Statistical processing

Source data

The main sources for compiling supply and use tables in current prices are the following:

• Accounts statistics for non-agricultural private sector (SBS)
• Sales by manufacturing industries (PRODCOM)
• General enterprise statistics
• Manufacturers' purchases of goods and services
• Accounts for public corporations
• Economic accounts for agriculture
• Government finance statistics
• Financial industries and FISIM compiled on a NA basis
• Accounts statistics for non-profit institutions serving households (NPISH)
• Energy accounts
• Balance of payments and external trade statistics
• Household budget survey

The main sources for the compilation of supply and use tables in previous year prices are:

• Producer price indices for goods and services
• Producer price indices for construction
• Construction cost indices
• Consumer price indices and net price indices (consumer price indices excluding taxes)
• Price indices for agricultural sales
• Wage indices
• Unit price indices from import and export statistics
• Volume indicators: Energy supply and use, transportation, final individual consumption expenditure of government

The balancing process of the SUTs serves as a central control of the quality and liability of the data. The compilation of SUTs is not solely to provide a reliable base for IOT, but also to provide a confrontation between estimates from different sources at a very detailed level. See also section 18.4.

The input-output table is almost entirely based on the SUTs. The only exceptions are the elements of Gross value added; Other taxes on production, Compensation of employees and Gross operating surplus and mixed income are all obtained from other sources in the national accounts.

Frequency of data collection

The supply and use tables play a central role in estimating the National Accounts Main Aggregates. Supply and use tables are therefore compiled every year in full detail like every year is a benchmark year. This implies that source data are collected and processed every year with no use of extrapolations of values from previous years. The Danish supply and use tables are released with a delay of 2.5 years, i.e. year t-3.

Preliminary annual supply and use tables are calculated every year for year t-2 at a lower level of detail based somewhat on extrapolations and structures from the most recent final SUT's, available at t-3.

The input-output tables are prepared once a year and disseminated at the same time as the final annual national accounts, and data for this process is collected as soon as the supply and use tables are available in a final version.

Data collection

There is no specific collection of primary data to build the supply and use tables. Data is collected in other parts of Statistics Denmark and delivered to the national accounts in datasets that have already been debugged and prepared.

Data for the input-output tables are available as prepared datasets as well.

Data validation

The initial data validation comprises formal checks including format of the files, internal consistency of the data and checking for any changes in the content of data. Then follows the main steps in the data validation process, which are the following:

• When targets (at the industry level) for total output, input, GFCF etc. are compiled a number of problems are revealed, investigated further and corrected if necessary.
• When the first version of the – unbalanced – SUT file is put together it is necessary to compare the initial estimates of supply for certain product groups with estimated use. A closer study often reveals errors in primary statistics or in the internal compilation process.
• Problems will usually be solved in cooperation with the relevant statistical sources domains. The inquiries are of considerable importance for the quality of the SUT and hence the national accounts.
• In recent years many of the problems have been related to globalization. A “large cases unit” (LCU), established in 2015, monitors the large multinational corporations and their complex business models (profiling) and confronts data reported by these units before they enter the national accounts.

Generally, it can be said that balancing of supply and use tables as a mean of data validation, provides a systematic confrontation of data that captures a lot of inconsistencies. One of the strongest cross-checks is comparing information on supply and demand at the product level (or groups of products).

The complete integration of the input-output tables with the final national accounts and supply and use tables means that the data validation of the input-output tables primarily consists of ensuring that all data found in both statistics are the same.

Upon receipt of Danish supply and use tables as well as input-output tables, Eurostat performs a further series of validity and consistency checks. The error messages and warnings that come back from Eurostat can be divided into three categories:

• Explainable deviations in Danish data from Eurostat's normal. These can be, for example, negative values ​​in certain investment categories. This occurs in Danish data when, for example, investment goods (transport equipment) or large consumer goods (e.g. yachts) are sold (disinvested). These deviations are explained to Eurostat and entered on a list of repeated deviations in the Danish data so that Eurostat does not have to notice them again the following year.

