The Life-Cycle Income Analysis Model (LIAM): A Study of a Flexible Dynamic Microsimulation Modelling Computing Framework

Transcription

1 INTERNATIONAL JOURNAL OF MICROSIMULATION (2009) 2(1) The Lfe-Cycle Income Analyss Model (LIAM): A Study of a Flexble Dynamc Mcrosmulaton Modellng Computng Framework Cathal O Donoghue, John Lennon and Stephen Hynes Rural Economy Research Centre (RERC), Teagasc, Ireland; emal: [email protected] ABSTRACT: Ths paper descrbes a flexble computng framework desgned to create a dynamc mcrosmulaton model, the Lfe-cycle Income Analyss Model (LIAM). The prncple computng characterstcs nclude the degree of modularsaton, parametersaton, generalsaton and robustness. The paper descrbes the decsons taken wth regard to type of dynamc model used. The LIAM framework has been used to create a number of dfferent mcrosmulaton models, ncludng an Irsh dynamc cohort model, a spatal dynamc mcrosmulaton model for Ireland, an ndrect tax and consumpton model for EU15 as part of EUROMOD and a prototype EU dynamc populaton mcrosmulaton model for 5 EU countres. Partcular consderaton s gven to ssues of parametersaton, algnment and computatonal effcency. Keywords: flexble; modular; dynamc; algnment; parametersaton; computatonal effcency 1. INTRODUCTION Populaton-based dynamc mcrosmulaton models are programs that are used to forecast populatons nto the future and to assess the mpact of economc and demographc change on publc polcy. In partcular these models have been used to analyse exstng polcy and to desgn polcy reforms n nter-temporal polces such as educaton, pensons, long-term care and spatal polcy. The objectve of ths dynamc modellng framework s to ncorporate a tme dmenson nto polcy analyss. Usng models based on crosssecton data smply allows one to look at the effect of polcy at one pont n tme. Usng crosssectonal data one s lmted n the smulaton of polcy nstruments whch depend on ntertemporal factors such as pensons. A dynamc mcrosmulaton lfe cycle model allows one to examne polcy over tme; for example lfe course redstrbuton, forecasts of cross-sectonal redstrbuton and the smulaton of pensons. Desgnng dynamc mcrosmulaton models s a large model buldng project nvolvng many dscplnes such as economcs, socal polcy, statstcs and computer scence. Ths paper descrbes an nnovatve mechansm for makng dynamc mcrosmulaton models easer to construct, usng a generalsed method. The result s the Lfe-cycle Income Analyss Model (LIAM). In addton we outlne a number of current applcatons of LIAM to further llustrate the flexblty of the approach adopted. The paper s desgned as follows. Secton 2 descrbes the objectves of the paper, wth secton 3 descrbng the man model features. Secton 4 overvews the dfferent types of process modules, whle secton 5 dscusses algnment. Secton 6 dscusses some effcency features. Secton 7 descrbes some of the mplementatons of LIAM and secton 8 concludes. 2. OBJECTIVES The constructon of a dynamc model s a very large task, both n terms of graspng the types and forms of behavour that take place over a lfetme and the effort n programmng thousands of lnes of code. When DMMs were frst developed, they represented advances n computer scence as well as n socal scence methodology. However, despte dynamc mcrosmulaton models (DMM) havng exsted snce the 1970s (Orcutt et al., 1986), developments n the feld of mcrosmulaton have progressed only slowly (O Donoghue, 2001a). Part of the reason has been the computatonal resource requrements. In many countres data lmtatons have also sgnfcantly lmted developments. Fortunately, n recent years, both dffcultes have started to be overcome. Computers have ncreased n speed, now allowng very powerful models to be constructed on Personal Computers. At the same tme the establshment of household panel datasets n many countres, for example the European Communty Household Panel Survey, the Brtsh Household Panel Survey and the German Soco-Economc Panel, alled to the ncreasng avalablty of admnstratve datasets, removed the barrer to the estmaton of dynamc behavoural processes. Even so, the spread of the DMM technology and the development of the feld has been relatvely slow. The models that are beng used at present are not dong very much more than the DYNASIM model n the late 1970 s. A large potental reason s the apparent beneft to cost rato. Many nsttutons, when faced wth the large cost of developng a dynamc model, feel the money better spent on other technques. One sgnfcant contrbutor to the cost of development s the cost n producng the computng envronment of the model. In addton, because the computng necessary to produce a

2 O DONOGHUE, LENNON AND HYNES The Lfe-Cycle Analyss Model (LIAM) 17 dynamc mcrosmulaton model s so complcated, computng development has often taken precedence over developng better behavoural equatons. It s therefore mportant to focus on ways of reducng the cost of buldng ths ntal framework. O Donoghue (2001a) surveys the dynamc mcrosmulaton models that have been constructed, descrbng n partcular the desgn choces that have been faced. Whle most models have been bult as stand-alone efforts, a number of attempts have been made to avod the start-up costs and learnng curve n buldng the model by utlsng the same framework for alternatve applcatons. There were some efforts n the 1970s to wrte generc mcrosmulaton computer software packages. However because of the complexty of the systems to be smulated, users typcally found that they had specalst requrements that these software packages could not cater for. (See, for example, Leombrun and Rchard, 2005.) Although not desgned wth objectve of constructng multple dynamc mcrosmulaton models, the code from CORSIM model (Caldwell, 1996) has been strpped down and used as a template n the constructon of the Canadan DYNACAN, Swedsh SVERIGE and the US Socal Securty Admnstraton models. Subsequently there have been four examples of programs that have been wrtten explctly for multple dynamc mcrosmulaton model constructon: ModGen (Wolfson and Rowe, 1998), UMDBS (Sauerber, 2002), GENESIS (Edwards, 2004) and LIAM the focus of ths paper. MODGEN s a computer language desgned to create mcrosmulaton models, and has been used to create a number of mcrosmulaton models (dynamc and statc) wthn the Canadan government, such as Lfepaths. UMDBS s a smulaton system developed at Darmstadt Unversty as part of academc research. It s mplemented n the object orented language Smalltalk and ts man applcatons are socoeconomc nvestgatons. GENESIS s a SAS based modellng framework beng used wthn the UK Department of Work and Pensons to create the Pensm2 penson age dynamc mcrosmulaton model and the state penson forecastng model. LIAM, unlke MODGEN, s a closed model, n whch spouses are drawn from ndvduals wthn the model populaton. In addton, LIAM s fully accessble to researchers, whereas GENESIS s currently avalable for nternal government use only. In ths paper we descrbe the LIAM framework whch was developed, roncally, because of the lmted resources avalable to the author. Dynamc models have typcally been constructed by governmental nsttutons (MOSART, SESIM, DYNACAN, PENSIM2) or by major research grants (SVERIGE, DYNASIM, POPSIM), although a number of models have been constructed as part of PhDs (Hardng, Baldn). Not beng funded by a major research grant or by a government nsttuton LIAM falls nto the latter low budget category, beng developed ntally as part of a PhD and latterly expanded wth small research grants and wth the assstance of a number of PhD students. As a result, t s freely acknowledged that current mplementatons of LIAM are relatvely basc compared to the exstng propretary models lsted above. But these shortcomngs can be overcome, subject to mproved data and fundng avalablty. The advantages already offered by LIAM le n ts flexblty and modularty, and ts objectve of provdng an unconstraned model development platform, adaptable to future uses and future proofed to allow for future enhancements. The ntal applcaton of LIAM was a sngle cohort lfe-course analyss of the redstrbutve mpact of the Irsh Tax-Beneft system, usng relatvely unsophstcated data and behavoural equatons. Subsequent developments (descrbed n more detal below) nclude mproved data (2-8 years n the panel data underlyng the behavoural estmatons), the addton of a graphcal user nterface, the move to a mult-cohort populaton model, and the use for alternatve polcy analyses such as spatal, ndrect taxaton and nternatonal comparsons. Future developments that are planned nclude mprovng the behavoural equatons to respond to changes n the polcy envronment such as labour supply retrement and mgraton. In order to avod n-bult software lmtatons nhbtng future model developments, careful thought s necessary n the desgn of a flexble modellng framework. There are a number of features that are desrable n such a framework: In order to deal wth new datasets wth ease, usng dfferent sets of varables should not be a problem. It should be easy to ncorporate new behavoural nformaton. Ablty to run on a personal computer usng standard nexpensve software. It should be straghtforward to make changes n the model model usng the framework, even f the model has not been used for a perod of tme, or s beng used by multple analysts. Ths mples transparency n the operaton of the framework and also flexblty n the way n whch behavour can be ncorporated n the model A framework that s robust to the modellng changes desred. Computatonal effcency as, despte computng tme decreasng wth the avalablty of cheaper and faster computers, computatonal demand has ncreased at a faster rate. A modellng envronment that allow the user to focus more on the estmaton of behavoural equatons rather than on computng ssues. Ablty to take account of, and examne, the feedback effects of polcy reforms.

