“…bales sold/ bought, HayP k is the annual price of hay in dollars per ton, CattQ k is the yearly number of calves, cull cows, and cull bulls sold that varies both by HSM and by calving season, CattP k is the nominal 4-500 lb. steer price 3 that varied by calving season (Table 2), FertM k and FertH k were binary (zero/one) variables denoting intermediate and highest fertilizer use (Table 1) in comparison to the least fertilizer use of the baseline, respectively, Weather k is a weather index indicating above/ below cattle cycle or period-specific annual forage production that averages to 1 for a particular cattle cycle or period (for details, see Tester et al, 2019), Season k is a binary variable for spring-or fall-calving season in a particular year, and ε k is the error term. Equation 2was then estimated for each of the three time periods, the 1990-2003 cattle cycle, the 2004-2014 cattle cycle, and finally pooled over both time periods as weather effects were modeled using matching time periods, and hence forage production could vary given an upward trend in weather effects that led to greater forage production over time.…”