## 4.1    First Stage

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---

### First-stage evidence
- Figure 2: positive first-stage correlations between the shift-share instrument and net immigration per capita across immigrant subgroups.
- Appendix Table A2: first-stage estimates reported.
- F statistics for first-stage partial correlations range from 21 to 43 across immigrant subgroups.
- Instrument is strong, with first-stage F statistics well above the standard rule of thumb of 10.

### Headline Inflation (Section 4.2)
- Two-stage least squares using the shift-share instrument with headline RPP inflation as the dependent variable (Table A3) yields:
  - Immigration reduces local inflation relative to other MSAs (column 1).
  - Effect almost doubled when considering only the working-age population (Ages 18 to 64) (column 2), suggesting labor supply is important.
  - Less educated immigrants in particular lower local prices; more highly-educated immigrants have no discernable impact on inflation (columns 3–6).
- Point estimates (Table 1, MSA-level Inflation (%)):
  - Immigration (% of Pop. in T-1): −0.657 (All) with robust standard error (0.241), IV F-statistic 42.66, Observations 3,588.
  - Immigration (% of Pop. in T-1): −1.096 (18 to 64) (0.420), IV F-statistic 26.62.
  - Immigration (% of Pop. in T-1): −2.402 (No HS) (1.050), IV F-statistic 27.81.
  - Immigration (% of Pop. in T-1): −2.032 (No College) (0.767), IV F-statistic 21.19.
  - Immigration (% of Pop. in T-1): −0.343 (At least HS) (0.384), IV F-statistic 27.62.
  - Immigration (% of Pop. in T-1): 0.256 (Some College) (0.467), IV F-statistic 37.04.
- Magnitude interpretation:
  - On average annual migrant inflows are equivalent to around 0.2% of the population, a rate which approximately doubled in 2022.
  - Marginal impact of such a doubling of immigration from the mean (or reducing immigration to zero) would lower (raise) inflation by about 0.1 to 0.2 p.p.
    - Footnote calculation: −0.657 × 0.2 ≃ −0.13.
    - Total contribution at the doubled level or increasing immigration by 0.4 p.p: −0.657 × 0.4 ≃ −0.3.
- Robustness:
  - Findings robust to controlling for US-born population growth, controlling for local unemployment, and restricting to the pre-COVID pandemic period (Table A5).
  - No evidence of spillovers to MSAs in the same state (Table A4).

### Validity (Section 4.3)

#### Pre-trends (4.3.1)
- Pre-trend tests follow Goldsmith-Pinkham et al. (2020) and Borusyak et al. (2024).
- IV specification estimated on inflation in lagged periods T ∈ {−1, −2, −3, −4} (Table 2).
- IV estimates on inflation in all lagged periods are insignificant; instrument is uncorrelated with pre-period inflation.
- Selected pre-trend point estimates and standard errors (Table 2):
  - Inflation (%) in T=−1: Immigration (% of Pop. in T-1) 0.327 (All) (0.221); 0.297 (18 to 64) (0.362); 0.290 (No HS) (0.673); 0.342 (No College) (0.539); 0.311 (At least HS) (0.364); 0.364 (Some College) (0.418).
  - Inflation (%) in T=−2: Immigration (% of Pop. in T-1) −0.111 (All) (0.250); −0.251 (18 to 64) (0.411); −1.133 (No HS) (0.952); −0.269 (No College) (0.607); 0.211 (At least HS) (0.429); −0.433 (Some College) (0.489).
  - Inflation (%) in T=−3: Immigration (% of Pop. in T-1) −0.085 (All) (0.252); −0.131 (18 to 64) (0.362); −0.527 (No HS) (0.714); 0.003 (No College) (0.534); −0.071 (At least HS) (0.423); 0.196 (Some College) (0.497).
  - Inflation (%) in T=−4: Immigration (% of Pop. in T-1) −0.043 (All) (0.225); −0.040 (18 to 64) (0.304); 0.782 (No HS) (0.579); 0.147 (No College) (0.343); −0.693 (At least HS) (0.518); −0.504 (Some College) (0.431).
- IV F-statistics across these specifications: 42.66, 26.62, 27.81, 27.62, 21.19, 37.04 (matching Table 1).

#### Rotemberg weights (4.3.2)
- Decomposition: estimated effect β̂ decomposed into weighted average of origin-country-specific just-identified estimates β̂c with weights α̂c.
- Top five origin country groups by Rotemberg weight (Table 3):
  - Mexico: α̂c 0.248; β̂c −0.774; Largest destination MSA Los Angeles-Long Beach-Anaheim, CA; Share of emigration to largest MSA 0.08.
  - Central America: α̂c 0.184; β̂c −1.015; Largest destination MSA Houston-The Woodlands-Sugar Land, TX; Share 0.09.
  - India: α̂c 0.131; β̂c −0.477; Largest destination MSA New York-Newark-Jersey City, NY-NJ-PA; Share 0.10.
  - West Indies: α̂c 0.105; β̂c −0.822; Largest destination MSA New York-Newark-Jersey City, NY-NJ-PA; Share 0.15.
  - Cuba: α̂c 0.085; β̂c −0.593; Largest destination MSA Miami-Fort Lauderdale-West Palm Beach, FL; Share 0.22.
- No single origin dominates: largest Rotemberg weight (Mexico) is less than 25 percent.
- β̂c estimates consistently negative across origin regions.
- Emigrant flows well-distributed: most important cities account for no more than one tenth of departing migrants for the three most influential countries (reported shares).

#### Correlation of Rotemberg weights with shifts and shares
- Correlation matrix (Table 4):
  - Corr(α̂c, ∆F c) = 0.784.
  - Corr(α̂c, Var(sh c)) = 0.217.
  - Corr(∆F c, Var(sh c)) = 0.116.
- Interpretation: results largely driven by the "shifts" (national immigrant flows). Shifts explain about 61% (=0.784^2) of the variation in the weights.

