Linkages and changing factor use in Indian economy: Implications of emerging trade pattern

Abstract

Globally, a greater component of trade in intermediates—parts and components—is a characteristic of the changing paradigm of international trade. Consequently, alongside the increasing trade openness of the Indian economy, the access to international factors of production has increased through their embodied use during the production of intermediates that are imported. Thus, the emerging trade pattern has the potential to impact the use of factors of production of domestic origin through linkages in the internal economy. This paper makes an assessment of the changing intensity of use of the two factors of production, viz., labor (L) and capital (K), in the economy. The analysis aims to provide an estimate of the impact of import utilization on the use of labor and capital. In the backdrop of a generally declining employment intensity, the employment foregone effect from the use of imported intermediate inputs is observed to have worsened over the period of study. Ironically, this has contributed to lower domestic employment, even in the traditionally labor-intensive sectors. The employment effect of import utilizations is also reflected in the declining share of labor income. The use of capital embodied in imported intermediates has contributed to increasing the capital intensity of the economy despite the low domestic capital investment. This underscores a greater dependency on capital-intensive imports. While import reliance has increased for both employment and the capital goods through their embodied use in the imported inputs, the dependency on imported capital has been stronger. A higher relative use of capital (K-to-L) indicates that the production method is relatively capital-intensive, thus requiring more capital goods and investment. The findings resolve the puzzle of India’s increasing relative use of capital alongside a slowdown of domestic investments in productive capital. The deficit on domestic investment has been compensated through import utilizations of capital goods.

Appendices

Appendix 1 Model formulation

A1.1 Basics of the input–output model

The I–O model represents intersectoral linkages through demand and supply relationships among sectors of the economy. The interactions are essentially transaction flows from a sector i to another sector j indicating value of commodity transaction from the ith input providing sector to the jth output producing sector. The mathematical representation of the model is conventionally through the use of matrices. The cost structure of a producing sector is presented in a column providing commodity flows of all inputs (material and service) used. The column also includes expenditure on account of the use of factors of production (i.e., value addition as a composite of labor and capital) and net taxes paid by the sector. The output supply of a sector under consideration can be consumed as intermediate input for sectors of the economy, or as a final good. The supply distribution is presented through the flows within a row corresponding to the sector.

Consider the economy with n (a positive integer) sectors inclusive of the production and service activities. Thus, in an economy the output of each sector (column vector X) is either consumed as an intermediate input (matrix Z of transaction flows) in the production process of another sector, or is consumed as a final good (column vector Y). Elements of the matrix Z (of size nXn) are X_ij representing the intersectoral intermediate flows from sector i to the sector j as follows:

$$Z = \left[ {X_{ij} } \right] = \left[ {\begin{array}{*{20}c} {X_{11} } & \cdots & {X_{1n} } \\ \vdots & \ddots & \vdots \\ {X_{n1} } & \cdots & {X_{nn} } \\ \end{array} } \right],\;{\text{where}}\;i,\;j = 1,2, \ldots ,n$$

(1)

$${\text{Similarly}},\;X = \left[ {X_{i} } \right] = \left[ {\begin{array}{*{20}c} {X_{1} } \\ \vdots \\ {X_{n} } \\ \end{array} } \right] \;{\text{and}}\;Y = \left[ {Y_{i} } \right] = \left[ {\begin{array}{*{20}c} {Y_{1} } \\ \vdots \\ {Y_{n} } \\ \end{array} } \right],\;{\text{where}}\;i = 1,2, \ldots ,n$$

(2)

The disposition of total output is compactly written in a matrix notation as:

$$\underbrace {Z}_{{{\text{intermediate}}\;{\text{consumption}} }}*\underbrace {i}_{{{\text{identity}}\;{\text{column}}\;{\text{vector}}}} + \underbrace {Y}_{{{\text{final}}\;{\text{use}}}} = \underbrace {X}_{{{\text{total}}\;{\text{output}}}}$$

(3)

The intersectoral relations in the economy are represented through the technical coefficient matrix, A (nXn) whose ijth element shows the amount of input from the ith sector required to produce one unit output of the jth sector. The matrix A is also called as the direct coefficient matrix or technology matrix as it shows the dependence of inter-industry flows on total output of each sector of the economy and is defined as:

$$A = \left[ {a_{{{\text{ij}}}} } \right] ,\;{\text{where}}\;a_{{{\text{ij}}}} = \frac{{X_{{{\text{ij}}}} }}{{X_{j} }},\;{\text{where}}\;i,\;j = 1,2, \ldots ,n$$

