition w.r.t. d t � � ( 1 + r ) ∂ V t + 1 � ∂ V t + 1 u c ( x t + d t � q t ) = β E t ∂ x t + 1 ∂ d t Borrow in period t because of possibility that need debt in period t + 1 : borrowing for a rainy day Alan, Crossley and Low (Cambridge) Rainy Days 25 October 2012 14 / 28
Precautionary Borrowing First-order condition w.r.t. d t � � ( 1 + r ) ∂ V t + 1 � ∂ V t + 1 u c ( x t + d t � q t ) = β E t ∂ x t + 1 ∂ d t Borrow in period t because of possibility that need debt in period t + 1 : borrowing for a rainy day Option value of holding debt: ∂ V t + 1 > 0 ∂ d t ... but ∂ V t + 1 ∂ x t + 1 higher because of presence of constraint in t + 1 Both precautionary borrowing and precautionary saving motives are present: I consumption in t could be lower or higher Alan, Crossley and Low (Cambridge) Rainy Days 25 October 2012 14 / 28
Solution Without Flow Credit Constraint Two motives for borrowing. As cash-on-hand rises: desire to leverage and buy risky asset Contrast with single asset model Alan, Crossley and Low (Cambridge) Rainy Days 25 October 2012 15 / 28
Solution With Flow Credit Constraint High x : constraint reduces equity investment (increases consumption) Alan, Crossley and Low (Cambridge) Rainy Days 25 October 2012 16 / 28
Data UK micro data (FES) 1976-2010: consumption, income etc Recessions: 1980-1981, 1990-1991, 2008-2009 Micro data: observe individual behaviour Synthetic cohort analysis Observe young/ middle aged/ old in each recession Alan, Crossley and Low (Cambridge) Rainy Days 25 October 2012 17 / 28
Estimates Saving Rates at Onset: what fraction of cohort income is saved ∆ Savings Rate Savings Rate Recession � 0.0390 ( . 0093 ) Recession Onset 0.0108 0.0115 ( . 012 ) ( . 0131 ) Recession Onset + 1 0.030 0.0224 ( . 012 ) ( . 0131 ) Recession Onset + 2 0.051 0.0211 ( . 014 ) ( . 0148 ) Recession Onset + 3 0.0118 -0.0365 ( . 014 ) ( . 0148 ) F-Test (p-value) 4.24 (0.004) 3.24 (0.0166) Same across age groups and across recessions Alan, Crossley and Low (Cambridge) Rainy Days 25 October 2012 18 / 28
Simulations Show calibration Show baseline life-cylce pro…les: consumption, savings, net worth, leverage Simulate behaviour in alternative recessions: I Recession occurs and lasts 2 periods: Fall in permanent income 1 Fall in permanent income and variance increase 2 Credit market constraint tightens in recession 3 I Asset price crash occurs at start of the recession E¤ects on di¤erent cohorts depending on age at onset (25,40,55) Alan, Crossley and Low (Cambridge) Rainy Days 25 October 2012 19 / 28
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