1. MEASURING POVERTY RATES IN CANADA USING POOLED OLS
MODEL
Abstract
The aim of this paper is to create an econometric model which can accurately predict the
Low Income Cut-Off after tax (LICO-AT) poverty rate in Canada using panel data which follows
provinces from 1994-2010. The variables used are the LICO-AT poverty rate, average market
income, average government transfers, low income transition exit and entry rates, persons with 0
to 8 year of education, food price index, shelter price index, non-permanent residents,
unemployment rate, and net interprovincial migrants. The paper first introduces the topic and its
importance, and then describes the data being used. Choosing between the pooled OLS, the fixed
effects and the random effects model, the best econometric model is determined and its results
are displayed after describing the data. The paper also employs the use of a quantile regression in
order to give a complete empirical analysis. In the end, it is concluded that the pooled OLS
model is the best model to predict the LICO-AT poverty rate in Canada and that the strongest
predictors are the low income transition exit and entry rates, average market income, and persons
with 0 to 8 years of schooling.
Introduction
Poverty in Canada has become a greater concern among Canadians in recent years with
many Canadians finding it difficult to keep up with the costs of living. In 2011 Canada ranked
24th out of 34 in lowest poverty rate among Organization for Economic Co-operation and
Development (OECD) countries with a poverty rate of 8.8% according to LICO-AT poverty line
measure. The LICO-AT is the level at which a family spends 63.6 per cent or more of its after
tax income on food, shelter, and clothing. The average gap between the LICO-AT poverty line
and household income below the LICO-AT is 33% (Citizens of Public Justice, 2012). Therefore
a low income family of four living in a city with a population of more than 500, 000 expected
income would be $24,458 which is $12,046 under the LICO-AT poverty line (Citizens of Public
Justice, 2012). Such a high poverty rate and significant depth of poverty for a country as wealthy
as Canada illustrates the lack of social welfare for the poorest Canadians.
2. The cost of poverty in Canada is very significant at $72 to $84 billion a year; for
Ontarians this means between $2,299 and $2,895 every year, and for British Columbians, this
equates to over $2,100 each year. The costs comprise of both private and social costs (Laurie,
2008). The private costs are the lost potential income and poverty induced costs that individuals
suffer while the social costs are the lost potential tax revenue and poverty induced costs that the
government suffers. The total cost of poverty considers remedial, intergenerational and
opportunity costs. Seven provinces have a poverty strategy (NL, NB, NS, QC, ON, MB, PE), and
four provinces/territories are in the process of creating a poverty plan (YK, NT, NU, AB).
Quebec released its first in 2002 and was the first province to do so, followed by Newfoundland
and Labrador in 2006. Ontario released its first in 2008 and in 2009 Manitoba, Nova Scotia and
New Brunswick released their first poverty reduction strategies; however there is currently no
federal poverty reduction strategy (House of Commons Committees, 2015). The table below
shows the LICO-AT poverty rates over time for different groups.
3. The table shows that the poverty rate is trending downward across provinces. This paper aims to
provide empirical results that will help explain the poverty rate and how best to address it.
This paper builds on a model found in Sinnathurai Vijayakumar‟s “An Empirical Study
on the Nexus of Poverty, GDP Growth, Dependency Ratio and Employment in Developing
Countries”. The study by Vijayakumar looks to find the link between poverty, economic growth,
agricultural and industrial employment and dependency ratio in developing countries and relies
on cross country data from forty one countries selected from Asia, Latin America and Sub-
Saharan Africa (Vijayakumar, 2013). Their paper concludes that stable economic growth based
on improved labour productivity and labour intensive technology is the best way to reduce
poverty among developing countries. This paper modifies the approach taken in Vijayakumar‟s
study by looking at provinces across time and using different variables but similarly accounting
for economic growth and employment in measuring poverty rates.
Data
The data this paper uses was taken from the Statistics Canada website and the
information needed to access this data is within the reference section of this paper. The
frequency of the data is yearly and covers the period 1994 to 2010 for the ten Canadian
provinces. Therefore the dataset contains 170 observations. The variables used are:
Description Variable name
LICO-AT Poverty Rate licoat
Average Market Income mi
Average Government Transfers gt
Low Income Transition Exit Rate litex
Low Income Transition Entry Rate liten
# of Persons with 0 to 8 years education
(x1000)
edu
Food Price Index fpi
Shelter Price Index spi
# of non-Permanent Residents npr
4. Net Interprovincial Migrants ipm
Unemployment Rate unemp
Province 1-10 from east to west. Code in Appendix
The average market income and the unemployment rate are closely related to Gross
Domestic Product growth rate and therefore can be seen as by-products of economic growth,
where strong positive growth increases the average market income and decreases the
unemployment rate. The variable edu is a proxy for persons with low literacy skills and the
variable npr is a proxy for recent immigrants.