(4)

$${\text{Thus}},\;A = Z*\hat{X}^{ - 1} \mathop \Rightarrow \limits_{{}} Z = A*\hat{X}$$

(5)

where $\widehat{\mathrm{X}}$ is a diagonal matrix of the sector outputs.¹⁹

Using Eq. (5) in Eq. (3), the output is expressed in terms of technology matrix as:

$$X = \left( {I - A} \right)^{ - 1} *Y$$

(6)

$${\text{Let}},\;L = \left( {I - A} \right)^{ - 1} = \left[ {r_{{{\text{ij}}}} } \right],\;{\text{where}}\;i,\;j = 1,2, \ldots ,n$$

(7)

The matrix L is called the Leontief inverse and shows the dependence of gross output (X) on final demand (Y). It is also referred to as the total requirement matrix and is inclusive of the indirect effects which occur due to multiple and nested rounds of interrelationship among sectors.

A1.2 Separating imported and domestically produced intermediate requirements

The separation of imported and the domestically produced intermediate inputs, as needed for implementation of the methodology adopted in the present paper, requires separating the transaction flows (X_ij) into two additive components. Individual transactions in the intermediate matrix are expressed as the sum of corresponding domestic and import flows. Thus, we write the following:

$$X_{{{\text{ij}}}} = D_{{{\text{ij}}}} + M_{{{\text{ij}}}}$$

(8)

Accordingly, the corresponding output coefficients of domestic and imports requirements can be written as:

$$D = \left[ {d_{{{\text{ij}}}} } \right],\;{\text{where}}\;d_{{{\text{ij}}}} = \frac{{D_{{{\text{ij}}}} }}{{X_{j} }},\;{\text{where}}\;i,\;j = 1,2, \ldots ,n$$

(9)

$${\text{and}}\;M = \left[ {m_{{{\text{ij}}}} } \right],\;{\text{where}}\;m_{{{\text{ij}}}} = \frac{{M_{{{\text{ij}}}} }}{{X_{j} }},\;{\text{where}}\;i,\;j = 1,2, \ldots ,n$$

(10)

$${\text{Thus}}\;{\text{referring}}\;{\text{to}}\;{\text{Eq}}\;\left( 8 \right),\;a_{{{\text{ij}}}} = d_{{{\text{ij}}}} + m_{{{\text{ij}}}}$$

(11)

Define, the total domestic requirement matrix of inputs as

$$S = \left( {I - D} \right)^{ - 1} = \left[ {s_{{{\text{ij}}}} } \right],\;{\text{where}}\;i,\;j = 1,2, \ldots ,n$$

(12)

An element s_ij provides the total input requirements of all domestically produced inputs (material and services) from sector i for a unit output in the jth sector.

A1.3 Estimating factor proportions

Factor requirements of domestically produced inputs

In an I–O framework, the direct factor coefficients are required to initiate the estimation of total factor use in a given sector. The direct factor coefficients, ${f}_{j}^{k}$, measure the amount of the kth production factor directly used for a unit output of the jth sector. For instance, a direct labor (capital) coefficient of a sector measures the amount of labor (capital) used directly in the sector activity. Since this information is not explicitly available for different factors of production from within the IOTT, the direct coefficient values are sourced from the KLEMS database of the RBI, 2020.²⁰ These coefficients are then integrated into the I-O model through their interaction with the total requirement matrix, S.²¹ Details are discussed as follows.