3 O DONOGHUE, LENNON AND HYNES The Lfe-Cycle Analyss Model (LIAM) FRAMEWORK FEATURES In ths secton we descrbe the man aspects of LIAM, focusng ntally on the general structure of the framework and then elaboratng the data structure and ssues relatng to modularsaton and parametersaton. Structure of Framework A dynamc mcrosmulaton model takes ndvdual objects (ndvduals, households, farms, companes) and smulates the probabltes of varous events occurrng at varous ponts n tme. Dynamc events may of course occur at the same pont n tme as other events. Fgure 1 descrbes the man operatons of the ageng component of the LIAM dynamc mcrosmulaton model. In ths context ageng s a generc term coverng any dynamc event that nvolves updatng object characterstcs over tme. Here the operaton of one partcular ageng module at one pont n tme s examned. In realty ths process occurs on a number of occasons as all the ndvduals n the database pass through a number of ageng modules at each pont n tme. Data for each person are frstly taken from the database, havng been transformed nto the model data-structure, whch s descrbed n more detal below. The ndvdual s then passed through each ageng module n turn. The ageng modules to be used are specfed as part of a parameter lst, whch allows the order and the types of the transton processes to be vared. Input parameters for each ageng module are stored n Mcrosoft EXCEL spreadsheets and are accessble va the user front end. Output from each ageng module s stored, n memory, n algnment storage matrces. For example, algnment regressons produce a determnstc component XB to whch s added a stochastc component,. These are stored n a dynamc data structure and ranked wth the hghest Z percent of values taken from the exogenous totals n the algnment process. If the ageng module s a transton between states, then the output wll be a probablty, otherwse f the ageng module s a transton between contnuous amounts, for example ncomes, the output s a real varable. When all ndvduals have been passed through the partcular ageng module, algnment occurs (see secton 5 below for a descrpton). Ths ensures that aggregates from the mcro model match macro aggregates. Fnally f a varable for any ndvdual changes then ths change s regstered n the database (.e. n both the physcal relatonal database, stored on the hard dsk n ASCII and the vrtual database stored n random access memory). In what follows the operatons of each of these components of the ageng module are unpacked n more detal. Data and Framework Data Structure In ths secton we descrbe how data s handled n LIAM. We descrbe the database used and how data are stored wthn the framework. The data structure or format of the data s very mportant as t determnes to a large extent the amount of memory requred to store the data, whch n turn nfluences the speed at whch the model can run. Fgure 1 Descrpton of a Dynamc Module

4 O DONOGHUE, LENNON AND HYNES The Lfe-Cycle Analyss Model (LIAM) 19 It also has mportant consequences for the flexblty of the model. Turnng frst to data storage, nput output data are stored n ASCII format. When storng output, varables are converted from real to nteger as ntegers requre less storage space than real numbers. Ths s acheved by multplyng output values by 100 and truncatng the result to zero decmal places. For storage we also adopt a relatonal database structure due to organsaton and memory handlng advantages. Fgure 2 descrbes the data-structure used by LIAM. Structurally the data s stored n a herarchy of object types (tobjt) such as person, household or frm. Each of these object types themselves conssts of a number of objects (tobj) such as the actual ncdence of a person or household. Events (tvar1) such as brths, tenure status or dentfcaton number then occur to objects. Each event can have a number of ncdences or values (tval). Wthn ths data-structure persons are consdered one set of objects and households another, wth the IDs of the member ndvduals of a household stored as events that can happen to households. Ths s because persons can be members of a number of dfferent households over tme, breakng down the tradtonal nestng of persons wth households assocated wth crosssectonal data structures. We explot the herarchcal nature of relatonal databases makng data storage event drven. Storng model output as consecutve crosssectons would result n severe neffcences, as each varable would be stored for each output perod, so for example a person s gender would be stored for each pont n tme. Makng data storage event drven, new data s stored only when a new event occurs and thus the data changes. Gender s therefore only stored at brth. One can make sgnfcant savngs n memory as a result. Each ndvdual varable, however, requres more nformaton than s the case n a cross-sectonal data structure. For each event t s necessary to know what event occurred (tvar1), when t occurred (tval.evtme), and the value of the event (tval.amount). There are a number of ways n whch data can be stored wthn LIAM tself durng the smulaton. If the model were open, as n the case of the DEMOGEN or LfePaths models n Canada, where new spouses are generated synthetcally when needed, then all of each ndvdual's transtons could be smulated ndependently of other ndvduals. Thus each ndvdual could be read from the database, ther lfe course smulated and then stored n the database one at a tme. LIAM, however, uses a closed model. Except for new brths or mmgrants, no new ndvduals are generated. Marrages, for example, lnk ndvduals already n the database. Ths method s more straghtforward to nterpret as t mrrors what happens n the real world. As a result of ths closed approach, ndvdual behavour can become dependent on the characterstcs and behavour of tobjt tobj *obj tobjt *next_ptr tobj tvar1 *st_var tobj *next_ptr tobj tvar1 *st_var tobj *next_ptr tobj tvar1 *st_var tobj *next_ptr tvar1 tval *st_val tvar1 *next_ptr tvar1 tval *st_val tvar1 *next_ptr tvar1 tval *st_val tvar1 *next_ptr tvar1 tval *st_val tvar1 *next_ptr tvar1 tval *st_val tvar1 *next_ptr tval nt evtme double amount, tval *next_ptr tval nt evtme double amount, tval *next_ptr tval nt evtme double amount, tval *next_ptr tval nt evtme double amount, tval *next_ptr tval nt evtme double amount, tval *next_ptr Fgure 2 Model data structure Notes: See text for explanaton of object and event types

