econometrics report poverty

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.

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.

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

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 = 10unemp 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 = 10spi 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 = 10fpi 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 = 10edu 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 = 10liten 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 = 10litex 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 = 10ipm 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 = 10npr 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 = 10mi 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 = 10gt 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 = 10licoat 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 = 10unemp 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 = 10spi 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 = 10fpi 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 = 10edu 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 = 10liten overall 3.453125 1.052934 .6 6.5 N = 160

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 2.49159895% 15.9 18 Skewness .129709590% 14.85 17.6 Variance 9.25672975% 13.25 16.9 Largest Std. Dev. 3.04248750% 10.8 Mean 10.84938

25% 8.6 5.2 Sum of Wgt. 16010% 7 5.1 Obs 160 5% 5.6 4.9 1% 4.9 3.9 Percentiles Smallest poverty rate

51

01

52

0

pove

rty r

ate

1995 2000 2005 2010year

prov = 1 prov = 2

prov = 3 prov = 4

prov = 5 prov = 6

prov = 7 prov = 8

prov = 9 prov = 10

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 unitsHadri (2000) panel unit root test for licoat

SerDep: controlling for serial dependence in errors (lag trunc = 2)Hetero: heteroskedastic disturbances across unitsHomo: homoskedastic disturbances across unitsH0: 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 unitsHadri (2000) panel unit root test for rlicoat

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) = 15.46Linear regression Number of obs = 160

Prob > F = 0.3119 F( 1, 9) = 1.148H0: no first-order autocorrelationWooldridge 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

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 = 100Linear regression Number of obs = 160

Prob > chi2 = 0.3691 chi2(1) = 0.81

Variables: fitted values of rlicoat Ho: Constant varianceBreusch-Pagan / Cook-Weisberg test for heteroskedasticity

Prob > F = 0.8939 F(3, 149) = 0.20 Ho: model has no omitted variablesRamsey RESET test using powers of the fitted values of rlicoat

-.4

-.2

0.2

.4

rlico

at

1995 2000 2005 2010year

prov = 1 prov = 2

prov = 3 prov = 4

prov = 5 prov = 6

prov = 7 prov = 8

prov = 9 prov = 10

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

Line

ar p

redi

ctio

n

1995 2000 2005 2010year

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 = 0.0000Random effects u_i ~ Gaussian Wald chi2(3) = 74.43

overall = 0.3378 max = 15 between = 0.2640 avg = 15.0R-sq: within = 0.3507 Obs per group: min = 15

Group variable: prov Number of groups = 10Random-effects GLS regression Number of obs = 150

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 = 0.0003Random effects u_i ~ Gaussian Wald chi2(3) = 18.61


Group variable: prov Number of groups = 10Random-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)

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 R2s 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)

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

licoat Summary Statistics by Province

licoat 16 9.575 2.103489 5.5 13.5 Variable Obs Mean Std. Dev. Min Max

-> prov = 4


-> prov = 3


-> prov = 2


-> prov = 1


-> prov = 8


-> prov = 7

licoat 16 10.79375 1.524235 8.8 14 Variable Obs Mean Std. Dev. Min Max

-> prov = 6


-> prov = 5

licoat 16 13.89375 1.770299 11 16.4 Variable Obs Mean Std. Dev. Min Max

-> prov = 10


-> prov = 9

Correlation Matrix

Province Dummies F-Test

liten Hausman Test

rspi 0.2221 0.0099 0.0566 1.0000 rfpi 0.2946 0.0249 1.0000 dipm -0.0272 1.0000 rnpr 1.0000 rnpr dipm rfpi rspi

rspi -0.2177 0.2336 -0.2933 0.2741 -0.2586 -0.1655 0.0452 rfpi -0.0237 0.1241 -0.4970 -0.1405 0.4900 0.5095 -0.0618 dipm -0.1874 -0.0089 0.0454 0.2123 -0.2135 0.0046 -0.0990 rnpr 0.0256 0.2784 -0.2758 0.0623 0.2180 0.1153 0.1114 dedu 0.1051 0.1169 -0.0340 0.0414 -0.0068 -0.0846 1.0000 dgt -0.0472 0.1125 -0.3094 -0.3102 0.4118 1.0000 runemp 0.2929 0.0543 -0.1420 -0.4743 1.0000 rmi -0.3360 0.1529 -0.0155 1.0000 liten 0.3453 -0.2595 1.0000 litex -0.3340 1.0000 rlicoat 1.0000 rlicoat litex liten rmi runemp dgt dedu

Prob > F = 0.2225 F( 9, 144) = 1.34

( 9) _Iprov_10 = 0 ( 8) _Iprov_9 = 0 ( 7) _Iprov_8 = 0 ( 6) _Iprov_7 = 0 ( 5) _Iprov_6 = 0 ( 4) _Iprov_5 = 0 ( 3) _Iprov_4 = 0 ( 2) _Iprov_3 = 0 ( 1) _Iprov_2 = 0

(V_b-V_B is not positive definite) Prob>chi2 = 0.9999 = 0.01 chi2(3) = (b-B)'[(V_b-V_B)^(-1)](b-B)

Test: Ho: difference in coefficients not systematic

B = inconsistent under Ha, efficient under Ho; obtained from xtreg b = consistent under Ho and Ha; obtained from xtreg litex -.0190625 -.0191217 .0000592 . rspi -9.23977 -9.22126 -.01851 . rfpi -.3057996 -.3041991 -.0016005 . random_group fixed_group Difference S.E. (b) (B) (b-B) sqrt(diag(V_b-V_B)) Coefficients

litex Fixed Effects Estimates

Program Code xtset province year xtsum sum licoat xtline licoat, overlay haudrilm licoat

haudrilm rlicoat reg rlicoat litex liten runemp rmi dgt dedu, robust xtserial rlicoat

litex liten runemp rmi dgt dedu xtreg rlicoat litex liten runemp rmi dgt dedu,fe xtreg rlicoat

litex liten runemp rmi dgt dedu xttest0 bootstrap, reps(100) dots: rlicoat litex liten

runemp rmi dedu d7 _Iprov_6 estat hettest ovtest xtline rlicoat xtline yhat

bootstrap, reps(100) dots:xtreg liten rfpi rspi litex quietly estimates store random_group

bootstrap, reps(100) dots:xtreg liten rfpi rspi litex,fe quietly estimates store

fixed_group hausman random_group fixed_group bootstrap, reps(100) dots:xtreg

litex dgt rmi rspi bootstrap, reps(100) dots:xtreg litex dgt rmi rspi,fe bsqreg rlicoat rmi dedu,

quantile(90) reps(100) by province: sum licoat corr rlicoat litex liten rmi runemp dgt

dedu rnpr dipm rspi rfpi

rho .29120886 (fraction of variance due to u_i) sigma_e 6.3094872 sigma_u 4.0442428 _cons 34.30817 .8973875 38.23 0.000 32.54933 36.06702 dgt 3.794942 1.303655 2.91 0.004 1.239825 6.35006 rmi 35.89295 19.57061 1.83 0.067 -2.464742 74.25063 rspi 52.20648 27.29443 1.91 0.056 -1.289613 105.7026 litex Coef. Std. Err. z P>|z| [95% Conf. Interval] Observed Bootstrap Normal-based (Replications based on clustering on prov)

corr(u_i, Xb) = 0.0957 Prob > chi2 = 0.0000 Wald chi2(3) = 22.91


Group variable: prov Number of groups = 10Fixed-effects (within) regression Number of obs = 160

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