What Accounts for the Growing Fluctuations in FamilyOECD Income March in the US? / 32

Transcription

1 What Accounts for the Growing Fluctuations in Family Income in the US? Peter Gottschalk and Sisi Zhang OECD March What Accounts for the Growing Fluctuations in FamilyOECD Income March in the US? / 32

2 Puzzle Variance of transitory log earnings grew primarily in 1970 s and early 1980 s What Accounts for the Growing Fluctuations in FamilyOECD Income March in the US? / 32

3 Puzzle Variance of transitory log family income grew throughout the period What Accounts for the Growing Fluctuations in FamilyOECD Income March in the US? / 32

4 Question and Objective Question addressed :What accounts for the di erences in recent trends in the variance of earnings and family income? Do these changes re ect changes in permanent income (i.e. non-mean reverting changes) transitory changes in income (i.e. mean reverting) What Accounts for the Growing Fluctuations in FamilyOECD Income March in the US? / 32

5 Question and Objective Objective Provide consistent links between family income instability and instability of income components Studies of family income instability are implicitly studies of changes in the joint distribution of income components j = 1..J : y = y j, (1) f (y 1...y J ) is pdf of joint distribution (2) Studies of individual components focus on the marginal distribution of each component What Accounts for the Growing Fluctuations in FamilyOECD Income March in the US? / 32

6 Overview of Presentation 1 Background 1 Why do we care about income instability? 2 What do these considerations imply about the income source? 2 Methodology 3 Data 1 Intuition of source of identi cation 2 Relationship between the joint distribution of income sources and the variance of the log family income? 3 Methods to identify and estimate permanent and transitory components of individual sources of income 4 Method to aggregate up to the permanent and transitory components of family income 4 Findings 5 Conclusions What Accounts for the Growing Fluctuations in FamilyOECD Income March in the US? / 32

7 Normative Implicit normative basis for interest in changes in variability of income and implied income concept 1 Risk aversion 1 Friedman s (1957) classic permanent income hypothesis 2 Aversion to uctuations in family income 1 No aversion to uctuations in earnings that are o set costlessly 1 Blundell et al. considerable consumption smoothing takes place in response to transitory shocks What Accounts for the Growing Fluctuations in FamilyOECD Income March in the US? / 32

8 Normative 1 Aversion to inequality 1 Yearly or lifetime depends on ability to save or borrow 1 If lifetime then no aversion to transitory uctuations 2 Aversion to uctuations in family income 1 No aversion to uctuations in earnings that are o set by transfers What Accounts for the Growing Fluctuations in FamilyOECD Income March in the US? / 32

9 Normative 1 Preference for mobility 1 Increases in transitory uctuations are a source of mobility 1 Shorrocks measure of mobility 2 Origin independence implies preference for fewer observations on diagonal of transition matrix 2 If rank reversal is preferred then aversion to increases in the variance of the permanentt component 3 Income concept is again family income What Accounts for the Growing Fluctuations in FamilyOECD Income March in the US? / 32

10 Positive 1 Understand the source of changes in the distribution of earnings 1 Original interest of Gottschalk Mo tt (1993) 2 Almost all explanations are implicitly about changes in the variance of the permanent component 1 Skill bias technological change 2 Immigration 3 Changes in institutions 3 Explanations for transitory very di erent 1 Changes in job transitions 2 Changes in unemployment dynamics / 32

11 Intuition Permanent component causes income to be correlated across time. Transitory component does not, if the lag is su ciently long for auto-correlated errors to die o So the permanent component is identi ed by su ciently far o diagonal elements of the covariance matrix / 32

12 Intuition Consider two extreme cases 1 Case A tns The variance of total income changes on the diagonal, 1 so the variance of either permanent or transitory income had to have changed 2 Since "long"covariances are zero, the variance of permanent income is zero 3 Therefore changes in cross-sectional variance re ects changes in variance of transitory income / 32

13 Intuition Case B tns The variance went up and then back down as in Case A But the covariances are not zero and changed along with the variances. This implies that the variance of permanent income changed What is not so obvious is that the cross sectional variance re ects only permanent variance If ρ (y it y is ) = 1 then σ (y it y is ) = σ (y is ) σ (y is ), which is satis ed / 32

14 Intuition Case C tns The covariances are same as in Case B But the variances are now higher. Subtract the variance in B from the variance in C to get the variance of the transitory component / 32

15 Intuition Summary of intuition Long covariances give the needed information to identify the variance of permanent income The variance of the transitory component is the additional to total variance / 32

16 Methods for Single Source of Income A bit more formally, let Yit k = Ỹt k + ε k it (3) ε k it = α k t µ k i + β k t νk it (4) Ỹ k t is the conditional mean log income from source k. ε k it. is the person speci c error component β k t νk it. is the transitory (i.e. mean reverting) component α k t µ k i, is the permanent (i.e. non-mean reverting) component Implied variances and covariances of ε it σ 2 ε it = α 2 t σ 2 µ + β 2 t σ2 ν (5) σ εit, ε is = α t α s σ 2 µ + β t β s σ νt ν s (6) / 32

