Product Variety, Trade Costs and the Standard of Living Across Countries … · 2020. 3. 1. · Feenstra (1994) the exact ... Wholesale & Retail margin 52% 47% 20% Transport margin

Product Variety, Trade Costs and theStandard of Living Across Countries

Alberto CavalloHarvard Business School, NBER

Robert C. FeenstraUC Davis and NBER

Robert InklaarUniversity of Groningen

March 2020

1 / 35

Motivation

I Penn World Table (PWT; Feenstra, Inklaar and Timmer, 2015)computes real GDP across countries, and is therefore comparing thecost of living between countries

I Current trade literature has focused on the impact of foreign tradecosts on the gains from trade (ACR 2012), comparing the cost ofliving in two equilibria within a country

I Is it possible to extend that literature to measure the cost of livingbetween countries?

I Cross-country productivity literature emphasizes differences indomestic trade costs (wholesale & retail margins, transport costs),and there is also the potential for product variety differences to belarge across countries due to size differences, etc.

I Goal of this paper:

I Extend existing literature to measure the relative importance ofdomestic trade costs, country size, and (endogenous) product varietyin determining cross-country differences in the cost of living

2 / 35

Literature Review

I Domestic trade costs:

I Anderson and van Wincoop (2004), Atkin and Donaldson (2015)

I Product variety and gains from trade:

I Feenstra (1994), Arkolakis (2010), ACR (2012)I Broda and Weinstein (BW, 2006), Ossa (2015), Giri, Yi, and

Yilmazkudayz (2020)

I Using International Comparisons Project (ICP) data to measuretrade elasticities:

I Eaton and Kortum (2002), Simonovska and Waugh (2014a,b)

I Using ICP/bar-code data to measure cost of living across countries:

I Neary (2004), Argente, Hsieh, Lee (2020), Cavallo, Diewert,Feenstra, Inklaar, Timmer (2018)

I Impact of variety on productivity across sectors or countries:

I Cuñat and Zymek (2018)

3 / 35

Theory: set-up

I Melitz-Chaney, but obtain ACR results in a slightly different way

I CES price index is defined over domestic and foreign varieties:

P =

Md ∞∫ϕd

pd (ϕ)1−σ g (ϕ) dϕ

[1− G (ϕd)]+ M∗x

∞∫ϕ∗x

p∗x (ϕ)1−σ g (ϕ) dϕ

[1− G (ϕ∗x )]

1

1−σ

I Treat domestic goods as “common” in the two equilibria, so fromFeenstra (1994) the exact price index between the two equilibria is

P ′

P=

(M ′dMd

) 11−σ(φ̃d

φ̃d

)−1︸︷︷︸

domestic goods price index

×(λ′dλd

) 1σ−1

︸︷︷︸gains from importing

4 / 35

”Overall” product variety and ACR gains

I Solve for the cut-off productivities in the two equilibria, and find:

Consumer “overall” product variety

(M ′d/λ

′d

Md/λd

)=

(X ′/w ′f ′dX/wfd

)I Allow for changes in the foreign variables (only) as in ACR and also

adopt a one-sector model with trade balance

=⇒(M ′

λ′d

)=

(Mdλd

)=⇒ with Pareto

(φ∗′dφ∗d

)−1=

(λ′dλd

) 1θ

I So the change in the cost of living between equilibria is:

P ′

P=

(λ′dλd

) 1θ

I Overall variety is constant with only a foreign shock and one sector(even though the number of varieties can change)

5 / 35

Allowing for changes in domestic variables

I In addition to iceberg foreign trade costs, we also introduce icebergdomestic trade costs τd ≥ 1

I Allow domestic trade costs, lower-bound to Pareto productivity Aand country size L to differ across equilibria (countries)

I Make two versions of an assumption on fixed costs:

Assumption 1. The fixed and sunk costs of producing for the homemarket are proportional: fd/f

id = fe/f

ie ∀i =′ and i = 1, . . . ,C

Assumption 1’. The fixed and sunk costs of producing for thehome market are proportional to Lα, fd/f

id = fe/f

ie = L

α/Liα,∀i =′ and i = 1, . . . ,C , with 0 ≤ α ≤ 1.

