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The TSCSREG Procedure

Example 20.1: Analyzing Demand for Liquid Assets

In this example, the demand equations for liquid assets are estimated. The demand function for the demand deposits is estimated under three error structures while demand equations for time deposits and savings and loan (S & L) association shares are calculated using the Parks method. The data for seven states (CA, DC, FL, IL, NY, TX, and WA) are selected out of 49 states. Refer to Feige (1964) for data description. All variables were transformed via natural logarithm. The first five observations of the data set A are shown in Output 20.1.1.


   data a;
      input state $ year d t s y rd rt rs;
      label d = 'Per Capita Demand Deposits'
            t = 'Per Capita Time Deposits'
            s = 'Per Capita S & L Association Shares'
            y = 'Permanent Per Capita Personal Income'
            rd = 'Service Charge on Demand Deposits'
            rt = 'Interest on Time Deposits'
            rs = 'Interest on S & L Association Shares';
   datalines;
      ... data lines are omitted ...
   ;


   proc print data=a(obs=5);
   run;

Output 20.1.1: A Sample of Liquid Assets Data
 
Obs state year d t s y rd rt rs
1 CA 1949 6.2785 6.1924 4.4998 7.2056 -1.0700 0.1080 1.0664
2 CA 1950 6.4019 6.2106 4.6821 7.2889 -1.0106 0.1501 1.0767
3 CA 1951 6.5058 6.2729 4.8598 7.3827 -1.0024 0.4008 1.1291
4 CA 1952 6.4785 6.2729 5.0039 7.4000 -0.9970 0.4492 1.1227
5 CA 1953 6.4118 6.2538 5.1761 7.4200 -0.8916 0.4662 1.2110

The SORT procedure is used to sort the data into the required time series cross-sectional format. Then PROC TSCSREG analyzes the data.


   proc sort data=a;
      by state year;
   run;
   
   title 'Demand for Liquid Assets';
   proc tscsreg data=a;
      model d = y rd rt rs / fuller parks dasilva m=7;
      model t = y rd rt rs / parks;
      model s = y rd rt rs / parks;
      id state year;
   run;

The income elasticities for liquid assets are greater than 1 except for the demand deposit income elasticity (0.692757) estimated by the Da Silva method. In Output 20.1.2, Output 20.1.3 and Output 20.1.4, the coefficient estimates (-0.29094, -0.43591, and -0.27736) of demand deposits (RD) imply that demand deposits increase significantly as the service charge is reduced. The price elasticities (0.227152 and 0.408066) for time deposits (RT) and S & L association shares (RS) have the expected sign and thus an increase in the interest rate on time deposits or S & L shares will increase the demand for the corresponding liquid asset. Demand deposits and S & L shares appear to be substitutes ( Output 20.1.2, Output 20.1.3, Output 20.1.4, and Output 20.1.6). Time deposits are also substitutes for S & L shares in the time deposit demand equation ( Output 20.1.5), while these liquid assets are independent of each other in Output 20.1.6 (insignificant coefficient estimate of RT, -0.02705). Demand deposits and time deposits appear to be weak complements in Output 20.1.3 and Output 20.1.4, while the cross elasticities between demand deposits and time deposits are not significant in Output 20.1.2 and Output 20.1.5.

Output 20.1.2: Demand for Demand Deposits -- Fuller-Battese Method
 
Demand for Liquid Assets

The TSCSREG Procedure
Fuller and Battese Method Estimation
Dependent Variable: d Per Capita Demand Deposits

Model Description
Estimation Method Fuller
Number of Cross Sections 7
Time Series Length 11
 
Fit Statistics
SSE 0.0795 DFE 72
MSE 0.0011 Root MSE 0.0332
R-Square 0.6786    
 
Variance Component Estimates
Variance Component for Cross Sections 0.03427
Variance Component for Time Series 0.00026
Variance Component for Error 0.00111
 
Hausman Test for Random Effects
DF m Value Pr > m
4 5.51 0.2385
 
Parameter Estimates
Variable DF Estimate Standard Error t Value Pr > |t| Label
Intercept 1 -1.23606 0.7252 -1.70 0.0926 Intercept
y 1 1.064058 0.1040 10.23 <.0001 Permanent Per Capita Personal Income
rd 1 -0.29094 0.0526 -5.53 <.0001 Service Charge on Demand Deposits
rt 1 0.039388 0.0278 1.42 0.1603 Interest on Time Deposits
rs 1 -0.32662 0.1140 -2.86 0.0055 Interest on S & L Association Shares

