The relationship between space, time, fertility, and employment: a fixed effectsspatial panel approach.

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1 1 The relatioship betwee space, time, fertility, ad employmet: a fixed effectsspatial pael approach. Alessadra Carioli 1 Daiel Devolder 2 Joaqui Recaño 2 L.J.G. va Wisse 3 1 Uiversity of Groige ad Netherlads Iterdiscipliary Demographic Istitute 2 Cetre d Estudis Demografics, Uiversitat Autooma de Barceloa 3 Netherlads Iterdiscipliary Demographic Istitute

2 Abstract Heterogeeity ad time depedecy are a challegig topic i demography. I this study, we aim to describe the spatial effect of socio-ecoomic idicators over the evolutio of fertility amog 910 Spaish muicipalities measured cross-sectioally at macro level i 1986, 1991, 2001 ad We apply a fixed effects spatial error model with GMM estimatio that exteds the cross-sectioal model of Kelejia ad Prucha (2010). Prelimiary aalysis fids strog spatial autocorrelatio for all the variables ad years take ito accout i the pael ad show sigificat clusters substatially trasformig over time. Ideed, durig these four decades major trasformatios took place i the family formatio process, geeratig sigificat chages i the effect of female participatio ito the labour force ad employmet as show by (Adsera, 2004). Moreover, such evolutio displays importat heterogeeity across areas revealig uderlyig leaders ad laggers i fertility behaviour chages. 2

3 Data ad Method 1. Data The data used for the aalysis come from microcesus data for years 1986, 1991, 2001 ad 2011.

3 3 Data ad Method 1. Data The data used for the aalysis come from microcesus data for years 1986, 1991, 2001 ad Data o the umber of births cosist of raw umbers of births by mothers age group (5 years age groups from 15 to 49) by sigle year ad by birth order (1 to 3+). For years 2001 ad 2011, data o births cotai also iformatio o mothers ad fathers atioality. Data o female populatio exposures cosist of populatio umbers by five-years age groups measured o the 1 st of March of each year. From 1998 to 2012 sigle year populatio estimates are available. For the previous period, , three caledar years measuremets are available: 1981, 1986 ad 1991, which were used to obtai iter year estimates. From 1998 owards data cotai iformatio o mothers ad fathers atioality. All data are grouped by 910 comarcas, which are admiistrative agglometarios of muicipalities, each geographical uit havig at least 20,000 ihabitats. 2. Measures I this study several fertility measures are computed to help ivestigatig spatial patters of fertility. These measures are costructed usig the data described i sectio 1. Some cosideratios are ecessary o the assumptios of data ad methods applied to obtai the idicators. The depedet variable used i this aalysis is the Priceto Idex for total birth order ad first birth order: I f = x B x p x F x where is the umber of births by wome i age group x, represets the Hutterites fertility for age group x ad the female populatio i age group x. The choice for I f istead of Total Fertility Rate relies o its stability, beig less affected by small chages i the umber of births by age ad by small ad scarcely populated rural areas births variability, as it is expressed as a proportio of Hutterites fertility. The explaatory variables cosidered are: 1. Mea Age at Childbearig, MAC for total birth order ad first birth order: MAC = x max x mi x max x mi x f (x) f (x) 2. Socio-ecoomic variables 2.1. Foreigers presece as % of the total; 2.2. Share of populatio with Primary Educatio by sex; 2.3. Share of populatio with Uiversity Educatio by sex; 2.4. Share of Uemployed by sex; 2.5. Share of Active by sex; 2.6. Share of populatio with permaet cotract (with social security beefits) by sex;

