# The PANEL 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. See Feige (1964) for data description. All variables were transformed via natural logarithm. The data set `A` is shown below.

```data a;
length state \$ 2;
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;
CA   1949  6.2785  6.1924  4.4998  7.2056 -1.0700  0.1080  1.0664
CA   1950  6.4019  6.2106  4.6821  7.2889 -1.0106  0.1501  1.0767
CA   1951  6.5058  6.2729  4.8598  7.3827 -1.0024  0.4008  1.1291
CA   1952  6.4785  6.2729  5.0039  7.4000 -0.9970  0.4492  1.1227
CA   1953  6.4118  6.2538  5.1761  7.4200 -0.8916  0.4662  1.2110
CA   1954  6.4520  6.2971  5.3613  7.4478 -0.6951  0.4756  1.1924

... more lines ...

```

As shown in the following statements, the SORT procedure is used to sort the data into the required time series cross-sectional format; then PROC PANEL analyzes the data.

```proc sort data=a;
by state year;
run;

proc panel 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 20.1.1, Output 20.1.2, and Output 20.1.3, 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. 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 (see Output 20.1.2, Output 20.1.3, and Output 20.1.5). Time deposits are also substitutes for S&L shares in the time deposit demand equation (see Output 20.1.4), while these liquid assets are independent of each other in Output 20.1.5 (insignificant coefficient estimate of RT, ). 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 20.1.1: Demand for Demand Deposits, Fuller-Battese Variance Component with Two-Way Random-Effects Model

The PANEL Procedure
Fuller and Battese Variance Components (RanTwo)

Dependent Variable: d Per Capita Demand Deposits

Model Description
Estimation Method RanTwo
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 20.1.2: Demand for Demand Deposits, Parks Method

The PANEL 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 40.0198 DFE 72
MSE 0.5558 Root MSE 0.7455
R-Square 0.9263

Parameter Estimates
Variable DF Estimate Standard
Error
t Value Pr > |t| Label
Intercept 1 -2.66565 0.4250 -6.27 <.0001 Intercept
y 1 1.222569 0.0573 21.33 <.0001 Permanent Per Capita Personal Income
rd 1 -0.43591 0.0272 -16.03 <.0001 Service Charge on Demand Deposits
rt 1 0.041237 0.0284 1.45 0.1505 Interest on Time Deposits
rs 1 -0.26683 0.0886 -3.01 0.0036 Interest on S & L Association Shares

Output 20.1.3: Demand for Demand Deposits, DaSilva Method

The PANEL 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

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 20.1.4: Demand for Time Deposits, Parks Method

The PANEL 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 34.5713 DFE 72
MSE 0.4802 Root MSE 0.6929
R-Square 0.9517

Parameter Estimates
Variable DF Estimate Standard
Error
t Value Pr > |t| Label
Intercept 1 -5.33334 0.6780 -7.87 <.0001 Intercept
y 1 1.516344 0.1097 13.82 <.0001 Permanent Per Capita Personal Income
rd 1 -0.04791 0.0399 -1.20 0.2335 Service Charge on Demand Deposits
rt 1 0.227152 0.0449 5.06 <.0001 Interest on Time Deposits
rs 1 -0.42569 0.1708 -2.49 0.0150 Interest on S & L Association Shares

Output 20.1.5: Demand for Savings and Loan Shares, Parks Method

The PANEL 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 39.2550 DFE 72
MSE 0.5452 Root MSE 0.7384
R-Square 0.9017

Parameter Estimates
Variable DF Estimate Standard
Error
t Value Pr > |t| Label
Intercept 1 -8.09632 1.0628 -7.62 <.0001 Intercept
y 1 1.832988 0.1567 11.70 <.0001 Permanent Per Capita Personal Income
rd 1 0.576723 0.0589 9.80 <.0001 Service Charge on Demand Deposits
rt 1 -0.02705 0.0423 -0.64 0.5242 Interest on Time Deposits
rs 1 0.408066 0.1478 2.76 0.0073 Interest on S & L Association Shares