Forecasting Method for General Aviation Aircraft and Their Activity

Transcription

1 5 commuter passenger traffic at Logan increased by 4 percent between 1977 and Such voatiity in the presence of not previousy experienced changes is, of course, difficut to forecast, and many projections made in the mid-s dramaticay underestimated growth of commuter traffic. However, aside from this type of unforeseeabe effect, many earier (i.e., ate 196s) forecasts systematicay overpredicted future activity. Athough this paper does not detai an expanation of these inaccuracies, the anaysis undertaken in this study isoated two principa causes. First, economic growth was projected to be much higher than the actua experience of the s. Second, eary forecasting modes had income easticities that are now beieved to be too high and air-fare easticities that are beieved to be too ow. Another finding during the course of the study has been the imited amount of consistent and reiabe data avaiabe for site-specific forecasts. Differences in the categorization of activity between data sources and between avaiabe and desired data items often constrain modeing efforts. For exampe, the adequacy of average yied as an expanatory variabe in demand-forecasting equations during years when the rate schedue is compex and demand oriented was subject to some doubt. Athough we found that average yied provides an adequate measure of fare eves and find no evidence of arge backcasting residuas when it is used, the unavaiabiity or the known inaccuracies and biases of data that measure both activity eves and causa factors often make informed judgment an appropriate forecasting too. ACKNOWLEDGMENT The forecasting project reported here was funded by the Massachusetts Port Authority under a panning grant from the Federa Aviation Administration. We woud ike to acknowedge the assistance provided by Mitche Keman and Cynthia Kagno of Chares River Associates. The opinions and concusions expressed or impied in the paper are ours and are not necessariy those of the Transportation Research Board, the Nationa Academy of Sciences, or the Massachusetts Port Authority. REFERENCES 1. Chares River Associates, nc. Logan nternationa Airport Passenger and Air Cargo Forecasts. Massachusetts Port Authority, Dec P.K. Vereger, Jr. Modes of the Demand for Air Transportation. Be Journa of Economics and Management Science, Vo. 3, 1972, pp Statistica Abstract of the United States. Bureau of the Census, U.S. Department of Commerce, R.W. Gimer. Services and Energy in U.S. Economic Growth. U.S. Department of Energy, notitute for Energy Anaysis, Oak Ridge, TN, Chares River Associates, nc. Review and Evauation of Seected Large-Scae Energy Modes. Eectric Power Research nstitute, Cambridge, MA, G. Deosaran, H. Sweezy, and R. Van Duzee. Forecasts of Commuter Airines Activity, Appendix C. Federa Aviation Administration, U.S. Department of Transportation, Rept. FAA-AVR-77-28, J. Rocks and H. Zabronsky. Study and Forecast of Genera Aviation Operations at 6 Medium-Hub Airports. Federa Aviation Administration, u.s. Department of Transportation, Rept. DOT-FAA- 77WA-726, Pubication of this paper sponsored by Committee on Aviation Demand Forecasting. Forecasting Method for Genera Aviation Aircraft and Their Activity BRUCE C. CLARK AND JAMES R. TANKERSLEY This paper describes the formuation and appication of a genera aviation (GA) forecasting mode within the context of the North Centra Texas regiona airport system panning process. The objective of the mode was to provide a means of forecasting registered county-eve GA aircraft ownership and the activity of those aircraft (hours fown) that aows pubic poicymakers and panners to assess the impact of poicy and economic growth aternatives on GA demand. The bottom-to-top econometric and time-series mode deveoped through this effort achieved these objectives with statistica resuts that varied across the 19 counties and four aircraft types. Finay, a feature of this mode uncom.mon to other GA forecasting modes is that the demand for aircraft is specified to be (among other things) a function of the demand for air trave (hours fown). The North Centra Texas Airport System Pan, adopted by the Regiona Transportation Poicy Advisory Committee (RTPAC) on November 16, 1974, presented the findings of a comprehensive two-year anaysis of existing and future activity in the 19-county area defined by the North Centra Texas and Texoma state panning regions. The pan identified existing airport faciities, forecast aviation demand through the year 199, and recommended the staged deveopment of a system of pubic airports (to incude improvements to both proposed and existing airports) to meet that demand. With the adoption of the pan, efforts of the RTPAC staff focused on assisting oca governments in pan impementation. n addition, efforts were made to update the pan in response to changing conditions within the aviation community and within oca communities. An outgrowth of these efforts was a reaization that the technica panning process underying the system pan did not aow for a rapid, comprehensive response to technica or poicy issues that were raised by eected officias, airport managers, and the genera pubic. For exampe, a major issue raised by groups opposed to new airports was whether there was a need

