## _wp16121

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---

### I. Introduction — overview and purpose
- Focus: document the rise in income polarization in the U.S. since the 1970s and explore potential macroeconomic impact on aggregate consumption.
- Income definition: household’s final disposable income, including salaries, wages, interest, etc., after taxes and transfers.
- Key observation: since the 1970s, real incomes of households in low to middle income brackets have stagnated while real incomes of households in the highest brackets rose sharply during 1970–2000 and have not changed considerably since 2000.
- Scope limitation: investigating root causes of rising income polarization is beyond this paper’s scope.

### II. Rising income polarization — empirical findings
- Middle-income share (households with 50-150 percent of median income) declined from about 58 percent in 1970 to 47 percent in 2014.
- During 1970-2000 more middle-income households moved up than down; since 2000:
  - 0.25 percent of households moved up from middle to high income.
  - 3¼ percent of households moved down from middle to low income.
- Robustness checks:
  - Alternative middle-income definitions (60-225 percent and 75-125 percent of median income) produce qualitatively similar polarization trends.
  - Adjusting for household size using OECD’s equivalence scale applied throughout; results without adjustment are qualitatively similar.
  - Using CPI versus PCE deflator does not qualitatively change results reported.

### III. Demographic patterns of polarization
- Polarization increased across age cohorts, education levels, and household head races (long-sample data for black and white only).
- Exception: polarization has somewhat decreased for households with female heads.
- Household-size adjustment: OECD’s equivalence scale (first household member = 1, each additional adult = 0.7, each child = 0.5) applied to all series.

### IV. Combined trends: polarization and income shares (1970–2014)
- Income shares interpretation: indicator of economic power of each income bracket.
- Historical pattern (1970s–late 1970s): middle- and high-income classes held broadly similar income shares slightly shy of 50 percent each.
- By 2014:
  - High-income class holds about 60 percent of total income.
  - Middle-income class holds about 35 percent of total income.
  - Low-income class income share stable at about 5 percent of total for 1970-2014.

### V. Polarization index — definition, properties, and examples
- Adopted index: Wolfson (1994) polarization index.
- Construction:
  - Based on area under the “polarization curve,” a rotation and rescaling of the Lorenz curve by median income.
  - Index equals 4 times the area between the polarization curve and the median tangent (area between curve and tangent at 50th percentile).
  - Index range: 0 (no polarity) to 1 (bipolarity).
- Conceptual properties:
  - Allows construction of a polarization ranking over distributions and is comparable across time without assuming cut-offs to define the middle-income class.
  - Maps into the Gini coefficient, but is less sensitive to income growth at the extreme top and bottom percentiles.
  - Focuses on relative size of income classes rather than their incomes; inclusion or exclusion of the top 1 percent does not materially change polarization trends.
- Illustrative example (from text):
  - Two households each with income $1 → polarization index = 0 (income share of bottom 50 percent = 0.5; Gini = 0).
  - Example where income share of the bottom 50 percent is equal to 0; the Gini coefficient is 0.5; yields P=4*(0.5-0-0.5/2)*1=1 (illustrating bipolarity).

### VI. Data sources, sample definitions, and handling
- Primary micro datasets: Current Population Survey (CPS), Panel Study of Income Dynamics (PSID), Survey of Consumer Finances (SCF).
- Sample periods:
  - Polarization and inequality trends: 1970–2014.
  - Econometric analysis of consumption (PSID): 1998-2013 (pre-crisis 1998-2006; crisis/post-crisis 2007-2013).
- Household-income group definitions:
  - Low Income: less than 50 percent of median income.
  - Middle Income: 50-150 percent of median income.
  - High Income: more than 150 percent of median income.
- Measurement notes:
  - PSID: family income constructed from taxable income of head and partner plus transfers; disposable income constructed using NBER TAXSIM (v.9).
  - PSID wealth constructed from asset and liability components; net worth available from 1998 to 2013.
  - PSID has only food expenditures prior to 1998; econometric analysis starts in 1998.
  - Consumption categories used: education, childcare, transportation, housing, and food; health care expenditures omitted.
  - CPS: FTOTVAL family income variable; top-coded prior to 1976 at 50,000 dollars.
  - SCF: five imputed versions used; average of Gini and Polarization Index across imputations used as final value.
- Sampling unit and family definitions:
  - CPS: housing unit/dwelling; household defined as all people who occupy a housing unit regardless of relationship.
  - PSID: family unit (FU); PSID follows families; multiple families may reside in same household.
  - SCF: primary economic unit (PEU) — individuals connected by financial interdependence.
- Common sample restrictions:
  1) head of household information present (income, age);
  2) head aged 24 to 64;
  3) head resides in the U.S.
- Additional exclusions and trimming:
  - Extremely poor families (< 2 dollars per day in real 2005 terms) dropped.
  - SCF: drop households with income in the top 1%.
  - “Trimmed” sample excludes observations exceeding top 1% thresholds from Alvaredo et al. (2015) and bottom 1%.
  - PSID-specific exclusions include SEO and Latino supplement samples, extreme income jumps (>500% or <-80%), and various data-missing conditions.

