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A Chain-Type price index for new business jet aircraft: industry-specific price indices yield valuable insights.

This paper presents a price index constructed to measure the real price and real output of corporate business jet aircraft. It employs a chained price index methodology to properly account for the effect of changes in aircraft quality and product lines on the price index. The index indicates that the average price level of corporate jets has significantly outpaced the general price level measured by the GDP deflator, nearly doubling the real price of the product over a 35-year period from 1968 to 2003, which could have negatively affected the demand for the product. Because the GDP deflator significantly understates the price increase in corporate jets, the industry's real output is overstated when its nominal sales are deflated with a general price index. The paper suggests that an industry-specific price index allows more accurate analyses of real economic activity of an industry. The methodology used in this paper could be useful for other industries where product price movements vary significantly from the changes in the general price level.


Measuring economic activity with price and quantity indexes has greatly enhanced the empirical content of economic analysis. The GDP deflator, for example, provides two critical pieces of information about the economy. First, it indicates the rate of inflation, or the real value (i.e., the purchasing power) of money over time. Second, it permits measurement of the real economic activity level measured in constant dollars (i.e., real GDP).

An individual industry's price index provides the same key pieces of information concerning economic activity of the industry. First, the average price of an industry's output relative to the overall price level is the real price of its output. As such, the trend and fluctuation in the real price of individual products indicate important characteristics of the market, such as, demand, competition, product innovations, and pricing strategies of the manufacturers.

Second, the index permits the measurement of real output of the industry. Real output to an individual industry is what real GDP is to an economy--a truer measure of economic activity of the industry than nominal output. It is therefore important to manufacturers, their marketing arms, employees, regulators, and consumers.

It is also important to recognize the potential value of a price index in investigating a host of research questions such as the demand for and the supply of products, the competitive nature of an industry, determinants of market shares, and the effectiveness of different pricing strategies. Indexes in themselves cannot answer these questions, but they are critical pieces of information when formulating tests of different theories and models of industry performance.

While individual industries have the same need to measure and analyze their economic activity, price indexes are not typically available at the industry level. (1) The Bureau of Economic Analysis updates price and output measures for industry groups to determine the contributions different industries make to overall output and price growth (Yuskavage, 1998; McCahill and Moyer, 2002). However, the industries are too broadly defined to provide average price measures for specific industries.

This article presents a price index for new business jet aircraft manufactured and sold by the general aviation industry. It also illustrates what can be done to calculate price indexes for other specific industries, data permitting.

Alternatives to Industry-Specific Price Indexes

Without a price index specific to an industry, there are three possible, but inadequate, methods of quantifying real industry activity over time. For business jet aircraft, one option is to use total units of aircraft delivered per quarter or year. This is an incomplete measure of real output because the industry regularly introduces new models that are entirely new or significantly modified, while discontinuing existing models that are no longer viable. Thus, the sales mix can change dramatically from year to year because of product introductions and deletions. (2)

Another approach is to deflate dollar sales using a broad measure of inflation such as the GDP deflator to derive a measure of real output. However, unless the GDP deflator and the industry's average price level follow a similar growth path, this measure of an industry's real output will not provide an accurate picture of real activity. If the deflator grows more slowly than average new business jet prices, for example, deflated dollar sales will overstate the real activity of the industry. Conversely, if the deflator grows faster, deflated industry dollar sales will understate real activity.

A third option is to select a numeraire or benchmark model and convert all models into numeraire equivalent units using price differences to account for differences among models. McDougall and Cho (1988), for example, used numeraire equivalent units to investigate the demand for general aviation aircraft. This approach works best if the numeraire model remains the most popular seller and different models share some common features. Unfortunately, these conditions no longer exist in the business aviation industry. Over the past ten years, the number of market segments in the business aviation industry has increased from three to at least eight and possibly ten, depending on how one wishes to categorize the very light jets under development and the very large business jets that include specially modified Boeing and Airbus aircraft. At the same time, competitive pressures have caused original equipment manufacturers to fill in market niches identified in the "price-performance" continuum, which further segments the traditional light, medium, and heavy jet markets.

