Spatial Sorting of Skills and Sectors Jonathan I. Dingel Chicago Booth Frontiers in Urban Economics November 2015 Spatial Sorting of Skills and Sectors My goal is to tackle three questions: I Why should we care? I How should we characterize skills and sectors? I What tools are available to model builders? Spatial distributions of skills and sectors Why should we care about the spatial distributions of skills and sectors? 1. They vary a lot 2. They covary with city characteristics 3. They’re often the basis for identification 4. They should help us understand how cities work Spatial distributions of skills and sectors I Public discussion describes US cities in terms of skills and sectors I Ranking cities by educational attainment is a popular media exercise I Place names are shorthand for sectors Educational attainment varies a lot across cities Share of population 25 and older with bachelor’s degree or higher 0.28 − 0.63 0.23 − 0.28 0.19 − 0.23 0.16 − 0.19 0.14 − 0.16 0.07 − 0.14 Data source: American Community Survey, 2005-2009, Series S1501 Plot: CBSAs for maptile Sectoral composition varies a lot across cities Employment share of Professional, Scientific, and Technical Services 0.06 − 0.26 0.04 − 0.06 0.03 − 0.04 0.03 − 0.03 0.02 − 0.03 0.01 − 0.02 Data source: County Business Patterns, 2009, NAICS 54 Plot: CBSAs for maptile They covary with city characteristics -1 -.5 Log (demeaned) skilled population share .5 -.5 0 Log (demeaned) skilled population share .25 -.25 0 1 .5 Populations of three educational groups across US metropolitan areas 10 12 14 16 Metropolitan log population 18 10 12 14 16 Metropolitan log population Bachelor's degree Bachelor's degree College dropout College dropout High school graduate High school graduate Data source: 2000 Census of Population microdata via IPUMS-USA 18 They covary with city characteristics 1 -1 -2 Log (demeaned) employment share -1 0 1 Log (demeaned) employment share -.5 .5 0 2 Employment in three occupations across US metropolitan areas 10 12 14 16 Metropolitan log population 18 10 12 14 16 Metropolitan log population 18 Computer and mathematical Computer and mathematical Office and administrative support Office and administrative support Installation, maintenance and repair Installation, maintenance and repair Data source: Occupational Employment Statistics 2000 10 12 14 16 Metropolitan log population 18 1 Log (demeaned) employment share -.5 0 .5 2 Log (demeaned) employment share 0 -1 1 -1 -1 -.5 -2 Log (demeaned) skilled population share .5 -.5 0 Log (demeaned) skilled population share -.25 0 .25 1 .5 They covary with city characteristics 10 12 14 16 Metropolitan log population 18 10 12 14 16 Metropolitan log population 18 10 12 14 16 Metropolitan log population 18 Bachelor's degree Bachelor's degree Computer and mathematical Computer and mathematical College dropout College dropout Office and administrative support Office and administrative support High school graduate High school graduate Installation, maintenance and repair Installation, maintenance and repair Skills and sectors are strongly linked to cities’ sizes (a) Confounds inference: Agglomeration benefits vs compositional effects (b) Confounds counterfactuals: Making NYC 10x larger raises finance’s share of national employment and GDP They’re often the basis for identification Recent JMPs by Notowidigdo, Diamond, and Yagan I Theory: all locations produce a homogeneous good I Empirics: exploit variation in industrial composition to estimate model parameters via shifts in local labor demand I Shift-share instrument: local composition × national changes What variation does the instrument exploit? I Skill mix vs industrial mix (e.g. endogenous local SBTC - Beaudry, Doms, Lewis 2010) I City characteristics covarying with skills and sectors highlight exclusion-restriction assumptions They should help us understand how cities work I Why do different people and different businesses locate in different places? I The answers should be crucial to understanding how cities work I Which elements of the Marshallian trinity imply we’ll find finance and dot-coms in big cities? I Coagglomeration (Ellison Glaeser Kerr 2010) and heterogeneous agglomeration (Faggio, Silva, Strange 2015) can provide clues I Theory is laggard: Most models of sectoral composition are polarized, with specialized cities that have only one tradable sector and perfectly diversified cities that have all the tradable sectors (Helsley and Strange 2014) Spatial distributions of skills and sectors How should we characterize skills and sectors? I Important question for both theory and empirics A richer depiction of firms and workers improves realism, but. . . I more types threaten to make theoretical models intractable I more types increase the burden of finding instruments While the trade-offs are specific to the research question under investigation, we can start by asking: Are two skill groups enough? Spatial equilibrium with two skill groups A simple starting point 1. Two skill groups, s ∈ {L, H} 2. Spatial equilibrium: Us (Ac , ws,c , pc ) = Us (Ac 0 , ws,c 0 , pc 0 ) ∀c, c 0 ∀s 3. Homotheticity: Us (Ac , ws,c , pc ) = ws,c A c pc These jointly imply that relative wages are spatially invariant wH,c 0 wL,c 0 wH,c wL,c = = and Ac pc Ac 0 pc 0 Ac pc Ac 0 pc 0 wH,c wH,c 0 = ∀c, c 0 ⇒ wL,c wL,c 0 Spatial equilibrium with two skill groups A simple starting point 1. Two skill groups, s ∈ {L, H} 2. Spatial equilibrium: Us (Ac , ws,c , pc ) = Us (Ac 0 , ws,c 0 , pc 0 ) ∀c, c 0 ∀s 3. Homotheticity: Us (Ac , ws,c , pc ) = ws,c A c pc These jointly imply that relative wages are spatially invariant wH,c 0 wL,c 0 wH,c wL,c = = and Ac pc Ac 0 pc 0 Ac pc Ac 0 pc 0 wH,c wH,c 0 = ∀c, c 0 ⇒ wL,c wL,c 0 Spatial variation in skill premia College Abilene, Akron, Albany, Albany--Schenectady--Troy, Albuquerque, Alexandria, Allentown--Bethlehem--Easton, Altoona, Amarillo, Anchorage, Ann