help: almon1 dialog:

Title

almon1: Shirley Almon Polynomial Distributed Lag Model

Table of Contents

Syntax

Description

Model

End Point Polynomial Restrictions Options

Other Options

Model Selection Diagnostic Criteria

Autocorrelation Tests

Heteroscedasticity Tests

Non Normality Tests

Saved Results

References

*** Examples

Author

Syntax

almon1 depvar indepvar [if] [in] , [ model(ols, als, gls, arch)

lag(#) pdl(#) endpr(0,1,2,3) order(#) noconstant nolag mfx(lin, log) tolog wvar(name)

iterate(#) technique(name) diag dn test ominv predict(new_var) resid(new_var) level(#) ]

Description

almon1 estimates Shirley Almon Polynomial Distributed Lag Model for many variables with the same lag order, endpoint restrictions, and polynomial degree order via (OLS - ALS - GLS - ARCH) Regression models.

almon1 used Allen McDowell (2004, p183) for polynomial order with some modifications to allow
inclusion or exclusion intercept, and also for estimation (ALS) and (ARCH) models.

almon1 can compute:

1- Autocorrelation, Heteroscedasticity, and Non Normality Tests.

2- Model Selection Diagnostic Criteria.

3- Marginal effects and elasticities in both short and long run.

4- Impact or short run multiplier, and long run or total distributed lag multiplier is the sum of lag coefficients for each variable. SUM(Coefs.) is called Long Run Dynamic Multiplier

5- Mean lag gives a measure of the speed of adjustment,it has a useful interpretation if lag coefficients are all positive, so the full time period to response is (Full Lag = Mean Lag +1)

6- Joint-F or Joint Chi2-Test to test the null hypothesis that all coefficients associated with the distributed lag variable are simultaneously equal to zero.

7- lag(#) order always starts from (0).

8- If pdl(0) and endpr(0) then unrestricted lag model is estimated.

9- Almon Polynomial Distributed Lag Model is useful in estimating supply response function for durable goods or perennial crops.

R2, R2 Adjusted, and F-Test, are obtained from 4 ways:

1- (Buse 1973) R2.

2- Raw Moments R2.

3- squared correlation between predicted (Yh) and observed dependent variable (Y).

4- Ratio of variance between predicted (Yh) and observed dependent variable (Y).

- Adjusted R2: R2_a=1-(1-R2)*(N-1)/(N-K-1).

- F-Test=R2/(1-R2)*(N-K-1)/(K).

Model

model description

ols Ordinary Least Squares (OLS)

als Autoregressive Least Squares (ALS)

gls Generalized Least Squares (GLS)

arch Autoregressive Conditional Heteroskedasticity (ARCH)

End Point Restriction Options

endpr Options Description

endppr(0) No Endpoint Polynomial Restrictions; the default
endppr(1) Left Side Endpoint Polynomial Restrictions
endppr(2) Right Side Endpoint Polynomial Restrictions
endppr(3) Left & Right Side Endpoint Polynomial Restrictions

Lag Length lag(#) must be greater than Polynomial Degree pdl(#)} by at lesat (1)

Endpoint restrictions may be specified for any polynomial. The use of Endpoint restrictions increases the number of restrictions imposed in the model.

Other Options

lag(#) Lag Length Order of Polynomial Distributed Lag Model; default (3)

pdl(#) Polynomial Degree Order (Pascal Triangle); default (2)

{almon1} estimates Almon polynomial distributed lag model at the same order with respect to: lag length, order of polynomial and Endpoint restriction on any independent variable in the model.

noconstant Exclude Constant Term from Equation

nolag Use Independent Variables in current period X(t), instead of lag X(t-1)

predict(new_var) Predicted values variable

resid(new_var) Residuals values variable

dn Use (N) divisor instead of (N-K) for Degrees of Freedom (DF) in (diag)

order(#) Lag Order for (ALS) and (ARCH) Models; default (1)

wvar(var) required variable name for Omega or Omega Inverse in (GLS) model

ominv Use Omega Inverse instead of Omega in (GLS) model

mfx(lin, log) functional form: Linear model (lin), or Log-Log model (log),
to compute Marginal Effects and Elasticities
- In Linear model: marginal effects are the coefficients (Bm),
and elasticities are (Es = Bm X/Y).
- In Log-Log model: elasticities are the coefficients (Es),
and the marginal effects are (Bm = Es Y/X).
- mfx(log) and tolog options must be combined, to transform variables to log form.