Methods for Constructing a Business Jet Price Index

This section describes various methods for constructing a business jet price index. The methods are widely known among economists and are similar to ones used by the U.S. Commerce Department for the National Income and Product Accounts. This discussion leads to a "chain type" index method to determine the average price level of new business jet aircraft relative to a base year. This index provides a basis for describing price trends of new business jets, fluctuations in the real output of the business jet industry, and how these movements relate to changes in the general price level and nominal industry sales. The discussion concludes with brief remarks on possible extensions and applications of this method to other segments of the general aviation industry.

A price index value for any year is expressed as a percentage of the average price level of the designated base year, which is assigned the value of 100 (percent). Thus, if the average price has increased by ten percent between the base year and year n, the price index value for year n is 110. Fixed-base or fixed-weighted indexes hold the base to the same year. A fixed-base index works best over relatively short periods, however, because the composition of products can change significantly over time. A fixed-base index cannot properly account for new product introductions and deletions that would take place over a long period. Nor can it capture the impact of price changes that cause purchasing patterns; that is, consumers increase purchases of goods whose prices have declined and reduce purchases of goods whose prices have increased.

Changes in product composition cause fixed-base indexes to misrepresent the true magnitude of average price changes. For example, a fixed-base Laspeyres index tends to overstate price increases because it uses the base period basket of goods and services as the weights. Thus, ceteris paribus, it fails to recognize the increased significance of goods whose relative prices have fallen and the decreased significance of goods whose prices have risen in the current consumer basket. The commonly referenced Consumer Price Index uses this method, presenting a long-held and much studied controversy over the extent to which the CPI overstates changes in the cost-of-living (Schultze, 2003). Partially in response to this controversy, the Labor Department recently introduced a supplemental index that provides some allowances for product substitution (Cage, Greenlees, and Jackman, 2003).

A fixed-base Paasche consumer price index, on the other hand, tends to understate price increases because it uses the current period basket of goods and services in weighting prices. As a result, products that have experienced a rapid price increase carry less weight. This type of index also is more costly to compute because it requires quantity data for each period.

Constructing a price index using a fixed base is particularly problematic for the business aviation industry because the industry's product composition has evolved significantly over the past 50 years from multi-engine piston aircraft to turbofan (turboprops) models in the 1970s to turbojet (jet) models in the 1980s. The pace of product development and proliferation of new models has accelerated with the introduction of very light and very heavy jet models and the continuing segmentation in the traditional light, medium and heavy categories of business jets.

An alternative to a fixed-base or fixed-weighted index is a chain system index. Irving Fisher (1927, p. 19) explained the alternative system, "By the 'chain of bases system' each year is taken as the base for calculating the index number of the next and the resulting figures are then linked together to form a 'chain' of figures." Fisher allowed that the chain system index "... makes less complicated the necessary withdrawal, or entry, or substitution of commodities, as time and change constantly require" (p. 309). But he dismissed this procedure to be of little or no real use primarily because the fixed-base system is "... simpler to conceive and to calculate, and means something clear and definite to everybody" (p. 312).

Despite Fisher's reservations, the chained system has gained acceptance as the pace of product turnovers has accelerated and data collection and analysis have become more manageable. The Bureau of Economic Analysis revived the chain system in 1992 and has since constructed chained price and quantity indexes for the National Income and Product Accounts (Triplett, 1992; Young, 1992). (3) Under the Bureau's procedure, a "Fisher Ideal" price index is first calculated between two consecutive years as the geometric mean of the annual-weighted Laspeyres and Paasche price indexes. The chain index for a given year is then determined by chaining (i.e., multiplying) the year-to-year Fisher Ideal indexes of all previous years. The Commerce Department now reports both the traditional fixed-weighted indexes and chain-type indexes for GDP and its components, with the latter more widely used now. The method of chaining year-to-year values allows for product substitution over time. It also helps reduce the upward bias in a price index caused by improvements in product quality: yearly improvements are relatively small compared with what can take place over a number of years.

The index presented here follows the BEA's annual-weighted price index procedure. The specific mathematical expressions used for calculating the indexes for business aircraft in year t are:

(1) Paasche Index = P[I.sub.t] = [[SIGMA] [P.sub.t] x [Q.sub.t]]/[[SIGMA] [P.sub.t-1] x [Q.sub.t]]

(2) Laspeyres Index = L[I.sub.t] = [[SIGMA] [P.sub.t] x [Q.sub.t-1]]/[[SIGMA] [P.sub.t-1] x [Q.sub.t-1]]

where [P.sub.t] and [Q.sub.t] are the prices and quantities of all business jet models sold in year t and [P.sub.t-1] and [Q.sub.t-1] are the previous year's prices and quantities. The cross products are summed over all models.

