## wp17244

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### Definitions and measurement framework
- Middle-income households: incomes between 50 and 150 percent of the median (national or state-level as specified).
- Low income: households with less than 50 percent of the median income.
- High income: households with more than 150 percent of the median income.
- Household income: total pre-tax earnings and transfers to the household head and the second adult (if any); real terms in 2005 dollars using the CPI.
- Household-size adjustment: OECD equivalence scale (1 for first member, 0.7 for each additional adult, 0.5 for each child).
- Polarization focus: distinct from inequality measures (e.g., Gini); decomposed into downward polarization (more households joining lower-income ranks) and upward polarization (more households joining upper-income ranks).
- Two indices developed:
  - Population-share index: share of household population not in the middle-income class (50–150 percent of median); downward = low-income share; upward = high-income share.
  - Hollowing-out (income-weighted) index: average deviations of incomes of middle-income households from the median based on Lorenz curve areas (index multiplied by 4 to normalize to 0-1 range); separable into downward and upward components.

### National trends (1970–2016) — magnitudes and dynamics
- 1970–2016 period change:
  - About 9.3 percent of U.S. households hollowed out of the middle-income class.
  - Of these, about 5.6 percentage points joined the low-income ranks.
  - Of these, about 3.7 percentage points joined the high-income ranks.
- Annual-average changes (intensity of polarization):
  - Middle-income hollowed out at about 0.2 percent of total household population per year since 1970.
  - During 2000-2016, of the 0.2 percent annual average hollowing out:
    - about 0.11 have joined the low-income class;
    - about 0.09 have joined the high-income class.
  - Average annual hollowing out into high-income class: 0.07 percent before 2000, 0.09 percent after 2000.
  - Average annual hollowing out into low-income class: 0.13 percent before 2000, 0.11 percent after 2000.
- Population-share index changes (1970–2016, national level):
  - Downward population-share index has grown by more than 30 percent.
  - Upward population-share index has grown about 15 percent.
  - Overall population-share index has grown about 30 percent.
- Hollowing-out index changes (1970–2016, national level):
  - Overall, downward, and upward hollowing-out indices have grown about 30-40 percent.
  - Upward hollowing-out index grew by about 56 percent during 1977–2016 (see contributions section).
  - Notable level shifts observed in early 1980s (sharp changes in Lorenz curve) and mid-1990s (temporary sharp rise in upward hollowing-out).

### State-level patterns and heterogeneity
- Median-state example (1977-1985 vs 2006-2016):
  - Average middle-income share: 56¼ percent for 1977-1985.
  - Average middle-income share: 50¼ percent for 2006-2016.
  - The 6 percentage points lower middle share associated with increases of 2¾ percentage points in high-income households and 3¼ percentage points in low-income households.
- Selected state-level hollowing-out (1977–2016) examples (percent of total household population hollowed out of middle):
  - Connecticut: 17.8 percent hollowed out; 12.2 percentage points joined high-income; 5.7 percentage points joined low-income.
  - New Hampshire: 15 percent hollowed out; 6.5 percentage points joined high-income; 8.5 percentage points joined low-income.
  - West Virginia: 15.5 percent hollowed out; 4.1 percentage points joined high-income; 11.4 percentage points joined low-income.
  - Arkansas: 1.3 percent hollowed out (least among states).
  - North Dakota: 2.2 percent hollowed out.
- Geography (2016 snapshot):
  - Eastern and some mid-western states show highest downward and upward polarization.
  - Coastal western and southern states moderate; remaining mid-west/center/north lowest.
- Cross-state median income patterns:
  - Richer states (higher median household income) tend to have larger middle-income class shares and smaller low- and high-income shares.
  - Example 2000-2016 averages: Maryland and Connecticut real median incomes of more than $35,000 in 2016; California and New York about $30,000 in 2016.
  - Higher median raises dollar cutoff for 150 percent of median, compressing high-income population share in richer states.

### Drivers and channels (state-level econometrics and decomposition)
- Conceptual determinants:
  - Personal characteristics: age, education, race, gender.
  - Job characteristics: sector, offshoring, routinization, manufacturing share, technology intensity.
- State-level empirical approach:
  - Panel of 50 states + D.C.; main sample 1977-2016; dynamic panel with state and time fixed effects estimated by System GMM.
  - Observations: 1,989 (full sample); 1,173 (1977-2000); 867 (2000-2016).
  - Variables standardized (reported coefficients standardized).
  - Lagged dependent variable coefficients (standardized):
    - Downward hollowing-out: 0.19*** (1977-2016), 0.23*** (1977-2000), 0.15*** (2000-2016).
    - Upward hollowing-out: 0.15*** (1977-2016), 0.18*** (1977-2000), 0.13*** (2000-2016).
- Key standardized state-level coefficients (1977-2016; significance shown in source):
  - Education:
    - Downward hollowing-out: -0.79*** (0.126).
    - Downward population-share: -0.73*** (0.127).
    - Upward hollowing-out: -0.84*** (0.132).
    - Upward population-share: -0.67*** (0.132).
    - Interpretation: higher average education strongly reduces both downward and upward polarization.
  - Offshoring:
    - Downward hollowing-out: 0.34*** (0.082).
    - Downward population-share: 0.28*** (0.087).
    - Upward hollowing-out: 0.32*** (0.082).
    - Upward population-share: 0.26*** (0.087).
    - Interpretation: higher offshoring levels associated with higher polarization.
  - Routinization:
    - Downward hollowing-out: 0.25*** (0.065).
    - Downward population-share: 0.23*** (0.074).
    - Upward hollowing-out: 0.22*** (0.071).
    - Upward population-share: 0.21*** (0.077).
    - Interpretation: higher routinization levels associated with higher polarization.
  - Share of non-white population:
    - Downward hollowing-out: 0.20*** (0.068).
    - Upward hollowing-out: 0.23*** (0.068).
    - Interpretation: conditional association of higher non-white share with higher polarization.
  - Age:
    - Downward hollowing-out: -0.14* (0.079).
    - Downward population-share: -0.24*** (0.062).
    - Upward population-share: -0.26*** (0.066).
    - Interpretation: higher average age tends to lower polarization; age stronger for upward polarization.
  - Share of manufacturing jobs → associated with lower downward hollowing-out in some specifications (manufacturing pays better ceteris paribus).
- Diagnostics (selected p-values reported in source):
  - AR(2) p-values (examples): 0.744, 0.879, 0.472, 0.540, 0.721, 0.863, 0.561, 0.187, 0.274, 0.658, 0.853, 0.636.
  - Sargan p-values (examples): 0.657, 0.001, 0.020, 0.794, 0.000, 0.003, 0.728, 0.000, 0.033, 0.582, 0.001, 0.004.

### Contributions to changes in polarization (Figure 14A summary)
- Downward hollowing-out index (1977–2016):
  - Grew by about 26 percent.
  - Job routinization and offshoring together account for about 15 percentage points of this increase, each bearing roughly half of this contribution.
  - Remaining 11 percentage points due to all other factors (including persistence, time fixed effects, minus countervailing effects from individual characteristics such as higher education).
- Upward hollowing-out index (1977–2016):
  - Grew by about 56 percent.
  - Job routinization and offshoring together account for about 30 percentage points of this increase, each bearing roughly half of this contribution.
  - Remaining 26 percentage points due to other factors (persistence, time fixed effects, minus countervailing individual characteristics).
- Comparison:
  - Upward hollowing out and its contributors are roughly double the size of downward hollowing out.
  - Population-share index contributions qualitatively similar to hollowing-out indices; for upward indices, hollowing-out contributions are about double those to population-share because of income-size effects in hollowing-out.

### Household-level evidence (OLS and quantile regressions)
- Dependent variable: household real size-adjusted income divided by state median (Y_i,s,t / Y_med_s,t).
- Regressors: age, gender, education, offshorability, routinizability, manufacturing indicator, technology dummies, race, and controls; methods include OLS and quantile regressions (Q(0.25), Q(0.50), Q(0.75)).
- OLS (standardized coefficients, full sample highlights from Table 2):
  - Age: 0.14*** (0.000)
  - Gender (male = 1): 0.13*** (0.000)
  - Education: 0.19*** (0.000)
  - Share of non-white population: -0.03*** (0.000)
  - Offshorability score: -0.06*** (0.000)
  - Routinizability score: -0.04*** (0.000)
  - Manufacturing (=1): 0.04*** (0.000)
  - Technology dummies: small positive standardized coefficients (0.01–0.02***) across categories.
- Quantile regression patterns (Table 3, full sample):
  - Age: Q(0.25) 0.08***; Q(0.50) 0.12***; Q(0.75) 0.15*** (all (0.000))
  - Gender (male = 1): Q(0.25) 0.07***; Q(0.50) 0.10***; Q(0.75) 0.14*** (all (0.000))
  - Education: Q(0.25) 0.11***; Q(0.50) 0.14***; Q(0.75) 0.19*** (all (0.000))
  - Offshorability score: Q(0.25) -0.03***; Q(0.50) -0.05***; Q(0.75) -0.07*** (all (0.000))
  - Routinizability score: Q(0.25) -0.01***; Q(0.50) -0.02***; Q(0.75) -0.04*** (all (0.000))
- Interpretation:
  - Household characteristics (age, education, gender) positively associated with household income relative to state median.
  - Offshorability and routinizability scores negatively associated with household income relative to median; effects larger at higher quantiles for offshorability.
  - Results robust across subsamples; coefficients generally stronger post-2000.
  - OLS results heavily influenced by high-income households; quantile regressions show heterogeneity across the distribution.