• Errors that occurred in connection with the transformation of Danish data into the format in which data must be reported, including the attachment of all necessary metadata. These errors are corrected as soon as information about them is received and the data is resent to Eurostat.

• Actual errors in supply and use tables and/or input-output tables. These errors are extremely rare, as they would normally have been discovered already in Statistics Denmark's work on compiling and publishing these tables. The few errors that have occurred have been quite small and have already been known to us. In the Danish national accounts, errors in already published data are only corrected in connection with the 5-yearly benchmark revisions, and it is therefore normally difficult to meet Eurostat's desire to correct such errors before the next benchmark revision.

Data compilation

The final year (t-3) supply and use tables (SUT) comprise 117 industries and approximately 2,350 products. Household consumption consists of 83 groups. Individual government consumption contains 32 COICOP-based groups, while non-profit institutions serving households (NPISH) consumption includes 10 COICOP-based categories. Government collective consumption is divided into 10 groups based on COFOG (see also S.3.2). Finally, investment is split into 13 categories, such as buildings, machinery, and R&D. For the first preliminary year (t-2), a more aggregated SUT is compiled, featuring 81 industries, 72 consumption groups, and around 350 products.

Current prices For the final year initial and independent estimates for GDP by the production approach (GDP(P)) and expenditure approach (GDP(E)) are compiled as described below:

• GDP(P): After initial processing of various primary source data (accounting statistics), the data are transferred to a common accounting plan and mapped to national accounts industries within the "Intermediate System". Conceptual adjustments are then made to align the figures with national accounts definitions for production and intermediate consumption.
• GDP(E): The largest share of expenditure-based GDP is calculated using direct estimates for the various expenditure components. The main exceptions are household final consumption expenditure on items such as hotel, restaurant, and dwelling services.

The SUT is then compiled through the following steps:

1. Target totals and product-level values that can be entered directly into the system as predetermined variables are collected. These include all energy-related data, which are compiled independently within the Energy Accounts system.
2. An initial version of the SUT is compiled in three steps:
3. The supply matrix, showing the supply of products by industry, is established. This matrix is normally fixed at this stage and left unaltered throughout the remaining SUT compilation process.
4. An initial version of the use table is created by inflating the previous year’s use table to current price levels. The new target totals for intermediate consumption by industry, final use by COICOP/COFOG groups, and investment categories are then used to update the initial use matrix via a vertical proportional distribution.
5. The intermediate and final use of products is updated through a proportional horizontal distribution of the total supply by product, balancing product supply and use. After this step, the column sums will usually deviate from the use-side targets. Total trade and transport margins, as well as total VAT, may also differ from their respective targets.
6. The initial SUT is adjusted manually to closely examine unresolved imbalances. In many cases, these imbalances reveal errors in primary data or calculations. Adjustments and corrections are entered to create a revised, though not yet final, version of the tables.
7. Discrepancies between totals and targets are eliminated, except where minor differences are deemed acceptable. Trade and transport margins, along with VAT, are adjusted to match their targets. This step is a largely automated process.
8. As a final step, exports by product are split into domestically produced goods and re-exports (imported goods). This split is based on the shares from the previous year. The original breakdown, dating several years back, was based on internal national accounts research. Recently, the size and distribution of re-exports were cross-checked against re-export data from the foreign trade statistics department at Statistics Denmark. The findings showed that the two sets of numbers were surprisingly close.

Previous years prices

All products in the current price SUT are included in the deflation process, and each product is assigned a price index at basic prices (covering production, imports, exports, and consumption). Price indices from the supply side—specifically from production and imports—serve as the primary source. A few exceptions exist, including energy, where volume indicators are used directly. Domestic use at basic prices is deflated using the implicit price index of the residual between total supply and exports, ensuring that each product balances at basic prices. Government individual consumption expenditure is deflated from the output side using volume indicators.

Because output and input are deflated independently, special indices for Gross Value Added (GVA) are not required; GVA is calculated directly through this double-deflation procedure.

