3. DYNAMIC CHARACTERISTICS OF

1. 3. DYNAMIC CHARACTERISTICS OF MODEL III 3.1 Dynamic Multipliers 3.1.1 Dynamic multipliers describe the incremental effects of a single-period change in the level of an exogenous variable on the time path of an endogenous variable. A single-period multiplier may be defined as d Xk+r / dWk, where Xk+r denotes an endogenous variable in period k+r, and r may take values from zero to infinity. The expression Wk denotes an exogenous variable in period k. 3.1.2 If r = o, the multiplier is called impact multiplier. This describes the current period or short-term effect of a change in the exogenous variable W on X. For r > o, the multiplier is called an interim multiplier which describes the effect on X in period k+r of a change in W in period k. The long-run or total (also referred to as the equilibrium) multiplier describes the effect over time (say zero to infinity) of a change in W on X. 3.1.3 The current period effects of a higher order policy factor changes are described by the impact multiplier. The subsequent effects of the same policy change are described by the interim multipliers. The summation over time of the interim multiplier effects generates the total multipliers. Appendix V presents the interim multiplier coefficients for a ten-year period for the Somali cereal sector generated from Model III. 3.2 Current Effects of Higher Order Policy Changes: Impact Multipliers 3.2.1 In general, one can obtain the impact multipliers directly from the reduced- form version of the models given in Table I, section 2.6. The reduced-form coefficients of each unchanged exogenous variable (r = o) is that variable's impact multiplier(18). 3.2.2 Assumptions: taking this into consideration, we may derive the current effects of a single shock in the major policy variables on cereal requirements, prices and domestic subsistence production. This requires that assumptions on the direction of policy variable changes be specified. Following are five major specifications that take into account the base-year period (1983) exogenous variables Y5, Y10 and Y11 magnitudes: 23