Capital Services & TFP in Belgium

The paper's core methodology involves a two-step process for constructing a volume index of capital services. First, productive capital stocks are estimated for each asset type. Two primary methodologies are employed: the geometric and hyperbolic age-efficiency profiles. These profiles model how an asset's productive efficiency declines over its service life. The choice of profile significantly impacts the subsequent results. The second step aggregates these individual capital stock estimates into an overall index. This aggregation uses the user cost of capital as weights, reflecting the cost of utilizing capital assets for a given period. The user cost calculation itself can employ either an ex-ante or ex-post approach, creating further variations in the final index. The paper examines the effects of these choices on the overall index and, crucially, on subsequent Total Factor Productivity (TFP) estimates.

The study compares two age-efficiency profiles: geometric and hyperbolic. The geometric profile assumes a constant rate of efficiency decline each year, with the largest decline occurring in the initial years. This profile, while simpler, may not accurately capture the nuances of asset depreciation. The hyperbolic profile, in contrast, offers a more nuanced representation of efficiency decline, often showing slower initial decline and a more rapid fall-off later in the asset's life. The paper highlights the sensitivity of capital stock estimations to the choice between these two profiles. This choice, in turn, impacts the growth rate of the capital services index and consequently the calculated TFP. Further variations within each profile arise from choices regarding the retirement function (e.g., lognormal, linear, delayed-linear) and maximum service life, demonstrating the need for careful consideration when selecting a methodology.

A critical element in constructing the volume index of capital services is the user cost of capital. The paper differentiates between two approaches: ex-ante and ex-post. The ex-ante approach uses the expected rate of return on capital, while the ex-post approach utilizes the realized rate of return. This difference in approach leads to variations in the calculated user costs, which serve as weights when aggregating the productive capital stocks. The study investigates how these different user cost approaches, when combined with the different age-efficiency profiles, affect the final volume index of capital services and the resulting TFP estimations. The ex-post approach, particularly, is highlighted as leading to more significant variations in TFP contributions, especially over shorter time periods.

The research focuses specifically on Belgium, using data from 1970 to 2004. The absence of official data on capital services flows in Belgium necessitates the use of constructed data. The data used incorporates various sources, including the National Bank of Belgium (NBB), the National Institute of Statistics (NIS), and OECD International Trade in Commodities Statistics (ITCS). The data construction process involved several assumptions to ensure coherence with National Accounts revisions (published in November 2006). The data spans a considerable period and incorporates multiple sectors and asset types, with specific consideration given to the challenges of measuring ICT investments (with adjustments made to account for only one officially recognized ICT asset in the Belgian National Accounts before 1995). This data construction process underlines the complexities involved in measuring capital services where official data is lacking.

The study begins by defining productive capital stock, emphasizing that it represents the quantity of services produced by an asset over time, not its price or value. This contrasts with simply using asset stocks, as is common in some productivity studies. The OECD recommends using capital services flows for productivity analysis, not just capital stocks. The calculation of productive capital stock is framed as a crucial step toward accurate measurement of total factor productivity (TFP). The document notes a lack of official data on capital services flows in Belgium, requiring the use of proxy measures and methodological choices that could affect the accuracy of the results. The study highlights that the service flows generated by an asset are often unobservable and need to be approximated, emphasizing the need for a robust methodology for capital services measurement.

Two key age-efficiency profiles are introduced: geometric and hyperbolic. The geometric profile assumes a constant annual rate of efficiency decline, simplifying calculations but potentially oversimplifying the depreciation process. The hyperbolic profile offers a more complex but potentially more accurate representation of efficiency decline, showing a slower initial decline and a faster decline later in the asset's life. The choice between these profiles significantly impacts the estimated productive capital stock. The document mentions that the geometric profile is frequently used due to its simplicity, while the hyperbolic profile provides a more nuanced approach. The selection of an appropriate profile is crucial for obtaining reliable estimates of productive capital stock, which are then used in calculating the volume index of capital services.

The research explores how various methodological choices affect the estimation of productive capital stock. These choices include the selection of the age-efficiency profile (geometric or hyperbolic), the specification of the retirement function (e.g., lognormal, linear, delayed-linear), and the determination of maximum service life. The results indicate that for the Belgian economy, productive capital stock levels and growth rates are generally higher when calculated using a hyperbolic age-efficiency profile compared to a geometric profile. However, the choice of retirement function also plays a considerable role. The study finds that using a linear retirement function tends to yield lower stocks and growth rates, while a delayed-linear function produces slightly higher growth rates than a lognormal function. These findings highlight the importance of carefully considering all methodological assumptions when estimating productive capital stock, as these choices directly influence the overall volume index of capital services and subsequent TFP calculations.

Within the context of the geometric age-efficiency profile, the paper explores the impact of different depreciation rate estimations. Two depreciation rates, labeled gamma 1 and gamma 2, are used. Gamma 1 uses average service lives provided by the National Bank of Belgium, while gamma 2 uses rates from the EUKLEMS project. While the choice between gamma 1 and gamma 2 does not impact the overall economy's volume index of capital services, it produces considerable differences in individual industry indices. The analysis shows the significance of using consistent and appropriate depreciation rates, demonstrating how a seemingly minor methodological choice can lead to diverse results across different sectors within the economy. This further underscores the need for a cautious approach to methodological choices and consistent application of parameters.

