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Working from this assumption and making further assumptions about people's skills and the effect that tax rates have on the incentive to earn, Mirrlees computed the top marginal tax rate for high-income earners.
While a more sophisticated model could interpolate between several close examples, such as with a k-nearest neighbour classifier, any such interpolation would require making further assumptions about the statistics of scenes, stimuli and perception.
Given the available information, and without making further assumptions
Without making further assumptions, W i can not be determined.
These data will also provide a basis for making further assumptions about cost impacts in other geographical locations.
Identifying individual cohort, period or age effects is impossible with making further assumptions, although this identifiability problem is not of concern when making projections.
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Then, making further assumption for the deterministic component of utility to be linear and additive in parameters, V iq = β' X iq, the probability in Equation (3) can be given as: P i q = exp ( β ′ X i q ) / ∑ j = 1 J exp ( β ′ X j q ) (4).
But in modelling future energy use, Aemo found the Coalition's current Direct Action policies would not achieve those reductions, and so made further assumptions about carbon abatement policy required in the electricity sector.
We now make further assumptions about channel gain information.
However, practicioners demand estimates for all respondents, so we have to make further assumptions in order to obtain parameter estimates for such cases as well.
Note that θ i ( h ) > 0 and θ i ( h ) ≈ h + O ( h 2 ) for small h > 0. It could be showed that the discrete-time analogue (3) converges to the continuous-time model (1) as h → 0. To investigate the stability and periodic oscillations of system (3), we make further assumptions.
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making further redundancies
making further refinements
making further additions
making further adjustments
making further waves
making further sales
making further gains
making further changes
making prior assumptions
making further arrests
making further investments
making further moves
making further comparisons
making further airings
making further announcements
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