Local multipliers of public employment: Long-run evidence from the late development of the Spanish public sector Jordi Jofre-Monseny 1 , Jos´e I. Silva2 , and Javier V´azquez-Grenno1 1 Universitat de Barcelona and Institut d’Economia de Barcelona 2 University of Kent and Universitat de Girona Preliminary Draft: May 22, 2014 Abstract In this paper we estimate long-run local multiplier effects of public administration employment. Specifically, we regress 1980-2001 private job changes in Spanish cities on contemporaneous changes in public administration jobs. The Spanish public sector developed with the advent of democracy after Franco’s death in 1975 and, thus, the period we study is characterized by a very large increase in public administration employment. Given path dependency in the location of public administration activities, our instrumental variables strategy uses the 1970 employment distribution to predict the location of public administration jobs in the 1980-2001 period. The results indicate that public employment crowds-in non-tradable jobs and crowds-out tradable jobs, changing the local industry mix. JEL Classifications: J45, H70, R12. Keywords: public employment, local multipliers, industry mix. 1 Introduction Public employment constitutes a significant fraction of employment in many countries around the world. In 2008, the employer of 15 percent of all US workers was the public sector. In Europe, Germany and Spain show a similar proportion, while public sector employment in France represents as much as 27 percent of total employment1 . Public employment is not evenly distributed across cities, with the public administration being typically clustered in a few (capital) cities. Brasilia and Ottawa, in Brazil and Canada respectively, are two very prominent examples of “government cities”. From the viewpoint of a city, what are the consequences of hosting public administration services on a large scale? And more specifically, what are the indirect employment effects of a local public sector expansion? Public employment will increase the demand for services such as housing, restaurants, bars, lawyers or hair-dressers, expanding private employment. This crowding-in effect is the focus of traditional Input-Output analysis. However, local wages and prices might respond to the positive labor demand shock. This price adjustment will tend to crowd-out private employment. Analyzing the equilibrium responses of private employment to public employment shocks is especially important for regional policy as public employment has been used to overcome spatial inequalities in different countries including Italy (Alesina et al., 2001), UK (Faggio and Overman, 2014) and Spain (Marqu´es-Sevillano and Rossell´o-Villallonga, 2004). Using city-level data from Spain, and using the empirical framework developed by Moretti (2010), we estimate the multiplier effects of public administration employment. Specifically, we regress 1980-2001 city-level changes in private jobs (in the tradable or the non-tradable sector) on contemporaneous changes in public administrative jobs. Besides trying to control for changes in private employment determinants, we also resort to an instrumental variables strategy that exploits path-dependency in the location of public administration jobs. The results indicate that adding public administrative jobs in a city increases employment in 1 International Labour Organization statistics - France’s figure corresponds to 2006. 2 the non-tradable sector and decreases employment in the tradable sector. Hence, hosting a large public administration changes a city’s industry mix favoring non-tradable over tradable activities. The estimates also imply that, at the aggregate level, public sector jobs crowd-in private jobs. Our paper is closely related to Faggio and Overman (2014) that estimates multiplier effects of public sector job relocations away from London. Their results, based on 20042008 employment changes at the British Local Authority level, indicate that overall private employment does not change with public employment although the industry mix is changed in favor of the non-tradable sector. We complement their study in several ways. First, we focus on employment changes in the very long-run, allowing for possible sluggish price adjustments. Second, the period we study is characterized by a very large increase in the Spanish public sector that followed the advent of democracy after Franco’s death in 1975. Specifically, between 1980 and 2001, the employment in the public administration increased from 523,434 to 1,258,512. This late development of the Spanish public sector enables us to use the geographical distribution of the pre-democratic and immature public administration in 1970 (with