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OCR for page 192
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
OCR for page 193
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 194
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ith model