### VII. PSID sample attrition and econometric sample sizes (1998–2013)
- PSID full-sample initial observations: 85,892
- Sequential drops and remaining counts (selected):
  - Drop 2013 (attrition weights not adjusted for 2013): Dropped 10,669 → Remaining 75,223
  - Drop SEO and Latino sample: Dropped 21,575 → Remaining 53,648
  - Age 24–64 restriction: Dropped 7,348 → Remaining 46,300
  - At least two observations required (panel): Dropped 5,915 → Remaining 34,862 (Full sample used for regressions)
  - Regression sample further restrictions:
    - Non-missing DI, wealth and expenditures + normalization 1/ c(t-2): Dropped 16,378 → Remaining 19,291
    - Instrument availability: Dropped 1,485 → Remaining 17,806
- Econometric sample size: approximately 3000-4000 observations per year where household is unit of observation (panel).

### VIII. PSID descriptive statistics (selected moments)
- Table 2.A Total Expenditures (Unconditional Weighted Mean) — selected items (values for years 2000, 2004, 2008):
  - Total Food: 7,238; 7,659; 8,180
    - At home: 5,119; 5,291; 5,854
    - Away from home: 2,024; 2,254; 2,227
    - Delivered: 129; 140; 120
  - Total Housing*: 19,326; 23,068; 26,127
    - Mortgage*: 8,411; 9,294; 10,540
    - Rent*: 1,450; 1,506; 1,801
    - Insurance: 432; 591; 706
    - Property Tax: 1,626; 2,053; 2,564
    - Utilities: 2,509; 2,536; 2,823
  - Total Transportation: 7,114; 8,208; 7,487
    - Loan Payment: 1,618; 1,840; 1,525
    - Down payment: 1,624; 1,750; 1,510
    - Lease payment: 491; 306; 265
    - Insurance: 1,436; 1,786; 1,725
    - Gasoline: 1,751; 2,280; 2,359
  - Education: 1,895; 2,249; 2,609
  - Childcare: 584; 504; 428
  - Total Expenditures (row): 36,154; 41,685; 44,829
  - N (sample counts for those years): 5,223; 5,520; 5,147
- Table 2.B Income, Wealth and Consumption — selected percentiles and means (years 1999, 2002, 2006, 2010):
  - Disposable Income p25: 29,054; 29,510; 32,859; 31,797
  - Disposable Income p50: 46,500; 49,683; 56,786; 60,098
  - Disposable Income p75: 68,306; 77,580; 91,754; 97,373
  - Disposable Income Mean: 53,804; 59,441; 70,696; 73,349
  - Net Worth without Home Equity Mean: 129,366; 179,240; 300,445; 271,105
  - Net Worth with Home Equity Mean: 183,156; 267,405; 439,068; 373,111
  - Expenditures Mean (annualized/divided by 0.7 shown in parentheses): 30,897 (44,139); 36,868 (52,669); 45,991 (65,701); 46,356 (66,223)
  - N (expenditures): 4,254; 4,443; 4,771; 4,553

### IX. Regression approach to estimate MPC out of permanent income (MPCP)
- Objective: measure MPCP and examine impact of polarization on aggregate consumption.
- Estimation approach:
  - PSID panel with an instrumental variables fixed effects specification.
  - Regress normalized changes in personal consumption expenditures on instrumented normalized changes in income.
  - Normalization: changes normalized by consumption two periods prior (e.g., changes from 2005 to 2007 normalized by consumption in 2003).
  - Controls: changes in real net worth, household size, region, age and age squared of household head, household fixed effects, yearly fixed effects; time-varying controls fully interacted with year dummies.
- Instrument for permanent income:
  - Average annual income of other households in the same region-age-family-size cohort (excluding household’s own income), with quadratic and cubic terms added as instruments.
  - First-stage F-Statistic of income on instrument: 618.10.
  - Kleibergen-Paap under-identification test: rejects null of under-identification.
  - Sargan-Hansen over-identification test: fail to reject joint null that instruments are valid.

