Geography, Depreciation, and Growth

By Solomon M. Hsiang and Amir S. Jina∗

Any visit to the seashore will confirm thatit is more difficult to build a large sandcas-tle if one locates the project too near thelapping waves of the ocean. The sandcas-tle may grow well initially, but eventually arouge wave washes out some portion of theprogress. It may be possible for the sand-castle to grow on net, so long as investmentin building outpaces losses to the waves, butit must be true that identical building effortwould lead to a larger castle were construc-tion sited on a portion of the beach furtherfrom the waves.

Beach-goers face depreciation of sandcas-tle investments by waves, with an averagerate of depreciation that is influenced bytheir location on the beach. We point outhere that similar dynamics apply to cap-ital accumulation, and thereby economicgrowth, which faces average rates of depre-ciation that differ by geography.

It has been previously proposed thatgeography influences economic growth formany reasons. For example, geographymay affect labor productivity via health,and trade costs via ruggedness and land-lockedness (Gallup, Sachs and Mellinger,1999); geography affected agricultural pro-ductivity during early stages of develop-ment which may have enduring influence(Nordhaus, 2006; Hornbeck, 2012); or geo-graphic conditions could influence the na-ture of persistent economic and politi-cal institutions (Acemoglu, Johnson andRobinson, 2002; Rodrik, Subramanian andTrebbi, 2004; Dell, 2010). Yet to our knowl-edge, prior work has neither suggested nordocumented that depreciation varies by lo-cation, and thus its potential role in influ-encing the wealth of nations has not beenconsidered nor explored.

∗ Hsiang: University of California, Berkeley, 2607Hearst Ave. Berkeley, CA 94720, shsiang@berkeley.edu.

Jina: University of Chicago, 5757 South University

Ave., Chicago, IL 60637, amirjina@uchicago.edu.

Previous analyses of comparative devel-opment seem to have sidestepped the ques-tion of location-dependent depreciation outof necessity because data on depreciationwere unavailable. For example, seminalwork by Mankiw, Romer and Weil (1992)stated

We assume that [depreciationrates] δ are constant across coun-tries.... [T]here is neither anystrong reason to expect deprecia-tion rates to vary greatly acrosscountries, nor are there any datathat would allow us to esti-mate country-specific depreciationrates.

We continue to lack generally comprehen-sive measures of capital depreciation, how-ever, the construction of new location-specific measures of tropical cyclone ex-posure (Hsiang, 2010) enables us to con-sider the potential impact of this singlesource of capital depreciation. Tropical cy-clones (hereafter “cyclones”) are the classof destructive storms that include “tropi-cal storms,” “hurricanes,” “typhoons,” and“cyclones”—all of which are the same phys-ical phenomena but differ in name based ontheir location and intensity.

To consider how cyclones affect localrates of depreciation, we first point out thatdepreciation rates may change across se-quential moments in time, holding a lo-cation fixed. In the beach-goers exampleabove, there may be moments with no de-preciation of a sandcastle (when no wavesare near) and there may be later brief mo-ments of rapid depreciation (when a waveis splashing against the sandcastle). Sim-ilarly, depreciation of capital acceleratesdramatically while it is exposed to a cy-clone, which may damage large portions ofbuildings, roadways, farmland, and otherdurable assets that depreciate much moregradually at other moments in time. We

1

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think most readers will be accustomed tothinking of depreciation as a slow processof capital degradation that does not varywith time, such as an iron bridge rust-ing gradually. To those readers we notethat these slow processes also vary overtime: the instantaneous rate at which abridge rusts may change dramatically de-pending on whether it is daytime, raining,or humid—however, because the process isso slow in absolute terms we have more diffi-culty discerning these fluctuations with thenaked eye.

For a unit of capital kx at location x thatis exposed to a time-varying depreciationrate δx(t), we are generally interested in theaverage “sandcastle depreciation rate” be-tween time s1 and s2:

(1) δ̄x ≈ 1

s2 − s1

∫ s2

s1

δx(t)dt.

