+ Aggregate Timber Supply
Aggregate Timber Supply
Summary 静给能值给坐)器的 tHeory ● Modeling approaches
Summary Theory Modeling approaches
1. Theory 能月辞口影 1.1 timer production function V=v(a,E,q 8.1 nE=maxa,e pv(a, E; e ru-weje rd 8.2 a(p, p, g=a: MBD(a, E; =MOC (a,E; q 8.3
1. Theory 1.1 timer production function 8.1 8.2 8.3 * ( , , ) : ( , ; ) ( , ; ) π max{α, } { ( , ; ) } (α, ; ) ∞ 0 γα a p p q a MBD a E q MOC a E q E pv a E q e wE e V v E q e e e j F raj ＝ ＝ ＝ － ＝ ＝ － －
1.2 Aggregate supply Aiv(a,E;q*hi=g(p, p) H harvest ccis where 8.4 0 othenwise k(a,E; g and S=g(p, p,1) 8.5 T(S,I,1,I,X,Y)=0 T(X,Y)=0 n8=h(p,v)=0 8.8 h(p, w,z) P s=g(P,w,Z) 8.10
1.2 Aggregate supply 8.4 8.5 8.6 8.7 8.8 8.9 8.10 ( , , ) ( , , ) ( , ) 0 ( , ) 0 ( , , , , ) 0 { ( , ; )} ( , , ) [ ] { ( , ; )} * ( , ) 1 1 1 1 , , 0 1 1 , , S g p w Z p h p w Z h p w T X Y T S I I X Y I V a E q and S g p p I where H S A v a E q H g p p i i i SR SR LR t t SR e I i J j if harvest occurs at p p i j otherwise I i J j e i j i j SR e ＝ ＝ ＝ ＝ ＝ ＝ ＝ ＝ ＝ ＝ ＝ ＝ － ＝ ＝ ＝ ＝ ∂ ∂π π π
2. Modeling approaches a Normative approaches ● Positive approaches e Timber supply an empirical analysis Contemporary research issues
2. Modeling approaches Normative approaches Positive approaches Timber supply :an empirical analysis Contemporary research issues
2.1 Normative approaches e Static engineering models e Intertemporal optimization p=a+ BY g-(Y) 8.12 Z=,(-B)-c(+y)-+Mn1(+n)m0813
2.1 Normative approaches Static engineering models Intertemporal optimization 8.11 8.12 8.13 + + + T i T i i i i Yi MT Z Y Y c p g Y p Y 1 ( 1) 1 1 1 ( ) ( )(1 ) (1 ) ( ) ＝ － － － ＝ － － ＋ ＋ ＋ ＝ ＝ α β γ γ α β
2.2 Positive approaches 只能能共影与 e Individual choice models e Aggregate supply models s-g(p; 1 ,Z) 8.14
2.2 Positive approaches Individual choice models Aggregate supply models S＝ g ( p ; I , Z ) 8.14
2.3 Timber supply an empirical analysis e Defining timber supply 8.15 π=h(p,w;z,t) S 6P=8(P;Z, 8.16 “=a0+a计+,4P+,a2+2bp1+2,b22+bp+cm8.17 Ss=8P=as+bs P s bp Pp mnzN+ bsa 2a +bsg 2g+C, t 6兀 Sp- 8p=ap+bppPp+ bps Ps+ nZn+baza+ bpg zg+ t 8.18 e Estimating the supply equations D=8(P,Pn,W,Y=1,) 8.19
2.3 Timber supply :an empirical analysis Defining timber supply 8.15 8.16 8.17 8.18 Estimating the supply equations 8.19 a b p b p b Z b Z b Z c t P S a b p b p b Z b Z b Z c t P S a a t a p a Z b p p b Z Z b p Z c tp g p Z t P S h p w Z t p pp p ps s pn n pa a pg g p P SR P S ss s sp p sn n sa a sg g s S SR S i i i i j ij i j j l jl j l i k ik i k j j j i t i i SR i i SR i SR + + + + + + + + + + + + ＝ ＝ ＝ ＝ ＝ ＋ ＋ ＋ ＋ ＋ ＋ ＋ ＝ ＝ ＝ δ δπ δ δπ 2 1 2 1 π ( ; , ) δ δπ π ( , ; , ) 0 ( , , , , ) , 1 D g p p w Y t i ＝ i fi i i t－
2.4 Contemporary research issues e Engineering approaches - Advantage for analyses of the long-run supply Not be well suited for short and medium-run analysis of market dynamics and policy effects e Positive econometric models of supply e To conduct modeling at finer scales and then aggregate the out comes to simulate supply responses To expand aggregate timber supply models to include additional information on the structure of timber inventory on the righthand side of the supply equation
2.4 Contemporary research issues Engineering approaches : -Advantage for analyses of the long-run supply -Not be well suited for short and medium-run analysis of market dynamics and policy effects Positive econometric models of supply To conduct modeling at finer scales and then aggregate the out comes to simulate supply responses To expand aggregate timber supply models to include additional information on the structure of timber inventory on the righthand side of the supply equation