### X. Empirical MPCP estimates (1998–2013) — exact reported values
- Simple scatter trend: MPCP ≈ 80 percent.
- OLS with fixed effects (whole sample): MPCP ≈ 40 percent.
- OLS bracketed MPCPs (1998-2013):
  - Low-income 60 percent.
  - Middle-income 40 percent.
  - High-income 30 percent.
- IV (2SLS) fixed-effects estimates (instrumented income):
  - Overall MPCP ≈ 100 percent for the whole sample (2SLS).
  - By bracket (2SLS): low-income 180 percent; middle-income 80 percent; high-income 50 percent.
  - Low-income 2SLS estimate imprecise with large standard errors.
- Pre/post-2007 split:
  - MPCPs for low, middle, and high income brackets estimated to be lower post crisis than pre crisis, though estimates have large standard errors.
- Polynomial (fractional polynomial around median) IV identification:
  - MPCPs estimated close to 100 percent for low-income brackets (imprecisely estimated) and decline to around 70 percent for higher income groups.
- Net worth response:
  - Net worth generally not a significant factor in consumption decisions when controlling for permanent income.
- Regression table notes (selected exact counts and statistics):
  - Number of Households: 6,170 (OLS), 4,868 (IV), 3,690 (IV Pre-2007), 3,213 (IV Post-2007).
  - Number of Observations: 19,291 (OLS), 17,806 (IV), 9,594 (IV Pre-2007), 6,426 (IV Post-2007).
  - Kleibergen-Paap LM Statistic examples: 84.11, 16.65, 71.57, 40.63.
  - R-Squared (OLS reported): 0.56 and 0.60 in specified columns.
  - Significance notation: *** p<0.01, ** p<0.05, * p<0.1.

### XI. Aggregate consumption effects of rising polarization (1998–2013)
- Identified forces affecting aggregate consumption over 1998-2013:
  1. Hollowing out: most middle-income outflows moved into the low-income class, ceteris paribus implying lower aggregate consumption.
  2. Composition effect: migration from middle to low income implies higher aggregate MPCPs (raising consumption).
  3. Behavioral change: overall decrease in MPCPs after controlling for income (lower responsiveness), which works against the composition effect and raises aggregate consumption relative to what composition alone would imply.
- Net result (Figure 17 analysis):
  - Total impact: lower level of aggregate consumption by around 3½ percent at the end of the sample (relative to the counterfactual where polarization remained at 1998 levels).
  - This cumulative consumption loss is split equally between lower MPCPs and lower median income levels.
  - The lost consumption is equivalent to more than one year of consumption, based on historical averages, over 15 years.

### XII. Main conclusions
- Income polarization has risen substantially in the past four decades—often faster than inequality as measured by the Gini coefficient; since the turn of the century most polarization has been towards lower incomes.
- Household consumption behavior shows heterogeneity across the income distribution and has become slightly less responsive to permanent income shocks over time (lower MPCPs).
- The hollowing out of the middle-income class combined with lower MPCPs reduced aggregate consumption by around 3½ percent by 2013 relative to a 1998-polarization counterfactual.

### XIII. Advantages, contributions, and suggested future research
- Advantages and contributions:
  - Household-level analysis aligns with availability of consumption data.
  - Documents rising polarization using a polarization index (Wolfson (1994)) in addition to bracket-based analysis.
  - Estimates marginal propensities to consume out of permanent income changes (MPCP) for low-, middle-, and high-income brackets.
  - Provides estimates for “lost aggregate consumption” in the U.S. due to increased polarization during 1998-2013 (initial year 1998; exercise period 1998-2013).
- Suggested avenues for future research:
  - Study root causes of rising income polarization (technological progress, declining unionization, taxation, international trade, education, immigration, household structure and demographics).
  - Develop a general equilibrium model to study macroeconomic effects of higher income polarization, incorporating consumption, investment, labor supply, tax and transfer policies, and relationship to GDP growth.
  - Analyze why MPCPs have decreased in recent years and whether these changes are temporary or permanent, and whether they stem from the global crisis or represent a secular trend.
  - Calculate the polarization index for other countries to enable cross-country comparisons of polarization trends.

*Source: Excerpt from _wp16121 - REFERENCES.*

### REFERENCES

### _wp16121 - REFERENCES

### I. Introduction — overview and purpose
- Focus: document the rise in income polarization in the U.S. since the 1970s and explore potential macroeconomic impact on aggregate consumption.
- Income definition: household’s final disposable income, including salaries, wages, interest, etc., after taxes and transfers.
- Key observation: since the 1970s, real incomes of households in low to middle income brackets have stagnated while real incomes of households in the highest brackets rose sharply during 1970–2000 and have not changed considerably since 2000.
- Scope limitation: investigating root causes of rising income polarization is beyond this paper’s scope.

### II. Rising income polarization — empirical findings
- Middle-income share (households with 50-150 percent of median income) declined from about 58 percent in 1970 to 47 percent in 2014.
- During 1970-2000 more middle-income households moved up than down; since 2000:
  - 0.25 percent (a quarter of one percent) of households moved up from middle to high income.
  - 3¼ percent of households moved down from middle to low income.
- Robustness checks:
  - Alternative middle-income definitions (60-225 percent and 75-125 percent of median income) produce qualitatively similar polarization trends.
  - Adjusting for household size using OECD’s equivalence scale is applied throughout; results without adjustment (not reported) are qualitatively similar.
  - Using CPI versus PCE deflator does not qualitatively change results reported.