tolog Convert dependent and independent variables
to LOG Form in the memory for Log-Log regression.
tolog Transforms depvar and indepvars
to Log Form without lost the original data variables

iterate(#) number of iterations; Default is iter(300)

technique(name) specifies how the likelihood function is to be maximized

technique(nr) Newton-Raphson (NR) algorithm ; The default.
technique(bhhh) Berndt-Hall-Hall-Hausman (BHHH) algorithm.
technique(dfp) Davidon-Fletcher-Powell (DFP) algorithm.
technique(bfgs) Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm.

Model Selection Diagnostic Criteria

- Log Likelihood Function LLF
- Akaike Information Criterion (1974) AIC
- Akaike Information Criterion (1973) Log AIC
- Schwarz Criterion (1978) SC
- Schwarz Criterion (1978) Log SC
- Amemiya Prediction Criterion (1969) FPE
- Hannan-Quinn Criterion (1979) HQ
- Rice Criterion (1984) Rice
- Shibata Criterion (1981) Shibata
- Craven-Wahba Generalized Cross Validation (1979) GCV

Autocorrelation Tests

Ho: No Autocorrelation - Ha: Autocorrelation
- Breusch-Godfrey LM Test (drop 1 obs)
- Breusch-Godfrey LM Test (keep 1 obs)
- Breusch-Pagan-Godfrey LM Test

Heteroscedasticity Tests

Ho: Homoscedasticity - Ha: Heteroscedasticity
- Engle LM ARCH Test
- Hall-Pagan LM Test: E2 = Yh
- Hall-Pagan LM Test: E2 = Yh2
- Hall-Pagan LM Test: E2 = LYh2

Non Normality Tests

Ho: Normality - Ha: Non Normality
- Jarque-Bera LM Test

Saved Results

almon1 saves the following in e():

*** Model Selection Diagnostic Criteria:
e(N) number of observations
e(r2bu) R-squared (Buse 1973)
e(r2bu_a) R-squared Adj (Buse 1973)
e(r2raw) Raw Moments R2
e(r2raw_a) Raw Moments R2 Adj
e(f) F-test
e(fp) F-test P-Value
e(wald) Wald-test
e(waldp) Wald-test P-Value
e(r2h) R2 Between Predicted (Yh) and Observed DepVar (Y)
e(r2h_a) Adjusted r2h
e(fh) F-test due to r2h
e(fhp) F-test due to r2h P-Value
e(r2v) R2 Variance Ratio Between Predicted (Yh) and Observed DepVar (Y)
e(r2v_a) Adjusted r2v
e(fv) F-test due to r2v
e(fvp) F-test due to r2v P-Value
e(sig) Root MSE (Sigma)
e(llf) Log Likelihood Function LLF
e(aic) Akaike Information Criterion (1974) AIC
e(laic) Akaike Information Criterion (1973) Log AIC
e(sc) Schwarz Criterion (1978) SC
e(lsc) Schwarz Criterion (1978) Log SC
e(fpe) Amemiya Prediction Criterion (1969) FPE
e(hq) Hannan-Quinn Criterion (1979) HQ
e(rice) Rice Criterion (1984) Rice
e(shibata) Shibata Criterion (1981) Shibata
e(gcv) Craven-Wahba Generalized Cross Validation (1979) GCV

*** Autocorrelation Tests:
e(lmabgd#) Breusch-Godfrey LM Test (drop i obs)
e(lmabgdp#) Breusch-Godfrey LM Test (drop i obs) P-Value
e(lmabgk#) Breusch-Godfrey LM Test (keep i obs)
e(lmabgkp#) Breusch-Godfrey LM Test (keep i obs) P-Value
e(lmabpg#) Breusch-Pagan-Godfrey LM Test AR(i)
e(lmabpgp#) Breusch-Pagan-Godfrey LM Test AR(i) P-Value

