The Hope Gap

The gap. The goal's growth minus pay growth over the chosen period, in percentage points a year. Home prices: FHFA House Price Index (counties: FHFA's annual county index). Pay: average weekly wages of all workers covered by unemployment insurance (BLS Quarterly Census of Employment and Wages), the broadest measure of local pay. Cost of living: the national Consumer Price Index (local indexes exist for only a few metros, so every area uses the national rate against its own pay).

Groups. A group's pay trend is the area's, plus how that group's earnings have grown relative to all workers in the same place: average monthly earnings of people who held the same job all quarter, by age, sex, education (workers 25 and older) and race and ethnicity, from the Census Bureau's Quarterly Workforce Indicators for the county (the state's figure where a county group is too small), compared over the same four-quarter periods. Choices in several of these are added together, an approximation for narrow groups. Housing status and income levels have no such series and use the area's pay trend. When only the lowest income level or tax bracket is chosen, people are measured against starter homes: Zillow's index for the cheapest third of homes, for its price and for how much faster or slower it has grown than typical homes (no such index before 2000, so “Since 1990” uses typical homes).

The tipping point and the Hope Gap. Without an end to the race (the paper's main model), people have a reason to stop only when the gap is larger than the square of the goal's typical yearly swing (the paper's finiteness line, ρ = D, once pay growth stands in for the growth of resources net of post-exit spending). That swing is the standard deviation of yearly changes in the home price index since 1990 for the area (for cost of living, of yearly changes in real pay). The Hope Gap is the tipping point minus the gap: positive while hope holds, negative past the tipping point. It does not depend on any assumption about people's preferences.

Standing. Owning a home: three years of household income divided by the typical home value (Zillow Home Value Index, or the Census median where Zillow has none), so 100% means a typical home costs three years of income (the price-to-income ratio of 3 that housing analysts have traditionally called affordable). Step 4 also shows the share who have stopped under a four-year rule, because this convention moves that share more than anything else. Each household's standing follows its income: incomes in the group are spread as in the area's Census income distribution, shifted for each age band and for the group's race and ethnicity, education and housing status using Census medians, and limited to the income levels or tax brackets chosen. Each person also has an age within their band. Cost of living: local pay against its 2019 level, divided by consumer prices against theirs.

Who. Head counts multiply the area's adults in the chosen ages by the shares of the chosen sex, race and ethnicity, education, housing status and income range. These shares are treated as independent, so counts for narrow groups are approximate.

People. How much falling behind stings and how much people weigh today over the future are set from the chosen ages, weighted by population; the table below lists the values. The directions come from the cited studies; the sizes are this tool's assumptions.

Working years. By default the race ends at about 67. That gives everyone a quitting point that depends on the working years they have left (the paper's Proposition 4, “A deadline”): it is computed for each person by solving the model backward from the end of the race, and it never falls as time runs out. People past the end age are not counted, and people who reach it during a scenario leave the count. Step 3 can move the end to 62 or 70, or remove it, which gives the paper's main model.

The simulation. Two thousand people spread across the group's standing and ages move month by month with the goal's trend and swings. Those below their quitting point have stopped. Scenarios and plans change the actual trend at once or over two years, and the quitting point moves with the trend. By default people take about a year to notice a change in the trend, an extension beyond the paper; Step 3 can set “At once”, exactly as in the paper, or about three years. Someone who has stopped starts again only if the quitting point falls below where they now stand. Without an end to the race, a scenario or plan that lifts the Hope Gap above zero takes the model outside its own assumption (the paper's ρ > D): there the race is worth staying in at any standing, so the quitting point is gone. With an end to the race, quitting points remain and fall as the trend improves.

Plans. Closing the gap means bringing the goal's growth down, or pay growth up, by the Hope Gap. Homes needed use a long-run price elasticity of housing demand of about −0.6 (Hanushek and Quigley 1980): each extra 1% of homes lowers prices about 1.7%; the range uses −0.4 to −1.0. Pay plans are priced as a credit that grows by the needed share of the group's median income each year. Help for people near the edge lifts their standing by 10%. Tax brackets are 2026 brackets for married couples filing jointly, converted to household income by adding the $32,200 standard deduction; single filers' dollar ranges are about half.

Limits. This is one decision, computed from the paper's model, applied to a group. With an end to the race, quitting points are computed on a coarser grid than the paper's tables, for speed; in tests across the range of settings this page offers, they agree with the paper's own computations to within 0.6 percentage points of standing, and usually closer. Group pay trends combine dimensions by adding them and come from jobs located in the area, not from where people live. It takes prices and pay as given, so it cannot show how disengagement feeds back into them. The quitting point moves fast near the tipping point, so the share who have stopped is less certain than the Hope Gap; the results show how much it changes if the trend is off by a quarter point, and under a four-year rather than three-year affordability rule. Read changes and comparisons more than levels.