# Location-Specific Adjustments in Population and Employment across Metropolitan America

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Bidirectional Population and Employment Change

## 3. The Adjustment Process

#### 3.1. Global Estimates

_{t}is taken to adjust to an estimate for current employment EMPLY*

_{t}and, similarly, current employment EMPLY

_{t}is taken to adjust to an estimate for current population POPUL*

_{t}. Since Carlino and Mills [19] analysts tend to make use of Census data, so the adjustment period is usually assumed to be a decade in length, but the most appropriate time lag is not really known. It remains unclear how important this time restriction is.

_{t}= a

_{1}+ b

_{1}POPUL

_{t}

_{-1}+ c

_{1}EMPLY*

_{t}+

**d**+ e

_{1}VECTR_{t-1}_{1}

_{t}= a

_{2}+ b

_{2}POPUL*

_{t}+ c

_{2}EMPLY

_{t-}

_{1}+

**d**+ e

_{2}VECTR_{t-1}_{2}

_{1}indicates the rate at which population numbers are adjusting to employment while the coefficient c

_{2}indicates the rate at which employment numbers are adjusting to population. The underlying supposition is that the incremental changes in both current population and employment will diminish over time, and a spatial equilibrium will be reached. The magnitudes of these two coefficients indicate the differential speeds of the two aspects of the overall joint adjustment. The estimates in reduced form for these two adjustment equations can be reached through substitution [17,18]. When making the various estimates for current employment and population, a series of exogenous (initial or prior) variables are typically placed in a contextual vector

**VECTR**. This vector is required because the twin distributions of errors are likely correlated so the estimates of those variables will be biased. The two reduced-form expressions are expressed as follows:

_{t-1}_{t}= g

_{1}+ h

_{1}POPUL

_{t}

_{-1}+ i

_{1}EMPLY

_{t-}

_{1}+

**j**+ k

_{1}VECTR_{t-1}_{1}

_{t}= g

_{2}+ h

_{2}POPUL

_{t-}

_{1}+ i

_{2}EMPLY

_{t-}

_{1}+

**j**+ k

_{2}VECTR_{t-1}_{2}

_{1}and h

_{2}become h

_{1}-1 and h

_{2}-1, respectively, in Equations (3) and (4), while all the other estimates exactly remain the same. Alternatively, in the logarithmic case, the modified equations—that now address growth instead of change—are once again h

_{1}-1 and h

_{2}-1, respectively. When three or more endogenous variables are estimated the issue of convergence can become somewhat problematic once the extra coefficients appear in the growth operator matrix. In any case, these new endogenous variables are typically chosen from those already included in the vector of exogenous variables.

**M***becomes increasingly similar. Moreover, their ratios (or shares) become identical to those uncovered in the so-called unit vector [48]. While the future values projected for the two endogenous variables are fixed throughout each projection period by the so-called “growth operator” matrix, these values are constantly updated by the subsequent rounds of matrix multiplication. Here the use of the projection matrix is much the same as that for the Markov models of population redistribution that are well known elsewhere [20,49,50].

#### 3.2. Local Estimates

_{st}= g

_{zs1}+ h

_{zs1}POPUL

_{st-1}+ i

_{zs1}EMPLY

_{st-1}+

**j**+ k

_{zs1}VECTR_{st-1}_{zs1}

_{st}= g

_{zs2}+ h

_{zs2}POPUL

_{st-1}+ i

_{zs2}EMPLY

_{st-1}+

**j**+ k

_{zs2}VECTR_{st-1}_{zs2}

_{st}and employment EMPLY

_{st}. As for stability, the discussion above, which pertained to global estimates made across all metropolitan areas, remains appropriate for the various place-specific estimates that are made by applying geographically weighted regression.