Anniston, Appleton--Oshkosh--Neenah, Asheville, Athens, Atlanta, Atlantic--Cape Auburn--Opelika, Augusta--Aiken, Austin--San Bakersfield, Baltimore, Bangor, Barnstable--Yarmouth, Baton Beaumont--Port Bellingham, Benton Bergen--Passaic, Billings, Biloxi--Gulfport--Pascagoula, Binghamton, Birmingham, Bloomington, Bloomington--Normal, Boise Boston, Boulder--Longmont, Brazoria, Bremerton, Bridgeport, Brockton, Brownsville--Harlingen--San Bryan--College Buffalo--Niagara Burlington, Canton--Massillon, Casper, Cedar Champaign--Urbana, Charleston--North Charleston, Charlotte--Gastonia--Rock Charlottesville, Chattanooga, Cheyenne, Chicago, Chico--Paradise, Cincinnati, Clarksville--Hopkinsville, Cleveland--Lorain--Elyria, Colorado Columbia, Columbus, Corpus Cumberland, Dallas, Danbury, Danville, Davenport--Moline--Rock Dayton--Springfield, Daytona Decatur, Denver, Des Detroit, Dothan, Dover, Duluth--Superior, Dutchess Eau El Elkhart--Goshen, Elmira, Erie, Eugene--Springfield, Evansville--Henderson, Fargo--Moorhead, Fayetteville, Fayetteville--Springdale--Rogers, Fitchburg--Leominster, Flagstaff, Flint, Florence, Fort Fresno, Gadsden, Gainesville, Galveston--Texas Gary, Glens Goldsboro, Grand Great Greeley, Green Greensboro--Winston-Salem--High Greenville, Greenville--Spartanburg--Anderson, Hagerstown, Hamilton--Middletown, Harrisburg--Lebanon--Carlisle, Hartford, Hattiesburg, Hickory--Morganton--Lenoir, Honolulu, Houma, Houston, Huntington--Ashland, Huntsville, Indianapolis, Iowa Jackson, Jacksonville, Jamestown, Janesville--Beloit, Jersey Johnson Johnstown, Joplin, Kalamazoo--Battle Kankakee, Kansas Kenosha, Killeen--Temple, Knoxville, Kokomo, La Lafayette, Lake Lakeland--Winter Lancaster, Lansing--East Laredo, Las Lawrence, Lawton, Lewiston--Auburn, Lexington, Lima, Lincoln, Little Longview--Marshall, Los Louisville, Lowell, Lubbock, Lynchburg, Macon, Madison, Manchester, Mansfield, McAllen--Edinburg--Mission, Medford--Ashland, Melbourne--Titusville--Palm Memphis, Merced, Miami, Middlesex--Somerset--Hunterdon, Milwaukee--Waukesha, Minneapolis--St. Missoula, Mobile, Modesto, Monmouth--Ocean, Monroe, Montgomery, Muncie, Myrtle Naples, Nashua, Nashville, Nassau--Suffolk, New Newark, Newburgh, Norfolk--Virginia Oakland, Ocala, Odessa--Midland, Oklahoma Olympia, Omaha, Orange Orlando, Owensboro, Panama Parkersburg--Marietta, Pensacola, Peoria--Pekin, Philadelphia, Phoenix--Mesa, Pine Pittsburgh, Pittsfield, Portland, Portland--Vancouver, Portsmouth--Rochester, Providence--Fall Provo--Orem, Pueblo, Punta Racine, Raleigh--Durham--Chapel Rapid Reading, Redding, Reno, Richland--Kennewick--Pasco, Richmond--Petersburg, Riverside--San Roanoke, Rochester, Rockford, Rocky Sacramento, Saginaw--Bay St. Salem, Salinas, Salt San Santa Sarasota--Bradenton, Savannah, Scranton--Wilkes-Barre--Hazleton, Seattle--Bellevue--Everett, Sharon, Sheboygan, Sherman--Denison, Shreveport--Bossier Sioux South Spokane, Springfield, Stamford--Norwalk, State Steubenville--Weirton, Stockton--Lodi, Sumter, Syracuse, Tacoma, Tallahassee, Tampa--St. Terre Texarkana, Toledo, Topeka, Trenton, Tucson, Tulsa, Tuscaloosa, Tyler, Utica--Rome, Vallejo--Fairfield--Napa, Ventura, Victoria, Vineland--Millville--Bridgeton, Visalia--Tulare--Porterville, Waco, Washington, Waterbury, Waterloo--Cedar Wausau, West Wheeling, Wichita, Wichita Williamsport, Wilmington--Newark, Wilmington, Worcester, Yakima, Yolo, York, Youngstown--Warren, Yuba Yuma, .8 .7 .6 .5 .4 .3 .2 Skill 11 12 13 14 15 16 MSA Paso, Crosse, Cloud, Joseph, Louis, Cruces, Vegas, Angeles--Long Claire, Angelo, Antonio, Diego, Francisco, Jose, Luis Moines, Lake Arbor, Bluff, Collins--Loveland, Lauderdale, Myers--Cape Pierce--Port Smith, Walton Wayne, Worth--Arlington, Bedford, Haven--Meriden, London--Norwich, Orleans, York, PA City, Charles, MI City, CA PA Palm IN Rock--North City, Falls, Haute, OH College, NV TX Barbara--Santa Cruz--Watsonville, Fe, Rosa, Gorda, Rapids, Bay, Forks, Junction, Rapids--Muskegon--Holland, Rouge, Bend, OK Mount, FL AZ TX Beach, MO TX City, DE OH OR NY MA--NH Christi, AL City, GA WI Harbor, County, FL CO CA Falls, OH WY MT GA TX IN PA NE--IA LA NE ME WA MA--NH CO MI City, GA AZ AL CA SC NH KS GA TX NJ LA OK CO City--Kingsport--Bristol, VA Obispo--Atascadero--Paso FL Beach, WI TX PA IL AL WA CA NJ MI MS TN TX WI IN Springs, CT ME MT TX AL SC WA VA WI City--Ogden, HI CA County, TN--AR--MS TN NM MO--IL AZ--UT NC MA CA AL IL NY WV--OH KY--IN MN MO SC City, IA premium OH NY AR MD IL GA KS MA--NH CA NC OH--KY--IN AL GA--AL OH WI LA IN WY WI--MN PA FL KY Beach--Boca IA--NE ID CA MN NY SD NC NY--PA WI VT TX--Texarkana, MI NV--AZ MA--CT FL SD LA PA NY Petersburg--Clearwater, log MT MO CT VA IL MA AR--OK WA WV AK PA NM CA Marcos, WI AL NJ CA NC Beach, KY TX IA NY FL IN NH NC PA--NJ MO--KS AL MS DC--MD--VA--WV FL NC MD--WV ND--MN NY MD IN CA TX PA NY FL TX LA IN NM AL LA UT City--Midland, TN--GA Lansing, MA NC IA IL SC PA Bernardino, CA May, Station, TX VA AZ OK MI CA CO FL River--Warwick, Paul, Arthur, CA TX GA--SC Falls, Beach--Newport NY FL Falls, IN NJ St. AL TX Haven, MN--WI Coral, City, WI CO ND--MN NY Charleston, Little OH OR ME Creek, Beach, TX NJ FL CT TX NJ population City, OH CO TX OR IL Lucie, DE--MD CT OR--WA MN--WI WV--KY--OH FL Maria--Lompoc, OH NY IL IA OH--WV CO OH TX WV--OH WI MI IN--KY MA UT CT--RI VA MA TX CA FL TN--KY TX Raton, Rock, NH--ME FL CA Hill, Island, OH LA MI Hill, CA CA AR WA FL Bay, Benito, TX MI NY NC MS WA WI NC NJ PA SC AR NC--SC FL PA IA--IL RI--MA FL AR TN--VA News, NJ Point, PA MI TX Robles, SC FLCAVA--NC NCCA wage premia are higher in larger cities .7 .8 Stamford--Norwalk, CT McAllen--Edinburg--Mission, TX Skill premium .5 .6 Danbury, CT Brownsville--Harlingen--San Benito, TX San Jose, CA .2 .3 .4 OrangeDallas, County, TXCA Houston, TX Bridgeport, CT Binghamton, NY