The Analysis and Forecast of Chinese Population

-- 自强不息，厚德载物 -- IE @Applied Statistics, Group Report 1

The Analysis and Forecast of Chinese Population

Group Members: 李文华 2009210538 杨丽丹 2009210561 宋芹 2009210568 杨春晖 2009220200

Instructor: 王凯波

2 -- 自强不息，厚德载物 -- IE @Applied Statistics, Group Report

OUTLINEPART 1:Introduction (Background, Objective, Terminology )PART 2:Descriptive Analysis

PART 3:Hypothesis Test of Male-Female Birth Rate (Descriptive date, Exploratory date , Cause analysis)

PART 4:Fertility Comparison (Descriptive date , Exploratory date , Cause analysis)

PART 5:Analysis of Ratio (Descriptive date , Exploratory date , Cause analysis)

PART 6:Analysis of Dead Rate (Descriptive date , Exploratory date , Cause analysis)

PART 7:Time Series Analysis of Total Population Size (Trend analysis, Model based analysis)

PART 8: Conclusion


INTRODUCTION--BackgroundINTRODUCTION--Background Before 1950 China had demographic characteristics of a pre-

modern society with high dead rates and high fertility rates. This situation produced certain stability in population size or, at least, leads to a slow increase.

After the foundation of The People’s Republic of China in 1949, China entered its demographic transition: first dead rates began to fall rapidly and second, fertility remained for many years at about an average of six children per woman. As a result of this China experienced rapid population growth due to the high number of children born, a sharp decline of baby dead rate.


INTRODUCTION-INTRODUCTION-China Population Development

China Population Development

0 20000 40000 60000 80000 100000 120000

春秋战国

秦汉

魏晋

隋唐

宋元（AD 1100）

明（AD 1600）

清（AD 1800）

清（AD 1840）

清（AD 1911）

1953

1977

1982

Population (10k persons)


INTRODUCTION-China Population INTRODUCTION-China Population TodayToday

Now China has a population over 1.3 billion (2007), that is nearly 1/5 the world population.

Most of the population are in the east (94%), which are more developed, and enjoying a relatively lower dead rate, and a lower baby dead rate


Our report would like to apply the statistics method with substantial evidence data got from CHINA POPULATION STATISTICS YEARBOOK (1995-2006) , and proceed the research and the analysis on the male-female birth rate, fertility rate and dead rate among different area (city, town, village), and different years, to have a trend analysis and prediction on the total China population.

INTRODUCTION--ObjectiveINTRODUCTION--Objective


INTRODUCTION--TerminologyINTRODUCTION--Terminology City, Town & Village 城市，乡镇，农村 : City and Town in China is

administratively defined as statutory cities and statutory towns judging from the population, economic, public finance and Infrastructure four aspects. Village is referred to the areas other than cities and towns.

Birth Rate (or crude birth rate) 出生率 :The number of live births per 1,000 population in a given year. Not to be confused with the growth rate.

Death Rate (or crude death rate) 死亡率 :The number of deaths per 1,000 population in a given year.

Sex Ratio 出生人口性别比 :The number of males per 100 females in a population.

Fertility Rate 生育率： The number of live births per 1,000 women ages 15-44 or 15-49 years in a given year.

----Definition from Administrative Office of the State Council &Population Reference Bureau, USA








PART 8: Conclusion


DESCRIPTIVE ANALYSIS-Variables Population size of China: Fertility rate ： ( 生育率 ) ‰ （ 1994-2005 ） Male-female birth rate ： F:100 （ 1994-2005 ） Male (female) ratio of a certain age: %

the percentage of the male number of total male population.

Death rate: ‰

41 10


The data were collected from internet ,such as CHINA POPULATION STATISTICS YEARBOOK (1995-2006) ( 中国人口统计年鉴 ) etc.

DESCRIPTIVE ANALYSIS-Data Sheet


Observation: Continuous increase since 1962 Increase rate decrease last 20 years

DESCRIPTIVE ANALYSIS-Population size


The age distribution of fertility is different. The birth peak for village comes earlier than city. And for all ages the village has higher birth rate.

DESCRIPTIVE ANALYSIS- Fertility rate

Observation


Jumping town data and stationary city and village data All exceed the rational range (102 to 107)

DESCRIPTIVE ANALYSIS- Male/female rate of newborn

Observation


• Does there are any gender choice?• Does female lives longer?

DESCRIPTIVE ANALYSIS- Male-Female rate & death rate(2005)








PART 8: Conclusion


Data selection ： mainly survey and observation• 10 variables• 27,000 data points

Data process• integrate original data(15 forms) into one form• recalculate them to get new data• select data points to build a new sample e.g. fertility rate , death rate

Male-Female Birth Rate--Data


Main basis of population balance, of great importance. Number of baby boys when 100 baby girls:

100baby boymale female ratebaby girl

(year:1994 -2005. type: city, town, village. 36 data points.)

