Output Quality, Skill Intensity, and Factor Contents of Trade: An Empirical Analysis Based on Micro-Data of the Census of Manufactures WIOD Conference on Industry‐Level Analyses of Globalization and its Consequences Technische Universitaet Wien, Vienna May 26-28, 2010 Kyoji Fukao (Hitotsubashi University and RIETI) Keiko Ito (Senshu University) 1
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Output Quality, Skill Intensity, and Factor Contents of Trade: An Empirical Analysis Based on Micro-Data of the Census of Manufactures WIOD Conference.
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Output Quality, Skill Intensity, and Factor Contents of Trade:
An Empirical Analysis Based on Micro-Data of the Census of Manufactures
WIOD Conference on Industry Level Analyses of‐Globalization and its Consequences
• Recent studies on intra-industry trade (IIT) have brought to light rapid increases in vertical IIT (VIIT) (for example, see Fukao, Ishido and Ito (2003) and Schott (2004)).
• Many theoretical models assume that developed economies export physical and human capital-intensive products of high quality and import unskilled labor-intensive products of low quality from developing economies.
• Through this mechanism, an increase in vertical IIT may have a large impact on factor demand and factor prices.
2
1. Introduction (Contd.)• Empirical studies use information on the unit value of
commodities as a proxy for product quality. • Most of empirical studies based on the unit value data
take the positive relationships between commodity prices and factor intensities as given.
• Yet, to the best of our knowledge, few studies have empirically examined the relationship between unit values of commodities and their factor contents at the factory level.
(Notes: Some recent studies try to take quality difference among firms (plants) into account. <Quality Heterogenous-Firms model> Baldwin & Harrigan 2007; Kugler & Verhoogen 2008; Hallak & Sivadasan 2009, etc.)
3
1. Introduction (Contd.)
• The Purposes of this study is: - To develop a theoretical framework to estimate
the relationship between the unit values of gross output and factor intensities
- To test whether factories that produce goods with a higher unit value tend to input more skilled labor and capital stock services, using micro data of the Census of Manufactures for Japan
-To calculate the factor contents of trade for Japan, based on the estimated relationship between the unit values and factor intensity.
4
2. Theoretical Analysis of Factor Contents in VIIT• We assume that factories, in order to produce
commodities of a high quality, engage in production processes that are intensive in both skilled labor and capital.
• Suppose that N commodities are produced in an industry. For each commodity, there is a continuum of different qualities.
• Each “commodity” in our model corresponds to one product item in the most detailed commodity classification of production and trade statistics and that products that differ only in quality are not recorded as different products in the statistics.
5
2. Theoretical Analysis of Factor Contents in VIIT (Contd.)
• Each commodity, (n, q), is produced by a Leontief-type constant-returns-to-scale production function.
)(,
)(,
)(,min
)( ,
,,
,
,,
,
,,,,,,
,
,,,,
ti
tiq
ti
tiq
ti
tiqStiqU
ti
tntitiq qh
M
qg
K
qf
LL
qe
caY
where LU, q, i, t, LS, q, i, t, Kq, i, t and Mq, i, t denote unskilled (blue-collar) labor, skilled (white-collar) labor, capital, and intermediate input. Yq, i, t denotes the gross output of factory i. a i, t denotes factory i’s total factor productivity (TFP) level in comparison with the industry average TFP level in year t.We express elasticity values by ηY=(qi, t de(qi, t))/(e(qi, t) dqi,
t), ηS=(qi, t df(qi, t))/(f(qi, t) dqi, t), ηK=(qi, t dg(qi, t))/(g(qi, t) dqi,
t), ηM=(qi, t dh(qi, t))/(h(qi, t) dqi, t), respectively.6
2. Theoretical Analysis of Factor Contents in VIIT (Contd.)
From our production function, we have the following factor demand relationships:
We assume that the price elasticity of demand for each factory’s output in this industry is constant and takes the same value for all factories producing commodity n.
)( ,,,,
,,,ti
tiqU
tiqS qfL
L
(3.3)
)( ,,,,
,,ti
tiqU
tiq qgL
K
(3.4)
)( ,,,,
,,ti
tiqU
tiq qhL
M
(3.5)
)( ,,,,,
,,,ti
tntitiq
tiqU qecaY
L (3.6)
7
2. Theoretical Analysis of Factor Contents in VIIT (Contd.)
From an unit production cost function and constant mark-up ratio, we have the following relationship between p and q.
