Estimating sectoral product quality under quality heterogeneity

Abstract

This paper estimates product quality at the sectoral level using data from a panel of twelve manufacturing sectors in nineteen OECD countries during the years 1995–2006. The author first derives a gravity model from a firm-heterogeneity model of trade, then measures product quality as the residual of the gravity model. In estimating the gravity model, the author employs the two-step procedure of Helpman et al. (Q J Econ 123(2):441–487, 2008) to correct for biases caused by selection in trade and firm heterogeneity. When aggregated into the country level, the used overall quality metrics do not systematically differ from Hallak and Schott’s (Q J Econ 126(1):417–474, 2011). In line with existing literature, sectoral quality estimates are found positively correlated with sectoral unit prices as well as countries’ income per capita. And the quality gap between rich and poor countries is more pronounced in capital- and skill-intensive sectors. In addition, the autor finds beta- and sigma-convergence in sectoral product quality across countries.

Appendices

Appendix 1: Data description and the sample of countries

1.1 Data for the calculation of A _is and c _is

Limitied by data availability, I only estimate sectoral product quality for nineteen OECD countries during the years 1995–2006.

Sectoral productivity, A _is , is measured as the Solow residuals and for this purpose, I use sectoral data of current value added, value added deflator, current fixed capital formation, gross fixed capital formation deflator, and total employment, all of which are from the STAN database, OECD (2008). To measure the real output, I first convert current value added into the real one in 2000 local currency using the value added deflator, which is then transformed into the US dollars using the exchange rate in the year 2000. Sectoral current fixed capital formation data are also transformed into the real one in 2000 US dollars in the same way and when the fixed capital formation deflator is missing for some sectors, the deflator for the whole manufacturing is used instead.²³

The real capital stock is calculated using the perpetual inventory method:

$$K_{is,t + 1} = (1 - \delta )K_{is,t} + I_{is,t} ,$$

(21)

where K _is,t and I _is,t are real capital stock and fixed capital formation, respectively, and δ is the depreciation rate. The initial capital stock is estimated as follows:

$$K_{is,1991} = \frac{{I_{is,1991} }}{{g_{is} + \delta }},$$

(22)

where g _is is the average growth rate of real fixed capital formation during the years 1991–2006 and following Unel (2008), I choose 8 % as the depreciation rate.

To measure the labor input, I multiply sectoral employment data by countries’ average annual working hours per worker since countries vary a lot in daily working hours (Unel 2008). The data of average annual hours worked per employee are available from the labor force statistics, OECD (2012).²⁴ In light of Harrigan (1997), I estimate the labor share, 1 − β _is , by running the following regression:

$$\alpha_{ist} = \alpha_{is} + \gamma_{s} \ln \left( {\frac{{K_{ist} }}{{L_{ist} }}} \right) + \varepsilon_{ist} ,$$

(23)

where α _ist is the share of labor compensation in the value added of sector s in country i at year t; K _ist and L _ist are real capital stock and total working hours, respectively. Then the predicted α _ist is used as the estimate of 1 − β _is at year t and the estimator is advantageous in that it is less noisy and less likely to exceed one (Unel, 2008). Finally, the sectoral productivity, A _is , is calculated by the Solow residual:

$$A_{is} = \frac{{Q_{is} }}{{K_{is}^{{\beta_{is} }} L_{is}^{{1 - \beta_{is} }} }},$$

(24)

and Q _is is the real value added in the sector.

To calculate c _is in (4), the wage rate w _i is measured by the labor compensation of the whole manufacturing divided by total manufacturing working hours, and then transformed into the US dollars using the exchange rate of that year. Following Caselli and Feyrer (2007) and Fadinger and Fleiss (2011), the rental price of capital, r _i , is estimated as follows:

$$r_{i} = \beta_{i} \frac{{GDP_{i} }}{{K_{i} }},$$

(25)

where β _i is one minus the labor share in national income of country i and the latter is calculated as the total labor compensation divided by total value added, which is then averaged across the years 1995–2006. The total labor compensation and value added data are from OECD (2008) and GDP _i is from the WDI in current US dollars. The real capital stock, K _i , is estimated using the perpetual inventory method.