only 296,207 employees) to predict city-level changes in public administration jobs in the 1980-2001 period. Finally, we formalize a stylized variant of the Roback (1982) spatial equilibrium model that can rationalize our empirical results and helps to clarify the channels through which public administration employment affects private employment in the tradable and non-tradable sectors so differently. Our paper also relates to an empirical (macroeconomics) literature studying the labor market effects of public employment at the national level. Edin and Holmlund (1997), using data for 22 OECD countries from the 1960s to 1990s, find that public sector employment reduces unemployment in the short-run (by 0.3 percent) and has no significant effect in the long-run. When focusing on the Swedish case, these authors conclude that the public sector growth over the 1960s and 1970s contributed to the low Swedish unemployment rate during those years. Using a longer OECD panel, Algan et al. (2002) find different conclusions, namely 3 that 100 new public jobs crowd-out 150 private sector jobs and increase unemployment by 30 workers. Our estimates are not directly comparable to these results since labor demand and supply elasticities at the local and national level are likely to differ. The remainder of this paper is organized as follows. In Section 2 we develop a stylized theoretical model that clarifies the mechanisms driving our empirical results. Section 3 presents and describes the data and variables used in the analysis and considers the historical circumstances around the late expansion of the Spanish public sector . Section 4 describes and justifies the econometric specifications and methods used in this study. Then, section 5 presents and discusses the results of the paper while Section 6 concludes. 2 A model of local multipliers In this section we develop a stylized variant of the Roback (1982) model to illustrate the mechanisms by which a shock in local public employment can affect the city’s private employment2 . We consider an economy comprised by many small cities (local labor markets). In each city, there are two competitive private sectors (tradable and non-tradable). The tradable (manufacturing) sector produces YT to be sold in the international market at unit price (PT = 1). The output of the non-tradable sector (YN T ) is consumed locally and, thus, its price (PN T ) is endogenously determined at the local level. The non-tradable good can be interpreted as housing. The two sectors employ homogeneous labor (NT and NN T ) and a sector-specific fixed factor of production (Z T and Z N T ) that can be interpreted as land in the presence of land use regulations. Markets are assumed to be perfectly competitive and capital returns accrue to absentee land owners. Output in the tradable and non-tradable sectors is produced under the following constant returns to scale production functions (YT = NTα ZT1−α ) and (YN T = NNη T ZN1−η T ) where α, η ∈ (0, 1). Labor is paid its marginal product, yielding the following labor demand 2 See Glaeser (2008) for a detailed exposition of Roback (1982) and variants of it. 4 functions for the tradable and non-tradable sectors: NT = NN T = 1 α−1 w ZT α 1 α−1 (1) 1 w η−1 ZNT η PN T 1 η−1 (2) In addition, we consider a public sector that employs local workers at the city wage level to provide a national public good (administration) that is not funded locally. We consider that public sector labor demand is exogenously given (NG ). Each (homogeneous) worker consumes tradable and non-tradable goods, supplies one unit of labor, and is perfectly mobile across cities. Hence, a worker’s utility depends on the wage and the price of the non-tradable good in the city. Since workers are perfectly mobile across industries and cities, (nominal) wages in a city will be the same in the three sectors (tradable, non-tradable and public) and utility levels will be equalized across cities. Specifically, the economy-wide utility level is (V¯ = V (1, PN T , w)). If the utility function is Cobb-Douglas the indirect utility function is: 1−ρ V = w(1 − ρ) ρ PN T ρ = V¯ (3) where 0 < ρ < 1 reflects the preference for the non-tradable good. Equation 3 indicates that wages need not be the same in all cities. However, low wages must be compensated by a low price of the non-tradable good if there are to be workers in a city. Finally, in equilibrium, local demand must equal supply in the non-tradable sector. The local expenditure in the non-tradable good is ρ w (NT + NN T + NG ) whereas the wage bill in the sector (w NN T ) amounts to η PN T YN T . Hence, market clearing in the non-tradable sector implies: 5 NN T = ηρ NT + NN T + NG (4) The non-tradable sector must concentrate a fixed share of total employment