4 Share of populatio with temporary cotract by sex; 2.8. Share of self-employed by sex; 2.9. Share of self-employed with employees by sex; Share of self-employed without employees by sex; Share of employed by sector (Primary, Secodary, Tertiary ad Costructios) by sex; 3. Rural-Urba idicator (umber of ihabitats per square km); 4. Distace from largest earest city; 5. Eastig ad Northig; 3. Method Spatial paels have recetly attracted much attetio, especially with the icreasig availability of micro ad macro-level pael data, especially i the field of ecoomics (see Baltagi:2007vz ad Driscoll & Kraay, 1995). Although spatial ecoometrics techiques are ot ew i demography, (Bocquet-Appel & Jakobi, 1996; 1998; Galloway, Hammel, & Lee, 1994; amog others: Kluseer, Szoltysek, & Goldstei, 2012; Szołtysek, Gruber, Klüseer, & Goldstei, 2010), spatial pael techiques are seldom applied to aalyse demographic pheomea, especially fertility. The spatial pael approach assumes that the structure of cross-sectioal correlatio is related to locatio ad distace amog areas ad it is defied accordig to a pre-specified metric give by a coectio or spatial matrix that characterizes the patter of spatial depedece accordig to prespecified rules. Cross-sectioal correlatio is represeted by meas of a spatial processes, which explicitly relate each area to its eighbors via a eighborhood matrix (Aseli, 1988; Aseli, Florax, & Rey, 2004; Cliff & Ord, 1981; Mora, 1950). I this study we defie the eighborhood relatioship to follow a First Order Rook, defied as a set of boudary poits b of uit i, which share a positive proportio of their boudary, thus havig legth l ij >0: w ij = 1 l ij > 0 (1) 0 l ij = 0 Oce the spatial eighbor list has bee defied, i spatial aalysis it is ecessary to set the weight matrix for each relatioship. The spatial weight matrix has bee costructed so that the weights for each areal item sum up to uity. 0 d 1,2 d 1, d W ij = 2,1 0 d 2,1!! "! (2) d m,1 d m,2 # 0 To establish the presece of sigificative ad o-radom spatial autocorrelatio we apply first Mora t I test for spatial autocorrelatio, to evaluate the stregth of spatial patters across the cosidered variables (Mora, 1950) ad is computed o the model s residuals. Mora s I is the idex obtaied through the product of the variable cosidered, let s call it y, ad its spatial lag, with the cross product of y ad adjusted for the spatial weights cosidered:

5 5 I = i=1 j=1 w ij i=1 j=1 w ij y)(y j y) i=1 y) 2 (3) where is the umber of spatial uits i ad j, y i is the i th spatial uit, is the mea of y, ad w ij is the spatial weight matrix, where j represets the regios adjacet to i. Mora s I ca take o values [- 1,+1], where 1 represets strog egative autocorrelatio, 0 o spatial autocorrelatio ad 1, strog positive spatial autocorrelatio. It is possible to break dow this measure its compoets i order to idetify clusters ad hotspots. Clusters are defied as observatios with similar eighbors, while hotspots are observatios with very differet eighbors (Aseli, 1995). The procedure is kows as Local Idicators of Spatial Associatio or LISA, where the Local Mora s I decomposes Mora's I ito its cotributios for each locatio. These idicators detect clusters of either similar or dissimilar values aroud a give observatio. The relatioship betwee global ad local idicators is quite simple, as the sum of LISAs for all observatios is proportioal to Mora's I. Therefore, LISAs ca be iterpreted both as idicators of local spatial clusters or as pipoitig outliers i global spatial patters. The measure for LISAs is defied as: I i = y) w ij y) i=1 j=1 y) (4) The aim of this prelimiary aalysis is to establish the presece of spatial autocorrelatio ad of spatial clusters. Oce this step is doe, we defie our spatial pael model as a fixed effects spatial error model, thus allowig for presece of edogeeity ad correlatio i the residuals: y ti = X ' ti β + u ti (i=1,,n; t=1,,t) (5) where y ti is the observatio o the i th comarca at time t, X ti is the k x 1 vector of observatios ad u ti the regressio error. I order to allow for edogeeity i the model, we choose a fixed effects approach usig a spatial error model, thus: u ti = µ + ε t (6) with: ε t = λw N ε t +ν t (7) where µ ' = (µ 1,...,µ N ) represets the radom effects for the selected geographical uits ad are assumed to be IIN(0,σ 2 ). λ is the scalar spatial auroregressive parameter ad it s λ <1, W N is the N x N spatial weights matrix with 0s diagoal elemets ad I λw N is o-sigular. ν t ' = (ν t1,...,ν tn ) with ν ti IIN(0,σ 2 ) ad idipedet of µ i. '

6 6 I this paper we will ot apply MLE as the umber of cross-sectioal uits is large (>400), thus we will use a geeralized method of momets, as suggested by Kapoor et al.(2007). This GM procedurehas the advatage of beig less demadig with respect to LME is specified for T fixed ad N, where the error specificatio i (7) follows a first-order spatial autoregressive process: u = λ(i T W N )u + ε (8) with: ε = (ι T I N )µ +ν (9) which allows also each geographical uit to be spatially correlated. To carry out the aalysis we use R package splm spgm estimatio method (G. Millo, Piras, & Millo, 2013), which estimates λ through GM ad the model coefficiets by a feasible GLS estimator. 4. Prelimiary Results 1. Mora s I is statistically sigificat ad o-radom for all variables cosidered uder Mote- Carlo bootstrap permutatio test, where the observatios are radomly assiged, ru for 999 simulatios. Table 1: Mora s I Mote Carlo bootstrap permutatio test for selected variables ad years. P- value < Variable Year Mora s I MC Lower Edu Me Lower Edu Wome Uiversity Edu Me Uiversity Edu Wome Activity Rate Me Activity Rate Wome Uemploymet Me Uempl. Wome Permaet Cotract Clusters are sigificat ad are preset for all four time frames for all cosidered variables. Cluster aalysis shows importat clusters, which ca vary across cesuses chagig mostly from North (Low-Low)-South(High-High) to East(Low-Low)-West(High-High) clusters, cetered aroud the capital, Madrid. Ideed, from empirical aalysis we ca deduce that i those years , two importat trasformatios took place: a. From high fertility i rural areas to high fertility i urba areas, mostly due to the cocetratio of migrats i metropolita areas after the mid 1990s;