### Heterogeneity by Goods vs Services (Section 4.4)
- Analysis uses four major subcomponents of the RPP (Table 5).
- Main findings:
  - When immigration increases, goods inflation falls (magnitudes similar to overall price change) and utilities inflation increases.
  - Effects largest for working-age immigrants, amplified for less educated immigrants, and mitigated for more educated immigrants.
  - Non-utilities, non-housing services show mixed results: no effect overall but disinflation for less educated immigrants and inflation for more educated immigrants.
  - Housing inflation (RPP) is statistically null; limitations of the RPP housing series are an important caveat.
- Selected point estimates (Table 5):
  - Panel A. Goods — Immigration (% of Pop. in T-1):
    - All: −0.697 (0.284) [∗∗]
    - 18 to 64: −1.064 (0.461) [∗∗]
    - No HS: −2.431 (1.068) [∗∗]
    - No College: −1.689 (0.746) [∗∗]
    - At least HS: −0.389 (0.468)
    - Some College: −0.327 (0.503)
  - Panel B. Services ex. Utilities and Housing — Immigration (% of Pop. in T-1):
    - All: 0.007 (0.246)
    - 18 to 64: −0.117 (0.378)
    - No HS: −2.239 (1.136) [∗∗]
    - No College: −1.125 (0.638) [∗]
    - At least HS: 0.792 (0.445) [∗]
    - Some College: 1.311 (0.565) [∗∗]
  - Panel C. Services: Utilities — Immigration (% of Pop. in T-1):
    - All: 1.709 (0.768) [∗∗]
    - 18 to 64: 2.336 (1.199) [∗]
    - No HS: 2.287 (1.616)
    - No College: 3.518 (1.720) [∗∗]
    - At least HS: 1.666 (1.300)
    - Some College: 0.653 (1.297)
  - Panel D. Services: Housing — Immigration (% of Pop. in T-1):
    - All: −1.119 (0.892)
    - 18 to 64: −1.864 (1.483)
    - No HS: −0.496 (2.837)
    - No College: −2.364 (2.193)
    - At least HS: −1.721 (1.445)
    - Some College: −0.776 (1.683)
- IV F-statistics and Observations match previously reported (IV F-statistic 42.66, 26.62, 27.81, 21.19, 27.62, 37.04; Observations 3,588 per column).

### Housing (Section 4.5)
- RPP housing index concerns motivate use of Zillow Home Value Index (ZHVI) and Zillow Observed Rent Index (ZORI).
- Using Zillow measures:
  - Immigration increases local housing inflation relative to other MSAs (Table 6).
  - Effect driven by high-education immigration (at least high school graduates).
  - Low-education immigration (no high school) has no statistically significant impact on housing inflation.
- Table 6 (Housing Inflation (%): IV), dependent variable log difference of Zillow Home Value Index (All Homes):
  - Immigration (% of Pop.) All: 2.470 (0.646) [∗∗∗]
  - Immigration (% of Pop.) 18 to 64: 3.319 (1.091) [∗∗∗]
  - Immigration (% of Pop.) No HS: −0.991 (1.188)
  - Immigration (% of Pop.) No College: 2.842 (1.358) [∗∗]
  - Immigration (% of Pop.) At least HS: 5.084 (1.343) [∗∗∗]
  - Immigration (% of Pop.) Some College: 4.284 (1.351) [∗∗∗]
  - IV F-statistics and sample: IV F-statistic 42.66, 26.62, 27.81, 27.62, 21.19, 37.04; Observations 3319 / 3319 / 3319 / 3319 / 3319 / 3319.
- Zillow rents (ZORI) results (Table 7, Rental Inflation (%): IV):
  - Immigration (% of Pop.) All: 2.076 (1.040) [∗∗]
  - Immigration (% of Pop.) 18 to 64: 3.506 (1.940) [∗]
  - Immigration (% of Pop.) No HS: 1.604 (1.187)
  - Immigration (% of Pop.) No College: 3.316 (1.566) [∗∗]
  - Immigration (% of Pop.) At least HS: 6.141 (4.595)
  - Immigration (% of Pop.) Some College: −0.138 (1.415)
  - Num. obs. 1454 (sample covers 306 MSAs and years from 2015 to 2022 for rent data).

### Dynamic responses (Section 4.6)
- Local projections follow Jordà (2005) to capture dynamics.
- Inflation rate dynamics (Figure 3a):
  - Replace dependent variable with t+h period equivalent for h = 0, 1, 2, 3.
  - Immigration lowers contemporaneous inflation but raises it thereafter; subsequent effects are statistically insignificant.
- Price level dynamics (Figure 3b):
  - Dependent variable is change in price level in period t+h relative to period t−1.
  - Immigration lowers overall price level contemporaneously; price level statistically indistinguishable from that in t−1 in future years.
- Persistence by category:
  - Except for housing, price level impact of immigration on all subcategories is transitory.
  - Housing prices:
    - Immigration increases housing prices persistently over time (positive and statistically significant impact as far as 4 years), driven by high-education immigration.
    - Low-education immigration has no impact on housing prices in the first year but lowers housing prices persistently starting in the second year (negative and statistically significant as far as 3 years).
    - Pattern consistent with a lagged impact from increased (low-education) labor supply to housing construction.
- Figures:
  - Figure 4 shows impacts on Zillow and RPP housing indices across lags/leads (periods −3 to 4) with panels for All Residents, No HS Diploma, No College, and Some College.

### Comparison to other estimates (Section 4.7)
- Cortes (2008):
  - Decennial census-based estimate converted to this paper’s units: roughly coefficient of −0.09.
  - About twenty times smaller than this paper’s most directly comparable estimates for low-education workers (between −2.0 and −2.4).
  - Interpretation: long-run estimates may miss important contemporaneous effects that fade; dynamic results support this.
  - Footnote reproduction: Cortes (2008) implies annual per-percentage impact ≃ −0.09 given described calculations.
- Lach (2007):
  - One percentage point increase in the immigrant-to-native ratio reduced grocery store goods prices by 0.5 percent point; result close to this paper’s findings for goods.
- Sample size and power:
  - Cortes (2008) and Lach (2007) have only 90 and 52 distinct values respectively for the dependent variable because variation in immigration is at city or city-decade level.
  - Present study has over 3,500 distinct values, providing increased statistical power.
- Key takeaway:
  - Measurement horizon matters: contemporaneous responses can be substantially larger than long-run estimates, consistent with dynamic evidence.