### III. Demographic patterns of polarization
- Polarization has risen across age cohorts, education levels, and household head races (data long-sample available for black and white only).
- Exception: polarization has somewhat decreased for households with female heads.
- All series displayed are adjusted for household size using OECD’s equivalence scale (methodology: first household member = 1, each additional adult = 0.7, each child = 0.5).

### IV. Combined trends: polarization and income shares
- Income shares interpretation: indicator of economic power of each income bracket.
- Historical pattern (1970s–late 1970s): middle- and high-income classes held broadly similar income shares slightly shy of 50 percent each.
- By 2014:
  - High-income class holds about 60 percent of total income.
  - Middle-income class holds about 35 percent of total income.
  - Low-income class income share stable at about 5 percent of total for 1970-2014.

### V. Comparison with other studies — reasons for material differences
- Pew (2015) and Rose (2016) find more polarization into high- than low-income class over comparable periods; this paper finds different long-horizon results (1970-2014) because:
  - Unit of analysis: this paper uses households; Pew and Rose report "adults in households." Double-weighting adults (e.g., married couples) biases distributions toward higher-income adults.
  - Household-size adjustment: this paper uses OECD’s equivalence scale; Pew and Rose divide household income by the square root of household members. Differences in equivalence scales produce different effective weights (Pew’s and Rose’s weights generally smaller than this paper’s, except for single-member households where weight = 1).
  - Sample restriction: this paper restricts household heads to ages 24-64 to focus on working families; other studies’ sample restrictions are not specified here.

### VI. Advantages and contributions of this paper
- Uses household-level analysis (aligns with availability of consumption data).
- Novelty: documents rising polarization using a polarization index (Wolfson (1994) index) in addition to bracket-based analysis — provides a single-number metric analogous to Gini for inequality.
- Estimates marginal propensities to consume out of permanent income changes (MPCP) for low-, middle-, and high-income brackets.
- Provides estimates for “lost aggregate consumption” in the U.S. due to increased polarization during 1998-2013 (initial year for exercise is 1998; exercise period 1998-2013).

### VII. Macroeconomic consequences — consumption analysis
- Method:
  - Estimate MPCP for low-, middle-, and high-income brackets using micro data (PSID) and an instrumental variables approach closest to McCarthy (1995).
  - Apply estimated MPCPs to income brackets while keeping aggregate income growth the same across brackets.
  - Compare resulting aggregate consumption to counterfactual with constant MPCPs and bracket sizes at initial year levels; cumulative difference interpreted as lost consumption due to changed MPCPs and higher polarization.
- Literature context:
  - Carroll (2009) reports MPCP between 70-90 percent (calibrated macro model).
  - Blundell et al. (2008), Heathcote et al. (2010a) use household panel data to estimate MPCP.
  - Souleles (1999), Parker et al. (2013) estimate MPC from anticipated transitory income shocks.
  - Jappelli and Pistaferri (2014) and McCarthy (1995) examine MPC using survey data.
- Advantage of current MPCP estimates: micro-data yields more observations and avoids aggregation issues.

### VIII. Index of income polarization — definition and interpretation
- Polarization index adopted: Wolfson (1994) index.
- Construction:
  - Based on area under the “polarization curve,” a rotation and rescaling of the Lorenz curve by median income.
  - Index equals 4 times the area between the polarization curve and the median tangent (area between curve and tangent at 50th percentile).
  - Index range: 0 (no polarity) to 1 (bipolarity).
- Interpretations and illustrative examples:
  - No polarity example: two households each with income $1 → polarization index = 0 (income share of bottom 50 percent = 0.5; Gini = 0).
  - Bipolarity example: two households, incomes $0 and $1 → polarization index equals (example truncated in source).

*Source: Excerpt from _wp16121 - REFERENCES.*

### 1. The income share of the bottom 50 percent is equal to 0; the Gini coefficient is 0.5;

### _wp16121 - 1. The income share of the bottom 50 percent is equal to 0; the Gini coefficient is 0.5;

### Polarization index versus Gini; conceptual properties
- Example values and formula: income share of the bottom 50 percent = 0; Gini coefficient = 0.5; mean equal to median (P=4*(0.5-0-0.5/2)*1=1).
- Key features of the polarization index:
  - Allows construction of a polarization ranking over distributions and is comparable across time without assuming cut-offs to define the middle-income class.
  - Maps into the Gini coefficient, but is less sensitive to income growth at the extreme top and bottom percentiles.
  - Focuses on measuring the relative size of different income classes rather than their incomes; inclusion or exclusion of the top 1 percent does not materially change polarization trends because they constitute only a small percent of the distribution.

