Is there a link between Immigration Policy and Inflation?

Inflation theories tend to cause a lot of debate, and the few responses I’ve gotten from economists on this question have been variations of “probably not”. Hoping people here have access to good quality heterodox research and studies that give a slightly better answer one way or another. My Google efforts have failed so far.

The conventional position on rising inflation as I understand it is:

Something causes Aggregate Demand to rise, or Aggregate Supply to drop, or both, for some sustained period, causing an increase in prices.

This “something” could be increased money supply or some policy which raises consumption, and therefore Aggregate Demand. If production cannot keep up with this increased demand, prices rise.

Similarly, production costs could go up because of supply-chain issues or higher wage demands, causing Aggregate Supply to drop. If consumer demand doesn’t cool off simultaneously, prices rise.

Alternatively, the Monetarist view is that an increase in money supply must be matched by a simultaneous increase in productivity. Unless the economy is able to produce more with less (via technology, efficiency, labor output etc.), the value backed by each currency unit goes down, and prices rise.

Further, higher prices, or even expectations that they will stay high, can result in an inflation spiral:

  1. Higher prices create higher wage demands to cover higher cost of living

  2. Higher wages result in higher costs of production

  3. Higher costs of production result in increased prices

  4. Go to Step 1.

The current tool to arrest this, at least in the U.S, is to raise interest rates. Which results in some combination of reducing money supply and lowering Aggregate Demand to bring prices back under control. But this often has the side affect of a recession—reducing new investment and spending (borrowing is expensive) and thereby reducing job and economic growth.

Whether or not this perfectly represents the views (I’m not an economist), there are a few variables which stand out regardless: higher wage demands and insufficient productivity.

Immigration Policy

Were there a steady influx of immigrants increasing labor supply, would it counter this increase in wage demands? Additionally if one agrees with the premise that immigrants tend to contribute across the skill spectrum and are a source of innovation, does greater immigration result in higher long-term productivity?

And therefore, could slowing down immigration i.e. tightening immigration policy, be a contributing cause for inflation? And increasing immigration be one additional tool to fight it?

To do a very cursory check to see if this was reflected in some data, I looked up Immigrant Share of Population in the U.S:

Which showed a steady decline to historic lows into the 70s inflation period. Additionally, there has been a slowing down of immigration post 2008, but especially in the last 5 years: Axios: Share of U.S. immigrant population drops for first time in 10 years:

And finally, unauthorized immigration trends from Pew:

None of this of course comes close to implying causality, but I found the trends at least worthy of investigation given the hypothesis. A hypothesis which passes the initial gut check for me.

Prima facie, it seems like it would have at least some impact—yet I find no mention of immigration in discussions around causes and solutions for inflation. eg. How the Great Inflation of the 1970s Happened.

So, is there are relevant theory that looks into the link between Immigration Policy and Inflation, or studies it empirically? And if so, has any causal relationship ever been found (one direction or the other)? And has it’s use as a tool to fight Inflation ever been tested?