Richland--Kennewick--Pasco, WA El Paso, TX San Francisco, CA Odessa--Midland, TX AL Huntsville, Miami, FL Birmingham, AL Ventura, CA Dothan, Panama ALCity, FL Newark, NJ Santa Cruz--Watsonville, CA Jackson, TN Fayetteville--Springdale--Rogers, AR Los York, Angeles--Long Beach, CA Ocala, FL Lawrence, MA--NH New NY Rochester, MN Austin--San Marcos, TX Gadsden, AL Trenton, NJ Sherman--Denison, TXWaco, TX TX Fort Worth--Arlington, TX NC--SC San Antonio, TX Amarillo, Corpus Augusta--Aiken, Christi, TX GA--SC West New Palm Charlotte--Gastonia--Rock Orleans, Beach--Boca LA Raton, FL Hill, FortAL AZ Walton Beach, FL Atlanta, GA Memphis, TN--AR--MS Decatur,Decatur, IL Yuma, Sacramento,NJTampa--St. CAHill, NC Petersburg--Clearwater, Santa Fe, NM Raleigh--Durham--Chapel FL Visalia--Tulare--Porterville, Jersey City, CANJ TX Melbourne--Titusville--Palm Bay, FLBergen--Passaic, Fort Lauderdale, FL San Diego, CA Sioux City, IA--NELongview--Marshall, Orlando, FLOH--KY--IN Washington, DC--MD--VA--WV Columbus, Lowell, MA--NH GA--AL Shreveport--Bossier City, LATN Cincinnati, Victoria, TX Boise Chattanooga, City, ID Bakersfield, Knoxville, TN--GA CA Oakland, CA Fort Smith, AR--OK Fort Pierce--Port St. Lucie, FL Phoenix--Mesa, AZ Galveston--Texas FL City, TX Little Rock--North LittleCA Rock, AR Alexandria, Benton LA Manchester, Harbor,Naples, MI NH Fresno, Greenville--Spartanburg--Anderson, SC Cumberland, Parkersburg--Marietta, MD--WV Las Cruces, NM WV--OH Hamilton--Middletown, OH Greensboro--Winston-Salem--High Point, NC Bloomington--Normal, IL TX Kalamazoo--Battle Creek, MI Glens Falls, NYLaredo, Akron, Boston, MA--NH Chicago, IL Albany, Wichita GA Falls, TXNCLubbock, Macon, GA Middlesex--Somerset--Hunterdon, NJ PA TX Tallahassee, Beaumont--Port Lafayette, FLJackson, LA Columbia, Mobile, AL SC Tulsa, TXOH OK NM Jacksonville, FL Pensacola, FL Albuquerque, Monmouth--Ocean, NJ Pittsburgh, Baltimore, MD Philadelphia, PA--NJ San Angelo, Jacksonville, TX MSArthur, Allentown--Bethlehem--Easton, PA Goldsboro, NC Savannah, Montgomery, GA ALCharleston--North Roanoke, NH Charleston, VA OH SC Columbus, St.Nassau--Suffolk, Louis, MO--IL NY Abilene, TX Nashua, Brazoria, VA TX WV Des Johnson Moines, Colorado City--Kingsport--Bristol, IASprings,Albany--Schenectady--Troy, COCharleston, Hartford, TN--VA CT Kansas Yuba Tuscaloosa, City, CA Lynchburg, AL NYCity, MO--KSRiverside--San Killeen--Temple, Harrisburg--Lebanon--Carlisle, PA Indianapolis, Cleveland--Lorain--Elyria, IN Beach--Newport OH Vineland--Millville--Bridgeton, NJ Canton--Massillon, Stockton--Lodi, OH CA VA Detroit, Bernardino, MI CA Hattiesburg, Jackson, MS MI Asheville, Dutchess NC County, Saginaw--Bay NYTX City--Midland, Omaha, Syracuse, NE--IA MIRichmond--Petersburg, NY Norfolk--Virginia News, VA--NC Williamsport, Florence, SC PA Gainesville, FL Peoria--Pekin, Provo--Orem, ILNY--PA UT Salt Lake City--Ogden, UT Rocky Tyler, Mount, Merced, TX NC CA Newburgh, Daytona Beach, FLTucson, Louisville, Rochester, KY--IN NY TX--Texarkana, AR Santa Modesto, Barbara--Santa Sarasota--Bradenton, CA Maria--Lompoc, Oklahoma FL CA City, OK Pine Lewiston--Auburn, Bluff, AR Texarkana, ME Redding, Myrtle Springfield, CA Beach, IL SC AZ Charlottesville, VA Fort Myers--Cape Coral, FL Nashville, TN River--Warwick, Cedar Waterbury, Rapids, Anchorage, IA OR CT AK Grand Providence--Fall Rapids--Muskegon--Holland, Denver, CO MI RI--MA South Bend, IN Lexington, Worcester, Wilmington--Newark, KYMA--CT DE--MD PuntaWI Gorda, Medford--Ashland, OR--WA Johnstown, PA Reading, Salinas, PA CA WA OHPortland--Vancouver, Wausau, Hagerstown, MDFLYakima, WA Hickory--Morganton--Lenoir, Davenport--Moline--Rock Ann Arbor, Island, NC MIMSDayton--Springfield, IA--IL Spokane, Milwaukee--Waukesha, WI Bremerton, Utica--Rome, WA Biloxi--Gulfport--Pascagoula, NY Boulder--Longmont, York, PALakeland--Winter CO Lansing--East Lansing, Haven, MI FL Greenville, Wheeling, NC Clarksville--Hopkinsville, WV--OH Fayetteville, NC Wichita, KS OH Flint, MI Brockton, NC Salem, MA NV TN--KY OR Toledo, Seattle--Bellevue--Everett, Joplin, MO Wilmington, Portland, ME Reno, Vallejo--Fairfield--Napa, Scranton--Wilkes-Barre--Hazleton, PA Minneapolis--St. Paul,WA MN--WI Elmira,Danville, Owensboro, NY Dover, KY VA Anniston, Bryan--College AL DE Station, TX Atlantic--Cape May, Baton NJ Rouge, LA CA MT Las Vegas, NV--AZ Green Lancaster, PA Bangor, ME Billings, Portsmouth--Rochester, NH--ME Kankakee, ILMonroe, Elkhart--Goshen, LA Charles, San Bay, Luis INWI Obispo--Atascadero--Paso London--Norwich, Wayne, CT--RI Robles, IN CA CT Buffalo--Niagara Springfield, MOFort New Youngstown--Warren, Haven--Meriden, OH Falls, NY La Jamestown, Crosse, Pueblo, WI--MN CO Lake LANew Mansfield, NY OH Santa Rosa, CA Sumter, SCFlorence, Kenosha, WI Erie, Huntington--Ashland, PA WV--KY--OH Casper, WY New AL Bedford, MA Eau Claire, WI Evansville--Henderson, IN--KY Honolulu, HI Pittsfield, MA Altoona, PA Grand Junction, Barnstable--Yarmouth, Champaign--Urbana, CO Houma, MA IL Topeka, Fargo--Moorhead, KS LA ND--MN Springfield, Tacoma, MAWA Sheboygan, WI Auburn--Opelika, Fitchburg--Leominster, Yolo,AL CA MA Olympia, Flagstaff, Rockford, IL Kokomo, IN Terre St.Haute, Cloud, INMN WA Lawton, OK AZ--UT Appleton--Oshkosh--Neenah, WI Columbia, Burlington, MO Racine, WI VT Greeley, Fort Collins--Loveland, CO Sioux Falls,CO SD Great Rapid Falls, St. City, Joseph, MTSDSteubenville--Weirton, MO College, OH--WV NE Eugene--Springfield, Gary, IN State Chico--Paradise, PA Lincoln, CA Madison, WIOR Athens, GA Janesville--Beloit, WI Duluth--Superior, MN--WI Sharon, PA Waterloo--Cedar Falls, IA Bloomington, IN Muncie, IN Lima, OH Missoula, Cheyenne, WY MT Grand Forks, ND--MNLafayette, IN Iowa City, IA Bellingham, WA Lawrence, KS 11 12 13 14 MSA log population 15 Davis and Dingel, “A Spatial Knowledge Economy”, 2013 16 Spatial variation in skill premia This pattern