I Assumption 1’ is motivated by Arkolakis (2010). Simonovska andWaugh (2014b) use the stronger version that α = 1.

6 / 35

Change in the real wages between equilibria, part (a)

Proposition 1

(a) Under Assumption 1, the ratio of the real wages between twoequilibria is:

w ′/P ′

w/P=

A′

A

(λ′d

λd

)−1/θ (τ′d

τd

)−1(M′d/λ

′d

Md/λd

) 1σ−1 (

X ′/w ′L′

X/wL

)−1/θ

I Domestic trade costs enter with the exponent of unity, whether theyapply to imports or not

I ”Overall” variety re-appears (due to differing country sizes), withexponent as in Feenstra (1994), BW (2006), Ossa (2015)

I We can think of the variety term as reflecting scale effects

I Final term reflects the trade balance with a single sector, or withmultiple sectors it reflects expenditure on that sector (X ) relative toaggregate expenditure (i.e. a budget share)

7 / 35

Change in the real wages between equilibria, part (b)

Proposition 1

(b) Under Assumption 1’, the ratio of wages between two equilibria is:

w ′/P ′

w/P=

A′

A

(λ′d

λd

)−1/θ (τ′d

τd

)−1(M′d/λ

′d

Md/λd

) 1σ−1−

1θ (

L′

L

) 1−αθ

,

and product variety is determined by:

M′d/λ

′d

Md/λd=

(L′

L

)1−α(X ′/w ′L′

X/wL

).

I ”Overall” variety term now has a different exponent that reflectsselection rather than scale effects

I Overall variety is related to country population and the budget sharefor each sector. So a “partial” scale effect still operates, though itwill have to prove itself using this regression.

I We will focus on measuring the cost of living from part (b).

8 / 35

Model-based cost of living and real consumption

I Adding a country supercript and solving for the price level from (b),

P i

P j=

(w i/Ai

w j/Aj

)(λii

λjj

) 1θ(τ ii

τ jj

)(M i/λii

M j/λjj

) 1θ−

1σ−1(Li

Lj

)− (1−α)θI Dual approach: w i/Ai = output price level, PLiy

I Wtih multiple sectors, the cost of living relative to the US is,

CoLi ≡(PLiy

)WTi×

S∏s=1

(λiisλUSs

)WTisθs(τ iisτUSs

)WTis ( M is/λiisMUSs /λUSs

)WTisθs− W

Tis

σs−1(

Li

LUS

)− (1−α)WTisθ (

PLNics

)WNisI W Tis , W

Nis are Sato-Vartia weights of traded and non-traded goods

I Compare this with PWT price level of consumption, which does not adjustfor foreign or domestic trade costs or variety differences across countries

9 / 35

Source of Parameters

I Scale effect α obtained from regression of overall variety onpopulation (or employment)

I Elasticity of substitution σs across broad sectors s taken frommedian estimates in BW (2006)

I Pareto parameter θs estimated using cross-country ICP prices as inEaton and Kortum (2002) and Simonovska and Waugh (2014b).

I In order to extend the gravity estimation from Eaton and Kortum(2002) to the Melitz-Chaney model, Simonovska and Waugh(2014b) assume:

Assumption 2. The fixed costs of domestic production in country,f id , equals the fixed costs of exporting to country i from any othersource country j , ∀i , j = 1, . . . ,C .

10 / 35

Sectoral Gravity Equation

Proposition 2.

(a) Under Assumptions 1 and 2, the value of exports, X ij , from country ito j relative to total expenditure X j in country j is

λij ≡ Xij

X j=

T i(w iτ ij

)−θC∑

k=1

T k (w kτ kj)−θ

where T i ≡ M ie(w i)1− θ

σ−1

(b) Under Assumptions 1’ with α= 1 and Assumption 2, and with thefixed costs of exporting paid in the destination country, then part (a)holds with T i ≡ M ie and the denominator is proportional to thecountry j price index raised to the power −θ:

