University of Groningen The Composition of Capital and ...

University of Groningen

The Composition of Capital and Cross-country Productivity ComparisonsInklaar, Robert; Gallardo Albarrán, Daniel; Woltjer, Pieter

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The Composition of Capitaland Cross-country ProductivityComparisons

Robert Inklaar and Pieter WoltjerUniversity of Groningen

Daniel Gallardo AlbarránWageningen University1

ABSTRACT

The role of physical capital is typically found to be limited in accountingfor differences in GDP per worker, but this result may be because capital iscustomarily assumed to be a homogenous unit. This assumption is misleading,as different types of capital assets have different marginal products and richercountries tend to invest more in high-marginal product assets. We take thisperspective to a global dataset, the Penn World Table, to improve cross-countryproductivity comparisons. We show that, properly measured, differences in cap-ital input can account for a greater share of income variation, but (total factor)productivity differences remain dominant.

Income levels differ greatly acrosscountries: the average income levelin 2011 in Denmark (at the 90thpercentile of the cross-country in-come distribution) was about 30 timeshigher than in Haiti (at the 10th per-centile). We can aim for a betterunderstanding of these differences bytrying to account for as much as pos-sible of these income differences us-

ing the tool of development account-ing. In development accounting, in-come differences are partly attributedto differences in observed levels of hu-man and physical capital with the re-mainder attributed to differences intotal factor productivity (TFP).2 Atypical result is that approximatelyhalf of income differences are due todifferences in (human and physical)

1 Prof. Dr. Robert Inklaar is a professor at the University of Groningen, Dr. Pieter Woltjer is a post-doctoral researcher at the University of Groningen, and Dr. Daniel Gallardo Albarrán is a post-doctoralresearcher at Wageningen University. The authors thank the editor and reviewers of this journal forhelpful comments as well participants at the Fifth World KLEMS Conference for their input. Emails:[email protected], [email protected], [email protected].

2 See in particular Caselli (2005) and Hsieh and Klenow (2010) for overview articles.

34 NUMBER 36, SPRING 2019

capital input and half due to TFP dif-ferences.Yet there are good reasons to be-

lieve that the role of physical capi-tal in development accounting is un-derestimated. This is, in part, be-cause usually only the contributionfrom standard ’National Accounts’ as-sets are considered, while there aregood reasons to expand asset cover-age to include other intangible as-sets (Chen, 2018) and subsoil as-sets (Freeman, Inklaar and Diewert,2018). But even when focusing onthe set of assets covered in the Na-tional Accounts, we may still be un-derestimating the role of (physical)capital.3 This is because countriesdiffer systematically in their invest-ment patterns: high-income countriestend to invest more in short-lived as-sets, such as computers and software,and less in long-lived assets like officebuildings or roads. These differencesare due to the higher relative cost ofshort-lived assets in low-income coun-tries (Hsieh and Klenow, 2007) andlack of complementary assets, such ashuman capital (Caselli and Wilson,

2004). Yet the impact of these differ-ences for development accounting arenot yet well understood.To gauge the impact of these dif-

ferences on comparative levels of cap-ital input and productivity, we relyon the conceptual tools introducedby Jorgenson and Nishimizu (1978)and in particular their methodology.4

These tools have—so far—only beenpartially implemented in comparingproductivity levels on a global scale.Most notably, the Penn World Ta-ble (PWT), (Feenstra, Inklaar andTimmer, 2015) compares productiv-ity across countries using a measureof capital input that does not appro-priately account for differences in themarginal product of the various capi-tal assets.5 In this article, we go a stepfurther by estimating the user costof capital and comparing the rentalprice of capital and the level of capi-tal services rather than capital stocks.While this is not the first article todo so, we cover a much broader set ofcountries than previously in the liter-ature, which means we can speak tothe broader development accounting

3 Note that this set has changed over time. In the accounting rules of the System of National Accounts(SNA) 1993, much of spending on software was recategorized from an expense to an investment and inthe SNA 2008, a major change was to recognize spending on research and development as an investment.Different countries follow different versions of the SNA, with very few still using SNA 1968 and approx-imately half of the countries using SNA 1993 and half using SNA 2008, according to the UN NationalAccounts Official Country Data.

4 See e.g. Jorgenson, Nomura and Samuels (2016), Inklaar and Timmer (2009) and Schreyer (2007) formore recent implementations of this methodology.

5 Feenstra et al. (2015) build on Diewert and Morrison (1986) and Caves, Christensen and Diewert (1982),who in turn build on Jorgenson and Nishimizu (1978).

