We can deduce from this passage that two features affect every country in the world. One is that each one has a government instituted by God and the other is that each Christian in every country has to recognise that his or her particular government has been appointed by the Lord. Because we live in a democracy we are often surprised by what Paul seems to be saying.
What authority was Paul speaking about as far as he and his readers were concerned? The answer is the Roman Empire, which was pagan, autocratic and cruel. Yet Paul recognised that Caesar was there because God had appointed him. So Paul is not speaking about a Christian government, even a nominal Christian one; nor is he speaking about a democratic government in our usual understanding of the term; and he is not speaking about a form of government who recognised that the church could bring benefits to society. Instead he was speaking about a government that opposed the Christian church and which would eventually bring about his execution. Even more striking, the government he has in mind was the government that put Jesus to death unjustly.
Remember that God raised up unbelieving rulers to fulfil part of his plans. We can take a couple of examples, each of whom was the most powerful individual in the world at their times. One of them was the Pharaoh who opposed the desire of the Israelites to return to the Promised Land. God raised him up, God gave him plenty warnings, but in the end he had to be defeated by God in order for the Israelites to be liberated. The other example is Cyrus the Persian, whom Isaiah predicted would set the Israelites free from their exile in Babylon, and he did because the sovereign God arranged it.
God also used the Roman empire to provide certain benefits for spreading the gospel. It has often been observed that the Roman roads made it easier for people to travel and the early Christians made use of them. Moreover, there was a common language (Greek) spoken throughout the empire, which made it easy to explain the gospel in every place. Further the Roman authorities had put in place a kind of peace in which strife and wars were prevented from causing any unease and disruptions to everyday life. Paul himself made use of the Roman justice system with regard to his first Roman imprisonment, and he was set free from it.
So God is in charge.