2 51 to buid new genera aviation (GA) airports if fue prices continued their rapid cimb: The assumption was that rapid fue price increases were equated to an equay rapid decine in GA activity. Another issue was what effect either deaying the construction of or not buiding a recommended airport woud have on existing faciities. n each case, neither the pan nor the technica panning process provided a mechanism for deveoping an anayticay based response to the issue raised. The identified weaknesses in the existing pan and panning process ed to the deveopment of a definition for a new technica GA airport system panning process for the North Centra Texas region. This paper presents one component of that process: a forecasting method for GA aircraft and their activity. A necessary feature of any aviation forecast is the identification and measurement of the factors that affect aviation growth. The indicators of regiona GA growth in this forecasting method are the number of aircraft (by type of aircraft) registered with the Federa Aviation Administration (FAA) and the hours fown by those aircraft. The mode is based on the hypothesis that regiona growth is, in genera, a function of fue costs, income, and genera credit conditions. As with most forecasting modes, data imitations prevent the method presented here from being a compete representation of a factors that affect GA growth. The utimate goa of a regiona aviation forecasting effort is the generation of airport-specific activity forecasts. Therefore, a bottom-to-top approach to forecasting was assumed in the mode's construction; i.e., the smaest geographic area was used for which sufficient data were avaiabe to support the forecasting effort. This was each of the 19 individua counties. When data imitations made direct estimates of county-eve activity impossibe, county-eve estimates were derived as margina products of regiona estimates. The forecasting mode presented here does not provide future estimates of oca and itinerant operations, which are variabes of interest to federa, state, and oca panners. There is a threefod reason for not forecasting aircraft operations directy. First, accurate historica operationa data at the eve of specificity required are simpy not avaiabe. Second, the costs associated with initiating such a data coection effort are beyond the financia resources of a regiona airport system panning effort. A third and more fundamenta reason for not forecasting operations directy is that, in the perception of the aircraft owner, the tota hours the aircraft has been fown represents the amount of avaiabe aircraft service that has been consumed over the ifetime of the aircraft. t can therefore be argued that the theoretica measure of GA activity is tota hours fown. Airport operations represent a compementary benefit in the consumption of GA hours fown and need not (and perhaps shoud not) be forecast directy. Since we recognized that (theory aside) we sti needed forecasts of airport operations for panning purposes, data by which forecasts of tota hours fown coud be converted to aircraft operations were derived from a survey of registered aircraft owners in the region performed by the North Centra Texas Counci of Governments (NCTCOG). Further, NCTCOG is deveoping a GA demand and assignment mode that wi aow county-eve aviation forecasts to be assigned to specific airports. This wi enabe panners to assess future needs at individua airports. FORECASTNG METHODS AVALABLE There are three estabished ong-term forecasting methods empoyed in GA forecasting at the regiona eve: (a) the regiona-share method, (b) the time-series (trend) method, and (c) the econometric method. t is common practice to use a three methods in a forecast to evauate the best method or combination of methods. This forma exercise has resuted in some genera agreement about the effectiveness of each method or combination of methods by aviation panners. More specificay, the consensus favors a combination of methods (b) and (c) whie regarding method (a) as more or ess a descriptive statistic. The regiona-share forecast is performed by observing aternative nationa forecasts from which one can compute the future aternative regiona forecasts by cacuating the region's percentage share of the nationa tota and extending the series into the future. The impication