# Presentation: 515112

## Deriving Detailed Time Series of Constant Price IO Tables 

- BEA Industry Accounts Directorate Users’ Conference
- October 26, 2007
- Douglas S. Meade
- meade@econ.umd.edu
- http://www.inforum.umd.edu

## Background

- The availability of the time series of 65-sector annual input-output (IO) tables from BEA has been a boon to users of industry data.
- Since 1967, Inforum has used IO data developed by OBE and BEA to build interindustry macro (IM) models that integrate IO and national accounts.
- The newest set of Inforum models is based on the 1997 NAICS benchmark and annual IO tables produced by BEA, and will soon incorporate the 2002 benchmark IO.
- Covered in this talk:
- Why derive these tables?
- What are the steps?
- What’s next?

## Why Detailed, Time Series of Constant Price IO?

- Detail – For many users of industry models and analysis, 65 sectors is not enough.  (Some examples: Defense, Health Care, Environmental, Energy, R&D and Technology, Industry Planning)
- Time Series – Consistent time series are necessary for econometric estimation.  Time series also show the presence of technical and structural change in the economy.
- Constant Prices – For impact analyses, analyses of technical relationships (energy, environmental, technology), the effects of inflation need to be removed to better understand what is happening.

## Inforum Users’ Needs

- Inforum incorporates IO data with National Accounts in a modeling framework that satisfies many users’ needs.
- Department of Commerce/ESA – Analysis of industry impacts of high energy prices, port closures and import restrictions.  Also provided support to *The Digital Economy*.
- Department of Defense, OSD/PA&E – Annual modeling support for DEPPS, which analyzes industry, state and occupational impacts of defense outlays.
- CMS – Long-term projections of health care expenditures, share of health care, medical care price growth, and effects of health care on aggregate productivity growth.
- Integra/Microbilt – Provide detailed industry forecasts for their clients to use for marketing, acquisition and planning.

## Inforum Users’ Needs (cont.)

- METI (a Japanese ministry) – Inforum provided updates of the U.S. Benchmark IO table.
- Booz-Allen Hamilton – Developed detailed scenarios of East Asia/US trade scenarios.
- Mitre – Analysis of alternative health care plans.
- Securing America’s Energy Future (SAFE) – Analysis of the effects of policies to reduce oil dependence.
- Price Waterhouse Coopers – Analysis of industry and distributional effects of proposed tax law changes.

## Examples of Detail Used by Inforum Clients

- Department of Defense – Tanks, ammunition, aircraft, missiles, communication equipment, navigation equipment.
- Department of Commerce – Steel products, autos, chemicals, semiconductors.
- CMS – Hospitals, physicians, nursing homes, pharmaceuticals, electro-medical equipment, surgical appliances, dental equipment.
- SAFE – Crude oil, gasoline, fuel oil, organic chemicals (ethanol), feed grains, food grains.

## Inforum Databases and Models

- Benchmark 495 – A time series of current and constant price IO tables derived from the 1997 benchmark table, the 1998 to 2005 series of Annual IO tables, and other sources.
- Iliad (360) – A direct aggregation of the 495, the Iliad model is a dynamic econometric model, forecasting final demands and output.  It works with the LIFT model.
- LIFT (111 commodities, 65 industries) – Inforum’s flagship model.  The LIFT model database integrates a current and constant IO framework with a PCE bridge, capital flow table, industry series of value added, employment and investment with the NIPA.  LIFT forecasts final demands, value added, prices, employment, and most major components of the NIPAs.

## Inforum Modeling Philosophy

**Bottom-up**
- Aggregates are summations of detailed industry results.
**Consistent**
- The integrated NIPA and IO framework ensures consistency.  The patterns of expenditures by industry affect employment by industry.  Prices reflect unit costs of materials, labor and other factor income (profits, depreciation, indirect taxes, etc.)
**Econometric Relationships**
- LIFT is based on empirically estimated relationships, using detailed historical data, based on time-series.
**Dynamic**
- LIFT models the economy year by year.  The time path of response is important.  Many equations use distributed lags, so effects of shocks build up and decay over time.  Input-output coefficients change over time, in response to estimated trends or exogenous assumptions.

