# The Balance Sheets of Low-Income Households: What We Know about Their Assets and Liabilities. Methods Used in the Literature

This appendix reports in some detail on the different methods the current literature uses to measure assets, debts, and net worth, such as means and medians.

Means. If we are looking at the asset holdings of 100 households, then the mean is the average asset holding for all 100. If there were \$1,000 in total assets spread across all 100 households, then \$10 would be the mean asset holding.

Per capita assets, debts, or net worth. Per capita is just like the mean, but for individuals rather than households. In our sample of 100 households with \$1,000 in assets total, if we knew that each household had four persons, then the amount of assets per capita would be \$2.50.

Medians. For the same group of 100, we sort them in ascending (or descending) order of asset values. Since there is an even number of households, the median is the value midway between households 50 and 51  meaning that fifty percent of the sample has assets holdings worth less than this median household and fifty percent has assets holdings worth more. When the total number is odd (for example, 99 households), the median is the middle value (household 50 of the 99). Note that the median value does not change even if we replace one of the households above the median with an extremely wealthy household, although the mean would change substantially.

Quintiles. Following the same principle as locating the median, here we divide the sample into equal fifths (20 households a piece), known as quintiles. The first or bottom quintile contains those households that have the least in asset holdings and the fifth or top quintile contains those that have the most. The median would fall in the middle of the third quintile. If we instead divided the sample into deciles or tenths, than each decile would contain ten households and the median would fall right between the fifth and the sixth decile. Alternatively, quartiles divide the distribution into fourths or 25 persons each in our example. The literature often uses quintiles of income or quintiles of net worth, but may refer to these quintiles as income percentiles.

Percentage of households holding an asset. This measure refers to the percentage of households within a defined group that hold a given asset with a positive value. Bank accounts are an exception, in that accounts with zero balances are included, the rationale being that while a respondents account may have been zero at the time of the survey, it was probably not at (or below) zero the entire month. Accounts that have negative balances are treated as drawing on a line of bank credit, which counts as a debt when the SCF totals up net worth.

Distribution of total assets, debts, or net worth. This measure is used when we want to know how much of an asset is concentrated in, say, each quintile of household income. In our example of 100 households, we might find that \$1,000 in total assets is distributed as follows: \$50 in the bottom quintile, \$100 in the second quintile, \$150 in the third quintile, \$250 in the fourth quintile, and \$450 in the top quintile.

Shares of assets, debts, or net worth. Based on the distribution in the preceding entry, suppose we then wanted to know what fraction or share of total assets was held by each quintile. We would simply divide the total asset amount of each quintiles holdings by the total asset amount for the sample (\$1,000) and arrive at the following shares: 5 percent for the first quintile, 10 percent for the second quintile, 15 percent for the third quintile, 25 percent for the fourth quintile, and 45 percent for the top quintile, summing to 100 percent.

Gini coefficients. The gini coefficient is a number between zero and one that is a measure of inequality. A gini of 0 indicates that an item like total assets, total debt, or total net worth is totally equally distributed  for example, in our sample 100 households, if total assets were \$1,000, each household would have \$10. A gini of 1 indicates that an item is maximally unequally distributed  for our example, the 100th household has all \$1,000 of assets and the other 99 households have nothing. Wolff (2004) examines the concentration of national wealth in the 2001 SCF and calculates a gini of 0.826.

Asset poverty measures. In this report, we rely on the definition in Caner and Wolff (2004), though they calculate asset poverty in several different ways. A household is asset poor if its access to wealth is insufficient to allow the household to meet basic needs over a certain period of time. Caner and Wolff, acknowledging that these specifications are somewhat arbitrary, consider three measures of wealth  net worth, net worth minus home equity, and liquid wealth (the value of cash and other assets that can be easily converted to cash). They rely on poverty thresholds (which increase with family size) for their definition of basic needs.[13] And they define a certain period of time as three months. Therefore, for this report, the asset poverty line is defined as the amount of assets a household would need to have available to liquidate in order to live at the designated poverty line for three months.

Asset poverty gap ratio. This ratio measures the per-household amount of wealth that would be required to raise all asset poor households to the asset poverty line, calculated as a share of the asset poverty line. In other words, a household at 40 percent of the asset poverty line would have an asset poverty gap ratio of 60.00 which would mean that an additional 60 percent of the asset poverty line would be required to bring this household up to the line.

Debt ratios. These ratios can be expressed in many ways. One way is to simply divide a households debts by its assets  this debt-to-asset ratio is sometimes called the leverage ratio and shows how extended (or over-extended) a household may be. Another ratio, which we call the debt service ratio or debt-to-income ratio, divides the payments necessary to service household debt by household income.

Bankruptcy filings. This measure of household financial distress can be expressed in several ways, one of which is simply the number of bankruptcy filings per 1 million persons.

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