is getting stronger over time Figure 3: Relative Skill Levels and Wages by City Size Over Time Panel A: Fraction College or More by City Size 0.4 2004-7 1999 0.3 1989 1979 0.2 0.1 0 2 4 6 8 10 City Size Panel B: College Log Wage Premium by City Size 2004-7 0.6 1999 1989 0.4 1979 0.2 0 2 4 6 8 10 City Size Notes: Panel A shows the fraction of total hours worked by all men and women with at least a college degree in Baum-Snow and and City Size”, 2013 each location type in each year. Pavan, Panel B shows “Inequality relative mean log wages for white men ages 25-54 working full time and full year with versus without college degrees. How to proceed? The data reject our simple model; skill premia are higher in larger cities wH,c wH,c 0 6= wL,c wL,c 0 Three possible routes to take 1. Non-homothetic preferences 2. Upward-sloping local labor supplies 3. More than two skill groups How to proceed? The data reject our simple model; skill premia are higher in larger cities wH,c wH,c 0 6= wL,c wL,c 0 Three possible routes to take 1. Non-homothetic preferences (Black, Kolesnikova, Taylor 2009) 2. Upward-sloping local labor supplies (Topel, Moretti, Diamond) 3. More than two skill groups (My focus today) How to proceed? The data reject our simple model; skill premia are higher in larger cities wH,c wH,c 0 6= wL,c wL,c 0 Three possible routes to take 1. Non-homothetic preferences (Black, Kolesnikova, Taylor 2009) ⇒ Do more skilled people find big cities less attractive for consumption? (Albouy, Ehrlich, Liu 2015, Handbury 2012) 2. Upward-sloping local labor supplies (Topel, Moretti, Diamond) 3. More than two skill groups (My focus today) How to proceed? The data reject our simple model; skill premia are higher in larger cities wH,c wH,c 0 6= wL,c wL,c 0 Three possible routes to take 1. Non-homothetic preferences (Black, Kolesnikova, Taylor 2009) ⇒ Do more skilled people find big cities less attractive for consumption? (Albouy, Ehrlich, Liu 2015, Handbury 2012) 2. Upward-sloping local labor supplies (Topel, Moretti, Diamond) ⇒ Relative prices and quantities imply higher relative demand for skilled in larger cities 3. More than two skill groups (My focus today) How to proceed? The data reject our simple model; skill premia are higher in larger cities wH,c wH,c 0 6= wL,c wL,c 0 Three possible routes to take 1. Non-homothetic preferences (Black, Kolesnikova, Taylor 2009) ⇒ Do more skilled people find big cities less attractive for consumption? (Albouy, Ehrlich, Liu 2015, Handbury 2012) 2. Upward-sloping local labor supplies (Topel, Moretti, Diamond) ⇒ Relative prices and quantities imply higher relative demand for skilled in larger cities 3. More than two skill groups (My focus today) Both 2 and 3 push us towards thinking about the complementarity between agglomeration and skills A continuum of skills Recent research works with a continuum of skills I High-dimensional: Infinite types of individuals I One-dimensional: Skills are ordered A few reasons to take this route 1. Dichotomous results depend on dichotomous definitions 2. Broad categories miss important variation 3. Continuum case can be quite tractable Two types in theory and practice Two-type models can be simple – but what about two-type empirics? I Omit types: Our plot of college wage premia was bachelor’s degrees vs HS diplomas – use only 45% of population to test price prediction I Convert quantities to “equivalents”: “one person with some college is equivalent to a total of 0.69 of a high school graduate and 0.29 of a college graduate” (Katz & Murphy 1992, p.68) Results may be sensitive to dichotomous definitions I Diamond (2015): “A MSA’s share of college graduates in 1980 is positively associated with larger growth in its share of college workers from 1980 to 2000” I Baum-Snow, Freedman, Pavan (2015): “Diamond’s result does not hold for CBSAs if those with some college education are included in the skilled group.” Two types in theory and practice Two-type models can be simple – but what about two-type empirics? I Omit types: Our plot of college wage premia was bachelor’s degrees vs HS diplomas – use only 45% of population to test price prediction I Convert quantities to “equivalents”: “one person with some college is equivalent to a total of 0.69 of a high school graduate and 0.29 of a college graduate” (Katz & Murphy 1992, p.68) Results may be sensitive to dichotomous definitions I Diamond (2015): “A MSA’s share of college graduates in 1980 is positively associated with larger growth in its share of college workers from 1980 to 2000” I Baum-Snow, Freedman, Pavan (2015): “Diamond’s result does not hold for CBSAs if those with some college education are included in the skilled group.” Dichotomous approach misses relevant variation I In labor economics, the canonical two-skill model “is largely silent on a number of central empirical developments of the last three decades”, such as wage polarization and job polarization (Acemoglu and Autor 2011) I There is systematic variation across cities in terms of finer observable categories: population elasticities for high school graduates (.925), associate’s degree (0.997), bachelor’s degree (1.087), and professional degree (1.113) (Davis and Dingel 2015) Do broad categories miss important variation? Contrasting views I “Workers in cities with a well-educated labor force are likely to have unobserved characteristics that make them more productive than workers with the same level of schooling in cities with a less-educated labor force. For example, a lawyer in New York is likely to be different from a lawyer in El Paso, TX.” (Moretti 2004, p.2246) I “Within broad occupation or education groups, there appears to be little sorting on ability” (de la Roca, Ottaviano, Puga 2014) Data sources for “no sorting” evidence I NLSY79: Longitudinal study of about 11,000 US individuals I Spanish tax