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Posted 03-08-2022 01:23 PM
(584 views)

In the SAS SAS/ETS® 13.2 User’s Guide: ..The SYSLIN Procedure page 2112 it defines predetermined variables as both exogenous and lagged endogenous variables. Next it defines instrument variables as predetermined variables. Is that statement indicating you have to include all exogenous variables as instrument variables when using 3SLS? thanks for the clarification in advance

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Could you please attach the part of the documentation that you are referring to?

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Could you please attach the part of the documentation that you are referring to?

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Hello pink_poodle. Thank you for your email. I provided a copy of the page

out of the SAS guide. Below that is my 3SLS code. scott

*Below is the copied text: *

*Page. 2112 F Chapter 29: The SYSLIN Procedure*

In this system, quantity demanded depends on price, income, and the price

of substitutes. Consumers

normally purchase more of a product when prices are lower and when income

and the price of substitute

goods are higher. Quantity supplied depends on price and the unit cost of

production. Producers supply more

when price is high and when unit cost is low. The actual price and quantity

sold are determined jointly by the

values that equate demand and supply.

Since price and quantity are jointly endogenous variables, both structural

equations are necessary to adequately

describe the observed values. A critical assumption of OLS is that the

regressors are uncorrelated with

the residual. When current endogenous variables appear as regressors in

other equations (endogenous

variables depend on each other), this assumption is violated and the OLS

parameter estimates are biased and

inconsistent. The bias caused by the violated assumptions is called

simultaneous equation bias. Neither the

demand nor supply equation can be estimated consistently by OLS.

*Variables in a System of Equations*

Before explaining how to use the SYSLIN procedure, it is useful to define

some terms. The variables in a

system of equations can be classified as follows:

• *Endogenous variables, *which are also called jointly dependent or

response variables, are the variables

determined by the system. Endogenous variables can also appear on the

right-hand side of equations.

•* Exogenous variables* are independent variables that do not depend on any

of the endogenous variables

in the system.

• *Predetermined variables *include both the exogenous variables and lagged

endogenous variables, which

are past values of endogenous variables determined at previous time

periods. PROC SYSLIN does not

compute lagged values; any lagged endogenous variables must be computed in

a preceding DATA step.

• *Instrumental variables* are predetermined variables used in obtaining

predicted values for the current

period endogenous variables by a first-stage regression. The use of

instrumental variables characterizes

estimation methods such as two-stage least squares and three-stage least

squares. Instrumental variables

estimation methods substitute these first-stage predicted values for

endogenous variables when they

appear as regressors in model equations.

Using PROC SYSLIN

First specify the input data set and estimation method in the PROC SYSLIN

statement. If any model uses

dependent regressors, and you are using an instrumental variables

regression method, declare the dependent

regressors with an ENDOGENOUS statement and declare the instruments with an

INSTRUMENTS statement.

Next, use MODEL statements to specify the structural equations of the

system.

The data is from an experimental auction: The endogenous variables are

winning prices. The instrument variables are lagged winning prices and

structural characteristics of the auction mechanism. Ten independent

auctions were held. So for instance, *Size* is the number of subjects in a

particular auction. Number of subjects participating varied across the ten

auctions held. The model statements represent the prices of the winning

bids for the 3 meat products being auctioned. Note: endogenous variables

are included on the right hand side of the model startment (bolded). The

other right hand side variables are exogenous variables representing

information from a demographic survey completed by subjects just prior to

the auction.

proc syslin data=a 3sls ;

*endogenous* prBIS prBF93 PrBF80;

*instruments * lagprbis lagpr80 lagpr93

dum80 dum93 *SIZE* dumround2 dumround3 dumround4 dumround5 ;

Beef80: model PrBF80= *prBIS prBF93* biscorrect B93correct BNI

b80text b80juice b80flav Q10 Q15 Q16 female /overid;

Beef93: model prBF93 = *prBIS PrBF80* biscorrect B80correct BNI

b93text b93juice b93flav Q10 Q15 Q16 female / overid;