(P j)−θ∝

C∑k=1

Mke

(w kτ ki

)−θ

11 / 35

Estimating sectoral gravity

I Trade elasticities, θs , are estimated from a gravity estimation:

ln

(λijsλiis

)= −θs

(ln τ ij − ln τ ii + D is − D js

)where λij are country i ’s consumption expenditure shares on goodsfrom j , and ln τ ij are trade costs

I Trade costs are unobservable, but can be inferred from observedprices (EK, 2002):

ln τ ij = maxn∈Ω(s)

{ln pjn − ln pin}

I DATA: ICP 2011 national item prices on global core list products,which are more disaggregate than the “basic heading” level prices

12 / 35

Sectoral gravity: estimates of θs

I Estimate using methods of Simonovska and Waugh (2014a,b)

Sector Code Traded share, % # Products θs Error σsTotal traded consumption 47 490 3.51 0.01Food, beverages & tobacco 01-02 100 205 3.46 0 4.2Clothing & footwear 03 97 47 2.96 0 3.5Furnishing 05 88 69 4.77 0 2.5Health 06 46 52 4 0.08 2.5Transport 07 59 31 11.43 0.33 7.8Recreation and culture 09 51 59 6.76 0.23 2.2Other goods 12 25 23 14.77 0.23 2.5

I Using basic headings, single θ = 4.58 (4.16 in Simonovska and Waugh, 201))

I Based on product items, single θ = 3.51 (greater price variability)

I Higher sectoral θs ⇒ systematic price differences between sectors

13 / 35

Cost of living: Data, 2011, 43 countries

I Output price level PLiy is from PWT 9.0

I Nontraded consumption prices PLNics and Sato-Vartia weights areconstructed from ICP2011 data

I Domestic goods’ share in consumption, λiis , is from WIOD

I Domestic trade costs are based on:

I I-O tables from WIOD: τ iis = consumption expenditure in s (gross oftaxes) divided by the basic-prices value of expenditures

I Data from surveys of wholesale and retail trade, for some countries

I Number of domestic varieties is based on number of domestic firmsfrom ORBIS, newly collected counts of barcodes acrosscountries

14 / 35

Domestic trade costs: Supply-Use Tables

Table: Margin Example: US and Netherlands, Supply-Use Table 2011

United States NetherlandsFood Clothing Fuel Food Clothing Fuel

Total margin 60% 58% 29% 52% 70% 71%

Domestic Trade & Transport 54% 49% 21% 35% 54% 8%Wholesale & Retail margin 52% 47% 20%Transport margin 2% 2% 1%

Taxes 6% 9% 8% 17% 16% 63%

15 / 35

Foreign and domestic costs and consumption price level

IND

IDN

TWN

BGR

CHN

RUS

ROU

POL

HUN

TUR

LTU

MEX

SVK

KOR

LVA

HRV

CZE

EST

MLT

PRTSVN

BRA

USA

CYP

GRC

ESP

DEU

ITA

AUT

NLD

GBR

FRA

BEL

CAN

IRL

FIN

LUX

SWE

JPNAUS

DNK

NOR

CHE

-.15

-.1-.0

50

.05

-1 -.5 0 .5log of consumption price level

Foreign trade costs

IND

IDN

TWN

BGR

CHN

RUS

ROU

POL

HUN

TUR

LTU

MEX

SVK

KOR

LVA

HRV

CZE

EST

MLT

PRTSVN

BRA

USA

CYP

GRCESP

DEU

ITAAUT

NLD

GBR

FRABEL

CAN

IRL

FIN

LUX

SWE

JPNAUS

DNK

NOR

CHE

-.2-.1

0.1

.2


Domestic trade costs

16 / 35


I The cost of living relative to the US, is

CoLi ≡(PLiy

)WTi×

S∏s=1

(λiisλUSs



)WTisθs− W

Tis

σs−1(

Li

LUS


PLNics

)WNisI Compare this with PWT price level of consumption, which does not adjust

for foreign or domestic trade costs or variety differences across countries

I Initially make this comparison using only the first three and the lastterms on the right-hand side

I So this initial calculation ignores the overall product variety term and thescale term (relative population)

