Local Ties in Spatial Equilibrium Mike Zabek Federal Reserve Board mike.zabek@frb.gov American Real Estate and Urban Economics Association 2020 National Conference May 28, 2020 Disclaimer: Any opinions and conclusions expressed herein are solely the responsibility of the author and do not necessarily represent the Federal Reserve Board, the US Census Bureau, the Federal Reserve System, the National Institutes of Health, or any other person or organization. Results have been reviewed to ensure that no confidential information is disclosed. Mike Zabek mike.zabek@frb.gov May 28, 2020 1 / 22
Spatial Equilibrium if People have Local Ties People have local ties Median US born adult lives about 50 miles from where they were born People are moving less often (Molloy, Smith and Wozniak, 2011; Ganong and Shoag, 2017; Kaplan and Schulhofer-Wohl, 2017; Coate and Mangum, 2018) Mike Zabek mike.zabek@frb.gov May 28, 2020 2 / 22
Spatial Equilibrium if People have Local Ties People have local ties Median US born adult lives about 50 miles from where they were born People are moving less often (Molloy, Smith and Wozniak, 2011; Ganong and Shoag, 2017; Kaplan and Schulhofer-Wohl, 2017; Coate and Mangum, 2018) Spatial Equilibrium models are extremely influential, and cannot match that fact (Rosen, 1979; Roback, 1982; Albouy, 2016) Mike Zabek mike.zabek@frb.gov May 28, 2020 2 / 22
Spatial Equilibrium if People have Local Ties People have local ties Median US born adult lives about 50 miles from where they were born People are moving less often (Molloy, Smith and Wozniak, 2011; Ganong and Shoag, 2017; Kaplan and Schulhofer-Wohl, 2017; Coate and Mangum, 2018) Spatial Equilibrium models are extremely influential, and cannot match that fact (Rosen, 1979; Roback, 1982; Albouy, 2016) What happens to spatial equilibrium if people have local ties? Mike Zabek mike.zabek@frb.gov May 28, 2020 2 / 22
Agenda Empirical Results 1 People Live Close to Where They Were Born (skipped) People Who Live in Depressed Places were Born There Places Lose Population Slowly (skipped) Less Migration in Places with More Locals (skipped) Model of Spatial Equilibrium with Local Ties 2 Model Results 3 Depressed Places have Lower Incomes and Migration Elasticities Hysteresis: Negative Shocks Make Incomes Lower and More Volatile Place-Based Subsidies can be Efficacious Local Ties are Persistent Conclusion 4 Mike Zabek mike.zabek@frb.gov May 28, 2020 3 / 22
Agenda Empirical Results 1 People Live Close to Where They Were Born (skipped) People Who Live in Depressed Places were Born There Places Lose Population Slowly (skipped) Less Migration in Places with More Locals (skipped) Model of Spatial Equilibrium with Local Ties 2 Model Results 3 Conclusion 4 Mike Zabek mike.zabek@frb.gov May 28, 2020 4 / 22
Share of Residents Born in the Same State Share Born Locally 80 − 100 70 − 80 60 − 70 50 − 60 40 − 50 20 − 40 0 − 20 Dallas, TX: 40 % Dayton, OH: 70 % Source: 2000 Census mapped to 1990 commuting zones People with local ties stay in depressed places Mike Zabek mike.zabek@frb.gov May 28, 2020 5 / 22
People who Live in Depressed Places were Born There Dayton, OH Dallas, TX 2 2 Population (millions) Population (millions) 1 1 0 0 1970 1980 1990 2000 2008 1970 1980 1990 2000 2008 Year Year Born Outside Born Locally Scatter of Ties Note: Commuting zones 5120 and 520. Mike Zabek mike.zabek@frb.gov May 28, 2020 6 / 22
Agenda Empirical Results 1 Model of Spatial Equilibrium with Local Ties 2 Model Results 3 Conclusion 4 Mike Zabek mike.zabek@frb.gov May 28, 2020 7 / 22
Model in of Local Ties in Spatial Equilibrium Workers choose a place to live Mike Zabek mike.zabek@frb.gov May 28, 2020 8 / 22
Model in of Local Ties in Spatial Equilibrium Workers choose a place to live Birthplaces reflect historical populations (previous shocks) Most workers prefer to live where they were born ( k = j ) But they trade off local ties, wages, rents, and amenities Mike Zabek mike.zabek@frb.gov May 28, 2020 8 / 22
Model in of Local Ties in Spatial Equilibrium Workers choose a place to live Birthplaces reflect historical populations (previous shocks) Most workers prefer to live where they were born ( k = j ) But they trade off local ties, wages, rents, and amenities In spatial equilibrium: Local firms in each area with changing productivities National firm combines local goods into a consumption good Housing is non-tradeable, has supply elasticity Mike Zabek mike.zabek@frb.gov May 28, 2020 8 / 22