It is this average rate that should affect cap-ital growth per capita, which in a Solowgrowth model is

(2)k̇xkx

=Ixkx

− δ̄x − nx − gx

where it is clear that changes in location-specific depreciation should affect percapita capital accumulation similarly tochanges in either population growth nx ortechnology growth gx. Ix is investment.

Anttila-Hughes and Hsiang (2011) com-bine estimates of household cyclone ex-posure from the Limited Information Cy-clone Reconstruction and Integration forClimate and Economics (LICRICE) modelwith Family Income and Expenditures sur-veys to estimate how exposure to cyclonesalters household assets in the Philippines.They find that higher exposure to cyclonesin the prior year increases the likelihoodthat a household is “conspicuously missing”otherwise durable assets, such as strongroofs, walls, or refrigerators. They inter-pret this finding as evidence that a frac-tion of assets are destroyed during cycloneevents and characterize the probability of

loss averaged across 14 types of assets as

(3) ˆ̄δCx (t) = −0.00069 · Cx(t)

where Cx(t) is the area-average maximumcyclone wind speed experienced by provincex in year t, measured in meters per second(m/s). We denote the component of to-tal depreciation attributed to cyclones δ̄Cxto distinguish it from other types of de-preciation that may also affect these as-sets. Given an average exposure of 16.9 m/sin their sample, the authors estimate thatthis portfolio of assets depreciate roughly1.2% per year on average due to cycloneexposure. This conclusion is broadly con-sistent with results from Hsiang and Narita(2012) who estimate country-level damageas a fraction of GDP using LICRICE, butthose results cannot be used to estimate de-preciation rates since the exposed capitalstock is unknown. To our knowledge, no

other study estimates any version of ˆ̄δCx , sowe rely on Equation 3 as our current bestestimate.

[Figure 1 here]

In Hsiang and Jina (2014) we extendedLICRICE to all countries for roughly 6,700cyclones observed globally during 1950-2008. Using these data, we ask whethergeographic heterogeneity in cyclone-drivendepreciation δ̄C is associated with lower av-erage growth rates, as predicted by a Solowgrowth model and illustrated in Equation 2.As shown by the west Pacific in Figure 1,the distribution of average cyclone exposureis heterogeneous across locations. This het-erogeneity is caused by differences in wherecyclones are formed—usually the tropicaloceans just north or south of the equator—and the wind patterns that drive thesestorms towards specific locations more fre-quently than others. These differences inaverage exposure can be striking—for ex-ample Singapore is almost never struck bystorms that either travel north or south ofit, while the northern Philippines are ex-posed to maximal winds over 30 m/s onaverage per year. According to Equation

3, this should generate a difference in ˆ̄δCx

VOL. VOL NO. ISSUE GEOGRAPHY, DEPRECIATION, AND GROWTH 3

for Singapore and the northern Philippinesof roughy 2.1% per year. Integrated overmultiple years, differences this large mayhave dramatic effects on the growth rate ofwealth, ceteris paribus.

Here we cannot satisfactorily achieve theceteris paribus assumption needed to fullyidentify the effect of δ̄Cx on the growth rateof capital, however a simple cross-sectionalanalysis does allow us to consider whetherthe magnitude of expected effects mightreasonably explain observed differences ingrowth rates between countries. To makesuch a comparison, we first compute the av-erage long-run rate of growth in GDP percapita for 34 cyclone-affected countries re-ported in the Penn World Tables (version7.1) during 1970-2008 (Summers and Hes-ton, 1991). To do this, we regress log GDPper capita on year and record the trend, θx,for each country. We then compare theselong-run growth rates to average sandcastledepreciation rates due to cyclones by com-

puting ˆ̄δCx for each country using Equation3 and annual cyclone data from Hsiang and

Jina (2014). Long-run average ˆ̄δCx is com-puted for 1950-2008.

