From the heightening rules:
Both prepared and spontaneous spellcasters can cast a spell at a higher spell level than that listed for the spell. This is called heightening the spell. A prepared spellcaster can heighten a spell by preparing it in a higher-level slot than its normal spell level, while a spontaneous spellcaster can heighten a spell by casting it using a higher-level spell slot, so long as they know the spell at that level (see Heightened Spontaneous Spells below). When you heighten your spell, the spell’s level increases to match the higher level of the spell slot you’ve prepared it in or used to cast it. This is useful for any spell, because some effects, such as counteracting, depend on the spell’s level.
So any spell can be heightened, in the least to make it more difficult to counteract. So 2nd level Fear does the same thing as 1st level, but is more difficult to counteract. What about 4th level fear? Well, the reading is actually a little ambiguous; I'm fairly confident the intent is that 4th level (and higher) Fear will use the 3rd level effect, so I'll make the argument for that interpretation from the text. Still from the heightening rules:
Some heightened entries specify one or more levels at which the spell must be prepared or cast to gain these extra advantages. Each of these heightened entries states specifically which aspects of the spell change at the given level. Read the heightened entry only for the spell level you’re using or preparing; if its benefits are meant to include any of the effects of a lower-level heightened entry, those benefits will be included in the entry.
So you would look at the Fear spell for Fear level 4; seeing none, you'd "count down" the spell levels until you found a heightened effect that applies, or you reach the base spell level. In this case, you'd see the 3rd level effect; the spell description here specifies what changes at the given level (3rd in this case). So you would use the 3rd level effect. If you were to use a lower spell level effect, it would state such.
Now, I do think that the text may be easier to interpret that a 4th level Fear acts as a 1st level Fear, but frankly that's just silly. It doesn't make sense that a 8th level Magic Missile would do the same damage as a 1st level Magic Missile, nor does it make sense that a level 10 Fear would affect less people than a level 3 Fear.
All spells can be heightened; use the latest applicable level. 2nd level Fear would have the same effect as 1st level, and 4th level Fear would have the same effect as 3rd level, both just being harder to counteract than the previous level.