For a kth factor of production, consider the diagonal matrix of direct coefficients, $\widehat{{f}^{k}}$ as shown in Eq. (15) where k = employment, labor, capital.²²

$$\widehat{{f}^{k}}=\left[\begin{array}{c}{f}_{1}^{k}\\ 0\\ \begin{array}{c}\vdots \\ 0\end{array}\end{array}\begin{array}{c}0\\ {f}_{2}^{k}\\ \begin{array}{c}\vdots \\ 0\end{array}\end{array}\begin{array}{c}\dots \\ \dots \\ \begin{array}{c}\ddots \\ \dots \end{array}\end{array}\begin{array}{c}0\\ 0\\ \begin{array}{c}0\\ {f}_{n}^{k}\end{array}\end{array}\right]$$

(13)

Let ${\mathrm{F}}_{j}^{k}$ denote the total use of kth factor required for production of one unit output of the jth sector. Following the methodology suggested by Riedel (1975), the value of ${\mathrm{F}}_{j}^{k}$ is obtained by interacting (multiplying) $\widehat{{f}^{k}}$ with the total domestic requirement matrix S and adding across rows within a column. Thus, for all k and j = 1,2,…,n, we write the following equation:

$$\left[ {F_{j}^{k} } \right] = \left[ {\begin{array}{*{20}c} {F_{1}^{k} } & {F_{2}^{k} } & {\begin{array}{*{20}c} \ldots & {F_{n}^{k} } \\ \end{array} } \\ \end{array} } \right] = \widehat{{f^{k} }}*S$$

$$\scriptsize = \underbrace {{\left[ {\begin{array}{*{20}c} {f_{1}^{k} } \\ 0 \\ {\begin{array}{*{20}c} \vdots \\ 0 \\ \end{array} } \\ \end{array} \begin{array}{*{20}c} 0 \\ {f_{2}^{k} } \\ {\begin{array}{*{20}c} \vdots \\ 0 \\ \end{array} } \\ \end{array} \begin{array}{*{20}c} \ldots \\ \ldots \\ {\begin{array}{*{20}c} { \ddots } \\ \ldots \\ \end{array} } \\ \end{array} \begin{array}{*{20}c} 0 \\ 0 \\ {\begin{array}{*{20}c} 0 \\ {f_{n}^{k} } \\ \end{array} } \\ \end{array} } \right]}}_{direct \ use\ of \ kth\ factor \ per\ unit \ output \ of \ sector\ j}$$

$$ *\underbrace {{\left[ {\begin{array}{*{20}c} {s_{11} } \\ {s_{21} } \\ {\begin{array}{*{20}c} \vdots \\ {s_{n1} } \\ \end{array} } \\ \end{array} \begin{array}{*{20}c} {s_{12} } \\ {s_{22} } \\ {\begin{array}{*{20}c} \vdots \\ {s_{n2} } \\ \end{array} } \\ \end{array} \begin{array}{*{20}c} \ldots \\ \ldots \\ {\begin{array}{*{20}c} { \ddots } \\ \ldots \\ \end{array} } \\ \end{array} \begin{array}{*{20}c} {s_{1n} } \\ {s_{21} } \\ {\begin{array}{*{20}c} \vdots \\ {s_{nn} } \\ \end{array} } \\ \end{array} } \right]}}_{total\ domestic\ input\ from \ sector\ i \ required \ for\ a\ unit \ output \ of \ sector \ j}$$

$$ = \underbrace {{\left[ {\begin{array}{*{20}c} {f_{1}^{k} s_{11} } \\ {f_{2}^{k} s_{21} } \\ {\begin{array}{*{20}c} \vdots \\ {f_{n}^{k} s_{n1} } \\ \end{array} } \\ \end{array} \begin{array}{*{20}c} {f_{1}^{k} s_{12} } \\ {f_{2}^{k} s_{22} } \\ {\begin{array}{*{20}c} \vdots \\ {f_{n}^{k} s_{n2} } \\ \end{array} } \\ \end{array} \begin{array}{*{20}c} \ldots \\ \ldots \\ {\begin{array}{*{20}c} { \ddots } \\ \ldots \\ \end{array} } \\ \end{array} \begin{array}{*{20}c} {f_{1}^{k} s_{1n} } \\ {f_{2}^{k} s_{21} } \\ {\begin{array}{*{20}c} \vdots \\ {f_{n}^{k} s_{nn} } \\ \end{array} } \\ \end{array} } \right]}}_{use\ of\ kth\ factor \ in\ domestic\ production\ of \ input\ i \ used\ in\ one\ unit\ of \ sector \ j}$$