## 4. Data, Variables, and Conjectures

## 5. Results

#### 5.1. Regression Estimates

_{t}

_{-1}falls from 0.944 (GS2SLS) to 0.913 (GWR) and the estimate on EMPLY

_{t}

_{-1}climbs from 0.055 to 0.086 in the population equation; at the same time, the estimate on POPUL

_{t}

_{-1}falls from 0.057 (GS2SLS) to 0.029 (GWR) and the elasticity estimate on EMPLY

_{t}

_{-1}climbs from 0.943 to 0.969 in the employment equation. Clearly, the four coefficients of the 2 by 2 endogeneity matrix are shifted away from an overall population effect toward an overall employment effect when using geographically weighted regression. As for the contextual effects only three differences are worthy of note. Again, looking across all 1508 observations, GWR generates a much greater effect (0.104 versus 0.066) for human amenities in the population equation, and much smaller effects for both self-employment (0.124 versus 0.170) and wages (−0.196 versus −0.238) in the employment equation. The estimates in Table 1 suggest that the gap in the human amenities effect narrowed in the middle years but the estimates in Table 2 suggest that the gap in the self-employment effect widened over time, while the gap in the wage effect narrowed over full study period. Other shifts are evident in specific time periods, including a rise in the importance of a prime workforce in the period 1995–2005 and a fall later in the period 2005–2015, but these are the three most pervasive shifts (Table 2).

#### 5.2. Stability

**M**= (h

_{1}, i

_{1}; h

_{2}, i

_{2}), where h represents population and i represents employment. The subscripts signify that two equations are being estimated, and the semi-colon simply delimits the separate rows for these equations [17,18]. When the eigenvalues (or characteristic roots) are real for the endogeneity matrix

**M**, convergence (eventually) must take place in the adjustment process and a long-run equilibrium exists. At the global equilibrium, estimated by OLS regression, or at each local equilibrium, estimated by GWR, the array of population coefficients in

**M***is just matched by the array of employment coefficients in that same matrix. The dominant (larger) eigenvalue is selected to indicate the correct solution for stability in the adjustment process [49,50].

_{t}

_{-1}in the current population equations; (ii) the estimates of EMPLY

_{t}

_{-1}in the current population equations; (iii) the estimates of POPUL

_{t}

_{-1}in the current employment equations; and (iv) the estimates of EMPLY

_{t}

_{-1}in the current employment equations. So, to clarify, r = 0.794 denotes the very strong association between the 377 estimates of POPUL

_{t}

_{-1}for the period 1990–2000 and the 377 estimates of POPUL

_{t}

_{-1}fifteen years later for the period 2005–2015. The own-variable correlations, all very high, were to be expected but the strong cross-variable correlations were not; however, these high latter figures appear to be in part due to the way GWR generates it place-specific estimates. The comparable correlations for the employment equations were also very strong. The only remarkable difference between the two sets of estimates was the drop in both the own- and cross-variable correlation coefficients for employment across the 377 metropolitan areas during the period 2000–2010, when the Great Recession was taking place. The strength of the association between the estimates of 2000 and those of 2010 were 0.868 (own) and 0.850 (cross) for the population equations, but these two figures dropped to 0.621 (cross) and 0.656 (own) for the employment equations. Nevertheless, the stability over time in the various place-specific estimates of population and employment was truly remarkable.

**M**are shown for each of the nation’s 15 largest metropolitan areas in Table 4, covering 1990 to 2000, and then in Table 5, covering 2005 to 2015. Even across this small number of metropolitan areas, a certain amount of variation is visible in the signs and the sizes of these key estimates. While stability occurs in all 15 instances, the property of sustainability is not universal (see below). In general, it should be noted that the variation in the estimates of the four estimates declined over time. Nevertheless, the pattern of coefficients for each large economy changed very little over the 25-year study period; for example, the figures for Boston changed marginally from

**M**= (0.9074, 0.1054; 0.0405, 0.9773) for 2000 to

**M**= (0.9310, 0.0672; 0.0252, 0.9800) for 2015. In fact, a simple 3-cluster classification based solely on these four coefficients is identical in those two separate time periods, where two other economies resemble New York, three others resemble Chicago, and the remaining seven are more like Los Angeles. This is another remarkable result given the shifts noted in the values and signs of the endogenous variables.

