Input–output overview

This page provides an overview of input–output analysis, establishing notations and conventions used in other pages. It then introduces the ADB MRIO tables and demonstrates how they are converted from Excel to Parquet files (process-mrios.ipynb) and how key values are extracted (summary-table.ipynb).

The input–output framework

Let there be $G$ economies in the world, indexed by $r,s = 1,...,G$. Production in each economy is divided into $N$ sectors, indexed by $i,j = 1,...,N$. Production is assumed to be done in fixed proportions, also called Leontief production, so that the output of an economy-sector $(r,i)$, denoted $x_{(r,i)}$, is given by

$$ \text{Purchases:} \qquad x_{(r,i)} = z_{(1,1),(r,i)} + z_{(1,2),(r,i)} + ... + z_{(s,j),(r,i)} + ... + z_{(G,N),(r,i)} + va_{(r,i)} $$

where $z_{(s,j),(r,i)}$ are inputs purchased by $(r,i)$ from $(s,j)$ and $va_{(r,i)}$ is $(r,i)$ value-added. One may also call $z$ "intermediate inputs" and $va$ "primary inputs". Note that variable subscripts denote flows from left to right, so that $z_{(s,j),(r,i)}$ means inputs are flowing from $(s,j)$ to $(r,i)$. An asterisk means all entities, as in $z_{(s,j),*}$ or $z_{*,(r,i)}$.

Output of $(r,i)$ is either consumed or used as inputs:

$$ \text{Sales:} \qquad x_{(r,i)} = z_{(r,i),(1,1)} + z_{(r,i),(1,2)} + ... + z_{(r,i),(u,i)} + ... + z_{(r,i),(G,N)} + y_{(r,i),1} + ... + y_{(r,i),u} + ... + y_{(r,i),G} $$

where $y_{(r,i),u}$ are $(r,i)$ output consumed in economy $u$. Market clearing is assumed to always hold, so the above equations are equal.

These relationships are more neatly presented in a table. For the case of three economies ${C, J, U}$ and two sectors ${1,2}$, the full table is as follows:

The $GN$ equations of purchases are arranged in columns while the $GN$ equations of sales are arranged in rows. It is clear that for larger $G$ and $N$, representation in table form becomes unwieldy. One fix would be to collect economy-specific terms into matrices and vectors:

Uppercase letters in bold denote matrices while lowercase letters in bold denote vectors. These may further be collected into larger matrices and vectors: all $\mathbf{Z}_{sr}$'s into the $GN \times GN$ matrix $\mathbf{Z}$, all $\mathbf{y}_{sr}$'s into the $GN \times G$ matrix $\mathbf{Y}$, all $\mathbf{va}_s$'s into the $1 \times GN$ vector $\mathbf{va}$, and all $\mathbf{x}_s$'s into the $GN \times 1$ vector $\mathbf{x}$. The sales equation may be rewritten as

$$ \mathbf{x} = \mathbf{Z} \cdot \mathbf{i}_{GN} + \mathbf{Y} \cdot \mathbf{i}_G, $$

where $\mathbf{i}_M = [1,1,...,1]'$ is a vector of 1's with length $M$ that serves to sum up $\mathbf{Z}$ and $\mathbf{Y}$ by rows. It will be useful to separately denote the vector $\mathbf{Y} \cdot \mathbf{i}_G$ as $\mathbf{y}$, so the above can be written more simply as

$$ \mathbf{x} = \mathbf{Zi} + \mathbf{y}. $$

Gross exports are the total sales of an economy-sector to another economy. To get an expression for this, the $\mathbf{Z}$ and $\mathbf{Y}$ matrices must be split between domestic and foreign sales:

$$ \begin{align} & \mathbf{Z} = \mathbf{Z}^d + \mathbf{Z}^f \\ & \mathbf{Y} = \mathbf{Y}^d + \mathbf{Y}^f \end{align} $$