INTERNATIONAL PRODUCTIVITY MONITOR 35

literature.6

In this study, we implement theuser cost/capital services methodol-ogy in a global setting over the pe-riod since 1950 and assess the impacton international differences in capi-tal input and productivity comparedwith the ’capital stock’ measure thatis used in recent versions of PWT. Inthis process, we improve measurementin three areas.First, PWT assumes that when a

country’s data are first observed, itsnominal capital-output ratio is 2.6,based on contemporaneous evidence(Feenstra et al. 2015). Using histor-ical series for 38 countries, we showthat across the development spec-trum, nominal capital-output ratioshave been increasing over time. Weimplement a method for estimatinginitial capital stocks using country-specific information, in combinationwith the observed global trend to al-low for more reliable estimation ofcapital input when a country’s dataare first observed.Second, the return on capital plays

an important role in the literature,in particular the Lucas (1980) para-dox of why capital is not flowing to-wards low-income countries. Morerecently, Caselli and Feyrer (2007)argue that, properly measured, the

marginal product of capital (MPK)does not vary with country incomelevel. Conversely, David, Henriksenand Simonovska (2016) argue that,over the long run, low-income coun-tries do have a higher MPK, withhigher risk explaining the Lucas para-dox. The method of Jorgenson andNishimizu (1978) requires an estimateof the internal rate of return on cap-ital (IRR), which is a more accuratemeasure of the return to capital thanthe MPK because it accounts for dif-ferences in the composition of the cap-ital stock. Our findings accord withthose of David et al. (2016), that low-income countries have higher (real)IRRs and we show that a single-yearcomparison of returns can easily bemisleading for the long-run patterns.Third, in PWT’s capital stock-

based methodology, the weight givento short-lived assets is too low com-pared to the conceptually appropri-ate capital services methodology. Weconfirm that high-income countriesinvest more in short-lived assets thanlow-income countries. By moving toa capital services methodology, capi-tal input of high-income countries isthus increased relative to capital in-put in low-income countries. We showthat, as a result, cross-country dif-ferences in capital input can account

6 The data we develop in this article are part of version 9.1 of the Penn World Table, available atwww.ggdc.net/pwt.


www.ggdc.net/pwt

for a greater share of cross-countryincome variation, increasing from 4.4to 7.5 per cent in 2011. Even then,though, productivity differences re-main the dominant source of incomevariation at 64.8 per cent.In the following sections we will

outline the conceptual framework fordevelopment accounting, productiv-ity measurement and capital measure-ment. We will then discuss our imple-mentation, with specific attention toour new method for estimating initialcapital stocks and the choices neces-sary to estimate capital services. Wefinally show results for the new capi-tal measures and the implications forthe importance of cross-country dif-ferences in capital input in accountingfor cross-country income differences.

Development Accounting

As detailed in Caselli (2005), thetypical starting point in developmentaccounting is an aggregate productionfunction for country m:

Ym = Amf(Km, Lm) = AmKαmL

1−αm

(1)

A country’s GDP, Y , is producedusing production function f with in-put of capital K and labour L andtotal factor productivity level A. Inequation (1) we assume a constant-

returns to scale Cobb-Douglas pro-duction function with a constant out-put elasticity of capital α for exposi-tional simplicity. In the next section,on productivity measurement, we willmove to a translog function. Simi-larly, the production function in equa-tion (1) shows overall capital inputand in the section on capital measure-ment, we will show how this is com-puted based on detailed asset stocksand their rental prices. Let a lower-case variable denote a quantity di-vided by country population, Pm, andlet us express quantities relative tothe United States, so that, for exam-ple, relative GDP per capita is definedym = Ym/Pm

YUS/PUS. We can then decom-

pose a country’s GDP per capita levelrelative to the United States into thecontribution from differences in factorinputs and differences in productivitylevels:

ym = Amkαml

1−αm (2)

As discussed in Hsieh and Klenow(2010), this accounting for differencesin GDP per capita levels answers thehypothetical question: by how muchwould GDP per capita increase if oneof the factor inputs or productivitywere to increase, holding constant theother two elements. This can be asensible hypothetical when comparinggrowth over a short period of timeas it is plausible to assume that the


economy has not yet moved from onesteady state to another. Yet whencomparing across countries, it seemsmore plausible that the comparison isbetween countries in a (Solow model)steady state, i.e. where the invest-ment response to the level of technol-ogy has worked itself out.Hsieh and Klenow (2010) argue

that a more sensible hypothetical ina cross-country context would be:

ym = A1

1−αm

(kmym

) α1−α

lm (3)

This rearranges the productionfunction in intensive form and the hy-pothetical question for this decompo-sition is how GDP per capita wouldchange if total factor productivityor labour input per capita were tochange, allowing capital per person toadjust in response. This reduces theeffect of differences in capital input,since part of the differences in capi-tal per worker are an endogenous re-sponse to differences in productivityand labour input, whose contributionsare, in turn, magnified.Given data for all terms of equa-

tion (3), we will assess the role of eachterm in accounting for income differ-ences by estimating the following re-

gressions:

11− α log (Am) = βA log (ym) + εAm

(4)

α

1− α log(kmym

)= βK log (ym) + εKm

(5)

log (lm) = βL log (ym) + εLm (6)

Since the sum of the dependentvariables equals the independent vari-able, the coefficients βA, βK and βL

add up to one and inform us of therelative importance of each term inaccounting for cross-country incomedifferences.7 We will implement equa-tion (3) for three alternative measuresof capital input and then compare βA

and βK for each alternative.