### Data sources and sample definitions
- Primary micro datasets used: Current Population Survey (CPS), Panel Study of Income Dynamics (PSID), Survey of Consumer Finances (SCF).
- Sample periods:
  - Polarization and inequality trends: 1970–2014.
  - Econometric analysis of consumption (PSID, expenditure data available): 1998-2013 (split into pre-crisis 1998-2006 and crisis/post-crisis 2007-2013).
- Variables used: total disposable income after taxes and transfers, personal consumption expenditures, net worth of households.
- Household-income group definitions used for descriptive analysis:
  - Low Income: less than 50 percent of median income.
  - Middle Income: 50-150 percent of median income.
  - High Income: more than 150 percent of median income.
- Notes on adjustments and sample handling:
  - Underlying income data for some CPS charts adjusted for household size using OECD's equivalence scale.
  - PSID econometric regressions do not adjust consumption data for household size; household size is controlled via dummies and fixed effects.
  - SCF and PSID comparisons: not adjusted for household size in some series due to differing household definitions.

### Polarization versus inequality trends (1970–2014)
- Both income inequality and polarization in the U.S. increased substantially since 1970.
- Polarization index trends:
  - Polarization index grew faster than the Gini coefficient during 1970–2014.
  - While the Gini coefficient was broadly flat since 2000, the polarization index notably increased following the Great Recession.
- Robustness to top-income exclusion:
  - Trimmed sample excluding the top 1 percent yields similar rising polarization trends, implying rising polarization is broad-based and not driven solely by the very rich.
- Gender breakdown:
  - For employed men (individuals), polarization rose sharply over the past four decades.
  - For employed women (individuals), income polarization increased only slightly over this period.
- Cross-data corroboration:
  - The rise in polarization is observed across CPS, PSID, and SCF.

### Macro implications — consumption and MPCPs (1998–2013)
- Purpose: determine how rising income polarization affects aggregate consumption by changing relative weights of income groups and examining changes in consumption responsiveness.
- Econometric scope: partial equilibrium analysis; regressions control for changes in real net worth, household size, region, age and age squared of household head, household fixed effects, and yearly fixed effects. Main instrument: average annual income of other households in same region-age-household-size cohort (and its squared and cubed terms).
- Empirical findings on MPCPs (marginal propensity to consume out of permanent income):
  - Simple scatter trend: MPCP ≈ 80 percent.
  - OLS with fixed effects (whole sample): MPCP ≈ 40 percent (noted as lower than 70-90 percent range in literature).
  - OLS bracketed MPCPs (1998-2013): low-income 60 percent; middle-income 40 percent; high-income 30 percent.
  - IV (2SLS) fixed-effects estimates (instrumented income):
    - Overall MPCP ≈ 100 percent for the whole sample (2SLS).
    - By bracket (2SLS): low-income 180 percent; middle-income 80 percent; high-income 50 percent (low-income estimate imprecise with large standard errors).
  - Pre/post-2007 split:
    - MPCPs for low, middle, and high income brackets are estimated to be lower post crisis than pre crisis, though estimates have large standard errors.
  - Polynomial (fractional polynomial around median) IV identification:
    - MPCPs estimated close to 100 percent for low-income brackets (imprecisely estimated) and decline to around 70 percent for higher income groups.
- Consumption response to net worth:
  - Net worth generally not a significant factor in consumption decisions when controlling for permanent income.
  - Estimates of MPC out of net worth by income level show very little impact of net worth on consumption when permanent income is controlled.

### Aggregate consumption effects of rising polarization (1998–2013)
- Identified forces affecting aggregate consumption over 1998-2013:
  1. Hollowing out: most middle-income outflows moved into the low-income class, ceteris paribus implying lower aggregate consumption.
  2. Composition effect: migration from middle to low income implies higher aggregate MPCPs (raising consumption).
  3. Behavioral change: overall decrease in MPCPs after controlling for income (lower responsiveness), which works against the composition effect and raises aggregate consumption relative to what composition alone would imply.
- Net result (Figure 17 analysis):
  - Total impact: lower level of aggregate consumption by around 3½ percent at the end of the sample (relative to the counterfactual where polarization remained at 1998 levels).
  - This cumulative consumption loss is split equally between lower MPCPs and lower median income levels.
  - The lost consumption is equivalent to more than one year of consumption, based on historical averages, over 15 years.

