The three recently announced candidate microlensing events toward the
Large Magellanic Cloud (LMC) could arise from compact objects in a thi
n disk, a thick disk, or a halo. We discuss five observations that cou
ld discriminate among these possibilities: (1) The optical depth to th
e LMC, which can be measured from the rate and duration of events. The
ratios of upper limits to the optical depths are 1:2.5:15 for the thi
n disk, thick disk, and halo models, so a large optical depth can rule
out the thin disk and thick disk models. (2) The ratios of the optica
l depths to the SMC and LMC for the three models: 0.6, 0.6, and 1-1.5.
(3) Deviations from the normal shape of the microlensing light curve,
caused by parallax effects. The ratios of the fraction of events with
detectable parallax effects are 70:15:1. If events are identified in
real time and are observed with high-precision relative photometry (ap
proximately 0.02 mag), then parallax effects can be measured for most
thin-disk events and approximately 15% of thick-disk events. (4) The c
haracteristic masses inferred from the mean duration of events. These
are in the ratio of 1.2:1:1.5, so this can be at most a marginal test
of the three models. (5) The ratios of optical depths to the bulge (in
excess of that produced by known stars) and to the LMC. These are 45,
5.5, and 1 for a thin disk, a thick disk, and a halo. At present the
observations favor a thick-disk or halo origin of the lenses, or simil
ar contributions from more than one structure, but do not exclude the
thin disk as the main contributor.