Measuring Productivity

A common justification for theCobb-Douglas function used in theprevious section is the work of Gollin(2002). He showed that the stan-dard estimate of the output elastic-ity of capital α, the share of capitalincome in GDP, does not systemat-ically vary with a country’s income

7 This is an alternative to the variance decomposition used in Caselli (2005), which has as a downside thatcovariances between inputs and productivity need to be allocated. The approach in equations (4), (5)and (6) is applied in the context of accounting for trade patterns in Redding and Weinstein (2018) andthe adding-up property means that no ad-hoc allocation of covariances is necessary.


level. However, when distinguish-ing multiple types of capital and/orlabour inputs, assuming that all in-put shares are identical is unlikelyto hold. Such a situation calls fora more flexible functional form andhere we follow Jorgenson and Nish-mizu (1978), Schreyer (2007), Feen-stra et al. (2015) and Inklaar andDiewert (2016) and assume a translogproduction function. This allows usto compare the level of factor inputs,Q, in country m relative to country cas:

logQm,c = αm,c[logKm − logKc]+

(1− αm,c)[logLm − logLc] (7)

with αm,c = 12( rmKm

rmKm+wmLm +rcKc

rcKc+wcLc ) the two-country averageshare of capital income in GDP.8 Thisimplementation of α implies assum-ing constant returns to scale, so thattotal income equals total cost, andperfect competition in factor marketsso that inputs are used up to thepoint where marginal product equalsmarginal costs. If, in addition, per-fect competition in output marketsis assumed, the resulting estimate oftotal factor productivity can be in-

terpreted as a measure of compara-tive technology. We follow much ofthe development accounting literatureand assume that labour input is well-captured by a measure of total hoursworked Hm multiplied by a humancapital index hm that depends on theaverage years of schooling and an (as-sumed) rate of return to schooling.9

In addition, note that this is (for ex-positional purposes) a two-input spec-ification, but a key feature of this ar-ticle is that we distinguish multipletypes of capital assets. Extendingequation (2) to cover multiple assetsKi is discussed below.Equation (2) shows the input in-

dex for a comparison between coun-tries m and c but with multiple coun-tries c = 1, . . . , C, the resulting indexwill be dependent on the base countryc. The solution is to make a multi-lateral comparison as discussed in, forexample, Inklaar and Diewert (2016).Given the translog production func-tion we assume, the multilateral inputindex can be expressed as:

logQm,· = αm,·[logKm − logK]+

(1− αm,·)[logLm − logL] (8)

8 As the equation for αm,c makes clear, this share—as all others in this article—is defined in terms ofcurrent price values.

9 We follow the standard implementation of Caselli (2005), though see Lagakos, Moll, Porzio, Qian andSchoellman (2018) for a broader view of human capital in a development accounting context.


Where αm,· is the average of thecapital income share in countrym andof the cross-country average capitalincome share, αm,· = 1

2( rmKmrmKm+wmLm +

1c

∑Cc=1

rcKcrcKc+wcLc ) and logK the cross-

country average of capital input lev-els, logK =1

c

∑c logKc. Equation (8)

gives the input index relative to a hy-pothetical average country, but thatindex can be recast relative to anyreference country, such as the UnitedStates.10

Measuring Capital

A key objective of this article isto estimate comparative capital in-put based on multiple capital assets,which involves estimating, for a rangeof capital assets i = 1, . . . , I, capitalinput Ki and rental prices ri. Follow-ing the framework of Jorgenson andNishimizu (1978)—and more recentlydiscussed in the OECD (2009) capi-tal manual—the asset rental price attime t can be approximated as:11

ri,t = pNi,t−1it + pNi,tδi−

pNi,t−1(pNi,t − pNi,t−1) (9)

where it is the required rate of re-

turn on capital (on which more be-low), pNi is the purchase price of asseti, and δi is the geometric depreciationrate.The quantity of capital input Ki is

typically not directly observable. In-stead it is based on estimated net cap-ital stocks Ni, which are in turn basedon the total accrued investment Ii de-preciated over time using the perpet-ual inventory method:

Ni,t = (1− δi)Ni,t−1 + Ii,t (10)

An important challenge in imple-menting equation (9) is the estimationof the capital stock in the initial year,Ni,1, which we discuss in detail below.Assuming that the flow of capital

inputs from a particular asset is pro-portional to the stock of that asset,Ni ∝ Ki, we can express the incomeflow from asset i as riNi and estimaterelative capital input for equation (8)as:

log (Km,·) =∑i

12(vi,m + vi,·)

(logNi,m + logNt)(11)

where vi,m = ri,mKi,m∑iri,mKi,m

is the share

10 The multilateral productivity measures we have introduced here, imply a small modification to the devel-opment accounting introduced in equations (4)-(6). Rather than relying on a single α, we use αm,·.