Visualizing this using the three-economy, two-sector example,

$$ \begin{bmatrix} \mathbf{Z}_{CC} & \mathbf{Z}_{CJ} & \mathbf{Z}_{CU} \\ \mathbf{Z}_{JC} & \mathbf{Z}_{JJ} & \mathbf{Z}_{JU} \\ \mathbf{Z}_{UC} & \mathbf{Z}_{UJ} & \mathbf{Z}_{UU} \\ \end{bmatrix} = \begin{bmatrix} \mathbf{Z}_{CC} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{Z}_{JJ} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{Z}_{UU} \\ \end{bmatrix} + \begin{bmatrix} \mathbf{0} & \mathbf{Z}_{CJ} & \mathbf{Z}_{CU} \\ \mathbf{Z}_{JC} & \mathbf{0} & \mathbf{Z}_{JU} \\ \mathbf{Z}_{UC} & \mathbf{Z}_{UJ} & \mathbf{0} \\ \end{bmatrix} $$

$$ \begin{bmatrix} \mathbf{y}_{CC} & \mathbf{y}_{CJ} & \mathbf{y}_{CU} \\ \mathbf{y}_{JC} & \mathbf{y}_{JJ} & \mathbf{y}_{JU} \\ \mathbf{y}_{UC} & \mathbf{y}_{UJ} & \mathbf{y}_{UU} \\ \end{bmatrix} = \begin{bmatrix} \mathbf{y}_{CC} & \mathbf{0} & \mathbf{0} \\ \mathbf{0} & \mathbf{y}_{JJ} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} & \mathbf{y}_{UU} \\ \end{bmatrix} + \begin{bmatrix} \mathbf{0} & \mathbf{y}_{CJ} & \mathbf{y}_{CU} \\ \mathbf{y}_{JC} & \mathbf{0} & \mathbf{y}_{JU} \\ \mathbf{y}_{UC} & \mathbf{y}_{UJ} & \mathbf{0} \\ \end{bmatrix} $$

The exports vector is defined as

$$ \mathbf{e} \equiv \mathbf{Z}^f \cdot \mathbf{i}_{GN} + \mathbf{Y}^f \cdot \mathbf{i}_{G} = \mathbf{Z}^f \mathbf{i} + \mathbf{y}^f. $$

It is also useful to construct an exports matrix $\mathbf{E}$ that identifies the destinations of each economy-sector's exports. This is done by post-multiplying an aggregator matrix to the $GN \times GN$ matrix $\mathbf{Z}^f$ to turn it into a $GN \times G$ matrix. Thus,

$$ \mathbf{E} \equiv \mathbf{Z}^f \cdot (\mathbf{I}_G \otimes \mathbf{i}_N) + \mathbf{Y}^f, $$

where $\otimes$ denote a Kronecker product. Written out,

$$ \begin{align*} \mathbf{E} & \equiv \begin{bmatrix} 0 & z_{C1,J1} + z_{C1,J2} & z_{C1,U1} + z_{C1,U2} \\ 0 & z_{C2,J1} + z_{C2,J2} & z_{C2,U1} + z_{C2,U2} \\ z_{J1,C1} + z_{J1,C2} & 0 & z_{J1,U1} + z_{J1,U2} \\ z_{J2,C1} + z_{J2,C2} & 0 & z_{J2,U1} + z_{J2,U2} \\ z_{U1,C1} + z_{U1,C2} & z_{U1,J1} + z_{U1,J2} & 0 \\ z_{U2,C1} + z_{U2,C2} & z_{U2,J1} + z_{U2,J2} & 0 \\ \end{bmatrix} + \begin{bmatrix} 0 & y_{C1,J} & y_{C1,U} \\ 0 & y_{C2,J} & y_{C2,U} \\ y_{J1,C} & 0 & y_{J1,U} \\ y_{J2,C} & 0 & y_{J2,U} \\ y_{U1,C} & y_{U1,J} & 0 \\ y_{U2,C} & y_{U2,J} & 0 \\ \end{bmatrix} \\ & = \begin{bmatrix} 0 & e_{C1,J} & e_{C1,U} \\ 0 & e_{C2,J} & e_{C2,U} \\ e_{J1,C} & 0 & e_{J1,U} \\ e_{J2,C} & 0 & e_{J2,U} \\ e_{U1,C} & e_{U1,J} & 0 \\ e_{U2,C} & e_{U2,J} & 0 \\ \end{bmatrix} = \begin{bmatrix} \mathbf{0} & \mathbf{e}_{CJ} & \mathbf{e}_{CU} \\ \mathbf{e}_{JC} & \mathbf{0} & \mathbf{e}_{JU} \\ \mathbf{e}_{UC} & \mathbf{e}_{UJ} & \mathbf{0} \\ \end{bmatrix} \end{align*} $$