(14)

$$= \left[ {\begin{array}{*{20}c} {\mathop \sum \limits_{i = 1}^{n} f_{i}^{k} s_{i1} } & {\mathop \sum \limits_{i = 1}^{n} f_{i}^{k} s_{i2} } & {\begin{array}{*{20}c} \ldots & {\mathop \sum \limits_{i = 1}^{n} f_{i}^{k} s_{in} } \\ \end{array} } \\ \end{array} } \right]$$

(15)

Summation of the elements within a column of the matrix on RHS of Eq. (15) provides ${F}_{j}^{k}$, as the total (direct and indirect) requirement of the kth factor through its use in production of all inputs used in one unit output of the sector represented in the column j. Equation (15) is further used to estimate total factor requirement to meet the final demand or any sub-component of final demand, e.g., exports (E).²³ Factor requirement for of the kth factor to meet the export demand, ${F}_{E}^{k}$ as given as:

$${F}_{E}^{k}=\left[{F}_{j}^{k}\right]*\widehat{E}=\left[\begin{array}{ccc}\sum_{i=1}^{n}{f}_{i}^{k}{s}_{i1}& \sum_{i=1}^{n}{f}_{i}^{k}{s}_{i2}& \begin{array}{cc}\dots & \sum_{i=1}^{n}{f}_{i}^{k}{s}_{in}\end{array}\end{array}\right]*\left[\begin{array}{c}{E}_{1 }\\ 0\\ \begin{array}{c}\vdots \\ 0\end{array}\end{array}\begin{array}{c}0\\ {E}_{2 }\\ \begin{array}{c}\vdots \\ 0\end{array}\end{array}\begin{array}{c}\dots \\ \dots \\ \begin{array}{c}\ddots \\ \dots \end{array}\end{array}\begin{array}{c}0\\ 0\\ \begin{array}{c}0\\ {E}_{n}\end{array}\end{array}\right]$$

(16)

Thus, we have,

$${F}_{E}^{k}=\left[\begin{array}{ccc}\left(\sum_{i=1}^{n}{f}_{i}^{k}{s}_{i1}\right)*{E}_{1 }& \left(\sum_{i=1}^{n}{f}_{i}^{k}{s}_{i2}\right)*{E}_{2 }& \begin{array}{cc}\dots & \left(\sum_{i=1}^{n}{f}_{i}^{k}{s}_{in}\right)\end{array}\end{array}*{E}_{n}\right]$$

(17)

The jth element of the row vector in the RHS of Eq. (17) represents the total factor use to meet export demand in the jth sector. Summing over the columns gives requirement of the kth factor to meet the overall exports in the economy, ${F}_{E}^{k}$ as:

$${F}_{E}^{k}=\sum_{j=1}^{n}\left(\left(\sum_{i=1}^{n}{f}_{i}^{k}{s}_{i1}\right)*{E}_{j}\right)$$

(18)

Factor requirements of imported inputs

On the other hand, factor use in imports is not explicitly known due to the unavailability of a foreign production technology matrix, separately for each import partner. Thus, we proxy the factor use in imports through measurement of factors in an equivalent export production (used to earn foreign exchange for purchasing imports). Thus, even though the total requirement coefficients used pertain to domestic technology, their use in the production of the export equivalent of imports provides the required estimate of imported factor use. The proxy computation requires to express imports as a function of — (i) export, and (ii) the production technology used in process of export production of an amount equivalent to imports.

In order to account for factor use in imported inputs, define ${M}_{i}=\sum_{j=1}^{n}{m}_{ji}$ as the direct requirement of all imported inputs (denoted by subscript j) in one unit production of output in the ith sector. Multiplying M_i with s_ij provides the (direct and indirect) import requirement in the ith input used in one unit output of the jth sector. Summing over all inputs (index i) provides the requirement of all imported inputs for a unit output of jth sector, M_j. This is given by the following expression:

$${M}_{j}=\sum_{i=1}^{n}\left({M}_{i}{s}_{ij}\right)=\sum_{i=1}^{n}\left(\sum_{j=1}^{n}{m}_{ji}{s}_{ij}\right)$$

(19)

Total import requirement for a unit export from the economy is based on the structure of the export basket and is represented by e_j as the export share of jth sector. Accordingly, imports requirement for producing export, e_j, of the jth sector are given by M_j*e_j. Further, summation over sector-wise requirements provides total import requirement for the production of exports as shown in Eq. (20).

$$M_{E} = \mathop \sum \limits_{j = 1}^{n} \left( {M_{j} *e_{j } } \right) = \underbrace {{\sum\limits_{j - 1}^{n} {\underbrace {{\left( {\mathop \sum \limits_{i = 1}^{n} \left( {\underbrace {{\mathop \sum \limits_{i = 1}^{n} \underbrace {{m_{ji} }}_{A}*S_{ij} }}_{B}} \right)*e_{j} } \right)}}_{C}} }}_{D}$$

(20)

where the expressions have the following representation:

• A: direct import use of jth input in a unit output of ith sector.