11 This formulation of the rental price abstracts from terms related to the tax treatment of investment andprofits.


of asset i in total compensation incountry m, vi,· = 1

c

∑c vi,c is the cross-

country average compensation shareand logNi = 1

c

∑c logNi,c the cross-

country average capital stock.It is helpful to contrast the concep-

tually preferred measure of equation(11) to current practice in the PennWorld Table, which for our analysis isthe status quo. PWT’s capital inputmeasure is a measure of the overallcapital stock:

logNm,· =∑i

12(wi,m + wi,·)

(logNi,m + logNi)(12)

where wi,m = pNi Ni∑ipNi Ni

is the shareof asset i in the total current-cost netcapital stock. The main differencewith our approach is that the mea-sure of capital input in equation (12)does not consider that different as-sets have different rental prices. Com-pared to equation (11), equation (12)overstates the importance of long-lived assets, which tend to have a rel-atively low rental price (because of alow δi) and a high share wi,m. Whenmoving from measuring capital usingequation (12) to equation (11), we ex-pect countries with a relatively highshare of long-lived assets to show adecline in relative capital input levels.

Data and Implementation

For implementing the developmentaccounting equation (3), our startingpoint is the Penn World Table. Ourmeasure of comparative GDP, pop-ulation, employment, average hoursworked, the share of labour incomein GDP and average years of school-ing are as described in Feenstra etal. (2015) and at www.ggdc.net/pwt.PWT (version 9.1) covers up to 182countries from 1950 to 2017, but themaximum number of countries in ouranalysis is 117, because for some wedo not have the requisite data to im-plement the development accountingmethod.For estimating capital input, the

starting point for both the currentPWT approach and our new anal-ysis is data on investment by assettype. Here, too, we use the same data,which distinguishes nine asset types:residential buildings, other struc-tures, information technology, com-munication technology, other machin-ery, transport equipment, software,other intellectual property productsand cultivated assets (such as live-stock for breeding and vineyards).12

As discussed in PWT documentation,these investment data are drawn fromcountry National Accounts data, sup-plemented by estimates based on to-

12 See also Table 3 in the results section.


www.ggdc.net/pwt

tal supply of investment goods (im-port plus production minus exports)and data on spending on informa-tion technology. Note that coverageis limited to assets currently coveredin the System of National Accounts.This means we omit land and inven-tories, as well as other forms of intan-gible capital—such as product designor organization capital—and subsoilassets—such as oil or copper.

Initial Capital StocksOur estimate of asset capital stocks

is based on the perpetual inventorymethod, so the capital stock at timet is based on all previous investments(equation 10). But given that we onlyobserve investment data for a limitedperiod of time (for PWT, 1950 is theearliest year), an important challengeis to estimate the capital stock in thefirst year of the data, Ni,1. There aretwo main approaches in the literature.The first is to assume the economy inthe steady-state of the Solow model attime t, in which case the initial stockis equal to:

Ni,1 = Ii,1gi + δi

(13)

where Ii,1 is investment in the ini-tial year and gi is an estimate ofthe steady-state growth rate of invest-ment in that asset, typically imple-mented as an average growth rate inthe first years of the observation pe-

riod.The second method is to use a data-

driven approach to select an initialcapital level. The nominal capital-output (pNN/pY Y ) ratio is a help-ful quantity in this approach. In theSolow model, the pNN/pY Y ratio isconstant while capital per worker in-creases with income, matching twoof the Kaldor facts, and observationalso shows this ratio to be bounded.Feenstra et al. (2015) observed inthe PWT data that (a) the pNN/pY Yratio did not vary systematically byincome level, and (b) the pNN/pY Yratio did not systematically changeover time. This motivated the choicefor selecting an initial pNN/pY Y ratiobased on contemporaneous data thatdid not vary across countries or overtime. In PWT versions 8.0, 8.1 and9.0, the initial current-cost net capitalwas set at a level of 2.6 times GDP atcurrent prices for each country. Thischoice can be justified if the maingoal is to select an Ni that does notsystematically over- or underestimatecapital input by income level, but thisapproach ignores country-specific in-formation.Recent data development has pro-

vided further scope for improvement.Gallardo Albarrán (2018) has col-lected investment data for 38 coun-tries across the world and spanningmuch of the development spectrum forthe period before 1950, with data cov-