5 O DONOGHUE, LENNON AND HYNES The Lfe-Cycle Analyss Model (LIAM) 20 other members of the sample. For example, algnment to requred global totals means that the chance of employment for an ndvdual s not ndependent of the rest of the populaton, but depends upon the aggregate outcomes of the whole labour market. Other operatons n the model that may depend on other ndvduals nclude the marrage market and other processes whch depend on spousal nformaton and algnment routnes. Although the model s not solely ndvdual based (t s a multlevel model comprsng Regons, Countes, Dstrcts, Households and Persons), a sde effect of the nter-person dependency engendered by the closed model approach s that t s necessary to store all ndvduals n memory durng the smulaton. To ths end, therefore, durng a model run the vrtual database stored n memory durng the operaton of the program mmcs the structure of the relatonal database stored on the hard dsk. Once the data have been read from the database nto memory, LIAM runs through each object type (person, famly and so on), n turn smulatng the lfe course events desred for each object of that type. Smulaton processes are therefore object-type specfc Typcally varables whch are components of the household data structure are declared n long lsts wthn a dynamc model. They may be ntalsed elsewhere and have other operatons carred out n other parts of the program. As the modellng framework s so large and complcated, t rapdly becomes dffcult to keep track of all the places n LIAM whch need to be altered when a new varable s ncluded. As a result, nstead of declarng varables wthn LIAM, we declare the lst of varables to be used separately n a parameter sheet (dyvardesc).liam then creates space for the varable, ntalses the data and carres out all necessary transformatons and operatons automatcally. Ths mnmses the number of model alteratons necessary when a new varable s ntroduced, keepng the framework entrely flexble wth regard to the set of varables used whlst mantanng ts robustness. For example, f the user wshes to ntroduce a new nstrument wth an output varable such as health status, then the user smply needs to ntroduce the varable nto the parameter sheet and LIAM wll do the rest, wthout the user havng to recode the framework tself. Another advantage of the flexble declaraton of varables s that, because varables are stored n vectors, new composte varables can be produced easly. For example, a complex varable lke dsposable ncome, f not smulated drectly, can be generated from the vector of ts components such as employment ncome and captal ncome. Another mportant advantage of the herarchcal method of data storage s the ease wth whch duraton nformaton can be accessed. As the date and value of each event s stored t s possble to determne such nformaton as duraton, duraton n the last 12 months, date an event frst occurred, date an event ended, duraton n a partcular state and so on. Informaton of ths knd s frequently requred by tax-beneft systems and other polcy analyss. Addtonally t s easy to access earler values of an event such as prevous earnngs. Populaton versus Cohort The ntal database depends on the purpose of the smulaton. One of the key dstnctons n the lterature s between longtudnal or sngle cohort models and populaton or cross-secton/multcohort models. However, ths dstncton s now largely redundant due to advances n computng power. From a computng perspectve, a cohort can smply be seen as an ntal sample of unrelated ndvduals aged 0, whle the populaton contans a sample of ndvduals of dfferent ages, some of whom are related. As a result, the computng framework has been developed to handle both types of analyss. Runnng LIAM as a dynamc populaton model requres that the ntal cross-secton s stored n the requred manner, whle runnng the model as a dynamc cohort model requres the model to frst generate an ntal cohort. Modularsaton The use of modularsaton s an mportant technque that helps acheve the objectves of flexblty, transparency and robustness that LIAM requres. Modularsaton means that components wthn the LIAM are desgned to be as autonomous as possble. Modules are the components where calculatons take place, each wth ts own parameters, varable defntons and self-contaned structure, wth fxed nputs and outputs. The result s a set of ndependent components that do not nteract wth each other drectly, allowng the framework to operate as a collecton of ndependent buldng blocks. Because each process module s entrely self contaned, each can be run ndependently, left out or replaced by an alternatve module. Constructng a program n ths way allows for the model to be easly expanded to deal wth new behavoural equatons or functons. Also, because t allows the user to focus on ndvdual components one at a tme, wthout nteracton wth the rest of the program, the robustness of the model can be mproved. Lnkages Many polcy nstruments depend upon multple unts of analyss. So, for example, pensons may depend upon ndvdual characterstcs such as contrbuton hstores, age and so on, taxaton may depend upon famly characterstcs such as both spouses ncomes, and socal protecton nstruments and welfare measures upon the household unt. Smlarly socologcal analyses and long-term care analyss may depend upon wder knshp networks. These lnkages are not strctly herarchcal (e.g. regon, household, famly, ndvdual). The may, n fact, consst of a web of lnkages (regon, frm, household, famly, ndvdual, mother, father, partner, chldren and so on). Ths mult-level structure wth ts complex

6 O DONOGHUE, LENNON AND HYNES The Lfe-Cycle Analyss Model (LIAM) 21 nteractons between levels s one of the man complcatons of mcrosmulaton models that make t dffcult to use person-based modellng frameworks. Whle t s not nfeasble to smulate usng non-herarchcal lnkages such as those between relatves across households usng other software packages such as socal smulaton and statstcal packages, the non-herarchcal structure often requres one to be "creatve" n desgnng the model due to nflexbltes n the model as they are often non-standard requrements. In contrast purpose desgned mcrosmulaton packages such as LIAM can have these data structures n-bult, mprovng the transparency and flexblty of the modellng envronment. In the LIAM framework, the mechansm of lnkng objects has been automated as a relatonal database. Potentally any object can be lnked to an object of ether the same or a dfferent object type. For example ndvduals of object type person (p) wll be lnked to ther household of object type (h), whle n turn the household s lnked wth the ndvduals n the household. Therefore calculaton of the number of persons n a household s a process carred out at the household level. Ths new household level varable, npers, can be accessed by ndvdual processes usng the prefx h_npers. (The actual prefx used s user-defned.) In smlar fashon lnkages can be made between objects of the same type. For example a chld can be lnked to parent s nformaton, accessng mother s educaton level usng m_edlevel and father s usng f_edlevel. In the ntal framework, there are no predefned lnkages as the objects can be of any type defned by the user. The user pre-defnes all lnkages usng the parametersaton descrbed below to essentally create a web of lnkages between objects; essentally defnng keys to lnk tables. As long as the nature of the lnkage s defned, t s then possble at any level of the model to access nformaton from another level. Ths s qute a powerful feature of the data-structure, savng both tme and memory. In the absence of these lnkages, such as h_npers, a new process would have to be smulated whch would store ths number of persons n a household as a person level varable p_hnpers (say), whch s analogous to a flat fle, where household level varables are stored at the person level. The use of lnkages or keys provdes the space savng advantages of a relatonal database and avods the smulaton of an extra process to convert the household varable to the person level. Creatng and Kllng Objects Whle creatng a new object (person, famly, household, enterprse) s tself not a very complcated task, creatng space and assgnng ntal default values, creatng a new object to mmc the brth of a new person s rather more complcated. As a result we have had to develop a specfc as opposed to generc new_brth functon. The assgnment of varable values such as sngle, age zero, no educaton and so on s straghtforward. However t s also desrable that the new chld nherts the lnkages of the parent. So, for example, the partner (f any) of the mother at brth becomes the chld s father. Smlarly other chldren of the mother become sblngs and the herarchcal lnkages such as the household, famly and regon of the mother are also nherted by the chld. Analogously, kllng a person s also more dffcult that kllng an object. The ndvdual needs to be extracted from the web of knshp networks and other lnkages of whch they form part. For example, the number of persons n a household decreases by one, whlst the spouse becomes a wdow. At the same tme bequest of accumulated wealth may need to be transferred and, n the case of pensons systems, contrbutons or enttlements may need to be transferred to survvng dependants. Agan the possble complexty of the operaton s far too dffcult to generalse, so agan object-specfc routnes have been requred. Mgraton Mgraton s another complex operaton. From the pont of vew of LIAM, emgraton s analogous to kllng someone. The reason for ths s that, n a natonal model, we do not track ndvduals whle they are abroad. (Techncally, as penson rghts can be accumulated overseas, one may need to smulate ther lfe-hstores whle overseas, but ths has been beyond the capacty of any exstng model.) A varaton of the pageant algorthm (Chénard, 2000) s used to ensure that the mgraton of famly unts results n natonal ndvdual level aggregates beng acheved. Immgraton, however, s a more dffcult stuaton. An mmgrant dffers from a new brth n that they have an accumulated set of characterstcs and potentally are accompaned by other famly members. One soluton s to smulate the range of characterstcs of new mmgrants on arrval. However the range of characterstcs s very broad and varable and so t would be very dffcult to retan the correct mult-dmensonal dstrbuton of characterstcs. To avod ths problem we sample (wth replacement) from a set of mmgrant households n the data. Thus whenever we need an mmgrant household we smply select a real (data-dependent) famly wth the actual characterstcs of a new mmgrant famly. In addton to preservng the multdmensonal dstrbuton, t saves substantal computng tme compared to havng to smulate all of the relevant mmgrant characterstcs. Parametersaton In order that modules and other components of LIAM can be changed wth ease, t s necessary to store model parameters externally. Therefore, where possble, parameters are not hard coded wthn the framework. Fgure 3 detals the set of parameters used by the modellng framework. The sets of parameters, representng the flow of

