During the last 40 years in America which party has been in favor of open trade?

I would say the Republicans have had consistent support for free trade. I found this comment in an article online…

“All of the eleven free trade agreements on which Congress has voted since 2001 enjoyed the near-unanimous support of House Republicans, who backed ratification more than 91 percent of the time. ”

Someone much smarter than me had this to offer to your question….

Free trade has, until recently, been a part of what has been known as the “Washington Consensus.” While the Washington Consensus itself refers to the position that development is fostered by pro-free trade positions, in general people ‘within the beltway’ were in favor of free trade, regardless of party.
That is not to say that NAFTA was uncontroversial. Most notably, Ross Perot—the Donald Trump of his era—ran primarily in opposition to NAFTA, and he drew support primarily from Republican voters. Likewise, both parties had anti-NAFTA elements.
A look at the roll call votes in the House and in the Senate show how divided the parties were. Republicans were generally more supportive both historically, at the time and currently of free trade, but the support was far from uniform. In the senate 48% of Democratic senators supported the bill, with the remainder opposed and one not voting, while 79% of Republican Senators supported the bill. On the House side, 39.5% of the Democratic members voted for NAFTA, while 75% of Republican members supported the implementation bill. The sole independent, Bernie Sanders, voted against.
Of note, the Senate did not have the votes to override the President, Bill Clinton, and so his support was crucial to passage. Furthermore, neither party had enough support internally to pass the bill without the other’s support. At the time the Democrats controlled both houses, too.
In the end, neither party owns NAFTA alone, which partly explains its resilience. The Democrats thoroughly controlled government, and NAFTA would neither have been negotiated nor passed without the leadership’s support. However, had the Republicans not been as enthusiastic in their support, the Democrats could not have overcome weakness in their coalition to pass the bill alone.

They each have, at various times. Republicans were early on (70s, even into the 80s), while the Unions (largely democrats) were not because of the assumed loss of jobs.

But, as @Cruiser notes, that changed (and continues to change) as the world situation changed.

My view is that trade policy in 2016 is less driven by basic economics (because basic economics says that trade without barriers is a good thing), and more driven by partisan posturing and politics.

That said, the death of the TPP is a good thing. It was a crappy treaty that negotiated away a lot of our rights to intellectual property.

As usual, I don’t think the real answer can be accurately answered as framed. Not only do Republicans and Democrats not have cohesive views, and not only are they mostly all beholden to corporations, but “in favor of open trade” is generally not the issue at hand. Each trade agreement comes with many other details. Most people are probably broadly “for trade” but what conditions govern trade, and related riders attached to trade agreements, are more of the issues of concern.

The TPP/TPIP is/was a corporate power grab, designed to overcome all sorts of laws that protect people and the environment from corporate abuses, and also to guarantee corporate profits and free them from restrictions and fines and legal actions.

^^What he said. An attempt to allow trans-national corporations to rise in power above nations.