INTERACTION EFFECTS OF PROMOTION, RESEARCH, AND PRICE SUPPORT PROGRAMS FOR U.S. COTTON

seasonally adjusted CI real nonagricultural research expenditures ($)

In addition to promotional and nonagricultural research expenditures (SAGPROM_t and
SAGNARES_t), other domestic demand shifters in the model include prices of competing fibers (PPOLY_t,
PRAYON_t), prices of other factors in textile manufacturing (DTEXW_t, DECI_t), and per capita real
disposable income (DPI_t). Proxies for the impact of the price of imports on domestic mill demand
include foreign income (FGDP_t) and the world price of cotton (WPCOT_t).

Our study focused on quantifying the impact of generic promotion and research on demand for
cotton. One complication we had to address is the timing of these explanatory variables. It is important
to allow for the possibility that their impact on consumption may be more complicated than simply
affecting consumption contemporaneously (i.e., in the same period that they occur). That is, the effects of
promotion and research on demand may be distributed over time. Unfortunately, economic theory does
not offer much guidance in determining the appropriate value for the number of periods that these effects
continue, m. Thus, it is necessary to consider alternative lag lengths for both advertising and research to
determine the “best” lag structure. With the correct lag length m* unknown, the number of regressors
that must be included in the model is also unknown. If the researcher chooses an m other than m*
(m ≠ m*) the parameter estimates of the model will either be biased or inefficient (imprecise). It will be
biased if m < m* because there are omitted variables, but it is inefficient if m > m* due to
overspecification of the model.

Thus, we embarked on grid search procedures for several types of distributed lag models (e.g.,
polynomial distributed lag, geometric lag) in an attempt to find the best model (see Murray et al. (2001)
for details on the grid search). In all cases of model selection across alternative specifications, we relied
on the Akaike Information Criteria (AIC), the Schwartz-Bayesian Criteria (SBC), the adjusted R² value
and the implied estimated economic effects (elasticities) to compare competing models and arrive at a
preferred model. Given the economic and statistical considerations as a whole, we arrived at a relatively
simple model with a 3-month lag on research, no lags on promotion, and no lags on cotton price. The

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