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Patents and Homelessness

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Economics · Paper

An econometric investigation testing the hypothesis that higher innovation rates, measured by patent filings, correlate with increased homelessness at the state level—exploring how economic growth and technological advancement impact housing insecurity.

Course: EC 15 Econometrics | Completed: Spring 2023 | Collaborator: Jaden Richardson

The Hypothesis

As innovation increases in a region (measured by patents filed), does homelessness increase as well? The intuition: patents signal economic growth and productivity, which can drive up cost of living, displace workers, and increase income inequality—all factors contributing to homelessness.

Goal: Move beyond correlation to establish whether this relationship is causal.

Data Overview

Geographic Scope: 51 US states/territories (including DC)
Time Period: 2014-2018 (annual observations)
Sample Size: n = 254 (5 years × 51 states, minus missing DC 2018 data)

Data Sources

Homelessness: HUD Annual Homelessness Assessment Report
Patents: Federal Reserve Bank of St. Louis (utility, plant, design, reissue patents by inventor residence)
Population: Census Bureau statistical estimates
Home Prices: Federal Housing Finance Agency House Price Index
Education: Department of Education high school graduation rates
Economic Activity: Bureau of Economic Analysis (GDP, personal expenditures)

Variable Summary

  • Homeless population: Mean 10,863 (SD 20,480), Range: 542 to 131,532
  • Patents filed: Mean 3,172 (SD 6,418), Range: 46 to 46,172
  • Population: Mean 6.35M (SD 7.17M)
  • House Price Index: Mean 239.9 (SD 57.8)
  • HS Graduation Rate: Mean 83.8% (SD 5.2%)
  • GDP: Mean $369.9B (SD $471.8B)

Methodology

Functional Form Selection

RESET test rejected linear specification (p < 0.00001), but visual inspection of scatterplot showed strong linearity. Compared log-log, log-linear, and linear-log transformations—chose linear specification based on interpretability and graphical fit.

Omitted Variable Bias Analysis

Systematically added controls to test direction of bias on patent coefficient:

Population: Expected positive bias (more people → more patents, more homeless). Actual: negative bias (coefficient decreased but stayed positive, suggesting negative correlation with patents).

Home Prices: Expected negative bias. Actual: positive bias—but coefficient became statistically insignificant (p = 0.607-1.112 across specifications), so removed from final model.

HS Graduation Rate: Expected negative bias. Actual: positive bias (graduation rate negatively correlated with patents—brain drain to other states?).

GDP: Expected positive bias. Confirmed—adding GDP cut patent coefficient by ~50%.

Personal Expenditures: Expected negative bias. Confirmed.

Final Specification (Table 3 in original paper)

Homeless = 45,432 + 0.902(Patents) - 0.004(Population) 
           - 54,568(HS Grad Rate) + 0.046(GDP) + 0.058(Personal Exp)

All coefficients significant at p < 0.01 except home prices (dropped).
R² = 0.80+ (explanatory power strong across all models).

Key Findings

Patent Effect

+0.902 homeless people per additional patent filed (p < 0.001)

Supports hypothesis: innovation proxies for economic activity that increases homelessness through cost-of-living pressures.

Other Notable Results

Population: Negative coefficient (-0.004) counterintuitive but economically negligible—starting from baseline 45,432 homeless with zero housed population, each 1,000 people only reduces homeless by 4.

HS Graduation Rate: -545 homeless per percentage point increase—actionable policy insight.

GDP: +0.046 homeless per $1M GDP increase—economic growth correlates with housing insecurity.

Personal Expenditures: +0.058 homeless per $1M increase—consumer spending (another growth proxy) also correlates with homelessness.

Robustness: Time Trend

Adding time variable (years since 2014) showed statistically significant decline in homelessness over time across all states (federal programs working?), but patent coefficient remained stable—conclusion robust to time trend.

Beta Coefficients: Relative Importance

Standardized coefficients revealed patents have smallest effect relative to graduation rate, expenditures, and population. Policy implication: while innovation matters, education and economic factors matter more.

Limitations

Violated OLS Assumptions

Randomness: Same states observed multiple times (panel structure) violates independence assumption.
Homoskedasticity: Breusch-Pagan test rejected (p < 0.0001)—used robust standard errors to correct.

Simultaneity / Reverse Causality

Does innovation → homelessness, or does homelessness → less innovation (perception of area as undesirable)? Likely bidirectional. Would need instrumental variables or natural experiment to isolate causal direction.

Measurement Error

Cannot verify data collection consistency across states—different localities may define/count homelessness differently (temporary housing vs. unsheltered vs. federal assistance recipients).

External Validity

Results specific to US states, 2014-2018. Different patent laws, housing markets, and social safety nets in other countries limit generalizability.

Sample Size

Limited to 5 years × 51 states due to data availability—larger panel would improve power.

Key Takeaways

Innovation has a dark side. Economic growth and technological advancement, while beneficial in aggregate, correlate with increased housing insecurity—the gains are not evenly distributed.

Education is policy-relevant. High school graduation rate showed the strongest standardized effect and is directly actionable through policy.

Home prices are surprisingly insignificant. Despite intuition, house price index showed no statistical relationship with homelessness once other factors controlled—suggests affordability is more complex than raw prices.

Growth ≠ equity. Both GDP and personal expenditures (measures of economic prosperity) predict higher homelessness, highlighting the paradox of growth without inclusive housing policy.

Skills Demonstrated

  • Econometric modeling (OLS regression, specification testing)
  • Hypothesis testing and statistical inference
  • Omitted variable bias analysis and control variable selection
  • Critical evaluation of assumptions (randomness, homoskedasticity)
  • Causal inference challenges (simultaneity, measurement error)
  • Data integration from multiple federal sources
  • Policy-relevant interpretation of coefficients
  • Robustness checks (time trends, standardized coefficients)

This study provides empirical evidence that innovation-driven economic growth, while economically beneficial, creates winners and losers—and without deliberate policy intervention, housing insecurity grows alongside prosperity.

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