### Interpretation (Section 5)
- Three key empirical results:
  - More immigration → lower local inflation relative to elsewhere (overall price level).
  - Product-specific responses: goods prices fall, services change little, utilities and housing increase (housing dependent on measure used).
  - Magnitude larger when immigrants have less education.
- Conceptual framework and mechanism:
  - Two-good region, convex and homothetic consumer preferences; non-homothetic production via different elasticities of supply.
  - Core insight: direction of relative local price changes is a function of relative supply elasticities; magnitude depends on elasticity of substitution between goods.
  - Algebraic decomposition (Appendix):
    - dlog(py/px)/dlogL1 = [εx/(1+εx) − εy/(1+εy)] (Direct effect) + (1+γ)^{-1} (Indirect effect)
    - εx, εy supply elasticities; γ decreasing function of elasticity of substitution; γ positive iff elasticity of substitution < 1; γ = −1 for perfect substitutes.
    - Direct effect: change in relative price if labor shares remained constant.
    - Indirect effect: labor reallocation induced by relative price changes.
    - Aggregate price level response: expenditure-share-weighted average of product-specific responses.
- How framework maps to findings:
  - Goods vs services: supply of goods more elastic than services → goods prices fall more.
  - Housing: very inelastic short-run supply → housing prices rise.
  - Education heterogeneity: less-educated labor more substitutable for capital → larger downward pressure where less-educated immigrants concentrate.
  - Dynamics/horizon: fixed capital assumption short-run; capital adjustment long-run can neutralize relative price effects (consistent with smaller long-run impacts except where land is fixed).
- Caveats and departures:
  - Trade linking relative price levels across regions.
  - Non-homothetic aggregate preferences if immigrant preferences differ.
  - Simple non-homothetic short-run framework remains coherent and parsimonious in interpreting empirical patterns.

### Conclusion (Section 6)
- Empirical summary:
  - Using a shift-share instrument, immigration reduces local inflation relative to other MSAs, strongest when immigrants are working-age and less educated.
  - Immigration lowers local goods inflation, increases housing inflation, negligible effect on services.
  - Less educated immigrants tend to be more disinflationary than more educated immigrants.
  - Longer-run price effects much smaller and typically statistically indistinguishable from zero; exception: housing, where effects can last several years depending on immigrant education composition.
- Interpretation and mechanism:
  - Inward immigration increases labor supply when production is non-homothetic in short run (capital fixed), leading to larger relative price declines in industries where labor is more substitutable for capital.
  - Observed patterns: goods prices decline, housing prices increase; less-educated immigrants lower prices, higher-educated immigrants raise them.
  - Long-run neutrality of relative prices (except sectors with fixed factors like land) consistent with capital adjustment eliminating non-homotheticities.
- Open questions and future research directions:
  - Use more detailed pricing data to identify specific goods and services most affected by immigration.
  - Analyze more recent consumer survey data to compare opinions on local prices with actual price changes in response to immigration.
  - Extend static mechanisms to a full dynamic stochastic general equilibrium model.

*Source: wpiea2025005-print-pdf*

### 4.1    First Stage

### 4.1    First Stage

### First-stage evidence
- Figure 2 shows positive first-stage correlations between the shift-share instrument and net immigration per capita across immigrant subgroups.
- Appendix Table A2 reports first-stage estimates.
- The F statistics for these first-stage partial correlations range from 21 to 43 across immigrant subgroups.
- The instrument is strong, with the first-stage F statistics well above the standard rule of thumb of 10.

### Headline Inflation (Section 4.2)
- Two-stage least squares using the shift-share instrument with headline RPP inflation as the dependent variable (Table A3) yields:
  - Immigration reduces local inflation relative to other MSAs (column 1).
  - The effect is almost doubled when considering only the working-age population (Ages 18 to 64) (column 2), suggesting labor supply is important.
  - Less educated immigrants in particular lower local prices; more highly-educated immigrants have no discernable impact on inflation (columns 3–6).
- Point estimates (Table 1, MSA-level Inflation (%)):
  - Immigration (% of Pop. in T-1): −0.657 (All) with robust standard error (0.241), IV F-statistic 42.66, Observations 3,588.
  - Immigration (% of Pop. in T-1): −1.096 (18 to 64) (0.420), IV F-statistic 26.62.
  - Immigration (% of Pop. in T-1): −2.402 (No HS) (1.050), IV F-statistic 27.81.
  - Immigration (% of Pop. in T-1): −2.032 (No College) (0.767), IV F-statistic 21.19.
  - Immigration (% of Pop. in T-1): −0.343 (At least HS) (0.384), IV F-statistic 27.62.
  - Immigration (% of Pop. in T-1): 0.256 (Some College) (0.467), IV F-statistic 37.04.
- Magnitude interpretation:
  - On average annual migrant inflows are equivalent to around 0.2% of the population, a rate which approximately doubled in 2022.
  - The marginal impact of such a doubling of immigration from the mean (or reducing immigration to zero) would lower (raise) inflation by about 0.1 to 0.2 p.p.
    - Footnote calculation: The impact of doubling or increasing immigration by 0.2 p.p. on inflation is −0.657 × 0.2 ≃ −0.13.
    - The total contribution of immigration at the doubled level (the 2022 level) or increasing immigration by 0.4 p.p to inflation is −0.657 × 0.4 ≃ −0.3.
- Robustness:
  - Findings are robust to controlling for US-born population growth, controlling for local unemployment, and restricting to the pre-COVID pandemic period (Table A5).
  - No evidence of spillovers to MSAs in the same state (Table A4).