[Figure 2 here]

Figure 2 displays the scatterplot of es-timated long-run average growth rates θ̂xagainst average predicted cyclone deprecia-

tion ˆ̄δCx for East Asia, the North Americanmainland (which includes Central Amer-ica), and Caribbean islands. In all threecases, higher predicted depreciation is cor-related with lower long-run growth rates.The association seems clearest for EastAsia, where there is substantial variance inpredicted depreciation, and least clear forthe Caribbean, where almost all islands arepredicted to lose roughly 0.75% of assetsper year on average to cyclones—exceptTrinidad and Tobago which faces less thanhalf that risk. The overall slope of the rela-tionship appears similar across these threeregions, although the vertical intercept dif-fers, perhaps because countries within eachregion share numerous geographic, cultural,and other economic attributes that differacross regions and are important for long-

run growth.

[Table 1 here]

To assess the overall strength of thisassociation globally, we pool these coun-tries with seven more from South Asia andOceania and estimate a regression that al-lows for unobserved regional heterogeneityin growth rates, but assume a global rela-tionship between long-run growth rates andpredicted cyclone depreciation. Indexingcountries by x and regions by r, we esti-mate the cross sectional regression

(4) θ̂xr = β · ˆ̄δCxr + µr + εxr

where µr are region fixed effects. We com-pute bootstrapped standard errors becauseof our small sample sizes. Table 1 reportsestimated regression coefficients β̂. In thesample pooling all five regions, we estimatethat increasing the average predicted cy-clone depreciation rate by one percentagepoint (i.e. each asset has an additional0.01 probability of being lost to a cyclonein each year) is associated with a declineof long-run average growth by 2.2 percent-age points per year. In this limited sampleof cyclone-exposed countries, the within-region R2 is 0.27, indicating that our esti-mate for cyclone depreciation rates predictsa substantial amount of the observed cross-country variation in their average growthrates. It is likely that this estimate suf-fers from some attenuation bias – since wemeasure cyclone exposure imperfectly – andprobably omitted variables bias as well –since there are important covariates thatare correlated with cyclone climate whichwe do not attempt to account for here.Nonetheless, it is notable that the negative

association between ˆ̄δCx and θ̂x appears in-dependently within different regions with arelatively stable magnitude always near −2(columns 2-6), although several of the es-timates are imprecise and not individuallysignificant.

The Solow model predicts that a regres-sion of long-run capital growth rates on av-erage sandcastle depreciation rates shouldrecover a coefficient of −1 (Equation 2).

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We do not observe total growth, but a re-gression of long-run income growth rateson the estimated component of deprecia-tion driven by tropical cyclone exposureconsistently recovers a coefficient of roughly−2, although no estimate can reject the hy-pothesis that the coefficient is −1. Thismight suggest that the long-run elasticityof income with respect to durable capi-tal is larger than unity, that we underes-timate depreciation from cyclones, or thatomitted variables that are positively cor-related with cyclone exposure also have anegative effect on long-run income growth.We think that all three explanations arelikely and the threat of omitted variablesbias is sufficient that the exact values re-trieved from these regressions should notbe interpreted too literally. However, wethink that the order of magnitude of theseestimates are reasonable and their consis-tent size in subsamples of data suggest theassociation is not entirely spurious. Thisleads us to propose that heterogeneousand geographically-dependent depreciationrates may play an important role in globalpatterns of economic development.

REFERENCES

Acemoglu, Daron, Simon Johnson,and James A Robinson. 2002. “Re-versal of fortune: Geography and institu-tions in the making of the modern worldincome distribution.” The QuarterlyJournal of Economics, 117(4): 1231–1294.

Anttila-Hughes, Jesse K., andSolomon M. Hsiang. 2011. “De-struction, Disinvestment, and Death:Economic and Human Losses Follow-ing Environmental Disaster.” Workingpaper.

Dell, Melissa. 2010. “The Persistent Ef-fects of Peru’s Mining Mita.” Economet-rica, 78(6): 1863–1903.

Gallup, John Luke, Jeffrey D Sachs,and Andrew D Mellinger. 1999. “Ge-ography and economic development.”International regional science review,22(2): 179–232.