The technical coefficient $a_{(s,j),(r,i)}$ is the share of inputs from $(s,j)$ in the output of $(r,i)$: $a_{(s,j),(r,i)} \equiv z_{(s,j),(r,i)}/x_{(r,i)}$. Collect all these into the $GN \times GN$ matrix of technical coefficients $\mathbf{A}$. This may be used to rewrite $\mathbf{x} = \mathbf{Zi} + \mathbf{y}$ as

$$ \mathbf{x} = \mathbf{Ax} + \mathbf{y}. $$

Solving for $\mathbf{x}$ gives

$$ \mathbf{x} = (\mathbf{I} - \mathbf{A})^{-1} \mathbf{y} = \mathbf{By}, $$

where the $GN \times GN$ matrix $\mathbf{B}$ is called the global Leontief inverse matrix.

VB decomposition

The equations $\mathbf{x} = \mathbf{Ax} + \mathbf{y}$ and $\mathbf{x} = \mathbf{By}$ are central to analyzing cross-economy and cross-sectoral linkages. It is clearer to see this if it is rewritten to isolate a single economy $s$:

$$ \begin{align} \mathbf{x}_s &= \sum^G_r \mathbf{A}_{sr} \mathbf{x}_{r} + \sum^G_r \mathbf{y}_{sr} \\ &= \sum^G_r \sum^G_u \mathbf{B}_{sr} \mathbf{y}_{ru} \end{align} $$

The first line says that $s$'s output $\mathbf{x}_s$ is used as intermediates in $r$'s production or sold as final goods to $r$ (for all $r=1,...,G$). The output of each $r$ can in turn be used as intermediates by other economies, whose outputs are then used by other economies, and so on in a potentially infinite series of production stages. The second line summarizes these to identify the final landing stage of $s$'s output. The product $\mathbf{B}_{sr} \mathbf{y}_{ru}$ is $s$ output that is "completed" into a final good by $r$, which then sends it to $u$ for final absorption.

In most analyses, value-added rather than output is the preferred metric. Define the vector $\mathbf{v}$ with $(s,i)$-th element $v_{(s,i)} \equiv va_{(s,i)}/x_{(s,i)}$. This gives the value-added-to-output ratio for each economy-sector. It follows that $\sum_{(s,j)} a_{(s,j),(r,i)} + v_{(r,i)} = 1$. Premultiplying this to the above converts everything to value-added terms:

$$ \mathbf{v}_s \mathbf{x}_s \equiv va_s = \mathbf{v}_s \sum^G_r \sum^G_u \mathbf{B}_{sr} \mathbf{y}_{ru} $$

This expression gives the value-added generated in economy $s$ that is eventually consumed in economy $u$. It can be tweaked to measure other flows. For example, $\mathbf{v}_s \mathbf{B}_{sr} \mathbf{y}_{ru}$ considers $s$ value-added embodied in final goods completed in $r$ that are sold to $u$. To measure $s$ value-added embodied in $r$'s total exports, one may instead write $\mathbf{v}_s \mathbf{B}_{sr} \mathbf{e}_{r*}$. These expressions are called VB decompositions and they serve to identify the value-added origins of certain quantities.

Even more specific flows may be derived by defining input use structures for domestic intermediates $\mathbf{Z}^d$ and foreign intermediates $\mathbf{Z}^f$ separately, yielding $\mathbf{A}^d$ and $\mathbf{A}^f$ where $\mathbf{A} = \mathbf{A}^d + \mathbf{A}^f$. Equation $\mathbf{x} = \mathbf{Ax} + \mathbf{y}$ can be rewritten as

$$ \mathbf{x} = (\mathbf{A}^d \mathbf{x} + \mathbf{y}^d) + (\mathbf{A}^f \mathbf{x} + \mathbf{y}^f). $$

Moreover, since $\mathbf{Z}^f \mathbf{i} = \mathbf{A}^f \mathbf{x}$, the exports vector can also be rewritten as

$$ \mathbf{e} = \mathbf{A}^f \mathbf{x} + \mathbf{y}^f. $$

Plugging this into the above and solving for $\mathbf{x}$,

$$ \begin{align} \mathbf{x} &= (\mathbf{A}^d \mathbf{x} + \mathbf{y}^d) + \mathbf{e} \\ &= (\mathbf{I} - \mathbf{A}^d)^{-1} (\mathbf{y}^d + \mathbf{e}) \\ &= \mathbf{B}^d (\mathbf{y}^d + \mathbf{e}). \end{align} $$