### Validity (Section 4.3)

H3: Pre-trends (4.3.1)
- Pre-trend tests follow Goldsmith-Pinkham et al. (2020) and Borusyak et al. (2024).
- IV specification estimated on inflation in lagged periods T ∈ {−1, −2, −3, −4} (Table 2).
- IV estimates on inflation in all lagged periods are insignificant; instrument is uncorrelated with pre-period inflation.
- Selected pre-trend point estimates and standard errors (Table 2):
  - Inflation (%) in T=−1: Immigration (% of Pop. in T-1) 0.327 (All) (0.221); 0.297 (18 to 64) (0.362); 0.290 (No HS) (0.673); 0.342 (No College) (0.539); 0.311 (At least HS) (0.364); 0.364 (Some College) (0.418).
  - Inflation (%) in T=−2: Immigration (% of Pop. in T-1) −0.111 (All) (0.250); −0.251 (18 to 64) (0.411); −1.133 (No HS) (0.952); −0.269 (No College) (0.607); 0.211 (At least HS) (0.429); −0.433 (Some College) (0.489).
  - Inflation (%) in T=−3: Immigration (% of Pop. in T-1) −0.085 (All) (0.252); −0.131 (18 to 64) (0.362); −0.527 (No HS) (0.714); 0.003 (No College) (0.534); −0.071 (At least HS) (0.423); 0.196 (Some College) (0.497).
  - Inflation (%) in T=−4: Immigration (% of Pop. in T-1) −0.043 (All) (0.225); −0.040 (18 to 64) (0.304); 0.782 (No HS) (0.579); 0.147 (No College) (0.343); −0.693 (At least HS) (0.518); −0.504 (Some College) (0.431).
- IV F-statistics across these specifications: 42.66, 26.62, 27.81, 27.62, 21.19, 37.04 (matching Table 1).

H3: Rotemberg weights (4.3.2)
- Decomposition of estimated effect β̂ into weighted average of origin-country-specific just-identified estimates β̂c with weights α̂c (Rotemberg weights).
- Top five origin country groups by Rotemberg weight (Table 3):
  - Mexico: α̂c 0.248; β̂c −0.774; Largest destination MSA Los Angeles-Long Beach-Anaheim, CA; Share of emigration to largest MSA 0.08.
  - Central America: α̂c 0.184; β̂c −1.015; Largest destination MSA Houston-The Woodlands-Sugar Land, TX; Share 0.09.
  - India: α̂c 0.131; β̂c −0.477; Largest destination MSA New York-Newark-Jersey City, NY-NJ-PA; Share 0.10.
  - West Indies: α̂c 0.105; β̂c −0.822; Largest destination MSA New York-Newark-Jersey City, NY-NJ-PA; Share 0.15.
  - Cuba: α̂c 0.085; β̂c −0.593; Largest destination MSA Miami-Fort Lauderdale-West Palm Beach, FL; Share 0.22.
- No single origin dominates: the largest Rotemberg weight (Mexico) is less than 25 percent.
- β̂c estimates are consistently negative across origin regions.
- Emigrant flows are well-distributed: even the most important cities account for no more than one tenth of departing migrants for the three most influential countries (reported shares).

H3: Correlation of Rotemberg weights with shifts and shares
- Correlation matrix (Table 4):
  - Correlation between α̂c and ∆F c is 0.784.
  - Correlation between α̂c and Var(sh c) is 0.217.
  - Correlation between ∆F c and Var(sh c) is 0.116.
- Interpretation: results are largely driven by the "shifts" (national immigrant flows). The shifts explain about 61% (=0.784^2) of the variation in the weights.

### Heterogeneity by Goods vs Services (Section 4.4)
- Analysis uses four major subcomponents of the RPP (Table 5).
- Main findings:
  - When immigration increases, goods inflation falls (magnitudes similar to overall price change) and utilities inflation increases.
  - Effects are largest for working age immigrants, amplified for less educated immigrants, and mitigated for more educated immigrants.
  - Non-utilities, non-housing services show mixed results: no effect overall but disinflation for less educated immigrants and inflation for more educated immigrants.
  - Housing inflation (RPP) is statistically null; limitations of the RPP housing series are an important caveat.
- Selected point estimates (Table 5):
  - Panel A. Goods — Immigration (% of Pop. in T-1):
    - All: −0.697 (0.284) [∗∗]
    - 18 to 64: −1.064 (0.461) [∗∗]
    - No HS: −2.431 (1.068) [∗∗]
    - No College: −1.689 (0.746) [∗∗]
    - At least HS: −0.389 (0.468)
    - Some College: −0.327 (0.503)
  - Panel B. Services ex. Utilities and Housing — Immigration (% of Pop. in T-1):
    - All: 0.007 (0.246)
    - 18 to 64: −0.117 (0.378)
    - No HS: −2.239 (1.136) [∗∗]
    - No College: −1.125 (0.638) [∗]
    - At least HS: 0.792 (0.445) [∗]
    - Some College: 1.311 (0.565) [∗∗]
  - Panel C. Services: Utilities — Immigration (% of Pop. in T-1):
    - All: 1.709 (0.768) [∗∗]
    - 18 to 64: 2.336 (1.199) [∗]
    - No HS: 2.287 (1.616)
    - No College: 3.518 (1.720) [∗∗]
    - At least HS: 1.666 (1.300)
    - Some College: 0.653 (1.297)
  - Panel D. Services: Housing — Immigration (% of Pop. in T-1):
    - All: −1.119 (0.892)
    - 18 to 64: −1.864 (1.483)
    - No HS: −0.496 (2.837)
    - No College: −2.364 (2.193)
    - At least HS: −1.721 (1.445)
    - Some College: −0.776 (1.683)
- IV F-statistics and Observations match those reported previously (IV F-statistic 42.66, 26.62, 27.81, 21.19, 27.62, 37.04; Observations 3,588 per column).

### Housing (Section 4.5)
- Due to concerns about the RPP housing index, two alternate measures are used: Zillow Home Value Index (ZHVI) and Zillow Observed Rent Index (ZORI).
- Using Zillow measures:
  - Immigration increases local housing inflation relative to other MSAs (Table 6).
  - Effect is driven by high-education immigration (at least high school graduates).
  - Low-education immigration (non high school graduates) has no statistically significant impact on housing inflation.
- Table 6 (Housing Inflation (%): IV), dependent variable log difference of Zillow Home Value Index (All Homes):
  - Immigration (% of Pop.) All: 2.470 (0.646) [∗∗∗]
  - Immigration (% of Pop.) 18 to 64: 3.319 (1.091) [∗∗∗]
  - Immigration (% of Pop.) No HS: −0.991 (1.188)
  - Immigration (% of Pop.) No College: 2.842 (1.358) [∗∗]
  - Immigration (% of Pop.) At least HS: 5.084 (1.343) [∗∗∗]
  - Immigration (% of Pop.) Some College: 4.284 (1.351) [∗∗∗]
  - IV F-statistics and sample: IV F-statistic 42.66, 26.62, 27.81, 27.62, 21.19, 37.04; Observations 3319 / 3319 / 3319 / 3319 / 3319 / 3319 (as reported).
- Zillow rents (ZORI) results (Table 7, Rental Inflation (%): IV):
  - Immigration (% of Pop.) All: 2.076 (1.040) [∗∗]
  - Immigration (% of Pop.) 18 to 64: 3.506 (1.940) [∗]
  - Immigration (% of Pop.) No HS: 1.604 (1.187)
  - Immigration (% of Pop.) No College: 3.316 (1.566) [∗∗]
  - Immigration (% of Pop.) At least HS: 6.141 (4.595)
  - Immigration (% of Pop.) Some College: −0.138 (1.415)
  - Num. obs. 1454 (sample covers 306 MSAs and years from 2015 to 2022 for rent data).