17 / 35

The impact of trade costs only on the cost of living

IND

IDN

TWN

BGRCHN

RUSROU

POL

HUNTUR

LTUMEXSVKKORLVAHRV

CZEESTMLT

PRTSVNBRA

USA

CYP

GRCESPDEU

ITAAUTNLDGBRFRABEL

CAN

IRLFIN

LUX

SWEJPN

AUSDNK NORCHE

45o

-1.5

-1-.5

0.5

log

of c

ost o

f liv

ing


IND

IDN

TWN

BGRCHN

RUS

ROUPOL

HUN

TUR

LTU

MEX

SVKKOR

LVA

HRV

CZEEST

MLT

PRTSVN

BRA

USA

CYP

GRCESPDEU

ITA

AUTNLD

GBR

FRA

BEL

CAN

IRLFIN

LUX

SWEJPN

AUSDNK

NORCHE

-.4-.3

-.2-.1

0.1

log(

Cos

t of L

ivin

g/C

onsu

mpt

ion

pric

e le

vel)


18 / 35

Cost of living only using foreign and domestic trade costs

I We find that the model-based cost-of-living is far below the PWTcost-of-living for many countries. Why is this?

I ICP and PWT:I PWT uses the United States as the base country, which has a high

domestic share, but this does not matter because the multilateralindex numbers are transitive

I PWT is also not very sensitive to breaking up the United States intoregions (e.g. states), and using any one as the base region

I Model-based cost of living:I Also transitive to using any comparison country

I But the home shares used the in model-base cost of living are verysensitive to breaking up the United States into regions

I Conclude: it is essential to incorporate product variety in order toget the model-based cost-of-living right!

19 / 35

Variety: Firm count and barcode data for 19 countries

I Barcode counts N is from Billion Price Project (Cavallo, et al., 2018)

I Available for five sectors: food, clothing, furniture, electronics andother products (missing health and transport)

I For food and electronics only, country of origin is being collectedmanually in retail stores: packages of 500 “randomly” selectedproducts are scanned in retailers from 19 countries (including US)

I Robustness: For the US, we can also compare the manually collectedcountry of origin with scraped data from Walmart and Samsclub

I Barcode share is B is , so domestically-produced barcodes are:

M is ≡ N isB is

I Outside of food and electronics, we assume B is ≈ λis , so that:

M is/λis ≈ N is

20 / 35

Domestically-produced varieties across countries

21 / 35

Variety: Firm count versus barcodes

AUSBRACAN

CHN

DEUESP FRA

GBR

GRC

IND

ITAJPN

KOR

MEX

NLDPOL

RUS

TUR

USA

AUT

BEL

BGR

CHE

CYP

CZE

DNKEST

FINHRV

HUN

IDNIRL

LTU

LUX

LVA

MLT

NOR

PRTROU

SVK

SVN

SWE

TWN

0.2

.4.6

.8


Firm count

IND

CHN

RUS

POL

TURMEX

KORBRA

USA

GRC

ESP

ITA

DEU

NLDFRA

GBRCAN

JPN

AUS

0.2

.4.6

.8


Barcodes

22 / 35

Scale Regression

Variety measure: Firm count Barcodes* Firm count Barcodes*Size measure: Employment Employment Population Population

log[Sizei/SizeUSA] 0.501*** 0.249*** 0.496*** 0.233***(0.0470) (0.0801) (0.0477) (0.0839)

log[ ExpenditureShareiExpenditureShareUSA

] 0.107 0.0841 0.106 0.0906

(0.0853) (0.116) (0.0864) (0.117)Constant -0.947*** -0.546*** -0.962*** -0.573***

(0.157) (0.166) (0.159) (0.169)

Observations 298 89 298 89R-squared 0.377 0.094 0.370 0.079

*: Excluding India

23 / 35

Scale Effect

IND

IND

IND

IND

IND

IND

IND

-8-6

-4-2

02

log

of re

lativ

e va

riety

-6 -4 -2 0 2log of relative population

All observations Excluding India

Firm count

INDIND

IND

IND

IND

-8-6

-4-2

02

log

of re

lativ

e va

riety

-6 -4 -2 0 2log of relative population

All observations Excluding India

Barcodes

24 / 35



CoLi ≡(PLiy

)WTi×

S∏s=1

(λiisλUSs



)WTisθs− W

Tis

σs−1(

Li

LUS


PLNics



I Now include all terms except for the scale term (relative population)