that depends positively on the consumer preferences for the non-tradable good (ρ) and on the labor income share in the non-tradable sector (η), implying that a positive shock in public employment (dNG ) has to equal ( η1ρ − 1) dNN T − dNT . Inserting 1, 2 and 3 in 4 and totally differentiating 4 yields dw/dNG , the change in the city wage given an increase in public employment dw 1 > 0 = ∂NN T ∂PN T 1 ∂NN T ∂NT dNG −1 + | ¯ − ηρ ∂w ∂PN T ∂w dV =0 {z } |∂w | {z } | {z } + In turns out that ∂NN T ∂w + + ∂NN T ∂PN T ∂PN T | ∂w dV¯ =0 (5) - is positive, indicating that labor demand in the non-tradable sector is increasing with wages. The reason for this counterintuitive result is that, for mobile workers to be indifferent across cities, the price of the non-tradable good must increase faster than wages (reducing “real” wages in terms of non-tradable goods) and this increases labor demand in the sector. Specifically, for workers’ utility to remain constant (dV¯ = 0), equation 3 implies that if the city wage increases by 1 percent, the non-tradable output price must increase by 1 ρ tradable sector will increase by percent, and, as a consequence, the employment in the nonρ−1 1 (η−1) ρ percent. Hence, it turns out that dw dNG > 0 which implies that: dPN T dNN T > 0; and > 0. dNG dNG 6 (6) In the tradable sector, dw dNG > 0 implies that dNT dNG < 0 as labor demand is downward sloping and, at the city level, the demand for the non-tradable good is completely elastic an given by PT = 1. 3 Data and variables 3.1 Data We primarily use employment data at the municipality level from Censuses carried out in 1970, 1980 and 2001. These data contain information on counts of employees by municipality and main economic activity (3-digit level) of the establishment in which the employee works. We construct city-wide employment levels using the 2008 urban area definitions built by the Ministry of Housing3 . We work with a total of 83 cities (urban areas) that in 2001 concentrated 67 percent of the population.4 The median city (Ourense) had 126,410 inhabitants in 2001. The size of the two largest cities - Madrid (5,135,225) and Barcelona (4,391,196)exceeds that of Soria (35,151) and Teruel (33,158) -the smallest two- by a factor of one hundred. In terms of outcome variables, we mostly consider (changes in) the employment in the tradable sector, NT , that we assimilate to manufacturing industries, and in the non-tradable sector (NN T ). Our main explanatory variable is the employment in the public administration sector (NG ). We focus on this specific component of public employment for two reasons. First, in contrast to other activities in which the public sector intervenes such as the health and education sectors, all public administration workers are public employees. Second, as will shown below, the geography of public administration employment does differ very markedly from the geography of population. To avoid a mechanical correlation between public administration and non-tradable employment, we leave out from the non-tradable sector those 3 4 The same definitions are used in De la Roca and Puga (2013). We do not consider Ceuta and Melilla, the two Spanish enclaves in North-Africa. 7 activities where the public sector plays a major role as employer or regulator such as in the R&D or the Radio and Television industries. We also exclude from our analysis the agricultural, farming, mining and energy industries. In the Appendix B we provide the details of the industry classifications (and bridges) used thorough the paper. 3.2 Public (administration) employment growth in Spain In Spain the development of the public sector took place surprisingly late. Figure 1 shows the evolution of tax revenue to GDP for Spain, France, Germany and the US between 1965 and 2006. In 1965, the fraction of output devoted to tax payments was 14.7 percent in Spain, a low figure compared to 24.7, 31.6 and 34.2, the corresponding figures for the US, Germany and France, respectively. By contrast, in 2006 (before the start of the financial crisis) tax revenue to GDP in Spain was 36.9, a fraction larger than that in the US (26.8) and Germany (35.7), although still smaller than that of France (44.4). This late development of the public sector in Spain coincides in time with the advent of democracy after Franco’s death in 1975. In fact, the growth of the public sector is most intense between 1975 and 1990, a period in which tax revenue to GDP increased from 18.4 to 32.5 percent. This process of growth in the tax revenue to GDP ratio was accompanied by a parallel increase in public employment. According to Census data, the number of public administration workers grew by 140 percent (from 523,434 to 1,258,512) between 1980 and 2001, while the population only grew by 8 percent during this period. The numbers of workers in the health and education sectors (where most workers are public employees) experienced a similar growth rate in this period (128 percent), going from 845,984 to 1,930,578. Hence, our period of study (1980-2001) is characterized by a very large increase in public employment. This is an attractive feature of the present study. 