As for sectoral elasticities of substitution, ɛ _s , I draw on estimates from Imbs and Mejean (2009), which are on the basis of 3-digit ISIC Rev.3. I calculate the elasticity of substitution for each 2-digit ISIC Rev.3 industry by averaging the elasticities of the 3-digit industries belonging to it. The elasticities of 2-digit industries are again averaged if the sector consists of two or more 2-digit industries.²⁵

1.2 Data for the extensive and intensive analysis

I extract the export data from the UN Comtrade database via the World Integrated Trade Solution (WITs) and the export data are based on 2-digit ISIC Rev.3 and summed up when the sector consists of two or more 2-digit industries. Comtrade claims that import data are more accurate than export data since governments use import value to calculate customs duty. However, import data cannot be used in this study since not many countries report their imports, especially in the first years of 1995–2006. Otherwise, some countries may export to all other countries that report imports and thus their fixed effects cannot be estimated in the extensive analysis. To mitigate the measurement errors in export data, I first choose the sample of exporting countries to include 85 countries that did not report their exports at most once during the years 1995–2006.²⁶ These countries are generally more important in world economy and their export data are of higher quality. Second, I drop export records whose value is less than the 15th percentile of the US’s in the sector in the year 2000.²⁷ This reduces the measurement errors since the least important small exports are more likely to be inaccurately reported.²⁸

The bilateral tariff data are from the TRAINS database via the WITs. The tariff is based on 2-digit ISIC Rev.3 which is then weight-averaged to the sectoral level if the sector consists of two or more 2-digit industries and the weight is the import value of the industry. I use the Most-favored Nation (MFN) tariff which is adjusted by any possible preferential rates between the trade pair. Note that countries that report their import tariffs are increasing over time and the sample of importing countries will be subject to constant change if I use all available tariff data, which will lead to biased estimators if the selection into reporting tariffs is not random.²⁹ Thus I limit the sample of importing countries to 45 countries that miss at most 2 years’ tariff during the years 1995–2006 when analyzing the intensive margin.³⁰ I extrapolate the missing tariff data by the average of neighboring 2 years’.

I extract other gravity variables from various sources. The bilateral distance data are from the CEPII database (Mayer and Zignago 2011). Other dichotomous variables from the CEPII database include dummies on sharing a common border, the same official language, the same legal origin, and having some colonial relationship (including colonial relationship post 1945, having the same colonizer post 1945, and ever in colonial relationship). The data on common currency and free trade agreements (FTA) are from De Sousa (2012). Dummies indicating if both countries are islands or landlocked are from Helpman et al. (2008).

1.3 The sample of countries in the analysis

The extensive analysis needs a sample including many countries and then there will be enough zero trade flows. Otherwise, some countries may export to (or import from) all other countries and thus their fixed effects cannot be estimated. However, I cannot include all available countries in the sample as countries that report exports are increasing over time and the problem of sample selection will emerge. Thus the sample of exporting countries includes 85 countries that fail to report at most one year’s data during the years 1995–2006. The sample of importing countries in the extensive analysis includes 149 countries, which is dictated by the availability of firm-entry cost data.

The sample of exporting countries in the intensive analysis is the same as in the extensive analysis. Since I use tariff data in the intensive analysis, the sample of importing countries consists of 44 countries whose tariff data are missing for at most 2 years during 1995–2006.

The samples of countries for the extensive as well as intensive analyses are listed in “Appendix 3”.

Appendix 2: The calculation of E[u _ijs |E _ijs  = 1] and E[φ _ijs |E _ijs  = 1]

2.1 Calculating E[u _ijs |E _ijs  = 1]

Rewrite (14) as $z_{ijs} = \left[ \cdot \right] + \bar{\omega }_{ijs}$, then E _ijs  = 1 implies that $z_{ijs} = \left[ \cdot \right] + \bar{\omega }_{ijs} > 0$. And thus $\bar{\omega }_{ijs} > - \left[ \cdot \right]$. Mathematically,

$$\left( {\begin{array}{*{20}c} {X_{1} } \\ {X_{2} } \\ \end{array} } \right)\sim N\left( {\left( {\begin{array}{*{20}c} 0 \\ 0 \\ \end{array} } \right),\;\left( {\begin{array}{*{20}c} 1 & \rho \\ \rho & 1 \\ \end{array} } \right)} \right) \Rightarrow E(X_{1} \left| {X_{2} > s} \right.) = \rho \frac{\phi (s)}{\varPhi ( - s)}.$$