### Dynamic responses (Section 4.6)
- Contemporaneous analysis may omit important dynamic responses; local projections follow Jordà (2005).
- Inflation rate dynamics (Figure 3a):
  - Replace dependent variable with t+h period equivalent for h = 0, 1, 2, 3.
  - Immigration lowers contemporaneous inflation but raises it thereafter; subsequent effects are statistically insignificant.
- Price level dynamics (Figure 3b):
  - Dependent variable is change in price level in period t+h relative to period t−1.
  - Immigration lowers the overall price level contemporaneously; price level is statistically indistinguishable from that in t−1 in future years.
- Persistence by category:
  - Except for housing, the price level impact of immigration on all subcategories is transitory.
  - Housing prices:
    - Immigration increases housing prices persistently over time (positive and statistically significant impact as far as 4 years), driven by high-education immigration.
    - Low-education immigration has no impact on housing prices in the first year but lowers housing prices persistently starting in the second year (negative and statistically significant as far as 3 years).
    - This pattern is consistent with a lagged impact from increased (low-education) labor supply to housing construction.
- Figures:
  - Figure 4 shows impacts on Zillow and RPP housing indices across lags/leads (periods −3 to 4), with panels for All Residents, No HS Diploma, No College, and Some College.

*Source: wpiea2025005-print-pdf - 4.1    First Stage*

### 4.7    Comparison to other estimates

### 4.7    Comparison to other estimates

### Comparison of estimated effects to prior literature
- Cortes (2008) — decennial census-based estimate: when converted to the paper’s units, roughly a coefficient of -0.09.  
  - This is about twenty times smaller than the paper’s most directly comparable estimates for low-education workers (between -2.0 and -2.4).  
  - Authors interpret this as evidence that long-run estimates may miss important contemporaneous effects that fade; the paper’s dynamic response results support this interpretation.
  - Footnote calculation reproduced in text: Cortes (2008) finds a 10 percent increase in low-skilled immigrants over a decade reduces immigrant-intensive services prices by 2 percent; with an expenditure share of around 3.5 percent this implies −2×0.035≃ −0.07 impact on the price level over ten years, or approximately 0.007 per year. With foreign-born share around 8 percent, a ten percent increase in immigrant population over a decade ≃ 0.08pp yearly increase in migrant inflows relative to population. Thus annual per-percentage impact ≃ −0.007÷0.08≃ −0.09.
- Lach (2007) — cross-sectional estimate for immigration from the former Soviet Union to Israel in 1990: a one percentage point increase in the immigrant-to-native ratio reduced grocery store goods prices by 0.5 percent point.  
  - This result is very close to this paper’s findings for goods (see Table 5 in source).
- Sample size and statistical power:  
  - Cortes (2008) and Lach (2007) have only 90 and 52 distinct values respectively for the dependent variable because variation in immigration is only at city or city-decade level, despite pooling across product categories.  
  - The present study has over 3500 distinct values, providing increased statistical power.

### Key takeaway
- The horizon over which immigration’s impact on prices is measured matters critically: contemporaneous responses can be substantially larger than long-run estimates, consistent with the paper’s dynamic evidence.

---

### 5    Interpretation

### Overview of empirical results to be interpreted
- Three key empirical results:
  - When a local area experiences more immigration, inflation is lower relative to elsewhere (overall price level).
  - Product-specific responses: goods prices fall, services change little, and utility and housing increase (with housing dependent on measure used).
  - The magnitude of local price response is larger when immigrants have less education.

### Conceptual framework and mechanism
- Model setting: region producing two goods, x and y, with convex and homothetic consumer preferences; all consumption produced locally for simplicity; non-homothetic production implemented via different elasticities of supply for the two goods.
- Core insight: direction of (relative) local price changes is a function of the relative elasticities of supply of different products; magnitude depends on consumers’ elasticity of substitution between them.
- Graphical intuition (Figure 5 in source): increase in labor supply (immigration) expands the production possibility frontier (PPF) unevenly toward the good with more elastic supply; the new efficient allocation depends on elasticity of substitution (from perfect complements to perfect substitutes extremes).
- Algebraic decomposition (closed-form result presented in Appendix in source):
  - dlog(py/px)/dlogL1 = [εx/(1+εx) − εy/(1+εy)] (Direct effect) + (1+γ)^{-1} (Indirect effect)
  - εx, εy are supply elasticities of goods x and y respectively.
  - γ is a decreasing function of the elasticity of substitution; γ is positive iff elasticity of substitution < 1, and γ = -1 in the case of perfect substitutes.
  - Interpretation:
    - Direct effect: change in relative price if labor shares in industries remained constant.
    - Indirect effect: reallocation of labor induced by relative price changes (toward the cheaper good if substitutes, away if complements).
  - Aggregate price level response: expenditure-share-weighted average of product-specific price responses.