## Deriving the Detailed Tables: The Ingredients

- 1997 Benchmark IO Table
- Preliminary outputs from 2002 Benchmark IO Table
- BEA Gross Output and prices time series
- BEA Annual IO time series
- Detailed imports and exports data from Census
- The NIPAs
- BEA GDP by Industry

## The Recipe

- Convert 1997 Benchmark and Annual IO to consistent basis.  Estimate detailed 495-order time series of make tables.
- Use BEA gross output and make table time series to estimate detailed time series of commodity output.  Control this ouput series to conform to the 2002 preliminary outputs, and interpolate the differences back between 1998 and 2001.
- Estimate detailed exports and imports from Census data, BEA end use, BOP and other sources.  Adjust to be consistent with Annual IO exports and imports.
- Calculate series of total supply.  Use this to derive estimates of PES and PCE, consistent with Annual IO.
- Derive core commodity by commodity intermediate flows, using Inforum product-to-product (PTP) algorithm.
- Derive detailed series of labor compensation, gross operating surplus and taxes on production and imports, consistent with BEA annual IO totals.

## The Recipe (cont.)

- Balance the 1998 to 2005 time series of detailed IO tables to row and column intermediate controls.  Hand-adjust where necessary.
- Derive series of detailed domestic price deflators, based mainly on gross output deflators
- Derive series of import deflators, using detailed Census quantity and price import data, BLS export/import price indexes and BEA merchandise trade deflators.
- Deflate commodity output using domestic price deflators.  Deflate imports with import deflators.  Derive weighted price for the other columns, as (out+im)/(out$+im$), where the ‘$’ suffice indicates constant price. Deflate each row of the table by this weighted deflator.
- Estimate time series of capital flow tables and PCE bridges in current and constant prices.

## The Inforum Commodity-by-Commodity Table

- From the BEA Use and Make tables, Inforum creates a commodity-by-commodity (CxC) direct requirements table, using an algorithm discovered by Almon (1967, 2000).
- This algorithm assumes that each commodity has its own typical “recipe” or mix of input requirements.  A column of the use table shows the input requirements for producing the product mix of that industry.  The Almon algorithm uses an iterative technique to derive the commodity recipe from the industry recipe.
- Such a CxC table is probably the most sensible form of direct requirements table for modeling or impact analysis, where the impacts or projections are from final demands by commodity.

## The Commodity-by-Commodity I-O Table

## Constant Price IO Coefficients

- In the constant price IO table, commodity output is deflated by the commodity output deflator, intermediate cells of the IO table are deflated by weighted domestic/import price deflators.
- The constant price IO coefficient is defined as constant price intermediate divided by constant price output.
- If relative prices change, there is no restriction that constant price coefficients sum to 1.0 down a column in years other than the base year for prices.  However, the table must add up down the column in current prices.

## Constant Price IO Illustration

## Projecting Constant Price IO Tables

- Time series of IO tables are extremely helpful for projecting future tables.  Inforum develops logistic curve forecasts that apply to all coefficients of a row.
- Historical ratios of actual intermediate/constant coefficient intermediate are formed, and regressed on a logistic function of time.  Logistic curves (“S curves”) approach a long-run asymptote.
- Actual intermediate I = q – f
- CCI = **A**q, where **A** is a constant matrix of intermediate coefficients
- Regress I/CCI on logistic function.

## Other Methods of Projecting IO Coefficients

- Price responsiveness can be incorporated for some intermediate inputs which have time series of price and consumption data available.  This can be done by estimating a cost function, or specifying price elasticities taken from other studies.  Different functional forms tested by Inforum include the CES, Translog and Diewert.
- Expert forecasts can be incorporated into the projected IO tables.  Inforum makes use of industrial, commercial and transportation energy consumption forecasts by EIA.  Special studies, such as that on electric vehicles, make use of engineering estimates of input costs.

## Future Work

- Incorporate the newly released 2002 Benchmark IO Table.
- Estimate separate deflators for exports, and possible PCE.
- Estimate the detailed table in layers (basic prices, commodity tax and margins).
- Work with BEA to obtain documentation on the construction of the annual gross output and price data.
- Work with BEA to obtain currently unpublished series of selected parts of the detailed annual IO database (for example, exports, imports and output would be particularly helpful).  Re-interpretation of the Information Quality Guidelines could bear fruit.