### Policy-relevant conclusions and caveats
- Main conclusions:
  - Income polarization has increased substantially over the last 4 decades at the U.S. state level; the middle-income class has generally hollowed out for a typical state.
  - Technology (job routinization) and international trade (job offshoring) can explain more than half of the rise in income polarization, with broadly equal contributions.
  - Routinization and international competition have accounted for around one-third of the income polarization seen over the past 40 years.
  - Household characteristics (age, education, race, gender) have been important drivers but on net have had a countervailing effect, largely because rising education levels improved incomes.
  - Richer states are less polarized (larger middle class share, smaller low/high shares).
- Suggested policy directions (not exhaustively tested in paper):
  - Access to better education.
  - Family-friendly benefits.
  - Skill-based immigration.
- Data and interpretation caveats:
  - CPS income data are pre-tax; future work could use combined CPS–IRS data to examine post-tax household income.
  - Missing explanatory variables for cross-state polarization (fiscal policy, infrastructure, regulation) noted for future research.
  - Some apparent level shifts (early 1980s, mid-1990s) may reflect CPS data issues (e.g., top-coding changes); careful interpretation required.

*Source: wp17244 (IMF Working Paper content extracted from the supplied PDF).*

### INTRODUCTION _______________________________________________________________________________ 3

### INTRODUCTION

### Background and definitions
- Middle-income households: those with incomes between 50 and 150 percent of the median income (national or state-level as specified).
- Low income: households with less than 50 percent of the median income.
- High income: households with more than 150 percent of the median income.
- Household income: total pre-tax earnings and transfers to the household head and the second adult in the household (if any); in real terms in 2005 dollars using the Consumer Price Index (CPI) as the deflator.
- Household-size adjustment: OECD equivalence scale that assigns a value of 1 to the first household member, 0.7 to each additional adult, and 0.5 to each child.

### National trends and magnitudes
- Since the 1970s the share of middle-income households (50-150 percent of the national median) has decreased by more than 10 percentage points (Alichi et al., 2016).
- Updated 1970–2016 trends (including 2015 and 2016 CPS data) show a marginal improvement in income polarization with an uptick in the share of the middle-income households and a downtick in the share of the low-income households.
- 1970–2016 period change:
  - About 9.3 percent of U.S. households hollowed out of the middle-income class.
  - Of these, about 5.6 percentage points joined the low-income ranks (less than 50 percent of median).
  - Of these, about 3.7 percentage points joined the high-income ranks (more than 150 percent of median).
- Annual-average changes (intensity of polarization):
  - Middle-income households hollowed out at a broadly constant rate of 0.2 percent of total household population per year since 1970.
  - During 2000-2016, of the 0.2 percent annual average hollowing out:
    - about 0.11 have joined the low-income class;
    - about 0.09 have joined the high-income class.
  - Average annual hollowing out into high-income class: 0.07 percent before 2000, 0.09 percent after 2000.
  - Average annual hollowing out into low-income class: 0.13 percent before 2000, 0.11 percent after 2000.

### State-level patterns and variation
- Focus shifts from national to state-level analysis; polarization pattern is prevalent across states but with significant variability.
- For the median state:
  - Average share of middle-income households was 56¼ percent for 1977-1985.
  - Average share of middle-income households was 50¼ percent for 2006-2016.
  - The 6 percentage points lower middle share was associated with increases of 2¾ percentage points in high-income households and 3¼ percentage points in low-income households over the period.
- Selected state-level examples for 1977–2016:
  - Connecticut: 17.8 percent of total household population hollowed out of the middle-income class; of these, 12.2 percentage points joined the high-income class and 5.7 percentage points joined the low-income class.
  - New Hampshire: 15 percent hollowed out; 6.5 percentage points joined the high-income ranks and 8.5 percentage points joined the low-income ranks.
  - West Virginia: 15.5 percent hollowed out; 4.1 percentage points joined the high-income ranks and 11.4 percentage points joined the low-income ranks.
  - Arkansas: 1.3 percent hollowed out (least among states).
  - North Dakota: 2.2 percent hollowed out.
- Observation on richer states (defined in this paper exclusively as those with higher median income):
  - States with higher median household income tend to have larger middle-income class population shares, and smaller low- and high-income class population shares.
  - Example median income comparisons (2000-2016 averages):
    - Maryland and Connecticut: real median incomes of more than $35,000 in 2016.
    - California and New York: real median incomes of about $30,000 in 2016.
  - Higher median raises the dollar cutoff for qualification as high income (150 percent of median), which tends to compress the high-income population share in richer states.

### Conceptual focus and measurement
- The paper focuses on income polarization (the “fattening” of the tails of the income distribution) distinct from general income inequality measures like the Gini coefficient.
- Polarization is decomposed into downward polarization (more households joining lower-income ranks) and upward polarization (more households joining upper-income ranks).
- Wolfson (1994) introduced the first univariate income polarization measure; alternative measures exist (Wang and Tsui (2000); Alesina and Spolaore (1997)).
- The paper presents two polarization indices (details in subsequent sections) and compares them to inequality measures.

### Key empirical findings on drivers
- Polarization indices show steady increase in polarization since the 1970s in the United States; both upward and downward polarization contributed.
- State-level econometric analysis suggests:
  - Technology, measured by job routinization, and international trade, measured by job offshoring, can explain more than half of the rise in income polarization, with broadly equal contributions.
- Household-level analysis indicates:
  - Household characteristics including education, age, race, and gender have been important drivers.
  - On net, household characteristics have had a countervailing effect on income polarization, mainly because rising education levels of households have led to better incomes.

### Structure of the paper (overview)
- Two-stage approach:
  - First: present two indices of polarization and compare them.
  - Second: identify potential drivers of polarization using state- and household-level empirical models.
- Appendices provide data, state-level polarization series, a discussion of Wolfson’s index, detailed regression tables, and contributions decomposition.

*Source: wp17244 - INTRODUCTION*

### Section II develops two indices to represent the level of income polarization. Section III offers

### wp17244 - Section II develops two indices to represent the level of income polarization. Section III offers

### Measuring income polarization
- Distinction between inequality and polarization:
  - Inequality indices (e.g., the Gini coefficient) focus on the distribution of incomes given the distribution of households.
  - Polarization indices give additional prominence to the median of the distribution as a benchmark to partition households.
- Wolfson (1994) index:
  - Based on mass of population above/below the median, weighted by distance from the median.
  - Drawback: median-only separator (two groups), cannot make statements about the middle-income class or break into downward/upward shifts of households.
- Empirical observation:
  - Figure 4 shows a steady trend increase in both the Gini coefficient and Wolfson’s measure of income polarization at the U.S. national level since 1970.

### Population-share Index
- Definition and construction:
  - Index defined as the share of the household population that is not in the middle-income class in each state s and year t:
    - Middle-income households are those whose real size-adjusted incomes fall between 50 to 150 percent of the median income.
    - Low-income households: real size-adjusted incomes less than 50 percent of the median.
    - High-income households: real size-adjusted incomes more than 150 percent of the median.
  - Downward and upward polarization can be separated:
    - Downward: share of low-income households in population.
    - Upward: share of high-income households in population.
- Key empirical findings (1970–2016, national level):
  - Overall, downward, and upward population-share indices have all seen notable increases since the 1970s.
  - Magnitudes:
    - Downward population-share index has grown by more than 30 percent during 1970-2016.
    - Upward population-share index has grown about 15 percent during 1970-2016.
    - Overall population-share index has grown about 30 percent during 1970-2016.
  - Interpretation: The U.S. income distribution has become more polarized by about 30 percent during 1970-2016 using this measure.
- Sectoral and demographic patterns (Figure 6 summary, 1970-2016):
  - Manufacturing and construction: share of middle-income class jobs fell; many replaced with both low- and high-income jobs in services.
    - About 18 percent of total households have lost their manufacturing sector jobs; of that 18 percent, 12 percentage points were middle income.
    - About a third of these households got high-income jobs in the services sector; most of the rest got services jobs in low- and middle-income ranks.
  - Private-sector middle-class salary jobs replaced by low-/high-income salary jobs or self-employed jobs.
  - Demographic shifts:
    - Aging of workers (especially since turn of the century): younger employees replaced by older ones.
    - Low-education middle-class jobs replaced with higher-education jobs in all income classes (education and aging were countervailing forces to polarization).
    - Male employment declined, concentrated in middle-income jobs; female employment rose across the entire income distribution.
    - Middle-income jobs of U.S.-born households replaced by jobs for foreign-born residents at both ends of income distribution.