**M**= (0.9418, 0.0568; 0.0432, 0.9648). Stability in the long run occurs for Chicago because the two roots can be shown to be real and the value of the dominant eigenvalue is λ = 1.0041. This local convergence leads to the specification of a place-specific unit vector, which indicates the relative importance of the two endogenous variables at the long-run equilibrium. Here the ratio between population and employment at this equilibrium is 0.9109 to 1.0000, meaning that the ratio, expressed in logarithms, in the unit vector is (0.4767; 0.5233). Once transformed into arithmetic format, this ratio is (0.4884; 0.5116), and both unit vectors indicate that employment clearly exceeds population at the long-run employment. As noted in the tables, all 15 of these large metropolitan areas have stable solutions for the two 10-year intervals of time. However, the composition of the unit vectors can be somewhat different in the various places; for instance, the coefficients for Seattle in the last period are

**M**= (1.0273, −0.0318; 0.0871, 0.9112), where λ = 0.9937, and the unit vector (in logarithmic format) is (0.4866, 0.5134). So, Chicago would be expected to have a slightly higher population-to-employment ratio than Seattle when convergence eventually occurs in both places.

#### 5.3. Sustainability

_{t}= σEMPLY

_{t}, where σ > 1 is a multiplier reflecting the relative size of the non-working or dependent population in the final year of the estimation period. Once the four coefficients of

**M**have been determined the growth operator matrix can be progressively powered to identify the rounds of adjustment that are expected to unfold over the subsequent 10 years, 20 years, and so on. If a fixed multiplier σ is used for each adjustment round after time t the future values for population and employment will fall (or rise) depending on how population and employment interact locally. On the other hand, this rather strict assumption could be modified to recognize that each place-specific multiplier σ could shrink, at its own distinctive rate, over the entire study period as some people continued to work while growing older and others took on multiple part-time jobs. In any case, the upcoming analysis will not address this possibility; instead, it will simply identify the point in time when employment is expected to exceed population using the multiplier value that existed at the final year of the estimation period.