of a constant market structure is the faw that aviation panners reject ( Regiona share is reay the outcome of regiona aviation growth. Consequenty, the resuts of regiona GA forecasts are often iustrated by computing the regiona share ony for purposes of comparison. A popuar forecasting method among aviation panners today is the time-series (trend) method. n this method, the variabe of interest is expressed as a function of time or as a function of its own variation over time. These modes take on a wide variety of functiona forms and incorporate different estimation methods. They can generay be cassified as deterministic or stochastic (~. The Box-Jenkins modes deveoped by FAA to forecast quartery itinerant and oca operations are exampes of s.tochastic modes <. n genera, deterministic and stochastic time-series modes do not predict w.e in the ong run because of their intrinsic naturei i.e., the forecast variabe is not reated to any causa variabe over time. For this reason, their use is generay confined to short-term forecasts. The econometric method is most often used to make ong-term forecasts. Econometric modes attempt to simuate economic behavior in the rea word based on we-estabished reationships with other variabes over time. An econometric mode may consist of one or more equations, and each equation may consist of one or more variabes. These modes are typicay constructed to expain the movement in one or more key variabes (endogenous variabes) by the movement in other outside variabes (exogenous variabes). By atering the vaues of the exogenous variabes in the mode, the forecaster can simuate rea-word events based on aternative assumptions about the future. The examination of aternative ong-term trends is a usefu panning exercise for estabishing confidence imits in the uncertain future. The forecasting mode constructed for GA activity combines both the econometric and the time-series methods in its structure. n this hybrid approach, the error terms in the econometric mode are used to construct a time-series mode, which in turn is used to adjust the origina econometric mode for any tempora systematic bias in the origina data (!. The resuting transformed mode is then used for forecasting. DATA SOURCES The FAA aircraft registration master fie provided data on the number of aircraft and reported hours fown by aircraft type and county. n addition,

3 52 Figure 1. Economic mode structure for, estimating GA activity. FUEL COST NDEX BY TYPE TRANSPORTATON COMFOOENT CONSUMER!>RCE NDEX REGC'AL AVERAC.. HOURS FLOWN BY TYPE DEFLATED NCOME PER HOUSEHOLD """' REPORTED HOURS FLOWN BY TYPE/ BY COUNTY REPORTNG ARCRAFT BY TYPE BY COUNTY ARCRAFT ELASTCTY COEFFCENTS BY TYPE/ BY COUNTY PRME NTEfEST i--- RATE DEFLATED PERSONAL NCOME BY COUNTY MARGNAL HOURS FLOWN BY TYPE BY COUNTY ARCRAFT BY TYPE BY COUNTY iours FLOWN BY TYPE/BY COONTY information from the fie on the make, mode, and year of manufacture of the regiona aircraft feet was used to identify fue-consumption rates of a sampe of GA aircraft to construct a fue cost index. Data on these variabes were avaiabe for December 31,, to December 31, Other data sources incuded a the items and the transportation component of the consumer price index (CP) from the Bureau of Labor Statistics for The Aircraft Bue Book was aso used to obtain fue-consumption rates (ga/h). County and regiona income data were taken from Saes and Marketing Management magazine's annua survey of buyer income. Finay, the prime rate of interest charged by banks was obtained from the 1978 economic report of the President. THE MODEL An iustration of the structura reationships in the GA forecasting mode is presented in Figure 1. This structure assumes that activity is determined by genera regiona economic conditions and those economic factors particuar to aviation. First a production reationship is estabished between reported hours fown and the number of aircraft units that report hours fown in each county. Aircraft eastic! ty coefficients are obtained from these estimates, which are used to caibrate regiona average hours fown at the county eve. Regiona average hours fown for each aircraft type is determined by a fue cost index, the transportation CP, and defated househod income. The caibrated average hours fown estimates (margina productivities) are used with defated county income and nationa prime-interest-rate data to forecast the number of aircraft by aircraft type in each county. Finay, the caibrated estimates of average hours fown are appied to the aircraft forecasts to obtain tota hours fown. Production Function The production function is specified in noninear form as foows: RH=a RA" (!) where RH = reported hours fown, RA = aircraft that report hours fown, and ao and a 1 = constants. The parameter a 1 is interpreted as the ong-term aircraft input