### Key empirical estimates and regression notes (selected exact values)
- Time spans: 1970–2014; 1998-2013; pre-crisis 1998-2006; post-crisis 2007-2013.
- MPCP estimates:
  - Scatter trend: about 80 percent.
  - OLS whole sample: around 40 percent.
  - OLS by bracket: low 60 percent; middle 40 percent; high 30 percent.
  - 2SLS whole sample: about 100 percent.
  - 2SLS by bracket: low 180 percent; middle 80 percent; high 50 percent.
  - Polynomial IV: low-income ≈ 100 percent (imprecise) down to ≈ 70 percent for higher income groups.
- Aggregate consumption decline due to rising polarization: around 3½ percent.
- Table 1 regression specifics (selected):
  - Number of Households: 6,170 (OLS), 4,868 (IV), 3,690 (IV Pre-2007), 3,213 (IV Post-2007).
  - Number of Observations: 19,291 (OLS), 17,806 (IV), 9,594 (IV Pre-2007), 6,426 (IV Post-2007).
  - Kleibergen-Paap LM Statistic examples: 84.11, 16.65, 71.57, 40.63.
  - R-Squared (OLS reported): 0.56 and 0.60 in specified columns.
  - Significance notation: *** p<0.01, ** p<0.05, * p<0.1.

### Main conclusions
- Income polarization has risen substantially in the past four decades—often faster than inequality as measured by the Gini coefficient; since the turn of the century most polarization has been towards lower incomes.
- Household consumption behavior shows heterogeneity across the income distribution and has become slightly less responsive to permanent income shocks over time (lower MPCPs).
- The hollowing out of the middle-income class combined with lower MPCPs reduced aggregate consumption by around 3½ percent by 2013 relative to a 1998-polarization counterfactual.

### Suggested avenues for future research (as listed)
- Study root causes of rising income polarization (possible contributors include technological progress, declining unionization, taxation, international trade, education, immigration, household structure and demographics).
- Develop a general equilibrium model to study macroeconomic effects of higher income polarization, incorporating consumption, investment, labor supply, tax and transfer policies, and relationship to GDP growth.
- Analyze why MPCPs have decreased in recent years and whether these changes are temporary or permanent, and whether they stem from the global crisis or represent a secular trend.
- Calculate the polarization index for other countries to enable cross-country comparisons of polarization trends.

*Source: IMF working paper content (excerpts provided).*

### 1995. Hence, we drop it from our general sample. An immigrant sample was added starting in 1997. We use

### _wp16121 - 1995. Hence, we drop it from our general sample. An immigrant sample was added starting in 1997. We use

### Sampling unit and family/unit definitions
- CPS sampling unit: a housing unit or dwelling; household defined as “all people who occupy a housing unit regardless of relationship.”
- PSID sampling unit: family unit (FU); PSID follows families and multiple families may reside in the same household (e.g., “split-off” families).
- SCF sampling unit: “primary economic unit” (PEU) — all individuals connected by financial interdependence.
- Analysis unit used:
  - CPS and PSID: family unit (FU) level (estimation and analysis performed at FU level).
  - SCF: PEU.
- Family definitions differ:
  - CPS family: “two or more people related by birth, marriage, or adoption residing in the same housing unit.”
  - PSID family: “a group of people living together [...]. They are almost always related by blood, marriage, or adoption. [...] Occasionally, unrelated persons can be part of an FU.” Cohabiting partners enter PSID families the same way as spouses.
  - SCF: married or cohabitating partners and their dependents are part of the PEU.
- Head of household definitions:
  - PSID: male older than 16 with the most financial responsibility; if no male fits, the female that fits is head.
  - CPS: interviews a “reference person” and defines relationships based on this person (variable “RELATE”).
  - SCF: head of PEU is male in mixed-gender partnership; oldest partner in same-gender partnership if couple is “economically dominant”; otherwise the most “economically dominant” individual.

### Income, net worth, and consumption measures
- CPS:
  - Family income variable: “FTOTVAL” (reported total family income including transfers).
  - Prior to 1976, FTOTVAL top-coded at 50,000 dollars; this censoring affects less than 0.5% of observations each year in the sample.
  - CPS imputes missing values for income; imputed values are retained.
  - CPS provides no asset holdings (aside from home ownership indicator) and no consumption expenditures.
- PSID:
  - Family income constructed from taxable income of head and partner plus transfers (alimony, child support, social security, worker’s compensation, VA pensions).
  - Taxable income components: labor income (wages and salaries, bonuses, tips, etc.), asset income (rental income, farm income, unincorporated business income, dividends, and interest), and taxable pension income (annuities and IRAs, pensions, other retirement accounts).
  - PSID provides information on unemployment compensation, property taxes, rent paid; used to compute federal and state taxes to construct disposable income (Federal and state taxes computed using the NBER TAXSIM (v.9) program).
  - Wealth (net worth) from PSID wealth supplements (1998 to 2013): assets — home equity, business/farm sale value, checking/savings/cash, stocks value, vehicles, annuities and IRAs, real estate sale value; liabilities — business/farm debts, real estate debt, credit card debt, student loans, health care bills, legal debts. Net worth = sum of these variables.
  - PSID has only food expenditures prior to 1998; econometric analysis starts in 1998.
  - Consumption categories used: education, childcare, transportation, housing, and food; health care expenditures omitted (only out-of-pocket expenses and insurance premiums present).
  - Rental services for homeowners imputed as value of main residence times a 4% interest rate.
  - Missing consumption values imputed using a left-censored Tobit regression of log expenditures in each category on a cubic in age and family size spline fully interacted with year dummies (as in Li et al. (2010)).
- SCF:
  - Reports total income for the PEU and imputes missing values, providing five imputed versions; the average of Gini and Polarization Index across imputations is used as final value.
  - SCF covers wealth more extensively but is less suitable for estimation needs due to relative infrequency, lack of a long panel dimension, and no expenditure information.