Hornbeck, Richard. 2012. “Nature ver-sus Nurture: The Environment’s Persis-tent Influence through the Moderniza-tion of American Agriculture.” AmericanEconomic Review: Papers and Proceed-ings, 102(3): 245–249.

Hsiang, Solomon M. 2010. “Temper-atures and Cyclones strongly associ-ated with economic production in theCaribbean and Central America.” Pro-ceedings of the National Academy of Sci-ences, 107(35): 15367–15372.

Hsiang, Solomon M., and Amir Jina.2014. “The Causal Effect of Environmen-tal Catastrophe on Long-Run EconomicGrowth: Evidence from 6,700 Cyclones.”NBER working paper 20352.

Hsiang, Solomon M., and DaijuNarita. 2012. “Adaptation to CycloneRisk: Evidence from the Global Cross-Section.” Climate Change Economics,3(2).

Mankiw, Gregory N., David Romer,and David N. Weil. 1992. “A Con-tribution to the Empiric of EconomicGrowth.” The Quarterly Journal of Eco-nomics, 107: 407–437.

Nordhaus, W. D. 2006. “Geography andmacroeconomics: New Data and newfindings.” Proceedings of the NationalAcademy of Sciences, 103(10).

Rodrik, Dani, Arvind Subramanian,and Francesco Trebbi. 2004. “Insti-tutions rule: the primacy of institu-tions over geography and integration ineconomic development.” Journal of eco-nomic growth, 9(2): 131–165.

Summers, Robert, and Alan Heston.1991. “The Penn World Table (Mark5): An Expanded Set of InternationalComparisons, 1950- 1988.” The Quar-terly Journal of Economics, 106: 327–68.

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0 4 8 12 16 20 24 28 32 36

100 120 140 160 180

−40

−20

20

40

annual average meters per second of cyclone wind

0

Longitude

Latit

ude

Figure 1. Annual average tropical cyclone windspeeds from 1950-2008 in the western tropical Pacific.

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CHN

JPN

KOR

LAO

MYS

PHL

SGP

THAVNM

-2

0

2

4

6

8

Avg

. ann

ual g

row

th r

ate

obse

rved

197

0-20

08 (

%)

0 .5 1 1.5

Avg. estimated depreciation rate, d

East Asia

BLZCANCRI

GTMHND

MEX

NIC

PAN

SLV

USA

-2

0

2

4

6

8

Avg

. ann

ual g

row

th r

ate

obse

rved

197

0-20

08 (

%)

0 .5 1 1.5

Avg. estimated depreciation rate, d

North American mainland

BHSBRBCUB

DOM

HTI

JAM

PRI

TTO

-2

0

2

4

6

8

Avg

. ann

ual g

row

th r

ate

obse

rved

197

0-20

08 (

%)

0 .5 1 1.5

Avg. estimated depreciation rate, d

Caribbean islands

Figure 2. Average growth rate versus average estimated depreciation rate for three regions.

Note: Taiwan omitted because it is an extreme outlier.

VOL. VOL NO. ISSUE GEOGRAPHY, DEPRECIATION, AND GROWTH 7

Table 1—Average growth rate (1970-2008) regressed on predicted average cyclone depreciation

(1) (2) (3) (4) (5) (6)

Predicted cyclone -2.20*** -2.07*** -1.70 -2.19 -1.31 -2.16**depreciation [0.75] [0.79] [1.51] [6.14] [2.36] [0.88]

Observations 34 27 18 8 10 9Within-region R2 0.27 0.26 0.07 0.11 0.05 0.44

East Asia Y Y YN. America Y Y Y YCaribbean islands Y Y Y YS. Asia YOceania Y

Note: Regressor is the average cyclone exposure times the marginal effect of cyclone exposure (Equation 3 estimatedby Anttila-Hughes and Hsiang (2011)). Regressand is the average long-run growth rate. Both regressor and regressandare in units of percentage points per year. Models with more than one region in the sample include region fixedeffects. Oceania includes AUS, NZL, PNG, and IDN. South Asia includes IND, LKA, and BGD. Bootstrappedstandard errors in brackets. *** p<0.01, ** p<0.05, * p<0.1