7 O DONOGHUE, LENNON AND HYNES The Lfe-Cycle Analyss Model (LIAM) 22 dyrunset Parameters dealng wth the data structure Parameters dealng wth smulaton process objtype dyvardesc objtype_x polparam agespne DATA transton lnkage lnk_xy algnment Model Fgure 3 Parameter Sheet Herarchy Notes: See text for explanaton of parameter types control n the model, are n some sense herarchcal. At the top level we have dyrunset parameters whch contan the parameters necessary to run the model, detalng drectores (locaton of nput and output fles), tme perod to be run and so on. The remanng parameters deal wth ether the data structure or the smulaton process. Dashed lnes n Fgure 3 ndcate ths dvson. On the data sde the hghest level parameters are contaned n objtype. Ths fle tells the model how many object types there are (regon, household, person and so forth). LIAM creates each object type based upon the lst defned here and assgns user-defned prefxes (for example, r,h and p). The framework then looks for fles objtype_x contanng the ncdences of each of the object types (r, h, p), whch n turn contan the dentfcaton numbers (IDs) of each object of that partcular object type. So objtype_p would contan the IDs of all persons. Related to the set of object types s a set of varables assocated wth each type n the dyvardesc fle. In ths fle, all varables used n LIAM are declared and descrbed. (In the front end, the parameter fles have equvalent menus.) It s, n essence a data dctonary, for the model. Ths fle contans nformaton on the followng attrbutes of each varable: varable name varable type (bnary, mult-category, contnuous) whether an ncome varable (monetary amount that can be added to other monetary amounts) ths prevents categorcal data beng summed; for example, addng gender to employment lmts of the varable (upper and lower bounds) for debuggng and valdaton whether or not a categorcal varables (f so how many categores and the lst of categores for tabulaton purposes), whether or not needs to be updated durng the smulaton to account for nflaton default values to be taken by new persons data descrpton (descrbes varable names) Assocated wth each varable, there s a data table contanng nformaton about the object(s) assocated wth the varable (who), the tme the event occurred (when) and the value of the varable (what). Whle each data table wthn an object type s lnked by the key or object ID, we need further nformaton to lnk objects of the same or other type. The lnkage parameters defne the set of possble lnks between objects. The user needs to defne a name for the lnkage (for example, ph person to household; hp household to person) and the equvalent orgn and destnaton types (p for lnk ph; h for lnk ph). These lnkages between objects are stored n the lnkage fle lnk_xy. Subsequently, for each lnkage lsted n lnk_xy, LIAM pars the relevant orgn objects and destnaton objects (for example chldren to parents) and stores the resultng orgn and destnaton IDs n a lnk-specfc fle (for example pc for chldren and parents). We now consder the set of parameters that defne the smulaton processes. The hghest level s the agespne or process spne/lst. In any smulaton

8 O DONOGHUE, LENNON AND HYNES The Lfe-Cycle Analyss Model (LIAM) 23 there s an mplct orderng, and events are trggered through condtons. The process spne contans the lst of modules to be run n the dynamc model, so that by varyng the order of the modules and varyng the content of the lst, one can vary the types of processes that can be run n the model. Ths feature explots the modularsaton nherent n LIAM, where because each process s seen as a separate buldng block, the number, type and order of processes can vary wthout havng to change the programme code. Each process or module has a correspondng parameter sheet n the parameter fle Transtons. These parameter fles tell the model the output varables of each process, the type of process, whether a process needs to be algned and the actual process parameters themselves, such as the transton rates, regresson equaton and polcy rules and so on. If a partcular process s to be algned, then LIAM wll look for an approprate set of algnment parameters. Sometmes ndvdual parameters may be requred to be changed between runs wthout any change to the set of processes. A reform to a penson smulaton module where the replacement rate was changed s an example. The polparam parameter set contans nformaton assocated wth each parameter for each possble system, where the system to be run s defned n the dyrunset parameters. 4. PROCESS MODULES Ths secton descrbes the man process types that can be used by LIAM. Ths refers to the collecton of operatons that are smulated on objects durng a smulaton. These nclude demographc processes such as brth, marrage, havng chldren and death, educaton, labour market processes such as employment and unemployment, the smulaton of ncomes and nteractons wth the tax-beneft system. In order to ad flexblty, we classfy processes under a number of headngs. In ths way, nstead of programmng each module separately, we only need to program the module type once. In order to run a module, we then only need a module name (whch s ncluded n the process spne), a module type to determne whch program to run and a set of parameters whch s fxed for every process type. At present there are 6 module types: transton matrces, n the form of a log lnear model (trap) transformatons (tran) regressons, both wth contnuous and lmted dependent varable (regr) macro algnment (dscussed n secton 5) (macro) marrage market (mmkt) tax-beneft system (tb) (actually a collecton of modules; we have lnked LIAM to the EUROMOD EU15 tax-beneft model and to other tax-beneft routnes) The frst component of a parameter fle contans detals about what condtons need to hold for the process to be run. At each pont (step) n tme, each ndvdual s passed through the module. If the condtons hold, then the module calculatons are carred out and the output passed to the algnment component of the module. The output for each ndvdual s stored untl all ndvduals have passed through the module. The algnment component then ensures that the aggregates correspond wth external control totals. Transton Matrces One of the most mportant processes n a dynamc model s the transton between dfferent dscrete states. Transton Matrces are often used to perform these operatons. They specfy the probablty of an ndvdual wth partcular crcumstances movng from state A to state B. In ths framework, transton matrces can be stored as log-lnear models (See, for example, Dobson, 1990). In ths way transton rates are decomposed nto average and relatve transton rates. As a result extra-relatve transton rates can be added wth ease. For example, f a mortalty rate on average fell by 0.1% every 10 years, then a tme-dependent relatve probablty parameter of could be added. Smlarly, ths approach allows the model bulder to combne nformaton from dfferent sources. So, for example, we combne actual age-gender specfc mortalty rates for 1991 taken from lfe-tables and use relatve mortalty rates taken from Nolan (1990) that ncorporate soco-economc relatve mortalty rates. Regressons The second type of transton process used s based upon standard regresson models. At present, ths type of module allows four types of dependent varable standard contnuous dependent varable log dependent varable, allowng for use of the log normal dstrbuton. logt dscrete choce dependent varable probt dscrete choce dependent varable Any varable n the model can be used as a dependent varable and any varable can be used as an explanatory varable. The error term can also vary. The default error term takes a normal dstrbuton wth ndependent dsturbances. Followng Pudney (1992), LIAM also allows for the error term to be decomposed nto ndvdual specfc (u n ) random effects and general error components (v nt ). However, more complcated error decompostons are also possble. Ths allows some degree of heterogenety to be assgned specfcally to ndvduals. So, for example, n determnng earnngs the ndvdual specfc error may represent some dfference n nnate ablty, whle the general error term represents random varaton over tme. Breakng up the varaton n ths manner wll tend to reduce wthn lfetme varaton and prevent to some degree the exstence of very unusual lfe paths.

