Example 8.5 Money Demand Model

This example estimates the log-log money demand equation by using the maximum likelihood method. The money demand model contains four explanatory variables. The lagged nominal money stock M1 is divided by the current price level GDF to calculate a new variable M1CP since the money stock is assumed to follow the partial adjustment process. The variable M1CP is then used to estimate the coefficient of adjustment. All variables are transformed using the natural logarithm with a DATA step. Refer to Balke and Gordon (1986) for a data description.

The first eight observations are printed using the PRINT procedure and are shown in Output 8.5.1. Note that the first observation of the variables M1CP and INFR are missing. Therefore, the money demand equation is estimated for the period 1968:2 to 1983:4 since PROC AUTOREG ignores the first missing observation. The DATA step that follows generates the transformed variables.

   data money;
      date = intnx( 'qtr', '01jan1968'd, _n_-1 );
      format date yyqc6.;
      input m1 gnp gdf ycb @@;
      m = log( 100 * m1 / gdf );
      m1cp = log( 100 * lag(m1) / gdf );
      y = log( gnp );
      intr = log( ycb );
      infr = 100 * log( gdf / lag(gdf) );
      label m    = 'Real Money Stock (M1)'
            m1cp = 'Lagged M1/Current GDF'
            y    = 'Real GNP'
            intr = 'Yield on Corporate Bonds'
            infr = 'Rate of Prices Changes';
   datalines;
   
   ... more lines ...   

The money demand equation is first estimated using OLS. The DW=4 option produces generalized Durbin-Watson statistics up to the fourth order. Their exact marginal probabilities (p-values) are also calculated with the DWPROB option. The Durbin-Watson test indicates positive first-order autocorrelation at, say, the 10% confidence level. You can use the Durbin-Watson table, which is available only for 1% and 5% significance points. The relevant upper () and lower () bounds are and , respectively, at 5% significance level. However, the bounds test is inconvenient, since sometimes you may get the statistic in the inconclusive region while the interval between the upper and lower bounds becomes smaller with the increasing sample size. The PROC step follows:

   title 'Partial Adjustment Money Demand Equation';
   title2 'Quarterly Data - 1968:2 to 1983:4';
   
   proc autoreg data=money outest=est covout;
      model m = m1cp y intr infr / dw=4 dwprob;
   run;