### Income Hollowing-out Index
- Rationale:
  - Population-share index captures population movements but not the strength of income shifts (how far incomes move).
  - Hollowing-out index captures average deviations of incomes of the middle-income class households from the median (income-weighted measure).
- Graphical intuition (Figure 7):
  - Compare actual Lorenz curve (CPS data for 2016) to 45-degree benchmark (zero polarity).
  - Blue box: area under benchmark Lorenz curve for middle-income class of benchmark (incomes between 25 to 75 percent of total income — equivalents of 50 to 150 percent of median for benchmark).
  - Yellow area: equivalent area for actual middle-income class population (50 to 150 percent of median).
  - Hollowing-out index = blue area minus yellow area; larger value means more hollowing-out (more polarized).
- Downward and upward components:
  - Break middle-income class into those below the median and those above the median.
  - Downward hollowing-out index: blue minus yellow area left of the vertical 0.5 line.
  - Upward hollowing-out index: blue minus yellow area right of the vertical 0.5 line.
- Empirical findings (1970–2016, national level):
  - Yellow area has shrunk from both left and right between 1970 and 2016, implying shrinking income share for middle-income class and increases in both upward and downward hollowing-out.
  - Overall, downward, and upward hollowing-out indices have grown about 30-40 percent during 1970-2016.
  - Notable level shifts:
    - Sharp upward level shift in hollowing-out indices in the early 1980s.
      - Left panel of Figure 8: sharp downward shift in the Lorenz curve during 1981–82, not reversed thereafter.
      - Suspected technical nature (e.g., changes in CPS top coding starting those years).
    - Temporary sharp rise in upward hollowing-out index in the mid-1990s.
      - Right panel of Figure 8: large downward shift in Lorenz curve in 1996–97, partially reversed later.

### Formal definition and state-level variation
- Formal index properties:
  - Hollowing-out index is based on Lorenz curve areas; index is multiplied by 4 to normalize to the 0-1 range.
  - L and H denote populations of households with incomes less than 50 and more than 150 percent of the median, respectively; y_i s,t denotes value of Lorenz curve at household i in state s at year t.
- State-level snapshots and dynamics:
  - Figure 9A (2016 snapshot):
    - States + District of Columbia = total of 51 units.
    - States divided into three equally-sized buckets of 17 states for downward and upward indices.
    - Top panel: downward polarization levels (red = 17 states with highest downward polarization; ivory = 17 states with lowest).
    - Bottom panel: upward polarization levels (dark green = 17 states with highest upward polarization; yellow = 17 states with lowest).
    - Observed geography: eastern and some mid-western states appear to have the highest levels of downward and upward polarization in 2016; coastal western and southern states moderate; remaining mid-west/center/north lowest.
  - Figure 9B (1977–2016 dynamics):
    - Indices normalized by their average value in 1977 (Index, 1977 Average = 100).
    - Average downward and upward hollowing-out indices for states have risen; ranges (dotted lines) indicate large heterogeneities across states.

### Comparison of the polarization indices
- Conceptual difference:
  - Hollowing-out index is income-weighted (captures income share: income times population of middle-income households).
  - Population-share index captures only population share of middle-income households.
  - Horizontal-axis cutoffs for the yellow area in Figure 7 correspond exactly to the population-share index cutoffs (household with 50 percent and 150 percent of median).
- Empirical comparison (Figure 10, state averages, 1977 onward):
  - Downward indices:
    - Both population-share and hollowing-out downward indices have broadly similar trends.
    - Both show a sharp rise in early-1980s and another sharp rise after the global financial crisis, with some correction thereafter.
    - Downward hollowing-out index generally less volatile than downward population-share index — indicating population increases at the bottom and relatively weak income growth; population effects more pronounced for the population-share index.
  - Upward indices:
    - Paths differ markedly. Incomes of high-income households grew much faster than their population shares.
    - Result: sharper rise in upward hollowing-out index (income-weighted) than upward population-share index.
    - Both upward indices also saw a sharp rise in the early-1980s and generally rose thereafter.

### Channels of income polarization
- Two conceptual sets of determinants:
  - Personal characteristics: age, education, race, gender.
  - Job characteristics: sector, industry, employment type, etc.
- Empirical approach:
  - Section III uses state-level estimation and household-level micro data to examine determinants of income polarization (Section III content indicated but results not included in supplied excerpt).
  - Figure 11 provides 4 scatterplots relating personal characteristics to the median income in different states to inform priors for regressions.
- Data note:
  - State-level study starts in 1977 due to availability issues of data for some states prior to 1977 and some top coding changes.

*Source: wp17244 (Section II excerpt, authors’ estimations using CPS data).*

### Appendix I.

### Appendix I

### Polarization indices and descriptive correlations
- Figure 10: Polarization Indices (Index, 1977 Average = 100) plotted for Downward and Upward series (1977–2015).
- Figure 11 (Averages over 2000-2016) unconditional correlations:
  - States with higher average age of household heads have higher median incomes.
  - States with more educated household heads have higher median incomes.
  - States’ median incomes do not vary much by their share of non-white population (unconditional).
  - States with relatively more single-female-headed households with children have lower median incomes.
- Combining Figures 3 and 11, priors:
  - Higher state education → higher median income → lower downward and upward polarization.
  - Higher average age and lower share of single females with children → lower downward and upward polarization.
  - No apparent unconditional link between share of non-whites and polarization.

### Job characteristics: definitions and distributions
- Variables used:
  - Share of manufacturing jobs in total employment (state-level).
  - Offshoring level: average of inverse offshorability scores of all jobs in each state and year multiplied by 100.
  - Routinization level: average of inverse routinizability scores of all jobs in each state and year multiplied by 100.
  - Offshorability and routinizability scores measure potential to be offshored/routinized; offshoring and routinization levels measure how much jobs have already been offshored/routinized.
- Distributional notes (Figure 12):
  - Median offshorability score is about 30.
  - Median offshoring level is about 3 (about the inverse of 30 times 100).
  - Similar inverse relationship between routinizability score and routinization level.
- Figure 13 (Averages over 2000-2016) unconditional correlations:
  - States with a higher share of manufacturing jobs have higher median incomes (manufacturing jobs pay better controlling for other factors).
  - States with higher offshoring and routinization levels have higher median incomes; remaining jobs are relatively less offshorable/routinizable and are better paid.

### Empirical strategy (state-level regressions)
- Panel: 50 U.S. states plus the District of Columbia; main sample 1977-2016; subsamples 1977-2000 and 2000-2016.
- Dependent variables: hollowing-out and population-share indices (downward and upward).
- Right-hand-side: averages of household and job characteristics at the state level.
- Model: dynamic panel with state fixed effects and time fixed effects estimated by System GMM (Blundell and Bond 1998).
- Standardization: variables standardized by subtracting sample mean and dividing by sample standard deviation (reported coefficients are standardized).
- Observations and cross-section:
  - Observations: 1,989 (full sample), 1,173 (1977-2000), 867 (2000-2016).
  - Number of states: 51.
- Lagged dependent variable coefficients (standardized):
  - Downward hollowing-out regressions: 0.19*** (1977-2016), 0.23*** (1977-2000), 0.15*** (2000-2016).
  - Upward hollowing-out regressions: 0.15*** (1977-2016), 0.18*** (1977-2000), 0.13*** (2000-2016).
  - Population-share indices show similar lag coefficients: 0.14***, 0.14***, 0.12*** (downward) and 0.15***, 0.19***, 0.09* (upward).

### Main state-level regression findings (standardized coefficients; statistical significance noted)
- Household characteristics (selected coefficients from Table 1):
  - Age:
    - Downward hollowing-out (1977-2016): -0.14* (0.079).
    - Downward population-share (1977-2016): -0.24*** (0.062).
    - Upward hollowing-out (1977-2016): -0.12 (0.094).
    - Upward population-share (1977-2016): -0.26*** (0.066).
    - Interpretation: higher average age tends to lower polarization; age is a stronger driver for upward polarization.
  - Education:
    - Downward hollowing-out (1977-2016): -0.79*** (0.126).
    - Downward population-share (1977-2016): -0.73*** (0.127).
    - Upward hollowing-out (1977-2016): -0.84*** (0.132).
    - Upward population-share (1977-2016): -0.67*** (0.132).
    - Interpretation: higher average education strongly reduces both downward and upward polarization.
  - Share of non-white population:
    - Downward hollowing-out (1977-2016): 0.20*** (0.068).
    - Downward population-share (1977-2016): 0.17** (0.068).
    - Upward hollowing-out (1977-2016): 0.23*** (0.068).
    - Upward population-share (1977-2016): 0.17** (0.068).
    - Interpretation: higher share of non-white population associated with higher polarization in conditional regressions.
- Job characteristics:
  - Offshoring:
    - Downward hollowing-out (1977-2016): 0.34*** (0.082).
    - Downward population-share (1977-2016): 0.28*** (0.087).
    - Upward hollowing-out (1977-2016): 0.32*** (0.082).
    - Upward population-share (1977-2016): 0.26*** (0.087).
    - Interpretation: higher offshoring levels (i.e., jobs already offshored/routinized) are associated with higher polarization.
  - Routinization:
    - Downward hollowing-out (1977-2016): 0.25*** (0.065).
    - Downward population-share (1977-2016): 0.23*** (0.074).
    - Upward hollowing-out (1977-2016): 0.22*** (0.071).
    - Upward population-share (1977-2016): 0.21*** (0.077).
    - Interpretation: higher routinization levels associated with higher polarization.
- Additional state-level findings (reported in Appendix IV, Tables 3A/3B and 4A/4B):
  - Higher share of manufacturing jobs → lower downward hollowing-out (manufacturing pays better ceteris paribus).
  - Higher share of female-headed households → higher downward hollowing-out.
  - Note: share-of-manufacturing is correlated with routinization and offshoring, so joint interpretation requires care; some models separate these variables.

### Comparison of drivers: downward vs upward polarization
- Broadly, drivers of upward income polarization are similar to those of downward income polarization.
- Two differences highlighted:
  - Age has a stronger role for upward polarization (experience matters more at the top).
  - Temporal shift: for all right-hand variables except age, coefficient sizes are larger for downward polarization in the pre-2000 sample but larger for upward polarization in the post-2000 sample:
    - Pre-2000: higher education relatively benefited low-income households more; international trade and routinization hurt low-income households relatively more.
    - Post-2000: this pattern flipped—higher education benefited low-income households less and international trade and routinization hurt low-income households relatively less than high-income households.
- Mechanism explanation using population-share index:
  - A determinant like higher education raises incomes across classes but disproportionately lifts low-income households into the middle, increasing middle-size relative to low and high and thereby reducing both downward and upward population-share indices.

