Local Ties in Spatial Equilibrium Mike Zabek Federal Reserve Board - - PowerPoint PPT Presentation

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

1

Empirical Results 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)

2

Model of Spatial Equilibrium with Local Ties

3

Model Results 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

4

Conclusion

Mike Zabek mike.zabek@frb.gov May 28, 2020 3 / 22

Agenda

1

Empirical Results 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)

2

Model of Spatial Equilibrium with Local Ties

3

Model Results

4

Conclusion

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

Dayton, OH: 70 % Dallas, TX: 40 %

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

1 2

Population (millions)

1970 1980 1990 2000 2008

Year Dayton, OH

1 2

Population (millions)

1970 1980 1990 2000 2008

Year Dallas, TX Born Outside Born Locally

Note: Commuting zones 5120 and 520.

Scatter of Ties Mike Zabek mike.zabek@frb.gov May 28, 2020 6 / 22

Agenda

1

Empirical Results

2

Model of Spatial Equilibrium with Local Ties

3

Model Results

4

Conclusion

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: uijk =

Real incomes

• ωj

+

Amenities

• Aj

+

Logit

• ξijk +

Local Ties

• ✶(k = j)µi

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: uijk =

Real incomes

• ωj

+

Amenities

• Aj

+

Logit

• ξijk +

Local Ties

• ✶(k = j)µi

Local Ties (µi) - 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: uijk =

Real incomes

• ωj

+

Amenities

• Aj

+

Logit

• ξijk +

Local Ties

• ✶(k = j)µi

Local Ties (µi) - 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: uijk =

Real incomes

• ωj

+

Amenities

• Aj

+

Logit

• ξijk +

Local Ties

• ✶(k = j)µi

Local Ties (µi) - 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

• 50

50 100 150 200

Change in Productivity (percent)

0.5 1 1.5 2

Population

Born Locally Born Outside

Calibration Mike Zabek mike.zabek@frb.gov May 28, 2020 10 / 22

Agenda

1

Empirical Results

2

Model of Spatial Equilibrium with Local Ties

3

Model Results 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

4

Conclusion

Mike Zabek mike.zabek@frb.gov May 28, 2020 11 / 22

Real Incomes and Migration Elasticities Are Lower in Depressed Places

• 50

50 100 150 200

Change in Productivity (percent)

• 25

25 50

Change in Real Wages (percent)

• 50

50 100 150 200

Change in Productivity (percent)

0.6 0.7 0.8 0.9 1

Migration Elasticity

Mike Zabek mike.zabek@frb.gov May 28, 2020 12 / 22

Agenda

1

Empirical Results

2

Model of Spatial Equilibrium with Local Ties

3

Model Results 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

4

Conclusion

Mike Zabek mike.zabek@frb.gov May 28, 2020 13 / 22

Impulse Responses after Equal Declines in Productivity

Productivity Share local

• 10

10 20 30

Year

• 1.5
• 1
• 0.5

Productivity (log deviations)

50 % 50 %

• 10

10 20 30

Year

40 50 60 70 80 90

Share Local (percent)

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

• 10

10 20 30

Year

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2

Population (log deviations)

35 % 30 %

• 10

10 20 30

Year

• 0.5
• 0.4
• 0.3
• 0.2
• 0.1

0.1

Real Incomes (log deviations)

19 % 24 % 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

Agenda

1

Empirical Results

2

Model of Spatial Equilibrium with Local Ties

3

Model Results 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

4

Conclusion

Mike Zabek mike.zabek@frb.gov May 28, 2020 16 / 22

A 10 pct Place-Based Subsidy

Setup: A subsidy equal to 10 percent of initial wages To places with low and high ties (percents born locally) Declines at 4 percent per year Present Discounted Value of percent changes with 2 pct discount rate Impacts on

1 Ratios of changes in incomes to populations ◮ Benefit (income increases) vs cost (population distortion)

Kline and Moretti (2014); Zabek (2018)

2 Changes in real incomes locally and in places paying for the subsidy Mike Zabek mike.zabek@frb.gov May 28, 2020 17 / 22

Ratio of Changes in Real Incomes to Population

40 50 60 70 80

Percent Born Locally

0.25 0.5 0.75 1

Income over Population Real incomes change by more than population in depressed places

