1 Basic concepts for quantitative policy analysis
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1 1 Basc concepts for quanttatve polcy analyss 1.1. Introducton The purpose of ths Chapter s the ntroducton of basc concepts of quanttatve polcy analyss. They represent the components of the framework adopted n the secton dedcated to modellng wth GAMS. More precsely, after the clarfcaton of the objectve of polcy analyss the steps n whch t s artculated are descrbed. Afterwards, ths Chapter llustrates the components of a model and dscusses the mportance of ts soluton wth respect to the observed values, that s of the base run. Fnally, the dfferent types of model are presented underlnng ther possble polcy evaluaton optons Steps n quanttatve polcy analyss Quanttatve polcy analyss nvolves quanttatve methods to: - Defne a polcy problem; - Demonstrate ts mpact; - Show potental solutons and polcy alternatves. It can be developed at three dfferent levels correspondng to the polcy levels. They are: - Mcroeconomc level, whch s focused on polces amed at ndvdual parts of the economy, such as, ndustres, busnesses and households; - Sector level, whch s targeted to nterventons drected to a specfc sector of the economy, for example, the maze sector; - Macroeconomc level, whch s centred on polces amed at the aggregate economy. In order to nvestgate the polcy mpact, quanttatve polcy analyss adopts a four-step approach llustrated n Fgure 1. Fgure 1 - Steps n quanttatve polcy analyss
2 The roots of the process are represented by the economc theory that, mplemented wth nformaton provded by hstorcal trends and experence, provdes gudelnes to help conceptualse and desgn polcy nterventons. For ths reason, quanttatve polcy analyss can be defnee as a process amed at quantfyng the varous mechansms analysed by theory. On the bass of a theory, quanttatve modellng desgns a model and estmate parameters and calbrate the model tself n orderr to provde the framework for polcy smulaton. Modellng and polcy smulaton are the two core elements of quanttatve polcy analyss. Modellng ncludes the constructon of a model and the computaton of the base run Constructon of a model Constructng a model conssts on the defnton of a theoretcal construct that represents the nvestgated economc process. It s made of equatons whch represent logcal and/or quanttatve relatonshps (equaltes or nequaltes) between a set of four components. They are: - Exogenous varables; - Endogenous varables; - Parameters; - Indces. The exogenous or ndependent varables are factors that affect a model wthout beng affected by the model. They are fxed n the sense that they cannot be manpulated wthn the economc model. The endogenous or dependent varables are those whose values are determnedd wthn the model. Parameters or coeffcents are fxed values that descrbe the effect of one exogenous varable on the endogenous varable. Let us consder a lnear model for the estmate of the quantty of meat demanded by a group of consumers (D) gven a certan level of prce (P), ncome (Y), the related prce and ncome
3 coeffcents (β, γ) and techncal effcency (α). Its mathematcal notatonn and the typology of components s represented n Fgure 2. Fgure 2 - Lnear demand model The exogenous varables and parameters can be further dstngushed n uncontrollable and polcy nstruments. They are both observable varables and coeffcents, but the latter are the objectve of the polcy nterventon. In addton, n the model the endogenous varable s selected to enter nto the defnton of crtera for polcy evaluaton. In our prevous example, let us assume that the government controls meat prce (polcy nstrument) and wants to change t n order to acheve a certan level of meat consumpton (crtera for polcy evaluaton). The other exogenous varables and the parameters are uncontrollable to the purpose of the polcy nterventon (Fgure 3) ). Fgure 3 - Lnear demand model wth uncontrolled varables and parameters and a polcy nstrument The ndces are used to specfy the elements of an array of numbers (varables and parameters). Turnng to the above descrbedd example, let us assume that the same model structure allows estmatng demand of the same group of consumers for not only meat but also maze. The model n Fgure 2 or 3 can be rewrtten as: D = α + β * P + γ * Y = meat, maze
4 In a model, equatons descrbe a system, namely a set of two or more smultaneous equatons wth the same set of unknowns. Let us consder a lnear model for the analyss of the market equlbrum for two commodtes, meat and fsh, wth demand (D), supply (S) and prces (P) the endogenous varables. The ndex s, whle the equatons are (1. Demand functon) ( ) (2. Supply functon) ( (3. Equlbrum condton) where a and f are the techncal coeffcents of the demand and supply equatons, respectvely, and b and z the prce coeffcents of demand and supply. The defnton of system of equatons provde an mportant rule n modellng desgn: n order to be solved, a system of equatons must be charactersed by a number of equatons equals to the number of endogenous varables. The model, n our example, s consstent n the sense that t has three unknown varables (D, S and P) and three equatons and, thus, t has a soluton. When the number of equatons s greater than the number of endogenous varables, the model s nconsstent, that s t provdes no soluton whle f the number of equatons s less than the number of endogenous varables, the model has an nfnte number of solutons Computaton of the base run Once the model s constructed, ts soluton for the observed values yelds the base run. Let us consder the lnear market equlbrum model specfed for meat and fsh n the prevous paragraph. Gven the observed values for the known components, the endogenous varables can be estmated as llustrated n the followng. The lner market equlbrum model components are - Two commodtes - The system of equatons, ( ) (