8 50 Figure 1: Public sector growth in Spain Franco’s death Tax revenue / GDP (%) 30 40 France Germany Spain 10 20 US 1965 1975 1985 1995 2005 Source: OECD Statistics. 3.3 The geography of public (administration) employment growth Public employment is not evenly distributed across Spanish cities, with administrative personnel showing substantial spatial concentration. The size of the public administration sector in a city is determined, to a large extent, by its political status. In Spain, there are provincial and regional capital cities. Provinces (and the associated capitals) were established in 1833 by Javier de Burgos and constituted the main territorial division of the country until the advent of democracy. Although provinces were not suppressed, 17 regions (Comunidades Aut´onomas) were built as aggregations of one or several provinces in 1981. Twenty years later, Spain was a decentralized country where its Comunidades Aut´onomas spending amounted to roughly 46 percent of total government spending5 . A similar picture is obtained if one looks at the distribution of public employees across layers of governments. In 2001, regional 5 Excluding social security spending. See Carri´on-i Silvestre et al. (2008) for a detailed explanation of the decentralization process. 9 governments employed 45 percent of public employees whereas the central government and local governments employed the remaining 34 and 21 percent6 . Figure 2 plots the presence of administrative personnel in all cities, distinguishing regional and provincial capitals, and non-capital cities. With two exceptions (Santiago de Compostela and M´erida7 ), the cities hosting regional governments are also provincial capitals. Two noncapital cities (El Ejido and Elda-Petrer) have the lowest presence of public administration employees in 2001 with about 1.7 employees per 100 inhabitants. At the other end, Soria and Teruel (two provincial capitals) have more than 7 public administration employees per 100 inhabitants. More generally, this figure corroborates that being a capital comes along with public employees, and the difference is especially large for small cities. Holding population size constant, the presence of public administrative personnel is similar in provincial and regional capitals. This suggests that the process of regional decentralization that took place in Spain between 1981 and 2001 was not accompanied by a significant relocation of administrative personnel from provincial to regional capitals. On the contrary, pre-democratic provincial capitals retained their share of public adminstration employment. On the one hand, provincial institutions (Diputaciones being the more prominent one) persisted into the new democratic regime. On the other hand, provincial capitals managed to pull regional public administration jobs. To analyze in a more systematic fashion if there is inertia in the location of public administrative personnel, we study what determines 1980-2001 changes in public administration jobs. Since population is likely to be the most important determinant, we start by considering that, at a given point in time, the number of public administrative personnel in a city is explained by a drift and its population, that is, NG = α + β P OP + , with α and β possibly being year-specific. Subtracting the 1980 from the 2001 level yields: 6 Registro Central de Personal, Ministerio de Hacienda y de Administraciones P´ ublicas. These two cities are historically important. While M´erida was the capital of the roman Lusitania province, Santiago is the destination of a major Catholic pilgrimage route. Moreover, these are the third cities in two bicephalic regions: Galicia (La Coru˜ na and Vigo) and Extremadura (C´aceres and Badajoz). 