Swiss Capital Stock & Services

The core objective of this research is to provide precise estimates of both aggregate net capital stock and aggregate capital services within the Swiss economy. The methodology employed is the perpetual inventory method, ensuring consistency in the approach. However, data limitations necessitate a two-tiered approach to the analysis. A two-asset breakdown (equipment and structures) covers the period from 1970 to 2005, while a more granular twelve-asset breakdown (nine categories of equipment and three of structures) is limited to the years 1990 to 2005. This data constraint is a crucial aspect of the study's scope and impacts the interpretations of the results. The study explores the sensitivity of its findings by systematically altering assumptions relating to initial capital stock levels, the lifespan of assets, the approach to calculating service prices, and the choice of ICT deflators. This thorough examination of the variables aims to establish the robustness of the estimates. A comparison with similar estimates generated by the Federal Statistical Office (FSO) is also included, highlighting differences in the methodologies and subsequent results. The introduction clearly sets the stage for the detailed analysis to follow.

The theoretical underpinnings of capital services measurement are rooted in the work of Dale Jorgenson and his collaborators from the 1960s. Their research established a method for deriving service prices, also known as the user cost of capital, even in the absence of direct observation. This seminal work is extended upon in the paper to calculate measures of capital input. Subsequent advancements in the field, including works by Jorgenson (1989), Hulten (1990), and Diewert and Schreyer (2006), are acknowledged as significant contributions to the methodology. Practical guidance on estimation procedures is drawn from OECD manuals (2001a and 2001b) and Schreyer et al. (2005). The conceptual distinction between the capital stock (a wealth perspective, representing physical assets at a specific point in time) and capital services (a production perspective, representing the service flow from these assets over a period) is established. The paper emphasizes that the growth rates of these two measures will coincide only when dealing with a homogeneous capital stock. This is unlikely in reality because capital goods are heterogeneous. The difference is particularly pronounced for Information and Communication Technology (ICT) goods, which exhibit shorter asset lives and a significant decline in relative prices over time.

The research acknowledges limitations in data availability. The study focuses on fixed produced assets and excludes inventories, land, and intangible assets, a key methodological choice influencing the overall results. The analysis uses two different investment data breakdowns: a two-asset breakdown (equipment and structures) for 1970-2005 and a twelve-asset breakdown (nine equipment categories and three structure categories) for the period 1990-2005. This difference in data granularity impacts the scope and depth of the analysis within these timeframes. The robustness of the capital estimates is examined through several alternative scenarios. These include exploring different assumptions regarding asset lifespan, initial asset stock values, the method of user cost of capital calculation, and the selection of price indices for ICT investment volumes. Additional variations include using quarterly measures of capital and estimates of capital services based on mid-year asset stocks. The challenges of measuring prices of goods with quality changes are also highlighted, with the study utilizing US Bureau of Economic Analysis (BEA) hedonic price indices for ICT goods to assess sensitivity in cases where Swiss-specific data is not readily available.

The study employs the perpetual inventory method to estimate the capital stock. This method involves accumulating past investments, adjusted for depreciation, to arrive at the current stock. The accuracy of this method relies heavily on the assumptions made about depreciation rates and the age-efficiency profiles of assets. Different age-efficiency profiles are discussed, including geometric, straight-line, and the 'one-hoss shay' profile, each reflecting a different pattern of asset efficiency decline over time. The paper emphasizes that age-efficiency profiles should not be confused with age-price profiles, which track the decline in asset prices with age (depreciation). Although distinct, they are related because an asset's price is essentially the present value of its future service flow. The choice of depreciation method significantly impacts the calculation of the capital stock, influencing the weights assigned to past investments in determining the overall value. The paper outlines how the weighted investment vintages, reflecting the relative efficiency of different investment years, are aggregated to obtain the final capital stock estimate.

The calculation of capital services necessitates determining the user cost of capital, which represents the rental price for utilizing capital goods over a given period. Because this cost is generally unobservable (as most capital goods are used by their owners), the paper utilizes an indirect approach to calculate the user cost. The user cost is intrinsically linked to asset prices within a competitive equilibrium. Therefore, it can be derived using equations incorporating variables such as nominal interest rates, asset prices of new and one-year-old assets, and depreciation rates. The paper introduces a convenient form of the user cost equation by incorporating depreciation and asset inflation. Depreciation, described as the reduction in market price due to aging, is modeled using the assumption of a constant depreciation rate for new assets. The resulting equation is then used to calculate a capital stock series at chained prices. The aggregation of capital services across different asset types necessitates data on the price of these services, which is essentially the user cost of capital, providing a method for consolidating heterogeneous assets into a single aggregate measure.

