Appendix

In the appendix I describe the methods and the data to obtain the parameter \(\theta\). Second, I include a data appendix with relevant summary statistics.

Estimation

In the following section I outline the methods, the additional data sources and the data manipulations I used to estimate \(\theta\). In particular, I motivate the IV estimation and describe the data imputation. Finally, I discuss the results.

I follow the approach of CDK to obtain an estimate of \(\theta\). Thus, I estimate the following equation. \[ ln x_{i,j}^k=\delta_{i,j}+\delta_{j}^k + \theta \ln z_{i,j}^k+\epsilon_{i,j}^k\] In the equation \(x_{i,j}^k\) denotes the trade flows between exporting country \(i\), importing country \(j\) in industry \(k\), \(\delta_{i,j}\) denotes an importer-exporter fixed effect, \(\delta_{j}^k\) denotes an importer-sector fixed effect, \(z_{i,j}^k\) denotes the productive efficiency and \(\epsilon_{i,j}^k\) denotes the error term. As in CDK I specify \(z_{i,j}^k\) as the inverse of producer prices.

The structural parameter \(\theta\) may be estimated with OLS under the condition that the econometric error term is exogenous. In the model the error term may be interpreted as a variable trade cost. Thus, the exogeneity condition requires for the three specifications that the inverse of total production cost, total domestic cost and total domestic factor cost is not correlated with variable trade cost.

Costinot, Donaldson, and Komunjer (2012) state two reasons why the condition may be violated. First, the condition may be violated because of a simultaneity bias. An example for a simultaneity bias is agglomeration effects.²⁶ The sign of the simultaneity bias is apriori ambiguous (Costinot, Donaldson, and Komunjer 2012).

Second, the exogeneity condition may be violated due to a measurement error. A measurement error of the international price data would downward bias the estimate of \(\theta\) under the condition that the measurement error is correlated with the true underlying variable (Greene 2003, 85).

I use an IV estimation strategy to address the two outlined problems. By instrumenting the inverse producer price with the instrument R&D expenditures, I attempt to isolate the variation of the regressor, which is exogenous to the econometric error term. Moreover, if the variation of the producer prices explained by R&D mainly affects our independent variable through productive efficiency, than the IV estimation identifies the effect of Ricardian sources of comparative advantage.

I motivate the choice of R&D expenditures as instrumental variable as follows. First, modelling productive efficiency as a process of R&D is in line with the approach of Costinot, Donaldson, and Komunjer (2012) and Eaton and Kortum (2002). A possible mechanism for R&D expenditures to affect the inverse of producer prices is that an increase in R&D expenditures may lead to innovations, which lead to more cost efficient production technologies. In the model a decrease in the cost of producing a good is directly passed through to the producer price, due to the assumption of perfect competition.

I can test the outlined mechanism, on the basis of the first stage regression of the inverse of producer prices on R&D expenditures. Under the outlined mechanism, I expect that the coefficient is positive and statistically significant. An empirical test of the exclusion assumption, which is that the instrument is exogenous to the econometric error term, is however not possible (Cameron and Trivedi 2005, 109).

Data

I use the following additional data sources to estimate \(\theta\). I use international producer price data for the year 2005 from the GGDC (Inklaar and Timmer 2014), R&D expenditures for the year 2005 from the (OECD 2013) ANBRED database and value-added trade and gross export data from the TiVA database. Further, to harmonize the level of aggregation of the international price data with the other data sources, I used value-added output data from the OECD STAN OECD (2013).

I combined the additional data sources with the value-added and gross export data from the TiVA using the ISIC Rev.3.1 two digits classification. In the cases in which the international price data is more disaggregated, I used a weighted average. Specifically, to merge two sectors I assigned to each sector a weight equal to the share of the sectors value-added output relative to the sum of value-added output of the two sectors. %Hence, I aggregated several prices from the service sectors using a weighted average.

Missing data imputation

Schafer and Olsen (1998) note that the following three concerns arise due to missing data: (1) efficiency losses, (2) complications in data handling and data analysis, (3) bias due to differences between the observed and unobserved data. For the estimation of \(\theta\) potential problems may arise due missing data because data on R & D expenditures is not available for some industries.. In particular, the missing data may cause a loss of efficiency in the first stage of the IV estimation, which would reduce the strength of the first stage association between R&D and the inverse of producer prices and hence upward bias the estimates of \(\theta\).

