Intertemporal Risk Management Decisions of Farmers under Preference, Market, and Policy Dynamics

but only the turning points for the first two years (β= 0.3 and 0.5, respectively) are observable
within the range ofβ. Third, for the last year when farming is about to end, the hedge ratio is
always around 25.5% for allβlevels, quite different from the other years, especially those for the
second to fourth year.

Sinceβis defined as the time discount factor, by postponing consumption to next period
the farmer only gets a fraction ( β) of the utility that he or she would get by consuming an equal
amount during the current period. Therefore with a higherβ, the farmer will have a greater
propensity to consume in the future instead of the current time period. In our case, as βbecomes
bigger or the future consumption is less discounted, the farmer values the future income and
income risk more than today’s, and hedging decreases in the early years. The hedge ratios are
increasing during the third until fifth year over all βvalues, and increasing for the first two years
before βgets to the turning point.

At a specific time preference level, the farmer tends to hedge more in earlier years due
to a preference for an early resolution of consumption risk. This pattern is more obvious in hedge
ratios whenβis low, but it then slowly changes as hedge ratios move to the turning point.
Intertemporal Substitutability

Optimal hedge ratios are generally sensitive to changes in intertemporal substitutability
as shown in figure 7. Hedging percentages are primarily increasing as ρ gets larger. The pattern
switches when ρreaches the turning point in the first and second year.

A larger ρrepresents a more substitution of consumption across years. Therefore,
optimal hedge ratios differ for large versus small ρ values across the first four years, most
noticeably in the third and fourth year. For a range between -5 to 0.8, the increase inρfor a

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