Thus, I have:

$$\begin{aligned} E[u_{ijs} \left| {E_{ijs} = 1} \right.] &= E[u_{ijs} \left| {\bar{\omega }_{ijs} > - [ \cdot ]} \right.] \hfill \\&= \sigma_{u} E\left[ {\frac{{u_{ijs} }}{{\sigma_{u} }}\left| {\frac{{\bar{\omega }_{ijs} }}{{\sigma_{\omega } }} > - \frac{[ \cdot ]}{{\sigma_{\omega } }}} \right.} \right] \hfill \\& = \rho \sigma_{u} \frac{{\phi ([ \cdot ]/\sigma_{\omega } )}}{{\varPhi ([ \cdot ]/\sigma_{\omega } )}} \hfill \\& = \rho \sigma_{u} \frac{{\phi (\varPhi^{ - 1} (\mathop {\Pr }\nolimits^{ \wedge }_{ijs} ))}}{{\varPhi (\varPhi^{ - 1} (\mathop {\Pr }\nolimits^{ \wedge }_{ijs} ))}} \hfill \\&= \rho \sigma_{u} \frac{{\phi (\varPhi^{ - 1} (\mathop {\Pr }\nolimits^{ \wedge }_{ijs} ))}}{{\mathop {\Pr }\nolimits^{ \wedge }_{ijs} }}, \hfill \\ \end{aligned}$$

where ρ is the correlation coefficient between u _ijs and $\bar{\omega }_{ijs}$.

2.2 Calculating E[φ _ijs |E _ijs  = 1]

Following Helpman et al. (2008), I approximate (15) by a polynomial to the order of three, i.e., φ _ijs  = d ₀ + d ₁ z _ijs  + d ₂ z ² _ijs  + d ₃ z ³ _ijs . Then,

$$E\left[ {\varphi_{ijs} |E_{ijs} = 1} \right] = d_{0} + d_{1} E\left[ {z_{ijs} |E_{ijs} = 1} \right] + d_{2} E\left[ {z_{ijs}^{2} |E_{ijs} = 1} \right] + d_{3} E\left[ {z_{ijs}^{3} |E_{ijs} = 1} \right].$$

Because z _ijs is subject to a normal distribution, E[z _ijs |E _ijs  = 1], E[z ² _ijs |E _ijs  = 1] and E[z ³ _ijs |E _ijs  = 1] are actually moments of a truncated normal distribution. Using the arithmetic of Dhrymes (2005), they can be calculated as follows:

$$E[z_{ijs} \left| {E_{ijs} = 1} \right.] = \hat{z}_{ijs} + \sigma_{\omega } u_{ijs}^{*} ,$$

$$E[z_{ijs}^{2} \left| {E_{ijs} = 1} \right.] = \hat{z}_{ijs}^{2} + \sigma_{\omega } \hat{z}_{ijs} u_{ijs}^{*} + \sigma_{\omega }^{2} ,$$

$$E[z_{ijs}^{3} \left| {E_{ijs} = 1} \right.] = \hat{z}_{ijs}^{3} + \sigma_{\omega } \hat{z}_{ijs}^{2} u_{ijs}^{*} + 3\sigma_{\omega }^{2} \hat{z}_{ijs} + 2\sigma_{\omega }^{3} u_{ijs}^{*} ,$$

where $\hat{z}_{ijs} = \sigma_{\omega } \varPhi^{ - 1} (\mathop {\Pr }\nolimits^{ \wedge }_{ijs} )$ and $u_{ijs}^{*} = \varphi \left( {\varPhi^{ - 1} \left( {{\hat{\text{P}}\text{r}}_{ijs} } \right)} \right)/{\hat{\text{P}}\text{r}}_{ijs}$. Thus, $E[\phi_{ijs} \left| {E_{ijs} = 1} \right.] = (d_{0} + d_{2} \sigma_{\omega }^{2} ) + (d_{1} + 3d_{3} \sigma_{\omega }^{2} )\hat{z}_{ijs} + d_{2} \hat{z}_{ijs}^{2} + d{}_{3}\hat{z}_{ijs}^{3}$ $+ (2d_{3} \sigma_{\omega }^{3} + d_{1} \sigma_{\omega } )u_{ijs}^{*} + d_{2} \sigma_{\omega } \hat{z}_{ijs} u_{ijs}^{*} + d_{3} \sigma_{\omega } \hat{z}_{ijs}^{2} u_{ijs}^{*}.$ I then write this equation as $E[\phi_{ijs} \left| {E_{ijs} = 1} \right.] = f_{0} + \sum\nolimits_{p = 1}^{3} {f_{p} \hat{z}_{ijs}^{p} } + \sum\nolimits_{q = 0}^{2} {g_{q} \hat{z}_{ijs}^{q} u_{ijs}^{*} }$, where f _p and g _q are coefficients.

