Filtering is the process of housing units changing price over time and therefore tending to be inhabited by people of different income/wealth than previously. A related but distinguishable concept is "chain of housing turnover", in which newly available homes (e.g. new construction) are moved into by households who formerly did or otherwise would occupy another existing local home; this home in turn is left available for another household to move into, etc. Housing turnover research such as [Kristof 1965] and [Mast 2019] suggest that new market-rate housing has a strong effect in creating new housing opportunity to other households far down the income scale.
History of concept
Originally and most commonly, 'filtering' it refers to "filtering-down," whereby housing that was built for or occupied by a higher-income group becomes less expensive and occupied by households of lower income. Ratcliffe  defined it as
"the changing of occupancy as the housing that is occupied by one income group becomes available to the next lower income group as a result of decline in market price."
However, Lowry  analyzed filtering as change in value which could be up or down:
"I propose to define 'filtering' simply as a change in the real value (price in constant dollars) of an existing dwelling unit. ... To analyze filtering as a market process, its causes and consequences, four basic constructs should be kept in mind: (1) An array of all dwelling units according to their real values ... (2) An array of all dwelling units according to their quality (by some quantifiable measure other than price). (3) An array of all households according to their real incomes ... (4) An array of supply prices of new dwelling units in each quality class...."
later the concept of gentrification has been described as "filtering up." [Goetze 1979]
At least back to the 1940s in the United States, the concept of filtering has been used to support the argument that private, or market-rate, housing development can meet housing needs of much of the population, even if it is often originally built for or occupied by higher-income residents. While often made, the argument mostly lacked good empirical proof until Rosenthal's study (see below).
Kristof (1965) NYC "chain of housing turnover" study 
from Frank S. Kristof, Frank S. "Housing Policy Goals and the Turnover of Housing." AIP Journal (now JAPA: Journal of the American Institute of Planners), Volume 31, 1965, Issue 3, Pages 232-245:
In the summer of 1963, a project was completed that illustrated the chain of housing turnover generated by people moving into newly constructed units.2l Starting with an interview sample of 64 initially-occupied new units, the survey required a visit to each housing unit left vacant by the household that occupied the new unit. The successor household (if there was one) was interviewed, and the characteristics of its present as well as that of its previous housing unit was obtained. Its previous housing unit was then visited and the new household occupying that unit was interviewed in the same manner. The chain was followed until it was broken. This occurred when a household in the sample had not left a unit vacant in the City or when the unit in the sample was found to have remained vacant, was demolished, or had been otherwise removed from the market.‘*
Although no claims are made about the representativeness of the sample, the implications that could be drawn from the survey data were quite dramatic. It was found, for every 10 newly constructed units in the sample, 24 families were able to make voluntary and presumably more satisfactory adjustments in their housing circumstances-10 by moving into the new units and 14 by moving into existing units made vacant by the housing turnover that ensued. The data further indicated that the chain of housing moves generated through new construction resulted in an improvement of the housing status of nearly all the families involved.
Rosenthal (2014) US-wide empirical study of filtering
Substantial evidence for filtering effects was presented in (Stuart Rosenthal, 2014), "Are Private Markets and Filtering a Viable Source of Low-Income Housing? Estimates from a 'Repeat Income' Model." in American Economic Review. https://drive.google.com/open?id=1tDFiyW5rVEUtx9rceWZjTDJPODX3NeEO. He dmonstrated that filtering occurs widely, although significantly less so in recent decades in high-cost, supply-constrained areas such as the Bay Area and Boston.
Comment from Dan Immergluck, 2 January 2017:
"I read Rosenthal piece as showing that incomes decline annually 7 times as fast as rents -->rent-to-income ratio increasing over time. And given high rents of new units being produced, I am not sure how this can be viewed as providing "affordable housing" to lower-income folks."