data 2004-2009: 150,375 workers (de la Roca and Puga 2015) Do broad categories miss important variation? National Longitudinal Survey of Youth 1979 I Bacolod, Blum, Strange (2009): “The mean AFQT scores do not vary much across [four] city sizes” within occupational categories I BBS observe only one sales person in MSAs with 0.5m – 1.0m residents (10th and 90th percentiles of AFQT are equal) table I Baum-Snow & Pavan (2012): Structural estimation of finite-mixture model implies “sorting on unobserved ability within education group. . . contribute little to observed city size wage premia.” I BSP use NLSY79 data on 1754 white men; 583 have bachelor’s degree or more; college wage premia don’t rise with city size table Spanish tax data (de la Roca and Puga 2015) I 150,375 workers and 37,443 migrations I Identification of sorting relies on random migration conditional on observables I Little sorting within five educational categories Bringing more data to bear on sorting I Baccalaureate and Beyond tracks a cohort graduating from four-year colleges in 1993 I In 2003, look at 2300 white individuals who obtained no further education after bachelor’s degree and now live in a PMSA I Look at variation in SAT scores across cities – all variation is within the finest age-race-education cell in typical public data sets I Mean SAT score in metros with more than 3.25m residents is 40 points higher than metros with fewer than 0.57m residents Sorting within observable demographic cells Mean SAT score in metros with more than 3.25m residents is 40 points higher than metros with fewer than 0.57m residents I Full distribution suggests stochastic dominance 0 .0005 Density .001 .0015 .002 .0025 I 500 1000 SAT score log pop > 15 14.3 > log pop > 13.25 Observations: 740, 710, 680, 640 Sample selection: TOOKSAT==1 & B3HDG03==1 & white==1 1500 15 > log pop > 14.3 log pop < 13.25 The continuum case Why work with a continuum? I Evidence for sorting on characteristics that are typically not observed I Need at least five types to capture sorting on observables in the sense of de la Roca and Puga (2015) I Modeling a finite, particular number of types is potentially painful Continuum case can be quite tractable I Recent work: Behrens, Duranton, Robert-Nicoud (2014), Davis and Dingel (2013, 2015), Gaubert (2015), Behrens and Robert-Nicoud (Handbook 2015) I These papers rely on tools from the assignment literature I Assignments of individuals/firms to cities, with endogenous city characteristics determined in equilibrium I Davis and Dingel (2015) speak to both skills and sectors Assignment models Many markets concern assignment problems I Who marries whom? (Becker) I Which worker performs which job? (Roy) I Which country makes which goods? (Ricardo) If relevant objects are well ordered, we can use tools from mathematics of complementarity to characterize equilibrium prices and quantities I Supermodularity (Topkis 1998) I Log-supermodularity (Athey 2002) Basis for today’s introduction I Sattinger - “Assignment Models of the Distribution of Earnings” I Costinot & Vogel - “Beyond Ricardo: Assignment Models in International Trade” I Davis & Dingel - “The Comparative Advantage of Cities” Differentials rents model In the spirit of Ricardo’s analysis of rent, start with land and labor: I A plot of land has fertility γ ∈ R I A farmer has skill ω ∈ R I Profits are π(γ, ω) = p · y (γ, ω) − r (γ) Which farmer will use which plot of land? I Farmers optimize: γ ∗ (ω) ≡ arg maxγ π(γ, ω) I Equilibrium prices r (γ) must support the equilibrium assignment of farmers to plots Supermodularity Definition (Supermodularity) A function g : Rn → R is supermodular if ∀x, x 0 ∈ Rn g (max (x, x 0 )) + g (min (x, x 0 )) ≥ g (x) + g (x 0 ) where max and min are component-wise operators. I Supermodularity means the arguments of g (·) are complements I g (x) is SM in (xi , xj ) if g (xi , xj ; x−i,−j ) is SM I g (x) is SM ⇐⇒ g (x) is SM in (xi , xj ) ∀i, j I If g is C 2 , ∂2g ∂xi ∂xj ≥ 0 ⇐⇒ g (x) is SM in (xi , xj ) Supermodularity implies PAM Positive assortative matching: I If g (x, t) is supermodular in (x, t), then x ∗ (t) ≡ arg maxx∈X g (x, t) is increasing in t I If y (γ, ω) is strictly supermodular (fertility and skill are complements), then γ ∗ (ω) is increasing I More skilled farmers are assigned to more fertile land Why? Suppose not: I Suppose ∃ω > ω 0 , γ > γ 0 where γ 0 ∈ γ ∗ (ω), γ ∈ γ ∗ (ω 0 ) I γ 0 ∈ γ ∗ (ω) ⇒ p · y (γ 0 , ω) − r (γ 0 ) ≥ p · y (γ, ω) − r (γ) ∀γ I γ ∈ γ ∗ (ω 0 ) ⇒ p · y (γ, ω 0 ) − r (γ) ≥ p · y (γ 0 , ω 0 ) − r (γ 0 ) ∀γ 0 I Summing: p · (y (γ 0 , ω) + y (γ, ω 0 )) ≥ p · (y (γ, ω) + y (γ 0 , ω 0 )) I Would contradict strict supermodularity of y (·) Ricardian trade model Costinot and Vogel (2015) survey Ricardo-Roy models I Ricardo: Linear production functions I Roy: Multiple factors of production (ω) Output in sector σ in country c is Z Q(σ, c) = A(ω, σ, c)L(ω, σ, c)dω Ω Ricardo 1817: England = c > c 0 = Portugal and cloth = σ > σ 0 = wine A(σ, c)/A(σ 0 , c) ≥ A(σ, c 0 )/A(σ 0 , c 0 ) Log-supermodularity (1/2) Definition (Log-supermodularity) A function g : Rn → R+ is log-supermodular if ∀x, x 0 ∈ Rn g (max (x, x 0 )) · g (min (x, x 0 )) ≥ g (x) · g (x 0 ) where max and min are component-wise operators. I Example: A : Σ × C → R+ , where Σ ⊆ R and C ⊆ R, with σ > σ 0 and c > c 0 A(σ, c)A(σ 0 , c 0 ) ≥ A(σ 0 , c)A(σ, c 0 ) I g (x) is LSM in (xi , xj ) if g (xi , xj ; x−i,−j ) is LSM I g (x) is LSM ⇐⇒ g (x) is LSM in (xi , xj ) ∀i, j I g > 0 and g is C 2 ⇒ ∂ 2 ln g ∂xi ∂xj ≥ 0 ⇐⇒ g (x) is LSM in (xi , xj ) Log-supermodularity (2/2) Three handy properties: 1. If g , h : Rn → R+ are log-supermodular, then gh is log-supermodular. 