25 / 35

Relative cost of living: barcode variety, no scale effect

IND

CHN

RUS

POL

TUR

MEX

KOR

BRAUSA

GRC

ESP

ITA

DEU

NLDFRA

GBRCAN

JPN

AUS

45o

-1-.5

0.5

1lo

g of

cos

t of l

ivin

g

-1.5 -1 -.5 0 .5log of consumption price level

IND

CHN

RUS

POL

TUR

MEX

KOR

BRA

USA

GRC

ESP

ITA

DEU

NLDFRA

GBR

CAN

JPN

AUS

-.2-.1

0.1

.2.3

log(

Cos

t of L

ivin

g/C

onsu

mpt

ion

pric

e le

vel)


26 / 35

Relative cost of living: firm-count variety, no scale effect

AUS

BRA

CAN

CHN

DEUESP

FRAGBRGRC

IND

ITA

JPN

KOR

MEX

NLD

POLRUS

TUR

USA

AUT

BEL

BGR

CHE

CYP

CZE

DNK

EST

FIN

HRV

HUN

IDN

IRL

LTU

LUX

LVA

MLT

NOR

PRT

ROU

SVK

SVN

SWE

TWN

45o

-1-.5

0.5

1lo

g of

cos

t of l

ivin

g


AUS

BRA

CAN

CHN

DEUESP

FRAGBR

GRC

IND

ITA

JPN

KOR

MEX NLD

POL

RUS TUR USA

AUT

BEL

BGR

CHE

CYP

CZE

DNK

EST

FIN

HRV

HUN

IDN

IRL

LTU

LUX

LVA

MLT

NOR

PRT

ROU

SVK

SVN SWE

TWN

-.20

.2.4

.6lo

g(C

ost o

f Liv

ing/

Con

sum

ptio

n pr

ice

leve

l)


27 / 35



CoLi ≡(PLiy

)WTi×

S∏s=1

(λiisλUSs



)WTisθs− W

Tis

σs−1(

Li

LUS


PLNics



I Now include all terms

28 / 35

Relative cost of living: barcode variety and scale

IND

CHN

RUS

POL

TUR

MEX

KOR

BRAUSA

GRC

ESP

ITA

DEU

NLDFRA

GBRCANJPN

AUS

45o

-1-.5

0.5

1lo

g of

cos

t of l

ivin

g


IND

CHN

RUS

POL

TUR

MEX

KOR

BRAUSA

GRC

ESP

ITA

DEU

NLDFRA

GBR

CAN

JPN

AUS

-.4-.2

0.2

.4lo

g(C

ost o

f Liv

ing/

Con

sum

ptio

n pr

ice

leve

l)


29 / 35

Relative cost of living: firm-count variety and scale

AUS

BRA

CAN

CHN

DEUESP

FRAGBRGRC

IND

ITA

JPN

KORMEX

NLD

POLRUS

TUR

USA

AUTBEL

BGR

CHE

CYP

CZE

DNK

EST

FIN

HRV

HUN

IDN

IRL

LTU

LUX

LVA

MLT

NOR

PRT

ROU

SVK

SVN

SWE

TWN

45o

-1.5

-1-.5

0.5

1lo

g of

cos

t of l

ivin

g


AUS

BRA

CAN

CHN

DEUESP

FRAGBR

GRC

IND

ITA

JPN

KOR

MEXNLD

POLRUSTUR

USA

AUT

BELBGR

CHE

CYP

CZE

DNKEST FIN

HRV

HUN

IDN

IRL

LTU

LUX

LVA

MLT

NORPRT

ROU

SVK

SVN

SWE

TWN

-.50

.51

log(

Cos

t of L

ivin

g/C

onsu

mpt

ion

pric

e le

vel)


