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Material Type: Notes; Professor: Koontz; Class: Agricultural Product Marketing; Subject: Agricultural and Resource Economics; University: Colorado State University; Term: Unknown 1989;
Typology: Study notes
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AREC 510 Lec I Systems Modelling PracticeExample Hog and Pork System – Harlow (USDA 1962)
Quarterly data Sow Farrowing
= f(SFt
, PHt-
, ..., PHt-
, PCt-
, ..., PCt-
, ...t-
Hog Slaughter
= f(SFt^
, ...t-
Quantity Pork
= f(HSt
, ...t
Cold Storage
= f(QPt
, CSt-
, PPt-
, ...t-
Price Pork
= f(QPt
/ N, CSt
/ N, QBt
/ N, QCt
/ N, Yt
)t
Price Hogs
= f(PPt^
, ...t
This is an example of a recursive system.
AREC 510 Lec I Dataex) Livestock -- HogsCommercial Slaughter, Weights, and Prices
Hogs
Barrows and GiltsSowsBoars and StagsOn-Farm
Federally Inspected Slaughter, Weights, and Prices
Hogs
Barrows and GiltsSowsBoars and Stags
ex) Livestock -- CattleCommercial and Federally InspectedCattle
Steers and HeifersCalves (<500 lbs)Cows (Beef or Dairy)Bulls Numbers, Weights, and Prices
AREC 510 Lec I Motivation
Demand: Q = f ( P )Supply: Q = g ( P )or Demand: P = f ( Q )Supply: Q = g ( P ) Q
AREC 510 Lec I
t^
t^
t
t^
t
α^
α βα β
α βα β
α α β
α α β
0
1 0 1 1
1 2 1
1
2 1
1
1
1 2 1 1
t^
t^
t
t^
t
β^
α βα β
β α β
α βα β
β^
α β
0
0 1 1 1
2 1
1
2 1 1 1
1 1
2 1 1
or Pt^ =^ π
π^11
X t
π^12
Y t
1t
Q^ t^
=^ π
π^21
X t
π^22
Y t
1t
This is the “Reduced-Form Model.” The reduced form of the system is obtained bysolving for the endogenous variables as a function of the exogenous variables anddisturbances. You can use OLS on the reduced form model but you – most likely –cannot get back to the elasticities – the structural model parameters.
AREC 510 Lec I Matrix B describes the system:1)^
If B is diagonal the model is a Seemingly Unrelated System.
Error terms are correlated E( u
u1t
)2t
If error terms are not correlated the problem contains two single equationmodels.
2)^
If B is upper or lower triangular the model is a Recursive System. OLS isappropriate. 3)^
If not 1) or 2) then the model is a Simultaneous System.
AREC 510 Lec I Identification ProblemOLS cannot be used to estimate the coefficients of the structural model. OLS can beused with the reduced form model.Can we derive estimates of the structural parameters from the reduced formparameters? This is the identification problem.Rules for IdentificationOrder Condition (Necessary Condition): The number of predetermined variablesexcluded from an equation is at least as large as the number endogenous variablesincluded in the equation less one.Rank Condition (Necessary and Sufficient Condition): There exists at least one non-vanishing determinant... (It’s important but not here.)
AREC 510 Lec I ex) Pt^
-^ β
-^ t γ^11
x^ 1t^
-^ γ^12
Y t
-^ γ
x 14 = u4t^
1t
Q^ t^
-^ β
-^ t γ^21
x^ 1t^
-^ γ^23
X t
-^ γ
x 24 = u4t^
2t
Eq
x^1
x^2
x^3
x^4
β^12
γ^11
γ^12
γ^14
β^21
γ^21
γ^23
γ^24
x^1
= intercept and x
= trend 4
AREC 510 Lec I Two-Stage Least Squares ExampleFirst Stage – Regress each endogenous variable on all the exogenous variables.
P = f ( X, Y, trend )Q = g ( X, Y, trend ) Second Stage – Use predicted values of endogenous variable in regression. (Over-identification helps...)Pt^ =^ α
α^1
Q t
α^2
Yt^
1t^
(Demand)
Q^ t^
=^ β
β^1
P t
β^2
Xt^
2t^
(Supply)
Consistent but inefficient.
AREC 510 Lec I Rational Expectations in Systems
AREC 510 Lec I Β^ Y
*^ +t
Xt^
t
*Yt
*^ t Ω t-
(naive expectations: Y
*^ = Yt
t-^
or distributed lag)
Assume that decision makers know the structure of the model and that there is fullinformation. They understand supply and demand functions – they cannot perfectlypredict the future.Solve the model for the expectation and then put expectation solution into model.Rational expectations models are simultaneous tests of rational expectations andproperly specified models.
AREC 510 Lec I 16
Two equation example: Q (^) t = a + b Pt + c Yt + u1t (Demand) Q (^) t = d + e Pt*^ + f Xt + u2t (Supply)
a + b Pt + c Yt + u1t = d + e Pt^ + f Xt + u2t b Pt - e Pt^ = a - d + c Yt - f Xt + u1t - u2t E(b Pt - e Pt) = E(a - d + c Yt - f Xt + u1t - u2t) (b - e) Pt^ = a - d + c Yt - f Xt
Q (^) t = (^) β 0 + β 1 Y $ t^ + β 2 X $ (^) t + β 3 X (^) t + u 2 t
Q (^) t = α 0 + α 1 Pt + α 2 Yt + u1t