*** Heteroscedasticity Tests:
e(lmharch) Engle LM ARCH Test AR(i)
e(lmharchp) Engle LM ARCH Test AR(i) P-Value
e(lmhhp1) Hall-Pagan LM Test
e(lmhhp1p) Hall-Pagan LM Test P-Value
e(lmhhp2) Hall-Pagan LM Test
e(lmhhp2p) Hall-Pagan LM Test P-Value
e(lmhhp3) Hall-Pagan LM Test
e(lmhhp3p) Hall-Pagan LM Test P-Value

*** Non Normality Tests:
e(lmnjb) Jarque-Bera LM Test
e(lmnjbp) Jarque-Bera LM Test P-Value

Matrixes
e(b) coefficient vector
e(V) variance-covariance matrix of the estimators

References

Shirley Montag Almon (1935–1975)
http://en.wikipedia.org/wiki/Shirley_Montag_Almon

Almon, Shirley (1965)
The Distributed Lag Between Capital Appropriations and Expenditures,
Econometrica, Vol. 33, No. 1, Jan.; 178-196.

Almon, Shirley (1968)
Lags Between Investment Decisions and Their Causes,
Rev. Econ. Stat., Vol. 50; 193-206.

Breusch, Trevor (1978)
"Testing for Autocorrelation in Dynamic Linear Models",
Aust. Econ. Papers, Vol. 17; 334-355.

Breusch, Trevor & Adrian Pagan (1980)
"The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics",
Review of Economic Studies 47; 239-253.

C.M. Jarque & A.K. Bera (1987)
"A Test for Normality of Observations and Regression Residuals"
International Statistical Review, Vol. 55; 163-172.

Damodar Gujarati (2004)
"Basic Econometrics"
4th Edition, McGraw Hill, New York, USA; 687.

Damodar Gujarati & Dawn C. Porter (2009)
"Basic Econometrics"
5th Edition, McGraw Hill, New York, USA; 645.

Engle, Robert (1982)
"Autoregressive Conditional Heteroscedasticity with Estimates of Variance of United Kingdom Inflation"
Econometrica, 50(4), July, 1982; 987-1007.

Frost, P.A. (1975)
"Some Properties of the Almon Lag Technique When One Searches for Degree of Polynomial and Lag,
J. Amer. Stat. Assoc., Vol. 70, March; 606-612.

Godfrey, L. (1978)
"Testing for Higher Order Serial Correlation in Regression Equations when the Regressors Include Lagged Dependent Variables",
Econometrica, Vol., 46; 1303-1310.

Greene, William (2007)
"Econometric Analysis",
6th ed., Upper Saddle River, NJ: Prentice-Hall; 387-388.

Griffiths, W., R. Carter Hill & George Judge (1993)
"Learning and Practicing Econometrics",
John Wiley & Sons, Inc., New York, USA; 602-606.

Harvey, Andrew (1990)
"The Econometric Analysis of Time Series",
2nd edition, MIT Press, Cambridge, Massachusetts.

McDowell, Allen (2004)
"From the Help Desk: Polynomial Distributed Lag Models",
Stata Journal, 4(2); 180–189.

Judge, Georege, R. Carter Hill, William . E. Griffiths, Helmut Lutkepohl, & Tsoung-Chao Lee (1988)
"Introduction To The Theory And Practice Of Econometrics",
2nd ed., John Wiley & Sons, Inc., New York, USA.

Judge, Georege, W. E. Griffiths, R. Carter Hill, Helmut Lutkepohl, & Tsoung-Chao Lee(1985)
"The Theory and Practice of Econometrics",
2nd ed., John Wiley & Sons, Inc., New York, USA; 615.

Kmenta, Jan (1986)
"Elements of Econometrics",
2nd ed., Macmillan Publishing Company, Inc., New York, USA; 718.

Maddala, G. (1992)
"Introduction to Econometrics",
2nd ed., Macmillan Publishing Company, New York, USA; 358-366.

Shehata, Emad Abd Elmessih (1996)
"Supply Response for Some Field Crops",
Cairo University - Faculty of Agriculture - Department of Economics - Egypt.

William E. Griffiths, R. Carter Hill and George G. Judge (1993)
"Learning and Practicing Econometrics",
John Wiley & Sons, Inc., New York, USA; 687.