### Model diagnostics and robustness
- AR(2) p-values (for selected regressions): 0.744, 0.879, 0.472, 0.540, 0.721, 0.863, 0.561, 0.187, 0.274, 0.658, 0.853, 0.636.
- Sargan p-values (for selected regressions): 0.657, 0.001, 0.020, 0.794, 0.000, 0.003, 0.728, 0.000, 0.033, 0.582, 0.001, 0.004.
- Full set of state-level results for downward indices: Appendix IV, Tables 3A and 3B.
- Full set of state-level results for upward indices: Appendix IV, Tables 4A and 4B.

### Contributions and next steps
- Contributions of each independent variable to changes in downward and upward hollowing-out indices calculated using estimated coefficients in Table 1; results reported in Figure 14A (columns in Figure 14A correspond to the regressions in Table 1).
- Subsequent empirical work in the document:
  - Subsection B: state-level regressions (presented here).
  - Subsection C: household-level regressions — dependent variable is households’ real size-adjusted incomes as a share of the median; aims to show robustness of determinants to index definition.

*Source: Appendix I, "wp17244 - Appendix I."*

### Appendix IV, Figures 3A, 3B, 4A, and 4B show the contributions for all of the models reported in Appendix IV,

### Appendix IV, Figures 3A, 3B, 4A, and 4B show the contributions for all of the models reported in Appendix IV,

### Contributions to Changes in Polarization Indices (Figure 14A — summary)
- Left panel (downward hollowing-out index, full sample 1977–2016):
  - The downward hollowing-out index grew by about 26 percent during 1977–2016.
  - Job routinization and offshoring are responsible for about 15 percentage points of this increase, each bearing roughly half of this contribution.
  - The remaining 11 percentage points of the increase are due to all other factors (including persistence of the dependent variable and the time fixed-effect minus countervailing effects from individual characteristics, most notably higher education).
  - Subsample results (1977–2000 and 2000–2016) show broadly similar relative contributions of technology, trade, and other factors to the full sample.
- Second panel from left (upward hollowing-out index, full sample 1977–2016):
  - The upward hollowing-out index grew by about 56 percent during 1977–2016.
  - Job routinization and offshoring are responsible for about 30 percentage points of this increase, each bearing roughly half of this contribution.
  - The remaining 26 percentage points of the increase are due to other factors, including persistence of the dependent variable and the time fixed-effect minus countervailing effects from individual characteristics (most notably higher education).
  - Subsample results (1977–2000 and 2000–2016) are similar to the full-sample results.
- Comparison and robustness:
  - Qualitatively, channels of downward and upward income hollowing out are similar.
  - Quantitatively, upward hollowing out and its contributors are roughly double the size of downward hollowing out.
  - The two right panels (population-share indices) report contributions for regressions where dependent variables are downward and upward population-share indices; contributions are qualitatively similar to hollowing-out indices.
  - For downward indices, hollowing-out and population-share indices are in the same ballpark quantitatively.
  - For upward indices, contributions to the hollowing-out index are about double the size of those to the population-share index (because income size effects are large in the hollowing-out index but do not affect the population-share index).

### Breakdown of Non-Technology/Non-Trade Contributors (Figure 14B)
- Time effects:
  - Time effects have significantly increased both hollowing-out and population-share indices.
- Household characteristics:
  - Education has played an important role, with its effect toward lowering the downward hollowing-out index.
- Net contribution:
  - On net, these components (time effects, lagged dependent variable persistence, education, age, race, and other household characteristics) have contributed to less than half of the increased polarization in the full sample and subsamples shown in Figure 14A.

### Household-level regressions: model and estimation approach
- Dependent variable:
  - Real size-adjusted household income of household i in state s in year t divided by median real size-adjusted income in state s in year t (Y_i,s,t / Y_med_s,t).
- Regressors:
  - Household characteristics: age, gender, education.
  - Job characteristics: technology (routinizability) and tradability (offshorability).
  - Additional controls: manufacturing indicator, race (share non-white), time fixed-effects, lagged dependent variable (persistence).
- Estimation methods:
  - Ordinary least squares (OLS) and quantile regression (mean, median, 25th and 75th quantiles).
  - Regressions run on pooled sample, imposing coefficients be the same across states and time.
- Purpose:
  - These regressions capture determinants of households’ incomes relative to the state median and serve as robustness checks for channels of income polarization.

### Key household-level regression results (Table 2 — OLS standardized coefficients, selected coefficients)
- Dependent variable: Real size-adjusted household income relative to the annual state median (1968–2016).
- Regression set 1 — selected standardized coefficients (Full sample column (1); significance levels shown as in table):
  - Age: 0.14*** (0.000)
  - Gender (male = 1): 0.13*** (0.000)
  - Education: 0.19*** (0.000)
  - Share of non-white population: -0.03*** (0.000)
  - Offshorability score: -0.06*** (0.000)
  - Routinizability score: -0.04*** (0.000)
  - Manufacturing (=1): 0.04*** (0.000)
  - Technology (High tech.=1): 0.02*** (0.000)
  - Technology (Medium-high tech.=1): 0.02*** (0.000)
  - Technology (Medium-low tech.=1): 0.01*** (0.000)
  - Technology (Low tech.=1): 0.01*** (0.000)
- Subsample and exclusion checks:
  - Columns (2)–(3) (pre- and post-2000) show same-sign coefficients and generally stronger coefficients post-2000.
  - Column (4) (full sample excluding high-income households) differs substantially from column (1).
  - Column (5) (full sample excluding low-income households) is very similar to column (1).
  - Conclusion: results in column (1) are heavily influenced by high-income households; hence quantile regressions are employed for more accurate estimates across the income distribution.

### Quantile regression summary (Table 3 — selected standardized coefficients)
- Quantiles reported: Q(0.25), Q(0.50), Q(0.75) across full sample, 1977–1999, and 2000–2015 subsamples.
- Regression set 1 — selected coefficients (Full sample):
  - Age: Q(0.25) 0.08*** (0.000); Q(0.50) 0.12*** (0.000); Q(0.75) 0.15*** (0.000)
  - Gender (male = 1): Q(0.25) 0.07*** (0.000); Q(0.50) 0.10*** (0.000); Q(0.75) 0.14*** (0.000)
  - Education: Q(0.25) 0.11*** (0.000); Q(0.50) 0.14*** (0.000); Q(0.75) 0.19*** (0.000)
  - Share of non-white population: Q(0.25) -0.03*** (0.000); Q(0.50) -0.03*** (0.000); Q(0.75) -0.03*** (0.000)
  - Offshorability score: Q(0.25) -0.03*** (0.000); Q(0.50) -0.05*** (0.000); Q(0.75) -0.07*** (0.000)
  - Routinizability score: Q(0.25) -0.01*** (0.000); Q(0.50) -0.02*** (0.000); Q(0.75) -0.04*** (0.000)
  - Manufacturing (=1): Q(0.25) 0.04*** (0.000); Q(0.50) 0.04*** (0.000); Q(0.75) 0.03*** (0.000)
  - Technology (High tech.=1): Q(0.25) 0.02*** (0.000); Q(0.50) 0.02*** (0.000); Q(0.75) 0.02*** (0.000)
- Interpretation:
  - Quantile regressions confirm drivers identified in OLS but reveal coefficient heterogeneity across income distribution.
  - Third quantile (Q(0.75)) results are very similar in size to OLS coefficients from Table 2.

### Main conclusions and policy-relevant findings
- Polarization trend:
  - Income polarization has increased substantially over the last 4 decades at the U.S. state level; the middle-income class has generally hollowed out for a typical state.
- Cross-state pattern:
  - Richer states (higher median household income) have a larger middle-income class and smaller population shares of low- and high-income households; i.e., richer states are less polarized.
- Contributions to rising polarization:
  - Technology (measured by job routinization) and international trade (measured by job offshoring) can explain more than half of the rise in income polarization, with broadly equal contributions.
  - Household characteristics (age, education, race, gender) have been important drivers but on net have had a countervailing effect (largely due to rising education levels improving incomes).
  - Routinization and international competition have accounted for around one-third of the income polarization seen over the past 40 years.
- Interpretation and caveats:
  - Technological change and globalization have increased living standards and boosted productivity and growth, but have had side-effects on income distribution and household welfare.
  - Suggested policy directions (not exhaustively tested in this work) could include access to better education, family-friendly benefits, skill-based immigration, etc.
  - Data limitations: CPS income data are pre-tax; future work could use combined CPS–IRS data to examine post-tax household income. Missing explanatory variables for cross-state polarization (fiscal policy, infrastructure, regulation) are noted for future research.
- Indices and contributions:
  - Two new indices of income polarization were developed that relate to sizes of low-, middle-, and high-income classes and variations in household incomes, and allow separate study of downward and upward hollowing out.

