Yes, Virginia, increased supply reduces price

From Do new housing units in your backyard raise your rents? by Xiaodi Li.

From the Abstract:

There is a growing debate about whether new housing units increase rents for immediately surrounding apartments. Some argue new market-rate development produces a supply effect, which should alleviate the demand pressure on existing housing units and decrease their rents. Others contend that new development will attract high-income households and new amenities, generating an amenity effect and driving up rents. I contribute to this debate by estimating the impact of new high-rises on nearby residential rents, residential property sales prices and restaurant openings in New York City. To address the selection bias that developers are more likely to build new high-rises in fast-appreciating areas, I restrict the sample to residential properties near approved new high-rises and exploit the plausibly exogenous timing of completion conditional upon the timing of approval. I provide event study evidence that within 500 ft, for every 10% increase in the housing stock, rents decrease by 1%; and for every 10% increase in the condo stock, condo sales prices decrease by 0.9%. In addition, I show that new high-rises attract new restaurants, which is consistent with the hypothesis about amenity effects. However, I find that the supply effect dominates the amenity effect, causing net reductions in the rents and sales prices of nearby residential properties.

As theory suggests, her empirical evidence supports that increased supply leads to lower cost.

The result is useful in addressing those who might believe otherwise.