By making a linear approximation of equation (3.3) and subtracting average values across all factories from both sides of the equation, we have
1lnlnln
)()()(lnlnln
,,
,,,,,,,,,
tnti
tMtittitStitUtitiq
ca
pqhrqgwqfwqep
tiSttiqS
tU
tS
tiqU
tiqS appL
L
L
L,,,
,
,
,,,
,,, lnlnlnlnln
8
2. Theoretical Analysis of Factor Contents in VIIT (Contd.)
tiKttiqK
tU
t
tiqU
tiq appL
K
L
K,,,
,,,,
,, lnlnlnlnln
tiMttiqM
tU
t
tiqU
tiq appL
M
L
M,,,
,,,,
,, lnlnlnlnln
titiYttiqYt
tU
tiq
tiqU aappY
L
Y
L,,,,
,
,,
,,, lnlnlnlnlnln
9
2. Theoretical Analysis of Factor Contents in VIIT (Contd.)
where
tMttttSttU
MtMtKttStStY
SS
pqhrqgwqfw
pqhrqgwqf
,,,
,,
*)(*)(*)(
*)(*)(*)(
tMttttSttU
MtMtKttStStY
KK
pqhrqgwqfw
pqhrqgwqf
,,,
,,
*)(*)(*)(
*)(*)(*)(
tMttttSttU
MtMtKttStStY
MM
pqhrqgwqfw
pqhrqgwqf
,,,
,,
*)(*)(*)(
*)(*)(*)(
tMttttSttU
MtMtKttStStY
YY
pqhrqgwqfw
pqhrqgwqf
,,,
,,
*)(*)(*)(
*)(*)(*)(
10
2. Theoretical Analysis of Factor Contents in VIIT (Contd.)
Since we assume constant returns to scale and a constant mark-up ratio, we have the following identity among the coefficients of the above four equations.
1*)(*)(*)(
*)(
*)(*)(*)(
*)(
*)(*)(*)(
*)(
,,,
,
,,,
,,,
,
MtMttttSttU
tMt
KtMttttSttU
tt
StMttttSttU
tStY
pqhrqgwqfw
pqh
pqhrqgwqfw
rqg
pqhrqgwqfw
wqf
(3.19)
This constraint means that a one percent increase in the unit price of output corresponds to a one percent increase in the unit production cost.We estimate the four equations under the constraint (3.19) using SUR techniques. 11
3. Factor Contents in Japan’s VIIT• Using equations (3.15) and (3.18), we can express the
ratio of the white-collar labor input to the output quantity for a factory which produces commodity (n, q) as follows:
where c’n, t denotes a commodity- and year-specific constant term.Let φD, n, t(pt) denote the distribution function of output quantity by all the factories producing commodity n in Japan over unit value p. Then, we can derive the following equation from the above equation:
YS
ttnttn
ttnS pcpY
pL ,,
,,
)(
)(
12
3. Factor Contents in Japan’s VIIT (contd.)
• In a similar way, we can derive
0 ,,,,,,,, )(
t
YS
p tttnDttntnDtnDS dpppcYL
0 ,,
0 ,,
,,
,,,,,,,,
)(
)(
t
YS
t
YS
p tttnDt
p tttnEt
tnD
tnDStnEtnES
dppp
dppp
Y
LYL
0 ,,
0 ,,
,,
,,,,,,,,
)(
)(
t
YS
t
YS
p tttnDt
p tttnIt
tnD
tnDStnItnIS
dppp
dppp
Y
LYL
13
4. Data• Census of Manufactures for Japan - Larger Establishment Sample: all mfg. plants with
30 or more employees - 6-digit commodity level information on shipment
and quantity Unit values can be calculated for 800 commodities out of 2,000 commodities
- Number of blue-collar and white-collar workers available for years 1981, 1984, 1987, and 1990.
• Trade Statistics for Japan - Values and quantities of exports and imports at
the HS 9-digit commodity level (7,000 commodities for exports and 9,000 commodities for imports)
14
4. Data (contd.)
• To estimate the relationship between the unit value of gross output and factor intensities, we select only single-product establishments, which we define as establishments where one commodity accounts for more than 60% of total shipments.
• By using the unit value and factor intensity
information taken form the CM and the TS, we calculate the factor contents of Japan’s trade, taking account of quality (price) difference between exported and imported goods.
