The ZHVI-by-race metric was created as an overlay to the published Zillow Home Value Index (ZHVI), using small area census owner-occupied housing unit estimates by race to draw conclusions about race-specific housing market performance. This is done in two ways: value-based estimation and ratio-based estimation, with different purposes for each method. 

In both cases, the aggregating and chaining methodology is meant to mirror the construction of ZHVI for the entire market, for harmonious estimates at the aggregated national/MSA/state level.

Approximate monthly ZIP-level owner-occupied housing units by race of householder and for “All Races”. This allows the weight of a ZIP code in estimation to change over time based on population and homeownership dynamics. LOESS prediction is used over ACS 5-year estimates for survey years and a combination of LOESS and linear prediction beyond the bounds of the survey years, extrapolating for: 

so that the population trend returns to the linear trend (over a relatively short time frame). Estimates are assumed to be centered in June, and other months are interpolated using a natural cubic spline. These owner-occupied housing unit estimates are only used as weights for smaller-area ZHVI trends and don’t have a direct impact in determining dollar values or rates of change in ZHVI.

ZIP weights by race are joined to ZIP ZHVI and the ZHVI of ZIP parent regions, using a single parent hierarchy. Value-based estimation determines:

• County typical home value by race for the most recent period using a weighted (homeowners by race) mean of ZIP ZHVI.
• Aggregated national/MSA/state typical home value by race for the most recent period using a weighted mean of county typical home value by race.
• County typical monthly appreciation by race for all periods using a weighted mean of month-over-month ZIP ZHVI.
• Aggregated national/MSA/state typical monthly appreciation by race for all periods using a weighted mean of county typical monthly appreciation by race.
• Aggregated home values chained back from current level using aggregated monthly appreciation.

The ratio-based estimation:

• Determines county typical home value by race for the most recent period using a weighted (homeowners by race) mean of ZIP ZHVI.
• Takes the county-level ratio of typical home values, comparing each race to the group of “All Races”.
• Determines aggregated national/MSA/state typical home value ratio by race for the most recent period using a weighted mean of county-level ratio by race.
• Multiplies the ratio of home values by the parent region ZHVI to get the standardized home value by race for the most recent period.
• Takes the difference between month-over month changes in ZIP ZHVI and month-over month changes in county ZHVI for all periods.
• Determines county relative monthly appreciation by race for all periods using a weighted mean of the difference between ZIP and county month-over-month appreciation.
• Determines aggregated national/MSA/state relative monthly appreciation by race for all periods using a weighted mean of county relative monthly appreciation by race.
• Adds the difference in the monthly appreciation by race to the parent region month-over-month ZHVI change to get the standardized appreciation by race for each period. 
• Chains aggregated home values back from current level using aggregated monthly appreciation.

We then adjust series for historical data “missingness” among ZIP codes. Some ZIPs do not have complete ZHVI series, and so historical estimates aggregating from ZIPs stray from the overall ZHVI. Some of this is controlled for by chaining back weighted changes rather than taking direct averages, but there is still some drift. Historical estimates by race are adjusted by the ratio of published ZHVI to estimated “All races” ZHVI, so that an adjustment is made for the overall drift and nothing else.