### How framework maps to empirical findings
- Goods vs services:
  - Labor and capital are closer substitutes in production of goods than services (literature cited in source), implying more elastic supply for goods.
  - With fixed capital in short run and increased labor availability, supply of goods is more elastic than services → relative price of goods drops more than services, consistent with empirical finding.
- Housing:
  - Supply of housing is very inelastic in short term (fixed land or construction materials) → housing prices rise.
- Education heterogeneity:
  - Less-educated labor is typically more substitutable for capital (literature cited), predicting more elastic supply for goods produced by less-educated workers and larger downward pressure on their relative prices. Empirical evidence: less-educated immigrants are more disinflationary.
- Dynamics / horizon:
  - Fixed capital assumption plausible in short run; if capital becomes infinitely elastic in long run (plausible at MSA level), long-run PPF expansion is homothetic and relative prices are unaffected. This aligns with empirical finding that long-run impacts on relative price levels are indistinguishable from zero for goods, services, and utilities — except housing and industries where land is fixed even in long run.

### Caveats and departures from the simple model
- Real-world complications include:
  - Trade linking relative price levels across regions.
  - Non-homothetic aggregate preferences if immigrants’ preferences differ sufficiently from natives’ preferences.
- Nonetheless, the simple non-homothetic short-run framework offers a coherent and parsimonious interpretation of the empirical patterns.

---

### 6    Conclusion

### Empirical summary
- Using a shift-share instrument, the paper finds:
  - Immigration reduces local inflation relative to other MSAs, with effects strongest when immigrants are working-age and have less educations.
  - Immigration lowers local goods inflation, increases housing inflation, and has a negligible effect on services.
  - For all products, less educated immigrants tend to be more disinflationary than more educated immigrants.
  - Longer-run price effects are much smaller and typically statistically indistinguishable from zero; exception: housing, where effects can last several years depending on immigrant education composition.

### Interpretation and mechanism
- Interpretation: inward immigration acts as an increase in labor supply when production is non-homothetic in the short run (capital and other factors fixed), leading to larger relative price declines in industries where labor is more substitutable for capital.
- Predicted and observed patterns:
  - Goods prices decline, housing prices increase.
  - Less-educated immigrants lower prices, higher-educated immigrants raise them.
  - Long-run neutrality of relative prices (except sectors with fixed factors like land) is consistent with capital adjustment eliminating non-homotheticities.

### Open questions and directions for further research
- Use of more detailed pricing data to identify specific goods and services most affected by immigration.
- Analysis of more recent consumer survey data to compare opinions on local prices with actual price changes in response to immigration.
- Extension of the static mechanisms to a full dynamic stochastic general equilibrium model.

*Source: wpiea2025005-print-pdf - 4.7    Comparison to other estimates*

### References

### wpiea2025005-print-pdf - References

### H3: Cited literature (selected)
- Empirical and theoretical studies on immigration and labor markets, including:
  - Altonji, J. G., & Card, D. (1991). The effects of immigration on the labor market outcomes of less-skilled natives.
  - Borjas, G. J. (2003). The labor demand curve is downward sloping: Reexamining the impact of immigration on the labor market. The Quarterly Journal of Economics,118, 1335–1374.
  - Card, D. (1990). The impact of the mariel boatlift on the miami labor market. ILR Review, 43, 245–257.
  - Clemens, M. A., & Hunt, J. (2019). The labor market effects of refugee waves: Reconciling conflicting results. ILR Review,72, 818–857.
  - Peri, G., Shih, K., & Sparber, C. (2015). Stem workers, h-1b visas, and productivity in us cities. Journal of Labor Economics,33, S225–S255.
  - National Academies of Sciences, Engineering, and Medicine. (2017). The economic and fiscal consequences of immigration. The National Academies Press.
- Methodological and econometric references:
  - Jordà, Ò. (2005). Estimation and inference of impulse responses by local projections. American economic review,95(1), 161–182.
  - Goldsmith-Pinkham, P., Sorkin, I., & Swift, H. (2020). Bartik instruments: What, when, why, and how. American Economic Review,110(8), 2586–2624.
  - White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica: journal of the Econometric Society, 817–838.
  - Borusyak, K., Hull, P., & Jaravel, X. (2024, December). A practical guide to shift-share instruments (Working Paper No. 33236). National Bureau of Economic Research. https://doi.org/10.3386/w33236
  - Caiumi, A., & Peri, G. (2024, April). Immigration’s effect on us wages and employment redux (Working Paper No. 32389). National Bureau of Economic Research. https://doi.org/10.3386/w32389

### H3: Thematic emphasis in references
- Labor-market impacts of immigration, including wage dynamics and labor demand elasticities.
- Capital-skill complementarity and structural transformation (Griliches 1969; Krusell et al. 2000; Chen 2020; Herrendorf et al. 2015).
- Local-price and inflation responses to immigration (Cortes 2008; Lach 2007; Cheremukhin et al. 2024).
- Instrumental-variable and shift-share methods for identification (Goldsmith-Pinkham et al. 2020; Borusyak et al. 2024).

### H3: Appendix Figures and Tables — descriptive notes
- Figure A1: Dynamic responses – Inflation
  - Estimates of Equation 1 using two-stage least-squares for lags of the dependent variable from periods −4 to 4.
  - Dependent variable: log difference of the BEA’s Implicit Regional Price Deflator (product of the region’s Regional Price Parity index and the U.S. PCE price index).
  - Each observation: MSA-Year pair.
  - Shift-share instrument: defined in Equation 4 using data from the American Community Survey.
  - Panels: (a) All Residents, (b) Working Age: 18 to 64, (c) No College, (d) Some College.
- Figure A2: Impulse Responses
  - Impulse responses following Jordà (2005) and Adämmer (2019) for a 1 p.p. shock to net immigration per capita.
  - Dependent variable: log Regional Price Parities by category.
  - Explanatory variable: net immigration divided by the population in T-1.
  - Panels: (a) Overall Inflation, (b) Goods, (c) Services ex. Housing and Utilities, (d) Utilities.
  - Each observation: MSA-Year pair. Shift-share instrument: Equation 4, American Community Survey.