The matrix $\mathbf{B}^d$ is called the local Leontief inverse matrix. Its interpretation is the same as the $\mathbf{B}$ matrix, except it assumes an input structure that precludes buying and selling inputs abroad. As such, only the block diagonal elements are non-zero. This isolates the purely domestic portion of production. Compare $\mathbf{v}_s \mathbf{B}_{ss} \mathbf{y}_{ss}$ and $\mathbf{v}_s \mathbf{B}^d_{ss} \mathbf{y}_{ss}$. While they both meaure $s$ value-added in its own final consumption, the first expression allows for some processing abroad while the second restricts it to purely domestic linkages. This will be crucial in disentangling direct and indirect trading.

Sector breakdown

Note that $\mathbf{v}_s \mathbf{x}_s$ ends up summing sector-level quantities into the aggregate level. However, breaking this down again by sectors is not straightforward as there are several approaches one can take. To see this, consider the case of $\mathbf{v}_C \mathbf{B}_{CJ} \mathbf{y}_{JU}$ — value-added from $C$ completed in $J$ and absorbed in $U$. Writing this out,

$$ \begin{bmatrix} v_{C1} & v_{C2} \\ \end{bmatrix} \begin{bmatrix} b_{C1, J1} & b_{C1, J2} \\ b_{C2, J1} & b_{C2, J2} \\ \end{bmatrix} \begin{bmatrix} y_{J1, U} \\ y_{J2, U} \\ \end{bmatrix}. $$

This results in the sum of four terms:

$$ v_{C1} b_{C1, J1} y_{J1, U} + v_{C1} b_{C1, J2} y_{J2, U} + v_{C2} b_{C2, J1} y_{J1, U} + v_{C2} b_{C2, J2} y_{J2, U} $$

Breaking this down by sector involves grouping these terms under either sector 1 and 2. There are two ways to do this:

	Sector 1	Sector 2
Option 1	$v_{C1} b_{C1, J1} y_{J1, U}$ $v_{C1} b_{C1, J2} y_{J2, U}$	$v_{C2} b_{C2, J1} y_{J1, U}$ $v_{C2} b_{C2, J2} y_{J2, U}$
Option 2	$v_{C1} b_{C1, J1} y_{J1, U}$ $v_{C2} b_{C2, J1} y_{J1, U}$	$v_{C1} b_{C1, J2} y_{J2, U}$ $v_{C1} b_{C1, J2} y_{J2, U}$

The first approach groups sectors by the origin of value-added. The second approach groups sectors by what $J$ exports to $U$. These are called, respectively, the sector breakdown by origin sector and by export sector. They are obtained by diagonalizing either $\mathbf{v}_C$ or $\mathbf{v}_{C} \mathbf{B}_{CJ}$. To demonstrate,

$$ \begin{alignat*}{3} & \hat{\mathbf{v}}_C \mathbf{B}_{CJ} \mathbf{y}_{JU} & &= \begin{bmatrix} v_{C1} & 0 \\ 0 & v_{C2} \\ \end{bmatrix} \begin{bmatrix} b_{C1, J1} & b_{C1, J2} \\ b_{C2, J1} & b_{C2, J2} \\ \end{bmatrix} \begin{bmatrix} y_{J1, U} \\ y_{J2, U} \\ \end{bmatrix}\\ & & &= \begin{bmatrix} v_{C1} ( b_{C1, J1} y_{J1, U} + b_{C1, J2} y_{J2, U} ) \\ v_{C2} ( b_{C2, J1} y_{J1, U} + b_{C2, J2} y_{J2, U} ) \\ \end{bmatrix} \\ \\ & \widehat{\mathbf{v}_C \mathbf{B}_{CJ}} \mathbf{y}_{JU} & &= \begin{bmatrix} v_{C1} b_{C1, J1} + v_{C2} b_{C2, J1} & 0 \\ 0 & v_{C1} b_{C1, J2} + v_{C2} b_{C2, J2} \\ \end{bmatrix} \begin{bmatrix} y_{J1, U} \\ y_{J2, U} \\ \end{bmatrix} \\ & & &= \begin{bmatrix} ( v_{C1} b_{C1, J1} + v_{C2} b_{C2, J1} ) y_{J1, U} \\ ( v_{C1} b_{C1, J2} + v_{C2} b_{C2, J2} ) y_{J2, U} \\ \end{bmatrix} \end{alignat*} $$