Model in of Local Ties in Spatial Equilibrium Workers choose a place to live Birthplaces reflect historical populations (previous shocks) Most workers prefer to live where they were born ( k = j ) But they trade off local ties, wages, rents, and amenities In spatial equilibrium: Local firms in each area with changing productivities National firm combines local goods into a consumption good Housing is non-tradeable, has supply elasticity Can extend to include durable housing, different skill levels Housing Government Production Worker Choice Calibration Mike Zabek mike.zabek@frb.gov May 28, 2020 8 / 22
Workers Choosing Where to Live Indirect utility of individual i , in area j , who was born in area k : Logit Local Ties Amenities Real incomes � �� � ���� ���� ���� u ijk = ω j + A j + ξ ijk + ✶ ( k = j ) µ i Mike Zabek mike.zabek@frb.gov May 28, 2020 9 / 22
Workers Choosing Where to Live Indirect utility of individual i , in area j , who was born in area k : Logit Local Ties Amenities Real incomes � �� � ���� ���� ���� u ijk = ω j + A j + ξ ijk + ✶ ( k = j ) µ i Local Ties ( µ i ) - Preference for living in your birthplace Differences are due to who chooses to live in j And how many people were born in k Mike Zabek mike.zabek@frb.gov May 28, 2020 9 / 22
Workers Choosing Where to Live Indirect utility of individual i , in area j , who was born in area k : Logit Local Ties Amenities Real incomes � �� � ���� ���� ���� u ijk = ω j + A j + ξ ijk + ✶ ( k = j ) µ i Local Ties ( µ i ) - Preference for living in your birthplace Differences are due to who chooses to live in j And how many people were born in k Distribution of attachments, indexed by i , is independent the birthplace ( k ) Mike Zabek mike.zabek@frb.gov May 28, 2020 9 / 22
Workers Choosing Where to Live Indirect utility of individual i , in area j , who was born in area k : Logit Local Ties Amenities Real incomes � �� � ���� ���� ���� u ijk = ω j + A j + ξ ijk + ✶ ( k = j ) µ i Local Ties ( µ i ) - Preference for living in your birthplace Differences are due to who chooses to live in j And how many people were born in k Distribution of attachments, indexed by i , is independent the birthplace ( k ) Local ties evolve over time – workers move to productive places and form ties Mike Zabek mike.zabek@frb.gov May 28, 2020 9 / 22
Productivity Increases Population, Decreases Local Ties 2 1.5 Population 1 0.5 0 -50 0 50 100 150 200 Change in Productivity (percent) Born Locally Born Outside Calibration Mike Zabek mike.zabek@frb.gov May 28, 2020 10 / 22
Agenda Empirical Results 1 Model of Spatial Equilibrium with Local Ties 2 Model Results 3 Depressed Places have Lower Incomes and Migration Elasticities Hysteresis: Negative Shocks Make Incomes Lower and More Volatile Place-Based Subsidies can be Efficacious Local Ties are Persistent Conclusion 4 Mike Zabek mike.zabek@frb.gov May 28, 2020 11 / 22
Real Incomes and Migration Elasticities Are Lower in Depressed Places 50 1 Change in Real Wages (percent) 0.9 Migration Elasticity 25 0.8 0 0.7 0.6 -25 -50 0 50 100 150 200 -50 0 50 100 150 200 Change in Productivity (percent) Change in Productivity (percent) Mike Zabek mike.zabek@frb.gov May 28, 2020 12 / 22
Agenda Empirical Results 1 Model of Spatial Equilibrium with Local Ties 2 Model Results 3 Depressed Places have Lower Incomes and Migration Elasticities Hysteresis: Negative Shocks Make Incomes Lower and More Volatile Place-Based Subsidies can be Efficacious Local Ties are Persistent Conclusion 4 Mike Zabek mike.zabek@frb.gov May 28, 2020 13 / 22
Impulse Responses after Equal Declines in Productivity Productivity Share local 90 0 Productivity (log deviations) 80 Share Local (percent) 50 % 70 -0.5 60 -1 50 % 50 -1.5 40 -10 0 10 20 30 -10 0 10 20 30 Year Year Idea: Shock the same area twice, same size shock. First shock changes the share local Mike Zabek mike.zabek@frb.gov May 28, 2020 14 / 22
Impulse Responses after Equal Declines in Productivity Population Real Incomes 0.1 0.2 0 Real Incomes (log deviations) 0 Population (log deviations) -0.1 19 % -0.2 35 % -0.2 -0.4 -0.3 -0.6 30 % 24 % -0.4 -0.8 -0.5 -1 -10 0 10 20 30 -10 0 10 20 30 Year Year Responses differ 1 First shock - Locals stay, real wages decline somewhat (persistently) 2 Second shock - Less migration, real wages decline by more Mike Zabek mike.zabek@frb.gov May 28, 2020 15 / 22
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