Mike Zabek mike.zabek@frb.gov May 28, 2020 18 / 22

Ratio of Changes in Real Incomes to Population

40 50 60 70 80

Percent Born Locally

0.25 0.5 0.75 1

Income over Population Real incomes change by more than population in depressed places Subsidies increase real incomes without distorting population (much)

Mike Zabek mike.zabek@frb.gov May 28, 2020 18 / 22

Changes in Real Incomes

40 50 60 70 80

Percent Born Locally

• 50

50 100 150

Real Incomes

Subsidized Place Other Places

Real incomes in depressed places increase by more

Mike Zabek mike.zabek@frb.gov May 28, 2020 19 / 22

Changes in Real Incomes

40 50 60 70 80

Percent Born Locally

• 50

50 100 150

Real Incomes

Subsidized Place Other Places

Real incomes in depressed places increase by more Subsidies to growing places increase real incomes everywhere Including the places that pay for them

Mike Zabek mike.zabek@frb.gov May 28, 2020 19 / 22

Agenda

1

Empirical Results

2

Model of Spatial Equilibrium with Local Ties

3

Model Results 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

4

Conclusion

Mike Zabek mike.zabek@frb.gov May 28, 2020 20 / 22

Convergence After a 50 % Decline in Productivity

200 400

Year

• 0.6
• 0.4
• 0.2

Population

200 400

Year

• 0.15
• 0.1
• 0.05

Real incomes Population declines by less than in steady state (too small by about 1/3)

Mike Zabek mike.zabek@frb.gov May 28, 2020 21 / 22

Convergence After a 50 % Decline in Productivity

200 400

Year

• 0.6
• 0.4
• 0.2

Population

200 400

Year

• 0.15
• 0.1
• 0.05

Real incomes Population declines by less than in steady state (too small by about 1/3) Real incomes decline by more than in steady state

Mike Zabek mike.zabek@frb.gov May 28, 2020 21 / 22

Convergence After a 50 % Decline in Productivity

200 400

Year

• 0.6
• 0.4
• 0.2

Population

200 400

Year

• 0.15
• 0.1
• 0.05

Real incomes Population declines by less than in steady state (too small by about 1/3) Real incomes decline by more than in steady state Convergence takes generations (takes a generation to halve the distance to steady state)

Mike Zabek mike.zabek@frb.gov May 28, 2020 21 / 22

Conclusion

Large differences in how many locals live in different places Depressed areas have more locals and less elastic migration

◮ Real wages can get quite low ◮ Labor demand shocks impact wages, not population ◮ Differences persist for generations

Place based subsidies have different effects

◮ Economically depressed places – increase local incomes ◮ Growing places – increase population and aggregate productivity Mike Zabek mike.zabek@frb.gov May 28, 2020 22 / 22

Albouy, David. 2016. “What are cities worth? Land rents, local productivity, and the total value of amenities.” The Review of Economics and Statistics, 98(3): 477–487. Coate, Patrick, and Kyle Mangum. 2018. “Fast Locations and Slowing Labor Mobility.” Andrew Young School of Policy Studies Research Paper Series No. 18-05. Ganong, Peter, and Daniel Shoag. 2017. “Why has regional income convergence in the U.S. declined?” Journal of Urban Economics. Kaplan, Greg, and Sam Schulhofer-Wohl. 2017. “Understanding The Long-Run Decline in Interstate Migration.” International Economic Review. Kline, Patrick, and Enrico Moretti. 2014. “People, Places and Public Policy: Some Simple Welfare Economics of Local Economic Development Programs.” Annual Review of Economics, 6: 629–62. Molloy, Raven, Christopher L Smith, and Abigail Wozniak. 2011. “Internal Migration in the United States.” Journal of Economic Perspectives, 25(3): 173–196. Roback, Jennifer. 1982. “Wages, rents, and the quality of life.” The Journal of Political Economy, 90(6): 1257–1278.

Mike Zabek mike.zabek@frb.gov May 28, 2020 0 / 22

Rosen, Sherwin. 1979. “Wage-based indexes of urban quality of life.” In Current Issues in Urban Economics. , ed. Mahlon Straszheim and Peter Mieszkowski. Baltimore, MD:Johns Hopkins University Press. Zabek, Mike. 2018. “Essays on Places and Economic Inequality.” PhD

• diss. University of Michigan.

Mike Zabek mike.zabek@frb.gov May 28, 2020 0 / 22