### Sample restrictions and trimming
- Common restrictions applied to each survey:
  1) head of household information present (income, age);
  2) head of household aged 24 to 64;
  3) head of household resides in the U.S.
- Additional exclusions:
  - Extremely poor families: less than 2 dollars per day in real 2005 terms dropped.
  - SCF: drop households with income in the top 1% (survey oversamples wealthy households).
  - “Trimmed” sample: excludes observations exceeding top 1% thresholds published by Alvaredo et al. (2015) and observations in the bottom 1%.
    - Trimming top 1% may lead to underestimation of the Gini Coefficient and consequently overestimation of the Polarization Index; predetermined thresholds from Alvaredo et al. are used.
  - PSID exclusions: SEO sample and Latino supplement sample (ran only from 1990 to 1995) excluded; PSID observations with large jumps in income (exceeding 500% or smaller than -80%) excluded.
- Econometric sample (PSID, 1998 onwards) additional restrictions:
  - Drop families where head is institutionalized, kept in house, or a student.
  - Treat families whose composition changes (e.g., divorce) as new families.
  - Drop observations missing age, marital status, race, gender, education or state (state required to compute state-level taxes).
  - Drop observations where head’s hourly earnings are less than half the federal minimum wage.
  - Drop observations where labor income positive but hours worked are zero.
  - Drop single heads with no children but childcare expenses exceeding 1% of total income.
  - After imputing missing expenditures, drop observations with expenditures exceeding income and wealth by 300%.
  - Drop observations where state tax burden is unavailable.
  - Drop families with only one observation remaining (panel regression requires at least two observations per family).
- Econometric sample size:
  - Econometric sample has approximately 3000-4000 observations per year where the household is the unit of observation.
- Specific PSID sample attrition (PSID 1998–2013):
  - Full Sample initial observations: 85,892
  - Drop 2013 (attrition weights not adjusted for 2013): Dropped 10,669 → Remaining 75,223
  - Drop SEO and Latino sample: Dropped 21,575 → Remaining 53,648
  - Age 24–64 restriction: Dropped 7,348 → Remaining 46,300
  - Living in US: Dropped 339 → Remaining 45,961
  - Partnered but missing partner’s age: Dropped 61 → Remaining 45,900
  - Missing age, marital status, race, gender, education or state: Dropped 1,777 → Remaining 44,123
  - Below half of federal minimum wage: Dropped 2,050 → Remaining 42,073
  - Labor income positive but hours worked are zero: Dropped 13 → Remaining 42,060
  - Income growth exceeds 500% and below -80%: Dropped 241 → Remaining 41,819
  - Expenditures exceed income and wealth by 300%: Dropped 37 → Remaining 41,782
  - Unmarried, No Children, Childcare Expenses > 1% of income: Dropped 3 → Remaining 41,779
  - State tax burden unavailable: Dropped 21 → Remaining 41,758
  - Student, Keeping house, Institutionalized: Dropped 981 → Remaining 40,777
  - At least two observations required: Dropped 5,915 → Remaining 34,862 (Full sample used for regressions)
  - Regression sample further restrictions:
    - Non-missing DI, wealth and expenditures + normalization 1/ c(t-2): Dropped 16,378 → Remaining 19,291
    - Instrument availability: Dropped 1,485 → Remaining 17,806