*Source: Appendix IV and related figures and tables in the supplied content.*

### References

### wp17244 - References

### References
- Full bibliography lists research cited in the paper, including working papers, journal articles, datasets, and software modules. Selected entries (as provided):
  - Abdih, Yasser, and Stephan Danninger, 2017, “What Do Industry and State Data Tell Us About the Decline of the U.S. Labor Share?” IMF working Paper No. 17/167 (Washington: International Monetary Fund).
  - Alichi, Ali, Korey Kantenga, and Juan Solé, 2016, “Income Polarization in the United States,” IMF Working Paper No. 16/121.
  - Alvaredo, Facundo, Anthony B. Atkinson, Thomas Piketty and Emmanuel Saez, 2015, The World Top Incomes Database, http://topincomes.g-mond.parisschoolofeconomics.eu/, Accessed 9/3/2015.
  - Arellano, M., and S. Bond, 1991, “Some Test of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations,” Review of Economic Studies, 58(2), pp. 277–97.
  - Autor, David H., Lawrence F. Katz and Melissa S. Kearney, 2006, “The Polarization of the U.S. Labor Market,” American Economic Review, 96(2), 189–94.
  - Blundell, Richard and Stephan Bond, 1998, “Initial Conditions and Moment Restrictions in Dynamic Panel Data Models,” Journal of Econometrics, 87(1), 115–43.
  - Carroll, Christopher D., 2009, “Precautionary Saving and the Marginal Propensity to Consume out of Permanent Income,” Journal of Monetary Economics, 56(6), 780–90.
  - Duclos, Jean-Yves, Joan Esteban, and Debraj Ray, 2004, “Polarization: Concepts, Measurement, Estimation,” Econometrica, Volume 72, Issue 6, November 2004, pp. 1737–72.
  - Heathcote, Jonathan, Fabrizio Perri and Giovanni L. Violante, 2010a, “Unequal We Stand: An Empirical Analysis of Economic Inequality in the United States: 1967-2006,” Review of Economic Dynamics, 13(1), 15–51.
  - Panel Study of Income Dynamics, Public Use Dataset, 2015, Produced and distributed by the Survey Research Center, Institute for Social Research, University of Michigan, Ann Arbor.
  - Survey of Consumer Finances, 2015. Produced and distributed by the Board of Governors of the Federal Reserve System.
  - UNCTAD (2002) Trade and Development Report, Annex 1 to Chapter III.
- (The full list in the source contains additional entries and software references used in the analysis.)

### Appendix I. Data — Variables and Construction
- Household-level variables (CPS, annual frequency):
  - Real, size-adjusted household income:
    - Nominal pre-tax household income, size-adjusted using OECD’s equivalence scale: assigns 1 to first household member, 0.7 to each additional adult, and 0.5 to each child.
    - Deflated using the consumer price index (CPI) to obtain real size-adjusted household income.
    - Sample restricted to households whose heads are 24-64 years old and have a nominal income (before size-adjustment) of at least $2 per day.
  - Age: two variables — age of household head and age of the second adult in the household (referred to as “relative”).
  - Education: years of schooling for household head and second adult.
  - Race: two dummies for household head and second adult (1 for white, 0 otherwise).
  - Gender: two dummies for household head and second adult (1 for male, 0 for female).
  - Manufacturing: two dummies for household head and second adult (1 for manufacturing job, 0 otherwise).
  - Technology: four dummies based on UNCTAD classification (high tech, medium-high tech, medium-low tech, low tech) for jobs in the manufacturing sector; set to zero if job not in manufacturing. Similar dummies for the second adult.
  - Routinizability and offshorability scores:
    - Constructed following Abdih and Danninger (2017), Autor and Dorn (2013), and Firpo et al. (2011), based on CPS and O*NET (1990–2016).
    - Routinizability score: composite of O*NET variables including “degree of automation”, “importance of repeating same tasks”, “structured versus unstructured work”, “pace determined by speed of equipment”, and “spend time making repetitive motions.” Assigned to household equal to index for household head.
    - Offshorability score: composite of O*NET variables including “face-to-face discussions”, “establishing and maintaining interpersonal relationships”, “assisting and caring for others”, “performing for or working directly with the public”, “coaching”, “developing others”, “inspecting equipment, structures, or material”, “handling and moving objects”, “controlling machines and processes”, “operating vehicles, mechanized devices, or equipment”, “repairing and maintaining mechanical equipment”, and “repairing and maintaining electronic equipment.” Assigned to household equal to index for household head.
    - Notes: Routinizability and offshorability scores cover all jobs (including services) and are partly based on perceptions or surveyed information rather than purely administrative data.

### Appendix I. Data — Summary Statistics (Household-Level) (1968-2016)
- Sources: Current Population Survey and author’s calculations.
- Variables, sample sizes, and statistics as provided:
  - Real income / median income (State-Year): Obs = 71,250,000; Mean = 124.3; Median = 100.0; Std.Dev. = 115.5; Min. = 0.4; Max. = 6,200.8
  - Age: Obs = 78,333,333; Mean = 43.3; Median = 43.0; Std.Dev. = 11.4; Min. = 24.0; Max. = 64.0
  - Gender (male = 1): Obs = 78,333,333; Mean = 0.7; Median = 1.0; Std.Dev. = 0.5; Min. = 0.0; Max. = 1.0
  - Education: Obs = 76,666,667; Mean = 13.1; Median = 13.0; Std.Dev. = 3.0; Min. = 0.0; Max. = 21.0
  - Share of non-white population: Obs = 78,333,333; Mean = 0.2; Median = 0.0; Std.Dev. = 0.4; Min. = 0.0; Max. = 1.0
  - Age (h. relative): Obs = 58,541,667; Mean = 37.7; Median = 38.0; Std.Dev. = 15.5; Min. = 0.0; Max. = 99.0
  - Gender (male = 1) (h. relative): Obs = 58,541,667; Mean = 0.3; Median = 0.0; Std.Dev. = 0.4; Min. = 0.0; Max. = 1.0
  - Education (h. relative): Obs = 52,291,667; Mean = 12.8; Median = 12.0; Std.Dev. = 2.8; Min. = 0.0; Max. = 21.0
  - Share of non-white population (h. relative): Obs = 78,333,333; Mean = 0.1; Median = 0.0; Std.Dev. = 0.3; Min. = 0.0; Max. = 1.0
  - Offshorability score: Obs = 61,875,000; Mean = 31.9; Median = 31.3; Std.Dev. = 4.8; Min. = 15.9; Max. = 47.9
  - Routinization score: Obs = 33,333,333; Mean = 30.6; Median = 30.6; Std.Dev. = 4.5; Min. = 15.9; Max. = 47.9
  - Offshorability score (h. relative): Obs = 61,875,000; Mean = 12.3; Median = 12.4; Std.Dev. = 1.9; Min. = 7.4; Max. = 20.2
  - Routinization score (h. relative): Obs = 33,333,333; Mean = 12.4; Median = 12.5; Std.Dev. = 2.0; Min. = 37.3; Max. = 720.18
  - Manufacturing (=1): Obs = 78,333,333; Mean = 0.16; Median = 0.00; Std.Dev. = 0.36; Min. = 0.00; Max. = 1.00
  - Manufacturing (=1) (h. relative): Obs = 58,541,667; Mean = 0.08; Median = 0.00; Std.Dev. = 0.28; Min. = 0.00; Max. = 1.00
  - Technology (High tech.=1) (h. head): Obs = 63,541,667; Mean = 0.02; Median = 0.00; Std.Dev. = 0.14; Min. = 0.00; Max. = 1.00
  - Technology (Medium-high tech.=1) (h. head): Obs = 63,541,667; Mean = 0.06; Median = 0.00; Std.Dev. = 0.24; Min. = 0.00; Max. = 1.00
  - Technology (Medium-low tech.=1) (h. head): Obs = 63,541,667; Mean = 0.03; Median = 0.00; Std.Dev. = 0.17; Min. = 0.00; Max. = 1.00
  - Technology (Low tech.=1) (h. head): Obs = 63,541,667; Mean = 0.08; Median = 0.00; Std.Dev. = 0.27; Min. = 0.00; Max. = 1.00
  - Technology (High tech.=1) (h. relative): Obs = 34,791,667; Mean = 0.02; Median = 0.00; Std.Dev. = 0.12; Min. = 0.00; Max. = 1.00
  - Technology (Medium-high tech.=1) (h. relative): Obs = 34,791,667; Mean = 0.04; Median = 0.00; Std.Dev. = 0.19; Min. = 0.00; Max. = 1.00
  - Technology (Medium-low tech.=1) (h. relative): Obs = 34,791,667; Mean = 0.01; Median = 0.00; Std.Dev. = 0.12; Min. = 0.00; Max. = 1.00
  - Technology (Low tech.=1) (h. relative): Obs = 34,791,667; Mean = 0.07; Median = 0.00; Std.Dev. = 0.26; Min. = 0.00; Max. = 1.00
- Appendix Table 1 referenced as summarizing these household-level sample statistics.

### Appendix I. Data — State-Level Data (1977–2016): Variables and Construction
- State-level data for each state and year 1977–2016 include:
  - Real size-adjusted household income: the weighted income share of low-, middle-, and high-income households.
  - Age: weighted average age of household heads; similar for second adult.
  - Education: weighted average years of schooling of household heads; similar for second adult.
  - Female share: weighted share of household heads who are female; similar for second adult.
  - Manufacturing: weighted population share of household heads with jobs in manufacturing; similar for second adult.
  - Technology: measures how high- or low-tech a job is.
  - Routinization and offshoring levels: the inverse of the weighted average scores for household heads multiplied by 100; similar variables for second adult.
- All weighted-sums and averages use the CPS population weights.