The panel summary statistics of these variables are:
within 1.31396 5.809375 11.75313 T = 16
between 3.476051 5.275 16.10625 n = 10
unemp overall 8.778125 3.559427 3.5 18.9 N = 160
within 14.23205 78.85437 145.2544 T = 16
between 2.335252 102.6125 110.95 n = 10
spi overall 105.1044 14.40452 80.6 151.1 N = 160
within 11.49651 84.625 127.0437 T = 16
between .850852 100.7313 103.5125 n = 10
fpi overall 102.3563 11.52499 83 128.2 N = 160
within 51.65664 17.5275 442.9275 T = 16
between 293.2316 10.2625 818.0938 n = 10
edu overall 215.1213 283.7982 7.6 1045.9 N = 160
within .9841851 1.309375 6.703125 T = 16
between .3932399 2.74375 4.1875 n = 10
liten overall 3.453125 1.052934 .6 6.5 N = 160
within 6.347922 16.19535 53.89535 T = 16
between 4.28211 29.5125 43.4875 n = 10
litex overall 36.13871 7.543389 19.5 59.9 N = 160
within 7571.809 -24006.56 25059.44 T = 16
between 8107.436 -9201.188 20799.63 n = 10
ipm overall 64.06875 10810.26 -20047 45795 N = 160
within 18663.17 -21633.41 108920.6 T = 16
between 53495 570.875 167134.2 n = 10
npr overall 36958.78 54222.28 273 239096 N = 160
within 5467.612 39393.75 69393.75 T = 16
between 9001.494 44268.75 69837.5 n = 10
mi overall 54031.25 10162.56 36200 85200 N = 160
within 442.2418 8235.625 10835.63 T = 16
between 1679.332 6625 12431.25 n = 10
gt overall 9091.875 1658.217 6200 13400 N = 160
within 2.344163 6.174375 16.00563 T = 16
between 2.038006 6.8 13.89375 n = 10
licoat overall 10.84938 3.042487 3.9 18.5 N = 160
Variable Mean Std. Dev. Min Max Observations
within 1.31396 5.809375 11.75313 T = 16
between 3.476051 5.275 16.10625 n = 10
unemp overall 8.778125 3.559427 3.5 18.9 N = 160
within 14.23205 78.85437 145.2544 T = 16
between 2.335252 102.6125 110.95 n = 10
spi overall 105.1044 14.40452 80.6 151.1 N = 160
within 11.49651 84.625 127.0437 T = 16
between .850852 100.7313 103.5125 n = 10
fpi overall 102.3563 11.52499 83 128.2 N = 160
within 51.65664 17.5275 442.9275 T = 16
between 293.2316 10.2625 818.0938 n = 10
edu overall 215.1213 283.7982 7.6 1045.9 N = 160
within .9841851 1.309375 6.703125 T = 16
between .3932399 2.74375 4.1875 n = 10
liten overall 3.453125 1.052934 .6 6.5 N = 160
5. The summary statistics for the licoat by province is given in the appendix. A detailed
look at the licoat summary statistics and a panel graph is given below. The graph shows a
downward trend.
A unit root test is conducted to see if licoat is stationary. The results rejected the null that
the data is stationary and so the growth rates of the licoat, named rlicoat, is taken and tested for a
unit root as well. The null is not rejected at that point and we conclude that the data is now
stationary.
99% 18 18.5 Kurtosis 2.491598
95% 15.9 18 Skewness .1297095
90% 14.85 17.6 Variance 9.256729
75% 13.25 16.9
Largest Std. Dev. 3.042487
50% 10.8 Mean 10.84938
25% 8.6 5.2 Sum of Wgt. 160
10% 7 5.1 Obs 160
5% 5.6 4.9
1% 4.9 3.9
Percentiles Smallest
poverty rate
5
101520
povertyrate
1995 2000 2005 2010
year
prov = 1 prov = 2
prov = 3 prov = 4
prov = 5 prov = 6
prov = 7 prov = 8
prov = 9 prov = 10
6. licoat Test for Unit root
rlicoat Test for Unit root
Unit root tests were conducted for each variable and all had to be first difference except
for liten and litex. An „r‟ before the variable name denotes growth rate while a „d‟ denotes
differenced. Note that dedu is in 10,000‟s in order to better scale the marginal effects.
