6. Anexos
6.3. Ámbito de conocimiento del medio
6.3.2. Conocimiento del medio social y cultural
Description of each variable and how it was obtained
Acronym Name Transformation Source
PIB Gross Domestic Product Millions of 1991 Colones 3 month average BCCR CO Private Consumption Millions of 1991 Colones 3 month average BCCR G Government Consumption Millions of 1991 Colones 3 month average BCCR IK Capital Investment Millions of 1991 Colones 3 month average BCCR DE Change in stocks Millions of 1991 Colones 3 month average BCCR X Exports Millions of 1991 Colones 3 month average BCCR XB Exports of Goods Millions of 1991 Colones 3 month average BCCR M Imports Millions of 1991 Colones 3 month average BCCR MB Imports of Goods Millions of 1991 Colones 3 month average BCCR IG Government Income Million Colones Deflated with PG Thru last month of quarter BCCR RA Customs Duties Million Colones Deflated with PG Thru last month of quarter BCCR RR Income Tax Million Colones Deflated with PG Thru last month of quarter BCCR RV Sales Tax Million Colones Deflated with PG Thru last month of quarter BCCR RC Consumption Tax Million Colones Deflated with PG Thru last month of quarter BCCR GG Draft Expenses Million Colones Deflated with PG Thru last month of quarter BCCR GT Transfer Expenses Million Colones Deflated with PG Thru last month of quarter BCCR GI Interest Expenses Million Colones Deflated with PG Thru last month of quarter BCCR GDI Internal Debt Interest Expenses Million Colones Deflated with PG Thru last month of quarter BCCR GDE External Debt Interest Expenses Million Colones Deflated with PG Thru last month of quarter BCCR GCB Bank Commission Expenses Million Colones Deflated with PG Thru last month of quarter BCCR M1 Monetary Balances Million Colones Deflated with PD 3 month average BCCR CR Total Net Internal Credit Million Colones Deflated with PD 3 month average BCCR DPC Savings Deposit in National Currency Million Colones Deflated with PD 3 month average BCCR DPD Savings Deposits in Dollars Million Colones Deflated with PD 3 month average BCCR RM International Reserves BCCR Million Colones Deflated with PD 3 month average BCCR dR Change in International Reserves (RM) BCCR PIBE United States GDP Billons of Dollars, 1991 Quarterly data 1/ INPE Inflation Measured with PDE
PDE United States GDP Deflator 1/ IPCE United States Consumer Price Index 2/ INE Inflation Measured with IPCE
PP Oil Price Dollars per Barrel Quarterly Average 3/ ie LIBOR Rate Quarterly Average 3/ tc Exchange Rate Colones per Dollar Thru last month of quarter BCCR dev Devaluation
i Passive Basic Rate BCCR
PD GDP Deflator
inp Inflation measured with PD PG Public Expenditure Deflator (G)
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ing Public Expenditure Inflation IPC Consumer Price Index
BCCR, INEC in Inflation measured with IPC
BCCR, INEC ipt Transactional Price Index
BCCR, INEC ipnt Non Transactional Price Index
BCCR, INEC w Minimum Salary Monthly Index BCCR
SOURCES:
1/ US Department of Commerce, Bureau of Economic Analysis. Http://www.bea.doc.gov/bea/dn/home/gdp.htm 2/ US Department of Labor: Bureau of Labor Statistics, http://research.stlouisfed.org
3/ Spot Oil Price: West Texas Intermediate, http://research.stlouisfed.org Source: Taken from Saborío (2004).
V. 3-Stage Least Squares
Why 3-Stage Least Squares?
When estimating equation systems we find the estimator of ordinary least squares
(OLS) is inconsistent given the existence of correlation between the errors and the
endogenous variables of each equation. The OLS estimator would be consistent if the system were completely recursive, but this is not the case.
One method to obtain consistent estimations, given this problem, is that of instrumental variables. Therefore, if the system is exactly identified, the number of exogenous variables excluded in each equation would be equal to the number of endogenous variables included, and therefore the former could be used as instruments of the latter.
In our case, the system is over identified, so using a single subset of exogenous variables as instruments for those correlated with the errors would not be the best choice. This because the information on the endogenous variables included in the other exogenous variables would not be taken into account.
The two-stage least square (2SLS) proposes using a linear combination of the exogenous variables as instruments. Thus, this method proposes that the adjusted values of the regression of these variables be used as instruments for the endogenous variables included in the equation against all exogenous variables. It can be demonstrated that the use of this method provides consistent estimations, although it should be noted that when estimating equation by equation, this method is of “limited information”.
81 The two-stage estimator, when estimating equation by equation, ignores the relation between the errors of different equations, and is therefore inefficient compared to a generalized least squares (GLS) estimator.
The three-stage least square (3SLS) method uses the information provided in the variance and covariance matrix of the errors to “gain efficiency”, i.e., it uses GLS together with the estimation of instrumental variables.
Therefore, the 3SLS estimator is consistent and it can be demonstrated that, among the estimators of instrumental variables that only use variables found within the system, is efficient.
In addition, if the disturbances are normal, the parameters estimated using this method have the same asymptotic distribution than the parameters calculated by FIML (“full-information maximum likelihood”), which is efficient among all estimators. The 2- and 3-stage estimators are, respectively.
j ! j 1 j ! j E 2 MC y Z Z Z
j 1 ! j 1 j 1 ! j E 3 MC y I Z Z I Z Where Zj
YjXj , j
jj ! and is the variance – covariance matrix of the errors, j refers to an equation in the system and the variables with “chapeau” refer to estimates.It can be noted that the difference in the parameters estimated is due to the inclusion of the variance – covariance matrix, as GLS is used, which is done to take the correlation between the errors of different equations into account.
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