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Rural Development Through Input–Output Modeling

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Advances in Modeling Agricultural Systems

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 25))

Abstract

Input–output (I-O) models developed in the late 1930s and ever since have been applied extensively. Though the contribution of I-O models in depicting economic transactions was recognized early on, computational constraints have limited their use. This is mainly because of huge data requirements, difficulties in computational handling, and lack of software developed and adjusted for I-O analysis. Today, I-O analysis can be applied extensively in regional and local economies and can provide valuable information on growth and investment priorities, sectoral interrelationships, and policy impacts. I-O analysis has been employed in research on both agriculture and rural development to evaluate the importance of agricultural activities, the interdependence among agriculture and the rest of the economy, the intensity of the rate of growth, and the impacts of policy interventions.

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Notes

  1. 1.

    Schaffer [44] refers some sources of models used in impact analysis (IMPLAN, RIMS, etc.). See also the works of Johnson and Otto [21] and Jordan and Brooks [22].

  2. 2.

    The analysis for Anatoliki Makedonia and Thraki region was taken as example in the present study, from a previous work of Mattas et al. [26], in which can be found more details; moreover, analysis of the tobacco sector in Greece can be found in Mattas et al. [25].

  3. 3.

    The mathematical presentation of the simple Leontief model can be found easily in the literature; for a thorough presentation, see [38].

  4. 4.

    Detailed discussion and application of various regionalization techniques, including GRIT, can be found in Refs. 19, 20, 27, 38, 49.

  5. 5.

    The original proposal of FLQ by Flegg et al. [10] was introduced in 1995. Since then, a dialogue was opened in the literature [3, 8, 9, 10, 11, 31] and the original version was improved and modified to the version appearing in Ref. 8.

  6. 6.

    A detailed description of the procedure for calculating I-O multipliers can be found among others in Refs. 27, 38.

  7. 7.

    The mathematical presentation of the GRIT can be found in Ref. 27, where each step’s equations are described in detail.

  8. 8.

    Employment is the measure used for the calculation of the LQs; it is the most commonly used measure due to its availability.

  9. 9.

    The use of the FLQ was supported above; for a more comprehensive analysis, see Ref. 27.

  10. 10.

    A detailed presentation of the I-O multipliers and linkages can be found in, among others, Refs. 27 and 38.

  11. 11.

    For more details about the mathematical programming model and the results, see Ref. 26.

  12. 12.

    As mentioned, the mathematical presentation of the GRIT technique and the calculation of the relevant linkage coefficients can be found in Ref. 41.

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Authors and Affiliations

  1. Department of Agricultural Economics, Aristotle University of Thessaloniki, Thessaloniki, Greece

    Konstadinos Mattas

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  1. Konstadinos Mattas
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  2. Efstratios Loizou
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  3. Vangelis Tzouvelekas
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Correspondence to Konstadinos Mattas .