Comment from YIMBYwiki, 2 January 2017:
"counterpoint to Dan: even if rent:income ratio or price:income ratio increases, the unit may still be affordable to the tenant. Higher-income/wealth renters typically spend lower % of income on housing, so the ratio might often increase a lot and still be affordable."
Comment from YIMBYwiki, 2 January 2017:
also, fwiw, the households occupying down-filtered units are affording them at least in the sense of being able to move into them. They could be cost-burdened, but otoh the fact they could get the unit suggests they met some income:rent standard of the landlord.
Comment from Dan Immergluck, 2 January 2017:
"In most cities the bulk of folks under 50% AMI cost burdened. That means most landlords are accepting high rent to income ratios. Often over 50%.
Look at recent work by
@jenny_schuetz. Esp at what this means in terms of residual incomes."
Mast (2019) chain-of-turnover study 
Mast, Evan. "The Effect of New Market-Rate Housing Construction on the Low-Income Housing Market." Upjohn Institute Working Paper 19307. July, 2019. https://www.dropbox.com/s/zuzxvupdbqcvhql/Mast%20Luxury%20Housing.pdf
Alternate terms / way of explaining filtering
"Taking pressure off the existing housing stock is normally how I phrase it. " - Laura Clark, YIMBY Action. 7 Dec 2017.
Sightline "Musical Chairs" concept and video.
Other ways new housing can affect affordability
Filtering is not the only way in which new market-rate housing may address affordability for other income groups, however. Other reasons are 1) fungibility/substitution, 2) adaptation; 3) helping to subsidize other housing.
1) Fungibility / substitution
(see also "chain of housing turnover" above)
The degree to which different housing units, or any good, may equivalently serve someone's needs is sometimes called fungibility, or substitutability. See Wikipedia: fungibility. In the case of market-rate housing, it is likely that often there is enough fungibility between available housing units that the buyer/renter, if that MR housing had not been developed, would have sought out another unit in the area, excluding or potentially displacing another, probably lower-income person, from that unit.
2) Adaptation 
Second, housing may be used differently or converted from its original intended use, possibly serving other and lower-income residents. Houses and apartments become shared between multiple tenants, either informally as house- or apartment-shares, or possibly by being divided into multiple legal residences. This can occur even with the first tenants of new housing, for example in San Francisco where vacant new "luxury" apartments are sometimes divided and shared between many tenants.
3) Funding for other housing
New market rate housing projects may include or generate funds for affordable housing through Inclusionary housing programs, through Impact fees, or more generally by increasing city and state tax bases to allow funding for other housing.
- Brummet & Reed on Effects of Gentrification (2019). https://philadelphiafed.org/-/media/community-development/publications/discussion-papers/discussion-paper_the-effects-of-gentrification-on-the-well-being-and-opportunity-of-original-resident-adults-and-children.pdf.
- Cortright, Joe. Urban myth busting: Why building more high income housing helps affordability. City Observatory. 20 Feb 2017.
[note, article states "the median value of rental housing declines by about 2.2% per year" citing [Rosenthal 2014], this seems to be a mistake. Dan Immergluck notes "Rosenthal paper says that 2.2% per year decline is in INCOMES of the tenants, NOT price/rent of unit. The decline in RENTS is closer to 0.3% per year."
- Ding, L., Hwang, J., and Divringi, E. (2016). Gentrification and residential mobility in Philadelphia. Regional Science and Urban Economics, 61:38–51. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5450830/.
- Dragan, K., Ellen, I. G., and Glied, S. A. (2019). Does gentrification displace poor children? New evidence from New York City Medicaid data. https://furmancenter.org/files/Does_Gentrification_Displace_Poor_Children.pdf.
- Ellen, I. G. and O’Regan, K. M. (2011b). How low income neighborhoods change: Entry, exit, and enhancement. Regional Science and Urban Economics, 41(2):89–97. https://www.sciencedirect.com/science/article/abs/pii/S0166046211000044.
- Freeman, L. (2005). Displacement or succession? Residential mobility in gentrifying neighborhoods. Urban Affairs Review, 40(4):463–49. https://journals.sagepub.com/doi/abs/10.1177/1078087404273341.