7 10 8 Figure 2: Public administration employees in 2001 per 100 inhabitants Soria 6 Teruel Madrid Santiago 2 4 Mérida Barcelona 0 Elda−Petrer El Ejido 11 13 Population in 2001 (logged) Provinvial capital Regional capital 15 Non−capital Source: Census and own elaboration. dNG,80−01 = (α01 − α80 ) + β01 (P OP01 − P OP80 ) + (β01 − β80 )P OP80 + (01 − 80 ) (7) where dNG,80−01 is the 1980-2001 increase in the city public adminstration employment. Given the aggregate increase in the Spanish pubic sector in the 1980-2001 period (i.e. β01 > β80 ), equation 7 implies that public administration employment growth will be larger the larger the baseline city size is (P OP80 ), and the larger the population growth in the period (P OP01 − P OP80 ). To assess if public administration jobs increased more in cities where the presence of administrative personnel was historically high, conditional on the population level in 1980 and the 1980-2001 population increase, Figure 3 shows the partial correlation between 1980-2001 changes in public administration jobs (NG,01 − NG,80 ) against public ad- 11 ministration employment in 1970(NG,70 ). Specifically, to partial out the correlation induced by the common influence of P OP01 and P OP01 − P OP80 , the plotted variables are the residuals of an equation against these two variables. The data shows a positive relationship with a Partial R-Squared of 12.5 percent, indicating that, indeed, cities with more public administrative personnel in 1970 attracted more public administrative jobs in the 1980-2001 period. This finding guides our instrumental variable strategy that we explain in detail below. 8000 4000 0 −4000 −8000 1980−01 change in public admin. jobs (resid.) Figure 3: Public admin. job increase (1980-01) versus 1970 public admin. jobs −8000 Partial R−squared = 0.125 −4000 0 4000 8000 Public admin. jobs in 1970 (resid.) Note: Both variables are the residuals of a regression on population in 1980 and the 1980-2001 population change. 4 Econometric specification We estimate the effects of 1980-2001 changes in public administration employment on contemporaneous changes in tradable and non-tradable (private) employment. The baseline specification is: 12 dNP,80−01 = δ + γ dNG,80−01 + η x + ξ80−01 (8) where P ⊂ (NT , NN T ). One possible problem with equation 8 is that shocks in private employment could be correlated with public adminstration employment changes. For instance, if governments use public employment as a redistributive tool to support lagging regions (Alesina et al. (2001)), public employment could be negatively correlated with employment changes in the private sector. It could also be the case that thriving cities have more tax revenues to hire administrative personnel and, as a consequence, positive shocks in private employment are positively correlated with public administration employment shocks. We deal with this potential problem in two ways. First, we will control for observed determinants of private employment growth (x) inasmuch as possible. Second, we will also resort to an instrumental variables strategy based on the observation that there is path-dependency in the location of public adminstration jobs as seen in section 3.3. Following Moretti (2010), we define our (shift-share) instrument (dN G,80−01 ) as: X N P Gi,70 NGi,01 i NGi,70 i dN Gi,80−01 = where i indexes cities and thus, P i ! − NGi,80 (9) N , is the national employment in the corresponding sector and year. Hence, the instrument first computes the public adminstration employment in 2001 that would be observed if each city would retain its 1970 national share in national public administration employment. Then, it predicts the 1980-2001 change by subtracting the observed public adminstration employment level in 1980. The instrument is arguably exogenous to the extent that is independent of private employment shocks that might have occurred in the 1980-2001 period. Figure 3 suggested that this instrument is relevant. We will return to this question below. 13 5 Results Before moving to the regression analysis, we start this section by plotting, in Figure 4 the 1980-01 changes in employment in the tradable (first panel) and non-tradable (second panel) sector versus contemporaneous changes in public adminstration jobs in all cities. Note that the two graphs differ in terms of the average increase in jobs in the vertical axis. Although positive, the average job increase in the tradable sector is small (1,396), with some cities like Bilbao or Oviedo-Gij´on loosing a large number of jobs in manufacturing industries . In contrast, all cities experience positive increases in non-tradable sector jobs (36,206) which reflects the ongoing tertiarization process of the Spanish economy. Turning to our research question, while there is a slightly negative association between changes in tradable and public administration jobs, the corresponding correlation between the non-tradable and the public administration sectors is clearly positive. The first two columns in Table 1 show the regression results of equation 8. Specifically, the table reports the coefficients measuring the impact of public administration job changes (dNGi,80−01 ) on tradable (column 1) and non-tradable (column 2) job changes over the same period of time. All these specifications include a a set of control variables, x, that include (1) the 1970-1980 change