Model and Estimation Results
The pooled OLS without province and time dummies show that litex, liten, rmi, runemp,
and dedu are significant at the 5% critical value, and dgt is significant at the 10% critical value.
All other variables were insignificant at the 10% critical value and were dropped from this
regression. The model has an R2
of 0.3527 which means it fits the data somewhat well. The rmi
and runemp has the greatest impacts on the rlicoat. An increase in average market income by 1
percentage point will decrease the growth rate of the poverty rate growth rate by 0.749
percentage points while an increase in the unemployment rate growth rate by 1 percentage point
SerDep 9.430 0.0000 2.460 0.0069
Hetero 25.162 0.0000 3.723 0.0001
Homo 26.600 0.0000 4.320 0.0000
eps Z(mu) P-value Z(tau) P-value
with 17 observations on 10 cross-sectional units
Hadri (2000) panel unit root test for licoat
SerDep: controlling for serial dependence in errors (lag trunc = 2)
Hetero: heteroskedastic disturbances across units
Homo: homoskedastic disturbances across units
H0: all 10 timeseries in the panel are stationary processes
SerDep 0.421 0.3368 2.077 0.0189
Hetero -0.832 0.7974 -0.513 0.6961
Homo -0.609 0.7287 -0.468 0.6801
eps Z(mu) P-value Z(tau) P-value
with 16 observations on 10 cross-sectional units
Hadri (2000) panel unit root test for rlicoat
7. increases the poverty rate growth rate by 0.25 percentage points. A test for serial correlation
concluded that there is no first order serial correlation. Also, the pooled OLS is favoured among
the fixed and random effects models since we cannot reject the null that u_i=var(u)=0 as shown
below.
Test for first order autocorrelation
Fixed effects test
Random effects test
Bootstrapping the regression and accounting for province and time dummy variables
provides a stronger pooled OLS model. The regression showed that province 6 (Ontario) and d7
(year 2001) are significant at the 5% critical value and the other dummies were insignificant at
the 10% critical value and thus dropped from the regression. The variable dgt was also dropped
for the same reason. The regression shows that Ontario has a higher poverty rate growth rate than
other provinces and that in 2001 there was a negative growth rate in the poverty rate. The model
_cons .0028678 .0476831 0.06 0.952 -.0913344 .09707
dedu .0011676 .0003661 3.19 0.002 .0004444 .0018908
dgt -.0354969 .0190191 -1.87 0.064 -.0730709 .0020771
runemp .2512018 .0995877 2.52 0.013 .0544573 .4479464
rmi -.7488357 .2811274 -2.66 0.009 -1.304228 -.1934432
liten .0278386 .007313 3.81 0.000 .013391 .0422861
litex -.0030385 .0008647 -3.51 0.001 -.0047468 -.0013302
rlicoat Coef. Std. Err. t P>|t| [95% Conf. Interval]
Robust
Root MSE = .07943
R-squared = 0.3527
Prob > F = 0.0000
F( 6, 153) = 15.46
Linear regression Number of obs = 160
Prob > F = 0.3119
F( 1, 9) = 1.148
H0: no first-order autocorrelation
Wooldridge test for autocorrelation in panel data
F test that all u_i=0: F(9, 144) = 1.10 Prob > F = 0.3637
Prob > chi2 = 0.7576
chi2(1) = 0.10
Test: Var(u) = 0
u 0 0
e .0062707 .0791875
rlicoat .0093787 .0968439
Var sd = sqrt(Var)
Estimated results:
rlicoat[prov,t] = Xb + u[prov] + e[prov,t]
Breusch and Pagan Lagrangian multiplier test for random effects
8. passed the test for heteroskedasticity and the Ramsey reset test showing that the model is well
specified.
The graphs below illustrate the actual rlicoat and the linear predictions generated by the model.
