  We establish estimates for the coalescence time of semi-infinite directed
geodesics in the planar corner growth model with i.i.d. exponential weights.
There are four estimates: upper and lower bounds on the probabilities of both
fast and slow coalescence on the correct spatial scale with exponent $3/2$. Our
proofs utilize a geodesic duality introduced by Pimentel and properties of the
increment-stationary last-passage percolation process. For fast coalescence our
bounds are new and they have matching optimal exponential order of magnitude.
For slow coalescence we reproduce bounds proved earlier with integrable
probability inputs, except that our upper bound misses the optimal order by a
logarithmic factor.