9 O DONOGHUE, LENNON AND HYNES The Lfe-Cycle Analyss Model (LIAM) 24 In the LIAM modellng framework, transtons occur at dscrete tme ntervals because of the weakness of the data and because of the desre to be able to algn the data. As Galler (1997) ponts out, the statstcal shortcomngs assocated wth the use of dscrete tme models make t s desrable to use short term dscrete tme perods such as a month. As the computng requrements can be substantal for monthly smulatons, LIAM s suffcently flexble to allow the user as the ablty to specfy the tme perod to be used and so monthly or annual perods can be smulated. For a fuller revew of the advantages and dsadvantages of contnuous tme versus dscrete tme, see O Donoghue (2001a). Transformatons Whle regresson models and transton matrces are stochastc processes, nvolvng a random component, some processes are determnstc. Examples nclude age, whch depends on the date of brth, wdowhood, whch depends on the death of a spouse and so on. Lkewse f an ndvdual moves from year 6 n educaton to year 7, years of educaton ncrease by 1. Wthn the transformaton-types handled by LIAM there are two types of determnstc transformaton, gen and fgen. The gen functons are of smpler types, utlsng calculaton routnes combnng sets of varables usng standard operatons ({+,-,*,/, max,mn,^,(,)}). The fgen set of functons represent ad-hoc programs. It s where we explot, for example, the relatonal database structure of the data n operatons such as the number of persons n a household, where the functon counts the number of objects of type person lnked to the object household as defned by the lnk_hp lnk fle. Smlarly t s where ad-hoc functons such as new_brth and kllperson are defned. Whle gen functons and predefned fgen functons are pre-coded and parametersed so that new users can employ them, new fgen functons such as the penson system of a new country need to be programmed by the user f the exstng functonalty does not allow t. Marrage Market If an ndvdual s selected to marry or form a partnershp a process s needed to determne whch spouse they wll take. The process used here s to take the characterstcs of the ndvdual chosen to marry and the characterstcs of each possble spouse and determne the lkelhood of a match. Smlar to the method used n other models such as the CORSIM model, ths s done usng a logt model that estmates the probablty of marrage between pars of ndvduals. The parameter fle therefore s dentcal to that used n the regresson process type. The module tself forms a matrx of the characterstcs of the n men and n women selected to marry. It estmates a probablty for each parng and assgns a match to the couples wth the hghest probablty of marryng. Bouffard et al. (2001) have dentfed some problematcal ssues assocated wth the marrage market, n partcular wth strange matches occurrng amongst the last people to be marred n a partcular smulaton. In order to avod these ssues, we allow the user to create a super-set of potental male partners, so that rather the last female n the marrage pool beng forced to select an unlkely match, there reman a number of males to choose from. In addton we employ the Order of Decreasng Dfferences algorthm proposed by Howard Redway at the UK Department for Work and Pensons, whch creates a measure of the dstance of an ndvdual from the centre of the populaton (or the average characterstc of the populaton) and frst selects for matchng the females wth the most unusual characterstcs, who are lkely to be the most dffcult to match. The logc s that those n the centre of the data are average people who are more lkely to fnd a good match than someone at the extremes. Polcy Processes The fourth process type s the smulaton of the tax-beneft system. Re-emphassng the desre to reuse code and, wherever possble to avod duplcaton, the dynamc framework has been made flexble enough to lnk wth other specalst programs such as pre-exstng tax-beneft models. As a result tax-beneft routnes from other models, such as EUROMOD, can be seamlessly accessed and thus used as module components of the dynamc model. Behavoural Response A desrable feature often gnored n dynamc mcrosmulaton models s the ablty to nclude feedback loops so that behavour can respond to changes n publc polcy. A crtcsm made by Ctro and Hanushek (1997) s that dynamc models are nsuffcently flexble to ncorporate the demands of behavoural response. In order to be able to smulate behavour, typcally the model needs to be able to call a polcy smulaton routne a number of tmes to quantfy the fnancal mpact of alternatve choces on the decson n questons such as the choce to work or retre. As a result the software framework has been desgned to be able to ncorporate feedback loops. The degree of modularsaton that exsts n the framework allows any number or order of modules to be run and for modules to be able to be run a number of tmes. For example, n O Donoghue (2001b) we mplemented a smple labour supply model where labour supply depended on the tax-beneft system. In order to have labour supply depend on tax-beneft polcy, the tax-beneft system needed to be run once as an nput nto the labour supply module and agan, after labour supply has been determned, n order recalculate taxes and benefts n the lght of the resultng behavoural decson. In O Donoghue (2001b) the model used the tax-beneft system as an nput nto decsons to work, decsons to seek part-tme employment versus full-tme employment and to become selfemployed. The tax-beneft system therefore

10 O DONOGHUE, LENNON AND HYNES The Lfe-Cycle Analyss Model (LIAM) 25 needed to be run 5 tmes to examne the mpact of the system on the choce faced by an ndvdual. In the case of spouses, whose behavour can be nter-dependent, the tax-beneft system needed to be smulated 17 tmes (4 decsons for each spouse, plus one run on the bass of resultng jont behavour). As a result ncorporatng behavoural response, although possble, can be computatonally expensve. Other possble behavoural routnes that could be ncluded are retrement decsons, consumpton and beneft take-up. Although computatonally expensve, the framework s suffcently flexble should the user requre and the computng power becomes avalable. Robustness Fnally, n order to avod robustness problems due to modules beng ncorrectly specfed, the model contans a debug devce whch ensures that all nputs requred by a module are actually avalable (.e. have ether been generated n the model or read from the database) before each module can be run. 5. ALIGNMENT The secton descrbes the algnment functon contaned n LIAM. The objectve of algnment s to ensure that output aggregates match external control totals. The reason ths s done s that mcro behavour (both socal and economc) s extremely complex and, mcro-theory beng lmted, the full varablty of the system (n ths case the lfe paths of ndvduals) cannot be accurately predcted. In addton, a household model only makes forecasts about a small part of the economy and largely gnores nteractons wth the rest of the world economy. Fnally, data taken from relatvely short perods of tme may not fully reflect dynamcs over tme. For all of the reasons dynamc mcro-models may not be able forecast aggregate characterstcs of the populaton well. Dscrete choce models In dscrete choce models the output for each ndvdual s a probablty. In order to use these models for predctve purposes, a decson rule s necessary. In other words, what forecasted probablty (or hgher) wll produce an event. In order to predct a state wth a logt (or probt) model, one draws a random number unformly dstrbuted number u. When u or logt -1 ( X ) -1 X u probt ( ), then a state s predcted to occur. Another use of algnment s n correctng for predctve falures of econometrc models. For example, when usng dscrete choce models such as logt or probt models, the predctve power s often poor. Duncan and Weeks (2000:292) hghlght that even n functonally well-specfed models, the predctve performance s poor, partcularly where some states are relatvely densely or sparsely represented n the data. Greene (1997:894) attrbutes ths to the fact that the maxmum lkelhood estmator s not chosen to maxmse a fttng crteron based on predcton of y, as t s n the classcal regresson (whch maxmses R 2 ). It s chosen to maxmse the jont densty of the observed dependent varable. Thus the further the probablty of an event occurrng s from 0.5, the less effectve these decson rules are at producng the desred result. As a result models may under or over predct the number of events. So, for example, f 5% of ndvduals of ndvduals should have the event, then the logt model may not necessarly produce 5% of events. Algnment, however, wll constran the event to occur to 5% of ndvduals. Ths s effectvely a calbraton mechansm and wll produce the correct proporton of events. Of course, care must be n ts use as algnment may lead to the dsgusng of errors n model specfcaton. The types of control totals that can be used to algn to nclude: The aggregate proporton/number n a state or movng between states The average event value The dstrbuton of values The average growth rate n the value of an event In ths paper we shall deal specfcally only wth the frst type A smple analogy for the relatonshp between algnment and the process modules s that the process modules, such as logt models, produce a rankng varable, whle the algnment mechansm selects the number of transtons. For example, n our econometrc model we may have an equaton of the probablty of dyng as descrbed n equaton (1), that depends on age, gender and whether an ndvdual s dsabled or not. Assumng that dsabled people have a hgher mortalty rate, then gven the same age and gender and dstrbuton, the mortalty dstrbuton for dsabled people wll be hgher: logt( p ) 3 Gender 1 4 Dsabled Dsabled 2 Age Age (1) The determnstc component of the model wll result n those wth a hgher rsk havng a better chance of the event occurrng, whle the stochastc part ( ) wll ensure that there s some varablty (so that not only those wth hgh rsk are selected). Ths model therefore produces the person-specfc rsk of dyng. In order to select the number of people that de, we use the algnment probabltes. Frstly ndvduals are grouped nto the approprate age