#### 5.4. Contextual Variables

## 6. Concluding Remarks

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- McCann, P. The Regional and Urban Policy of the European Union; Edward Elgar: Cheltenham, UK, 2015. [Google Scholar]
- Borchert, J. Major control points in American economic geography. Ann. Assoc. Am. Geogr.
**1978**, 68, 214–232. [Google Scholar] [CrossRef] - Pred, A. Urban Growth and the Circulation of Information; Harvard University Press: Cambridge, MA, USA, 1973. [Google Scholar]
- Berry, B.; Horton, F. Geographic Perspectives on Urban Systems; Prentice-Hall: Englewood Cliffs, NJ, USA, 1970. [Google Scholar]
- Cadwallader, M. Urban Geography: An Analytical Approach; Prentice-Hall: Upper Saddle River, NJ, USA, 1996. [Google Scholar]
- Arnott, R.; McMillen, D. (Eds.) A Companion to Urban Economics; Blackwell: Oxford, UK, 2008. [Google Scholar]
- Glaeser, E. Triumph of the City; Penguin Press: New York, NY, USA, 2011. [Google Scholar]
- Whisler, R.; Waldorf, B.; Mulligan, G.; Plane, D. Quality of life and the migration of the college-educated: A life-course approach. Growth Chang.
**2008**, 39, 58–94. [Google Scholar] [CrossRef] - Corcoran, J.; Faggian, A. (Eds.) Graduate Migration and Regional Development; Edward Elgar: Cheltenham, UK, 2017. [Google Scholar]
- Gordon, I.; Champion, T.; Coombes, M. Urban escalators and interregional elevators: The difference that location, mobility, and sectoral specialisation make to occupational progression. Environ. Plan. A
**2015**, 47, 588–606. [Google Scholar] [CrossRef] - Bosworth, G.; Venholst, V. Economic linkages between urban and rural regions—what’s in it for the rural? Reg. Stud.
**2017**, 52, 1–12. [Google Scholar] [CrossRef] - Kotkin, J. The Human City; Agate B2: Chicago, IL, USA, 2016. [Google Scholar]
- Moretti, E. The New Geography of Jobs; Houghton Mifflin Harcourt: New York, NY, USA, 2012. [Google Scholar]
- Bartik, T. Who Benefits from State and Local Economic Development Policies? W.E. Upjohn Institute: Kalamazoo, MI, USA, 1991.
- DiPasquale, D.; Wheaton, W. Urban Economics and Real Estate Markets; Prentice-Hall: Englewood Cliffs, NJ, USA, 1996. [Google Scholar]
- Mulligan, G.; Reid, N.; Lehnert, M. Metropolitan innovation in the New Economy. Urban Sci.
**2017**, 1, 18. [Google Scholar] [CrossRef] [Green Version] - Mulligan, G.; Nilsson, H.; Carruthers, J. Population and employment change in U.S. metropolitan areas. In Population, Place, and Spatial Interaction; Franklin, R., Ed.; Springer Nature: Singapore, 2019; pp. 95–113. [Google Scholar]
- Mulligan, G.; Nilsson, H. Recent population and employment change in U.S. metropolitan areas. In Development Studies in Regional Science; Chen, Z., Bowen, W., Whittington, D., Eds.; Springer Nature: Singapore, 2020; pp. 429–447. [Google Scholar]
- Carlino, G.; Mills, E. The determinants of county growth. J. Reg. Sci.
**1987**, 27, 135–152. [Google Scholar] [CrossRef] [PubMed] - Rogers, A. Matrix Analysis of Interregional Population Growth and Distribution; University of California Press: Berkeley, CA, USA, 1968. [Google Scholar]
- Fotheringham, S.; Brunsdon, C.; Charlton, M. Quantitative Geography; Sage Publications: London, UK, 2000. [Google Scholar]
- Florida, R. The Rise of the Creative Class; Basic Books: New York, NY, USA, 2002. [Google Scholar]
- Noah, T. The Great Divergence; Bloomsbury Press: New York, NY, USA, 2012. [Google Scholar]