Multiple imputation is a Bayesian technique to impute missing data by simulated draws from the posterior predictive distribution.²⁷

In the following, I outline multiple imputation based on (R. J. A. Little and Rubin 2002, 209–11).

Missing data techniques assume that the missing observations of a variable are random variables with a statistical distribution. Multiple imputation as other missing data imputation techniques assume that the probability of a missing observation depends only on the observed data and not on the missing data.

The idea of multiple imputation is to relate the observed posterior distribution to the complete-data posterior distribution, which would be observed in the absence of missing data. The main result of (Rubin 1987) is that the posterior distribution of a statistical quantity may be simulated by first imputing the missing observations with repeated draws from the predictive posterior distribution of the missing data given the observed data and then drawing the statistical quantity from its complete data posterior distribution.²⁸

Multiple imputation produces valid interference from a frequentist perspective (R. J. A. Little and Rubin 2002, 90).

The choice of multiple imputation is based on the following reasons. First, techniques ignoring the missing observations such as complete case analysis or case-wise deletion, require a stronger assumption about the missing data. Specifically, they require that the missing data is a random subset of all observations Bhaskaran and Smeeth (2014)}. Multiple imputation offers a simple and general approach and it correctly accounts for the uncertainty induced by missing observations (Schafer and Olsen 1998).

After the imputation complete-data methods can be used on the imputed data-sets and the results may be combined using Rubin’s rules (Rubin 1987). Specifically, I obtain an estimate of a statistical quantity \(\bar{Q}_m\), by taking the mean of the estimates obtained within each imputed data set \(\bar{Q}_m=1/m \sum_{l=1}^m Q_{l}\), where \(Q_1 \dots Q_m\) denotes the estimate obtained within each data set. The associated variance is the combination of the variance estimates within each imputed data set and the variance between the imputations. Formally, $ T_m={V_m}+ ({m+1}/m)B_m , B_m=1/{m-1}{l=1}^m (Q_l-Q_m)^2 , ,{V_m}=1/m * {l=1}^m V_l $.

To overcome possible shortcomings of multiple imputation, I combine it with predictive mean matching (PMM). PMM is a nearest neighbour matching technique. Its use in the context of multiple imputation is attributed to Rubin (1986) and R. J. A. Little (1986). Unlike multiple imputation, which is based on a normality assumption, PMM imputes missing data with random draws from the closest observations in the observed data. As a consequence, it is well suited to impute skewed variables (White, Royston, and Wood 2011). This approach is relevant to our imputation as R&D expenditure is highly skewed.

Under PMM the missing observation \(y_i\) of unit \(i\) is imputed using a random draw from the observations \(y_j\) of those units \(j\), which have the smallest distance between its predicted value \(\hat{y_j}\) to the predicted value for unit \(\hat{y_i}\) based on a regression of \(\boldsymbol{Y}\) on some covariates \(\boldsymbol{X}\). In particular, I impute each missing value with a random draw from the ten closest observations. This choice rests on the recommendations of the simulation study by (Morris, White, and Royston 2014).

The imputation is conducted as follows. First, I impute the outcome variable of the first stage regression, the log of the inverse of the international producer prices, using country and sector fixed effects. Second, I impute the log of R&D expenditure using country and sector fixed effects and the log of the inverse of the international producer prices. I impute both variables using the country and sector fixed effects, to account for time-invariant determinants of both at the country and sector level. Similarly, Costinot, Donaldson, and Komunjer (2012)} imputed the log of R&D expenditures with the predicted values from a regression on country and sector fixed effects.

I impute the outcome variable based on the following arguments. First, R. J. Little (1992)} argued that if both the regressors and the outcome variable have missing values, the latter may provide additional information to impute the regressors. Second, the simulation study of Moons et al. (2006) found that the results of multiple imputation of covariates with missing observations were biased if the outcome variable was not used in the imputation.