More elaborate decompositions allow for more approaches. For example, consider $\mathbf{v}_C \mathbf{B}^d_{CC} \mathbf{A}_{CJ} \mathbf{B}^d_{JJ} \mathbf{y}_{JU}$ — value-added from $C$ sent as intermediates to $J$, who completes it into final goods that are then exported to $U$. In this case, sectors may be broken down by (1) value-added origin, (2) the sector in $C$ that exports to $J$, (3) the sector in $J$ that imports from $C$, and (4) the sector in $J$ that exports to $U$. The particular sector breakdown chosen will depend on the research question at hand.

The ADB MRIO

The Asian Development Bank (ADB) Multiregional Input–Output (MRIO) Database is a time series of intercountry input–output tables. Originally an extended version of the World Input–Output Database, 2013 release, it is now maintained and updated yearly by a dedicated team in ADB. Information on cross-sectoral linkages are provided for 72 countries and economies plus a residual “Rest of the world” entity. Each country is divided into 35 sectors, based on Table A2 of Timmer, et al. (2015). There are five final demand categories: household final consumption expenditure (FCE), non-profit institutions serving households FCE, government FCE, gross fixed capital formation, and changes in inventories. A schematic representation of each MRIO table is given below.

Officially published national supply–use tables (SUTs) and/or input–output tables (IOTs) serve as benchmarks in the construction of the ADB MRIO. In each national SUT or IOT, sectoral and product classifications are harmonized to follow the 35 sectors, and whenever necessary, SUTs are transformed into IOTs following the industry technology transformation assumption discussed in European Commission (2008). Published estimates of gross output, gross value added, taxes less subsidies on products, imports, and exports sourced from national statistical agencies and central bank databases are used as control totals. The structure of imports and exports are based on bilateral trade data extracted from the United Nations COMTRADE Database and government trade and balance of payments statistics. Once the national IOTs are integrated into the MRIO, accounts for the sectors of “Rest of the world” are manually and systematically adjusted to ensure consistency with economy–sector totals in the MRIO.

Processing from Excel

Loading the raw Excel file of the MRIO using Pandas results in an unwieldy table:

The notebook process-mrios.ipynb converts this to a machine-readable format:

The cleaned tables are then saved as space-efficient Parquet files in data/interim/.

Extracting key values

The notebook summary-table.ipynb extracts the following key values for each country-sector from the cleaned MRIO tables:

x: total output
zuse: intermediate use
va: value added
zsales: intermediate sales
y: final sales
ez: exports of intermediates
ey: exports of final goods
e: total exports

The tables are first queried using DuckDB's SQL functionality.

import pandas
import duckdb

mrio = duckdb.sql(
    f"""
    SELECT * EXCLUDE(C0)
    FROM read_parquet('../data/interim/{inputfolder}/{file}')
    """
).df()
mrio = mrio.values

Vectors and matrices of interest are then extracted. The custom function zeroout() is described in detail here.

import numpy as np
from functions import zeroout

x = mrio[-1][:(G*N)]
Z = mrio[:(G*N)][:, :(G*N)]
zuse = np.sum(Z, axis=0)
zsales = np.sum(Z, axis=1)
va = np.sum(mrio[-7:-1][:, :(G*N)], axis=0)
Y_big = mrio[:(G*N)][:, (G*N):-1]
Y = Y_big @ np.kron(np.eye(G), np.ones((f, 1)))
Zd = zeroout(Z @ np.kron(np.eye(G), np.ones((N, 1))), inverse=True)
Yd = zeroout(Y, inverse=True)
y = np.sum(Y, axis=1)
ez = np.sum(Zd, axis=1)
ey = np.sum(Yd, axis=1)

The output from this notebook is saved as summary.csv in data/final/.

MRIO countries and sectors

Countries

The MRIO identified 62 countries and economies and a residual Rest of the World entity. In 2022, it was expanded to separately identify an additional 10 countries (numbers 63-72 below).