30 / 35

Cost of Living Decomposition 1I First we run:

lnCoLi = α0 + β0 lnPLic + �

i0, i = 1, . . . ,C

I Define Z ik , k = 1, . . . , 6 as (in logs):

lnZ i1 = WTi lnPLiy

lnZ i2 =S∑

s=1

WTis

θsln(λiis /λ

USs

)

lnZ i3 =S∑

s=1

WTis ln

(τ iisτUSs

)

lnZ i4 =S∑

s=1

WTis

[1

θs−

1

σs − 1

]ln

(M is/λ

iis

MUSs /λUSs

)

lnZ i5 = −(1 − α)WTis

θsln(Li/LUS

)lnZ i6 =

S∑s=1

WNis ln(PL

Nics )

I Then we also run: lnZ ik = αk + βk lnPLic + �

ik , k = 1, . . . , 6

I Because lnCoLic =6∑

k=1lnZ ik , then α0 =

6∑k=1

αk , β0 =6∑

k=1βk

31 / 35

Regression table 1

Variety: No variety FirmCount Barcode Firmcount BarcodeScale effect: n.a. No No Yes Yes

Explanatory variable: log(PLc)

CoL 1.224 1.228 1.147 1.278 1.186(0.039) (0.050) (0.080) (0.073) (0.081)

PLy 0.429 0.429 0.444 0.429 0.444(0.024) (0.024) (0.012) (0.024) (0.012)

Foreign trade costs -0.062 -0.062 -0.066 -0.062 -0.066(0.014) (0.014) (0.016) (0.014) (0.016)

Domestic trade costs 0.114 0.114 0.120 0.114 0.120(0.027) (0.027) (0.028) (0.027) (0.028)

Variety 0.004 -0.058 0.004 -0.058(0.036) (0.049) (0.036) (0.049)

Scale 0.050 0.039(0.036) (0.015)

Non-traded prices 0.708 0.344 0.432 0.206 0.398(0.089) (0.096) (0.076) (0.069) (0.061)

32 / 35

Cost of Living Decomposition 2

I Take the difference between the model-based cost-of-living and the PWTrelative price of consumption:

∆CoLi ≡ CoLi − PLic

I Also combine the various PWT price terms to get

∆P i ≡W Ti lnPLiy +S∑

s=1

W Nis ln(PLNics )− lnPLic , i = 1, . . . ,C

I The we run∆P i = α0 + β0∆CoL

i + �i0, i = 1, . . . ,C

I Also define∆Z ik ≡ Z ik − PLic , k = 2, . . . , 5

I Then we also run:

∆ lnZ ik = αk + βk∆CoLi + �ik , k = 2, . . . , 5

33 / 35

Regression table 2

Variety: No variety FirmCount Barcode Firmcount BarcodeScale effect: n.a. No No Yes Yes

Explanatory variable: log(PLc)

Prices 0.708 0.344 0.432 0.206 0.398(0.089) (0.096) (0.076) (0.069) (0.061)

Foreign trade costs -0.215 -0.149 -0.111 -0.116 -0.128(0.050) (0.034) (0.059) (0.023) (0.055)

Domestic trade costs 0.507 0.241 0.328 0.157 0.327(0.077) (0.081) (0.069) (0.056) (0.062)

Variety 0.564 0.351 0.430 0.288(0.104) (0.078) (0.072) (0.087)

Scale 0.322 0.115(0.025) (0.087)

Number of countries 43 43 19 20 21

34 / 35

Conclusions

I We have extended ACR to allow for comparisons of equilibria bothwithin and between countries

I We have compared a model-based cost-of-living to the consumptionprice from PWT for 43 countries

I In this comparison it is essential to also correct for ”overall” productvariety (using the count of domestic varieties / home share)

I Empirical resultsI Using barcode data to count variety for 19 countries, the

model-based cost of living is reasonably close to the PWT price levelof consumption (but slightly worse using the firm count)

I Using firm data to count variety, the other 24 countries in thesample have a PWT price level relative to the US that is sometimessubstantially above the the model-based cost of living.

I For those other 24 countries, the US enjoys relatively more gainsfrom variety.

35 / 35

Documents

Product Variety, Trade Costs and the Standard of Living Across Countries … · 2020. 3. 1. · Feenstra (1994) the exact ... Wholesale & Retail margin 52% 47% 20% Transport margin