Golf superstar is Kiwi to her core like all who have grown up in this country.

In the days before the Olympics I quietly hoped our flag might be carried into the stadium by Lydia Ko. It turned out she wasn't going to be there for the opening ceremony but it would have been nice.

She is after all our sporting superstar. For all our celebrating of her achievements so far, I doubt we really comprehend what it means to have the world No 1 in a truly global sport. I don't know how many women in the world play golf but I imagine it is quite a few more than the number of women or men who play rugby, cricket or netball, sail yachts, run, row or race on bikes. It may be as many as play tennis.

It takes unimaginable dedication on the part of a child prodigy, and parents and coaches, to launch a professional tennis player from this country where competition is limited. I imagine it is the same in golf. We have never produced a world No 1 in tennis. If we did, Sky would carry every ATP final she reached, and all her matches in the majors.

Ko is Serena Williams, and she is ours. Definitely ours.

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Some of us have a lot to learn from her. When she was breaking into the big time, still at school, we used to speculate in the paper that her Korean heritage would reclaim her, that the sponsorship she could command in Korea would eclipse the money she could make from here. She has recently let us now how hurtful that was.

And of course it would be, if you had grown up in New Zealand, loved this country and could not imagine representing any other. When she turned up at the Olympics this week wearing the silver fern and talking about the thrill of playing for her country this time, she sounded as genuine as always. I need to take her lesson to heart. I'm inclined to suppose immigrants' primary identity remains their ethnicity rather than their adopted nationality. Hence they call themselves New Zealand Chinese rather than Chinese New Zealanders. But everything Ko says and does tells me she is unequivocally a Kiwi and that this is so for all Asian New Zealanders of her generation.

Nearly a quarter of Auckland's population is Asian now, a ratio that will not surprise anybody at the city's secondary schools and universities. New Zealand over the past five years has had one of the highest immigration rates in the developed world. Immigrants are attracted to a relatively strong economy and they make it stronger.

They contribute to the rise in house prices, too, but that is also happening in countries with lower immigration rates. It's caused by the reluctance of central banks to realise that low interest rates and excessive liquidity are not going to generate economic growth. All they have done is inflate asset values, especially property, and our problem is pronounced because we tax property too lightly, which immigrants quickly discover.

But there are worse problems we could have. It wasn't very many years ago that we were worried about the exodus of our kids, which incidentally continues. Policy analysts Julie Fry and Hayden Glass in a recent book, Going Places, Migration, Economics and the Future of New Zealand (BWB Texts, 2016) point out we still have a net loss of New Zealand-born people every year. It seems we also have one of the highest emigration rates in the developed world. Our "diaspora" is second only to Ireland's, they say.

We have a turnover of population much greater than we realise, which makes our political stability and good government all the more remarkable. Our immigration debate has not descended to the level of a Brexit or Trump. We sense, I think, that we constantly need to replace our newly and highly educated people who leave for bigger places. We need to keep bringing in skilled immigrants and Fry and Glass suggest we are not doing that well enough.

They find New Zealand's immigrants in the skilled category are low skilled compared with those attracted by Australia and Canada. They think we've been too insistent on them having prearranged jobs, which tend to be mostly in trades and services. They want to see more entrepreneurs who might invest in "transformational" technology and export products. Long-term business visas were abolished two years ago when it was discovered almost 40 per cent of the business created was in retail or hospitality.

I"m not so sure that matters. To keep young people here we need more people. Even at present rates, the population will not reach five million until 2025 and six million in the 2060s. In the meantime, life is better for Asian food halls, Iranian barbers and Brazilian waiters because our changing face remains Kiwi at heart.