Methods - Reconciliation

This paper describes and illustrates a generalized least squares (GLS) reconciliation method that can efficiently incorporate all available information on initial data in reconciling a large system of disaggregated accounts and can accurately estimate industry distribution of statistical discrepancy. The GLS reconciliation method is applied to reconciling the 1997 GDP-by-industry accounts and the Input-output accounts. The GDP-by-industry accounts measure GDP by industry using industry gross income, and the input-output accounts measure GDP by industry as the residual between gross output and intermediate inputs. The GLS method produced balanced estimates and estimated the industry distribution of the statistical discrepancy. The results show that using reliability to reconcile different accounts produces statistically meaningful balanced estimates. The study demonstrates that reconciling a large system of disaggregated accounts is empirically feasible and computationally efficient.

The Bureau of Labor Statistics (BLS) prepares the Consumer Price Index for All Urban Consumers (CPI-U), and the Bureau of Economic Analysis prepares the Personal Consumption Expenditures (PCE) chain-type price index. Both indexes measure the prices paid by consumers for goods and services. Because the two indexes are based on different underlying concepts, they are constructed differently, and tend to behave differently over time. From the first quarter of 2002 through the second quarter of 2007, the CPI-U increased 0.4 percentage point per year faster than the PCE price index. This paper details and quantifies the differences in growth rates between the CPI-U and the PCE price index; it provides a quarterly reconciliation of growth rates for the 2002:Q1-2007:Q2 time period.

There are several factors that explain the differences in growth rates between the CPI and the PCE price index. First, the indexes are based on difference index-number formulas. The CPI-U is based on a Laspeyres index; the PCE price index is based on a Fisher-Ideal index. Second, the relative weights assigned to the detailed item prices in each index are different because they are based on different data sources. The weights used in the CPIU are based on a household survey, while the weights used in the PCE price index are based on business surveys. Third, there are scope differences between the two indexes—that is, there are items in the CPI-U that are out-of-scope of the PCE price index, and there are items in the PCE price index that are out-of-scope of the CPI-U. And finally, there are differences in the seasonal-adjustment routines and in the detailed price indexes used to construct the two indexes.

Over the 2002:Q1-2007:Q2 time period, this analysis finds that almost half of the 0.4 percentage point difference in growth rates between the CPI-U and the PCE price index was explained by differences in index-number formulas. After adjusting for formula differences, differences in relative weights—primarily “rent of shelter”—more than accounted for the remaining difference in growth rates. Net scope differences, in contrast, partly offset the effect of relative weight differences.
 

As part of the U.S. Bureau of Economic Analysis’ integration initiative (Yuskavage, 2000; Moyer et al., 2004a, 2004b; Lawson et al., 2006), the Industry Accounts Directorate is drawing upon the Stone method (Stone et al., 1942) and Chen (2006) to reconcile the gross operating surplus component of value-added from the 2002 expenditure-based benchmark input-output accounts and the 2002 income-based gross domestic product-by-industry accounts. The objective of the reconciliation is to use information regarding the relative reliabilities of underlying data in both the benchmark input-output use table and the gross domestic product-by-industry accounts in a balanced input-output framework in order to improve intermediate input estimates and gross operating surplus estimates in both accounts. Given a balanced input-output framework, the Stone method also provides a tool for balancing the benchmark use table.

This paper presents work by the Industry Accounts Directorate to develop and implement the reconciliation and balancing model. The paper provides overviews of the benchmark use table and gross domestic product-by-industry accounts, including features of external source data and adjustment methodologies that are relevant for the reconciliation. In addition, the paper presents the empirical model that the Industry Accounts Directorate is building and briefly describes the technology used to solve the model. Preliminary work during development of the model shows that reconciling and balancing a large system with disaggregated data is computationally feasible and efficient in pursuit of an economically accurate and reliable benchmark use table and gross domestic product-by-industry accounts.