PROC PDLREG: Industrial Conference Board Data :: SAS/ETS(R) 9.22 User's Guide

The PDLREG Procedure

Example 20.1 Industrial Conference Board Data

In this example, a second-degree Almon polynomial lag model is fit to a model with a five-period lag, and dummy variables are used for quarter effects. The PDL model is estimated using capital appropriations data series for the period 1952 to 1967. The estimation model is written

$\text{[math]}$
$\text{[math]}$

where CE represents capital expenditures and CA represents capital appropriations.

title 'National Industrial Conference Board Data';
title2 'Quarterly Series - 1952Q1 to 1967Q4';

data a;
   input ce ca @@;
   qtr = mod( _n_-1, 4 ) + 1;
   q1  = qtr=1;
   q2  = qtr=2;
   q3  = qtr=3;
datalines;

   ... more lines ...

proc pdlreg data=a;
   model ce = q1 q2 q3 ca(5,2) / dwprob;
run;

The printed output produced by the PDLREG procedure is shown in Output 20.1.1. The small Durbin-Watson test indicates autoregressive errors.

Output 20.1.1 Printed Output Produced by PROC PDLREG

National Industrial Conference Board Data

Quarterly Series - 1952Q1 to 1967Q4

The PDLREG Procedure

Dependent Variable	ce

Ordinary Least Squares Estimates
SSE	1205186.4	DFE	48
MSE	25108	Root MSE	158.45520
SBC	733.84921	AIC	719.797878
MAE	107.777378	AICC	722.180856
MAPE	3.71653891	HQC	725.231641
Durbin-Watson	0.6157	Regress R-Square	0.9834
		Total R-Square	0.9834

Parameter Estimates
Variable	DF	Estimate	Standard Error	t Value	Approx Pr > \|t\|
Intercept	1	210.0109	73.2524	2.87	0.0061
q1	1	-10.5515	61.0634	-0.17	0.8635
q2	1	-20.9887	59.9386	-0.35	0.7277
q3	1	-30.4337	59.9004	-0.51	0.6137
ca**0	1	0.3760	0.007318	51.38	<.0001
ca**1	1	0.1297	0.0251	5.16	<.0001
ca**2	1	0.0247	0.0593	0.42	0.6794

Estimate of Lag Distribution
Variable	Estimate	Standard Error	t Value	Approx Pr > \|t\|	0 0.2444
ca(0)	0.089467	0.0360	2.49	0.0165	\|*************** \|
ca(1)	0.104317	0.0109	9.56	<.0001	\|***************** \|
ca(2)	0.127237	0.0255	5.00	<.0001	\|********************* \|
ca(3)	0.158230	0.0254	6.24	<.0001	\|*************************** \|
ca(4)	0.197294	0.0112	17.69	<.0001	\|********************************* \|
ca(5)	0.244429	0.0370	6.60	<.0001	\|*****************************************\|

The following statements use the REG procedure to fit the same polynomial distributed lag model. A DATA step computes lagged values of the regressor X, and RESTRICT statements are used to impose the polynomial lag distribution. Refer to Judge et al. (1985, pp. 357–359) for the restricted least squares estimation of the Almon distributed lag model.

data b;
   set a;
   ca_1 = lag( ca );
   ca_2 = lag2( ca );
   ca_3 = lag3( ca );
   ca_4 = lag4( ca );
   ca_5 = lag5( ca );
run;

proc reg data=b;
   model  ce = q1 q2 q3 ca ca_1 ca_2 ca_3 ca_4 ca_5;
   restrict   - ca + 5*ca_1 - 10*ca_2 + 10*ca_3 - 5*ca_4 +   ca_5;
   restrict     ca - 3*ca_1 +  2*ca_2 +  2*ca_3 - 3*ca_4 +   ca_5;
   restrict  -5*ca + 7*ca_1 +  4*ca_2 -  4*ca_3 - 7*ca_4 + 5*ca_5;
run;

The REG procedure output is shown in Output 20.1.2.

Output 20.1.2 Printed Output Produced by PROC REG

National Industrial Conference Board Data

Quarterly Series - 1952Q1 to 1967Q4

The REG Procedure

Model: MODEL1

Dependent Variable: ce

Analysis of Variance
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	6	71343377	11890563	473.58	<.0001
Error	48	1205186	25108
Corrected Total	54	72548564

Root MSE	158.45520	R-Square	0.9834
Dependent Mean	3185.69091	Adj R-Sq	0.9813
Coeff Var	4.97397

Parameter Estimates
Variable	DF	Parameter Estimate	Standard Error	t Value	Pr > \|t\|
Intercept	1	210.01094	73.25236	2.87	0.0061
q1	1	-10.55151	61.06341	-0.17	0.8635
q2	1	-20.98869	59.93860	-0.35	0.7277
q3	1	-30.43374	59.90045	-0.51	0.6137
ca	1	0.08947	0.03599	2.49	0.0165
ca_1	1	0.10432	0.01091	9.56	<.0001
ca_2	1	0.12724	0.02547	5.00	<.0001
ca_3	1	0.15823	0.02537	6.24	<.0001
ca_4	1	0.19729	0.01115	17.69	<.0001
ca_5	1	0.24443	0.03704	6.60	<.0001
RESTRICT	-1	623.63242	12697	0.05	0.9614*
RESTRICT	-1	18933	44803	0.42	0.6772*
RESTRICT	-1	10303	18422	0.56	0.5814*

* Probability computed using beta distribution.

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