erage varying between countries, fromSweden (data starting in 1800) to Ko-rea (data starting in 1911). As a re-sult, the pNN/pY Y ratio we observein 1950 for these 38 countries can betaken as reliable initial capital stocks.The data for these 38 countries thusprovides a more extensive basis forassessing the stylized facts underly-ing PWT, in particular the findingthat there is no time trend in thepNN/pY Y .Chart 1 plots the pNN/pY Y ratio

for the 38 countries since 1950. A firstimportant observation is that thereis a time trend: the pNN/pY Y ra-tio increases from, on average, 2.2 in1950 to 3.5 in 2017 for an increaseof approximately 0.02 per year. Sec-ond, this chart illustrates the largecross-country variation, with 1950 ra-tios varying between 0.9 and 4.0. Thechoice of 2.6 in recent PWT versionsis thus only (somewhat) appropriateon average.To estimate initial capital stocks for

the countries without long-run (pre-1950) investment data in a way thatdoes justice to the rising trend andthe cross-country variation, we devisea new procedure, which we illustratein Chart 2. First, we determine thepoint in each country’s time series atwhich the choice of the initial capi-tal stock has faded enough in impor-tance; we denote this point by t∗. Todetermine t∗, we estimate pNN/pY Y

ratios based on extreme initial stocks:an pNN/pY Y ratio of 0.5 on the lowend and an pNN/pY Y ratio of 4 on thehigh end. These extremes are inspiredby the extremes in Chart 1. Point t∗ ischosen as the first year for which thedifference in estimated capital stocksfrom both extremes is less than 10 percent. This point can come sooner orlater depending on the composition ofthe capital stock (short- vs. long-livedassets) and the growth rate of invest-ment. In the example for Turkey inChart 2, t∗ = 1990, which means thatfrom 1990 onwards, the choice of theinitial capital stock is practically im-material.The next step in the procedure is

to take the mid-point pNN/pY Y ra-tio at year t∗ and project this levelbackwards using the average annualchange in the pNN/pY Y ratio of 0.02from Chart 1. We realize this growthrate will not be appropriate for eachcountry, but over time frames of 30-40 years, most countries do show in-creases in the pNN/pY Y ratio. Com-pared to assuming a single initialpNN/pY Y ratio for every country, thisprocedure does more justice to eachcountry’s experiences.We were able to apply this proce-

dure successfully for 92 countries. Forsome countries the available invest-ment series were too short in length toconverge to within our defined band-width, so no t∗ could be determined.


Chart 1: Capital-to-Output Ratios, 1950-2017

Notes: Annual capital-to-output ratios for 38 countries for which long run (pre-1950) investment data areavailable.

For those cases we base the startinglevel of the pNN/pY Y ratio on the av-erage observed for that year for the130 countries for which we have esti-mates of the pNN/pY Y ratio.

Rental PricesRecall that the rental prices are de-

termined by the required rate of re-turn on capital, the depreciation rateand a revaluation term, reflecting thechange in the asset price. The reval-uation term as specified in equation(9) is not ideal in practice, because

asset prices can be quite volatile. Es-pecially in the case of structures, withits low depreciation rates, this canbe problematic and lead to negativerental prices.13 To avoid this, weuse a five-year moving average for thechange in asset prices:

pKi,t = pNi,t−1it + pNi,tδk−

pNi,t−115

(t∑

τ=t−4pNi,τ

) (14)

13 See also Inklaar (2009).


Chart 2: Example of Estimation Procedure Initial Capital-to-Output Ratio, Turkey

Notes: The starting pNN/pY Y ratio for the upper bound is 4.0. The lower bound starts at 0.5. ’t∗’ marksthe year where the lower- and upper bound converge to within a margin of 10 per cent. The slope of thedashed line represents the assumed growth of the pNN/pY Y ratio at 0.02 per annum between the first year[1950] and t∗ [1990]. The solid black line shows the resulting capital-output ratio based on the estimate forthe initial pNN/pY Y ratio.

In the standard Jorgensonian ap-proach to rental prices, the requiredrate of return on capital is chosen toexhaust the income left after subtract-ing labour income from GDP. Thisgives an internal rate of return oncapital and an important advantageis that this return sets ’pure profits’to zero and is thus consistent withthe maintained assumption of per-fect competition. An important draw-back, in a global context, is that in

some countries the rents from extract-ing natural resources like oil and gasis a sizeable fraction of GDP (Lange,Wodon and Carey, 2018). For thosecountries, computing the internal rateof return based on the income thatdoes not flow to labour would sub-stantially overestimate the requiredrate of return on assets.14 So instead,we determine the income flowing tocapital as nominal GDP minus labourincome minus natural resource rents:

14 Ideally, natural resources should be recognized as production factors in their own right. That is beyondthe scope of this article but see Freeman, Inklaar and Diewert (2018).