Examples

clear all

db almon1

sysuse almon1.dta , clear

* (1) Ordinary Least Squares (OLS)

almon1 y x , model(ols) lag(3) pdl(2) mfx(lin)

almon1 y x

almon1 y x , model(ols) lag(3) pdl(0) end(0) mfx(lin)

almon1 y x z , model(ols) lag(3) pdl(2) end(0) mfx(lin)

almon1 y x z , model(ols) lag(4) pdl(3) end(0) mfx(lin)

tsset t

reg y l(0/3).x

almon1 y x , model(ols) lag(3) pdl(0) end(0)

almon1 y x , model(ols) lag(3) pdl(2) end(0)

almon1 y x , model(ols) lag(3) pdl(2) end(1)

almon1 y x , model(ols) lag(3) pdl(2) end(2)

almon1 y x , model(ols) lag(3) pdl(2) end(3)

almon1 y x , model(ols) lag(3) pdl(2) end(0) test mfx(lin)

almon1 y x , model(ols) lag(3) pdl(2) end(0) test mfx(log) tolog

almon1 y x , model(ols) lag(3) pdl(2) end(0) test mfx(lin) predict(Yh) resid(Ue)

* (2) Autoregressive Least Squares (ALS)

almon1 y x , model(als) lag(3) pdl(2) end(0) test mfx(lin)

almon1 y x , model(als) lag(3) pdl(2) end(0) test mfx(lin) order(1)

almon1 y x , model(als) lag(3) pdl(2) end(0) test mfx(lin) order(2)

* (3) Generalized Least Squares (GLS)

almon1 y x , model(gls) lag(3) pdl(2) wvar(x)

almon1 y x , model(gls) lag(3) pdl(2) wvar(x) ominv

* (4) Autoregressive Conditional Heteroskedasticity (ARCH)

almon1 y x , model(arch) lag(4) pdl(2) end(0) test mfx(lin)

almon1 y x , model(arch) lag(4) pdl(2) end(0) test mfx(lin) order(1)

almon1 y x , model(arch) lag(4) pdl(2) end(0) test mfx(lin) order(2)

* Example from Damodar [2009, p. 651].

clear all

sysuse almon2.dta , clear

almon1 y x , model(ols) lag(3) pdl(2) end(0)

* Example from Griffiths, Hill and Judge [1993, p. 687].

clear all

sysuse almon3.dta , clear

almon1 y x , model(ols) lag(8) pdl(2) end(0)

clear all

sysuse almon1.dta , clear

almon1 y x , model(ols) lag(3) pdl(2) end(0) test mfx(lin) predict(Yh) resid(Ue)

. clear all
. sysuse almon1.dta , clear
. almon1 y x , model(ols) lag(3) pdl(2) end(0) test mfx(lin) predict(Yh) resid(Ue)

==============================================================================
*** Shirley Almon Polynomial Distributed Lag Model ***
==============================================================================
*** Ordinary Least Squares (OLS) ***
*** No Endpoint Polynomial Restrictions ***
------------------------------------------------------------------------------
- Lag Length: Lag(3) - Polynomial Degree PDL(2) - Endpoint Restriction End(0)
------------------------------------------------------------------------------
Sample Size = 32 | Sample Range = 4 - 36
Wald Test = 1848.5961 | P-Value > Chi2(3) = 0.0000
F-Test = 616.1987 | P-Value > F(3 , 28) = 0.0000
R2 (R-Squared) = 0.9851 | Raw Moments R2 = 0.9999
R2a (Adjusted R2) = 0.9835 | Raw Moments R2 Adj. = 0.9999
Root MSE (Sigma) = 2.8448 | Log Likelihood Function = -76.7249
------------------------------------------------------------------------------
- R2h= 0.9851 R2h Adj= 0.9835 F-Test = 616.20 P-Value > F(3 , 28) 0.0000
- R2v= 0.9851 R2v Adj= 0.9835 F-Test = 616.20 P-Value > F(3 , 28) 0.0000
------------------------------------------------------------------------------
Akaike Criterion AIC = 161.4498 | Schwarz Criterion SC = 167.3128
------------------------------------------------------------------------------
- Joint F-Test Restriction x = 616.199 P > F(3, 28) 0.0000
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x |
--. | 1.202501 .2993337 4.02 0.000 .5893435 1.815658
L1. | .6681351 .27373 2.44 0.021 .1074245 1.228846
L2. | .0904505 .2717045 0.33 0.742 -.4661109 .6470119
L3. | -.530553 .3083609 -1.72 0.096 -1.162202 .1010957
|
_cons | 68.57335 6.809186 10.07 0.000 54.62537 82.52134
------------------------------------------------------------------------------