Table 1 presents the cross-sectional results of the estimates of \(\theta\) for the year 2005. Table 1 is divided into three subtables for each of the three dependent variables, gross exports, backward value-added and forward value-added. Across tables, I present the OLS estimates in column 1. I present the IV estimates with the instrument “R&D expenditure” in columns 2-4. In columns 2-3, I present the IV estimates using the complete sector coverage and a restricted sample without primary sectors. In column 5, I present the IV estimates including only high income countries based on the World Bank classification for 2005.

The OLS estimates for gross exports and backward value-added trade show a statistically significant positive coefficient. The IV estimates in the columns 2-4 are significantly increased relative to column 1. The estimated \(\theta\) in column 2-4 is between 12.63 and 14.68. The significant increase of the IV estimate compared to the OLS estimate, confirms that the regressor is endogenous (Hausman 1978).

The IV estimates of \(\theta\) across the samples for the dependent variables “gross exports” and “backward value-added trade” show the following results. Overall, the estimates of \(\theta\) for both dependent variables are very close and the difference is statistically not significant. Second, the sample including only high-income countries and excluding the primary sectors shows a statistically significant increase of \(\theta\)..²⁹ A higher estimate of \(\theta\) implies a decreased dispersion of production costs within sectors. The result is in line with our expectations, since the sample includes only high income countries.

The estimates of \(\theta\) on the basis of FVAT are not significant based on OLS. As for the other two dependent variables the IV estimates for \(\theta\) are significantly increased. Third, the estimate of \(\theta\) for the sample including only high-income countries shows in contrast to the results for EXGR and BVAT no significant difference compared to the other samples.

Directly comparing the estimate of \(\theta\) on the basis of gross exports to the result of Costinot, Donaldson, and Komunjer (2012), I find that the IV results in column 2-3 are not statistically different from CDKs results (\(\theta_{CDK}\) 11.1 SE 0.981). However, the authors’ favourite estimate of \(\theta\) is \(6.58\) on the basis of openness corrected exports. The authors use openness corrected gross exports to account for trade selection, which downward biases the productive differences.³⁰

For two reasons I decided to use gross exports and value added trade without correcting for openness. First, data on the import penetration ratio is only available for the manufacturing sectors, which would reduce the sample size considerably. Second, I was unable to obtain a similar correction for VAT.

Cross-section results I

	OLS	Full Sample	Without primary sectors**	Without primary sectors high***
Dep. var.	log EXGR 2005
θ	0.434	12.653	11.424	14.689
SE*	(0.067)	(1.331)	(1.422)	(2.130)
Exporter Importer FE	Yes	Yes	Yes	Yes
Importer Sector FE	Yes	Yes	Yes	Yes
Observations	18143	18143	16582	14449
R-squared	0.771	0.197	0.321	0.141
F-stat 1st stage		151.41	125.6	85.24
*HC robust	standard errors	in parentheses
**Without primary	sectors	excludes	the sectors mining &	agriculture
***high denotes	highly	developed	countries

Cross-section results II

	OLS	Full Sample	Without primary sectors**	Without primary sectors high***
Dep. var.	log BVAX 2005
θ	0.476	12.911	11.762	15.080
SE*	(0.066)	(1.34)	(1.447)	(2.18)
Exporter Importer FE	Yes	Yes	Yes	Yes
Importer Sector FE	Yes	Yes	Yes	Yes
Observations	18143	18143	16582	14449
R-squared	0.775	0.18	0.304	0.128
F-stat 1st stage		151.41	125.6	85.24
———————-	—————–	—————-	—————————	———————————–
*HC robust	standard errors	in parentheses
**Without primary	sectors	excludes	the sectors mining &	agriculture
***high denotes	highly	developed	countries

Cross-section results III

	OLS	Full Sample	Without primary sectors**	Without primary sectors high***
Dep. var.	log FVAX 2005
θ	0.019	9.286	10.325	10.218
SE*	(0.045)	(0.868)	(1.291)	(1.199)
Exporter Importer FE	Yes	Yes	Yes	Yes
Importer Sector FE	Yes	Yes	Yes	Yes
Observations	18143	18143	16582	14449
R-squared	0.882	0.475	0.431	0.488
F-stat 1st stage		151.41	125.6	85.24
*HC robust	standard errors	in parentheses
**Without primary	sectors	excludes	the sectors mining &	agriculture
***high denotes	highly	developed	countries

Results: First stage

The results of the first stage regression address two concerns about the validity of the IV regression: the relevance of the instrument and whether the instrument affects the endogenous regressor in the hypothesized way.