### H3: Key summary statistics (Table A1)
- Sample size: N = 36,140 observations.
- Inflation (%): Mean 1.8, Std. Dev. 2.6, Pctl. 25 0.17, Median 1.53, Pctl. 75 3.2.
- Population: Mean 4,991,411, Std. Dev. 2,193,774, Pctl. 25 388,531, Median 752,193, Pctl. 75 4,986,0540
  - Note: preserve exact separators as in source: "4,99141111938853175219377469860540" appears concatenated; the table lists "Population36149914111938853175219377469860540" — the source formatting is irregular. The table entry as printed:
    - Population36149914111938853175219377469860540
- Foreign-born Share: Mean 0.110, Std. Dev. 0.077, Pctl. 25 0.055, Median 0.084, Pctl. 75 0.14.
- Age 18 to 64 Share: Mean 0.62, Std. Dev. 0.034, Pctl. 25 0.60, Median 0.62, Pctl. 75 0.63.
- At least High School Share: Mean 0.56, Std. Dev. 0.048, Pctl. 25 0.54, Median 0.56, Pctl. 75 0.58.
- Some College Share: Mean 0.33, Std. Dev. 0.062, Pctl. 25 0.29, Median 0.33, Pctl. 75 0.37.
- Net Immigration per cap.: Mean 0.0019, Std. Dev. 0.012, Pctl. 25 −0.0044, Median 0.0018, Pctl. 75 0.0082.
- Net Immigration (Age 18-64) per cap.: Mean 0.0012, Std. Dev. 0.01, Pctl. 25 −0.0039, Median 0.0014, Pctl. 75 0.0065.
- Net Immigration (At least HS) per cap.: Mean 0.0015, Std. Dev. 0.0089, Pctl. 25 −0.0032, Median 0.0015, Pctl. 75 0.0061.
- Net Immigration (Some college) per cap.: N = 3614, Mean 0.00095, Std. Dev. 0.0067, Pctl. 25 −0.0026, Median 0.00096, Pctl. 75 0.0044.

### H3: First-stage and IV diagnostics (Table A2)
- Shift-Share Instrument coefficients (regressing Immigration (% of Pop. in T-1) on instrument):
  - All: 0.616 ∗∗∗ (std. err. 0.087)
  - 18 to 64: 0.568 ∗∗∗ (0.096)
  - No HS: 0.449 ∗∗∗ (0.164)
  - No College: 0.568 ∗∗∗ (0.123)
  - At least HS: 0.536 ∗∗∗ (0.096)
  - Some College: 0.796 ∗∗∗ (0.103)
- Observations: 4,443 across columns.
- IV F-statistics:
  - All: 42.66
  - 18 to 64: 26.62
  - No HS: 27.81
  - No College: 21.19
  - At least HS: 27.62
  - Some College: 37.04
- Significance notation: ∗ p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.

### H3: Main IV estimates — MSA-level inflation (Table A3)
- Immigration (% of Pop. in T-1) coefficients on MSA-level Inflation (%):
  - All (col 1): −0.657 ∗∗∗ (0.241)
  - 18 to 64 (col 2): −1.096 ∗∗∗ (0.420)
  - No HS (col 3): −2.402 ∗∗ (1.050)
  - Only HS (col 4): −1.728 ∗ (0.971)
  - Some College (col 5): 0.256 (0.467)
- IV F-statistic reported as in Table A2 (e.g., All: 42.66).
- Observations: 3,588; sample covers 306 MSAs and years 2009 to 2022.
- Notes: Dependent variable is the log difference of BEA’s Implicit Regional Price Deflator. Shift-share instrument: Equation 4, ACS.

### H3: Spillovers and robustness (Tables A4–A5)
- Table A4 (Spillovers): Including State Immigration (% of Pop. in T-1) alongside MSA Immigration:
  - MSA Immigration coefficients:
    - All: −0.721 ∗∗ (0.320)
    - 18 to 64: −1.158 ∗∗ (0.526)
    - No HS: −3.557 (3.025)
    - No College: −2.004 ∗∗ (0.891)
    - At least HS: −0.480 (0.493)
    - Some College: −0.060 (0.572)
  - State Immigration coefficients (corresponding columns): e.g., All: 0.156 (0.422); 18 to 64: 0.153 (0.713); No HS: 1.632 (2.779); etc.
  - IV F-statistics vary, e.g., All: 21.96; 18 to 64: 13.33; Some College: 8.66.
  - Observations: 3,588.
- Table A5 (Robustness): Panels A–D with alternative samples and controls.
  - Panel A: Restrict to pre-pandemic period (before 2020), Observations = 2,828.
    - Immigration (% of Pop. in T-1) coefficients:
      - All: −0.476 ∗ (0.243)
      - 18 to 64: −0.750 ∗∗ (0.351)
      - No HS: −3.314 ∗ (1.796)
      - No College: −1.470 ∗∗ (0.647)
      - At least HS: −0.248 (0.351)
      - Some College: −0.216 (0.496)
  - Panel B: Control for % growth of the US-born population (sample 2009 to 2022).
    - All: −0.724 ∗∗∗ (0.264)
    - 18 to 64: −1.312 ∗∗ (0.531)
    - No HS: −2.432 ∗∗ (1.060)
    - No College: −2.132 ∗∗∗ (0.818)
    - At least HS: −0.341 (0.381)
    - Some College: 0.256 (0.465)
  - Panel C: Control for MSA Unemployment Rate.
    - All: −0.759 ∗∗∗ (0.238)
    - 18 to 64: −1.309 ∗∗∗ (0.435)
    - No HS: −3.362 ∗∗ (1.517)
    - No College: −2.681 ∗∗∗ (1.000)
    - At least HS: −0.405 (0.361)
    - Some College: 0.283 (0.440)
  - Panel D: Control for Lagged MSA Unemployment Rate.
    - All: −0.760 ∗∗∗ (0.238)
    - 18 to 64: −1.324 ∗∗∗ (0.439)
    - No HS: −3.552 ∗∗ (1.636)
    - No College: −2.741 ∗∗∗ (1.028)
    - At least HS: −0.369 (0.350)
    - Some College: 0.298 (0.434)
  - Observations for Panels B–D: 3,588. Significance notation: ∗ p<0.1; ∗∗ p<0.05; ∗∗∗ p<0.01.