17 Methods for Single Source of Income Estimation Estimation methods #1 Parametric Statistical Model Make assumptions about time series properties of µ it and v it Use GMM to estimate parameters of the model using all T (T + 1)/2 covariances #2 Smoothing method Moving window Permanent component variance of individual mean incomes Transitory component variance of deviations around individual means / 32

18 Methods for Single Source of Income Estimation #3 Semi- parametric method what we use in this paper No restrictions on time series properties of µ it and v it Estimation Use su ciently long lags to eliminate transitory component (i.e. σ νt ν s = 0). So σ εit, ε is = α t α s σ 2 µ + β t β s σ νt ν s (7) reduces to Take logs σ εit, ε is = α t α s σ 2 µ (8) ln σ εt, ε s = ln σ 2 µ + ln α t + ln α s (9) Minimize distance between empirical and theoretical covariances 2 min ln(sˆεt,ˆε s ) ln σ 2 µ + ln α t + ln α s (10) / 32

19 Methods for Single Source of Income Estimation Rewrite as the projection ln(sˆεt,ˆε s ) = ln σ 2 µ + ln α t + ln α s + ɛ (11) The parameters (σ 2 µ and α 0 s) are obtained from the regression ln(sˆεt,ˆε s ) = γ 0 + T j=1 γ s D s + 2 (12) since E ( ˆγ 0 ) = ln σ 2 µ and E ˆγ j = ln αj Recover transitory component as di erence between total and permanent variances / 32

20 Methodology for Multiple Sources of Income Variance of ln family income Variance log family income is a nonlinear function of variances and covariances of subcomponents of log income. Using Taylor series it can be shown that σ 2 (Y k t ) K k=1 " E (yk ) 2 σ 2 (Y k E (y T ) y k income from source k t ) + K l=1! # E (y k ) E (y l ) (E (y T )) 2 σ(yt k, Yt l ) (13) Y k t log income from source k E (y k ) E (y T ) mean of source k relative to total income σ 2 (Y k t ) variance of log income from source k So σ 2 (Y k t ) depends on full covariances structure across sources / 32

21 Methodology for Multiple Sources of Income Covariance structure across income sources Consider two income sources( k = m, f ) and two periods. Yit m = α m t µ m i + β m t νm it (14) Yit f = α f t µ f i + β t ν f it (15) Implies the following 4x4 covariance matrix Y m t Y m s Y f t Y f s Y m t α 2 mt σ 2 µm α mt α ms σ 2 µm α mt α ft σ 2 µ (fm) α mt α fs σ 2 µ (fm) Y m s α 2 ms σ 2 µm α ms α ft σ 2 µ (fm) α ms α fs σ 2 µ (fm) Y f t α 2 ft σ2 µf α ft α fs σ 2 µf Y f s α 2 fs σ2 µf The 2x2 sub-matrix in upper right gives the correlations in income sources that also a ect the variance of log family income / 32

22 Data Panel Study of Income Dynamics (PSID) Income year (skipped interview every other year after 1996) Sample Families with male household heads age Exclude over-sampled (SEO, Latino) Trim 1% from top and bottom of marginal distributions of each income source in each year / 32

23 Trends in Marginal Distribution of Family Income Steady increase in variance of total income re ects continued increase in both permanent and transitory variance / 32

24 Trends in Marginal Distribution of Head s Earnings Male Head Earnings Increase in total and transitory variances concentrated in 1970 s and early 80 s / 32

25 Trends in Marginal Distribution of Spouse s Earnings Spouses earnings Continued increase in variance of total family income can t be explained by spousal earnings since both total and transitory variances decline / 32

26 Trend in Marginal Distribution of Other Income Other income Large increase in both total and transitory variances starting in the mid-1980 s (note scale) Recent decline in transitory variance / 32

27 Trends in Covariance of Head and Spouse Log Earnings The covariance between the transitory earnings of heads and spouses increased over the recent period. This rising covariance is consistent with a decline in the ability to share risk and an increase in instability of family income / 32

28 Trends in Covariance of head s earnings and other income The increase in the positive covariance between head s earnings and other transitory income also contributed to the increase in family income instability / 32

29 Relative Importance of Changes in Variances and Covariances Use the approximation to the variance of log family income shown earlier to estimate the partial impact of changes in the variances and covariances 2 σ 2 (Y T ȳ1 ) σ 2 (Y 1 ) (16) To reduce impact of noise is de ned by the change in variances (or covariances) averaged over 3 years Summing across impact of all variances and covariances will not exactly match observed change in variance log family income because Approximation holds only in limit ȳ T Variances and covariances require samples of positive income from those source Trimming eliminates di erent sample members / 32

30 Relative Importance of Changes at Intensive Margin / 32

31 Relative Importance of Changes at Intensive Margin / 32

32 Conclusions and Next Steps Conclusions Transitory variance of head s earnings stopped growing in mid-1980 s while family income instability continued to rise Largely a result of increases in covariances in transitory across income sources Next Steps Estimate covariance structure of the extensive margin Bound potential selection e ects (much harder) / 32