Yale law professor, and mother of two girls, Amy Chua gave the world a new type of mother role model in her memoir Battle Hymn of the Tiger Mother: someone who insisted on several hours of music practice every day, banned sleepovers and wasn't happy with anything less than an A+ for schoolwork. Bryan Caplan, economics professor and father-of-three, whose new book says nature will always win over nurture, is an exponent of "serenity parenting", the belief that parents should stop hothousing their children. Can either of them change the other's mind? Emine Saner listens in.

Bryan Caplan: I'm wondering why genes play so little part in your story. You mention them a few times, but there isn't much about how your kids are the children of law professors and best-selling authors, and this might have something to do with their success.

Amy Chua: My book isn't about success or biology. It's just a memoir. I was raised by really strict Chinese immigrant parents and I tried to do the same with my two daughters. It worked in some ways, and not in others.

BC: Two passages stuck with me. You write about how your husband was raised in a very liberal way, and yet you describe this parenting as "doomed to fail". It didn't fail with your husband – he is a professor and bestselling author.

AC: Some people are just self-motivated – my husband was. I also believe there are many children for whom parental involvement is key. I had academic parents and I was a good student, but when I was 14, I got into a bad crowd, my grades starting falling. My father used some tough language on me, and now, as an adult, I am so grateful. Some people don't need parental commitment, they will still come out great, but for others, parents can be critical in providing moral and academic guidance.

BC: Most of my book is based on a summary of 40 years of adoption and twin studies – the usual result is parents just don't have much effect on their kids. In your book you have lots of great stories about how you influenced your kids, and I believe you did for a while, but what the adoption and twin evidence says is that the feeling that parents are changing their kids is based on an illusion. There is a big short-run effect, but the long-run effect is very different.

AC: My daughter Sophia would half-agree with you: somebody asked her if she would still be the same student had I not had high expectations, and she said yes. But she also said she would never have developed her love of music if it wasn't for me. My husband was given a choice by his mother when he was about six – do you want to start playing the violin or do you want to play with your friends? He chose his friends, of course. He still came out great, but he regrets that he doesn't read music. I feel a responsibility that doesn't seem to operate with you – I need to prepare my daughters for the world so they can have the opportunities.

BC: I'm very involved with my kids and we enjoy doing things together. We have a lot of common interests so I don't have to drag them to do things – we play games, we read comics. If you and your daughters enjoy music together, that is fantastic, but there is a lot in your book that makes it sound like there was a lot of suffering and anger that outweighed the happiness.

AC: My book is a bit of a spoof. I don't write about all the fun we had. I would be confident that we have just as much fun in my family as yours. In fact, because I'm strict and my kids don't spend as much time at other people's houses we have more family time to do things.

BC: You had a schedule in the book – one that I remember had "one hour of fun family time", and that was optional.

AC: That was a joke. It was a schedule for Saturday, and that was a day when we drove Lulu to Julliard [performing arts conservatory]. There is truth in jest; our Saturdays were crazy for two years. Those were the months before my daughter had a total rebellion. I pulled back after that, though not entirely – I still insisted on academic excellence, but I gave Lulu more choice and freedom.

BC: It seems your daughter beat you at your own game. It wasn't like you changed your mind about it.

AC: Parenting is the hardest thing I have ever done. I tried to find the balance between the strict, traditional Chinese way I was raised, which I think can be too harsh, and what I see as a tendency in the west to be too permissive and indulgent. If I could do it all again, I would, with some adjustments.

BC: Assuming that Lulu doesn't go back to the violin, why would you put her through all those years of arguing?

AC: Lulu actually did come back to the violin, on her own terms. She did not want me involved, she wanted to choose her own music, not play for two hours but play for 20 minutes every few days. Now she does it out of fun and love.

BC: I'm a huge classical music fan, but I'm grateful my parents didn't push me to learn an instrument, because I think I'd hate music if they had.

AC: That shows you can't win as a parent, because my husband wishes he had been pushed.

Emine Saner: Bryan, how would you describe your parenting style?

BC: I have three sons – eight-year-old identical twins and a baby. I'm not permissive, we do have discipline, but the point is to make sure they treat people decently. Once my kids were born, I realised that all these things that people say about parenting are wrong according to the best science. Parents seem to think their kids are like clay, that you mould them into the right shape when they're wet. A better metaphor is that kids are like flexible plastic – they respond to pressure, but when you release the pressure they tend to pop back to their original shape. I don't know Amy and her kids, but from my reading of the book the mother-daughter relationship seemed strained for many years, and that's sad.

AC: I instilled a sense of respect and discipline that will last them a lifetime. I don't think just by doing fun things and praising kids all the time that they develop that inner strength. When my kids wanted to give up on things, I wouldn't let them, and those are lifelong lessons. The reason my daughters say they would be strict parents themselves is because that represents a mother who loved her children more than anything.

BC: The feeling that parents have to do all this stuff for their kids, or else they are letting the kids down, is a big factor in people not wanting to have kids. In developed nations, birth rates are low, and I think that is due to people feeling having kids is a cross to bear. It's a lot easier to have more kids if you are honest with your limitations, realise they are their own people and their success in life is largely up to them and not you.

Battle Hymn of the Tiger Mother by Amy Chua is published by Bloomsbury. Selfish Reasons to Have More Kids: Why Being a Great Parent is Less Work and More Fun than You Think by Bryan Caplan is published by Basic Books