11 O DONOGHUE, LENNON AND HYNES The Lfe-Cycle Analyss Model (LIAM) 26 and gender groups. As everyone n the relevant group wll have the same age and gender, they only dffer by the determnstc component for dsabled people, ß 1 x Dsabled + ß 4 x Dsabled x Age, and the stochastc component. The object then s to select to de the people n the group wth the hghest probabltes of dyng. If ß 1 s postve, proportonally more dsabled wll de than non-dsabled. As a result we see that the output of the model equaton s used to rank the ndvduals to whom the event occurs, but to leave the decson of experences the event to the algnment process. Implementaton In ths secton we descrbe a practcal method for rankng ndvduals for algnment. We take as our reference pont a logstc model: p logt -1 ( ) (2) X Utlsng the model logt ( p * ) X wll result n those wth the hghest rsk always beng selected for the event. Contnung our example above, the dsabled, all other thngs beng equal, would be selected to have a de. In realty those wth the hghest rsk wll on average be selected more than those wth lower rsk, rather than smply selected those wth the hghest rsk. As a result some varablty needs to be ntroduced. Models based on the CORSIM framework such as the DYNACAN model (Chénard, 2000) utlse the followng method. Frstly, predcted probablty s produced usng our econometrc model: -1 X p* logt ( ). Next, a random number, u, s drawn from a unform dstrbuton, and subtracted from the predcted probablty, p *, to produce a rankng varable, r = p * u. Ths value s then used to rank ndvduals so that the top x% of values are selected. A concern about ths method s that the range of possble rankng values s not the same for each pont. In other words, because the random number u [0,1] s subtracted from the determnstcally predcted p *, then the rankng value takes the range r [-1,1]. However the rankng value for each ndvdual wll only take a possble range r [u 1, u ]. So, for example, f p * s small, say = 0.1, the range of possble rankng values s [-0.9, 0.1]. At the other extreme f p * s large, say = 0.9, then the range of possble rankng values s [-0.1, 0.9]. Thus because there s only a small over lap for these extreme ponts, even f a very low random varable s selected, then an ndvdual wth a small p * wll have a very low chance of beng selected. Ideally the range of possble rankng values should be the same, so that for each ndvdual, r [a,b], wth ndvduals wth a low p * beng clustered towards the bottom and those wth a hgh p * beng clustered towards the top. We now consder an alternatve method. Ths method takes a predcted logstc varable: logt (p ) X. Next, a random number s drawn taken from the logstc dstrbuton. Ths s added to the predcton, gvng logt (p ). The resultng nverse logt, p logt -1 ( X ) s then used to rank ndvduals and smlarly the top x% of households are selected. The rank produced by the two methods s not the same. The second method wll be more lkely to select cases at extreme ponts than the frst, whle frst method wll select more ponts wth central values of p *. Macro Algnment There are a number of levels at whch algnment can occur. At the lowest level, algnment refers to the decson rule used n a dscrete choce model. The next level, descrbed above n our mortalty example, whch s called the meso-level, concerns the dea that the aggregates for partcular groups (n ths case gender and age) should match desred external totals. Meso-level algnment and the use of algnment as a decson rule can however be combned nto one stage. Sometmes the desred targets are narrower than the algnment targets we use. Extendng our mortalty algnment example, suppose we algn mortalty by age, gender and occupaton. We wsh to nclude occupaton n the algnment as occupatonal structure s very mportant for other characterstcs n the model, and because there are known to be sgnfcant dfferentals n occupatonal mortalty rates. However f one of the core targets n the model s to acheve the mortalty dstrbuton suppled by external sources such as offcal populaton projectons, whch may be dsaggregated only by age and gender, then our meso-algnment may produce dfferent aggregates. Ths wll happen f our underlyng occupaton dstrbuton s dfferent to the one mplct n the offcal forecasts. It may therefore be desrable to adjust the results agan to acheve these targets. Ths process s known as macro algnment. Another example follows on from the meso-algnment n the smulaton of transtons between employment states. Macro algnment s then used to constran total employment rates. See Appendx 1 for the steps nvolved n the macro algnment process. Behavoural Change Handlng behavoural nteractons n the model resultng from alternatve scenaros s another ssue one needs to consder when decdng on an

12 O DONOGHUE, LENNON AND HYNES The Lfe-Cycle Analyss Model (LIAM) 27 algnment strategy. One potental soluton s to compare the average (pre-algnment) event value, such as the average transton rate or average earnngs n the baselne scenaro, wth the average n the alternatve scenaro. One potental method s to ncrease algnment values by proportonal dfference. Ths s a method utlsed n some dynamc models. However, ths approach assumes that all processes are unconstraned. In some cases, such as mortalty rates, ths may be a realstc assumpton. One may expect that an exogenous ncrease n human captal wll reduce total mortalty rates. In ths case shftng down the algnment totals s approprate. Other processes face market or other nsttutonal constrants, ssues that are only partally smulated n the model. One example nvolves the labour market, where there s a behavoural change n labour partcpaton n response to a tax change. If labour supply ncreases, then wages would fall and employment ncrease. Ths s smlar to shftng the algnment probabltes. However one would have to shft earnngs as well. Unfortunately, due to rgdtes n the labour market, ths may not necessarly happen. Labour demand may be fxed, n whch case we may just smply see that as more women supply labour, they smply replace people n the labour market who are less employable. Ths s smlar to not shftng algnment at all. In cases where there are market nteractons such as ths, t may be useful to ncorporate a model of the market that would nform the response of algnment totals to economc and demographc totals. At present the framework makes no explct ncorporaton of behavoural change n the algnment structure. Future work on macro-mcro lnkages wll attempt to address ths. 6. EFFICIENCY In ntal versons of the LIAM framework, developments focused on functonalty and not speed. So for each process the model passed through all the objects of the object type, checked to see f a condton was true and, f true, performed the calculaton f(xß+ ) before, f necessary, usng algnment to produce the predcted value of the process. In ths secton we descrbe a number of mprovements n computatonal effcency, relatve to ths ntal approach, that have been made recently. A frst effcency savng reles on the fact that most processes are relatvely stable and so do not change much year on year. Because of ths, elgblty condtons are unlkely to change much year on year. For example, for lone parent brths the model used to check to see f an object was female, sngle and of chld bearng age. It dd ths for each year and for every person. Ths s neffcent as gender doesn t change, so there s no need to repeatedly check whether a male can have a chld. Smlarly martal status elgblty does not need to be retested annually, gven that martal status changes only nfrequently. In the same way, the age range condton (chld bearng age) only changes twce over a lfetme. A key speed mprovement, therefore, has been to calculate the condtons for all people n the frst year of the smulaton and then only to recalculate the condton f an nput varable to the condton changed. The same s true when calculatng regressons. Most regressons are of the form f, j X j j f ( A Agan, by calculatng the value of the expresson n the frst year, when X j changes to X j * one only needs to apply the followng transformaton f ( A X X ). j j * j j The same speed effcences can be found for transformatons, algnment and tabulatons. For example, when algnng by age-group, sex and educaton level, or creatng output tables by these components, most of these categores do not change much f at all durng the smulaton. It s therefore computatonally qute expensve to dentfy, say, all year old males wth unversty educaton each perod of the smulaton to perform an algnment. Rather, by computng the group membershp at the outset and only changng group membershp when a characterstc changes, we sgnfcantly reduce the computatonal costs. These mprovements were appled by creatng a data structure that lnks every varable to the processes whch utlse the varable. When the value of the varable changes, then the related condtons, regressons, transformatons etc are updated. The move from perodc smulatons to ntalsaton plus smulaton only when nputs change transfers some of the computng cost from the smulaton perod to the start. Intalsaton becomes a good deal longer as, rather than smulatng equatons where condtons are met (for example, only smulatng work equatons for those who are n-work the prevous perod), we must now smulate all equatons (.e. smulate the equatons condtonal on workng and condtonal on not workng n the prevous perod). On the other hand, as all that s beng calculated s X j, j j, no algnment needs to occur at ths stage. The net result s much less loopng through the data and sgnfcant overall economes of scale. As development of the program occurred ncrementally and dfferent versons have been run on dfferent machnes and wth dfferent specfcatons, t has been qute dffcult to gauge )

