Agglomeration Economies and a Test for Optimal City Sizes in Japan

Summary

"Agglomeration Economies and a Test for Optimal City Sizes in Japan" (Journal of the Japanese and International Economies, Vol. 10, No. 4, December 1996, pp. 379–398, DOI 10.1006/jjie.1996.0022) is by Yoshitsugu Kanemoto (University of Tokyo), Toru Ohkawara (Socio-Economic Research Center, Central Research Institute of Electric Power Industry), and Tsutomu Suzuki (Institute of Socio-Economic Planning, University of Tsukuba). A pre-publication working-paper version (dated April 1996, presented at the 9th TCER-NBER-CEPR Trilateral Conference in Tokyo and the Urban Economics Workshop in Kyoto) is freely available as University of Tokyo CIRJE Discussion Paper 96-F-9. Kanemoto is a leading Japanese urban and public economist whose 1980 book Theories of Urban Externalities is itself an early contributor to the theoretical literature the Henry George Theorem (HGT) belongs to; the paper's HGT derivation cites Arnott & Stiglitz (1979) directly. The paper is significant for the Georgist case not because it is a landmark or highly authoritative venue in the way the Mirrlees Review is, but because — as both the authors and Richard Arnott's own 2004 retrospective on the theorem note — it is, to date, essentially the only empirical attempt to operationalize the HGT as a real-world test of whether an actual city is optimally sized.

The Core Argument and Findings

1. Two stated aims. The paper (a) estimates aggregate production functions for Japanese metropolitan areas to measure the magnitude of agglomeration economies, using a custom-built metropolitan-area dataset (Japan, unlike the U.S., publishes economic data only for legal jurisdictions, not metro areas, so the authors constructed "Integrated Metropolitan Area" data by an iterative commuting-based procedure); and (b) uses those estimates to test whether Japanese cities — especially Tokyo, then the subject of a national policy debate about relocating the capital because of perceived overcrowding — are "too large."

2. Why a direct HGT test is not possible, and what the authors do instead. The authors state plainly that "a direct test of the Henry George Theorem is very difficult because good land rent data are not available and we have to rely on land price data instead," and that converting Japanese land prices into land rents is "bound to be inaccurate" because the price/rent ratio is extremely high and volatile (it moved from 2.48× GNP in 1970 to 5.35× in 1990 and back to 4.01× in 1993, computed from Japan Economic Planning Agency national income accounts). Instead of a direct rent-equals-spending test, they compute, for 17 Japanese metropolitan areas with over one million residents, the ratio of total land value to the total "Pigouvian subsidy" (the estimated aggregate agglomeration-economy benefit implied by their production-function estimates) and ask whether this ratio is systematically higher for Tokyo — the top of Japan's urban hierarchy — than for other cities. Their reasoning (following Kanemoto's own 1980 theoretical work) is that agglomeration economies plus multiple equilibria in city formation mean equilibrium city sizes tend to be too large everywhere, but the divergence from the optimum should be largest for the city hardest to "duplicate," i.e. Tokyo.

3. The empirical estimates. Estimating Cobb-Douglas-style aggregate production functions with 1985 cross-sectional data, they find agglomeration economies are small for cities under 200,000 population, largest for cities between 200,000–400,000 (where doubling city size raises productivity by roughly 25% in their baseline specification), and moderate (~7%) for cities above 400,000.

4. The land-rent/Pigouvian-subsidy test. Averaged across the 17 metro areas, total land value exceeds the total estimated Pigouvian subsidy by a factor of roughly 145 (Cobb-Douglas case) to 293 (modified Cobb-Douglas case) — the authors note this would imply an implausibly low user cost of capital if taken as a literal HGT violation, but caution their land-value estimates are "quite crude." Tokyo's own ratio came out slightly below the 17-city average in both specifications (144.6 vs. 145.4 average in the simple case; 247.1 vs. 292.8 in the modified case). The authors' own conclusion: "there is no evidence supporting the hypothesis that Tokyo is too large" relative to other major Japanese cities — directly contradicting the premise of the contemporary Japanese policy debate about relocating the capital out of Tokyo. They add an important caveat: because the test is a ratio, and Tokyo's population (32 million) was more than double that of the next-largest metro area (Osaka, 14 million), the same ratio finding could still coexist with a much larger absolute gap between land rent and public spending for Tokyo than for smaller cities — so the paper does not rule out that Tokyo (and other Japanese cities generally) could be oversized in absolute terms, only that Tokyo is not distinctively more oversized than its peers.

5. The authors' own honesty about the result's limits. The paper explicitly frames itself as exploratory: "This article is a first attempt at an empirical test of the Henry George Theorem and there is ample room for improvements." They flag their land-value estimates as "quite crude" (substantially higher than Japan Economic Planning Agency prefecture-level figures) and list unresolved methodological problems, including the difficulty of separating development costs, discount rates, and rural-rent baselines from raw land-price data.

