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The Full Model

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Dynamic Macroeconomic Models in Emerging Market Economies

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Abstract

In this chapter, the theoretical framework of the fully fledged FHSAM is finalized. It maintains certain basic assumptions in the advanced model, such as household heterogeneities (social stratification and/or classification) and nominal rigidity in the non-housing market, and improves the structure of the model economy by installing the financial market. On the supply side, two markets are contained in the full model: the goods market (the non-housing market producing consumption goods, intermediate goods and business investment; the housing market producing real estate for household borrowers and household lenders. In addition, the full model contains an explicit financial market linking household deposits (the bank lending supply) and the firms calling for loans to pay their working capital expenditure (bank lending demand). The theoretical summary and hypotheses of the fully FHSAM are discussed in the second section of this chapter.

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Notes

  1. 1.

    For details of the discussion on the nature of interest rates, see Böhm-Bawerk and Smart [1], Keynes [2], Hayek [3] and Woodford [4].

  2. 2.

    For more details on CSV, see the contributions proposed by Townsend [5], Boyd and Smith [6] and Winton [7].

  3. 3.

    For details of the Modigliani–Miller theorem, see the work proposed by Modigliani and Miller [9].

  4. 4.

    For relevant literature on this issue, see the studies conducted by Diamond and Rajan [15], Bernanke [16, 17] and Iyer et al. [18].

  5. 5.

    See the works of Sachs et al. [19] and Peek and Rosengren [20].

  6. 6.

    See the work proposed by Borensztein and Lee [21].

  7. 7.

    See the work of Chanlau and Chen [22].

  8. 8.

    For details on the description of function \(\Psi (R_{t}^{d})\), see the work of Chowdhury et al. [23].

  9. 9.

    Clearly, the \(GDP_{t}\) is defined here in real terms.

  10. 10.

    The definition of \(WC_{t}\) is as in Eq. 8.33. The term \(WC_{t}r_{t}^{l}\) is the wholesale firms’ repayment for loan to support their working capital expenditures.

  11. 11.

    To avoid duplication, we only derive the steady-state values of variables for the full model. The reduced-scale solutions can be easily made to get the steady-state values for the advanced model, which is a simpler version.

  12. 12.

    The upper index ‘ss’ is the symbol of steady-state value for the parameter to which it is attached.

  13. 13.

    Some may argue that according to labour laws and related regulations, workers are protected from working more than 8 hours per day, but the situation in emerging market economies is tricky. Because of the ineffective administrative efforts, the absence of strong workers’ union, the inferior bargaining position of employees and even the willingness of workers themselves to earn extra gain, a large portion of rural workers exceed the 8 hours per day limit. The situation gets even worse in lower-end industries like construction, in which rural workers play the majority part. For supporting evidence, see the studies conducted by Velasquez [24], Brown et al. [25], Chan and Ngai [26], Burra [27], Rocha and Debert [28] among many others. Similar conclusion concerning this issue is drawn in the advanced model. Moreover, FHSAM allows modeller to modify such steady-state values of working hour, within the range of (0, 1). Researchers can assign values to \(n^{ss}\) based on their judgement.

  14. 14.

    These equations are derived using equations described in the relevant subsections above, given steady values already known. The ‘great ratio’ method adopted in solving steady-state values for basic model has been used as well.

  15. 15.

    The appendix to this chapter provides the details of how to find steady-state values for all the variables in the model.

  16. 16.

    In particular, this cost is composed of several important economic components such as auditing, accounting and legal costs. This cost can be interpreted as bankruptcy cost, in that if entrepreneur defaults and then claim bankruptcy, financial intermediates must pay such cost and only receive the wreck value of such entrepreneur, who gets nothing.

  17. 17.

    Because the cost for banks to raise such fund is the deposit rate paying to the households, the cost of loan is equal to the interest rate, \(r_{t}\), which is assumed to be risk free.

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Authors and Affiliations

  1. Beijing, China

    Daniel Lukui Jia

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Appendix

Appendix

MATLAB is adopted to find the steady-state values for the full model (the solution of the advanced model can be easily achieved using a similar and simpler program). The MATLAB codes are shown as follows.

function y=fun(x);

y(1) = x(2)+x(3)+x(4)-x(1);

y(2) = wlhss*nlhss+wbhss*nbhss+crwss+x(12)-x(1);

y(3) = (mu1/mu4)*(rhss*x(5))/rlss-x(12);

y(4) = (mu2/mu4)*x(5)*rhss-x(6);

y(5) = x(10)+x(11)+crwss+x(12)+kcss*deltakc+x(5)*deltakh+x(6)-yss;

y(6) = rhss/(mu4*(ncwss\(\wedge \) mu1)*(x(6)\(\wedge \) mu2)*(x(5)\(\wedge \)(mu4-1)))-x(7);

y(7) = 1/x(8)+(((1-betabh*bbh)/(1-bbh))/(x(11)))*m*(x(7)/rss) +betabh*(((1-betabh*bbh)/(1-bbh))/(x(11)))*x(7)*(1-deltah)-x(7)* ((1-betabh*bbh)/(1-bbh))/(x(11))-(betabh* ((1-betabh*bbh)/(1-bbh))/(x(11)))*m*x(7);

y(8) = 1/x(9)+(betalh*((1-betalh*blh)/(1-blh))/(x(10)))*(1-deltah)*x(7) -x(7)*((1-betalh*blh)/(1-blh))/(x(10));

y(9) = x(11)+x(7)*x(8)*deltah+m*x(7)*x(8)+x(3)-wbhss*nbhss-m*x(7)*x (8)/rss-x(3)*rdss;

y(10)= x(10)+x(7)*x(9)+x(15)+kcss+x(6)+x(5)+x(14)+x(2)-wlhss*nlhss -(1-deltah)*x(7) *x(9)-(x(15)+x(16))-(rcss+(1-deltakc))*kcss -(rhss+(1-deltakh)) *x(5)-x(6)-(xss-1)*(yss/xss)-x(14)*rss-x(2)*rdss;

y(11)= (ncwss\(\wedge \) mu1)*(x(6)\(\wedge \) mu2)*(x(5)\(\wedge \) mu4)-deltah*(x(9)+x(8));

y(12)= x(7)*deltah*(x(9)+x(8))+yss-x(6)-x(13);

y(13)=x(3);

y(14)= x(14)-m*x(7)*x(8)/rss;

y(15)= x(16)-(mu3/mu4)*rhss*x(5);

y(16)= x(15)-betalh*x(16)/(1-betalh);

x0=[5 2 0 1 10 10 1 5 5 1 1 1 2 5 1 1];

% BC Dlh Dbh Bcb kh kb ph hbh hlh clh cbh ccw GDP Llh pl rl

options = optimset(’MaxIter’,1e8,’MaxFunEvals’,1e8,’TolFun’,1e-8);

x=fsolve(@fun,x0,options);

BCss=real(x(1));

Dlhss=real(x(2));

Dbhss=real(x(3));

Bcbss=real(x(4));

khss=real(x(5));

kbss=real(x(6));

phss=real(x(7));

hbhss=real(x(8));

hlhss=real(x(9));

clhss=real(x(10));

cbhss=real(x(11));

ccwss=real(x(12));

GDPss=real(x(13));

Llhss=real(x(14));

plss=real(x(15));

rlss=real(x(16));

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Jia, D.L. (2020). The Full Model. In: Dynamic Macroeconomic Models in Emerging Market Economies. Palgrave Macmillan, Singapore. https://doi.org/10.1007/978-981-15-4588-7_8

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