7 7 b. massive female etrace ito the labor force trasformed the dyamics of childcare, thus i a first phase, female activity had a egative impact, while i a secod phase this relatioship reversed. 3. Prelimiary aalysis of cross sectioal data uderlie the importat role of labour idicators i explaiig fertility chages. For istace female activity rate has a egative effect o fertility util the late 1990s, whe wome started eterig the labor force i sigificative umbers. This effect becomes positive i the lastest period, i areas with cosiderable female participatio to the labor force (North-East area), while for areas with higher uemploymet ad more traditioal family roles, South, the effect stays egative. This multifaceted effect of activity rate is mirrored by me uemploymet rates, which also egatively impact fertility i reacher areas with lower uemploymet rates, but ot i areas with high uemploymet (South). Table 2. Prelimiary exploratory SAR model estimatio for selected variables. YEAR VARIABLES Model 1 Model 2 Model 3 Model 4 Model 5 YEAR VARIABLES Model 1 Model 2 Model 3 Model 4 Model Itercept 0.46*** 0.142*** 0.141*** 0.12*** 0.404*** 2001 Itercept 0.284*** 0.087*** 0.11*** 0.191*** 0.218*** Uempl. Me Self Empl. Wome *** *** Uempl. Me Self Empl. Wome *** 0.002*** MAC MAC *** MAC First *** MAC First *** Adj.r Adj.r Itercept 0.463*** 0.117*** 0.123*** 0.18*** 0.381*** 2011 Itercept 0.135*** 0.097*** Uempl. Me Self Empl. Wome *** Northig Eastig 0.003*** 0.124** * MAC * MAC *** 0.131*** MAC First *** MAC First Adj.r Adj.r *** p-value<0.0001

8 8 Map 1: Priceto Idex ad Female Activity Rate LISA cluster map (right), year Clusters p value>0.5 High Low Low High Low Low High High Refereces Adsera, A. (2004). Chagig Fertility Rates i Developed Coutries. The Impact of Labor Market Istitutios. Joural of Populatio Ecoomics, 17(1), doi: /s x Aseli, L. (1988). Spatial Ecoometrics: Methods ad Models. Kluwer Academic Publishers. Aseli, L. (1995). Local Idicators of spatial associatio-lisa. Geographical Aalysis, 27, Aseli, L., Florax, R. J. G. M., & Rey, S. J. (2004). Advaces i Spatial Ecoometrics: Methodology, Tools ad Applicatios. Berli. Bocquet-Appel, J.-P., & Jakobi, L. (1996). Barriers to the spatial diffusio for the demographic trasitio i Wester Europe. Spatial Aalysis of Biodemographic Data, Bocquet-Appel, J.-P., & Jakobi, L. (1998). Evidece for a spatial diffusio of cotraceptio at the oset ofthe fertility trasitio i victoria Britai. Populatio, (1), Cliff, A. D., & Ord, J. K. (1981). Spatial Processes: Models ad Applicatios. Lodo, Eglad: Pio Ltd. Driscoll, J., & Kraay, A. (1995). Spatial Correlatios i Pael Data. Galloway, P. R., Hammel, E. A., & Lee, R. D. (1994). FertilityDeclie i Prussia, : A Pooled Cross-SectioTime SeriesAalysis. Populatio Studies, 48(1), Kapoor, M., Kelejia, H. H., & Prucha, I. R. (2007). Pael data models with spatially correlated error compoets. Joural of Ecoometrics, 140(1), doi: /j.jecoom Kluseer, S., Szoltysek, M., & Goldstei, J. R. (2012). Towards a Itegrated Uderstadig of Demographic Chage ad its Spatio-Temporal Dimesios:Cocepts, Data Needs ad Case Studies. Die Erde, 143(1-2), Millo, G., Piras, G., & Millo, M. G. (2013). Package splm, Mora, P. A. P. (1950). Notes o cotiuous stochastic pheomea. Biometrika, 37, Szołtysek, M., Gruber, S., Klüseer, S., & Goldstei, J. R. (2010). Spatial Variatio i Household Structure i 19 th-cetury Germay.

Properties and Hypothesis Testing

Properties and Hypothesis Testing Chapter 3 Properties ad Hypothesis Testig 3.1 Types of data The regressio techiques developed i previous chapters ca be applied to three differet kids of data. 1. Cross-sectioal data. 2. Time series data.