easticity coefficient. n genera, input easticity of any factor of production measures the percentage response of output from a percentage change in the factor of production. Thus, aircraft easticity provides a measure of the sensitivity of hours fown from a change in the regiona aircraft feet size. To perform regression anayses, Equation 1 is inearized by ogarithmic transformation into Jn RH = na + a 1 nra (2) f we assume that Equation 2 represents the true reationship between tota hours fown and tota aircraft, Equation 1 can be rewritten as foows: where H represents tota hours fown and A represents tota aircraft. According to genera-production theory, abor and other resources as we as capita a:re incuded in the production function. These constitute the variabe production inputs in the short term when the capita stock is assumed constant. n this case, abor (piots) and other resources (fue) are not known. The omission of these variabes from the equation may resut in biased estimates of aircraft eastici tyi i.e., the norma probabiity distribution of a1 may not have as its mean vaue the true popuation vaue of a 1 However, the effect of the specification bias must be weighed against the foowing:. The magnitude of any possibe specification bias that resuts from omission of variabes is unknown. 2. Any unknown bias that resuts from omission of variabes impies the presence of muticoinearity in the regression coefficients and resuts in biased east-squares parameter estimates if the variabe is incuded (5). 3. The objective in for-;casting is to obtain estimates of minimum-variance parameters and not necessariy unbiased estimates of parameters. (3)

4 53 n practice, it is the extent of the bias that is most important in mode specification. f a high correation exists between aircraft and piots, the coefficient u 1 wi be biased whether or not piots are incuded in the equation. With reference to statement 3, a biased regression coefficient that resuts from an omitted variabe has been proved to be more efficient (has smaer variance) than the regression-coefficient estimate when the omitted variabe is incuded in the equation (~). For forecasting purposes, minimum-variance estimators are typicay chosen over a other estimators in sma sampes because they are more precise than an unbiased estimator with high variance. Another factor that potentiay affects the easticity coefficients is the type of use to which the region's aircraft feet is appied. n the course of mode deveopment, aircraft use was carefuy examined and utimatey rejected by NCTCOG staff in the specification of the production function. County cross-tabuations of hours fown by primary use yieded sampe sizes in many counties that were too sma for accurate modeing and prediction. n addition, most aircraft types were found to be dominated by one or two primary uses; e.g., air-taxi and executive uses are predominant for jet aircraft and persona and instructiona uses are predominant for singe-engine piston-powered aircraft (. _, p. 1). This suggests that, for a given aircraft typer changes in use are minima over time. Differences in equipment, piot-icensing requirements, and aircraft performance may present imitations to an aircraft's use. Therefore, it was assumed that changes in primary use for each aircraft type woud not be significant during the forecast period. Demand Equation for Ave r age Hours Fown The equation for regiona been specified to incude effects on GA activity. functiona form appears as H/ A = ~o - ~ 1 F/TCP + ~ 2 NC/HH where average hours fown has both price and income Specificay, its H reported hours fown in the region, A airqraft that report, F = regiona fue cost index, TCP! ~ regiona transportation component of the CP, NC regiona income defated by CP for a goods, and HH number of househods in the region. The ratio F/TCP! represents the rea cost of aircraft operation ahd thus its expected sign is negative. Since GA operating costs are not incuded in TCP!, the ratio is a good measure of the reative impact of changes in aviation variabe costs to other transportation costs. When F increases reative to TCP!, average hours fown decreases, and when TCP! increases reative to F, average hours fown increases. Thus, a substitutiona reationship is hypothesized between genera aviation and other modes of transportation. The expected sign of NC/HH is positive. The hypothesis here is that as income per unit (househod) increases, average hours fown increases. Average hours fown is used as the measure of GA activity demand ony because tota hours fown is not known. Treating reported hours fown as a sampe drawn from the regiona popuation of aircraft owners, the appropriate measure of demand (4) is the average or mean vaue of the sampe. The assumption invoved here is that the sampe average is equa to the popuation