15
Table 5. Summary table of the unit value analysis: The case of cotton tubular knit fabric
Unit value data of the Census of Manufactures 1990Commodity classification name in the Census of Manufactures Cotton tubular knit fabricCommodity code 1451-11Number of factories whose data were used 14Number of white-collar workers per one million yen gross output 0.0066Number of blue-collar workers per one million yen gross output 0.0167Capital stock (in million yen) per one million yen gross output 0.1257Average unit value (million yen per ton) 1.3571Standard deviation of unit value (million yen per ton) 1.6016Average of natural log of unit value 0.0393Standard deviation of natural log of unit value 0.6073
Total value of exports (million yen) 203.110Total value of exports/total volume of exports (million yen) 2.482Weighted average of unit value of exports (weight: value of exports) 2.488
Total value of imports (million yen) 543.365Unit value (Total value of imports/total volume of imports, million yen per ton) 1.344Weighted average of unit value of imports (weight: value of imports) 1.400
16
5. Empirical Results on the Relationship between Output Unit Values and Factor Intensities
• Estimate equations (3.15)-(3.18) by SUR estimations subject to the constraint expressed by equation (3.19)----using factory-level data from the Census
tiSttiqS
tU
tS
tiqU
tiqS appL
L
L
L,,,
,
,
,,,
,,, lnlnlnlnln
tiKttiqK
tU
t
tiqU
tiq appL
K
L
K,,,
,,,,
,, lnlnlnlnln
tiMttiqM
tU
t
tiqU
tiq appL
M
L
M,,,
,,,,
,, lnlnlnlnln
titiYttiqYt
tU
tiq
tiqU aappY
L
Y
L,,,,
,
,,
,,, lnlnlnlnlnln
17
Table 1. Relationship between factor intensity and unit price: Seemingly Unrelated Regression estimations with constraint
Table 4. Relationship between factor intensity and unit price: Seemingly Unrelated Regression estimations without constraint, based on data offactories belonging to firms with no additional factory and whose headquarters are located in the same place
Appendix Table 2. Relationship between factor intensity and unit production cost: Seemingly Unrelated Regression estimations without constraint
5. Robustness checks: Relationship between Unit Production Costs and Factor Intensities
22
Appendix Table 3. Relationship between factor intensity and unit price: Seemingly Unrelated Regression estimations with constraint--- Including multi-product establishments ---
5. Robustness checks: Relationship between Output Unit Values and Factor Intensities including Multi-Product Establishments
23
6. Calculated Factor Contents in VIIT (contd.)• Using unit value information taken from the CM and
the trade statistics as well as data on factor intensities, we estimate the factor contents of Japan’s VIIT.
• For number of white-collar workers embodied in Japan’s exports for commodity n are calculated as:
0 ,,
0 ,,
,,
,,,,,,,,
)(
)(
t
YS
t
YS
p tttnDt
p tttnEt
tnD
tnDStnEtnES
dppp
dppp
Y
LYL
24
Estimated
Unknown
6. Calculated Factor Contents in VIIT (contd.)
• Assuming that φE, n, t(pn, t) and φI, n, t(pt) follow a log normal distribution,
μE : log of unit value of Japan’s exports
μD : average of the factory-level unit values in logarithm
σE : standard deviation of the distribution functions of exports
σD : standard deviation of the distribution functions of all shipments by single-product factories
222
,,
,,,,,,,, 2
1exp DEYSDEYS
tnD
tnDStnEtnES Y
LYL
25
6. Calculated Factor Contents in VIIT (contd.)• Due to data constraints, we use average unit value
differences (μE – μD, μI – μD) at the broad industry level.
• Average difference between ln(unit value for exporting factories) and ln(unit value for non-exporting factories), calculated using the CM for 2001-2004.
• Average difference between ln(export unit value) and ln(import unit value), calculated using the TS
2001-2004 Average 1990Census of Manufactures Trade Statistics Trade Statistics
Export -
Import**
Export -
Import**
Estimate relative unit values for domestic shipments, exports, and imports
** Average value of HS 6-digit commodity-level "ln(export unit value)-ln(import unit value)" using the HS 6-digitcommodity-level trade values as weights.
Notes: * Average value of 6-digit commodity-level "ln(unit value for exporting factories)-ln(unit value for non-exportingfactories)" using the 6-digit commodity-level shipments as weights.
Tables 8 & 9. Estimated factor contents of net exports
• As for the relationship b/w the unit value of a product and its white-collar labor intensity, the significant and positive relationship we find is important empirical evidence which supports the assumption widely employed in theoretical models.
• On the other hand, we find that the widely employed assumption that commodities with higher prices are more physical capital-intensive does not always hold.
• The results of the factor contents of trade estimation suggests that the implication of international trade on the domestic factor markets should be very different if we take account of VIIT.
29
8. Extensions• Incorporate headquarter-level data in our analysis in
order to take account of white-collar tasks provided by headquarters. Using information from “Kigyo Katsudo Kihon Chosa (BSBSA)?
• What is the definition of “skill”? We may use the wage information as a proxy of skill.
• Distinguish between intra-firm trade and inter-firm trade? If we can match the trade statistics with the firm- or plant-level data, it would be possible. (c.f. France, U.S.)