- Fallah, B.; Partridge, M.; Rickman, D. Geography and high-tech employment growth in U.S. counties. J. Econ. Geogr.
**2014**, 14, 683–720. [Google Scholar] [CrossRef] [Green Version] - Mulligan, G.; Reid, N.; Carruthers, J.; Lehnert, M. Exploring innovation gaps in the American space economy. In Regional Research Frontiers; Jackson, R., Schaeffer, P., Eds.; Springer International: Cham, Switzerland, 2017; Volume 1, pp. 21–50. [Google Scholar]
- Beale, C. Rural and Nonmetropolitan Population Trends of Significance to National Population Policy; Economic Research Service: Washington, DC, USA, 1972. [Google Scholar]
- Frey, W. The new urban revival in the United States. Urban Stud.
**1993**, 30, 741–774. [Google Scholar] [CrossRef] [Green Version] - Carruthers, J.; Vias, A. Urban, suburban, and exurban sprawl in the Rocky Mountain West: Evidence from regional adjustment models. J. Reg. Sci.
**2005**, 45, 21–48. [Google Scholar] [CrossRef] - Muth, R. Migration: Chicken or egg? South. Econ. J.
**1971**, 37, 295–306. [Google Scholar] [CrossRef] - Carruthers, J.; Mulligan, G. The regional adjustment model: An instrument of evidence-based policy. In Handbook of Regional Growth and Development Theories, 2nd ed.; Capello, R., Nijkamp, P., Eds.; Edward Elgar: Cheltenham, UK, 2019; pp. 607–627. [Google Scholar]
- Borts, G.; Stein, J. Economic Growth in a Free Market; Columbia University: New York, NY, USA, 1964. [Google Scholar]
- Isserman, A. Population Change and the Economy: Social Science Theories and Models; Kluwer-Nijhoff: Boston, MA, USA, 1986. [Google Scholar]
- Greenwood, M. Research on internal migration in the United States: A survey. J. Econ. Lit.
**1975**, 13, 397–433. [Google Scholar] - Graves, P. A re-examination of migration, economic opportunity, and the quality of life. J. Reg. Sci.
**1976**, 16, 107–112. [Google Scholar] [CrossRef] [Green Version] - Graves, P. A life-cycle empirical analysis of migration and climate, by race. J. Urban Econ.
**1979**, 6, 135–147. [Google Scholar] [CrossRef] [Green Version] - Sjaastad, L. The costs and returns of human migration. J. Political Econ.
**1962**, 70, 80–93. [Google Scholar] [CrossRef] - Rosen, S. Wage-based indexes of urban quality of life. In Current Issues in Urban Economics; Mieszkowski, P., Straszheim, M., Eds.; Johns Hopkins University Press: Baltimore, MD, USA, 1979; pp. 74–104. [Google Scholar]
- Roback, J. Wages, rent, and the quality of life. J. Political Econ.
**1982**, 90, 1257–1278. [Google Scholar] [CrossRef] - Herzog, H.; Schlottman, A. What can be learned from the recent migrants? Growth Chang.
**1986**, 17, 37–50. [Google Scholar] [CrossRef] - Boarnet, M. An empirical model of intrametropolitan population and employment growth. Pap. Reg. Sci.
**1994**, 73, 135–152. [Google Scholar] [CrossRef] - Mueser, P.; Graves, P. Examining the role of economic opportunity and amenities in explaining population redistribution. J. Urban Econ.
**1995**, 37, 176–200. [Google Scholar] [CrossRef] - Glaeser, E. The Economics Approach to Cities; Working paper 13696; National Bureau of Economic Research: Cambridge, MA, USA, 2007. [Google Scholar]
- Steinnes, D.; Fisher, W. An econometric model of intraurban location. J. Reg. Sci.