13 O DONOGHUE, LENNON AND HYNES The Lfe-Cycle Analyss Model (LIAM) 28 the mpact of the speed mprovements. However a conservatve estmate s that the run tme s 10% of what t was and potentally as low as 5%. So the qualtatve concluson s that the gans are hghly sgnfcant. Another, although less sgnfcant, speed mprovement was obtaned by storng varables n a statc rather than n a dynamc data structure (.e. as an array rather than a lst). As the set of varables does not vary wthn a run of the model, there s no gan to usng a dynamc lst; nstead a speed penalty s mposed as the lst needs to be traversed to fnd a partcular varable as opposed to smply usng the array ndex to dentfy the varable. Whle attenton was pad n the orgnal datastructure to the memory effcency of the datastructure by storng only new events, lttle attenton was pad to the space taken wthn ths structure, whch proved very costly. For example all ncdences of values were stored as doubles or real numbers, even though the majorty of varables were bnary varables that could be stored as a char. To mprove ths we ntroduced a new category n the data dctonary whch specfed what type of varable to be used, so that bnary varables only took up a fracton of the space requred to store a double. Also we stored real and categorcal numbers as ntegers. Real numbers were converted to ntegers by multplyng by 1000 and retanng only the nteger element of the number. Integers take half as much space as a double. We also conducted an audt of the entre data-structure, strppng out as much superfluous memory requrements as possble. Ths has been partcularly mportant for allowng for much bgger datasets to be smulated on a laptop wth lmted RAM. Somethng we have not explored yet s the further speed mprovement that could be found by creatng sub-sets of objects assocated wth each condton. At present, the model needs to scroll down through the whole dataset for each process. If condtons are updated dynamcally, then the sub-groups where the condton s true can be updated dynamcally, resultng n calculatons only takng place on the subset. When the condton changes then, ths updates the set of objects where the condton s true. Therefore n dong smulatons, the model wll only smulate over the set of objects elgble to be smulated. At present all processes are run n seres. In other words each process s completely smulated before movng on to the next process. Ths requres a data pass for each process. Ths s necessary for processes that are algned as the decson about who makes a transton wll depend upon all objects and not on ndvdual objects. However some processes, such as transformatons and unalgned processes, do not need to be done serally. Effcences could be ganed by smulatng these processes n parallel. For example, f age s smulated for an ndvdual, then age squared and age band could be calculated usng age as nput for each ndvdual before contnung on to the next ndvdual, cuttng the number of data passes and mprovng the speed of the model. Other examples nclude the calculaton of duratons and lagged values of varables. As always n mcrosmulaton models, there s a trade-off between flexblty, complexty and performance. Parametersaton may sometmes result n enhanced complexty and thus reduced transparency and ease of use of the model. In the LIAM structure, ths has been less of an ssue as the parametersaton allows for the same code to be reused over and over wthout recodng, so to some extent mprovng the transparency. There are, however, some performance overheads noted elsewhere n the paper, where the degree of parametersaton and generalsaton may ncrease the number of operatons requred and thus ncrease the tme to run a smulaton. Ths ncrease must be weghed up aganst the complexty of creatng a dynamc model wthout an exstng framework. 7. IMPLEMENTATIONS OF THE FRAMEWORK In ths secton we descrbe a number of mplementatons of the LIAM framework. Thus far there have been four mplementatons of the model a. Lfe-cycle redstrbuton n the Irsh Tax- Beneft system - Irsh Dynamc Cohort Mcrosmulaton Model b. Redstrbutve mpact of Indrect Taxes n Europe dynamc mcrosmulaton of expendtures n the EUROMOD framework. c. Spatal Polcy Analyses Smulaton Model of the Irsh Local Economy (SMILE) d. Cross-natonal comparsons of the dstrbutonal mpact of pensons and the ncentve to retre mult-country dynamc mcrosmulaton model EU 6 th Framework project, Old Age Income Mantenance Polces (AIM). Model (a) was the bass of the author s PhD and has been used to examne the lfe-course redstrbutve mpact of the Irsh Tax-Beneft System (O Donoghue, 2002) and the redstrbutve mpact of penson reform (O Donoghue, 2005). The mplementaton was a sngle cohort model takng 1000 people aged 0 and smulatng ther entre lfe-hstory before lnkng wth the EUROMOD tax-beneft model to smulate the taxbeneft system. A feedback loop was used to ncorporate the mpact of tax-beneft polcy on labour supply decsons. Whle model (a) utlsed an external tax-beneft mcrosmulaton model to provde tax-beneft smulatons for use n the dynamc mcrosmulaton model, model (b) takes nputs from the dynamc mcrosmulaton framework nto a statc tax-beneft model. As part of the EU taxbeneft model EUROMOD, there was a desre to

14 O DONOGHUE, LENNON AND HYNES The Lfe-Cycle Analyss Model (LIAM) 29 examne the mpact of ndrect taxaton on redstrbuton (O Donoghue et al., 2004). However, most of the databases used as nputs nto the model dd not contan expendture nformaton. The LIAM framework was used to smulate a system of equatons smulatng total expendture and budget shares of twenty groups of goods on the bass of nformaton contaned n the ncome surveys used n the model. Indrect taxes were then smulated usng the EUROMOD framework. Ths model used datasets of up to 50,000 households smulatng ndrect taxes for one fscal year. In recent years parallel mcrosmulaton modellng has been used for geographcal and spatal analyss (See Clarke, 1996 and Holm et al, 1996). Snce 2002, a team comprsng the Unversty of Leeds, the Natonal Unversty of Ireland Galway and Teagasc have been developng model (c), the Smulaton Model of the Irsh Local Economy (SMILE), usng the LIAM framework wth the prncple objectve of carryng out spatal analyss n Ireland (O Donoghue et al., 2005). Examples nclude modellng the mpact of local area demographc changes on welfare, modellng the spatal mpact of rural polcy reforms, dentfyng agr-toursm hotspots. A future goal s to model the spatal behavoural mpact of publc nfrastructure developments such as road buldng programs. The frst component of the model s developed outsde the framework, requrng the statstcal matchng of ndvdual tabular local area census nformaton wth mcro-level household data to produce the base dataset. Ths s done usng a statstcal matchng algorthm. The LIAM framework s used to smulate typcal dynamc mcrosmulaton varables such as demographc and labour market varables. Partcular advancements from ths model nclude regonal labour markets, mcro-farm level producton functons and spatal behavoural models. The model s currently under development. At present t s splt nto around 30 county models of about 70,000 persons each and smulates spatal-based polcy at the local level. The fourth mplementaton of LIAM, also n development, s beng used to carry out crossnatonal comparsons of the dstrbutonal mpact of pensons n a selecton of countres n the EU (Belgum, Germany, Ireland, Italy and Sweden). In addton a comparatve analyss wll be carred usng a sem-structural retrement decson module based upon dscounted ncome and penson wealth streams. Ths model smulates over the 50 year horzon , usng crosssectons of about 10-15,000 ndvduals. 8. CONCLUSIONS Whle there have been substantal numbers of papers descrbng analyses carred out by models developed usng LIAM, relatvely lttle has been wrtten on the techncal development of the models. In ths paper we have dscussed some of the methodologcal nnovatons underpnnng the LIAM dynamc mcrosmulaton framework. The key feature of LIAM s the extensve use of parametersaton. Parametersaton of the man features of the dynamc model allows for the programme code whch runs transtons, algnment and transformatons to be reused for dfferent purposes. When addng new varables to the model, alteratons need to be made only n one place, n a parameter fle, makng the model easer to change and reducng the possblty of error. Ths ads model flexblty, as code does not need to be reprogrammed when parameters change. Ths n turn mproves the durablty of models developed usng LIAM, as t allows new parameters to be ncluded when better nformaton becomes avalable. Ths s perhaps the most mportant feature of the LIAM, allowng the framework to be used to develop model applcatons for a wde varety of purposes. It also allows for ease of expanson as mproved data and mcro-behavour become avalable. In addton, by defnng the data structure outsde the model, n a parameter fle, model transparency and robustness s mproved. A second key feature of LIAM s modularsaton. Sx generc module types have been dentfed and developed, whch between them are desgned to cover the full range of model functonalty requred n a dynamc mcrosmulaton model. Because these modules are fully parametersed, n LIAM one can declare a new module by smply takng an exstng module as a template and changng the parameters as requred. Smlarly, because module run-order and type s parametersed, the model can handle any number of modules n any order wthout the need for extra programmng, provded the functonalty of the new module maps onto one of the exstng generc module types. New modules can be added to a model wthout affectng ts ntegrty as, n LIAM, all modules are desgned to work ndependently of each other. Ths further adds to the robustness of the model. Also, by allowng the user to focus on small sectons of code at tme, modularsaton mproves the transparency of the model. The thrd aspect of LIAM hghlghted n ths paper s ts handlng of algnment. As well revewng the ratonale for algnment, we have set out the crcumstances n whch the use of generc or event specfc functons are most approprate for the mplementaton of algnment. We have also set out n detal the process requred to algn aggregate outcomes to the proporton or number of objects n, or movng between, gven states, ncludng consderaton of herarchcal (meso/macro) algnment. The fnal aspect of LIAM hghlghted n ths paper s the range of effcency mprovements, n both speed and memory usage, that have been mplemented as a result of lessons learnt whlst developng the framework. The man mprovement has been move from the evaluaton of functons