After individual productive capital stocks are estimated (using either geometric or hyperbolic age-efficiency profiles), they must be aggregated to create a comprehensive measure of capital services for the entire economy. This aggregation process forms the volume index of capital services. The key to this aggregation is the use of user costs of capital as weights for each asset type. The user cost of capital, essentially the rental price of capital services, reflects the marginal productivity of each asset type under conditions of competitive markets and equilibrium. By using user cost weights, the volume index effectively accounts for the differing productive contributions of various heterogeneous capital investments, creating a single measure representative of the overall capital input to output growth. This index then becomes a critical input for analyzing total factor productivity (TFP).

The calculation of the user cost of capital presents a crucial methodological choice: the ex-ante or ex-post approach. The ex-ante approach uses the expected rate of return on capital, while the ex-post approach uses the realized rate of return. These different approaches generate different user cost figures. The study notes that the Australian Bureau of Statistics and the US Bureau of Labor Statistics employ a method requiring constant returns to scale, competitive markets, and an equality between expected and realized rates of return. This highlights a potential challenge of perfectly aligning ex-ante and ex-post estimations. The paper investigates the impact of this choice on the volume index, finding that the ex-post approach, when used with hyperbolic age-efficiency profiles, leads to a higher growth rate of the volume index of capital services compared to using the geometric profile. The ex-ante approach, however, yields more similar results across both profiles, especially for the entire Belgian economy, although some sector-specific differences remain.

The study's results demonstrate the sensitivity of the volume index of capital services to various methodological choices. Using an ex-post approach, the volume index calculated with a hyperbolic age-efficiency profile shows a higher growth rate than that calculated with a geometric profile. This holds true for the entire Belgian economy over the period 1970–2004 but is less consistent across all sectors. The choice between ex-ante and ex-post user costs also plays a significant role, with the ex-post approach generating more significant variations in the index, particularly in shorter time periods. Similarly, the retirement function influences growth rates, with delayed-linear functions generating slightly higher growth rates than lognormal functions, and linear functions having the lowest impact. The study finds that while the choice of depreciation rate (gamma 1 vs gamma 2) within the geometric profile has little influence on the total economy's volume index, it generates notable differences across specific industries. In essence, the calculated volume index, and its subsequent effect on TFP estimates, is highly sensitive to the selection of numerous methodological aspects.

The study's conclusions emphasize the sensitivity of capital services and total factor productivity (TFP) measurements to methodological choices. The use of a hyperbolic age-efficiency profile, particularly with an ex-post user cost approach, consistently results in higher estimates of productive capital stock and, notably, a higher growth rate in the volume index of capital services over longer periods (1970-2004). However, this pattern is less consistent over shorter periods and across all sectors. Conversely, with an ex-ante approach, the geometric profile often shows slightly higher growth rates in the volume index. The findings highlight that long-run TFP estimates are relatively robust across different methodologies. However, short-term TFP estimates exhibit greater sensitivity to methodological choices, particularly regarding the selection of the age-efficiency profile, the ex-ante vs ex-post user cost calculation, and the specific retirement function used. This underscores the importance of careful consideration of these choices when conducting productivity analysis.

The variations in the volume index of capital services, stemming from different methodological choices, directly influence the calculated TFP contribution to GDP growth. While long-run TFP estimates show relative consistency across methodologies, shorter-term estimates (such as those for 2000-2004) exhibit greater variability. For the entire Belgian economy during 2000-2004, the annual TFP contribution ranged from 0.04% to 0.27%, depending on the specific methodological assumptions. The study notes that larger variations in TFP contribution arise when using an ex-post user cost. In the case of a hyperbolic profile, increasing the maximum service life or the β parameter (indicating slower efficiency loss) decreases the TFP contribution due to a higher capital contribution. The choice of depreciation rate (gamma 1 vs. gamma 2) within the geometric profile does not impact overall TFP for the entire Belgian economy but does affect TFP growth estimates within specific sectors. These findings highlight the importance of considering the chosen methodology when analyzing the contribution of TFP to economic growth.

The research utilizes data from multiple sources, including the National Bank of Belgium (NBB), the National Institute of Statistics (NIS), and OECD International Trade in Commodities Statistics (ITCS), reflecting both published and unpublished data. The dataset spans a considerable period (1853-2004 at constant prices, and 1970-2004 at current prices) across 29 sectors and up to 9 product categories. The data on ICT investments required particular attention because Belgium’s National Accounts only recognized one ICT asset (software) before 1995. The data construction involved specific assumptions to align with the revision of national accounts published in November 2006. The study acknowledges that the absence of official data on capital services flows in Belgium necessitated the use of constructed data, potentially introducing uncertainties into the analysis. The findings highlight the need for more complete and consistent official data on capital services for future studies to enhance the robustness of productivity analysis. The paper’s use of multiple data sources and modifications made to ensure data coherence underlines the effort and complexities in constructing reliable datasets for economic research.