**1974**, 14, 65–80. [Google Scholar] [CrossRef] - Steinnes, D. Causality and intraurban location. J. Urban Econ.
**1977**, 4, 69–79. [Google Scholar] [CrossRef] - Clark, D.; Murphy, C. Countywide employment and population growth. J. Reg. Sci.
**1996**, 36, 235–256. [Google Scholar] [CrossRef] - Mulligan, G.; Vias, A.; Glavac, S. Initial diagnostics of a regional adjustment model. Environ. Plan. A
**1999**, 31, 855–876. [Google Scholar] [CrossRef] - Hoogstra, G.; Dijk, J.; Florax, R. Do jobs follow people or people follow jobs? A meta-analysis of Carlino-Mills studies. Spat. Econ. Anal.
**2017**, 4, 357–378. [Google Scholar] [CrossRef] - Mulligan, G.; Nilsson, H. Recent population and employment change in U.S. metropolitan areas: Endogenizing self-employment and patents. In Unlocking the Potential of Regions Through Entrepreneurship and Innovation; Bernhard, I., Ed.; University West: Trollhättan, Sweden, 2019; pp. 309–329. [Google Scholar]
- Rogers, A. Matrix Methods in Urban and Regional Analysis; Holden-Day: San Francisco, CA, USA, 1971. [Google Scholar]
- Keyfitz, N.; Caswell, H. Applied Mathematical Demography, 3rd ed.; Springer: New York, NY, USA, 2005. [Google Scholar]
- Lu, B.; Charlton, M.; Harris, P.; Fotheringham, S. Geographically weighted regression with a non-Euclidean distance metric: A case study using hedonic house price data. Int. J. Geogr. Inf. Sci.
**2014**, 28, 1–25. [Google Scholar] [CrossRef] - Bureau of Economic Analysis. Interactive Tables: Personal Income and Employment. Available online: https://www.bea.gov/regional/index/htm (accessed on 1 November 2018).
- U.S. Census Bureau. Available online: https://www.census.gov (accessed on 1 November 2018).
- Carruthers, J.; Mundy, B. Environmental Valuation; Ashgate: Burlington, VT, USA, 2006. [Google Scholar]
- Savageau, D.; Boyer, R. Places Rated Almanac, 4th ed.; Macmillan: New York, NY, USA, 1993. [Google Scholar]
- BizEE Degree Days. Available online: https://www.degreedays.net (accessed on 1 November 2018).
- Mulligan, G.; Carruthers, J. Amenities, quality of life, and regional development. In Investigating Quality of Urban Life; Marans, R., Stimson, R., Eds.; Springer: New York, NY, USA, 2011; pp. 107–133. [Google Scholar]
- U.S. Patent and Trade Office. Calendar Year Patent Statistics. Available online: https://www.uspto.gov/web/offices/ac/ido/oeip/taf/reports_cbsa.htm (accessed on 1 November 2018).
- Mulligan, G. Revisiting patent generation in U.S. metropolitan areas: 1990–2015. Appl. Spat. Anal. Policy. accepted for publication on 13 July 2020. [CrossRef]
- Kirzner, I. Competition and Entrepreneurship; University of Chicago: Chicago, IL, USA, 1973. [Google Scholar]
- Godin, K.; Clemens, J.; Veldhus, N. Measuring Entrepreneurship: Conceptual Frameworks and Empirical Indicators; Fraser Institute: Vancouver, BC, Canada, 2008. [Google Scholar]
- Kelejian, H.; Prucha, I. Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances. J. Econom.
**2010**, 157, 53–67. [Google Scholar] [CrossRef] [Green Version] - Kaldor, N. The irrelevance of equilibrium economics. Econ. J.
**1972**, 82, 1237–1255. [Google Scholar] [CrossRef] - Perloff, H.; Dunn, E., Jr.; Lampard, E.; Muth, R. Regions, Resources and Economic Growth; Resources for the Future: Washington, DC, USA, 1960. [Google Scholar]
- Nourse, H. Regional Economics; McGraw-Hill: New York, NY, USA, 1968. [Google Scholar]
- Shearer, C.; Shah, I.; Friedhoff, A.; Berube, A. Metro Monitor 2018. Available online: https://www.brookings.edu/research/metro-monitor-2018 (accessed on 1 November 2018).