average for the region. At the county eve, approximatey 5-6 percent of aircraft owners reported hours fown, but the sampe sizes at the county eve for the ess-popuated counties are very sma. Therefore, average hours fown is estimated at the regiona eve in order to use a arger sampe size. To measure the variabe cost impact on the demand for hours fown, a regiona fue cost index was constructed for the period The construction of this index served two purposes: (a) to convert the cost per gaon of fue into a measure of the cost per hour of fying over time and (b) to account for changes in fue consumption rates per fight hour due to variations in the number of aircraft types over time. Specificay, the Ratchford C) index was used for this purpose, and it appears as foows: where F fue cost index, ci fue consumption rate (ga/h) for the ith aircraft make and mode, G regiona price per gaon of aviation gasoine or kerojet fue, Hi hours fown by the ith aircraft make and mode, and t time. D~mand Equation for Aircra.ft nvestment Unike other regression modes used to forecast the GA feet, the aircraft demand equation incuded in this mode specifies GA aircraft to be (among other things) a function of GA activity (,!!). n this context, the demand for aircraft can be considered as a derived demand for air trave. n other words, the desired stock of aircraft does not refect the demand for aircraft per se but a demand for the fow of services that aircraft can provide over time, i.e., hours fown. The theory empoyed in the aircraft investment equation is a variant of the genera fexibe acceerator mode deveoped by Jorgenson and Siebert C.~ n this mode, a variabe reationship is derived from the production function, which reates the increase in hours fown to the eve of the regiona aircraft stock. First, it is assumed that the aircraft stock wi expand unti the margina product of aircraft equas the rea user cost of aircraft. n the competitive case, the rea margina user cost of adding one more aircraft to the regiona aviation feet is equa to the market price of aircraft. The margina product of aircraft derived from the production function is as foows: Then, in user equiibrium, rea margina user cost is equa to margina product: :1 (H/ A) = (C/P) (7) where C is the price of aircraft and P is the CP. When we sove for A in Equation 7, the equiibrium capita stock is as foows: A=a: 1 PH/C (8) (5) (6)

5 54 As number of hours fown increases, the aircraft stock increases by the mutipe of 1, and as the cost of aircraft (C increases, the aircraft stock decreases. n this form, the number of aircraft is reated to 1 ts own activity as we as to its market vaue. n genera form, the compete specification of the aircraft demand equation (which incudes other variabes) is as foows: A= A(H, C, P, R, Y, At_ 1 ) (9) The specific form of demand in Equation 8 requires aircraft to be a function of tota hours fown (H). However, average hours fown was actuay used in the estimation procedure since tota hours fown is unknown. The additiona variabes are the prime interest rate (R), county-eve defated income (Y), and a stock-adjustment variabe <At-1> The interest rate is hypothesized to have a negative impact on the growth in the aircraft stock because purchases of most durabe assets are sensitive to changes in the price of credit. The number of aircraft shoud aso be positivey reated to economic activity. An increase in income shoud resut in an increase in aircraft demand. The stock-adjustment principe in At-1 is incuded to determine the time rate of change in the aircraft stock as it adjusts to new eves of demand. The stock-adjustment principe is intended to measure the response of the aviation industry to a change in aircraft demand. t is assumed that net additions to the aircraft stock refect the desired demand for a minimum aircraft feet size. When demand is stabe, the stock-adjustment coefficient obtained when regressing aircraft in the present period against aircraft in the previous period is positive and ies between and 1 <.~.>. f this vaue is greater than 1 1 the demand for aircraft becomes exposive and increases at an exponentia rate. When the stock-adjustment coefficient is ess than O, the demand for aircraft becomes osciatory; i.e., it periodicay fuctuates rather than increases at a steady rate. nitiay, the agged vaue of aircraft was incuded in the demand equation but was dropped when both exposive and osciatory resuts were obtained. t is often assumed in this type of investment growth mode that the prices of capita goods increase at the same rate as does the genera price eve. When this occurs, the ony fuctuation in the capita stock resuts from changes in the use of the stock. n terms of Equation 8, when P and C increase at the same rate, the rea price of aircraft is constant and ony variations in hours fown