Output 20.1.3: Demand for Demand Deposits -- Parks Method
 
Demand for Liquid Assets

The TSCSREG Procedure
Parks Method Estimation
Dependent Variable: d Per Capita Demand Deposits

Model Description
Estimation Method Parks
Number of Cross Sections 7
Time Series Length 11
 
Fit Statistics
SSE 73.3696 DFE 72
MSE 1.0190 Root MSE 1.0095
R-Square 0.9263    
 
Parameter Estimates
Variable DF Estimate Standard Error t Value Pr > |t| Label
Intercept 1 -2.66565 0.3139 -8.49 <.0001 Intercept
y 1 1.222569 0.0423 28.87 <.0001 Permanent Per Capita Personal Income
rd 1 -0.43591 0.0201 -21.71 <.0001 Service Charge on Demand Deposits
rt 1 0.041237 0.0210 1.97 0.0530 Interest on Time Deposits
rs 1 -0.26683 0.0654 -4.08 0.0001 Interest on S & L Association Shares

Output 20.1.4: Demand for Demand Deposits -- Da Silva Method
 
Demand for Liquid Assets

The TSCSREG Procedure
Da Silva Method Estimation
Dependent Variable: d Per Capita Demand Deposits

Model Description
Estimation Method DaSilva
Number of Cross Sections 7
Time Series Length 11
Order of MA Error Process 7
 
Fit Statistics
SSE 21609.8923 DFE 72
MSE 300.1374 Root MSE 17.3245
R-Square 0.4995    
 
Variance Component Estimates
Variance Component for Cross Sections 0.03063
Variance Component for Time Series 0.000148
 
Estimates of Autocovariances
Lag Gamma
0 0.0008558553
1 0.0009081747
2 0.0008494797
3 0.0007889687
4 0.0013281983
5 0.0011091685
6 0.0009874973
7 0.0008462601

 
Demand for Liquid Assets

The TSCSREG Procedure
Da Silva Method Estimation
Dependent Variable: d Per Capita Demand Deposits

Parameter Estimates
Variable DF Estimate Standard Error t Value Pr > |t| Label
Intercept 1 1.281084 0.0824 15.55 <.0001 Intercept
y 1 0.692757 0.00677 102.40 <.0001 Permanent Per Capita Personal Income
rd 1 -0.27736 0.00274 -101.18 <.0001 Service Charge on Demand Deposits
rt 1 0.009378 0.00171 5.49 <.0001 Interest on Time Deposits
rs 1 -0.09942 0.00601 -16.53 <.0001 Interest on S & L Association Shares

Output 20.1.5: Demand for Time Deposits -- Parks Method
 
Demand for Liquid Assets

The TSCSREG Procedure
Parks Method Estimation
Dependent Variable: t Per Capita Time Deposits

Model Description
Estimation Method Parks
Number of Cross Sections 7
Time Series Length 11
 
Fit Statistics
SSE 63.3807 DFE 72
MSE 0.8803 Root MSE 0.9382
R-Square 0.9517    
 
Parameter Estimates
Variable DF Estimate Standard Error t Value Pr > |t| Label
Intercept 1 -5.33334 0.5007 -10.65 <.0001 Intercept
y 1 1.516344 0.0810 18.72 <.0001 Permanent Per Capita Personal Income
rd 1 -0.04791 0.0294 -1.63 0.1082 Service Charge on Demand Deposits
rt 1 0.227152 0.0332 6.85 <.0001 Interest on Time Deposits
rs 1 -0.42569 0.1262 -3.37 0.0012 Interest on S & L Association Shares

Output 20.1.6: Demand for Savings and Loan Shares -- Parks Method
 
Demand for Liquid Assets

The TSCSREG Procedure
Parks Method Estimation
Dependent Variable: s Per Capita S & L Association Shares

Model Description
Estimation Method Parks
Number of Cross Sections 7
Time Series Length 11
 
Fit Statistics
SSE 71.9675 DFE 72
MSE 0.9995 Root MSE 0.9998
R-Square 0.9017    
 
Parameter Estimates
Variable DF Estimate Standard Error t Value Pr > |t| Label
Intercept 1 -8.09632 0.7850 -10.31 <.0001 Intercept
y 1 1.832988 0.1157 15.84 <.0001 Permanent Per Capita Personal Income
rd 1 0.576723 0.0435 13.26 <.0001 Service Charge on Demand Deposits
rt 1 -0.02705 0.0312 -0.87 0.3891 Interest on Time Deposits
rs 1 0.408066 0.1092 3.74 0.0004 Interest on S & L Association Shares

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