OLS | 2GLS | GWR | OLS | 2GLS | GWR | |
---|---|---|---|---|---|---|

90-00 | 95-05 | |||||

Constant | 2.609 * | 2.276 * | 1.569 | 1.167 * | 1.024 * | 0.328 |

POPUL | 0.894 * | 0.888 * | 0.872 | 0.945 * | 0.950 * | 0.903 |

EMPLY | 0.109 * | 0.111 * | 0.132 | 0.050 | 0.044 | 0.090 |

HAMEN | 0.083 * | 0.093 * | 0.114 | 0.142 * | 0.143 * | 0.117 |

CDGDY | −0.009 | −0.006 | −0.018 | 0.005 | 0.006 | −0.013 |

HDGDY | −0.067 * | −0.060 * | −0.062 | −0.057 * | −0.054 * | −0.056 |

00−10 | 05−15 | |||||

Constant | 1.285 * | 1.092 * | 0.369 | 0.489 | 0.320 | 0.769 |

POPUL | 0.982 * | 0.997 * | 0.967 | 0.965 * | 0.974 * | 0.911 |

EMPLY | 0.018 | 0.002 | 0.033 | 0.029 | 0.019 | 0.087 |

HAMEN | 0.135 * | 0.133 * | 0.141 | −0.010 | −0.009 | 0.044 |

CDGDY | 0.012 | 0.015 ** | 0.007 | 0.031 * | 0.033 * | 0.034 |

HDGDY | −0.031 * | −0.026 * | −0.025 | −0.005 | −0.001 | −0.015 |

OLS1 | 2GLS | GWR | OLS1 | 2GLS | GWR | |
---|---|---|---|---|---|---|

90-00 | 95-05 | |||||

Constant | 2.985 * | 2.509 * | 0.373 | 1.914 * | 1.600 * | 1.115 |

POPUL | −0.020 | −0.028 | −0.017 | 0.039 | 0.050 | 0.028 |

EMPLY | 1.023 * | 1.027 * | 1.120 | 0.955 * | 0.942 * | 0.962 |

WAGES | −0.397 * | −0.296 * | −0.261 | −0.142 * | −0.089 | −0.099 |

PWFOR | 0.290 * | 0.173 * | 0.331 | 0.015 | −0.038 | 0.239 |

PROFS | 0.040 * | 0.040 * | 0.031 | 0.066 * | 0.062 * | 0.059 |

PATEN | 0.015 ** | 0.017 * | 0.013 | −0.002 | 0.000 | −0.004 |

PROPR | 0.124 * | 0.081 * | 0.121 | 0.117 * | 0.092 * | 0.144 |

00−10 | 05−15 | |||||

Constant | 0.040 | −0.193 | 1.004 | −0.384 | −0.727 | 1.350 |

POPUL | 0.141 * | 0.159 * | 0.113 | 0.061 | 0.080 | −0.009 |

EMPLY | 0.846 * | 0.827 * | 0.881 | 0.939 * | 0.919 * | 1.015 |

WAGES | −0.229 * | −0.189 * | −0.246 | −0.186 * | −0.136 * | −0.179 |

PWFOR | 0.393 * | 0.350 * | 0.361 | 0.341 * | 0.288 * | 0.227 |

PROFS | 0.135 * | 0.130 * | 0.100 | 0.115 * | 0.110 * | 0.091 |

PATEN | −0.006 | −0.004 | 0.002 | 0.010 | 0.012 ** | 0.012 |

PROPR | 0.211 * | 0.187 * | 0.135 | 0.200 * | 0.176 * | 0.096 |

2000 | 2005 | 2010 | 2015 | 2000 | 2005 | 2010 | 2015 | |

POPUL_{t} | ||||||||

POPUL_{t}_{-1} | POPUL_{t}_{-1} | POPUL_{t}_{-1} | POPUL_{t}_{-1} | EMPLY_{t}_{-1} | EMPLY_{t}_{-1} | EMPLY_{t}_{-1} | EMPLY_{t}_{-1} | |

2000 | 1.000 | 0.920 | 0.868 | 0.794 | 1.000 | 0.919 | 0.850 | 0.810 |

2005 | 0.920 | 1.000 | 0.961 | 0.844 | 0.919 | 1.000 | 0.957 | 0.853 |

2010 | 0.868 | 0.961 | 1.000 | 0.915 | 0.850 | 0.957 | 1.000 | 0.917 |

2015 | 0.794 | 0.844 | 0.915 | 1.000 | 0.810 | 0.853 | 0.917 | 1.000 |

EMPLY_{t} | ||||||||

POPUL_{t}_{-1} | POPUL_{t}_{-1} | POPUL_{t}_{-1} | POPUL_{t}_{-1} | EMPLY_{t}_{-1} | EMPLY_{t}_{-1} | EMPLY_{t}_{-1} | EMPLY_{t}_{-1} | |

2000 | 1.000 | 0.926 | 0.621 | 0.822 | 1.000 | 0.911 | 0.656 | 0.867 |

2005 | 0.926 | 1.000 | 0.727 | 0.885 | 0.911 | 1.000 | 0.796 | 0.910 |

2010 | 0.621 | 0.727 | 1.000 | 0.856 | 0.656 | 0.796 | 1.000 | 0.842 |

2015 | 0.822 | 0.885 | 0.856 | 1.000 | 0.867 | 0.910 | 0.842 | 1.000 |

POPUL_{t} | POPUL_{t} | EMPLY_{t} | EMPLY_{t} | |||

Metro | POPUL_{t}_{-1} | EMPLY_{t}_{-1} | POPUL_{t}_{-1} | EMPLY_{t}_{-1} | Stable | Sustain |

New York | 1.017 | −0.015 | 0.020 | 0.970 | Yes | Yes |

Los Angeles | 0.779 | 0.223 | −0.098 | 1.100 | Yes | Yes |

Chicago | 0.847 | 0.137 | −0.027 | 1.028 | Yes | No |

Dallas | 0.900 | 0.093 | 0.033 | 0.976 | Yes | No |

Houston | 0.716 | 0.283 | −0.106 | 1.102 | Yes | Yes |

Philadelphia | 0.899 | 0.140 | 0.048 | 0.984 | Yes | Yes |

Washington | 0.867 | 0.131 | 0.009 | 0.995 | Yes | No |

Miami | 0.810 | 0.186 | −0.053 | 1.049 | Yes | Yes |

Atlanta | 1.118 | −0.108 | 0.148 | 0.862 | Yes | Yes |

Boston | 0.907 | 0.105 | 0.041 | 0.977 | Yes | Yes |

San Francisco | 0.851 | 0.147 | −0.063 | 1.065 | Yes | Yes |

Phoenix | 0.833 | 0.161 | −0.050 | 1.048 | Yes | Yes |

Riverside | 0.790 | 0.217 | 0.127 | 0.895 | Yes | Yes |

Detroit | 0.801 | 0.204 | −0.138 | 1.143 | Yes | Yes |

Seattle | 1.032 | −0.035 | 0.063 | 0.928 | Yes | Yes |

POPUL_{t} | POPUL_{t} | EMPLY_{t} | EMPLY_{t} | |||
---|---|---|---|---|---|---|

Metro | POPUL_{t}_{-1} | EMPLY_{t}_{-1} | POPUL_{t}_{-1} | EMPLY_{t}_{-1} | Stable | Sustain |