- Goetze, Understanding Neighborhood Change, 1979.
Apparent first use of "filtering up" as a term or definition for gentrification.
- Gray, Nolan. "How Luxury Units Turn Into Affordable Housing: Building more high-end apartments doesn’t sound like a quick fix for the affordable housing crisis. But maybe you just have to look harder." Citylab, June 5, 2019. [discussing Mast 2019 paper]. https://www.citylab.com/perspective/2019/06/housing-supply-debate-affordable-home-prices-rent-yimby/591061.
- Hertz, Daniel. "What filtering can and can’t do." City Observatory, 10.11.2015. http://cityobservatory.org/what-filtering-can-and-cant-do/.
- Kristof, Frank S. "Housing Policy Goals and the Turnover of Housing." AIP Journal (now JAPA: Journal of the American Institute of Planners), Volume 31, 1965, Issue 3, Pages 232-245. https://doi.org/10.1080/01944366508978170. PDF: https://drive.google.com/open?id=1xaM4ODiP9KUJH-Gjgqr53Xzl2tWhrlRg.
- Lehner, Josh. “Why Housing Supply Matters.” Oregon Office of Economic Analysis (State of Oregon). December 14, 2017
“Last week, I was a panel member for the YIMBY (Yes In My Back Yard) breakout discussion at the Oregon Leadership Summit. The group overall discussed the lack of supply, the importance of affordability, some regulations, market conditions, public policies and the like. It was a wide-ranging and informative session, if I may say so myself. Today I want to recap a few things, and take another stab at visualizing the importance of housing supply and the role of filtering.”
“Housing does filter. New construction is always expensive and always aimed at the upper third or so of the market. That said, over time as housing depreciates, it does become more affordable. This filtering does not happen overnight. It is a long-run process. Filtering is also the major way to provide reasonably priced workforce housing for those making in and around the median family income. There is not nearly enough public money to fund the affordability gap,
“Finally, what follows is another effort to show how filtering works in the real world. What the charts below show is the current housing stock in the Portland metro based on the recently released 2016 American Community Survey data. The first chart shows the housing stock divided into thirds based on home values or monthly rents*. Then we look at when these units were built by decade.”
- Lowry, Ira S. "Filtering and Housing Standards: A Conceptual Analysis." Land Economics, Vol. 36, No. 4 (Nov., 1960), pp. 362-370
- Mast, Evan. "The Effect of New Market-Rate Housing Construction on the Low-Income Housing Market." Upjohn Institute Working Paper 19307. July, 2019. https://www.dropbox.com/s/zuzxvupdbqcvhql/Mast%20Luxury%20Housing.pdf
- Nathanson, C. (2019). Trickle-down housing economics. Working Paper https://static1.squarespace.com/static/58d44831ebbd1a1fe2ff449d/t/5df967a60004cd5b04df01b5/1576626086993/TrickleDownHousingEconomics.pdf.
- Ratcliff, Richard Updegraff. "The Economics of the Housing Problem: Preliminary Draft." (1945)
- Ratcliff, Richard Updegraff. Urban Land Economics (1949).
- Rosenthal, Stuart S. . "Are Private Markets and Filtering a Viable Source of Low-Income Housing? Estimates from a 'Repeat Income' Model." American Economic Review, 104(2): 687-706 (February 2014). DOI: 10.1257/aer.104.2.687. Preprint (2013): http://faculty.maxwell.syr.edu/rosenthal/recent%20papers/Is_Filtering_a_Viable_Source_of_Low-Income_Housing_%206_18_13.pdf.https://drive.google.com/open?id=1tDFiyW5rVEUtx9rceWZjTDJPODX3NeEO.
- Zuk, Miriam, and Karen Chapple. "Housing Production, Filtering and Displacement: Untangling the Relationships." Berkeley Institute of Government Studies - Research Brief, May 2016.