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Most parents tell lies to their children as a tactic to change their behaviour, suggests a study of families in the United States and China.

The most frequent example was parents threatening to leave children alone in public unless they behaved.

Persuasion ranged from invoking the support of the tooth fairy to telling children they would go blind unless they ate particular vegetables.

Another strategic example was: "That was beautiful piano playing."

The study, published in the International Journal of Psychology, examined the use of "instrumental lying" - and found that such tactically-deployed falsehoods were used by an overwhelming majority of parents in both the United States and China - based on interviews with about 200 families.

The most commonly used lie - popular with both US and Chinese families - was parents pretending to a child that they were going to walk away and leave the child to his or her tantrum.

"The pervasiveness of this lie may relate to the universality of the challenge parents face in trying to leave a place against their child's wishes," say the researchers.

Another lie that was common in both countries was the "false promise to buy a requested toy at some indefinite time in the future".

Researchers established different categories of these untruths.

There were "untrue statements related to misbehaviour", which included: ''If you don't behave, I will call the police," and: "If you don't quiet down and start behaving, the lady over there will be angry with you.''

If these seem rather unheroic examples of parenting by proxy threat, there are some more startling lies recorded.

Under the category of "Untrue statements related to leaving or staying" a parent was recorded as saying: "If you don't follow me, a kidnapper will come to kidnap you while I'm gone."

There were also lies motivated by protecting a child's feelings - labelled as "Untrue statements related to positive feelings."

This included the optimistic: "Your pet went to live on your uncle's farm where he will have more space to run around."

A rather self-serving untruth was used for a quick getaway from a toy shop: ''I did not bring money with me today. We can come back another day."

There was also a selection of lies relating to "fantasy characters", also used to enforce good behaviour, such as in the run-up to Christmas.

The study found no clear difference between the lies used by mothers and fathers, according to researchers, who were from psychology departments at the University of California San Diego in the US, Zhejiang Normal University, Jinhua in China and the University of Toronto, Canada.

Although levels of such "instrumental lying" were high in both countries, they were highest in China.

The study found there was an acceptance of such lies among parents when they were used as a way of reinforcing desirable social behaviour.

For example, the lie told to children that they would grow taller for every bite of broccoli was seen as encouraging healthy eating habits.

The study raises the longer-term issue of the impact on families of such opportunistic approaches to the truth. It suggests it could influence family relationships as children get older.

The researchers, headed by Gail D. Heymana, Anna S. Hsua, Genyue Fub and Kang Leeac, concluded that this raises "important moral questions for parents about when, if ever, parental lying is justified".