An empirical analysis of Halifax municipal water consumption

Figures & data

Table 1. Summary statistics.

	Mean	Standard Deviation	Minimum	Maximum	No.
Consumption^1	10,491,587	593,688	9,301,224	11,661,285	52
Customers	72,792	3693	65,960	79,384	52
Real Price^2	$1.23	$0.32	$0.66	$1.67	52
Employment	191,762	14,104	164,400	213,900	52
Population	374,877	12,591	353,490	398,049	52
Cooling Degree Days	28	33	0	90	52
^1Cubic metres consumed.^2Real Canadian dollars per cubic metre.

Figure 1 Time series of variables considered for statistical analysis.

Table 2. (a) Long-run cointegrating equations for 2SLS.

Dependent Variable: LOG(C/CSM)
Method A: Two Stage Least Squares with Instrumental Variables (2SLS)
Sample: 1996Q2–2009Q1
Included observations: 52
Variable	Coefficient	Std. Error	t-Statistic	Prob.
Constant	5.841118	0.290177	20.12947	0.0000
LOG(P-Fitted)	–0.459810	0.067873	–6.774557	0.0000
LOG(E/POP)	1.205643	0.414082	2.911607	0.0054
LOG(CLIM-CDD)	0.007899	0.004071	1.940212	0.0582
R-squared	0.683565	Mean dependent var.		4.970420
Adjusted R-squared	0.663788	Std. dev. dep. variable		0.089204
S.E. of regression	0.051724	Durbin-Watson statistic		1.908911
Sum squared residual	0.128417	Second stage SSR		0.108385
F-statistic	37.05918	Prob. (F-statistic)		0.000000
Seasonal unit root F	9.334572	Significance level		0.050000

Table 2. (b) Long-run cointegrating equations for OLS.

Dependent Variable: LOG(C/CSM)
Method B: Ordinary Least Squares (OLS)
Sample: 1996Q2–2009Q1
Included observations: 52
Variable	Coefficient	Std. Error	t-Statistic	Prob.
Constant	5.364783	0.216738	24.75236	0.0000
LOG(P)	–0.338242	0.047814	–7.074172	0.0000
LOG(E / POP)	0.529496	0.310225	1.706812	0.0943
LOG(CLIM-CDD)	0.008392	0.003818	2.197990	0.0328
R-squared	0.721123	Mean dependent var.		4.970420
Adjusted R-squared	0.703693	Std. dev. dep. variable		0.089204
S.E. of regression	0.048557	Durbin-Watson statistic		1.933079
Sum squared residual	0.113175	Log likelihood		85.59683
F-statistic	41.37295	Prob. (F-statistic)		0.000000
Seasonal unit root F	11.30590	Significance level		0.050000

Figure 2 Residuals of the long-run cointegrating equation.

Table 3. Short-run error correction equation.

Dependent Variable: D[LOG(C/CSM)]
Method: Least Squares
Sample (adjusted): 1996Q3–2009Q1
Included observations: 51 after adjustments
Variable	Coefficient	Std. Error	t-Statistic	Prob.
Constant	–0.005932	0.006794	–0.873175	0.3871
D[LOG(P-Fitted)]	–0.307930	0.055154	–5.583132	0.0000
D[LOG(E/POP)]	2.081462	0.483277	4.306979	0.0001
D[LOG(CLIM-CDD)]	–0.002615	0.003265	–0.800915	0.4273
U-Resid(–1)	–0.755348	0.164172	–4.600942	0.0000
R-squared	0.618567	Mean dependent var.		–0.005152
Adjusted R-squared	0.585398	Std. dev. dep. variable		0.071920
S.E. of regression	0.046309	Schwarz inf. criterion		–3.024678
Sum squared resid.	0.098647	Hannan-Quinn criterion		–3.141700
Log likelihood	86.95886	Durbin-Watson statistic		1.978498
F-statistic	18.64943	Prob. (F-statistic)		0.000000
Seasonal unit root F	10.54786	Significance level		0.050000

Table 4. Halifax municipal water customers equation.

Dependent Variable: LOG(CSM)
Method: Least Squares
Sample (adjusted): 1996Q2–2009Q1
Included observations: 52
MA Backcast: 1996Q1
Variable	Coefficient	Std. Error	t-Statistic	Prob.
Constant	–5.626068	0.884228	–6.362691	0.0000
LOG(POPULATION)	1.169585	0.112589	10.38811	0.0000
LOG(EMPLOYMENT)	0.148841	0.050596	2.941777	0.0050
MA(1)	0.812438	0.081444	9.975471	0.0000
R-squared	0.991491	Mean dependent var.		11.19410
Adjusted R-squared	0.990959	Std. dev. dep. variable		0.050950
S.E. of regression	0.004845	Schwarz inf. criterion		–7.597984
Sum squared residual	0.001127	Hannan-Quinn criterion		–7.690537
Log likelihood	205.4501	Durbin-Watson statistic		1.766018
F-statistic	1864.253	Prob. (F-statistic)		0.000000
Seasonal unit root F	35.28709	Significance level		0.050000