_cons -.027534 .0434783 -0.63 0.527 -.1127499 .0576819
d7 -.0692612 .02439 -2.84 0.005 -.1170648 -.0214577
_Iprov_6 .035415 .017645 2.01 0.045 .0008315 .0699985
dedu .0012524 .0004431 2.83 0.005 .0003839 .0021209
runemp .2394088 .0972868 2.46 0.014 .0487302 .4300874
rmi -.6185302 .3048785 -2.03 0.042 -1.216081 -.0209793
liten .0321315 .0063844 5.03 0.000 .0196183 .0446447
litex -.0026439 .0008548 -3.09 0.002 -.0043192 -.0009686
rlicoat Coef. Std. Err. z P>|z| [95% Conf. Interval]
Observed Bootstrap Normal-based
Root MSE = 0.0781
Adj R-squared = 0.3503
R-squared = 0.3789
Prob > chi2 = 0.0000
Wald chi2(7) = 115.89
Replications = 100
Linear regression Number of obs = 160
Prob > chi2 = 0.3691
chi2(1) = 0.81
Variables: fitted values of rlicoat
Ho: Constant variance
Breusch-Pagan / Cook-Weisberg test for heteroskedasticity
Prob > F = 0.8939
F(3, 149) = 0.20
Ho: model has no omitted variables
Ramsey RESET test using powers of the fitted values of rlicoat
-.4-.2
0
.2.4
rlicoat
1995 2000 2005 2010
year
prov = 1 prov = 2
prov = 3 prov = 4
prov = 5 prov = 6
prov = 7 prov = 8
prov = 9 prov = 10
9. The liten and litex are significantly tied to the rlicoat and further investigation into these
variables is necessary. The Hausman test concludes that a random effects model is best to
estimate the liten, shown in appendix, but it is inconclusive in choosing between random effects
and fixed effects for estimating the litex. The random effects model for both is considered here,
however the fixed effects estimates for the litex are in the appendix. It is seen that rfpi, rspi, and
litex have a negative effect on the liten while rspi, dgt, and rmi have a positive effect on the litex.
All explanatory variables are significant at the 10% critical value.
-.2-.1
0
.1.2
1995 2000 2005 2010
year
prov = 1 prov = 2
prov = 3 prov = 4
prov = 5 prov = 6
prov = 7 prov = 8
prov = 9 prov = 10
rho .16860615 (fraction of variance due to u_i)
sigma_e .76150814
sigma_u .34293188
_cons 5.007358 .3364286 14.88 0.000 4.34797 5.666746
litex -.0190625 .0091377 -2.09 0.037 -.0369721 -.001153
rspi -9.23977 2.680549 -3.45 0.001 -14.49355 -3.985991
rfpi -.3057996 .040824 -7.49 0.000 -.3858131 -.2257861
liten Coef. Std. Err. z P>|z| [95% Conf. Interval]
Observed Bootstrap Normal-based
(Replications based on clustering on prov)
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
Random effects u_i ~ Gaussian Wald chi2(3) = 74.43
overall = 0.3378 max = 15
between = 0.2640 avg = 15.0
R-sq: within = 0.3507 Obs per group: min = 15
Group variable: prov Number of groups = 10
Random-effects GLS regression Number of obs = 150
10. A quantile regression on the rlicoat‟s 90th
percentile shows that only the variables rmi and
dedu are significant in explaining the top decile of rlicoat. Both are significant at the 1% critical
value while the other variables failed to be significant at the 10% critical value.
Conclusion
The paper finds that the LICO-AT poverty rate is affected by economic growth, number
of persons with low literacy skills, and the low income transition exit and entry rates.
Furthermore, the food and shelter price indexes, and average government transfers indirectly
impact the poverty rate through the low income transition exit and entry rates. Surprisingly,
recent immigrants and interprovincial migration are not significant in explaining poverty rates.
For policy purposes, investigating why Ontario has a higher poverty rate on average than
the other provinces is worthwhile. Also exploring what caused a significant drop in poverty rates
across all provinces in 2000/2001 is also worthwhile. The quantile regression shows that
economic growth and decreasing the number of persons with low literacy skills is the best way to
combat high poverty rates. Therefore policy makers should focus on educating those with less
than 8 years of schooling if they wish to reduce high poverty rates.
rho .29749699 (fraction of variance due to u_i)
sigma_e 6.3094872
sigma_u 4.1059273
_cons 34.23936 .8679427 39.45 0.000 32.53822 35.94049
rmi 36.90001 19.73829 1.87 0.062 -1.786316 75.58634
dgt 3.819456 1.400359 2.73 0.006 1.074803 6.564109
rspi 54.4588 27.01747 2.02 0.044 1.505542 107.4121
litex Coef. Std. Err. z P>|z| [95% Conf. Interval]
Observed Bootstrap Normal-based
(Replications based on clustering on prov)
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0003
Random effects u_i ~ Gaussian Wald chi2(3) = 18.61
overall = 0.0956 max = 16
between = 0.1989 avg = 16.0
R-sq: within = 0.0866 Obs per group: min = 16
Group variable: prov Number of groups = 10
Random-effects GLS regression Number of obs = 160
_cons .1087695 .0143534 7.58 0.000 .0804189 .13712
dedu .0019875 .0006194 3.21 0.002 .0007642 .0032109
rmi -1.025309 .2219883 -4.62 0.000 -1.463778 -.5868403
rlicoat Coef. Std. Err. t P>|t| [95% Conf. Interval]
Min sum of deviations 4.805109 Pseudo R2 = 0.1205
Raw sum of deviations 5.463407 (about .0779615)
.9 Quantile regression, bootstrap(100) SEs Number of obs = 160
> ....................................)