in population, (2) the 1970-1980 employment change in the own sector (tradable or non-tradable), (3) the 1980 population level, (4) the 1980 own sector employment level and, (5) a prediction of the 1980-2001 own sector employment change defined as: dN P i,80−01 = X k X N P ki,80 Nki,01 i Nki,80 i ! − X Nki,80 (10) k where k indexes narrowly defined industries in the relevant sector (tradable or nontradable). The predicted employment change in 9 captures the component of the 1980-2001 local employment shock (in the tradable or non-tradable sector) explained by city’s industry mix in 1980 interacted with 1980-2001 fate of industries at the national level. That is, Bil14 Oviedo−Gijón Bilbao 0 5000 10000 change in public administration jobs 15000 0 5000 10000 change in public administration jobs 15000 0 change in non−tradable jobs 20000 40000 60000 80000 100000 −50000 change in tradable jobs −30000 −10000 10000 Figure 4: Changes in tradable and non-tradable jobs (1980-01) versus contemporaneous changes in admin. jobs Note: Cities with more than 1,000,000 excluded for the sake of presentation (Madrid, Barcelona, Sevilla & Valencia). 15 bao’s loss of tradable jobs between 1980-2001 is partly explained because one of the industries in which Bilbao was specialized in 1980 (the iron and steel industry) lost 38 percent of the jobs at the national level during this period. Table 1: The multiplier effects of public administration jobs Tradable (dNT,80−01 ) Public admin (dNG,80−01 ) Public admin pred (dN G,80−01 ) Public admin (dNG,80−01 ) Partial R-Squared F stat Kleibergen-Paap rk LM stat Non-tradable (dNN T,80−01 ) OLS -0.599** 1.701*** (0.288) (0.474) Reduced-form estimates -0.232*** 0.942*** (0.090) (0.222) 2SLS -1.956** 3.616** (0.868) (1.580) 0.09 0.26 4.15 (0.04) 8.01 (0.00) 4.79 (0.03) 7.29 (0.01) Notes: 1) Coefficients are the effects of public administration job changes (19802001) on contemporaneous changes in tradable (col. 1) and non-tradable (col. 2- jobs and in population (col. 3). 2) In the first two columns, the regressions include, as controls, the 1970-1980 change in population, the 1970-1980 employment change in the own sector (tradable or non-tradable), the 1980 population level, the 1980 own sector employment level, and, the prediction of the 1980-2001 own sector employment change as defined in the text. 3) Robust standard errors in parenthesis. 4) ***, **, * denote statistical significance at the 1, 5 and 10 percent. The first panel in the Table 1 reports Ordinary Least Squares (OLS) estimates. These results indicate that more public administration jobs reduce employment in the tradable sector. Specifically, the estimates imply that one additional public administration job causes 0.6 job losses in the tradable sector. In contrast, public administration employment expands employment in the non-tradable sector. Here, one public job creates 1.7 additional jobs. These results imply that placing public administrative personnel in a city changes the city’s industry mix by crowding-out employment in the manufacture and expanding it in nontradable sectors. Since the positive effect on the non-tradable sector dominates the negative effect on the tradable sector, one extra public adminstration job has a positive effect on the 16 total private employment. The second panel shows the estimates of regressions where the explanatory variable of interest, i.e. public administration jobs (dN Gi,80−01 ), has been replaced by the instrument (dN G,80−01 ) isolating the variation explained by the fact that, due to path dependency, public administration grew more in cities that in 1970 had a large public administration. These (reduced-form) estimates indicate that the higher the predicted public administration job increase, the lower the employment increase in the tradable sector and the higher the increase in the non-tradable sector. Hence, these estimates are qualitatively similar to their OLS counterparts. Finally, the third panel shows the 2-Stage Least Squares (2SLS) results. In addition to being a valid instrument, dN G,80−01 must also be relevant. The last three rows report FirstStage statistics. The partial R-squared values are relatively large and both the F- and the Kleibergen and Paap (2006) rk LM- statistics are significant at the 5 percent level. However, the F-test values are lower than 10, and evidence the limited strength of our instrument which results in relatively imprecise 2SLS estimates (the standard errors increase by a factor of 3 with respect to the OLS estimates). Despite this, the 2SLS (and the reduced-form) estimates are qualitatively similar to their OLS counterparts. Besides public administration, the public sector (including its firms) is active in other sectors of the