15 Natural resource rents are from the World Development Indicators.


rtNt ≡ pYt Yt − wtLt − pZZ.15 The(nominal) internal rate of return oncapital is then determined to ensurecapital compensation adds up to to-tal capital income:

it =rtNt −

∑i p

Ni,tδiNi,t∑

i pNi,t−1Ni,t

+

∑i p

Ni,t−1

15(∑t

τ=t−4 pNi,τ )Nk,t∑

i pNi,t−1Ni,t

(15)

For a cross-country comparison ofthe returns to capital we also estimatethe real internal rate of return (R), anew variable in PWT version 9.1:16

Rt =rtNt −

∑i p

Ni,tδiNi,t∑

i pNi,tNi,t

(16)

The rental prices are also relevantfor comparing the level of capital in-put in different countries. In the orig-inal PWT method (i.e. equation 12),capital stocks are made comparableacross countries using data on therelative prices of investment goods,pNi,m/p

Ni,US. Yet when comparing cap-

ital input according to equation (11),

the appropriate price comparison isbased on the rental price from equa-tion (14), so pKi,m/pKi,US. This adjuststhe relative price of investment goodsfor differences across countries in theuser cost of capital. Since we assumethe same depreciation rate for a givenasset in all countries, differences in theuser cost of capital are due to differ-ences in the (country-level) internalrate of return it and due to differ-ences in the (five-year average) rateof asset price inflation. Especiallyfor computers, communication equip-ment and software, cross-country dif-ferences in asset price inflation (or de-flation) can be affected by the degreeto which country statistical agenciesadjust for quality change. So as inprevious versions of PWT, we applyUS asset price changes, adjusted fordifferences in the change in the overalldeflator for gross fixed capital forma-tion, to all countries.

Results

In this section, we first discuss howour new initial capital stock estimatesinfluence capital-output ratios andhow they compare to the pNN/pY Yratios in the previous PWT. Next,

16 Note we also used the asset-specific investment price for the current year (pNi,t) instead of the previousyear in the denominator for the calculation of the real IRR. Rapid inflation would otherwise cause thereal IRR to fluctuate wildly. The correlation between the mean real IRR based on current year and pre-vious year prices for countries who experienced below-average price changes is 0.998, for countries withabove-average inflation this correlation is 0.794. The correlation between the standard deviations is 0.934and 0.223 respectively. For the latter set of countries the standard deviation based on the previous-yearmethod is much higher; 0.290 versus 0.055 for the current-year method.


we analyze the variation in the in-ternal rates of return across countriesand over time. Finally, we implementthe development accounting proce-dure from equations (3-6) to assess towhat extent our new, more conceptu-ally appealing measure of capital in-put can account for more of the cross-country variation in income levels.

Capital-Output RatiosFor selected years, Table 1 sum-

marizes the pNN/pY Y ratios basedon the new, country-specific initialcapital stocks compared to the previ-ous method, where all countries hadthe same initial capital-output ra-tio. For our full sample of coun-tries, the rising trend in the pNN/pY Yratios observed in Chart 1 is con-firmed: the average pNN/pY Y ratioclimbs from 2.1 in 1950 to 3.5 in2000.17 The standard deviation, min-imum and maximum values confirmthat there are indeed sizable varia-tions in the pNN/pY Y ratios betweencountries. The comparison betweenthe ’new’ and ’original’ initializationshows the average adjustment in thepNN/pY Y ratios is most pronouncedfor earlier years. This is to be ex-pected, as the pNN/pY Y ratios de-pend ever less on the initial stock.Already by 1990, the differences be-

tween the new and original initial cap-ital stocks have mostly disappeared.The standard deviation and range ofpNN/pY Y ratios for the original se-ries remain lower for the original ini-tial stocks, which reflects that the newinitialization allows for variation inthe starting capital-to-output ratiosreflecting country-specific factors.

Internal Rates of ReturnChart 3 shows the development

over time of the real internal rate ofreturn Rt from equation (16). As dis-cussed above, Rt is a proxy for the(expected) real returns to capital. Werun an ordinary least squares regres-sion of Rt on country and year dum-mies and plot year dummies with their95-per cent confidence interval in theleft panel Chart 3. This show the av-erage Rt declining from 20.0 per centin 1950 to 11.7 per cent in 2017. Thedistribution of Rt is skewed to theright, so the trend in the median isinformative as well. To that end, theright panel of Chart 3 shows the re-sults from a least median squares re-gression of Rt on country and yeardummies. This shows the median de-creasing from 14.4 per cent in 1950 to8.5 per cent in 2017.Table 2 reports the real IRR across

three country groups (distinguished

17 Note that the sample of countries for which we can estimate the capital stocks changes over time. Thetrend increase can still be observed if we hold the sample constant, however.


Table 1: Comparison of pNN/pY Y Ratios Between New- and OriginalInitiatlization, Selected Years

Year Countries New initialization Original initializationMean Stdev. Min. Max. Mean Stdev. Min. Max.

