Does squatting help reduce fat in the hips and thighs?
Nope, not directly at least.
It cannot be said enough: You cannot spot reduce or target fat loss.
You can target muscle growth.
The reasons for this are the SAID principle [Systematic Adaptations to Imposed Demands], and the basic ways that your body's energy systems work.
Fat is your body's fuel tank. It's a very efficient way of storing energy long term.
Muscle is a tissue that makes you move by contracting itself on demand.
Muscles grow because of the SAID principle. If you impose a force on them, they will adapt to the forces that they are forced to work. So by doing squats, your butt, thighs, and other muscles will be utilized and adapt to the demands you're putting on them. Muscle also keeps a store of slightly more volatile energy within them called glucose (in glycogen stores) that it can use on demand.
Fat is used when your body needs more energy. 60% of the energy you use while fasted and at rest comes from fat. When you are active, less energy is used by fat initially because it's harder to access, your muscles have their own energy stores inside of them. However, your body will ramp up fat energy conversion as you exercise in case you continue to exercise to the point that the glycogen stores run low. After about an hour or two of constant aerobic exercise (depending on how hard you're going and how fit you are) you'll be using more fat than glucose as energy.
When you're done working out, your body's priorities will be to replenish it's glycogen stores and to adapt to the demands you placed on it. Glycogen stores can be replenished by fat being synthesized by your body into glucose.
Simultaneously, whenever you eat, some of that food will turn into fat. It is a simple fact of nature. Your body is a brilliant biological machine, but it's component parts aren't smart on their own. They can't see or communicate with each other as effective as we can. The way that cells signal they need something is through hormones - chemicals they dump into the blood stream. In order for the nutrients to enter the cell, they have to engage with the proper receptors. Cells that need nutrients will activate more receptors.
Everything that happens in your body is due to chance and opportunity.
Fat accumulates where it does on your body because of chance - where the fat goes first and how it runs into the cells.
My point here is that working a muscle has no effect on where the fat comes from. Chances are it will be most noticeably lost in sections of your body that get fat first because there's more of it there to be lost.
Now, even though your body will use fat to replenish itself after a workout, if you eat too much - more than you've burned throughout the day - it will keep more of the food in fat simply because it doesn't need it right now.
The key to losing fat is through dietary restrictions.
Building muscle can help, so long as you maintain those dietary restrictions.
Muscle burns a few more calories a day than other tissues, and it's good for your bones and joints to perform resistance exercises. Exercise is not a bad thing, it's just not the ideal single strategy for losing fat, and it's not a way to target fat.