account for the vari ati on i n aircraft. This hypothesis was tested by eaving C and P in the equation. Generay, this ratio varied ony sighty and was found to be insignificant. Therefore, aircraft price (book vaue) and CP were excuded from the fina mode. Estimates of the propensity to own aircraft can be read directy from the mode by observing the coefficient of income. These propensities vary by county and by aircraft type. Since the expected sign of the propensity to own aircraft is positive, an increase in income wi resut in an increase in aircraft ownership and a decrease in income wi resut in a decrease in aircraft ownership. This represents the direct reationship between genera aviation and the regiona economy. The fina form of the investment demand equation used in the county-eve forecasts is (O) where a 1 is the aircraft easticity coefficient. By substituting future vaues of H/A, Y, and R into Equation 1, the forecast vaues for aircraft wi be obtained. Forecast vaues for average hours fown (H/A) are taken from the average hours fown in Equation 4. '.'he specification of future vaues for Y and R constitutes the judgmenta assumptions made. FOiECAST ASSUMPTONS AND RESULTS Aternative Energy Scenarios to Address Fue Uncertainties The ong-run projections of fue prices in the mode were provided by the U.S. Department of Energy (DOE) 1977 annua report to the Congress (1). n genera, the prices of aviation gasoine an~kerojet fue are expected to increase dramaticay through 1982 as a resut of phased decontro of domestic crude-oi prices, the continued decine in domestic petroeum reserves, and higher pricf!s for imported oi. ncuded in this report are aternative energy scenarios for prices of a fues used in a sectors of the economy. The two extreme cases--high energy demand and ow suppy and ow energy demand and high suppy--were used in the GA forecast to derive regiona aternative projections of aviation demand. The two scenarios refer to the overa energy suppy and demand in the economy and shoud not be confused with the suppy and demand for aviation fue excusivey. As mentioned earier, the fue cost indices measure changes in fue prices and fue consumption rates over time. An examination of changes in fue efficiency from and 1977 indicated a sow but consistent trend toward better fue efficiency in genera aviation. Reativey greater changes were found in the turboprop and turbojet category due primariy to weight reductions in newer modes (11). f the present trend continues, reductions in consumption (ga/h) may ony amount to 5-1 percent for a of genera aviation. Therefore, it is expected that improvements in fue efficiency wi not offset future price increases in fue. [This has aso been assumed by others (1, pp ).] Throughout the forecast period, it must be assumed that fue suppies wi be avaiabe. Currenty, there are no actua data on tota fue consumption by the aviation industry. However, there are three factors whose consideration ends some judgmenta credibiity to this assumption. First, on theoretica grounds, it is reasonabe to expect some increase in fue suppies as a resut of crude-oi decontro. Even in the high-demand and ow-suppy scenario deveopment by DOE, an increase in fue suppies is expected. Second, the current government fue-aocation program favors the production of distiates, which incudes kerojet fue, over motor gasoine (11_, p. 3). The aocation of distiates has been set equa to 1978 production eves as opposed to an aocation reduction for gasoine. Finay, aviation gasoine price contros were ifted in February Economic Growth Economic growth in the region is expected to sow through the remainder of 1979 and during a of 198. Regiona famiy income adjusted for infation is projected to decine by 2.8 percent over this period and afterwards to increase at its historica rate of 1. 5 percent. The growth of tota infation-adjusted persona income for most counties is expected to sow to an average of from zero to 2 percent in 1979 and to return to individua

6 55 historica growth rates by The primary cause of the expected decine in economic growth is the anticipation of doube-digit infation through nfation is expected to average 1.5 percent during the period , the primary cause being rising energy prices and previousy buit-up infationary expectations. Prime nterest Rate t is assumed that the prime interest rate charged by banks wi reach its peak in 1979 and the average for the year wi be percent. Any decine in the prime rate wi be sow through 1982, primariy as a resut of high infation. The average for the 198s shoud be about 8. 