2. If g : Rn → R+ is log-supermodular, then G (x−i ) ≡ is log-supermodular. R 3. If g : Rn → R+ is log-supermodular, then xi∗ (x−i ) ≡ arg maxxi ∈R g (xi , x−i ) is increasing in x−i . g (xi , x−i )dxi Assignments with factor endowments (Costinot 2009) Primitives: I Technologies A(ω, σ, c) = A(ω, σ) ∀c I Endowments L(ω, γL,c ) Profit maximization by firms: p(σ) ≤ min{w (ω, c)/A(ω, σ)} ω∈Ω Ω(σ, c) ≡ {ω ∈ Ω : L(ω, σ, c) > 0)} ⊆ arg min{w (ω, c)/A(ω, σ)} ω∈Ω A(ω, σ) is strictly log-supermodular in (ω, σ) ⇒ I Ω(σ, c) is increasing in σ by property 3 of LSM I High-ω factors are employed in high-σ activities Equilibrium: I FPE w (ω, c) = w (ω) I Continuum ⇒ Σ(ω, c) = Σ(ω) singleton Output quantities (Costinot 2009) Labor market clearing: Z L(ω, σ, c)dσ = L(ω, γL,c ) ∀ω, c Σ L(ω, γL,c ) is strictly log-supermodular: High-γL,c locations are relatively abundant in high-ω factors Z Q(σ, c) = A(ω, σ)L(ω, σ, c)dω ZΩ = A(ω, σ)L(ω, γL,c )dω by Σ(ω, c) singleton Ω(σ) Rybczynski: A(ω, σ) and L(ω, γL,c ) SLSM ⇒ Q(σ, γL,c ) SLSM by properties 1 and 2 of LSM Comparative Advantage of Cities: Theory I Davis and Dingel (2015) describe comparative advantage of cities as jointly governed by individuals’ comparative advantage and locational choices I Cities endogenously differ in TFP due to agglomeration I More skilled individuals are more willing to pay for more attractive locations I Larger cities are skill-abundant in equilibrium I By individuals’ comparative advantage, larger cities specialize in skill-intensive activities I Under a further condition, larger cities are larger in all activities 1 0 -1 -3 I Compare elasticities of different skills, sectors Steeper slope in log-log plot is higher elasticity 10 12 14 16 18 Metropolitan log population Elasticities may be positive for all Professional, Scientific & Technical Services sectors -2 I I .5 Elasticity test of variation in relative population/employment 0 I -.5 Characterize the comparative advantage of cities with two tests -1 I 2 Use US data on skills and sectors Log (demeaned) employment share I Log (demeaned) employment share 1 3 Comparative Advantage of Cities: Empirics (1/2) 10 12 14 16 Metropolitan log population 18 Professional, Scientific & Technical Service Finance & Insurance Finance & Insurance Manufacturing Manufacturing Comparative Advantage of Cities: Empirics (2/2) Pairwise comparison test (LSM) I The function f (ω, c) is log-supermodular if c > c 0 , ω > ω 0 ⇒ f (ω, c)f (ω 0 , c 0 ) ≥ f (ω 0 , c)f (ω, c 0 ) I Our theory says skill distribution f (ω, c) and sectoral employment distribution f (σ, c) are log-supermodular I For example, population of skill ω in city c is f (ω, c). Check whether, for c > c 0 , ω > ω 0 , f (ω, c) f (ω, c 0 ) ≥ 0 f (ω , c) f (ω 0 , c 0 ) Are larger cities larger in all sectors? I Check if c > c 0 ⇒ f (σ, c) ≥ f (σ, c 0 ) Theory Model components Producers I Skills: Continuum of skills indexed by ω (educational attainment) I Sectors: Continuum of sectors σ (occupations, industries) I Goods: Freely traded intermediates assembled into final good I All markets are perfectly competitive Places I Cities are ex ante identical I Locations within cities vary in their desirability I TFP depends on agglomeration of “scale and skills” Z A(c) = J L, j(ω)f (ω, c)dω ω∈Ω Individual optimization Perfectly mobile individuals simultaneously choose I A sector σ of employment I A city with total factor productivity A(c) I A location τ (distance from ideal) within city c The productivity of an individual of skill ω is q(c, τ, σ; ω) = A(c)T (τ )H(ω, σ) Utility is consumption of the numeraire final good, which is income minus locational cost: U(c, τ, σ; ω) = q(c, τ, σ; ω)p(σ) − r (c, τ ) = A(c)T (τ )H(ω, σ))p(σ) − r (c, τ ) Sectoral choice I Individuals’ choices of locations and sectors are separable: arg max A(c)T (τ ) H(ω, σ)p(σ) −r (c, τ ) = arg max H(ω, σ)p(σ) σ | σ {z } | {z } locational sectoral I H(ω, σ) is log-supermodular in ω, σ and strictly increasing in ω I Comparative advantage assigns high-ω individuals to high-σ sectors I Absolute advantage makes more skilled have higher incomes (G (ω) = maxσ H(ω, σ)p(σ) is increasing) Locational choice I A location’s attractiveness γ = A(c)T (τ ) depends on c and τ I T 0 (τ ) < 0 may be interpreted as commuting to CBD, proximity to productive opportunities, or consumption value I More skilled are more willing to pay for more attractive locations I Equally attractive locations have same rental price and skill type I Location in higher-TFP city is farther from ideal desirability γ = A(c)T (τ ) = A(c 0 )T (τ 0 ) A(c) > A(c 0 ) ⇒ τ > τ 0 I Locational hierarchy: A smaller city’s locations are a subset of larger city’s in terms of attractiveness: A(c)T (0) > A(c 0 )T (0) Equilibrium distributions I Skill and sectoral distributions reflect distribution of locational attractiveness: Higher-γ locations occupied by higher-ω individuals who work in higher-σ sectors I Locational hierarchy ⇒ hierarchy of skills and sectors I The distributions f (ω, c) and f (σ, c) are log-supermodular if and only if the supply of locations with attractiveness γ in city c, s(γ, c), is log-supermodular γ 1 V if γ ≤ A(c)T (0) A(c) A(c) s(γ, c) = 0 otherwise ∂ where V (z) ≡ − ∂z S T −1 (z) is the supply of locations with innate desirability τ such thatT (τ ) = z When is s(γ, c) log-supermodular? Proposition (Locational attractiveness distribution) The supply of locations of attractiveness γ in city c, s(γ, c), is log-supermodular if and only if the supply of locations with innate desirability T −1 (z) within each city, V (z), has a decreasing elasticity. I Links each city’s exogeneous distribution of locations, V (z), to endogenous equilibrium locational supplies s(γ, c) I Informally, ranking relative supplies is ranking elasticities of V (z) γ ∂ ln V A(c) ∂ ln s(γ, c) γ ⇒ = s(γ, c) ∝ V A(c) ∂ ln γ ∂ ln z I Satisfied by the canonical von Thünen/monocentric geography The Comparative Advantage of Cities Corollary (Skill and employment distributions) If V (z) has a decreasing elasticity, then