economy, namely, health, education, railway transportation, air transportation, postal services and telecommunications, public sewage, libraries and museums, and diplomatic representations. Although these activities employ both private and public employees, the public sector plays a major role in all these (regulated) industries. Therefore, in Table 2 we redo the analysis considering this broader definition of public sector. The results are qualitatively similar to our baseline estimates that only considered public administration. Nevertheless, the instrument relevance increases significantly when using this broader definition, increasing the precision of the 2SLS estimates. Here, the OLS and the 2SLS results are very close, suggesting that, controlling for determinants of private em17 Table 2: Multiplier effects: Broader public sector definition Tradable (dNT,80−01 ) Public admin (dNG,80−01 ) Public admin pred (dN G,80−01 ) Public admin (dNG,80−01 ) Partial R-Squared F stat Kleibergen-Paap rk LM stat Non-tradable (dNN T,80−01 ) OLS -0.583*** 1.429*** (0.147) (0.185) Reduced-form estimates -0.210*** 0.408*** (0.057) (0.139) 2SLS -0.757*** 1.252*** (0.197) (0.313) 0.415 0.332 29.90 (0.00) 30.66 (0.00) 11.44 (0.00) 10.538 (0.00) Notes: 1) Coefficients are the effects of public administration job changes (19802001) on contemporaneous changes in tradable (col. 1) and non-tradable (col. 2- jobs and in population (col. 3). 2) In the first two columns, the regressions include, as controls, the 1970-1980 change in population, the 1970-1980 employment change in the own sector (tradable or non-tradable), the 1980 population level, the 1980 own sector employment level, and, the prediction of the 1980-2001 own sector employment change as defined in the text. 3) Robust standard errors in parenthesis. 4) ***, **, * denote statistical significance at the 1, 5 and 10 percent. ployment changes, shocks in private employment are not correlated with public employment changes. 6 Summary and final remarks In this paper we have estimated the long-run effects of public administration employment on private employment, distinguishing between the effects on the tradable and non-tradable sectors. Specifically, we examine employment changes in Spanish cities between 1980 and 2001, a period of time characterized by a very large increase in public employment in Spain. Exploiting path dependency in the location of public administration activities, our instrumental variables strategy uses the 1970 employment distribution across cities to predict the location of public administration jobs in the 1980-2001 period. Our results indicate that public administration employment has a positive multiplier effect for the non-tradable sector 18 (restaurants, bars, hair-dressers, etc.) and a negative effect for the tradable sector. A stylized variant of the Roback (1982) spatial equilibrium model can rationalize these results. An additional public worker increases the demand for non-tradable goods (e.g. restaurants, bars or hair-dressers). However, public employment also shifts the labor demand curve outwards, increasing wages which tends to reduce employment. For workers to be indifferent across cities, the price of non-tradable goods must increase faster than wages since workers only spend a fraction of their income in non-tradable goods. As a result, employment in the non-tradable sector increases with public employment. For the non-tradable sector, more public workers do not significantly raise demand and, therefore, employment is reduced as wage are higher. 19 References Alesina, A., Danninger, S., and Rostagno, M. (2001). “Redistribution Through Public Employment: The Case of Italy.” IMF Staff Papers, 48 (3), 2–44. Algan, Y., Cahuc, P., and Zylberberg, A. (2002). “Public employment and labour market performance.” Economic Policy, 17 (34), 7–66. Carri´on-i Silvestre, J. L., Espasa, M., and Mora, T. (2008). “Fiscal Decentralization and Economic Growth in Spain.” Public Finance Review, 36 (2), 194–218. De la Roca, J., and Puga, D. (2013). “Learning By Working In Big Cities.” Working Papers 2013-1301, CEMFI. Edin, P.-A., and Holmlund, B. 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(1982). “Wages, rents, and the quality of life.” Journal of Political Economy, 90 (6), 1257–1278. 20 A Appendix: The Model A.1 Production in the tradable sector The production function for firms in the tradable sector is Cobb-Douglas with constant returns to scale: 1−α YT = NTα Z T (A-1) where α (0, 1), Z T represents land used in the tradable sector which we assume is fixed. NT is the labor in tradable sector. We assume that firms are competitive and maximize profits over NT . 