5 percent as compared with the average 7.9 percent during the s. Resuts from the mode indicate that interest rates had a sight dampening effect on regiona aircraft investment. Forecast Resuts The mode structure described provides county-eve estimates of aircraft types. For the 19-county North Centra Texas area, this provided 152 separate sets of forecast resuts. For the purposes of reporting the mode resuts, the 19-county forecasts have been summed to refect a regiona forecast. Figures 2-9 provide a graphic presentation of the forecasts for the North Centra Texas and Texoma state panning regions. Athough the curves exhibit an overa upward trend over the forecast period, each refects the anticipated negative infuences of rapid increases in fue prices due to dereguation in the eary 198s couped with continued high infation. For exampe, the tota regiona aircraft stock is expected to grow at an annua rate of percent over the seven-year period from 1978 to 1984, compared with a 6. percent annua growth rate from 1971 to Most important, the distinguishing feature of Figure 3. Estimated tota hours fown by singe-engine piston aircraft , Low Energy Demand/ / / High Suppy ~ f' i,,,_,.j / f', 1 -, ',1.,, ",.,;.,,' '.. ' Low Suppy Figure 2. Estimated number of singe-engine piston aircraft = ~ (,,) 35.. c 3 1,~,,,;,,ii Low Energy Demand/ 1 ~1 High Suppy ~,;, ; 1 1,,, ' 1,,,,',t/,#1,/,~,' Low Suppy 1975 Figure 4. Estimated number of mutiengine pistpn aircraft. =? (,,) 6 Ci ,;j'. f,,'-' ;'1 Low Energy Demand/ { High Suppy 11o.,..,... "" ~,., ~~/,.# "'., ' J 1,,,,, r/ "fie. '/ ~.,... Low Suppy

7 56 this mode--the infuence of hours fown on aircraft stock--is ceary refected in each pair of figures. With the exception of turboprop aircraft, the curves for hours fown and for number of aircraft are identica in shape for each type of aircraft. Empiri.ca Resuts The empirica resuts of the appication of the GA forecasting mode to Daas County are provided in Equations 11-26, which are categorized by aircraft type. The t-statistic for each estimated coefficient is in brackets after each coefficient. Other statistics incuded are the adjusted coefficient of determination (R 2 ), the mean-square error (MSE), and the F-test for the origina east-squares estimates. n addition, the error modes for each equation appear in backward-shift operator notation, in which B = et-1 and B 2 = et-2 and the autoregressive parameters for the error process Ut are incuded. Singe-Engine Aircraft nh = 2.93[1.565) [4.694) na (11) Figure 5. Estimated tota hours fown by mutiengine piston aircraft. 6 5 iii 'ti i 4 C : E. ~ 3 :J: 2, '' Low Energy Demand/ /'' High Suppy~,1, ii/,~,,,1, ;',,' i"'.--1), J_,~., Low Suppy where R 2 is O. 72, MSE is.3, F is 22.3, and (1 -.7B) n U 1 =,ne 1 (12) A= (-2.975) [1.8) (H/A) +. 18Y[8.229) -.29R[-.252] (13) where R 2 is.97, MSE is , F is 42.12, and Mutiengine Aircraft (14) nh = -.419(-.16) [2.854} na (15) where R 2 is.43, MSE is.9, F is 8.14, and the error mode is as foows: (1 +.27B)n U 1 = ne 1 (16) A= (-.975) +.228(2.162) (H/A) Y[2.564] +.578R[.253] (17) Figure 7. Estimated tota hours fown by turboprop aircraft. Figura 6. Estimated number of turboprop aircraft i ~ c so 15..,..,,,_..,,.,.._// Low Suppy f,' ',f/,,, /, ;~'...,. ~ ' "=''' Low Energy Demand/ High Suppy iii 'ti c ft C :.c!:. C : :J: 2 1 ~,, i 1' ~',,,. ' Low Energy Demand/ / High Suppy , f.._, 1 -,,.-/J} t' ~' ;'" ',, ',, ' \ \,_,,, ' ' Low Suppy '

8 57 where R 2 is.93, MSE is , F is 2.34, and Equations give the resuts for average hours fown. regiona Turboprop Aircraft (18) nh = 7.148[6.919] +.698[2.249] na (19) where R 2 is.26, MSE is.42, F is 5.6, and the error mode is as foows: (1+.1 B) nu 1 = ne 1 (2) A= -15.6[-6.44) -.61 [-2.98) (H/A) +.!6Y[1.477) +.845R[3.627) (21) where R 2 is.99, MSE is 2.574, F is , and Turbojet Aircraft (22) nh = 4.445[1.965) [2.37] na (23) where R 2 is.29, MSE is.67, F is 5.62, and the error mode is as foows: ( -.25B) n U 1 = ne 1 (24) A= [-5.222) +.129[4.137](H/A) +. 25Y[6.155] R[-3.54] (25) where R 2 is.97, MSE is 3.84, F is 45.79, and (26) Singe-Engine Aircraft H/A = [4.118) [-1.954) GF/TCP +.29[.756) NC/HH (27) where R 2 is.2, MSE is , F is 2.17, and Mutiengine Aircraft H/A = [-.43] -.39[-.283] GF/TCP +.23[1.552] NC/HH (28) (29) where R 2 is.26, MSE is , F is 2.53, and Turboprop Aircraft (3) H/A = [7.484) - 8.2(-4.771) KF/TCP (31) where R 2 is.69, MSE is 859.7, Fis 22.76, and Turbojet Aircraft (32) H/A = [5.49) (-3.344) KF/TCP (33) where R 2 is.48, MSE is , F is 11.18, and (34) Figure 8. Estimated number of turbojet aircraft N ~; ",,' "', i' Low Energy Demand/ 1f,' High Suppy ~ 1 # f' 1 /,. 1', \,,,;' ;' '' ' t,' H;g~oo<gy Demood Low Suppy Figure 9. Estimated tota hours fown by turbojet aircraft. ii 'C ~ 16 C) :: ~ ~ 12 J: 8 4 i ' ' ' ',, ' ; t' Low Energy Demand/ f i / 1 High Suppy " f f '""'""'' i ;' t' ;t ~- "\/ \_,,~ t 1 1' J Low Suppy a