Appendix 3: The list of countries

#	Country	#	Country	#	Country
1	Albania*	51	Greece*$	101	Panama
2	Algeria	52	Guatemala	102	Paraguay*$
3	Angola	53	Guinea*	103	Peru*
4	Argentina*$	54	Guinea-Bissau	104	Poland*$
5	Armenia	55	Guyana	105	Portugal*$
6	Australia*$	56	Haiti	106	Qatar
7	Austria*$	57	Honduras	107	Republic of Congo
8	Azerbaijan*	58	Hong Kong*	108	Romania*
9	Bahrain	59	Hungary*$	109	Russia*
10	Bangladesh*	60	Iceland*	110	Rwanda
11	Belarus	61	India*	111	Saudi Arabia
12	Belgium$	62	Indonesia*$	112	Senegal*
13	Belize	63	Iran	113	Sierra Leone
14	Benin	64	Ireland*$	114	Singapore*
15	Bolivia*$	65	Israel *	115	Slovakia*$
16	Bosnia and Herzegovina	66	Italy*$	116	Slovenia*$
17	Botswana	67	Jamaica	117	South Africa*
18	Brazil*$	68	Japan*$	118	South Korea*
19	Bulgaria*	69	Jordan*	119	Spain*$
20	Burkina Faso*	70	Kazakhstan	120	Sri Lanka
21	Burundi	71	Kenya	121	Suriname
22	Cambodia	72	Kuwait	122	Swaziland
23	Cameroon	73	Kyrgyz Republic	123	Sweden*$
24	Canada*$	74	Laos	124	Switzerland*$
25	Cape Verde	75	Latvia *$	125	Syria
26	Central African Rep.*	76	Lebanon	126	Taiwan
27	Chad	77	Lesotho	127	Tajikistan
28	Chile*$	78	Lithuania*$	128	Tanzania
29	China*$	79	Luxembourg$	129	Thailand*
30	Colombia*$	80	Macedonia*	130	The Bahamas
31	Costa Rica$	81	Madagascar*	131	The Gambia
32	Cote d’Ivoire*	82	Malawi*	132	The Netherlands*$
33	Croatia*	83	Malaysia*	133	The Philippines*$
34	Czech Republic*$	84	Mali*	134	Togo*
35	Denmark*$	85	Mauritania	135	Trinidad and Tobago
36	Djibouti	86	Mauritius*	136	Tunisia*
37	Dominican Republic$	87	Mexico*$	137	Turkey*
38	Ecuador*$	88	Moldova*	138	Uganda*
39	Egypt*	89	Mongolia*	139	Ukraine*
40	El Salvador	90	Morocco*	140	United Arab Emirates
41	Equatorial Guinea	91	Mozambique	141	United Kingdom*$
42	Estonia*$	92	Namibia	142	United States*$
43	Ethiopia*	93	Nepal	143	Uruguay*$
44	Fiji	94	New Zealand*$	144	Uzbekistan
45	Finland*$	95	Nicaragua	145	Venezuela*
46	France*$	96	Niger	146	Vietnam
47	Gabon	97	Nigeria$	147	Yemem
48	Georgia*	98	Norway*	148	Zambia*
49	Germany*$	99	Oman*	149	Zimbabwe
50	Ghana	100	Pakistan

1. The countries in this table are the sample of importing countries in the extensive analysis. In addition, the countries marked by * are the sample of exporting countries in the extensive as well as intensive analyses. The countries marked by $ are the sample of importing countries in the intensive analysis