f (ω, c) and f (σ, c) are log-supermodular. I Larger cities are skill-abundant in equilibrium (satisfies Assumption 2 in Costinot 2009) I Locational productivity differences are Hicks-neutral in equilibrium (satisfies Definition 4 in Costinot 2009) I H(ω, σ) is log-supermodular (Assumption 3 in Costinot 2009) Corollary (Output and revenue distributions) If V (z) has a decreasing elasticity, then sectoral output Q(σ, c) and revenue R(σ, c) ≡ p(σ)Q(σ, c) are log-supermodular. The Comparative Advantage of Cities Corollary (Skill and employment distributions) If V (z) has a decreasing elasticity, then f (ω, c) and f (σ, c) are log-supermodular. I Larger cities are skill-abundant in equilibrium (satisfies Assumption 2 in Costinot 2009) I Locational productivity differences are Hicks-neutral in equilibrium (satisfies Definition 4 in Costinot 2009) I H(ω, σ) is log-supermodular (Assumption 3 in Costinot 2009) Corollary (Output and revenue distributions) If V (z) has a decreasing elasticity, then sectoral output Q(σ, c) and revenue R(σ, c) ≡ p(σ)Q(σ, c) are log-supermodular. When are bigger cities bigger in everything? We identify a sufficient condition under which a larger city has a larger supply of locations of a given attractiveness Proposition For any A(c) > A(c 0 ), if V (z) has a decreasing elasticity that is less than γ -1 at z = A(c) , s(γ, c) ≥ s(γ, c 0 ). Now apply this result to the least-attractive locations, so larger cities are larger in all skills and sectors Corollary If V (z) has a decreasing elasticity that is less than -1 at −1 γ (ω) z = K A(c) = A(c) , A(c) > A(c 0 ) implies f (ω, c) ≥ f (ω, c 0 ) and f (M(ω), c) ≥ f (M(ω), c 0 ) ∀ω ∈ Ω. Empirical approach and data description Empirical tests Our theory says f (ω, c) and f (σ, c) are log-supermodular. Two tests to describe skill and sectoral employment distributions: I Elasticities test: I I I I Compare population elasticities estimated via linear regression More skilled types should have higher population elasticities More skill-intensive sectors should have higher population elasticities Pairwise comparisons test: I I I I Compare any two cities and any two skills/sectors Relative population of more skilled should be higher in larger city: f (ω,c 0 ) (ω,c) c > c 0 , ω > ω 0 ⇒ ff(ω 0 ,c) ≥ f (ω 0 ,c 0 ) Relative employment of more skill-intensive sector should be higher (σ,c) f (σ,c 0 ) in larger city: c > c 0 , σ > σ 0 ⇒ ff(σ 0 ,c) ≥ f (σ 0 ,c 0 ) “Bin” together cities ordered by size and compare bins similarly Data: Skills I Proxy skills by educational attainment, assuming f (edu, ω, c) is log-supermodular in edu and ω (Costinot and Vogel 2010) I Following Acemoglu and Autor (2011), we use a minimum of three skill groups. Population share .37 Share US-born .78 Some college .31 .89 Bachelor’s or more .32 .85 Skill (3 groups) High school or less Skill (9 groups) Less than high school High school dropout High school graduate College dropout Associate’s degree Bachelor’s degree Master’s degree Professional degree Doctorate Population share .04 .08 .25 .23 .08 .20 .08 .03 .01 Share US-born .29 .73 .88 .89 .87 .86 .84 .81 .72 Notes: Sample is individuals 25 and older in the labor force residing in 270 metropolitan areas. Data source: 2000 Census of Population microdata via IPUMS-USA Data: Sectors I I I SOC 45 37 35 47 51 29 21 25 19 23 19 industrial categories (2-digit NAICS, 2000 County Business Patterns) 22 occupations (2-digit SOC, 2000 BLS Occupational Employment Statistics) Infer sectors’ skill intensities from average years of schooling of workers employed in them Occupational category Farming, Fishing & Forestry Cleaning & Maintenance Food Preparation & Serving Related Construction & Extraction Production Healthcare Practitioners & Technical Community & Social Services Education, Training & Library Life, Physical & Social Science Legal Occupations Skill intensity 8.7 10.8 11.5 11.5 11.5 15.6 15.8 16.3 17.2 17.3 NAICS 11 72 23 56 48 52 51 55 54 61 Industry Forestry, fishing, hunting & agriculture support Accommodation & food services Construction Admin, support, waste mgt, remediation Transportation & warehousing Finance & insurance Information Management of companies & enterprises Professional, scientific & technical services Educational services Data source: 2000 Census of Population microdata via IPUMS-USA Skill intensity 10.5 11.8 11.9 12.2 12.6 14.1 14.1 14.6 15.3 15.6 Empirical results Three skill groups Dependent variable: ln f (ω, c) βω1 High school or less × log population βω2 Some college × log population βω3 Bachelor’s or more × log population (1) All (2) US-born Population share Share US-born 0.954 0.895 .37 .78 (0.0108) (0.0153) .31 .89 .32 .85 0.996 0.969 (0.0105) (0.0122) 1.086 1.057 (0.0153) (0.0162) Nine skill groups Dependent variable: ln f (ω, c) βω1 Less than high school × log population βω2 High school dropout × log population βω3 High school graduate × log population βω4 College dropout × log population βω5 Associate’s degree × log population βω6 Bachelor’s degree × log population βω7 Master’s degree × log population βω8 Professional degree × log population βω9 PhD × log population (1) All (2) US-born Population share Share US-born 1.089 0.858 .04 .29 (0.0314) (0.0239) .08 .73 .25 .88 .23 .89 .08 .87 .20 .86 .08 .84 .03 .81 .01 .72 1.005 0.933 (0.0152) (0.0181) 0.925 0.890 (0.0132) (0.0163) 0.997 0.971 (0.0111) (0.0128) 0.997 0.965 (0.0146) (0.0157) 1.087 1.059 (0.0149) (0.0164) 1.095 1.063 (0.0179) (0.0181) 1.113 1.082 (0.0168) (0.0178) 1.069 1.021 (0.0321) (0.0303) Spatial distribution of skills in 1980 Dependent variable: ln f (ω, c) βω1 Less than high school × log population βω2 High school dropout × log population βω3 Grade 12 × log population βω4 1 year college × log population βω5 2-3 years college × log population βω6 4 years college × log population βω7 5+ years college × log