(3) Fisher Ideal Price Index = F[I.sub.t] = (P[I.sub.t] x L[I.sub.t])[.sup.1/2]

(4) Chained Price Index = C[I.sub.t] = (F[I.sub.t] x F[I.sub.t-1] x F[I.sub.t-2] x ..... F[I.sub.2] x F[I.sub.1]) x 100

The value of the Fisher index for the first year is set equal to 1.

The Industry and the Data

Airplane makers worldwide delivered 2,686 general aviation aircraft in 2003, with factory billings reaching approximately $10 billion (General Aviation Manufacturers Association, 2003). General aviation aircraft are classified into three broad categories: single and multiple piston engine, turboprop, and turbojet. Turbojet airplanes are the most important products of the industry. They are bigger, faster, and deliver a more comfortable flying experience than other types of aircraft. The business jet sector is the most active and innovative part of the general aviation industry, today producing more than 25 models of varying size and capability. Manufacturers shipped 502 business jets in 2003 valued at approximately $8 billion, a figure amounting to 80 percent of the entire industry sales. The price index constructed here focuses on the business jet segment.

The data used to calculate the chained price index for business jet aircraft consist of shipments and prices for all jet models produced and sold from 1968 to 2003. The shipment data are taken from industry sources, and prices are taken from the Aircraft Bluebook Price Digest. Because manufacturers tend to establish new aircraft prices once a year, the chained price index is calculated on an annual rather than quarterly basis.

The business jet manufacturing sector has been a growth industry with healthy competition. Combined with the rapid technological progress made in the field, these factors have created a dynamic environment of product development and innovation. Over the 1970s, product development was seen in the modern light jet segment with the introduction of the Citation I and II, Lear 35 and 36, Falcon 10, and IAI 1124. As the light jet market became more competitive and business travel needs expanded, manufacturers shifted to the medium-size jet segment during the 1980s with the introduction of the Citation III, the Lear 55, and the Falcon 50, which replaced the earlier Falcon 20. The 1990s brought another cycle of product development. To meet market demand for faster, more comfortable aircraft with longer range, manufacturers rolled out a number of large business jets including the Falcon 2000 and 900EX, the Canadair 600 series, and the very heavy Gulfstream V, Global Express (GX), and Boeing business jets. By the end of the 1990s, the number of large and very large units delivered exceeded the number of medium sized business jets shipped. Over the past 20 years, the business jet industry has undergone significant structural change and consolidation as it undertook unprecedented product innovation and development to meet changing market demands.

Product entry and exit create problems when constructing a price index. Prices of new models are not available for the proceeding year. This does not affect the Laspeyres index, but causes a discrete upward shift in the Paasche index for the introduction year. Examination of equation (1) shows that the numerator, but not the denominator, of the Paasche index increases for the year when a new model is introduced. It is reasonable to hold the price consequence of a new model until the second year. Computationally, this is equivalent to assuming that the pre-introductory price is the same as the first year price.

The discontinuance of existing models affects the Laspeyres index since there is no current price of a model discontinued in the previous year. The denominator of the index carries the value of the previous year's models, but not the numerator. Once again, it seems reasonable to neutralize the price impact of model changes for the first year by assuming that a post-discontinuation price is the same as a model's last year price.

Once the Paasche and Laspeyres values are calculated, constructing the chained price index for business jets is straightforward. Using Equation 3, the Fisher index from 1968 to 2003 is calculated using the geometric means of the Laspeyres and Paasche indexes. These values are then accumulated per Equation 4 to give a chained index value for each year. The resulting series measures the average price level against the base year of 1968.