### Appendix I. Data — Summary Statistics (State-Level) (1977-2016)
- Sources: Current Population Survey and author’s calculations.
- Appendix Table 2 statistics (Variables, Obs, Mean, Median, Std.Dev., Min., Max.):
  - Index Hollowing-out (downward): Obs = 2,040; Mean = 116.0; Median = 116.5; Std.Dev. = 12.8; Min. = 78.7; Max. = 156.1
  - Index Hollowing-out (upward): Obs = 2,040; Mean = 129.4; Median = 134.2; Std.Dev. = 30.3; Min. = 34.0; Max. = 217.0
  - Population share index (downward): Obs = 2,040; Mean = 117.6; Median = 118.0; Std.Dev. = 16.1; Min. = 62.2; Max. = 174.9
  - Population share index (upward): Obs = 2,040; Mean = 107.6; Median = 107.3; Std.Dev. = 10.3; Min. = 75.1; Max. = 147.8
  - Age: Obs = 2,040; Mean = 43.0; Median = 42.9; Std.Dev. = 1.5; Min. = 37.5; Max. = 47.4
  - Education: Obs = 2,040; Mean = 13.4; Median = 13.6; Std.Dev. = 0.7; Min. = 10.8; Max. = 15.9
  - Share of non-white population: Obs = 2,040; Mean = 15.8; Median = 12.9; Std.Dev. = 13.2; Min. = 0.1; Max. = 73.7
  - Share of females (h. head): Obs = 2,040; Mean = 35.5; Median = 36.3; Std.Dev. = 11.3; Min. = 9.8; Max. = 60.8
  - Share of single females with children (h. head): Obs = 2,040; Mean = 11.0; Median = 10.9; Std.Dev. = 2.5; Min. = 3.1; Max. = 21.6
  - Offshoring: Obs = 2,040; Mean = 3.2; Median = 3.2; Std.Dev. = 0.1; Min. = 2.9; Max. = 3.6
  - Routinization: Obs = 2,040; Mean = 8.3; Median = 8.3; Std.Dev. = 0.2; Min. = 7.8; Max. = 9.0
  - Share of manufacturing employees: Obs = 2,040; Mean = 14.6; Median = 13.4; Std.Dev. = 7.5; Min. = 1.1; Max. = 38.7
  - Share of high tech. sector employees: Obs = 2,040; Mean = 1.6; Median = 1.2; Std.Dev. = 1.4; Min. = 0.0; Max. = 10.3
  - Share of medium-high tech. sector employees: Obs = 2,040; Mean = 4.5; Median = 3.8; Std.Dev. = 3.5; Min. = 0.0; Max. = 23.1
  - Share of medium-low tech. sector employees: Obs = 2,040; Mean = 2.0; Median = 1.7; Std.Dev. = 1.6; Min. = 0.0; Max. = 10.8
  - Share of low tech. sector employees: Obs = 2,040; Mean = 6.5; Median = 5.8; Std.Dev. = 3.6; Min. = 0.6; Max. = 21.9

### Appendix Figures and Time-Series Ranges
- Appendix Figure 1A: State-Level Household Characteristics (Period averages) — period averages shown for Age, Education, Share of non-white population, Share of females (h. head), Share of single females with children (h. head) across periods 1977-85, 1986-95, 1996-05, 2006-16.
- Appendix Figure 1B: State-Level Job Characteristics (Period averages) — period averages shown for Offshoring, Routinization, Share of manufacturing employees, Share of high tech. sector employees, Share of medium-high tech. sector employees, Share of medium-low tech. sector employees, Share of low tech. sector employees across periods 1977-85, 1986-95, 1996-05, 2006-16.
- Figures use CPS and author’s calculations.

### Overview of the CPS (used in the analysis)
- CPS characteristics and usage:
  - CPS is monthly at the national level; sampling unit is all individuals in a dwelling (household).
  - CPS dates back to 1962 and samples about 50,000 households monthly.
  - The analysis uses CPS from 1968 to 2016.
  - CPS rotation: households rotate out for 8 months after 4 months in survey and then after 4 more months are rotated out permanently.
  - The CPS March Supplement (Annual Social and Economic Supplement) includes detailed income questions about the previous year; annual income for previous year is constructed from it.
  - Data labeling: variables are labeled with survey’s publication year rather than survey year. Example: data labeled with 2017 were results of survey conducted in 2016 but published in 2017. Throughout the paper, data are lagged and presented labeled by the same year (e.g., “2016” refers to survey about household information for 2016 published in 2017).
- Sampling unit definitions:
  - Household: all people who occupy a housing unit regardless of relationship.
  - Family (FU) level: a family consists of two or more people related by birth, marriage, or adoption residing in the same housing unit.
  - Main reference is the head of household; regression analysis includes variables related to the second adult in household.
- Income variable:
  - Variable used: “FTOTVAL” — reported total family income and includes transfers.
  - Prior to 1976, FTOTVAL top-coded at 50,000 dollars; censoring affects less than 0.5 percent of observations each year in the sample, so no correction for top-coding is applied.
  - CPS imputes missing values for income; imputed values are retained (not dropped).
  - Family income composition: taxable labor income, asset income, taxable pension income; transfers include alimony, child support, social security, worker’s compensation, VA pensions.
  - CPS provides no information on asset holdings aside from home ownership; analysis limited to income polarization (no wealth polarization).
- Sample restrictions applied:
  - For each survey, keep observations where:
    1) information for the head of household (income, age) is available;
    2) head of household is aged 24 to 64;
    3) head of household resides in the U.S.
  - Drop extremely poor families as defined by less than 2 dollars per day in real 2005 terms.

*Source: wp17244 - References*

### Appendix II. Income Polarization by State

### Appendix II. Income Polarization by State

### Methodology and definitions
- Charts are compiled using CPS data.
- Income is adjusted for household size using OECD’s equivalence scale.
- Middle income (class) consists of households falling within 50-150 percent of median income.
- Figures show "Change in Number of Households (Percent of total households)" by income class (Low income, Middle income, High income) for time segments labeled in charts (e.g., 1977-2016, 1977-2000, 2000-2006, 2006-2016). Exact numerical entries for each state are listed below as presented in the source.