==============================================================================
*** Model Selection Diagnostic Criteria
------------------------------------------------------------------------------
* Stata Method
- Akaike Information Criterion (1974) AIC = 161.4498
- Schwarz Criterion (1978) SC = 167.3128
-------------------------------------------------------------------------
- Log Likelihood Function (LLF) = -76.7249
---------------------------------------------------------------------------
- Akaike Information Criterion (1974) AIC = 9.0923
- Akaike Information Criterion (1973) Log AIC = 2.2074
- Corrected Akaike Information Criterion AICC = 10.5738
---------------------------------------------------------------------------
- Schwarz Criterion (1978) SC = 10.9206
- Schwarz Criterion (1978) Log SC = 2.3906
---------------------------------------------------------------------------
- Final Prediction Criterion (1969) FPE = 9.1043
- Hannan-Quinn Criterion (1979) HQ = 9.6616
- Rice Criterion (1984) Rice = 9.4415
- Shibata Criterion (1981) Shibata = 8.8514
- Craven-Wahba Generalized Cross Validation (1979) GCV = 9.2488
------------------------------------------------------------------------------

==============================================================================
*** Autocorrelation Tests - (Model= ols)
------------------------------------------------------------------------------
Ho: No Autocorrelation - Ha: Autocorrelation
------------------------------------------------------------------------------
- Rho Value for Order(1) AR(1)= 0.5062
- Breusch-Godfrey LM Test (drop 1 obs) AR(1)= 8.4650 P-Value >Chi2(1) 0.0036
- Breusch-Godfrey LM Test (keep 1 obs) AR(1)= 8.7436 P-Value >Chi2(1) 0.0031
- Breusch-Pagan-Godfrey LM Test AR(1)= 2.9570 P-Value >Chi2(1) 0.0855
------------------------------------------------------------------------------

==============================================================================
*** Heteroscedasticity Tests - (Model= ols)
------------------------------------------------------------------------------
Ho: Homoscedasticity - Ha: Heteroscedasticity
------------------------------------------------------------------------------
- Engle LM ARCH Test AR(1) E2=E2_1-E2_1= 0.7476 P-Value > Chi2(1) 0.3872
------------------------------------------------------------------------------
- Hall-Pagan LM Test: E2 = Yh = 0.1063 P-Value > Chi2(1) 0.7444
- Hall-Pagan LM Test: E2 = Yh2 = 0.0904 P-Value > Chi2(1) 0.7637
- Hall-Pagan LM Test: E2 = LYh2 = 0.1239 P-Value > Chi2(1) 0.7248
------------------------------------------------------------------------------
- Harvey LM Test: LogE2 = X = 0.0362 P-Value > Chi2(2) 0.9821
- White Test -Koenker(R2): E2 = X = 0.0758 P-Value > Chi2(1) 0.7831
- White Test -B-P-G (SSR): E2 = X = 0.0647 P-Value > Chi2(1) 0.7993
------------------------------------------------------------------------------

==============================================================================
*** Non Normality Tests - (Model= ols)
------------------------------------------------------------------------------
Ho: Normality - Ha: Non Normality
------------------------------------------------------------------------------
- Jarque-Bera LM Test = 0.2503 P-Value > Chi2(2) 0.8824
- White IM Test = 1.6090 P-Value > Chi2(2) 0.4473
- Geary LM Test = -3.0347 P-Value > Chi2(2) 0.2193
------------------------------------------------------------------------------

*** Marginal Effect - Elasticity (Model= OLS): Linear *

+----------------------------------------------------------------------------+
| Variable | Marginal Effect(B) | Elasticity(Es) | Mean |
|-------------+--------------------+--------------------+--------------------|
| x | 1.2025 | 0.6735 | 196.6850 |
| L.x | 0.6681 | 0.3710 | 194.9896 |
| L2.x | 0.0905 | 0.0498 | 193.2746 |
| L3.x | -0.5306 | -0.2896 | 191.6763 |
+----------------------------------------------------------------------------+
Mean of Dependent Variable = 351.1539