• One-way ANOVA: Male-female birth rate versus type (city, town and village)

Population Balance: Male-Female Birth Rate

0 : C T VH


Population Balance: Male-Female Birth Rate

Conclusions and cause analysis:

Three types own significant difference of gender balances and choices.P-value = 0.000<0.05

Boy preference: village (highest) town city (lowest)

• Viewpoint that Man is superior to woman• The farm work and lifestyle• Education• Medical technique (helps sharpen the

gender choice)








PART 8: Conclusion


• Main basis of population balance, of great importance.• number of babies per 1000 women from age 15-49:

Population replacement: Fertility rate

(year:1994 -2005. type: city, town, village. 2520 original points.)

5040302010

200

150

100

50

0

Age

Y-Da

ta

Ci ty f erti l i ty rateTown f erti l i ty rateVi l l age ferti l i ty rate

Vari abl e

Scatterpl ot of Ci ty fert i l i , Town ferti l i , Vi l l age fert vs Age

2004

5040302010

20

15

10

5

0

Age

Y-Da

ta

Ci ty ferti l i ty rateTown ferti l i ty rateVi l l age ferti l i ty rate

Vari abl e

Scatterpl ot of Ci ty ferti l i , Town ferti l i , Vi l l age fert vs Age

2003

5040302010

200

150

100

50

0

Age

Y-Da

ta

Ci ty f erti l i ty rateTown f erti l i ty rateVi l l age ferti l i ty rate

Vari abl e

Scatterpl ot of Ci ty fert i l i , Town ferti l i , Vi l l age fert vs Age

2002

5040302010

200

150

100

50

0

Age

Y-Da

ta

Ci ty ferti l i ty rateTown ferti l i ty rateVi l l age ferti l i ty rate

Vari abl e

Scatterpl ot of Ci ty ferti l i , Town ferti l i , Vi l l age fert vs Age

2001


• Two-way ANOVA: Fertility rate versus type (city, town and village), year

• Intersection of type and year


Conclusions and cause analysis:It proves that one-child policy in our country works a lot. Small rise and fall around 2003 result from the very epidemic SARS around 2003,which reduced the contact and pregnant chances.

Both significant!

type difference: village> town> cityyear difference: negative trend



Fertility peak (highest fertility age) versus type, year

•The age peak is around 24• Fertility peak decreases (city changes most. village most stable)•The village peak is the highest

Data processyear(2001-2005), age( with highest fertility), type (city, town and village)

Build up a new sample "fertility peak”

• Scatter plot of fertility peak








PART 8: Conclusion


ANALYSIS of RATIO

Step 1: Data collection

Take city male ratio for example

City male ratio=


Step 2: Descriptive date analysis

sexarea

MFVTCVTC

0. 52

0. 51

0. 50

0. 49

0. 48

rati

oBoxpl ot of rati o

ANALYSIS of RATIO

In city, both male and female ratios are near 0.5. But the difference between male ratio and female ratio is getting larger and larger from town to village. Basically, there are more male than female in society. That is the reason why it is hard for many young men to find “Mrs. Right”.


Step 3 Exploratory date analysis

0. 0080. 0040. 000- 0. 004- 0. 008

99

90

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10

1

Resi dual

Perc

ent

0. 510. 500. 49

0. 006

0. 003

0. 000

- 0. 003

- 0. 006

Fi t t ed Val ue

Resi

dual

0. 0060. 0040. 0020. 000-0. 002-0. 004-0. 006

8

6

4

2

0Resi dual

Freq

uenc

y

30282624222018161412108642

0. 006

0. 003

0. 000

- 0. 003

- 0. 006

Obser vat i on Or der

Resi

dual

Normal Probabi l i ty Pl ot Versus Fi ts

Hi stogram Versus Order

Resi dual Pl ots for rati o

ANALYSIS of RATIO


VTC

0. 515

0. 510

0. 505

0. 500

0. 495

0. 490

0. 485

area

Mean

FM

sex

I nteracti on Pl ot for rati oDat a Means Conclusion:

•In city, male ratio is equal to female ratio. But it is larger than female ratio in town and village.•The difference between male ratio and female ratio is getting larger and larger from city to village.

ANALYSIS of RATIOStep 3 Exploratory date analysis


Step 4 Cause analysis

City people•Just have one kid•Higher education•Higher pressures in life•Dink family

Reason 1

Town and village people

•More than one kid•value the male child only

Reason 2

And this phenomenon in village is more serious than that in town, so the difference between male ratio and female ratio in village is larger than that in town.