### State-level changes in household income shares (exact values as listed)
- Alabama: 0.5, -7.3, 6.8, -0.4, -2.2, 2.6, -2.1, 0.6, 1.5, 3.0, -5.6, 2.7
- Alaska: 2.0, -8.2, 6.2, -1.6, -1.9, 3.5, 3.5, -3.8, 0.3, 0.1, -2.4, 2.4
- Arizona: 7.3, -14.1, 6.8, 4.6, -9.7, 5.1, 1.8, -4.9, 3.0, 0.9, 0.4, -1.3
- Arkansas: 2.6, -1.3, -1.3, 2.3, -1.5, -0.8, -0.2, 1.5, -1.3, 0.5, -1.3, 0.8
- California: 5.1, -11.4, 6.3, 4.1, -9.7, 5.6, 1.8, -1.8, 0.0, -0.8, 0.1, 0.7
- Colorado: 3.5, -4.6, 1.0, 2.7, -4.5, 1.8, 1.0, -1.0, 0.0, -0.1, 0.9, -0.8
- Connecticut: 5.7, -17.8, 12.2, 3.6, -8.9, 5.3, 1.5, -3.9, 2.4, 0.6, -5.1, 4.5
- Delaware: 8.7, -10.4, 1.6, 4.4, -0.8, -3.6, 0.7, -4.0, 3.3, 3.6, -5.6, 2.0
- District of Columbia: 6.4, -10.6, 4.3, 2.2, -5.3, 3.1, -0.0, 1.8, -1.8, 4.1, -7.1, 2.9
- Florida: 2.0, -6.0, 4.0, 1.9, -4.4, 2.5, 0.3, -2.1, 1.7, -0.3, 0.5, -0.2
- Georgia: 2.0, -6.0, 4.0, 1.9, -4.4, 2.5, 0.3, -2.1, 1.7, -0.3, 0.5, -0.2
- Hawaii: 1.6, -4.1, 2.6, -2.4, 0.9, 1.5, 1.6, -1.1, -0.5, 2.3, -3.9, 1.6
- Idaho: 5.1, -13.5, 8.4, 2.6, -8.5, 5.8, 1.9, -0.8, -1.1, 0.6, -4.2, 3.6
- Illinois: 4.7, -8.8, 4.0, 2.9, -6.3, 3.3, 0.1, -0.9, 0.8, 1.7, -1.6, -0.1
- Indiana: 7.1, -9.0, 1.9, 5.0, -4.0, -1.0, -0.6, -1.5, 2.1, 2.7, -3.5, 0.8
- Iowa: 5.6, -9.4, 3.8, 1.6, -2.5, 0.9, 0.3, -3.9, 3.6, 3.8, -3.1, -0.7
- Kansas: 5.6, -9.3, 3.7, 0.5, -6.1, 5.6, 4.3, -0.3, -4.0, 0.8, -2.9, 2.1
- Kentucky: 5.6, -9.3, 3.7, 0.5, -6.1, 5.6, 4.3, -0.3, -4.0, 0.8, -2.9, 2.1
- Louisiana: 2.7, -6.4, 3.7, 2.6, -5.8, 3.3, 0.2, 0.0, -0.3, -0.1, -0.6, 0.7
- Maine: 1.5, -7.6, 1.5, 2.9, -6.9, 4.0, 2.6, 2.4, -5.0, 0.6, -3.1, 2.5
- Maryland: 1.5, -3.8, 2.3, -2.3, 0.3, 2.0, 1.4, -3.7, 2.3, 2.4, -0.4, -2.0
- Massachusetts: 4.2, -9.3, 5.2, 3.6, -5.1, 1.5, 1.7, -2.0, 0.3, -1.1, -2.3, 3.4
- Michigan: 4.2, -9.3, 5.2, 3.6, -5.1, 1.5, 1.7, -2.0, 0.3, -1.1, -2.3, 3.4
- Minnesota: 5.9, -11.9, 6.0, 0.8, -6.8, 6.0, 0.5, 0.4, -1.0, 4.6, -5.5, 0.9
- Mississippi: 5.1, -7.1, 4.3, 2.2, -5.3, 3.1, -0.0, 1.8, -1.8, 4.1, -7.1, 2.9
- Missouri: 5.1, -7.1, 4.3, 2.2, -5.3, 3.1, -0.0, 1.8, -1.8, 4.1, -7.1, 2.9
- Montana: 3.2, -5.2, 1.9, -3.8, -0.8, 4.6, 5.1, -4.7, -0.4, 2.0, 0.3, -2.3
- Nebraska: 5.3, -8.0, 2.6, 2.0, -4.5, 2.6, 1.6, 1.4, -3.1, 1.8, -4.9, 3.1
- Nevada: 2.5, -4.9, 2.4, 3.7, -5.6, 1.9, -1.0, -0.4, 1.4, -0.2, 1.2, -0.9
- New Hampshire: 1.5, -9.6, 8.1, 0.4, -6.5, 6.0, 0.7, -3.0, 2.3, 0.4, -0.1, -0.3
- New Jersey: 8.5, -15.0, 6.5, 4.9, -9.8, 4.9, -0.8, 0.9, -0.1, 4.4, -6.1, 1.7
- New Mexico: 4.5, -7.2, 2.7, 2.1, -3.2, 1.1, 2.3, -2.4, 0.2, 0.1, -1.6, 1.5
- New York: 1.4, -3.4, 1.9, 1.0, 2.2, -3.2, -1.7, -3.2, 4.9, 2.2, -2.4, 0.2
- North Carolina: 3.8, -7.1, 3.3, 2.3, -4.8, 2.5, 0.4, -0.6, 0.2, 1.2, -1.8, 0.6
- North Dakota: 3.6, -9.0, 5.3, 3.2, -6.6, 3.4, 1.6, -2.7, 1.1, -1.2, 0.3, 0.9
- Ohio: 2.8, -2.2, -0.6, 0.2, 3.2, -3.4, 2.6, -2.7, 0.0, 0.0, -2.8, 2.8
- Oklahoma: 6.7, -9.0, 2.3, 3.9, -4.8, 0.9, -0.8, -0.4, 1.2, 3.5, -3.8, 0.3
- Oregon: 8.4, -10.2, 1.8, 7.8, -9.9, 2.2, -2.6, 3.2, -0.7, 3.2, -3.5, 0.3
- Pennsylvania: 6.5, -11.6, 5.1, 2.9, -3.1, 0.2, 2.4, -6.2, 3.7, 1.1, -2.3, 1.2
- Rhode Island: 6.5, -11.6, 5.1, 2.9, -3.1, 0.2, 2.4, -6.2, 3.7, 1.1, -2.3, 1.2
- South Carolina: 4.3, -7.6, 3.3, 3.5, -5.2, 1.6, -0.5, 0.3, 0.1, 1.2, -2.8, 1.6
- South Dakota: 3.4, -9.4, 6.0, 3.4, -6.3, 2.9, 0.5, -1.6, 1.1, -0.4, -1.5, 2.0
- Tennessee: 7.8, -6.5, -1.3, 4.9, -0.6, -4.3, 0.4, -0.8, 0.3, 2.4, -5.1, 2.6
- Texas: 3.3, -5.0, 1.8, -0.1, 3.6, -3.5, 1.1, -5.4, 4.3, 2.2, -3.2, 1.0
- Utah: 1.7, -6.7, 5.1, -3.2, -1.4, 4.7, 2.7, 0.1, -2.7, 2.3, -5.4, 3.1
- Vermont: 3.9, -7.7, 3.8, 2.7, -8.1, 5.5, 0.4, 1.2, -1.6, 0.8, -0.7, -0.0
- Virginia: 3.9, -7.7, 3.8, 2.7, -8.1, 5.5, 0.4, 1.2, -1.6, 0.8, -0.7, -0.0
- Washington: 5.0, -5.6, 0.6, 4.4, 1.7, -6.1, 2.2, -6.6, 4.4, -1.6, -0.7, 2.3
- West Virginia: 5.1, -9.0, 4.0, -0.4, -0.0, 0.4, 2.6, -3.1, 0.6, 2.9, -5.8, 2.9
- Wisconsin: 5.1, -9.0, 4.0, -0.4, -0.0, 0.4, 2.6, -3.1, 0.6, 2.9, -5.8, 2.9
- Wyoming: 6.5, -11.3, 4.8, 3.3, -5.2, 2.0, 0.8, -0.2, -0.6, 2.4, -5.8, 3.4
- Additional entries (labeled in source): West Virginia: 11.4, -15.5, 4.1, 8.7, -7.9, -0.8, 0.8, -4.0, 3.1, 1.9, -3.6, 1.7
- Wisconsin (additional): 6.3, -6.4, 0.2, 1.8, -3.3, 1.5, 2.0, -2.0, 0.0, 2.5, -1.1, -1.4
- Wyoming (additional): 8.2, -13.5, 5.2, 3.8, -5.9, 2.1, 0.5, -2.7, 2.2, 3.9, -4.9, 1.0

(Note: numbers are presented exactly as they appear in the source for each state's charted series.)

### Supplementary notes on interpretation
- The charts depict percentage-point changes in the share of households classified as Low income, Middle income, and High income across the sample periods shown in each state's panel.
- Middle income is defined as households with income between 50-150 percent of median income (OECD equivalence scale adjustment applied).

*Sources: Current Population Survey and author’s calculations.*

### Appendix Table 4A. State-level Regressions: Upward Hollowing-out Index

### Appendix Table 4A. State-level Regressions: Upward Hollowing-out Index (1977-2016; standardized coefficients)

### Key regression estimates (System GMM; columns (1)–(8))
- Lagged dependent variable: 0.15***, 0.16***, 0.15***, 0.15***, 0.15***, 0.14***, 0.15***, 0.15*** (standard errors: (0.034)(0.034)(0.034)(0.033)(0.033)(0.033)(0.035)(0.035))
- Household characteristics:
  - Age: -0.23***, -0.22***, -0.24***, -0.16**, -0.17**, -0.18***, -0.24***, -0.22*** (standard errors: (0.064)(0.069)(0.062)(0.077)(0.074)(0.057)(0.067)(0.063))
  - Education: -0.53***, -0.52***, -0.73***, -0.26***, -0.36***, -0.70***, -0.26***, -0.11* (standard errors: (0.109)(0.107)(0.127)(0.074)(0.094)(0.118)(0.073)(0.068))
  - Share of non-white population: 0.17**, 0.23***, 0.17**, 0.21**, 0.23**, 0.11, 0.18**, 0.10 (standard errors: (0.067)(0.087)(0.068)(0.096)(0.099)(0.071)(0.071)(0.062))
  - Share of females (head): 0.41*** (standard error: (0.133)) — appears in one specification
  - Share of single females with children (head): 0.26*** (standard error: (0.055)) — appears in one specification
- Job characteristics:
  - Offshoring: 0.32***, 0.28***, 0.37*** (standard errors: (0.083)(0.087)(0.091)) — significant positive association in selected specifications
  - Routinization: 0.29***, 0.23***, 0.06 (standard errors: (0.076)(0.074)(0.073)) — positive and significant in some specifications
  - Share of manufacturing employees: -0.21***, -0.23*** (standard errors: (0.076)(0.066)) — negative and significant
- Manufacturing by technological intensity (selected coefficients):
  - Share of high tech. sector employees: 0.06 (standard error: (0.051))
  - Share of medium-high tech. sector employees: -0.10* (standard error: (0.056))
  - Share of medium-low tech. sector employees: -0.05 (standard error: (0.052))
  - Share of low tech. sector employees: -0.16*** (standard error: (0.056))
- Constant terms (by column): 1.02***, 1.03***, -1.61***, -1.18***, 0.79***, -1.45***, 0.56***, 0.84*** (standard errors: (0.153)(0.164)(0.191)(0.212)(0.161)(0.192)(0.163)(0.133))

### Model and diagnostic statistics
- Observations: 1,989 (reported across columns)
- Number of states: 51
- AR(2) p-values (by column): 0.5090, 0.7480, 0.5400, 0.7990, 0.8740, 0.5270, 0.6340, 0.862
- Sargan p-values (by column): 0.7600, 0.8290, 0.7940, 0.8230, 0.8370, 0.7660, 0.8430, 0.871

### Notes on Appendix Figure 4A (Contributions to Change in Upward Hollowing-Out Index)
- Figures display percentage-point contributions over periods: 1977-2016, 1977-2000, 2000-2016.
- Components shown include: Lag dep. var. (persistence), Const., Time-F.E., Age, Education, Share non-white pop., Share manuf. employees, Offshoring, Routinization, and Net change.
- Notes: coefficients estimation come from Table 7A using state averages for the sample period.