• B: direct and indirect import requirement of all inputs per unit output of jth sector.

• C: import requirement for export of jth sector.

• D: sum of import requirements for all exports.

Equation (20) provides an export equivalence of imports. It shows the amount of imports purchased with the foreign exchange earned from the exports. In other words, M_E is the amount of exports (exchanged) for imports. It may be clarified here that although value of imports are directly available, their factor use cannot be assessed directly due to difference in production technology in the country of origin. Therefore, an export proxy of the import value is used to estimate the factor equivalence in the domestic production.

Estimating import use in production of exports

The use of factor imports in the production of additional exports to exchange for the imported inputs is given by ${F}_{E}^{k}* {M}_{E}$ in the first round of import use. However, the production of exports (to finance the imports) in turn requires the use of imported inputs. This imposes a requirement of ${M}_{E}* {M}_{E}$ units of import, entailing an export equivalent of $\left({F}_{E}^{k}* {M}_{E}\right)*{M}_{E}$ to finance the additional imports. This nesting of import use gives rise to a second round of requirements and continues further. Similarly, the effect of following rounds is measured by multiplying successive terms with ${M}_{E}$. Thus, the multiple round effect of import use is:

$${F}_{E}^{k}+\left({F}_{E}^{k}* {M}_{E}\right)+\left({F}_{E}^{k}* {M}_{E}*{M}_{E}\right)+\dots =\frac{{F}_{E}^{k}}{1-{M}_{E}}$$

(21)

since 0 $\le {M}_{E}\le 1$

It may be noted that the ratio on the RHS of Eq. (21) is a constant, independent of any sector. However, the ratio is different for a given factor of production. The ratio is the value of kth factor required to produce one unit of export in exchange for import. On multiplying the ratio with the import requirement in the jth sector (M_j), we get the factor use equivalent of import.

Factor requirements due to domestic and imported all inputs

The estimate of actual factor use of the kth factor in the jth sector, ${\tilde{F }}_{j}^{k}$, is the sum of – (i) factor use in the production of all domestically produced intermediate inputs (${F}_{j}^{k})$(using Eq. (18)), and (ii) factor use in the imports of jth sector (${M}_{j})$, which is estimated by multiplying M_j with multiple round effects of factor use in production of exports to (earn foreign) exchange to pay for imported inputs (in Eq. (21)).

$${\tilde{F }}_{j}^{k}={F}_{j}^{k}+{M}_{j}\left(\frac{{F}_{E}^{k}}{1-{M}_{E}}\right)$$

(22)

Equation (22) is used separately for the each of the factors of production.

Appendix 2 Description of sectors and broad groups

S. No	Description
1	Agriculture, hunting, forestry, and fishing
2	Mining and quarrying
3	Food products, beverages and tobacco
4	Textiles, textile products, leather and footwear
5	Wood and products of wood
6	Pulp, paper, paper products, printing and publishing
7	Coke, refined petroleum products and nuclear fuel
8	Chemicals and chemical products
9	Rubber and plastic products
10	Other nonmetallic mineral products
11	Basic metals and fabricated metal products
12	Machinery, nec
13	Electrical and optical equipment
14	Transport equipment
15	Manufacturing, nec; recycling
16	Electricity, gas and water supply
17	Construction
18	Trade
19	Hotels and restaurants
20	Transport and storage
21	Post and telecommunication
22	Financial services
23	Business service
24	Public administration and defense; compulsory social security
25	Education
26	Health and social work
27	Other services
	Groups
1–27	All
1	Agriculture
2	Mining
3–15	Manufacturing
16–27	Services

1. nec not elsewhere classified.
2. Source Das et al. 2015.