1−α max{NTα Z T NT − wNT } (A-2) The first order condition (FOC) for labor in the tradable sector is: 1−α αNTα−1 Z T − w = 0 then, labor demand in the tradable sector is given by: w = αZ T NT or 21 1−α (A-3) NT = A.2 1 α−1 w ZT α 1 α−1 (A-4) Production in the non-tradable sector The production function for firms in non-tradable sector also is Cobb-Douglas with constant returns to scale: 1−η YN T = NNη T Z N T , (A-5) where η (0, 1), Z N T represents land used in the non-tradable sector which we assume is fixed. NN T is labor in tradable sector. We assume that non-tradable firms are competitive and maximize profits over NT , yielding the following FOC for labor: 1−η ηPN T NNη−1 T ZNT − w = 0 (A-6) then, labor demand in the non-tradable sector is: w = ηPN T ZNT NN T 1−η (A-7) or η−1 NN T = w ZNT PN T η 22 1 ! η−1 (A-8) A.3 Consumers Each homogeneous consumer supplies one unit of labor, is perfectly mobile across cities and consumes non-tradable and tradable goods: U = CNρ T CT1−ρ (A-9) with ρ (0, 1). Given A-9, the indirect utility function is given by A-10. Perfect mobility implies that local prices (wages and the price of non-tradable goods) must adjust to equalize utility across cities. V¯ is the economy-wide utility level consumers can achieve: 1−ρ V = w(1 − ρ) ρ ρ PN T = V¯ (A-10) V¯ (A-11) then, ρ−1 w = (1 − ρ) ρ −ρ PN T or PN T = ρ A.4 w (1 − ρ)1−ρ V¯ ρ1 (A-12) Market clearing in the non-tradable sector Utility maximization implies that a fraction ρ of total labor income is spent on non-tradable goods, 23 ρ w (NT + NN T + NG ) = PN T YN T (A-13) We can express the FOC for labor as: w NN T = PN T YN T η (A-14) doing some algebra and combining the equations A-13 and A-14 yields: NN T = ηρ NT + NN T + NG A.5 (A-15) Comparative statics Plugging A-4, A-8 and A-12 into(A-15) defines: φ(w, NG ) = (1 − η ρ) NN T (w, PN T (w)) − η ρ (NT (w) + NG ) = 0 (A-16) Taking the total derivative in equation A-16 yields: dφ = (1 − η ρ) ∂NN T ∂NN T ∂PN T + ∂w ∂PN T ∂w dw − η ρ dNG − η ρ which can be rearranged as: 24 ∂NT dw = 0 (A-17) ∂w dw = dNG 1 1 ηρ − 1 ∂N∂wN T + ∂NN T ∂PN T | ∂PN T ∂w dV¯ =0 − ∂NT ∂w In order to know the sign of the expression A-18 we need to know the sign of the sign of ∂NN T ∂w + ∂NN T ∂PN T | . ∂PN T ∂w dV¯ =0 In order to sign + and (A-19) + - ∂NN T ∂w ∂NT ∂w Note that: −α w α−1 ∂NT ZT = < 0 ∂w (α − 1)α | α{z } | {z } (A-18) ∂NN T ∂PN T | ∂PN T ∂w dV¯ =0 we can plug PN T (equation A-12) into NN T (equation A-8) obtaining: " NN T = Z N T 1 # β−1 w (A-20) 1 βδ( wv (1 − δ)1−δ ) δ Then, we can take the derivative of equation A-20 with respect to w which yields: β # 1−β 1 β−1 1 − 1δ 1 ZNT w > 0 1 1 w w 1−δ ) δ β−1 β δ)1−δ ) δ δ( (1 − δ) v | {z } | βδ( v (1 −{z {z } } | {z } | " - + + (A-21) - Given the sign of the derivatives of the equations A-19 and A-21, it turns out that: dw 1 = > 0 ∂NN T ∂NT 1 ∂NN T ∂PN T dNG −1 + | ¯ − ηρ ∂w ∂PN T ∂w dV =0 |∂w {z } | {z } | {z } + + 25 - B Appendix: Industry classifications Description Broad' public sector Public administration Education Primary Secondary Tertiary Health Railway transportation Air transportation Postal services & telecommunication Public sewage Libraries, archives & museums Diplomatic representations Tradable sector CNAE 52 (1970) CNAE-74 (1980) 81 821 . . . 822 711 717 731-734 522 . . 20-39 CNAE-93 (2001) 91 931,932, 933, 934 931 932 933 934 941-945 711-712 741-742, 753 761-762 921 967 990 22, 24, 25-49 75 801-804 801 802 803 851 601 621-623 641-642 900 925 990 15-39 CNAE-74 to CNAE-93 bridge for narrowly defined industries Description CNAE 52 (1970) 413 416 415 411-412 414 417-419, 420-421, 423 422 424-428 429 431-437,439,453-455 441,442, 456 451-452 461-467 471-472 473 475 474 114 130 140 251-253, 255 254 481 482 246 241 247 242 243 245, 249 221-223 312-316, 319 321-326, 329 345 330 341-343, 346,347 353 393 399 361 362 363 371-372 381 382 383 389 468 491 492 494 495 CNAE-74 (1980) 151 152 153 154 155 156-158 157 159 160 171-177, 182 181, 183, 191,192 193 201-205 211 212 221 222 231 232 233 241-247 244 251 252 261 262-264 265 266 268 271-273 281-287 291-296 297 300 311-316 333 334 335 341 342 343 351 352 353 354 355 361 362 363 364 365 366, 371, 372 CNAE-93 (2001) CNAE-74 to CNAE-93 bridge for narrowly defined industries Non-tradable sector 611, 612, 621, 622, 623, 624, 625, 626, 627, 628, 629, 631, 632, 633, 634, 635, 636, 638, 639, 641, 642, 643, 644, 649, 713, 714, 718, 719, 721, 722, 726, 727, 729, 825, 826, 829, 831, 833, 841, 842, 843, 844, 845, 846, 849 26 50 61-64, 67 65,66 602 754 756 811-814, 819 821-823 831 832 833 861, 869 834 854 855 851-853 856, 859 845 841-842, 846 843 844 922 946 961-963 980 971-973, 979,849 45 50-51-52 55 721-723, 729, 751 631 634 651-652 660 671 672 701 702 703 711 712 713 714 721-726 741 742-743 744 747 852 921 950 632, 745, 746, 748, 924, 493, 930
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