1950 55 2.1 0.9 0.5 4.0 2.6 0.0 2.6 2.61960 110 2.2 1.0 0.6 7.0 2.5 0.8 1.0 6.91970 156 2.1 0.9 0.6 5.4 2.4 0.6 0.8 4.91980 156 2.5 1.0 0.5 5.6 2.7 0.9 0.6 5.21990 180 3.0 1.6 0.6 18.2 3.1 1.6 0.6 17.42000 180 3.5 2.5 0.7 25.0 3.4 2.3 0.8 22.72011 180 3.3 2.5 1.0 30.2 3.3 2.3 1.0 27.62017 180 3.4 2.0 1.0 19.3 3.3 1.9 1.0 17.7Note: The ’new initialization’ relies on the procedure described in the ’starting stocks’ sectionabove to estimate the initial N/Y ratio for each country separately. The ’original initialization’assumes the initial level of N/Y for each country is equal to 2.6, mirroring the method usedfor previous versions of the PWT. Both the ’new’ and ’original’ series apply the same PIMprocedure, discussed above, to construct the capital stocks and N/Y ratios for all subsequentyears.

Chart 3: Real Internal Rate of Return Time Trend, 1950-2017

0.05

.1.15

.2.25

.3

1950 1960 1970 1980 1990 2000 2010

Mean0

.05

.1.15

.2.25

.3

1950 1960 1970 1980 1990 2000 2010

Median

Note: The chart shows the coefficients and 95 per cent confidence interval for year dummies in an ordinaryleast squares regression of Rt from equation (16) regressed on country and year dummies (left panel) andthe year dummies from the same regression but then estimated using least median squares. The samplesize increases over time from 55 countries in 1950 to 135 in 2017.


Table 2: Real Internal Rate of Return by Income Group

Portfolio 1950-2017 1970-2017 2011(1) (2) (3) (4) (5)

1 0.124*** 0.112*** 0.110*** 0.105*** 0.1012 0.139*** 0.127*** 0.128*** 0.124*** 0.1203 0.094* 0.078** 0.090 0.084 0.086US 0.078 0.057 0.075 0.068 0.075

Year dummies N Y N Y N

Observations 7,586 7,586 6,080 6,080 135Adjusted R2 0.11 0.15 0.1 0.11 0.05Notes: The portfolios are based on the approach of David et al. (2016),appendix F. The portfolio categories for countries missing in the Davidet al. dataset were estimated based the mean GDP p. capita observedbetween 1950 and 2008. In 2011 the (unweighted) average log of GDP p.capita for portfolio 1 was [8.1], for portfolio 2 [9.5], for portfolio 3 [10.5],and for the US [10.8]. *** p < 0.01; ** p < 0.05; * p < 0.10.

by income level) for different periods,with or without year dummies, mir-roring the approach of David et al.(2016). The results show that forthe 1950-2017 period, the real IRRfor the low- and middle-income coun-tries was significantly higher thanthat observed for the United States.The implicit return to capital forhigh-income countries (other than theUnited States) was also higher, butthis is only significant at the 10 percent level. The result for low- andmiddle-income countries holds up ifwe include year dummies or limit theperiod to 1970-2017. If we focus on2011 alone, the differences betweenthe real IRR across the different coun-try groupings are no longer signifi-cant. More in general, the explana-tory power of these models is lim-ited, so other factors must have alsobeen important. For one, the year-to-year variation in the IRR will de-pend on the state of the business cy-cle, as during downturns the realized

returns on capital are typically lower.The low explanatory power can alsopoint to the importance of omittedassets, such as land and inventories(e.g. Inklaar, 2009). All this doessuggest that drawing conclusions on asingle cross-section worth of data, asin Caselli and Feyrer (2007) can leadto missing out on patterns that areclear in the data once more years aretaken into account.

Capital ServicesUsing the internal rate of return

discussed above and the asset-specificrates of depreciation listed in Table3, we estimate the rental price ofcapital and the capital compensationshares (vi) for the nine assets in ourdataset and compare them to the av-erage share in current-cost net capitalstocks (wi).Table 3 summarizes these shares for

all countries and years in our sam-ple. As is to be expected, vi ex-ceeds wi for assets with higher de-


Table 3: Depreciation, Shares and the Relationship with Income Level

Asset Depreciation Stock Services Services/Stock CoefficientRate Share, wi Share, vi Share, vi/wi log(GDP/capita)(1) (2) (3) (4) (5)

