Indexing Capital Gains to Inflation

The code for these calculations can be found here.

The IRS public-use microdata (PUF) reports net long-term capital gains or losses for each tax unit but does not include holding period, cost basis, or the number of underlying transactions. We impute these using data from the IRS Statistics of Income’s Sales of Capital Assets (SOCA) study, which tabulates holding period, sales price, and cost basis for the universe of capital asset transactions on individual tax returns.

We draw on SOCA Table 4, which reports the number of transactions, aggregate sales price, cost basis, and gain or loss amount by holding period bucket, separately for gain and loss transactions. The nine long-term holding period buckets are: under 18 months, 18 months to 2 years, 2–3 years, 3–4 years, 4–5 years, 5–10 years, 10–15 years, 15–20 years, and 20 years or more.

From SOCA Table 4 (averaging over the 2013–2015 panel, the most recent available), we compute:

• Gain-dollar-weighted holding period distribution (πᵍ): the share of total long-term gain dollars falling in each holding period bucket. We use the gain amount column directly rather than computing gain as sales minus basis, since the two differ due to passthrough income and mutual fund distributions that appear in the gain column but have no corresponding sale (see SOCA Table 4 footnotes).
• Loss-dollar-weighted holding period distribution (πₗ): the analogous shares for loss transactions. Losses are more concentrated at shorter holding periods than gains (gain-weighted mean of about 12 years vs. about 6 years for losses).
• Basis-to-sale ratio by holding period bucket, separately for gain and loss transactions.

For each PUF record with nonzero net long-term capital gains or losses, we assign a continuous holding period in two steps:

1. Draw a holding period bucket. For records with net gains, we draw from the gain-dollar-weighted distribution πᵍ. For records with net losses, we draw from the loss-dollar-weighted distribution πₗ. Every record faces the same distribution regardless of gain size or income.
2. Smooth within the bucket. For the first eight buckets, we draw from a shifted Weibull distribution (shape 0.77, scale 9.15) truncated to the bucket's interval. The Weibull, fit to the overall SOCA holding period distribution, is right-skewed: within any bucket, draws cluster toward the lower bound. For the top bucket (20 years or more), the Weibull's heavy tail produces unrealistically long holding periods. Instead, we draw from an exponential distribution with rate parameter pinned so that the density is continuous at the 20-year boundary. This yields a gain-dollar-weighted mean of about 35 years in the top bucket and an overall mean of about 11 years.

Given the assigned holding period \(h\), we compute cost basis from the basis-to-sale ratio (BSR).

For gains, we estimate \(\text{BSR}(h)\) using an OLS model fit to the SOCA Table 4 panel (all available years, 1985–2015):

\begin{align} \log(\text{BSR}) = \alpha_h + \beta \cdot h \cdot \log(1 + R) \end{align}

where \(\alpha_h\) is a bucket fixed effect and \(R\) is the trailing annualized S&P 500 total return over the holding window ending in the sale year. This specification allows the basis-to-sale ratio to vary with market conditions: assets sold after strong market trends lower BSR (more of the sale price is gain), while assets sold after a downturn have higher BSR. We predict ratios for our imputation base year (2017) at the nine bucket knot points and interpolate across holding periods. For projection years beyond 2017, we scale basis using the ratio of the predicted weighted-average BSR in year \(y\) to that in 2017. Basis is then:

\begin{align} \text{basis} = \text{gain} \times \frac{\text{BSR}(h)}{1 - \text{BSR}(h)} \end{align}

For losses, we use the loss-transaction basis-to-sale ratio from SOCA Table 4, which exceeds 1 by definition. Loss basis is:

\begin{align} \text{basis} = |\text{loss}| \times \frac{\text{BSR}_{\text{loss}}(h)}{\text{BSR}_{\text{loss}}(h) - 1} \end{align}

One limitation is that the SOCA data are transaction-level while the PUF is tax-unit-level. SOCA reports holding period and basis for individual asset sales, separately for gain and loss transactions. The PUF reports only the net long-term gain or loss across all of a tax unit's transactions. We assign a single holding period and basis to each tax unit's net amount, drawing from the SOCA gain-transaction distribution if the net is positive and the loss-transaction distribution if the net is negative. This treats each tax unit as if it had a single representative transaction, when in practice a unit with a net gain may also have loss transactions with different holding periods, and vice versa.

A second possible limitation is that we impute holding period distribution without conditioning on taxpayer-level income or net gain size. In practice, SOCA Table 2 shows that the composition of gains shifts toward longer holding periods at higher AGI levels. We tested a conditional model that incorporated this gradient, but it produced similar revenue and distributional estimates, so we use the simpler unconditional approach.