Appendix 3: Decomposition of the NPC

The annual change in the nominal protection coefficient (NPC) can be decomposed into its component parts using a difference equation (Jaeger and Humphreys, 1988). If we start with the basic NPC equation, i.e.

NPC_t = P_t^d/(E_tP_t^w),

where P_t^d is the domestic producer price for a given commodity,

E_t is the official exchange rate, and P_t^w is the border equivalent price for the commodity, all for period t. The total derivative for the above is:

dNPC = (1/EP^w)dP^d - (P^d/(E²P^w))dE - (P^d/(EP^w2))dP^w,

which for small changes is approximated with first differences by:

NPCt+1 - NPCt = (Pdt+1 Ptd)/(EtPtw)
	- (Et+1 - Et)Ptd/(PtwEt2)
	- (Pwt+1 - Ptw)Ptd/(EtPtw2)