Good question. I recommend reading "Poor Economics" for a background on these questions.
Not a full response, but two points.
1. Giving has less impact - as an LMIC resident you probably have less money so giving directly has lower impact. Also you can buy goods at that price anyway.
2. Improving policy has more impact - You can influence your government in ways that rich countries cannot. You likely also have access to more parts of your own society to study different perspectives. Poor Economics discusses tools for changing policy in LMIC's better than I can.
LMIC - low and middle-income countries.
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