Dummy Amazon boxes with GPS tracking devices are being installed by police in the US in order to catch thieves taking them from outside peoples houses.

The increasing number of online shoppers over recent years has led to a rise in thefts of packages from unsuspecting residents during the festive period.

In Jersey City, across the Hudson River from New York, police are teaming up with Amazon to install doorbell cameras and plant the boxes at homes across the city.

After setting their trap earlier this week, officers did not have to wait long for someone to take the bait.

"We had a box out on the street for three minutes before it was taken," said police captain James Crecco, who is overseeing the operation. "We thought it was a mistake at first."

The suspect was caught, Mr Crecco added.

Exact figures on thefts are hard to come by, but one survey suggested up to 26 million Americans have had a holiday package stolen from their home. That would be the equivalent of one in 12 Americans.

Amazon — which is providing equipment free for the Jersey City program — declined to provide figures on how many packages are reported stolen or missing, as did UPS and FedEx.

"We absolutely report them to local law enforcement when we hear of them, and we encourage our customers to do the same," UPS spokesman Glenn Zaccara said.

Jersey City police chief Michael Kelly said the locations for cameras and boxes were selected using the city's own crime statistics and mapping of theft locations provided by Amazon.

"Most of the package thefts we've made arrests on revolve around (closed-circuit TV) or private surveillance cameras that give us a still image," Mr Kelly said. "With the bait packages, some will be under video surveillance, and some will have GPS."

No homeowner is immune. Mr Crecco said his mother was a victim of a package theft. So was mayor Steven Fulop, according to his spokeswoman.

Members of the police department who live in the city volunteered to have the cameras and boxes placed at their homes.

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Mr Kelly said the program has undergone a legal review and has been approved by a municipal prosecutor. He said the city is hoping to expand the programme with assistance from Amazon.

The online retailer declined to answer questions about the anti-theft programme, but said in a statement: "We appreciate the increased effort by local law enforcement to tackle package theft and remain committed to assisting however we can."

Similar programmes have been tried in other cities including Albuquerque, New Mexico, and Hayward, California.

E-commerce sales have been growing faster than sales at brick-and-mortar retailers for several years. Online sales in the US are forecast to increase 14.8 per cent from last year, to $124bn (£99bn), for November and December, according to Adobe Analytics, which tracks online spending.

The Postal Service expects to deliver about 900 million packages, and United Parcel Service forecasts it will handle about 800 million parcels between Thanksgiving and Christmas.

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That is causing a spike in deliveries to houses and apartments. Sometimes the residents are not home or not aware that a package has been dropped off.

The delivery companies provide services that could offer some protection against porch thefts. The boldest might be Amazon's Key service, in which homeowners pay to have a cloud-connected lock and camera installed at the front door, allowing an Amazon delivery person to unlock the door and slide the package inside.

Plenty of people went on social media to raise privacy and security objections after Amazon announced that service, but the company is betting that others will decide it is convenient.

Some other strategies for foiling snatch-and-run thieves require picking up packages at a company store, which defeats the purpose of at-home delivery.

To avoid parcels being left outside during extended absences, the post office has long allowed customers to set up hold-mail requests.

UPS and FedEx let customers sign up for alerts about deliveries and give them the chance to reschedule or change the drop-off address even for deliveries already on their way.

They let customers leave detailed instructions for drivers about where around the house to leave a package.

The delivery companies will also let customers pick up packages at other businesses. FedEx, for example, uses nearby shops.