15 O DONOGHUE, LENNON AND HYNES The Lfe-Cycle Analyss Model (LIAM) 30 on a unversal, perodc, bass, to an ntal unversal evaluaton followed by reevaluaton only for those objects to whom the functon apples, and for whom values n relevant elements of ther attrbute set have changed. Secondary mprovements have been lnked to more effcent data storage, ncludng the converson of all data, ncludng floatng pont data, to nteger format. We do not clam that LIAM s ether the fastest or most effcent dynamc mcrosmulaton model currently n use. But unfortunately the methodologcal underpnnngs of many models reman undocumented or are set out only n nhouse documentaton. In ths paper we have attempted to publcly document some of the ssues that have arsen n the creaton of the LIAM framework, wth the hope that other model bulders can learn from our experences. Although the framework s not an attempt at wrtng a mcrosmulaton programmng language, t has allowed for a varety of dfferent applcatons to be constructed wthout the need for extensve recodng. In addton, as we have shown, t has been possble to use ths framework as a template for other dynamc models, because the model tself s entrely ndependent of data and behavoural equatons to be used. To promote collaboraton and further development, LIAM s avalable to researchers on request. Acknowledgements The authors gratefully acknowledges fnancal assstance from the Postgraduate Fellowshp of the Economc and Socal Research Insttute, Dubln, the Irsh Department of Agrculture Rural Stmulus Fund, Center for Research on Pensons and Welfare Polces (CERP), Unversty of Turn, the NUIG Mllennum fund, the Combat Poverty Research Fund and the Targeted Soco-Economc Research programme of the European Commsson (CT ), the AIM project fnanced under the 6 th Framework Research Program of the European Commsson and the IDARI project fnanced under the 5 th Framework Research Program of the European Commsson. We are very grateful for the assstance of Donal Kelly, who substantally mproved the code of ths model. We are also grateful for comments provded by Geert Bryon, Jane Falkngham and semnar partcpants n LSE, Nordc Mcrosmulaton Workshop Copenhagen, AIM workshop Madrd and colleagues n Teagasc, the DWP and NUIG. The authors reman responsble for all remanng errors. REFERENCES Bouffard N, Easther R, Johnson T Morrson R J and Vnk J (2001) Matchmaker, matchmaker, make me a match, Brazlan Electronc Journal of Economcs, 4(2). Caldwell S B (1996) Health, wealth, pensons and lfe paths: the CORSIM dynamc mcrosmulaton model, n Hardng A (Ed.) Mcrosmulaton and Publc Polcy, Amsterdam: Elsever, Chénard D (2000) Indvdual algnment and group processng: an applcaton to mgraton processes n DYNACAN, n Mtton L, H Sutherland and M Weeks (Eds.) Mcrosmulaton modellng for polcy analyss: challenges and nnovatons, Cambrdge: Cambrdge Unversty Press, Ctro C F and Hanushek E A (Eds.) (1997) Assessng Polces for Retrement Income: Needs for Data, Research, and Models, Washngton DC: Natonal Research Councl. Clarke G P (1996) (Ed.) Mcrosmulaton for Urban and Regonal Polcy Analyss, London: Pon. Dobson A (1990) Generalsed Lnear Models. London: Chapman and Hall. Duncan A and Weeks M (2000) Smulatng transtons usng dscrete choce models, n Mtton L, H Sutherland and M Weeks (Eds.), Mcrosmulaton Modellng for Polcy Analyss: Challenges and Innovatons, Cambrdge: Cambrdge Unversty Press, Edwards S (2004) GENESIS: SAS based computng envronment for dynamc mcrosmulaton models, Mmeo, Department of Work and Pensons, London. Galler H (1997) Dscrete-tme and contnuoustme approaches to dynamc mcrosmulaton reconsdered, NATSEM Techncal Paper 13, Natonal Centre for Socal and Economc Modellng, Unversty of Canberra, Australa. Holm E, Lndgren U, Makla K and Malmberg G (1996) Smulatng an entre naton, n Clarke G P (Ed.), Mcrosmulaton for Urban and Regonal Polcy Analyss, London: Pon, Immervoll H and O'Donoghue D (2001) Towards a mult-purpose framework for tax-beneft mcrosmulaton: a dscusson by reference to EUROMOD, a European tax-beneft model, EUROMOD Workng Paper, EM2/01, Department of Appled Economcs, Unversty of Cambrdge. Leombrun R and Rchard M (2005) An agentbased mcrosmulaton of labour force partcpaton. Some results for Italy, mmeo, LABORatoro R. Revell, Unversty of Turn. Nolan B (1990) Inequty n the Fnancng and Delvery of Health Care n Ireland, ESRI Workng Paper 16, Economc and Socal Research Insttute, Dubln. O Donoghue C (2001a) Dynamc Mcrosmulaton: A Survey, Brazlan Electronc Journal of Economcs, 4(2). O Donoghue C (2001b) Redstrbuton n the Irsh Tax-Beneft System, Unpublshed PhD thess, London School of Economcs, UK. O Donoghue C (2002) Redstrbuton over the lfetme n the rsh tax-beneft system: an applcaton of a prototype dynamc mcrosmulaton model for Ireland, Economc and Socal Revew, 32(3), O Donoghue C (2005) Assessng the mpact of pensons polcy reform n Ireland: the case of ncreasng the penson age n Fornero E and P Sestto (Eds.) Penson Systems: Beyond Mandatory Retrement, Cheltenham: Edward Elgar,

16 O DONOGHUE, LENNON AND HYNES The Lfe-Cycle Analyss Model (LIAM) 31 O Donoghue C, Baldn M and Mantovan D (2004) Modellng the redstrbutve mpact of ndrect taxes n Europe: an applcaton of EUROMOD, EUROMOD Workng Paper no. 7/01, Department of Appled Economcs, Unversty of Cambrdge. O Donoghue C, Ballas D, Clarke G and Lennon J (2005) Locaton choce decsons n Ireland, paper presented to the conference Modellng Urban Socal Demographcs, Unversty of Surrey, Guldford. Orcutt G, Merz J and Qunke H (Eds.) (1986) Mcroanalytc Smulaton Models to Support Socal and Fnancal Polcy, Amsterdam: North- Holland. Pudney S E (1992) Dynamc smulaton of pensoner s ncomes: methodologcal ssues and a model desgn for Great Brtan, Dept. of Appled Economcs Dscusson paper, MSPMU 9201, Unversty of Cambrdge. Sauerber T (2002) UMDBS - a new tool for dynamc mcrosmulaton, Journal of Artfcal Socetes and Socal Smulaton, 5(2). Wolfson M and Rowe G (1998) LfePaths toward an ntegrated mcroanalytc framework for soco-economc statstcs, paper presented to the 26th General Conference of the Internatonal Assocaton for Research n Income and Wealth, Cambrdge, UK. Appendx 1 Macro algnment n LIAM In LIAM, macro algnment occurs as follows: 1. Specfy algnment sheets, that need to be the same shape for each process (but macro can be a subset), as does the predctor 2. Create a temporary set of algnment structures of type talgn (= n+1, where n s the number of processes to be macro algned - structure (0) s to store the macro level) 3. For each sub process, run through condtons and count the number of people (level.nper) who meet condtons who are n each algnment cell (we don't store predcted probablty at ths pont as we don't know t - maybe smply assgn zero and use the exstng code) 4. For macro process, do the same 5. Multply the cell p tmes the number n cell N = np, the number to be selected n cell 6. If the sub-processes are more dsaggregated than the macro level, collapse to the lower level by summng N over the hgher level (e across educaton levels) 7. Now we have the N's for the 2 dmensonal table for macro and each sub-process. Sum over sub-processes to get expected overall N_t and compare wth the Macro N_m 8. To adjust multply the hghest level of the macro sheet (n ths case level 2) n each of the sub-process by N_m/N_t 9. Backup orgnal Algnment numbers (to be used n the followng year) 10. Store new Algnment totals n the sub-process algnment structures