### H3: Housing-price impacts by Zillow series (Table A6)
- Dependent variable: Housing Inflation (%): IV estimates for Zillow Home Value Index by percentile ranges.
- Panel A: Top-tier Zillow Home Value Index: 65th to 95th percentile range.
  - Immigration (% of Pop.) coefficients:
    - All: 2.600 ∗∗∗ (0.635)
    - 18 to 64: 3.684 ∗∗∗ (1.094)
    - No HS: 0.780 (1.044)
    - No College: 3.743 ∗∗∗ (1.427)
    - At least HS: 4.857 ∗∗∗ (1.283)
    - Some College: 4.152 ∗∗∗ (1.279)
- Panel B: Zillow Home Value Index: 35th to 65th percentile range.
  - Immigration (% of Pop.) coefficients:
    - All: 2.470 ∗∗∗ (0.646)
    - 18 to 64: 3.319 ∗∗∗ (1.091)
    - No HS: −0.991 (1.188)
    - No College: 2.842 ∗∗ (1.358)
    - At least HS: 5.084 ∗∗∗ (1.343)
    - Some College: 4.284 ∗∗∗ (1.351)
- Panel C: Bottom-tier Zillow Home Value Index: 5th to 35th percentile range.
  - Immigration (% of Pop.) coefficients:
    - All: 3.912 ∗∗∗ (0.874)
    - 18 to 64: 5.106 ∗∗∗ (1.490)
    - No HS: −1.740 (1.528)
    - No College: 4.153 ∗∗ (1.768)
    - At least HS: 7.970 ∗∗∗ (1.926)
    - Some College: 6.408 ∗∗∗ (1.679)
- IV F-statistics: same pattern as Table A2 (e.g., All: 42.66; Some College: 37.04).
- Observations: 33,193 / 33,193 / 33,193 across reported panels (format in source: Observations331933193319331933193319).

### H3: Notes on estimation and data
- Dependent variables across tables include log differences of BEA’s Implicit Regional Price Deflator, Regional Price Parity index, and Zillow Home Value Index series.
- Each observation is an MSA-Year pair.
- Shift-share instrument: defined in Equation 4 and uses data from the American Community Survey.
- Robust standard errors are reported throughout.

### H3: Appendix B — Simple model (summary of setup and main analytical results)
- B.1 Set up
  - Two goods produced in a region: x and y, wholly consumed locally.
  - Aggregate production technologies (decreasing returns to scale, labor only):
    - X = A L_x^α (Equation 6)
    - Y = B L_y^β (Equation 7)
    - Curvatures: α, β < 1.
  - Perfect competition, price equals marginal cost:
    - P_x = 1/α W A^(−1/α) X^(1/α−1) (Equation 8)
    - P_Y = 1/β W B^(−1/β) Y^(1/β−1) (Equation 9)
  - Firms’ markups: 1/α − 1 and 1/β − 1; rebated to households.
- B.1.2 Preferences
  - L households, each supplies inelastically one unit of labor.
  - CES preferences across goods; households maximize:
    - U_i = [η_x X^ρ + η_y Y^ρ]^(1/ρ) subject to P_X X + P_Y Y = (1+θ) W L
  - θ is average markup across sectors, Θ defined in Equation 10:
    - Θ = Λ[1/α − 1] + (1−Λ)[1/β − 1] (Equation 10)
  - Define σ = 1/(1−ρ).
  - Demand curves (Equations 11–13):
    - X = [η_x / P_x]^σ θ W L P^(1−σ) (Equation 11)
    - Y = [η_y / P_y]^σ θ W L P^(1−σ) (Equation 12)
    - P^(1−σ) = η_x^σ (P_X)^(1−σ) + η_y^σ (P_Y)^(1−σ) (Equation 13)
- B.1.3 Equilibrium
  - Labor market clearing:
    - L_x = Λ L (Equation 14)
    - L_y = (1−Λ) L (Equation 15)
  - Equilibrium unknowns: {X, Y, L_x, L_y, P, P_X, P_Y, W, Λ, Θ} satisfy Equations (6)–(15).
- B.2 Differential form
  - Log-log derivatives notation: lower case variables denote d log / d log L.
  - System of linear simultaneous equations (Equations 16–23):
    - x = α λ + α (16)
    - y = −β Λ^* λ + β (17)
    - p_x = w + [(1−α)/α] x (18)
    - p_y = w + [(1−β)/β] y (19)
    - y = −σ p_y + θ + w − (1−σ) p + 1 (20)
    - x = −σ p_x + θ + w − (1−σ) p + 1 (21)
    - θ = Θ^* λ (22)
    - p = s_x p_x + s_y p_y (23)
  - Definitions:
    - Λ^* = Λ/(1−Λ)
    - Θ^* = (β−α)/(β(1−α)Λ + α(1−β)(1−Λ))
    - s_x and s_y are expenditure shares of X and Y.
  - Solution for λ given in text:
    - λ = −(α−β)(1−σ) / [α + β Λ^* + σ μ]  where μ = (1−α) + Λ^*(1−β).
  - Relative price result:
    - p_y − p_x = (α−β)[1 + (1−σ) μ / (α + β Λ^* + σ μ)]
  - Relation to supply elasticities:
    - ε_x = α/(1−α), ε_y = β/(1−β); γ = (1−σ μ)/(α + β Λ^* + σ μ).
- B.3–B.4 Microfoundations: elasticity of supply and fixed capital
  - B.3 illustrates how a large number of small firms with CES technologies (labor and capital) and fixed capital at the firm level can rationalize the aggregate DRS production technology to first order.
  - Flexible factor usage: with CRS and variable capital, marginal cost η is independent of scale; aggregation yields:
    - L_y = (Y/B) [β p_y / B w]^(σ_y)
    - K_y = (Y/B) [(1−β) p_y / B r]^(σ_y)
    - σ_y = 1/(1−ρ_y).
  - B.4 Production with fixed factor: capital fixed at firm level leads to marginal cost η that is increasing in output y:
    - d log η / d log y = 1/σ_y [1/ν − 1] > 0, where ν = 1 − (1−β) (k_i / (B y_i))^(σ_y−1)/σ_y, bounded above by 1.
  - Aggregation holds even with fixed capital: aggregate relationships given (see text), and firms’ capital-output ratio k_i / y_i is constant across firms (function of p_y and w).
  - Connection to aggregate DRS technology: approximate the CES-with-fixed-capital aggregate by Y = ˜B L^{˜β} near L^*_y with formulas for ˜β and ˜B given in the text.

*Immigration and Local Inflation Working Paper No. WP/2025/005*

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_Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025005-print-pdf.pdf_