	MRIO code	Name		MRIO code	Name
1	AUS	Australia	38	SVK	Slovak Republic
2	AUT	Austria	39	SVN	Slovenia
3	BEL	Belgium	40	SWE	Sweden
4	BGR	Bulgaria	41	TUR	Turkey
5	BRA	Brazil	42	TAP	Taipei,China
6	CAN	Canada	43	USA	United States
7	SWI	Switzerland	44	BAN	Bangladesh
8	PRC	People's Republic of China	45	MAL	Malaysia
9	CYP	Cyprus	46	PHI	Philippines
10	CZE	Czech Republic	47	THA	Thailand
11	GER	Germany	48	VIE	Viet Nam
12	DEN	Denmark	49	KAZ	Kazakhstan
13	SPA	Spain	50	MON	Mongolia
14	EST	Estonia	51	SRI	Sri Lanka
15	FIN	Finland	52	PAK	Pakistan
16	FRA	France	53	FIJ	Fiji
17	UKG	United Kingdom	54	LAO	Lao People's Democratic Republic
18	GRC	Greece	55	BRU	Brunei Darussalam
19	HRV	Croatia	56	BHU	Bhutan
20	HUN	Hungary	57	KGZ	Kyrgyz Republic
21	INO	Indonesia	58	CAM	Cambodia
22	IND	India	59	MLD	Maldives
23	IRE	Ireland	60	NEP	Nepal
24	ITA	Italy	61	SIN	Singapore
25	JPN	Japan	62	HKG	Hong Kong, China
26	KOR	Republic of Korea	63	ARG	Argentina
27	LTU	Lithuania	64	COL	Colombia
28	LUX	Luxembourg	65	ECU	Ecuador
29	LVA	Latvia	66	ARM	Armenia
30	MEX	Mexico	67	GEO	Georgia
31	MLT	Malta	68	EGY	Egypt
32	NET	Netherlands	69	KUW	Kuwait
33	NOR	Norway	70	SAU	Saudi Arabia
34	POL	Poland	71	UAE	United Arab Emirates
35	POR	Portugal	72	NZL	New Zealand
36	ROM	Romania	73	RoW	Rest of the world
37	RUS	Russia

Sectors

MRIO code	Name	Short name	ISIC 3.1
c1	Agriculture, hunting, forestry, and fishing	Agriculture	A-B
c2	Mining and quarrying	Mining	C
c3	Food, beverages, and tobacco	Food & beverages	D15-16
c4	Textiles and textile products	Textiles	D17-18
c5	Leather, leather products, and footwear	Leather	D19
c6	Wood and products of wood and cork	Wood	D20
c7	Pulp, paper, printing, and publishing	Paper	D21-22
c8	Coke, refined petroleum, and nuclear fuel	Refined fuels	D23
c9	Chemicals and chemical products	Chemicals	D24
c10	Rubber and plastics	Rubber	D25
c11	Other non-metallic mineral	Other minerals	D26
c12	Basic metals and fabricated metal	Metals	D27-28
c13	Machinery, not elsewhere classified	Other machinery	D29
c14	Electrical and optical equipment	Electricals	D30-33
c15	Transport equipment	Transport equipment	D34-35
c16	Manufacturing, not elsewhere classified; recycling	Other manufacturing	D36-37
c17	Electricity, gas, and water supply	Utilities	E
c18	Construction	Construction	F
c19	Sale and repair of motor vehicles and motorcycles; retail sale of fuel	Sale of motor vehicles	G50
c20	Wholesale trade, except of motor vehicles and motorcycles	Wholesale trade	G51
c21	Retail trade and repair, except of motor vehicles and motorcycles	Retail trade & repair	G52
c22	Hotels and restaurants	Hotels & restaurants	H
c23	Inland transport	Inland transport	I60
c24	Water transport	Water transport	I61
c25	Air transport	Air transport	I62
c26	Other supporting transport activities	Other transport services	I63
c27	Post and telecommunications	Telecommunications	I64
c28	Financial intermediation	Finance	J65-67
c29	Real estate activities	Real estate	K70
c30	Renting of machinery & equipment and other business activities	Other business services	K71-74
c31	Public administration and defence; compulsory social security	Public administration	L
c32	Education	Education	M
c33	Health and social work	Social work	N
c34	Other community, social, and personal services	Other personal services	O
c35	Private households with employed persons	Private households	P

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