9 58 Tabe 1. Sensitivity anaysis of dependent variabes for seected years. Percentage Change from Baseine Forecast Reative to a 1 % ncrease in Fue Cost ndex Depende11t Variabe Percentage Change from Baseine Forecast Reative to a % ncrease in Defated County ncome Aircraft Singe-engine Mutiengne..... Turboprop..... Turbojet Hours fown Singe-engine Mutiengine Turboprop Turbojet U These equations indicate that the rea cost of aviation fue has a significant impact on average hours fown. However, the t-statistics for each equation are ony asymptoticay vaid for the transformed equations. The ow adjusted R'-vaues indicate that the equations have itte expanatory power, which may be due to (a) the sma. number of observations, (b) omission of other reevant data (such as fue avaiabiity), or L) measurement error in average hours fown due to incompete reporting of hours fown. n ahy event, the objective of econometric forecasting is not to maximize the adjusted R 2 but to minimize the error variance (13). n addition, muticoinearity was found to be present in the turboprop and turbojet equations between the rea cost of fue and average defated income per househod. The atter variabe was dropped from these equations since the purpose of the forecast was to examine the aternative energy scenarios projected by DOE. '.'he strength of the GA forecasting mode ies in the individua county estimates of the demand equations for hours-fown production functions and for aircraft investment. Comparisons of the mean-square errors of the county versus the regiona demand equations for aircraft investment found the error of the county estimates to be smaer than that of the regiona estimates for each type of aircraft. n order to measure the responsiveness of the mode to the forecast assumptions, a sensitivity anaysis was undertaken to assess (a) the reative impacts of the exogenous variabes and (b) the effect of a possibe deviation in the forecast assumptions. The percentages reported in Tabe 1 are interpreted as easticity coefficients. They are derived by aowing the exogenous variabe of interest (the fue cost index or persona defated income) to increase by 1 percent above the baseine forecast whie a other exogenous variabes in the mode are hed constant. This reveas the responsiveness of the endogenous variabes to the specified exogenous variabes. A tabe for the prime interest rate is not incuded because a 1 percent change in this variabe was discovered to have no effect on any dependent variabe. CONCLUSON The forecasting mode defined in this paper aowed the deveopment of a quantitative means of assessing the impact of major economic forces that infuence GA growth. Perhaps more important, experience gained through deveopment of the mode ed to greater recognition by a parties of the roe of genera aviation within the North Centra Texas region. From an anaytica viewpoint, it is cear that there is considerabe room for improvement and refinement in the mode's structure and statistica strength. However, whie we recognize that the research conducted to date on the deveopment of county-based GA torecast modes has been imited and, further, that the funding made avaiabe through FAA for the Continuous Airport System Panning Process program has been imited, the mode is nevertheess offered as a usefu first step in a continuing effort to strengthen the anaytica basis for conducting regiona airport system panning. REFERENCES 1. Proc., Third Annua FAA Forecast Conference (Washington, DC, June 1978). Federa Aviation Administration, U.S. Department of Transportation, 1978, pp R.S. Pindyek and P.L. Rubinfed. Econometric Modes and Economic Forecasts. McGraw-Hi, New York, FAA Aviation Forecasts: Fisca s Federa Aviation Administration, U.S. Department of Transportation, Sept A.R. Gaant and J.J. Goebe. Noninear Regression with Autoregressive Errors. Journa of the American Statistica Association, Vo. 71, 1976, pp P. Roa and R.L. Mier. Appied Econometrics. Wadsworth Pubishing Co., Bemont, CA, 1971, pp S.G. Vahovich. Genera Aviation Aircraft: Owner and Utiization Characteristics. Federa Aviation Administration, u.s. Department of Transportation, Nov. 1976, Chapter 6, Section B.T. Ratchford. A Mode for Estimating the Demand for Genera Aviation. Transportation Research, Vo. S, Aug. 1974, pp T.F. Henry, J.C. Tom, and R.A. Jeter. Federa Aviation Forecasts: Fisca s Federa Aviation Administration, U.S. Department of Transportation, Sept. 1977, pp D. Jorgenson and J. Siebert. nvestment :ehavior in u. s. Manufacturing, Econometrica, Vo. 35, 1967, pp Annua Report to Congress: Projections of Energy Suppy and Demand and Their mpacts. U.S. Department of Energy, DOE/EA-3612, Vo. 2, 1977, pp Aircraft Bue Book. Aircraft Deaers Service Association, Aurora, co, Weeky Announcements. Energy nformation Administration, U.S. Department of Energy, Aug J.S. Armstrong. Long-Range Forecasting: From Crysta Ba to Computer Wiey, New York, Pubication of this paper sponsored by Committee on Aviation Demand Forecasting.