---

### Appendix Table 4B. State-level Regressions: Upward Population-Share Index (1977-2016; standardized coefficients)

### Key regression estimates (System GMM; columns (1)–(8))
- Lagged dependent variable: 0.14***, 0.16***, 0.15***, 0.15***, 0.15***, 0.14***, 0.15***, 0.15*** (standard errors: (0.033)(0.033)(0.034)(0.032)(0.032)(0.033)(0.033)(0.033))
- Household characteristics:
  - Age: -0.25***, -0.24***, -0.26***, -0.18**, -0.19***, -0.20***, -0.26***, -0.25*** (standard errors: (0.067)(0.071)(0.066)(0.077)(0.074)(0.060)(0.071)(0.066))
  - Education: -0.49***, -0.47***, -0.67***, -0.24***, -0.34***, -0.64***, -0.24***, -0.10 (standard errors: (0.112)(0.112)(0.132)(0.076)(0.097)(0.121)(0.078)(0.072))
  - Share of non-white population: 0.18***, 0.23***, 0.17**, 0.21**, 0.23**, 0.11, 0.18**, 0.10* (standard errors: (0.068)(0.086)(0.068)(0.095)(0.097)(0.071)(0.072)(0.061))
  - Share of females (head): 0.37*** (standard error: (0.131)) — appears in one specification
  - Share of single females with children (head): 0.25*** (standard error: (0.053)) — appears in one specification
- Job characteristics:
  - Offshoring: 0.30***, 0.26***, 0.35*** (standard errors: (0.082)(0.087)(0.089))
  - Routinization: 0.26***, 0.21***, 0.03 (standard errors: (0.078)(0.077)(0.074))
  - Share of manufacturing employees: -0.21***, -0.24*** (standard errors: (0.074)(0.064))
- Manufacturing by technological intensity (selected coefficients):
  - Share of high tech. sector employees: 0.05 (standard error: (0.048))
  - Share of medium-high tech. sector employees: -0.11** (standard error: (0.052))
  - Share of medium-low tech. sector employees: -0.03 (standard error: (0.052))
  - Share of low tech. sector employees: -0.16*** (standard error: (0.055))
- Constant terms (by column): -1.29***, -1.26***, -1.39***, -0.99***, 0.81***, 0.80***, -0.66***, -0.84*** (standard errors: (0.196)(0.201)(0.195)(0.216)(0.168)(0.173)(0.207)(0.169))

### Model and diagnostic statistics
- Observations: 1,989 (reported across columns)
- Number of states: 51
- AR(2) p-values (by column): 0.5780, 0.8050, 0.6580, 0.7790, 0.8040, 0.6260, 0.6540, 0.752
- Sargan p-values (by column): 0.5690, 0.6350, 0.5820, 0.6370, 0.6210, 0.5460, 0.5810, 0.707

### Notes on Appendix Figure 4B (Contributions to Change in Upward Population-Share Index)
- Figures display percentage-point contributions over periods: 1977-2016, 1977-2000, 2000-2016.
- Components shown include: Lag dep. var. (persistence), Const., Time-F.E., Age, Education, Share non-white pop., Share manuf. employees, Offshoring, Routinization, and Net change.
- Notes: coefficients estimation come from Table 7B using state averages for the sample period.

---

### Appendix V. Household-level Regression Tables — Tables 5A–6B (Selected estimates and diagnostics)

### Appendix Table 5A. Household-Level Regressions (Standardized Coefficients)
Dependent variable: Real Size-Adjusted Household Income Relative to the Annual State Median (1968-16). Robust standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1.

- Core individual and household predictors (reported consistently across OLS specifications and subperiods):
  - Age: 0.14*** (full sample OLS Std; standard error: (0.000)), with subperiods 0.13*** (1977-1999) and 0.16*** (2000-2015).
  - Gender (male = 1): 0.13*** (full sample), 0.11*** (1977-1999), 0.14*** (2000-2015) (standard errors: (0.000) across reported cells).
  - Education: 0.19*** (full sample), 0.16*** (1977-1999), 0.28*** (2000-2015) (standard errors: (0.000)).
  - Share of non-white population: -0.03*** across specifications (standard errors: (0.000)).
- Household relative measures (h. relative indicate household relative to state median household characteristics):
  - Age (h. relative): 0.13*** (standard error: (0.000))
  - Gender (male = 1) (h. relative): 0.11*** (standard error: (0.000))
  - Education (h. relative): 0.20*** (standard error: (0.000))
  - Share of non-white population (h. relative): -0.02*** (standard error: (0.000))
- Occupation/industry task measures:
  - Offshorability score: -0.06***, Offshorability score (h. relative): -0.06*** (standard errors: (0.000))
  - Routinization score: -0.04***, Routinization score (h. relative): -0.01*** to 0.01*** depending on specification (standard errors: (0.000))
  - Manufacturing (=1): 0.04***; Manufacturing (h. relative): 0.04*** (standard errors: (0.000))
- Technology indicators (household head and household relative):
  - Technology (High tech.=1, h. head): 0.02***; Technology (Medium-high tech.=1, h. head): 0.02***; Technology (Medium-low tech.=1, h. head): 0.01***; Technology (Low tech.=1, h. head): 0.01*** (standard errors: (0.000))
  - Technology (High tech.=1, h. relative): 0.02***; Technology (Medium-high tech.=1, h. relative): 0.02***; Technology (Medium-low tech.=1, h. relative): 0.01***; Technology (Low tech.=1, h. relative): 0.02*** (standard errors: (0.000))
- Constants by reported block: 0.09***, 0.11***, 0.02***, 0.09***, 0.12***, 0.02***, 0.09***, 0.11***, 0.02***, -0.00***, 0.02***, -0.08***, 0.09***, 0.11***, 0.02*** (standard errors: (0.000))
- Observations (in millions) across reported panels: 1,281; 736; 546; 1,281; 736; 546; 1,281; 736; 546; 2,255; 1,325; 930; 1,370; 784; 586
- R-squared values (selected columns): 0.172, 0.193, 0.159, 0.167, 0.188, 0.155, 0.173, 0.194, 0.160, 0.177, 0.207, 0.163, 0.169, 0.190, 0.154

### Appendix Table 5B. Household-Level Quantile Regressions on the Median (Q(0.50); standardized coefficients)
Dependent variable: Real Size-Adjusted Household Income Relative to the Annual State Median (1968-16). Robust standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1.

- Median quantile (Q(0.50)) highlights (full sample and subperiods):
  - Age: 0.12*** (full sample), 0.11*** (1977-1999), 0.12*** (2000-2015) (standard errors: (0.000))
  - Gender (male = 1): 0.10*** (full sample), 0.09*** (1977-1999), 0.09*** (2000-2015) (standard errors: (0.000))
  - Education: 0.14*** (full sample), 0.12*** (1977-1999), 0.21*** (2000-2015) (standard errors: (0.000))
  - Share of non-white population: -0.03*** across most specifications (standard errors: (0.000))
  - Offshorability score: -0.05*** to -0.04*** (standard errors: (0.000))
  - Routinization score: -0.02*** to -0.01*** (standard errors: (0.000))
  - Manufacturing (=1): 0.04*** (standard errors: (0.000))
- Observations (in millions) match Table 5A: 1,281; 736; 546; 2,255; 1,325; 930; 1,370; 784; 586

### Appendix Table 6A. Household-Level Quantile Regressions on the 25th Percentile (Q(0.25); standardized coefficients)
Dependent variable: Real Size-Adjusted Household Income Relative to the Annual State Median (1968-16).

- Q(0.25) highlights:
  - Age: 0.08*** (full sample), 0.08*** (1977-1999), 0.08*** (2000-2015) (standard errors: (0.000))
  - Gender (male = 1): 0.07***, 0.06***, 0.06*** (standard errors: (0.000))
  - Education: 0.11***, 0.09***, 0.15*** (standard errors: (0.000))
  - Share of non-white population: -0.03*** to -0.02*** (standard errors: (0.000))
  - Offshorability score: -0.03*** (standard errors: (0.000))
  - Routinization score: -0.01*** to 0.01*** (standard errors: (0.000))
  - Manufacturing (=1): 0.04*** (standard errors: (0.000))
- Observations (in millions): same panel counts as above.

### Appendix Table 6B. Household-Level Quantile Regressions on the 72nd Percentile (Q(0.72); standardized coefficients)
Dependent variable: Real Size-Adjusted Household Income Relative to the Annual State Median (1968-16).

- Q(0.72) highlights:
  - Age: 0.15***, 0.14***, 0.16*** across full sample and subperiods (standard errors: (0.000))
  - Gender (male = 1): 0.14***, 0.12***, 0.13*** (standard errors: (0.000))
  - Education: 0.19***, 0.16***, 0.31*** (standard errors: (0.000))
  - Share of non-white population: -0.03*** to -0.04*** (standard errors: (0.000))
  - Offshorability score: -0.07***, -0.07***, -0.07*** (standard errors: (0.000))
  - Routinization score: -0.04*** to -0.03*** (standard errors: (0.000))
  - Manufacturing (=1): 0.03*** (standard errors: (0.000))
- Constant (Q(0.72) panels): 0.37***, 0.39***, 0.27***, 0.37***, 0.40***, 0.27***, 0.37***, 0.40***, 0.27***, 0.26***, 0.28***, 0.17***, 0.37***, 0.39***, 0.27*** (standard errors: (0.000))
- Observations (in millions): same series as above.

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*Sources: Current Population Survey and author’s estimations (tables and figures extracted from the source content).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp17244.pdf_