Appendix: The Code of the GAUSS Computer Package

Appendix: The Code of the GAUSS Computer Package

/* Gauss program for regionalizing the National I-O table for Anatoliki Makedonia and Thraki region (1998, 34 sectors), using the GRIT technique, and estimating the I-O multipliers *//* PHASE 1: LOAD BASIC TABLES AND DATA IN TXT FORMAT *//*format /mat /on /mb1 /ros 16,8;*/format /rds 12,5;outwidth 240;m=34;/* set the dimension (number of sectors) in the national transactions table */n=3;/* set the dimension (number of categories) of the final demand and final payments matrix */loadm TrNt[ ]=c:\gauss\kapnos\reg\TrNt.txt; TrNt=reshape(TrNt,m,m);  /* LoadNational Transactions Matrix mxm*/loadm FDNt[ ]=c:\gauss\kapnos\reg\FDNt.txt; FDNt=reshape(FDNt,m,n);  /* Load National Final Demand Matrix mxn */loadm FPNt[ ]=c:\gauss\kapnos\reg\PrdnNt.txt;FPNt=reshape(FPNt,m,n);/* Load National Final Payments Matrix for Greece mxn */ loadm EmpNt[ ]=c:\gauss\kapnos\reg\EmpNt.txt; PrdnNt=reshape(PrdnNt,m,1);   /* Load National Sectoral Output mx1 */loadm EmpNt[ ]=c:\gauss\kapnos\reg\EmpNt.txt;  EmpNt=reshape(EmpNt,m,1);   /* Load National Employment Vector m sectors */loadm EmpRg[]=c:\gauss\kapnos\reg\EmpRg.txt;  EmpRg=reshape(EmpRg,m,1);   /* Load Regional Employment Vector m sectors */ /* PHASE 2: COMPUTATION OF THE LOCATION QUOTIENTS */ /* Step 2.1: Computation of the Employment-Based CILQ Type (the FLQ) */EmpRatio=EmpRg./EmpNt;C1=reshape(Empratio',m,m);CILQ0=(EmpRatio./C1)*0.34181; /* CILQ Matrix before adjustment*//* Replace the values of CILQ which are greater than 1 with 1 */CILQ=zeros(m,m);    i=0;     do while i<m;     i=i+1;    j=0;     do while j<m;      j=j+1;       if CILQ0[i,j]>1;         CILQ[i,j]=1;        else;        CILQ[i,j]=CILQ0[i,j];      endif;   endo;endo;/* Step 2.2: Estimation of the Employment-Based SLQ */SL0=(EmpRg./sumc(EmpRg))./(EmpNt./Sumc(EmpNt));SL1=reshape(SL0,m,m);SLF=zeros(m,m);     i=0;     do while i<m;     i=i+1;    j=0;     do while j<m;    j=j+1;     if SL1[i,j]>1;        SLF[i,j]= 1;     else;     SLF[i,j]=SL1[i,j];    endif;  endo;endo; /* PHASE 3: APPLICATION OF THE GRIT TECHNIQUE STEPS */ /* Step 3.1: Sectoral Aggregation (No Need for Aggregation in the Current Study)*/ /* Step 3.2: Reallocation of International Trade */TrNt1=TrNt[8:25,.];/* Partitioned Transactions with Secondary Sectors */d1=ones(1,rows(TrNt1))*TrNt1;/*primary sectors (1-7), sec(8-25), ter (26-34)*/d2=d1+FpNt[.,2]';TrNt2=TrNt1*diagrv(zeros(m,m),d2)*inv(diagrv(zeros(m,m),d1));/* National Transactions SubMatrix Adjusted for International Trade (mxn) */TrNt3=TrNt[1:7,.]|TrNt2|TrNt[26:34,.];/* National Transactions Matrix Adjusted for International Trade (nxn) *//* Step 3.3: Computation of the National Matrices (There Are No Nonexistent Sectors) */DRMNt=(TrNt3)*inv((diagrv((zeros(m,m)),(PrdnNt))));/*National Direct Requirements Matrix mxm *//* Step 3.4: Computation of Regional Matrices */DRMRg=CILQ.*DRMNt;/* Regional Direct Requirements Matrix mxm */ImpRgCf1=(sumc(drmnt-drmrg));/*Regional Imports Coefficients vector adjusted for CILQ mx1*/Print; print "Direct Requirements Regional for AMT"; print DRMRg;/* Step 3.5: Sectoral Aggregation – Definition of the Regional Classification Scheme*/C3=eye(m);C4=C3-DRMRg;LEONTIEFRg=inv(C4);/* Regional Leontief Inverse Matrix mxm */PrdnRg=(PrdnNt).*(EmpRg./EmpNt);/* Regional Sectoral Output mx1 */TransRg=DRMRg*diagrv(zeros(m,m),PrdnRg);/* Regional Transactions Matrix */ImpRgf=ImpRgCf1.*PrdnRg;/* Regional Imports Vector mx1, from coefficients to values */Print; print "Leontief Regional for AMT"; print LEONTIEFRg;Print; print "Regional Sectoral Output"; print PrdnRg;format /rds 14,3;Print; print "Regional Transactions Matrix for AMT"; print TransRg;/* Step 3.6: Computation of the Complete Regional Input–Output Table */ /*Final Demand and Primary Inputs Computation */ /* Regionalization of the Household Income Using Employment Ratios and an Employment-Based SLQ */SLQH0=(Emprg./sumc(EmpRg))./(EmpNt./sumc(EmpNt));r0=(EMPRg)./(EMPNt); r1=FpNt;SLQHd=zeros(m,1); i=0;  do while i<m;  i=i+1;    if SLQH0[i,1]>1;    SLQHd[i,1]= r0[i,1] ; else;   SLQHd[i,1]=r0[i,1]*SLQH0[i,1]; endif;endo;HousRg=r1[.,1].