------------------------------------------------------------------------------
* Variable Mean Lag Full Lag SUM(Coefs.) Std. Err. T-Test P>|t|
------------------------------------------------------------------------------
x -0.5191 0.4809 1.4305 0.0356 40.1586 0.0000
------------------------------------------------------------------------------

------------------------------------------------------------------------------
* Variable Marginal Effect (B) | Elasticity (Es)
Short Run Long Run | Short Run Long Run
------------------------------------------------------------------------------
x 1.2025 1.4305 | 0.6735 0.8047
------------------------------------------------------------------------------

Author

Emad Abd Elmessih Shehata
Professor (PhD Economics)
Agricultural Research Center - Agricultural Economics Research Institute - Egypt
Email: emadstat@hotmail.com
WebPage at IDEAS: http://ideas.repec.org/f/psh494.html
WebPage at EconPapers: http://econpapers.repec.org/RAS/psh494.htm

ALMON1 Citation

Shehata, Emad Abd Elmessih (2014)

ALMON1: "Stata Module to Estimate Shirley Almon Polynomial Distributed Lag Model"

Online Help:

*** Distributed Lag Models
almon1 Shirley Almon Polynomial Distributed Lag Model (ALMON1)
almon Shirley Almon Generalized Polynomial Distributed Lag Model (ALMON)
dlagaj Alt France-Jan Tinbergen Distributed Lag Model (DLAGAJ)
dlagdj Dale Jorgenson Rational Distributed Lag Model (DLAGDJ)
dlagfd Frank De Leeuw Inverted V Distributed Lag Model (DLAGFD)
dlagif Irving Fisher Arithmetic Distributed Lag Model (DLAGIF)
dlagmf Milton Fridman Partial Adjustment-Adaptive Expectations
Distributed Lag Model (DLAGMF)
dlagmn Marc Nerlove Partial Adjustment Distributed Lag Model (DLAGMN)
dlagrs Robert Solow Pascal Triangle Distributed Lag Model (DLAGRS)
dlagrw Rudolf Wolffram Segmenting Partial Adjustment Distributed Lag (DLAGRW)
dlagtq Tweeten-Quance Partial Adjustment Distributed Lag Model (DLAGTQ)

*** Demand System Models
dsles Linear Expenditure System (LES) (DSLES)
dseles Extended Linear Expenditure System (ELES) (DSELES)
dsqes Quadratic Expenditure System (QES) (DSQES)
dsrot Rotterdam Demand System (DSROT)
dsroti Inverse Rotterdam Demand System (DSROTI)
dsaidsla Linear Approximation Almost Ideal Demand System (AIDS-LA) (DSAIDSLA)
dsaidsfd First Difference Almost Ideal Demand System (AIDS-FD) (DSAIDSFD)
dsaidsi Inverse Almost Ideal Demand System(AIDS-I) (DSAIDSI)
dsarm Primal Armington Demand System (DSARM)
dsengel Engel Demand System (DSENGEL)
dsgads Generalized AddiLog Demand System (GADS) (DSGADS)
dstlog Transcendental Logarithmic Demand System (DSTLOG)
dsw Working Demand System (DSW)

pfm Production Function Models (PFM)

ffm Profit Function Models (FFM)

cfm Cost Function Models (CFM)

iic Investment Indicators Criteria (IIC)

iot Leontief Input - Output Table (IOT)

index Index Numbers (INDEX)

mef Marketing Efficiency Models (MEF)

pam Policy Analysis Matrix (PAM)
pem Partial Equilibrium Model (PEM)

*** Financial Analysis Models
fam Financial Analysis Models (FAM)
xbcr Benefit-Cost Ratio (XBCR)
xirr Internal Rate of Return (XIRR)
xmirr Modified Internal Rate of Return (XMIRR)
xnfv Net Future Value (XNFV)
xnpv Net Present Value (XNPV)
xpp Payback Period (XPP)

*** Trade Models
wtm World Trade Models (WTM)
wtic World Trade Indicators Criteria (WTIC)
wtrgc World Trade Regional Geographical Concentration (WTRGC)
wtsgc World Trade Sectoral Geographical Concentration (WTSGC)
wtrca World Trade Revealed Comparative Advantage (WTRCA)