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Appendix C Statistical Analysis of Technology, Sales, and Prices The sales model underlying the estimated effects given in Table 8.3 is given by: Si—be + ~ pi Xij + ci where Si measures sales of the ith model, Xi, is the jth characteristic of the ith model, and Bj captures the effect of the jth characteristics on sales. As specified here the equation is a reduced form. It is derived from a set of structural equations relating supply and demand to the price of a vehicle and its characteristics. Solving for price and sales in equilibrium yields the reduced form relating sales to characteristics. The price equation is expressed similarly: Pi Co + ~\j;Xij + Hi, where Pi is the transaction price, ui is an error term, Xi is as defined as before, and of is the effect of the jth characteristic on prices. The list price is added to the price model to give perspective on the importance of demand and supply effects. The specification of the basic models is presented in Table C.1. As given there, many of the variables in the analysis are easily defined and readily available. For sales, prices, and age data, however, a number of assumptions were necessary. Price data for domestic cars were readily available only for models with automatic transmission, power steering, power brakes, and air conditioning. Prices of imported products, however, were readily available for models with standard equipment--generally a manual transmission, without the power accessories. We followed this convention in both list and first-year prices. Sales data were available only for the model line (e.g., Citation) and were not broken down by engine type or other features. Finally, model age 192

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193 TABLE C. 1 Basic Estimating Equations Fully Specified Sales and Discount Equation (1977, 1979) Si = ao + a1 MPGi + a2RNGi + as VOLWTi + a4 REPli + as REP2i + as DIESEL Pi + a7 FWDi + as AGEi + as JAPAN + ale JAPCAP + all USA + al2 SUBCOMP was determined by using trade reports and expert commentary on new models to determine when a major redesign took place. The results are presented in Tables C.3 and C.4. In the price results we find evidence of a change in the valuation of technology regardless of whether the list price is included. F-tests of the hypothesis that the Hi is equal in the two years are reported in Table C.2. We see that once technology characteristics come into the picture we can reject the equality hypothesis. The sales r esults are much weaker. The large standard errors on the coefficients make clear that the equality hypothesis cannot be rejected. In general, however, the data provide little information about the effect of technology on sales. TABLE C.2 Tests of Equality of the 1977-1979 Coefficients Equation and degrees of freedoma Calculated Critical Ratio F-Statistic (95 percent confidence level) 1. (5,117) 1.37 2.67 2. (6,115) 2.18 2.52 3. (9,109) 3.88 2.23 4. (10,107) 3.33 2.17 5. (12,103) 2.31 2.07 6. (13,101) 2.08 2.03 a The equation numbers correspond to the equations in Table C.3 in this volume.

OCR for page 192
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