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The PDLREG Procedure

Example 15.2: Money Demand Model

This example estimates the demand for money using the following dynamic specification:

m_{t} = a_{0} + b_{0} m_{t-1} +
\sum_{i=0}^5{c_{i} y_{t-i}} +
\sum_{i=0}^2{d_{i} r_{t-i}} +
\sum_{i=0}^3{f_{i} p_{t-i}} +
 u_{t}

where

mt = log of real money stock (M1)
yt = log of real GNP
rt = interest rate (commercial paper rate)
pt = inflation rate
ci, di, and fi  (i>0) are coefficients for the lagged variables

The following DATA step reads the data and transforms the real money and real GNP variables using the natural logarithm. Refer to Balke and Gordon (1986) for a description of the data.

   data a;
      input m1 gnp gdf r @@;
      m    = log( 100 * m1 / gdf );
      lagm = lag( m );
      y    = log( gnp );
      p    = log( gdf / lag( gdf ) );
      date = intnx( 'qtr', '1jan1968'd, _n_-1 );
      format date yyqc6.;
      label m    = 'Real Money Stock (M1)'
            lagm = 'Lagged Real Money Stock'
            y    = 'Real GNP'
            r    = 'Commercial Paper Rate'
            p    = 'Inflation Rate';
   cards;
      ... data lines are omitted ...
   ;
   
   proc print data=a(obs=5);
      var date m lagm y r p;
   run;

Output 15.2.1 shows a partial list of the data set.

Output 15.2.1: Partial List of the Data Set A
 
Obs date m lagm y r p
1 1968:1 5.44041 . 6.94333 5.58 .
2 1968:2 5.44732 5.44041 6.96226 6.08 0.011513
3 1968:3 5.45815 5.44732 6.97422 5.96 0.008246
4 1968:4 5.46492 5.45815 6.97661 5.96 0.014865
5 1969:1 5.46980 5.46492 6.98855 6.66 0.011005

The regression model is written for the PDLREG procedure with a MODEL statement. The LAGDEP= option is specified to test for the serial correlation in disturbances since regressors contain the lagged dependent variable LAGM.

   title 'Money Demand Estimation using Distributed Lag Model';
   title2 'Quarterly Data - 1968Q2 to 1983Q4';
   
   proc pdlreg data=a;
      model m = lagm y(5,3) r(2, , ,first) p(3,2) / lagdep=lagm;
   run;

The estimated model is shown in Output 15.2.2 and Output 15.2.3.

Output 15.2.2: Parameter Estimates
 
Money Demand Estimation using Distributed Lag Model
Quarterly Data - 1968Q2 to 1983Q4

The PDLREG Procedure

Dependent Variable m
  Real Money Stock (M1)
 
Ordinary Least Squares Estimates
SSE 0.00169815 DFE 48
MSE 0.0000354 Root MSE 0.00595
SBC -404.60169 AIC -427.4546
Regress R-Square 0.9712 Total R-Square 0.9712
Durbin h -0.7533 Pr < h 0.2256
 
Variable DF Estimate Standard Error t Value Approx
Pr > |t|
Intercept 1 -0.1407 0.2625 -0.54 0.5943
lagm 1 0.9875 0.0425 23.21 <.0001
y**0 1 0.0132 0.004531 2.91 0.0055
y**1 1 -0.0704 0.0528 -1.33 0.1891
y**2 1 0.1261 0.0786 1.60 0.1154
y**3 1 -0.4089 0.1265 -3.23 0.0022
r**0 1 -0.000186 0.000336 -0.55 0.5816
r**1 1 0.002200 0.000774 2.84 0.0065
r**2 1 0.000788 0.000249 3.16 0.0027
p**0 1 -0.6602 0.1132 -5.83 <.0001
p**1 1 0.4036 0.2321 1.74 0.0885
p**2 1 -1.0064 0.2288 -4.40 <.0001
 
Restriction DF L Value Standard Error t Value Approx
Pr > |t|
r(-1) -1 0.0164 0.007275 2.26 0.0223

Output 15.2.3: Estimates for Lagged Variables
 
Money Demand Estimation using Distributed Lag Model
Quarterly Data - 1968Q2 to 1983Q4

The PDLREG Procedure

Estimate of Lag Distribution
Variable Estimate Standard Error t Value Approx
Pr > |t|

-0.196           0                   0.2686
y(0) 0.268619 0.0910 2.95 0.0049 |                |************************|
y(1) -0.196484 0.0612 -3.21 0.0024 |****************|                        |
y(2) -0.163148 0.0537 -3.04 0.0038 |   *************|                        |
y(3) 0.063850 0.0451 1.42 0.1632 |                |******                  |
y(4) 0.179733 0.0588 3.06 0.0036 |                |****************        |
y(5) -0.120276 0.0679 -1.77 0.0827 |       *********|                        |

 
Money Demand Estimation using Distributed Lag Model
Quarterly Data - 1968Q2 to 1983Q4

The PDLREG Procedure

Estimate of Lag Distribution
Variable Estimate Standard Error t Value Approx
Pr > |t|

-0.001            0                  0.0018
r(0) -0.001341 0.000388 -3.45 0.0012 |*****************|                       |
r(1) -0.000751 0.000234 -3.22 0.0023 |        *********|                       |
r(2) 0.001770 0.000754 2.35 0.0230 |                 |***********************|
 
Estimate of Lag Distribution
Variable Estimate Standard Error t Value Approx
Pr > |t|

-1.104                           0   0.2634
p(0) -1.104051 0.2027 -5.45 <.0001 |********************************|        |
p(1) 0.082892 0.1257 0.66 0.5128 |                                |***     |
p(2) 0.263391 0.1381 1.91 0.0624 |                                |********|
p(3) -0.562556 0.2076 -2.71 0.0093 |                ****************|        |

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