Relation to the Georgist Case

This paper supports the Georgist case only narrowly and conditionally. It does not show that land rent in Japanese cities equals or could fund observed public spending — the direct HGT prediction — because the authors explicitly say they could not test that directly given available data. What it does show is an indirect, comparative test: using the best available (if "crude," in the authors' words) proxy data, Tokyo's land-value-to-agglomeration-benefit ratio was not exceptional relative to other large Japanese cities, which the authors interpret as absence of evidence that Tokyo specifically violates the HGT's optimal-size logic more than its peers do. For the Georgist case this is a modest, technical data point: it is consistent with the HGT's underlying land-rent/public-benefit linkage being a real empirical regularity (rents track agglomeration benefits fairly uniformly across a city hierarchy) rather than a claim that any given city's land rent could currently finance its public goods bill. It should be read as a proof-of-concept that the HGT is empirically approachable at all — which, per Arnott (2004), remained a rare achievement even eight years later — rather than as a confirmation that observed land rents in Japan (or anywhere) are adequate to fund public expenditure.

Nuances and Limits

• Not a direct test of the HGT's rent-equals-spending identity. The authors substitute a ratio-comparison-across-cities design specifically because they say a direct test is infeasible with available land-rent data; readers should not treat this as "confirming" the HGT numerically.
• Land value, not land rent, is the underlying data, converted via assumptions about development costs, discount rates, and rural-rent baselines that the authors themselves call difficult to estimate reliably; Japan's land price/rent ratio was unusually high and volatile in the period studied (the late-1980s bubble and its unwind), which the authors flag as a specific source of unreliability in the conversion.
• The "no evidence Tokyo is too large" finding is relative, not absolute. Because the comparison is a ratio and Tokyo is far larger in absolute terms than any other Japanese city, the same finding is compatible with Tokyo's absolute land-rent/public-spending gap being much larger than smaller cities' — the paper explicitly says this cannot be ruled out.
• The paper remained unpublished in its most detailed working-paper form for some time and, per Arnott (2004), required "a long chain of questionable assumptions" to move from the generalized theoretical HGT to this specific test — including treating the theorem as applying city-by-city rather than to an entire spatial "replication unit," and assuming a constant land-value/shadow-loss ratio is meaningful across a heterogeneous urban hierarchy. See Arnott (2004) for the fullest published critique of these assumptions.
• Cross-sectional, single-year (1985) data — the test speaks to Japan's mid-1980s urban hierarchy specifically, not a general or contemporary claim about optimal city size anywhere else.
• The authors' own framing is that this is a first attempt, not a settled result — later work (e.g. Behrens, Kanemoto & Murata (2015), co-authored by Kanemoto himself) extends the theoretical side of this research program but does not, to this wiki's knowledge, repeat or update the empirical Tokyo test with better rent data.

Bears On

• Outcome: Public goods can be funded from the land rent they create — this paper is the first (and, per Arnott 2004, still rare) attempt to give the Henry George Theorem an empirical test rather than leaving it purely theoretical; its finding (no evidence Tokyo specifically over-violates the theorem's logic relative to peer cities) is weak, indirect, and self-described as provisional support for the plausibility of the underlying rent/public-benefit link, not a measurement of whether land rent could actually fund public goods in any city.
• Concept: Henry George Theorem — supplies the one empirical application discussed in the theoretical literature on the theorem.
• Research: Arnott (2004), "Does the Henry George Theorem Provide a Practical Guide to Optimal City Size?" — Arnott's paper is the fullest published critical assessment of this study's assumptions and gives it a qualified endorsement ("its conclusion should be respected until a sounder procedure is developed").
• Objection: Land value can't be assessed accurately — the authors' own admission that available Japanese land-price data could only crudely proxy land rent, and that separating development costs, discount rates, and rural-rent baselines is difficult, is a direct real-world illustration of this objection from economists sympathetic to the HGT's logic.

See Also

• Henry George Theorem
• Arnott & Stiglitz (1979): Aggregate Land Rents, Expenditure on Public Goods, and Optimal City Size
• Does the Henry George Theorem Provide a Practical Guide to Optimal City Size? (Arnott 2004)
• The Henry George Theorem in a Second-Best World (Behrens, Kanemoto & Murata 2015)
• Objection: Land value can't be assessed accurately

Sources

1. Yoshitsugu Kanemoto, Toru Ohkawara & Tsutomu Suzuki (1996), "Agglomeration Economies and a Test for Optimal City Sizes in Japan," Journal of the Japanese and International Economies 10(4): 379–398. DOI: 10.1006/jjie.1996.0022 — used for the published citation (title, authors, journal, volume/issue/pages) and confirmed via the publisher (ScienceDirect/Elsevier) record.
2. Yoshitsugu Kanemoto, Toru Ohkawara & Tsutomu Suzuki, "Agglomeration Economies and a Test for Optimal City Sizes in Japan," CIRJE Discussion Paper 96-F-9, University of Tokyo, April 1996. Free PDF — the pre-publication working-paper text; fetched and read directly in this session. Used for the abstract, introduction, methodology (the Integrated Metropolitan Area construction, the Henry George Theorem discussion, the reasons a direct test is infeasible), the Table 4–6 data (land value/GNP ratios, land value vs. Pigouvian subsidy by city), the specific finding on Tokyo's ratio versus the 17-city average, and the authors' own conclusion and caveats, including the direct quotations above.
3. Richard Arnott (2004), "Does the Henry George Theorem Provide a Practical Guide to Optimal City Size?" The American Journal of Economics and Sociology 63(5): 1057–1090 — used for the characterization of this paper as the sole available empirical HGT application as of 2004, and for the critical assessment of its assumptions; see wiki summary.