The table shows that the F-statistic of the excluded instrument in the first stage is very high. This implies that the instrument is highly relevant. Further, the first stage shows a statistical significant positive effect of R&D on the inverse of producer prices, which confirms the expected positive effect of R&D.

	Full Sample	Without primary sectors	Without primary sectors high
Log of R&D	0.022	0.023	0.02
SE	0.002	0.002	0.002
Exporter Importer FE	Yes	Yes	Yes
Export Sector FE	Yes	Yes	Yes
Observations	19343	17661	15283
F (excl. dummies)	125.6	88.17	85.24
Imputations	29	29	29

ISIC and ISO 3 Alpha Classification

ISIC Code	Short	Description
01-05	Agriculture products	Agriculture, hunting, forestry and fishing
10-14	Mining products	Mining and quarrying
15-16	Food sector	Food products, beverages and tobacco
17-18	Textile products	Textile and textile products
19	Leather products	Leather and footwear
17-19	Textiles & Leather products	Textiles, textile products, leather and footwear
20	Wood products	Wood and products of wood and cork
21-22	Paper products	Pulp, paper, paper products, printing and publishing
23	Fuel products	Coke, refined petroleum products and nuclear fuel
24	Chemical products	Chemicals and chemical products
25	Plastic products	Rubber and plastics products
26	Mineral products	Other non-metallic mineral products
27-28	Metals	Basic metals and fabricated metal products
29	Machinery	Machinery and equipment, nec
30-33	Electrical	Electrical and optical equipment
34-35	Transport	Transport equipment
36-37	Misc. Manufacturing	Manufacturing nec; recycling
40-41	Electricity	Electricity, gas and water supply
45	Construction	Construction
50-52	Trade	Wholesale and retail trade; repairs
55	Gastronomy	Hotels and restaurants
60-64	Communication	Transport and storage, post and telecommunication
65-67	Finance	Financial intermediation
70-74	Real estate	Real estate, renting and business activities
75-95	Social	Community, social and personal services

ISO 3	Country	COU	Country
ARG	Argentina	ITA	Italy
AUS	Australia	JPN	Japan
AUT	Austria	KOR	Korea
BEL	Belgium	LTU	Lithuania
BGR	Bulgaria	LUX	Luxembourg
BRA	Brazil	LVA	Latvia
CAN	Canada	MEX	Mexico
CHE	Switzerland	MYS	Malaysia
CHL	Chile	NLD	Netherlands
CHN	China	NOR	Norway
COL	Colombia	NZL	New Zeeland
CYP	Cyprus	PHL	Philippiens
CZE	Czech Republic	POL	Poland
DEU	Germany	PRT	Portugal
DNK	Denmark	ROU	Romania
ESP	Spain	ROW	Rest of the World
EST	Estonia	RUS	Russian Federation
FIN	Finland	SGP	Singapore
FRA	France	SVK	Slovakia
GBR	United Kingdom	SVN	Slovenia
GRC	Greece	SWE	Sweden
HKG	Hong Kong	THA	Thailand
HRV	Croatia	TUN	Tunisia
HUN	Hungary	TUR	Turkey
IDN	India	TWN	Taiwan
IND	Indonesia	USA	United States of America
IRL	Ireland	VNM	Vietnam
ISR	Israel	ZAF	South Africa

Data Appendix

Summary statistics in \(\theta\) sample

	Mean	Std_Dev	Min	Max	N
Log BVAT	2.443	2.867	-4.605	10.754	17453
Log EXGR	2.742	2.871	-4.605	11.108	17505
Log FVAT	3.000	2.351	-4.605	10.739	15999
Log inv. prod. prices	0.267	0.274	-0.672	1.167	18444
Log R&D	17.801	2.441	10.745	24.759	17313

	Log EXGR	Log BVAT	Log FVAT	Log inv. prod. prices	Log R& D
log gross exports	1	-	-	-	-
log backward value-added trade	0.996	1	-	-	-
log forward value-added trade	0.872	0.89	1	-	-
Log inv. prod. prices	-0.092	-0.1	-0.211	1	-
Log R&D	0.434	0.446	0.488	-0.2	1