population (1) All (2) US-born Population share Share US-born 0.975 0.892 .09 .72 (0.0236) (0.0255) .12 .91 .33 .93 .10 .94 .12 .91 .12 .92 .12 .90 1.006 0.983 (0.0157) (0.0179) 0.989 0.971 (0.00936) (0.0111) 1.047 1.033 (0.0144) (0.0151) 1.095 1.076 (0.0153) (0.0155) 1.091 1.073 (0.0153) (0.0157) 1.113 1.093 (0.0202) (0.0196) 1.4 Occupations’ elasticities and skill intensities Population elasticity 1 1.2 Computer & Mathematical Business & Financial Operations Architecture & Engineering Legal Life, Physical, & Social Science Arts, Design, Entertainment, Sports, & Media Protective Service Office & Administrative Support Management Transportation & Material Moving Personal Care & Service Cleaning & Maintenance Construction & Extraction Production Food Preparation & Serving Related Sales & Related Education, Training, & Library Installation, Maintenance, & Repair Healthcare Practitioners & Technical Healthcare Support Community & Social Services .8 Farming, Fishing, & Forestry 6 8 10 12 14 16 18 Skill intensity (employees' average years of schooling) 20 1.6 Industry population elasticities and skill intensities Population elasticity 1.2 1.4 Management of companies and enterprises Professional, scientific and technical services Admin, support, waste mgt, remediation services Educational services Finance and insurance Information Transportation and warehousing Real estate and rental and leasing Wholesale trade Arts, entertainment and recreation Construction 1 Other services (except public administration) Accommodation and food services Utilities Manufacturing Retail trade Health care and social assistance .8 Mining Forestry, fishing, hunting, and agriculture support 10 12 14 Skill intensity (employees' average years of schooling) 16 Summary I Spatial distributions of skills and sectors are prominent in public discussion of cities, exploited for identification in empirical work, and potentially key to understanding agglomeration processes I We need models with more than two skills groups and more than perfectly specialized/diversified cities I Recent research exploits tools from assignment literature to characterize spatial sorting of skills and sectors I Assignment mechanisms can be used in quantitative work via assumptions on components observed and unobserved by the econometrician – Fréchet distribution is most popular Thank you Bacolod, Blum, Strange on AFQT scores Table 5 Agglomeration and the AFQT and Rotter scores: Distributions for selected occupations and city size categories. Panel A. 10th & 90th Percentiles of AFQT Score MSA Size Panel B. 10th & 90th Percentiles of Rotter Score MSA Size Occupation Small Medium Large Very Large Small Medium Large Very Large Managers 51.99 69.65 62.92 79.22 60.75 60.9 74.1 81.43 60.32 68.81 69.74 81.45 47.48 58.01 39.73 57.01 42.4 51.75 34.54 45.41 75.67 75.67 57.33 58.88 38.52 52.54 67.28 79.89 34.18 55.98 60.54 68.11 56.78 66.61 42.02 64.81 79.22 86.96 70.92 72.93 59.79 81.77 63.82 75.67 82.27 82.27 21.05 54.9 29.72 61.59 26.8 42.58 35.99 55.4 53.53 77.7 61.02 65.34 54.14 57.04 52.01 81.6 37.9 70.32 34.46 57.92 52.77 69.49 36.37 82.29 62.95 87.59 44.98 60.03 70.4 88.25 50.88 81.96 62.92 86.18 27.21 64.57 24.13 67.99 15.22 63.56 11.83 53.21 47.25 58.03 61.97 76.31 57.37 69.24 46.84 85.74 34.05 75.89 19.58 65.6 44.92 74 24.6 91.72 49.67 94.93 41.62 82.56 45.13 93.61 34.51 86.44 66.41 96.12 10.71 80.6 12.71 74.14 8.89 68.33 5.55 64.15 63.06 92.92 51.23 83.92 34.1 77.37 30.44 93.88 14.65 83.85 14.74 73.21 33.86 84.39 0.47 0.55 0.47 0.53 0.57 0.57 0.45 0.49 0.51 0.54 0.49 0.56 0.53 0.58 0.51 0.56 0.46 0.51 0.52 0.55 0.52 0.52 0.53 0.54 0.49 0.5 0.47 0.55 0.49 0.6 0.51 0.56 0.5 0.54 0.46 0.52 0.49 0.53 0.6 0.6 0.47 0.6 0.45 0.52 0.42 0.42 0.49 0.64 0.45 0.55 0.48 0.58 0.48 0.63 0.45 0.51 0.48 0.51 0.52 0.54 0.42 0.61 0.45 0.62 0.5 0.59 0.48 0.56 0.43 0.65 0.42 0.58 0.49 0.62 0.46 0.55 0.43 0.62 0.44 0.5 0.42 0.66 0.41 0.62 0.46 0.7 0.43 0.67 0.47 0.49 0.46 0.59 0.53 0.58 0.42 0.62 0.41 0.62 0.44 0.67 0.45 0.6 0.37 0.68 0.41 0.63 0.42 0.62 0.4 0.6 0.38 0.62 0.42 0.59 0.38 0.7 0.38 0.68 0.39 0.69 0.4 0.72 0.44 0.6 0.41 0.57 0.4 0.63 0.38 0.67 0.37 0.7 0.39 0.68 0.4 0.65 Engineers Therapists College Professors Teachers Sales Persons Food Services Mechanics Construction Workers Janitors Natural Scientists Nurses Social Workers Technicians Administrative Support Personal Services Total Notes. The first row reports the 10th percentile, while the second row reports the 90th percentile. Small MSA size: population between 100,000 and 500,000; Medium: between 500,000 and 1 million; Large: between 1 million and 4 million; Very Large: more than 4 million. College wage premia in NLSY vs Census Baum-Snow & Pavan 2000 Census 2000 Census Table 1, column 1 PMSA CMSA Non-Hispanic white males with fewer than 15 years of work experience Medium-city college wage premium .09 0.0978 0.0937 (0.00578) Large-city college wage premium N Individuals observed R2 p-value for equal premia .05 17991 1257 (0.00613) 0.145 0.154 (0.00565) (0.00551) 301326 301326 0.197 0 301326 301326 0.202 0 Robust standard errors in parentheses Notes: This table describes full-time, full-year employees ages 18-55. Following BSP, “college graduate” means anyone with a bachelor’s degree or greater educational attainment. Large means population greater than 1.5m. Medium means population .25m to 1.5m. Small includes rural areas. The premia in the first column are obtained by differencing the numbers for high-school and college graduates’ log wages in the first column of BSP’s Table 1. Note that they report results for temporally deflated panel data, while we report cross-sectional results. BSP assign individual to metropolitan statistical areas using the 1999 boundary definitions, but they do not specify whether they use consolidated MSAs or primary MSAs for large cities. Hence we report both.