New Business Jet Price Index, 1968-2003

The chained price index of new business jets determined from the above method is plotted in Figure 1 along with the GDP deflator (rescaled to the base year of 1968) for the 1968-2003. (The actual price index data, along with shipment and value data, may be obtained from the author at The average price level of new business jets has grown significantly during the period, with the 2003 level nearly eight times that of the 1968 average price. Business jet prices also have increased faster than the general price levels. For the 35-year period from 1968 to 2003, the GDP deflator grew at an average annual rate of 4.2 percent. Over the same period, the average price for new business jets increased at an average annual rate of 6.1 percent, with the divergence beginning in the mid-1970s. Between 1968 and 2003, the Consumer Price Index (CPI) increased at an average annual rale of 4.9 percent; and the Producer Price Index (PPI) for capital equipment increased at an average annual rate of four percent. The difference is even greater when the business jet industry is compared with overall manufacturing. According to a Commerce Department study, average prices of manufactured goods grew at an average annual rate of 3.2 percent between 1977 and 1996 (Yuskavage, 1998), while business jet prices increased at an average annual rate of 6.8 percent during the same period.

The difference between business jet price inflation and overall inflation is the percentage change in the real price of business jets. Since the overall inflation measured by the GDP deflator grew at an average of 4.2 percent per year, the annual average rate of price increase of 6.1 percent implies that the real price of business jets has increased an average of 1.9 percent per year over the 35-year period. At the 1.9 percent annual growth, it would take approximately 38 years for the real business jet price to double. In 38 years, it would take twice as many goods and services to buy a business jet as it does now, if the historical real price growth rate were to continue.

The industry's strong pace of real price increase is unusual in the manufacturing sector, where pricing power has all but vanished. The consolidation of the industry around a smaller number of firms (i.e., the emergence of an oligopolistic industry structure); stronger brand identity; increased product differentiation brought on by new product development; and the expansion of markets through product refinements and new forms of ownership, such as fractional shares; are likely to have contributed to the favorable price appreciation for the industry's product.

Nominal and Real Values of Jet Sales

In addition to determining the real price level of business jets, the price index helps determine the real output of the industry. Most business jet deliveries come from current production since the production planning process is organized around customer demand. Thus, since inventory change need not be considered, sales values provide a reasonably accurate measure of industry output.

The real output of the business jet industry is determined by dividing the nominal sales (i.e., output) by the chained price index, with the base year set at 1996. Real output in billions of chained 1996 dollars are plotted in Figure 2 along with the nominal annual sales in billions of current dollars. From 1968 to 2003, real output grew at an average annual rate of three percent, with growth concentrated in the early 1980s and the late 1990s. Over the entire period, many years displayed negative growth in real output. For example, the industry achieved real output of five billions of chained 1996 dollars in 1981, but it took more than 15 years (1997) for the industry to surpass that historic high. This is a much different picture than presented by nominal output figures. The path for nominal business jet output shows almost uninterrupted growth, except for the mid-1980s and since 2001. Over the entire 35-year period, nominal business jet output grew at an average rate of 9.2 percent.

Another frequently used indicator of the industry's economic conditions is the total number of jets (units) shipped and delivered during a year. However, this measure ignores changes in product mix. Thus, it is worth examining whether units provide an adequate description of the industry's real output. For the purpose of comparison, both the annual units and the real output figures are indexed to the 1996 figures, 1996=100 percent, resulting in indexes of unit and real output. Figure 3 plots the deliveries and real output indexes.

According to the unit index, the industry appears to have been quite robust during the late 1970s and early 1980s. The 1981 unit index was 179.8 percent of the 1996 level, indicating that the number of business aircraft delivered in 1981 was nearly 80 percent higher than 1996 deliveries. However, the real output index for the year 1981 was only 35.6 percent higher than the base-year value. (Notice also how total units show six years of robustness while the output index shows only three years of robustness compared to the base-year performance). These differences reflect the shift in product mix from small to medium jets that has occurred since the early 1980s.

Similarly, the difference between the unit and output indexes after 1996 reflect the shift in product mix to heavy and very heavy business jets. Between 1996 and 2001, the unit index increased to 239.7 percent of the 1996 level, but the real output index increased to 267.1 percent of the 1996 base value. For 2003, the unit index indicates that the industry's real economic activity stood at 158.4 percent of the 1996 level, not a bad improvement. However, the real output index suggests that industry performance in 2003 is even better than this with real output at 176.5 percent of the 1996 level. Because of changes in product mix, the unit index tended to overstate real industry output between 1968 and 1985 and understate real output after 1996. In short, total units delivered present a distorted picture of real output of the industry.