### PSID descriptive statistics and expenditure/income/wealth moments (selected figures)
- Table 2.A Total Expenditures (Unconditional Weighted Mean) — selected items (values shown for years 2000, 2004, 2008):
  - Total Food: 7,238; 7,659; 8,180
    - At home: 5,119; 5,291; 5,854
    - Away from home: 2,024; 2,254; 2,227
    - Delivered: 129; 140; 120
  - Total Housing*: 19,326; 23,068; 26,127
    - Mortgage*: 8,411; 9,294; 10,540
    - Rent*: 1,450; 1,506; 1,801
    - Insurance: 432; 591; 706
    - Property Tax: 1,626; 2,053; 2,564
    - Utilities: 2,509; 2,536; 2,823
  - Total Transportation: 7,114; 8,208; 7,487
    - Loan Payment: 1,618; 1,840; 1,525
    - Down payment: 1,624; 1,750; 1,510
    - Lease payment: 491; 306; 265
    - Insurance: 1,436; 1,786; 1,725
    - Gasoline: 1,751; 2,280; 2,359
    - Repairs: 129; 133; 150
    - Parking: 60; 55; 59
    - Bus and Train: 72; 73; 82
    - Taxicab: 15; 22; 17
    - Other Transit: 180; 164; 122
  - Education: 1,895; 2,249; 2,609
  - Childcare: 584; 504; 428
  - Total Expenditures (row): 36,154; 41,685; 44,829
  - N (sample counts for those years): 5,223; 5,520; 5,147
  - Note: (*) categories are significantly higher than Li et al. 2010 as a result of the econometric sample selection.
- Table 2.B Income, Wealth and Consumption — selected percentiles and means
  - Disposable Income (p25, p50, p75, Mean) across years 1999, 2002, 2006, 2010:
    - p25: 29,054; 29,510; 32,859; 31,797
    - p50: 46,500; 49,683; 56,786; 60,098
    - p75: 68,306; 77,580; 91,754; 97,373
    - Mean: 53,804; 59,441; 70,696; 73,349
  - Net Worth without Home Equity (p25, p50, p75, Mean) for 1999, 2002, 2006, 2010:
    - p25: 4,100; 4,500; 5,000; 3,700
    - p50: 22,025; 28,000; 35,000; 30,000
    - p75: 95,300; 119,000; 191,500; 195,000
    - Mean: 129,366; 179,240; 300,445; 271,105
  - Net Worth with Home Equity (p25, p50, p75, Mean) for same years:
    - p25: 12,500; 19,081; 26,500; 15,000
    - p50: 64,000; 89,500; 139,000; 98,300
    - p75: 177,500; 250,000; 390,000; 347,500
    - Mean: 183,156; 267,405; 439,068; 373,111
  - Expenditures (percentiles and means in brackets annualized/divided by 0.7 shown in parentheses) for years 1999, 2002, 2006, 2010:
    - p25: 18,668 (26,669); 21,430 (30,614); 24,970 (35,671); 26,266 (37,523)
    - p50: 26,985 (38,500); 31,988 (45,697); 38,904 (55,557); 40,300 (57,571)
    - p75: 37,849 (54,070); 46,674 (66,667); 56,614 (80,887); 57,668 (82,383)
    - Mean: 30,897 (44,139); 36,868 (52,669); 45,991 (65,701); 46,356 (66,223)
    - N: 4,254; 4,443; 4,771; 4,553
  - Note: Expenditures cover the categories mentioned. Li et al. (2010) show these expenditures cover up to roughly 70% of total expenditures using the Consumer Expenditure Survey for validation. Expenditures divided by 0.7 are shown in parentheses.

### Regression appendix — estimating MPC out of permanent income (MPCP)
- Objective: measure marginal propensity to consume out of permanent income (MPCP) to examine impact of polarization on aggregate consumption.
- Estimation approach:
  - Use PSID panel and an instrumental variables fixed effects specification.
  - Regress normalized changes in personal consumption expenditures on instrumented normalized changes in income.
  - Normalization: changes in consumption, income, and net worth from, e.g., 2005 to 2007 are normalized by consumption in 2003 (ratio of change in income relative to an initial level of consumption).
  - Fixed effects remove time-invariant household characteristics; controls for time-varying household characteristics (family size, region, age and age squared of head) fully interacted with year dummies.
  - Identification uses within-household time variation.
- Instrument for permanent income:
  - Average annual income of all other households in the same region-age-family-size cohort (excludes the household’s own income).
  - Validity requires: 1) measurement error not systematic across households; 2) covariance of transitory income changes constant across households and time (regional macroeconomic conditions affecting cohort households similarly over time).
  - Relevance: permanent income changes correlated across similar households (region-age-family-size cohorts).
  - Quadratic and cubic terms of the same instrument used as additional valid instruments.
- First-stage statistics and instrument tests:
  - First-stage F-Statistic of income on instrument: 618.10 (shows relevance).
  - Kleibergen-Paap under-identification test: rejects null of under-identification (evidence in favor of identification).
  - Sargan-Hansen over-identification test: fail to reject joint null that set of instruments is valid (evidence in favor of instrument validity).
- Heterogeneity in MPCP:
  - Allow MPCP to vary across income distribution:
    - Interact changes in income with indicator variables for household position in income distribution.
    - Interact changes in income with continuous variables indicating distance from median income (polynomial expansion in distance from median income).
  - Median income used is median for all households in the sample each year (PSID not representative at state level). Defining median at state level and restricting to at least 40 observations yields similar results in most cases.

*Source: Excerpt from the provided PSID/CPS/SCF methods and appendices in the supplied content.*

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