Information equipment 31.5 0.2 1.1 4.8 0.574*** (0.0126)Communication equipment 11.5 1.3 2.3 1.8 0.251***(0.0144)Other machinery 12.6 11 17.4 1.6 -0.005 (0.0054)Transport equipment 18.9 4.4 8.2 1.8 -0.055*** (0.0061)Software 31.5 0.2 0.9 3.9 0.720*** (0.0144)Other intellectual property 15 1.2 2.5 2.1 0.555*** (0.0200)Cultivated assets 12.6 0.1 0.2 2.3 -0.852***(0.0436)Residential structures 1.1 39.1 28.6 0.7 0.024*** (0.0049)Other construction 3.1 42.4 38.7 0.9 -0.054*** (0.0047)Notes: The table shows (1) the asset-specific rates of depreciation; (2) the assets’ average share in the totalcurrent-cost net capital stocks (for all years and countries in our sample); (3) the assets’ average share in capitalcompensation; (4) the ratio between the capital services and the capital stock share; and (5) the beta coefficientsfor a regression of the log of GDP per capita on the log of nominal capital compensation (pKi Ki) over nominaloutput (pY Y ). Robust standard errors in parentheses, *** p < 0.01; ** p < 0.05; * p < 0.10.

preciation rates (and for assets whereprice deflation was more pronounced,notably IT-equipment). For exam-ple, capital compensation for othermachinery accounts for 17.4 per centon average, compared to the 11 percent of the capital stock share, re-flecting the higher service flow fromsuch assets. In the final column weregress the nominal capital-to-outputratio for each asset on log GDP percapita. The coefficients show thathigh-income countries, on average,have higher stocks of short-lived as-sets and low-income countries havehigher stocks of transport equipment,cultivated assets and other construc-tion. This result mirrors similar ear-lier findings (e.g. Caselli and Wil-son, 2004; Hsieh and Klenow, 2007)and suggests that employing a cap-ital services input measure will leadto relatively higher levels of capitalinput in high-income countries. Theonly exception to this pattern is res-idential structures, whose stocks in-

crease with income levels. Despitethis, we would expect that capitalinput is more important in account-ing for cross-country income differ-ences when based on our new measureof capital services compared with theearlier capital stock measure.

Development AccountingTable 4 shows the results from es-

timating equations (4-6) on data for2011. The first row shows capitalinput measured as in equation (12),Nm,·, and uses the original initial cap-ital stocks, i.e. assuming a nomi-nal capital-output ratio of 2.6 in thefirst observed year. The second rowstill uses Nm,· from equation (12) butbased on the new estimates of the ini-tial capital stock. The final row isbased on Km,·, from equation (11).The coefficient on labour input, βL

is constant across the rows as mea-surement is unchanged. Changing theprocedure for estimating the initialstock has very little impact on βK and


Table 4: Development accounting results for 2011

Capital input, βK Labour Input, βL Total Factor Productivity, βA

Nm,·, original initial stocks 0.044 0.277*** 0.679***(0.0330) (0.0241) (0.0445)

Nm,·, new initial stocks 0.050 0.277*** 0.673***(0.0340) (0.0241) (0.0457)

Km,· 0.075** 0.277*** 0.648***(0.0311) (0.0241) (0.0376)

Notes: The table show the beta coefficients for regression of capita input, labor input and productivity onGDP per capita, see equations (4-6), where instead of a single α, we use each country’s share of capitalincome in GDP, αm,·. Nm,· is computed as in equation (12), Km,· as in equation (11). Data are for 117countries. Standard errors between parentheses. *** p < 0.01; ** p < 0.05; * p < 0.10.

βA, which was to be expected fromTable 1 since by 2011 there is little dif-ference between the two approaches.Going from Nm,· to Km,· does havea substantial impact: βK increasesfrom 0.050 to 0.075, indicating thatthe new capital input measure canaccount for considerably more of thecross-country variation in income lev-els. At the same time, the effect onβA is (relatively) smaller, going from0.681 to 0.647. So, despite accountingfor more of the cross-country incomevariation, productivity differences re-main the dominant sources of incomedifferences.

Conclusions

In this article, we have addressedtwo important shortcomings in themeasurement of capital input in thewidely-used Penn World Table. First,we have estimated initial capitalstocks based on better data andan improved procedure that doesmore justice to country-specific ex-periences. Second, we have imple-mented a capital services methodol-

ogy in accordance with standard pro-ductivity measurement theory. Bydoing so, we are able to account formore of the cross-country variationin income levels. This is becausehigh-income countries tend to investmore in short-lived assets with highermarginal products.Applying the capital services/rental

prices methodology on a global scalefor comparisons across countries high-lights the challenges in this methodol-ogy. As discussed, the role of naturalresources in generating income can-not be ignored, as otherwise the re-turn that is imputed to fixed assetsis considerably overestimated, in par-ticular in resource-rich countries suchas Qatar or Saudi Arabia. A relatedchallenge is that we omit land and in-ventories from the set of assets due tolack of reliable data, and that, too,biases the estimated return on capitaland can thus influence the compari-son of capital input across countries.Yet we feel our current analysis servesa useful purpose in highlighting thesechallenges and pointing the way forfuture research in this area. And de-


spite measurement shortcomings, ourimproved capital input measure canaccount for more of the cross-countrydifferences in income levels.

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