The paper addresses the calculation of aggregate depreciation, highlighting its dynamic nature due to varying depreciation rates across asset classes and the changing composition of the capital stock over time. Geometric and constant depreciation rates are assumed, specifically a double-declining balance method (δi = 2/Ni, where Ni is the asset's lifespan). The assumptions about asset lives are largely based on those of the FSO (2006a), with one exception. The paper details starting values for asset stocks estimated using artificial investment data constructed for periods before the readily available data, using the GDP growth rate as a proxy for investment growth during these earlier years. The rate of return (rt) is determined endogenously, assuming that the total value of capital services equals the total profits generated by the capital stock. Mixed income, including income from self-employed individuals, is also considered and estimated based on average employee compensation. Asset prices (Pit) are derived by dividing nominal investment series by their real investment counterparts. For the period 1970-1989, artificial series for nominal investment were constructed, implying constant relative prices within asset categories. This detailed explanation illustrates how the complex interaction of various factors and assumptions contributes to the final estimates.

The analysis reveals a consistent upward trend in both aggregate capital services and the capital stock throughout the study period. For the entire period (1970-2005), the average annual growth rate for aggregate capital services is 2.65%, while the capital stock shows an average annual growth of 2.54%. However, the annual growth rates exhibit fluctuation, ranging from approximately 0% to 6%. A noteworthy observation is that the growth of capital services appears to lag behind the growth of the capital stock by one period, an observation requiring further investigation into the underlying factors and dynamics. This initial overview sets the stage for a deeper dive into the specifics of capital composition and its influence on the growth rates of each measure. The overall positive growth underscores the consistent expansion of the Swiss economy's productive capacity, but the nuances within these growth patterns are important for a comprehensive understanding.

A significant finding is the substantial difference in growth rate weights assigned to structures and equipment in the aggregation of both capital services and the capital stock. This difference reflects the heterogeneous nature of the capital stock. While the wealth composition (average wealth split) between structures and equipment is roughly 69% to 31%, the profit distribution is more evenly split (48% to 52%). This implies that equipment plays a larger role in determining the growth of capital services compared to its contribution to the overall wealth. The disparity highlights the role of depreciation rates and inflation in shaping the relative weights. Equipment, characterized by faster depreciation, receives more weight in profit aggregation. Conversely, structures, which experienced higher inflation, receive a more significant weight in overall wealth aggregation. The discrepancy in these weights emphasizes the importance of a detailed asset breakdown in accurately assessing capital growth dynamics.

A more detailed analysis, examining sub-periods within the overall timeframe (1970-2005), reveals a notable divergence in growth rates between capital services and the capital stock. For instance, from 1990 to 2005, aggregate capital services grew at 2.38% annually, while the capital stock grew at a slower 1.90% rate. This period also witnessed faster equipment stock growth (2.50%) compared to structure stock growth (1.67%). Simultaneously, the relative price of equipment goods (higher depreciation rates) declined during this period. The effect of this relative price decrease is pronounced, leading to high rental-price-to-asset-price ratios and higher shares in profits compared to wealth shares for equipment. This highlights the significance of considering relative prices and depreciation in understanding the discrepancy between capital services and capital stock growth, especially concerning the impact of equipment and Information and Communication Technology (ICT) goods. The analysis underscores the importance of detailed sub-period analyses to capture the changing dynamics of the Swiss economy's capital stock and its services.

A closer examination of individual asset growth rates reveals that software and computers exhibit the highest growth rates. Concurrently, these assets also possess the highest rental price-to-asset price ratios, reflecting their relatively short asset lives and a substantial decrease in relative prices over time. This suggests a direct link between these assets and the discrepancy between aggregate capital services growth and capital stock growth. Despite these high growth rates, the weights of software and computers in the aggregate measures remain relatively modest, indicating their contribution to overall growth is significant but not dominant. The share of profits attributable to software showed a notable increase (from 3.3% in 1990 to 6.1% in 2005), whereas the share for computers decreased slightly (from 3.5% to 3.2%). The share of wealth, however, showed a small increase for software and a decrease for computers. This detailed asset-level analysis emphasizes how the interaction of growth rates, asset lives, and relative price changes influence the overall dynamics of capital services and stock.