Input-output-tables

The Danish input-output tables are based almost entirely on the supply and use tables. Compilation broadly follows Eurostat and UN manual guidelines. Transforming supply and use tables into input-output tables requires a few strong assumptions regarding product flows in the economy. Therefore, choosing the transformation method is a critical aspect of the compilation process. The relevant manuals outline four different methods based on various assumptions. Statistics Denmark produces input-output tables using Method D. This method assumes that "each product has its own fixed sales structure, regardless of which industry produces it." For example, if Industry 1 produces 80% of a product and Industry 2 produces the remaining 20%, all users of this product are assumed to source 80% from Industry 1 and 20% from Industry 2. While this does not always hold true in reality, it is considered the method that introduces the least distortion to the supply and use data. Method D results in an industry-by-industry input-output table.

1. First step: The basic price supply table is split into a domestically produced component and an imported component. Statistics Denmark does not compile a full matrix of imports by intermediate or final use categories. Instead, we use a vector of imports by product (approximately 1,950 products) and a corresponding vector of customs duties on those imported products. Consequently, we calculate a vector of import coefficients to determine the imported share of supply for each product. Since exports are already split into domestic output and re-exports in the supply and use tables, we only need to calculate imports for domestic intermediate and final use. The formula is structured as follows: import_coefficients = (imports - re-exports) / ((domestic output - exports) + (imports - re-exports)) In matrix formulation, the use matrix (excluding exports) is pre-multiplied by a diagonal matrix containing this vector to generate the import matrix. The domestically produced component is the remaining part of the initial use matrix.

2. Second step: The two new use tables are transformed from a product-by-use category format into an industry-by-use category table using Method D. To achieve this, a market-share matrix is calculated from the supply matrix. This product-by-industry market-share matrix shows the proportion of each product produced across the 117 industries. For products not produced in Denmark, rows in the matrix initially contain only zeros. To address this, we maintain and update a list of all products in the system alongside their "characteristic industry"—meaning the industry where the product most likely would have been produced. For instance, bananas are included on this list; though not produced in Denmark, their characteristic industry is Agriculture. Using the market-share matrix, we transform both the domestic use table and the imported use table from products to industries. Thus, for imported products that are also produced in Denmark, we assume they are distributed across foreign industries in the same relative proportions as domestic production. This means that if Industry 1 in Denmark produces 80% of a product and Industry 2 produces the remaining 20%, we assume that 80% of our imports of this product originate from the foreign equivalent of Industry 1 and 20% from Industry 2. If an imported product is not produced in Denmark at all, we assume it is imported entirely from its designated characteristic industry.

3. Third step: The remaining price layers between basic and purchasers' prices must be incorporated into the table. Since the column sums in an input-output table are in purchasers' prices, information regarding margins and taxes must be added alongside the basic price cells. The Danish supply and use table system includes data for each product on basic prices, wholesale and retail margins, product taxes, VAT, and purchasers' prices. The Danish tables do not include separate transport margins, as these are treated as part of wholesale trade margins. Therefore, this text refers exclusively to trade margins. We then compile matrices for margins, product taxes, and VAT using roughly the same methodology as the basic price matrices.The matrix of trade margins is aggregated and allocated to the following three industries:

4. G45 (450000): Wholesale and retail trade margins from the sale of motor vehicles and related items.

5. G46 (460000): Wholesale trade margins.
6. G47 (470000): Retail trade margins.

Wholesale trade margins are allocated to G46, and retail trade margins to G47. The share of margins allocated to G45 is determined through a calculation that reallocates specific margins from G46 and G47, based on past investigations into which products are fully or partially sold by enterprises residing within industry G45. The matrices for net product taxes and VAT are likewise summed and placed at the bottom of the input-output table.

To produce input-output tables in previous years' prices, the exact same procedure is carried out using the supply and use tables in previous years' prices.

As an example of how these input-output tables are applied, Statistics Denmark publishes calculations of import-adjusted growth contributions using the input-output method. This method utilizes the input-output tables and models to calculate the direct and indirect imports generated by individual final demand components. These imports are subsequently deducted from the respective final use components to isolate the Danish-produced share of final demand. Based on these components, which combined constitute Danish GDP, the final contribution of each final demand component to total GDP growth can be determined.

Adjustment

All relevant adjustments are described in the sections above.