Counting varieties: the Feenstra premise, three decades later

Feenstra’s 1994 AER paper shows that conventional import-price indices understate welfare because they assume a fixed set of varieties and cannot price the entry of new ones. He gives the correction (a CES expenditure function with variety-varying adjustment) and illustrates the size of the bias on six goods. The Feenstra premise — that the variety count keeps rising — is straightforward to check in the BACI HS6 panel: count distinct (country, product) pairs with positive exports, every year.

Published result

Feenstra (1994, AER) starts with a Sato-Vartia (1976) CES price index and extends it to allow the set of varieties being priced to change over time. The closed-form correction depends on the elasticity of substitution σ and on a ratio of expenditure shares on “common” goods across periods. Applied to six US import goods (men’s leather shoes, portable typewriters, silver bullion, carbon-black, gold bullion, stainless steel bars) for 1964–1987, the correction shows that new-variety entry biased the conventional BLS import price index upward by a non-trivial margin — several percentage points over the sample. The broader point, which became foundational for Broda & Weinstein (2006), is that variety growth is persistent, pervasive, and welfare-relevant. Measuring variety requires either product-level entry data (Feenstra’s 7-digit TSUSA) or a coarser but more comprehensive HS6 panel (our approach here).

Our re-estimate

BACI 202501 covers 1995–2024 at HS6. We count, each year, the number of distinct (country_code, product_code) pairs with strictly-positive export value. This is not the Feenstra price-index correction (that requires unit-value variance across source origins and a fitted σ — the Broda-Weinstein extension). It is the underlying count of “active” country-product varieties in world trade each year, which is the premise the Feenstra correction builds on.

Numerical comparison

Feenstra-Markusen-Rose (2001) λ ratio, USA imports

Feenstra’s (1994) correction factor for new-variety entry has the explicit form (λt-1/λt)1/(σ−1), where λ_t = (value of “common” varieties in period t) / (value of all varieties in t). A variety is “common” if it traded in both periods. Feenstra-Markusen-Rose (2001, JIE) operationalise this at country-of-origin × HS code. At σ = 4 (the median Broda-Weinstein 2006 estimate), each one-percentage-point drop in λ implies roughly a 0.33% welfare gain from new varieties. Below: λ and the implied cumulative Feenstra correction for USA imports at HS6 × source-country, 1995 → selected years.

λ approaches 1 when variety churn is low (every HS6×source present in t was also present in t−1). The gap 1 − λ is the fraction of year-t import value in varieties that did not exist a year earlier. At σ = 4, the Feenstra-Markusen-Rose welfare correction is (1 − λ)/3 in log points: the implicit upward bias in conventional BLS-style fixed-basket price indices.

USA new-variety gains · σ sensitivity vs Broda-Weinstein (2006)

Broda & Weinstein (2006, QJE) apply the Feenstra (1994) correction to 15,000+ HS10-by-source varieties of US imports 1972-2001 and report a cumulative upward bias in the conventional import price index of 2.6% of GDP at σ = 4 (their median-fitted elasticity, Table IV). Our λ series above is much flatter because HS6 (5,022 codes) is two orders of magnitude coarser than HS10 × source. Still, the formula Δlog Wt = −log(λnew,t/λold,t)/(σ − 1) (Feenstra-Markusen-Rose 2001) applied to our sample lets us bracket the bias under alternative σ choices and compare the implied gain to Broda-Weinstein’s.

Annual new-variety gain trajectory · σ sensitivity

The cumulative bars above compress 28 annual steps into a single number per σ. The year-by-year series reveals when variety churn actually happened: whether it was a smooth drip of new Chinese HS6 exports through the 2000s, a step jump at WTO accession, or a post-2015 slowdown. Plotting (1 − λt)/(σ − 1) for each year and each σ isolates the time-series fingerprint of Feenstra’s bias term.

Where did the new varieties land? HS6 ubiquity distribution shift

Figure 1 counts varieties; the σ-sensitivity figures price them. Neither tells us where in the product space the variety growth lives. A direct way is the ubiquity distribution (Hidalgo & Hausmann 2009 use the same statistic on the product side): for each HS6 product, count how many countries actively export it. Variety growth can come from new HS6 codes entering with few exporters (frontier widening), from existing rare-products picking up additional exporters (filling the long tail), or from already-ubiquitous products getting still more exporters (densification). Comparing the 1996 ubiquity histogram to the 2024 one tells us which channel drove the +37% pair count in Figure 1.

Why it might differ

Five reasons our variety count is not directly comparable to Feenstra’s (or Broda-Weinstein’s). First, unit: Feenstra’s varieties are source-country-specific 7-digit TSUSA goods imported by the US; ours are (country-of-export, HS6) cells worldwide. HS6 is coarser than TSUSA 7-digit by roughly a factor of 3–4, so our count understates the truly fine-grained variety concept. Second, geography: Feenstra studies US imports; we count world-wide active exporter-product pairs, which is a different object — it doubles every pair (CHN exports HS 611030 to USA and USA imports HS 611030 from CHN are two data points in Feenstra’s source-specific setup but one (CHN, 611030) in ours). Third, threshold: we count any positive export value; BACI’s HS6 detection threshold after reconciliation is roughly $1,000 of annual flow, which is more permissive than the dollar thresholds typical in US customs data. Fourth, period difference: Broda-Weinstein show US import variety tripled from 1972 to 2001; our 1995–2024 window starts at a much higher base and shows the smaller additional growth of a mature trading system. Fifth, sample composition: BACI includes 1995 data from 213 reporters and 2024 data from 226, so some of the growth is new reporter entry (the Baltics, Central Asia, small Pacific islands) rather than existing reporters widening their basket.

The Feenstra claim — that the set of traded varieties grows over time, and that a fixed-set price index misses welfare gains from entry — passes its qualitative test on the 1995–2024 BACI panel: varieties grew 36.7%, with most of the gain front-loaded in the 1995–2008 period. The rate of new-variety entry has slowed since 2010, which is itself an economically interesting pattern — consistent with Bergin, Feenstra & Hanson (2011, AER) on the maturation of China’s variety frontier and with Yi (2003, JPE) on the vertical-specialisation ceiling.

BibTeX

@article{feenstra_1994,
  author  = {Feenstra, Robert C.},
  title   = {New Product Varieties and the Measurement of International Prices},
  journal = {American Economic Review},
  volume  = {84},
  number  = {1},
  pages   = {157--177},
  year    = {1994},
  jstor   = {2117976}
}

For the within-product quality-ladder complement, see /quality. Return to the replication gallery.