New York | 1.021 | −0.025 | 0.081 | 0.917 | Yes | No |

Los Angeles | 0.838 | 0.162 | −0.079 | 1.087 | Yes | No |

Chicago | 0.942 | 0.056 | 0.043 | 0.964 | Yes | No |

Dallas | 0.937 | 0.062 | 0.034 | 0.974 | Yes | No |

Houston | 0.879 | 0.119 | −0.041 | 1.049 | Yes | No |

Philadelphia | 0.932 | 0.064 | 0.018 | 0.983 | Yes | Yes |

Washington | 1.022 | −0.026 | 0.011 | 0.999 | Yes | No |

Miami | 0.852 | 0.148 | −0.057 | 1.067 | Yes | No |

Atlanta | 1.031 | −0.034 | 0.083 | 0.914 | Yes | Yes |

Boston | 0.931 | 0.067 | 0.025 | 0.980 | Yes | No |

San Francisco | 0.817 | 0.182 | −0.117 | 1.123 | Yes | No |

Phoenix | 0.823 | 0.176 | −0.107 | 1.114 | Yes | Yes |

Riverside | 0.830 | 0.167 | −0.097 | 1.101 | Yes | Yes |

Detroit | 0.824 | 0.172 | −0.102 | 1.107 | Yes | Yes |

Seattle | 1.027 | −0.032 | 0.087 | 0.911 | Yes | Yes |

Region | Name | HAMEN | CDGDY | HDGDY |
---|---|---|---|---|

1 (15) | New England | 0.098 | −0.197 | −0.326 |

2 (41) | Mideast | 0.055 | −0.045 | 0.085 |

3 (121) | Southeast | 0.000 | −0.007 | 0.005 |

4 (39) | Southwest | −0.216 | 0.234 | 0.112 |

5 (59) | Great Lakes | 0.069 | 0.002 | 0.012 |

6 (33) | Plains | 0.204 | −0.197 | −0.236 |

7 (22) | Rocky Mountain | −0.174 | 0.227 | 0.091 |

8 (47) | Far West | −0.045 | −0.044 | 0.031 |

Nation | Base Score | 0.000 | 0.000 | 0.000 |

(377) | Actual Estimate | 0.1040 | 0.0025 | −0.0398 |

Region | Name | WAGES | PWFOR | PROFS | PATEN | PROPR |
---|---|---|---|---|---|---|

1 (15) | New England | 0.131 | 0.084 | −0.244 | −0.153 | −0.118 |

2 (41) | Mideast | −0.053 | −0.028 | 0.082 | 0.090 | 0.034 |

3 (121) | Southeast | −0.032 | 0.003 | 0.022 | 0.028 | 0.025 |

4 (39) | Southwest | 0.093 | 0.004 | 0.003 | −0.218 | −0.064 |

5 (59) | Great Lakes | 0.076 | −0.101 | 0.093 | −0.005 | −0.026 |

6 (33) | Plains | 0.039 | −0.063 | −0.114 | 0.000 | −0.055 |

7(22) | Rocky Mountain | 0.077 | 0.084 | −0.013 | −0.089 | −0.061 |

8(47) | Far West | −0.147 | 0.110 | −0.084 | 0.126 | 0.097 |

Nation | Base Score | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |

(377) | Actual Estimate | −0.1962 | 0.2898 | 0.0704 | 0.0056 | 0.1246 |

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## Share and Cite

**MDPI and ACS Style**

Mulligan, G.F.; Carruthers, J.I.
Location-Specific Adjustments in Population and Employment across Metropolitan America. *Urban Sci.* **2021**, *5*, 24.
https://doi.org/10.3390/urbansci5010024

**AMA Style**

Mulligan GF, Carruthers JI.
Location-Specific Adjustments in Population and Employment across Metropolitan America. *Urban Science*. 2021; 5(1):24.
https://doi.org/10.3390/urbansci5010024

**Chicago/Turabian Style**

Mulligan, Gordon F., and John I. Carruthers.
2021. "Location-Specific Adjustments in Population and Employment across Metropolitan America" *Urban Science* 5, no. 1: 24.
https://doi.org/10.3390/urbansci5010024