*SLQHd;/* Regional Household Income Vector mx1 */IPRg=(ones(1,m))*TransRg;/* Regional Sectoral Intermediate Purchases 1xm */OPRg=PrdnRg-sumc(TransRg)-HousRg-ImpRgf;/* Regional Other Payments Vector mx1 */FpRg=HousRg+ImpRGf+OPRg;/* Regional Final Payments mx3 *//*PrdnRg-(OPRg+HousRg+ImpRGf+IPRg'); */Print; print "Regional Final Payments for AMT"; print FpRg;ISRg=sumc(TransRg ′);/* Regional Sectoral Intermediate Sales kx1 */FDi=PrdnRg-ISRg;format /rds 16,5;/* Regionalization of Private Consumption Vector Using Employment Ratios and an Employment-Based SLQ */SLQF0=(EmpRg./sumc(EmpRg))./(EmpNt./sumc(EmpNt));r3=(EmpRg)./(EmpNt); r2=FdNt;SLQC=zeros(m,1);  i=0;   do while i<m;    i=i+1;    if SLQF0[i,1]>1;    SLQC[i,1]= r3[i,1] ;   else;    SLQC[i,1]=r3[i,1]*SLQF0[i,1];   endif;endo;ConsRg=r2[.,1].*SLQC;/* Regional Sectoral Private Consumption kx1 *//* Regionalization of Exports Vector Using Employment Ratios and anEmployment-Based SLQ */SLQE=zeros(m,1); i=0;  do while i<m;  i=i+1;   if SLQF0[i,1]>1;      SLQE[i,1]= r3[i,1] ;    else;      SLQE[i,1]=0;   endif;endo;ExpRg=r2[.,2].*SLQE;/* Regional Sectoral Exports kx1 */OFDRg=PrdnRg-ISRg-ExpRg-ConsRg;/* Regional Other Final Demand kx1 */FDRg=ConsRg+ExpRg+OFDRg;/* Regional Final Demand kx3 */Print; print "Regional Final Demand for AMT"; print FDRg;" Regional Final Demand ";?;" Int Sales Consumption Exports Other FD Output ";ISRg˜ConsRg˜ExpRg˜OFDRg˜PrdnRg;?;?;" Regional Final Payments ";?;" Int Purchases Households Imports  Other FP Output ";IPRg ′˜HousRg˜ImpRGf˜OPRg˜PrdnRg; /* PHASE 4: COMPUTATION OF THE I-O MULTIPLIERS */b1=ones(1,m);FDShare=FDRg/sumc(FDRg);FPShare=FPRg/sumc(FPRg);SecId=seqa(1,1,m);/* Step 4.1: Chenery and Watanabe Linkage Indices (or Direct Coefficients) */CH1=B1*DRMRg;  /* Output Backward linkages */CH2=DRMRg*B1';  /* Output Forward Linkages */print;print"Chenery and Watanabe Linkages";print; print" Sector Backward Forward";print SecId˜CH1′˜CH2;print "Total " OCH1˜OCH2;/* Step 4.2: Rasmussen and Hirschman Linkage Indices (or I-O Multipliers)*/B2=B1*LeontiefRg;/* Output Backward linkages or OUTPUT MULTIPLIERS */B4=HousRg./PrdnRg;/* Income technical coefficients or DIRECT INCOME EFFECT */B5=B4′*LeontiefRg;/* Simple Income Multiplier or TOTAL INCOME EFFECTS */B6=B5′./B4;/* TYPE I INCOME MULTIPLIERS */B7=EmpRg./PrdnRg;/* Employment technical coefficients or DIRECT EMPLOYMENT EFFECT */B8=B7′*LeontiefRg;/* Simple Employment Multiplier or TOTAL EMPLOYMENT EFFECTS */B9=B8′./B7;/* TYPE I EMPLOYMENT MULTIPLIERS */B3=LeontiefRg*B1';/* Output Forward Linkages */B10=LeontiefRg*B4;/* Income Forward Linkages */B11=LeontiefRg*B7;/* Employment Forward Linkages */?;print;print"Rasmussen and Hirschman Linkages";print; print"Backward";print;print" Sector Output Income Employment Type I Income Type I Employment";print SecId˜B2′˜B5′˜B8′˜B6˜B9;print " Type I     " OB2˜OB5˜OB8˜OB6˜OB9;print; print "direct effects";print; print "B4 Direct Income Effect, B7 Direct Employment Effect";print SecId˜B4˜B7;?;print; print"Forward";print; print" Sector Output Income Employment ";print SecId˜B3˜B10˜B11;print " Type I     " OB3˜OB10˜OB11;CLOSEALL;END;

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Mattas, K., Loizou, E., Tzouvelekas, V. (2009). Rural Development Through Input–Output Modeling. In: Advances in Modeling Agricultural Systems. Springer Optimization and Its Applications, vol 25. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-75181-8_13

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