Bison: model prBIS = *prBF93 PrBF80* b80correct b93correct BNI

bistext bisjuice bisflav Q10 Q15 Q16 female Dumbybis /overid;

run;

Sorry for taking so long to reply. Work has been very busy.

out of the SAS guide. Below that is my 3SLS code. scott

*Below is the copied text: *

*Page. 2112 F Chapter 29: The SYSLIN Procedure*

In this system, quantity demanded depends on price, income, and the price

of substitutes. Consumers

normally purchase more of a product when prices are lower and when income

and the price of substitute

goods are higher. Quantity supplied depends on price and the unit cost of

production. Producers supply more

when price is high and when unit cost is low. The actual price and quantity

sold are determined jointly by the

values that equate demand and supply.

Since price and quantity are jointly endogenous variables, both structural

equations are necessary to adequately

describe the observed values. A critical assumption of OLS is that the

regressors are uncorrelated with

the residual. When current endogenous variables appear as regressors in

other equations (endogenous

variables depend on each other), this assumption is violated and the OLS

parameter estimates are biased and

inconsistent. The bias caused by the violated assumptions is called

simultaneous equation bias. Neither the

demand nor supply equation can be estimated consistently by OLS.

*Variables in a System of Equations*

Before explaining how to use the SYSLIN procedure, it is useful to define

some terms. The variables in a

system of equations can be classified as follows:

• *Endogenous variables, *which are also called jointly dependent or

response variables, are the variables

determined by the system. Endogenous variables can also appear on the

right-hand side of equations.

•* Exogenous variables* are independent variables that do not depend on any

of the endogenous variables

in the system.

• *Predetermined variables *include both the exogenous variables and lagged

endogenous variables, which

are past values of endogenous variables determined at previous time

periods. PROC SYSLIN does not

compute lagged values; any lagged endogenous variables must be computed in

a preceding DATA step.

• *Instrumental variables* are predetermined variables used in obtaining

predicted values for the current

period endogenous variables by a first-stage regression. The use of

instrumental variables characterizes

estimation methods such as two-stage least squares and three-stage least

squares. Instrumental variables

estimation methods substitute these first-stage predicted values for

endogenous variables when they

appear as regressors in model equations.

Using PROC SYSLIN

First specify the input data set and estimation method in the PROC SYSLIN

statement. If any model uses

dependent regressors, and you are using an instrumental variables

regression method, declare the dependent

regressors with an ENDOGENOUS statement and declare the instruments with an

INSTRUMENTS statement.

Next, use MODEL statements to specify the structural equations of the

system.

The data is from an experimental auction: The endogenous variables are

winning prices. The instrument variables are lagged winning prices and

structural characteristics of the auction mechanism. Ten independent

auctions were held. So for instance, *Size* is the number of subjects in a

particular auction. Number of subjects participating varied across the ten

auctions held. The model statements represent the prices of the winning

bids for the 3 meat products being auctioned. Note: endogenous variables

are included on the right hand side of the model startment (bolded). The

other right hand side variables are exogenous variables representing

information from a demographic survey completed by subjects just prior to

the auction.

proc syslin data=a 3sls ;

*endogenous* prBIS prBF93 PrBF80;

*instruments * lagprbis lagpr80 lagpr93

dum80 dum93 *SIZE* dumround2 dumround3 dumround4 dumround5 ;

Beef80: model PrBF80= *prBIS prBF93* biscorrect B93correct BNI

b80text b80juice b80flav Q10 Q15 Q16 female /overid;

Beef93: model prBF93 = *prBIS PrBF80* biscorrect B80correct BNI

b93text b93juice b93flav Q10 Q15 Q16 female / overid;

Bison: model prBIS = *prBF93 PrBF80* b80correct b93correct BNI

bistext bisjuice bisflav Q10 Q15 Q16 female Dumbybis /overid;

run;

Sorry for taking so long to reply. Work has been very busy.

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I do not have a deep understanding of the subject. To me what it’s saying is when exogenous variables are used to predict endogenous variables they are called instrumental. It seems to imply that exogenous variable should be listed as instrumental when used for predicting endogenous variables.

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