The growth rates for prices and real output presented in this discussion suggest that the average annual growth rate of 9.2 percent in nominal sales over the past 35 years can be decomposed into an annual real growth rate of three percent and a 6.1 percent annual rate of price inflation. Furthermore, this rate of inflation for business jets can be decomposed into the 4.2 percent average annual growth attributable to general inflation and a 1.9 percent average annual rate of real price increase for business jets.

Concluding Remarks

The price indexes constructed for business jet aircraft provide useful insights concerning the real and nominal economic output of this segment of the general aviation industry. It also illustrates how such indexes can be constructed and used in other industries and segments of industries.

This paper clearly shows that, for a dynamic, innovative, and volatile industry such as the general aviation industry, total units sold are not a proper measure of real industry output because aggregate units fail to reflect changing product lines. Neither would a real dollar output determined from a common price index be an adequate measure of real output of the business jet industry, because of the significant differences observed between the average price changes of business jets and those of the general price level.

While nominal output measured by current dollar sales grew at an average annual rate of 9.2 percent between 1968 to 2003, approximately two-thirds of the growth came from price increases rather than from increases in real production. Further, the price growth exceeded general inflation by almost two percent per year. The two percent real price increase of business jets over a 35-year period is quite surprising, given the competitiveness and productivity increases the manufacturing sector has experienced in recent years. The exceptional real price increases suggest that the industry has benefited from market strength, likely associated with expanding markets and the introduction of new and refined products that are valued by business customers as productive tools. The two percent real price increase over the 35 years, however, has made business jets almost twice as expensive in terms of other products: in 2003 it takes twice the quantity of other goods than was needed to buy a business jet in 1968.

As long as the business jet industry is able to deliver new products that provide increased value to current owners/operators and expand business applications, the industry should be able to keep the real price of its output rising. However, given the increasingly competitive global market economy, it may be difficult for the industry to keep its real prices high in the future. Even if the industry is able to increase prices beyond the general price level, it is questionable whether such price increases will translate to higher revenues and profits to the industry, as higher real prices invariably create resistance from customers.

The real output and the real price determined from the price index help describe more clearly the reality of the market, the competitiveness of the industry, and the pricing power and behavior of the plane makers. The real variables would also provide empirical data needed for constructing and testing industry models for analysis and prediction.

This paper is an application of the national income accounting method of chained price indexes to an industry. The results provide useful information for the industry that would not have been available otherwise. Other industries could also make use of similar methodologies and assess their economic activities and market conditions. Data requirements would be considerable, however, because it would take both price and quantity data to construct a chain-type price index for an industry. Price data are more readily available than quantity data; but without detailed quantity information, it would impossible to account for changing product composition in a price index.


An earlier version was presented at the June 2004 meeting of the Transportation Research Board, National Research Council, Washington, D.C. I would like to thank Gerald McDougall, Philip L. Hersch, Steve Hines, and the participants of the meeting for their help and comments. Detailed comments and suggestions received from the editor and an anonymous referee have vastly improved the paper. I am grateful to them. Any errors in the paper are solely mine.


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McDougall, Gerald S. and Dong W. Cho. 1988. "Demand Estimates for New General Aviation Aircraft: A User-Cost Approach." Applied Economics. 20:3, pp. 611-21.

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Dong W. Cho is a professor of economics at Wichita State University. He earned a Ph.D. from the University of Illinois and a B.A. from Seoul National University. He has frequently provided economic analyses to the general aviation industry, and his research in the field appeared in Applied Economics and Logistics and Transportation Review. His research in forecasting evaluation was published in Journal of Economics and Business, Business Economics, and International Journal of Forecasting.

(1) Interest in creating industry price indexes is growing. Dow Jones & Co. is reportedly considering launching a monthly price index for U.S. steel products (Glader, 2004). The index is designed to add transparency to volatile steel prices.

(2) Currently there are 30 new business jets under development. See

(3) The BEA initially proposed two alternatives to the fixed-weighted index: the chain-type annual-weighted price index and the benchmark-years-weighted price index. In the former, weights change each year; in the latter, weights change each benchmark year at about 5-year interval (Young, 1992).
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Author:Cho, Dong W.
Publication:Business Economics
Geographic Code:1USA
Date:Jan 1, 2006
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