5 - the observed varables a techncal coeffcent of the demand equaton f techncal coeffcent of the supply equaton b prce coeffcent of demand z prce coeffcent of supply - the value of the observed varables (789:) 1.07 =>?' :' 1.03 =>?' 0.47 ) 789:' 1.08 ) =>?' 4.87 For the computaton of the base run for meat: - Frst, substtute the observed values n the model 789:' 1.07@ :' (a) ( 789:' :' (b) 789:' ( 789:' (c) - Second, solve the model as follows. Substtute n equaton c, equaton a and b Calculate meat equlbrum prce 1.07@ :' :' 1.07@ ' 789:' :' 789:' Substtute meat prce n equaton a and b and calculate demand and supply that mast be equal because ths quantty s the meat equlbrum quantty For the computaton of the base run for fsh: 789:' 1.07@ ( 789:' Frst, substtute the observed values n the model
6 (=>?) =>?' (A) ( =>?' =>?' (B) =>?' ( =>?' (C) - Second, solve the model as follows. Substtute n equaton C, equaton A and B Calculate fsh equlbrum prce 1.012@3.09 =>?' = =>?' 1.012@ ' =>?' =>?' =>?' Substtute fsh prce n equaton A and B and calculate demand and supply that mast be equal because ths quantty s the fsh equlbrum quantty Table 1 summarzes the base run. =>?' 1.012@ ( =>?' Table 1 - Base run for meat and fsh Equlbrum value Meat Fsh Prce Quantty Importance of the base run Calculatng the base run has dfferent purposes. Two of them have a specfc mportance. The soluton of a model for the observed values can be adopted: - for the valdaton of the model; - as a benchmark aganst whch to measure the mpact of counterfactual polcy scenaros. The objectve of the valdaton of a model s to seek to mnmze the dfference between the observed values of the endogenous varable and ts estmated value. The valdaton technques can be classfed n: - Econometrc approaches, wth whch the accuracy of the model s verfed by statstcal crtera of goodness of ft;
7 - Calbraton procedures, adoptedd when the number of avalable observed values s not enough to apply econometrc technques. The second purpose of the base run s to represent the benchmark aganst whch to measure the mpact of alternatve smulated polces or shocks. Ths s a very mportant pont. It means that n order to understand the effect of a smulaton on an endogenous varable, the value of the mpact varable after the smulaton must be compare wth ts base run value and not wth ts observed value. An example allows clarfyng the ssue. Fgure 4 llustrates the hstorcal trend n producton of maze n a hypothetcal country where two drought perods brake the normal producton years. Let us model ths trend wth a lnear model where producton of maze (y) s a functon of labor (x) that s where a s equal to and b to Fgure 4 - Data on producton of maze n a hypothetcal country ( ) Frst drought Second drought Hstorcal data on producton Fgure 5 compare the base run wth the observed hstorcal data Fgure 5 - Data on producton of maze n a hypothetcal country and base run ( )
8 Frst drought Second drought Hstorcal data on producton Lneare Base (Hstorcal run data on producton) Let us ntroduce a polcy amed at ncreasng producton as descrbed by the polcy mpact lne n Fgure 6. Fgure 6 - Data on producton of maze n a hypothetcal country, base run and polcy mpact lne ( ) Base run If we compare the 2007 observed value wth ts value n the same year after the polcy nterventon we make a mstake because the shock s calculated wth a model that predct a level of producton, n that year, represented by the base run. In other words, the effect of a polcy must be assessed aganst the state predcted by the model that descrbe how the observed economc process evolves
9 wthout the mplementaton of any shock. In our example, the comparson must be between the base run and the polcy mpact lnes Taxonomy of models Models can be classfed nto four typologes, namely conceptual, analytcal, stylzed and appled models (Fgure 7). A model s a smplfed framework desgned to llustrate a complex observed economc process. Theoretcal framework and mathematcal methods allow to flter out ts nessental detals and to represent the nvestgated real complex process n terms of stylzed facts, that s to desgn a conceptual model. Ths latter allows descrbng the observed economc process. Focusng on few mportant assumptons and casual mechansms, castng economc relatonshps nto a form susceptble to mathematcal analyss leads to analytcal models. They are sutable for the nvestgaton of the mplcatons of varous sets of postulates wth a few assumptons as possble about the magntudes of parameters. Attachng numbers to an analytcal model and relatng them to the economc performance allows desgnng a stylzed model. Ths typology of framework can be adopted not only to nvestgate the sze of varous effects but also to analyse problems that are too dffcult to solve analytcally or that have ambguous analytcal answers and hence depend on partcular parameter values. Fgure 7 - Taxonomy of models and polcy evaluaton optons
10 Includng n stylzed model more detals and mportant features of a partcularr economy or stuaton lead to an appled model. An example can better clarfy the dstncton between a stylzed and appled model: the former may refer to a group of countres, for nstance the Ol-mportng countres, whle the appled model s related to a specfc country n a group, such as Saud Araba. The specfc features of the above mentoned models made them sutable for dfferent purposes. A conceptualse model allows descrbng the observed economc process, an analytcal model s useful for strategc plannng that s for the defnton and analyss of strateges (general, undetaled plan of acton over the long tme perod n order to acheve the overall organzaton s goals), whle stylzed and appled models are ndcated for polcy analyss, that s for the nvestgaton of partcular nterventons amed at specfc targets.
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