The study conducts a sensitivity analysis to assess the robustness of its results. It begins by examining the impact of altering the assumptions about initial capital stock values and the service lives (asset lives) of various assets. The analysis considers different starting values and finds that the growth rates of capital services are not significantly altered by changes in these assumptions. The choice of asset lives is crucial because different countries adopt varying assumptions; this study utilizes the asset lives employed by the Federal Statistical Office (FSO). The insensitivity to changes in starting values and asset lives suggests that the model's conclusions are not unduly influenced by these specific parameter choices. The relative stability of results across different assumptions strengthens the overall robustness of the findings. The methodology used to arrive at these alternative assumptions and the procedures for incorporating them into the model are not explicitly detailed, but the results clearly show insensitivity to these choices.

Next, the sensitivity of the results to the method of calculating the user cost of capital is investigated. The benchmark results are based on an endogenously derived rate of return. However, alternative approaches are explored by using exogenous rates of return and comparing the results obtained with the use of real versus nominal user costs of capital. The use of an exogenous rate of return is presented as an alternative, though it has its own limitations, namely the possibility of negative user costs of capital and the ambiguity surrounding which market interest rate to select. The paper presents the results of these different calculations to assess the impact on the calculated dynamics of aggregate capital services. While the alternative methods produce some differences, these changes are described as modest, implying that the conclusions are not heavily reliant on the specific method employed. The relatively small impact underscores the robustness of the overall conclusions.

The paper then investigates the sensitivity to the measurement of Information and Communication Technology (ICT) prices, acknowledging the challenges in measuring prices for goods with quality changes. The study uses hedonic price indices for ICT goods developed by the US Bureau of Economic Analysis (BEA) as an alternative to Swiss data. Three variants of these US price deflators are considered (unadjusted; adjusted using the USD-CHF exchange rate; adjusted for the price level ratio between the two countries). The results are compared with those derived using the Swiss national accounts' price deflators for the same ICT categories. The substantial difference in price deflators for computers, with the US indices falling more rapidly than the Swiss deflator, highlights the potential for significant bias in the results if the choice of price index is not carefully considered. The analysis shows that using US-based ICT price indices considerably increases the growth rate of aggregate capital services but has a more modest impact on capital stock growth. The paper also explores the use of mid-year asset stocks and quarterly data for estimating capital services and stock, demonstrating that these alternative approaches also contribute to a broader understanding of the sensitivities of the results.

The study explicitly compares its findings with those of the Federal Statistical Office (FSO) of Switzerland. Both sets of estimates use the perpetual inventory method, geometric depreciation rates, and a Törnqvist index for aggregation across different asset types. They also utilize similar investment data and exclude inventories and land from their calculations. Despite these shared methodological elements, key differences exist. The FSO assumes that capital services in a given period are directly proportional to the asset stock at the end of that period (K i,t = A i,t), while this study assumes proportionality to the asset stock at the end of the previous period (K i,t = A i,t−1). This difference in timing assumptions significantly affects the calculated capital services. Additionally, the FSO employs a truncated depreciation method, removing assets from the stock once their efficiency falls below 10% of their initial level, while this research incorporates assets even as their weight diminishes over time. These differences in treatment of depreciation and timing lead to discrepancies in the final estimates.

The differences between the FSO estimates and those presented in this study are further analyzed. A key difference stems from how the two approaches handle the timing of capital services. The FSO links capital services to the asset stock at the end of the period, while this study uses the stock at the end of the previous period. To account for this timing difference, the study shifts its own capital services estimates by one period, allowing for a fairer comparison of the underlying trends. Other minor discrepancies exist in the treatment of pre-1948 data for structures investment. The FSO uses a regression-based approach linking investment to GDP, while this study assumes that the growth in construction investment mirrored the growth in real GDP during the 1820-1948 period. Despite these methodological nuances, a visual comparison of the growth rates (presented in Figure 13) demonstrates that the differences between the FSO estimates and those in this study are remarkably small after adjusting for the timing discrepancy in capital service calculations. This supports the overall reliability and validity of the methodology employed in this research, even when compared against the established FSO estimates.