(bootstrapping ................................................................
(fitting base model)
. bsqreg rlicoat rmi dedu, quantile(90) reps(100)
11. There are a few limitations to this paper and model. The first is that the sample size is
inadequate and the results rely heavily on bootstrap estimations. Secondly, the regressions do not
have very high R2
s and therefore leaves much of the poverty rate unexplained. Also using edu
and npr as proxies for number of persons with low literacy and number of recent immigrants
hinders accurate estimations. Lastly, the difficulty in explaining what drives low income
transition entry and exit rates is a fundamental problem in the paper‟s overall analysis. This
paper does attempt to address this problem by choosing to avoid using instrumental variables and
instead running random effects regressions on the variables. Overall the paper provides a strong
starting point in empirically investigating the factors that affect the poverty rates in Canada.
Bibliography
Citizens of Public Justice. (2012). Poverty Trends Scorecard.
House of Commons Committees. (2015). Federal Poverty Reduction Plan: Working in
Partnership Towards Reducing Poverty in Canada. PARLIAMENT of CANADA.
Laurie, N. (2008). The Cost of Poverty. Toronto: Ontario Association of Food Banks.
Vijayakumar, S. (2013). An Empirical Study on the Nexus of Poverty, GDP Growth,
Dependency Ratio and Employment in Developing Countries. Journal of Competitiveness, 67-
82.
Statistics Canada. Table 326-0021 - Consumer Price Index, annual (2002=100 unless otherwise
noted)
Statistics Canada. Table 282-0002 - Labour force survey estimates (LFS), by sex and detailed
age group, annual (persons unless otherwise noted)
Statistics Canada. Table 202-0806 - Transitions of persons into and out of low income, by
selected characteristics, annual
Statistics Canada. Table 202-0802 - Persons in low income families, annual
Statistics Canada. Table 202-0702 - Market income, government transfers, total income, income
tax and after-tax income, by economic family type, 2011 constant dollars, annual
Statistics Canada. Table 051-0020 - Number of non-permanent residents, Canada, provinces and
territories, annual (persons)
Statistics Canada. Table 051-0012 - Interprovincial migrants, by age group and sex, Canada,
provinces and territories, annual (persons)
12. Statistics Canada. Table 282-0004 - Labour force survey estimates (LFS), by educational
attainment, sex and age group, annual (persons unless otherwise noted)
Appendix
Province Code
Newfoundland 1
Prince Edward Island 2
Nova Scotia 3
New Brunswick 4
Quebec 5
Ontario 6
Manitoba 7
Saskatchewan 8
Alberta 9
British Columbia 10
13. licoat Summary Statistics by Province
licoat 16 9.575 2.103489 5.5 13.5
Variable Obs Mean Std. Dev. Min Max
-> prov = 4
licoat 16 10.575 2.29187 7.7 14.1
Variable Obs Mean Std. Dev. Min Max
-> prov = 3
licoat 16 6.8 1.761817 3.9 9.5
Variable Obs Mean Std. Dev. Min Max
-> prov = 2
licoat 16 11.075 3.31572 6.4 16.1
Variable Obs Mean Std. Dev. Min Max
-> prov = 1
licoat 16 9.9375 2.093442 6.4 14.2
Variable Obs Mean Std. Dev. Min Max
-> prov = 8
licoat 16 12.3875 2.493425 8.5 16.5
Variable Obs Mean Std. Dev. Min Max
-> prov = 7
licoat 16 10.79375 1.524235 8.8 14
Variable Obs Mean Std. Dev. Min Max
-> prov = 6
licoat 16 13.34375 3.080686 8.9 18.5
Variable Obs Mean Std. Dev. Min Max
-> prov = 5
licoat 16 13.89375 1.770299 11 16.4
Variable Obs Mean Std. Dev. Min Max
-> prov = 10
licoat 16 10.1125 2.987502 5.7 14.8
Variable Obs Mean Std. Dev. Min Max
-> prov = 9