ANALYSIS of RATIO








PART 8: Conclusion


ANALYSIS of DEAD RATE

Take city male dead rate for example

City male dead rate ratio=

Step 1: Data collection


sexarea

MFVTCVTC

0. 45

0. 40

0. 35

0. 30

0. 25

0. 20

dead

rat

e

Boxpl ot of dead rate

Step 2: Descriptive date analysis


Observation:male dead rate is higher than female’s. And there is another conclusion that the dead rate is increasing from city to village


0. 0300. 0150. 000- 0. 015- 0. 030

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Perc

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0. 400. 350. 300. 250. 20

0. 02

0. 01

0. 00

- 0. 01

- 0. 02

Fi t t ed Val ue

Resi

dual

0. 020. 010. 00- 0. 01- 0. 02

4. 8

3. 6

2. 4

1. 2

0. 0

Resi dual

Freq

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30282624222018161412108642

0. 02

0. 01

0. 00

- 0. 01

- 0. 02

Obser vat i on Or der

Resi

dual



Resi dual Pl ots for dead rate




Conclusion:•Male dead rate is higher than female dead rate•Dead rate is increasing from city to village

VTC

0. 40

0. 35

0. 30

0. 25

0. 20

area

Mean

FM

sex

I nteracti on Pl ot for dead rateDat a Means




reason•Male just have one X chromosome•Main labor force in society•Bad habit: smoking drinking•Accident, crime

1:Male dead rate is higher City

• Higher education• Better living standard• Better medical care• Better work condition

It is increasing from city to village

generally speaking, city better than town and village; and town is a little better than village.

Step 4 Cause analysis









PART 8: Conclusion


TOTAL POPULATION SIZE PREDICT-Guideline

The analysis here is based on the population data since the foundation of China, and based on 58 year’s population data we could do trend analysis and prediction in qualitative or quantitative analysis.

Trend analysis Linear, exponential, quadratic and S-curve Deviation analysis

ARIMA Stationary Model determination based on ACF/PACF Prediction and deviation analysis


Continuous increase and a odd decrease point were observed in annually collected population data. From the Figure, we see the increase rate declined in last 20 years.

China’s population has reached 132,129*104(2007) , we still face the serious population problem and also aging population problem too.

TOTAL POPULATION SIZE PREDICT- Trend object


TOTAL POPULATION SIZE PREDICT- Result of trend analysis

• Linear, exponential, quadratic and S-curve models were used to analysis the increase features. Parameters estimation is based on OLS methods.

• 4 results were evaluated in 3 elementary indexes as MAD, MAPE, MSE. The result tells us that S-curve models fits China’s increase sharply then slowly reality.

544842363024181261

1400001300001200001100001000009000080000700006000050000

I ndex

Popu

lati

on s

ize MAPE 2

MAD 1633MSD 3932649

Accuracy Measures

ActualFi ts

Vari abl e

Trend Anal ysi s Pl ot f or Popul ati on si zeLi near Trend ModelYt = 51011 + 1458*t

544842363024181261

150000

125000

100000

75000

50000

I ndex

Popu

lati

on s

ize MAPE 4

MAD 3525MSD 19641671

Accuracy Measures

ActualFi ts

Vari abl e

Trend Anal ysi s Pl ot for Popul ati on si zeGrowth Curve Model

Yt = 56244. 4 * ( 1. 01628**t )

544842363024181261

1400001300001200001100001000009000080000700006000050000

I ndex

Popu

lati

on s

ize MAPE 2

MAD 1494MSD 3454107

Accuracy Measures

ActualFi ts

Vari abl e

Trend Anal ysi s Pl ot for Popul at i on si zeQuadrat i c Trend Model

Yt = 49384 + 1618. 1*t - 2. 668*t **2

60544842363024181261

1400001300001200001100001000009000080000700006000050000

I ndex

Popu

lati

on s

ize

I ntercept 49784Asymptote 164704Asym. Rate 1

Curve Parameters

MAPE 2MAD 1189MSD 2225774

Accuracy Measures

ActualFi tsForecasts

Vari abl e

Trend Anal ysi s Pl ot f or Popul ati on si zeS- Curve Trend Model

Yt = (10**6) / (6. 07150 + 14. 0151*(0. 961598**t ) )


TOTAL POPULATION SIZE PREDICT-Evaluation of 4 models

Method Equation MAPE MAD MSDlinear Yt = 51011 + 1458*t 2 1633 3932649

exponential growth Yt = 56244.4 * (1.01628**t) 4 3525 19641671quadratic trend Yt = 49384 + 1618.1*t - 2.668*t**2 2 1494 3454107

S-curve Yt = (10**6) / (6.07150 +14.0151*(0.961598**t))

2 1189 2225774

Trends analysis’s use is to predict future. So we focus on the most recent regression deviation to evaluate these four models. That means we only take the deviation from 2000~2007.

Method MAPE MSE MADlinear 1.8 8193544 2385

exponential groth 6.4 80808235 8344 quadratic trend 1.2 3602967 1518

S-curve 0.7 1144129 872

Year 2008 2009 2010 2011 2012Population size (unite:1*104)

134975 135918 136836 137731 138603


TOTAL POPULATION SIZE PREDICT-ARIMA Description

ARIMA is developed by Box and Jenkins in 1970s, and it is a famous model in time serious analysis combined auto regression, moving average and also difference operation to treat unstationary time series data.

ARIMA （ p ， d ， q ） , is determined in 3 step: Stationary transfer Model determination Parameters estimation


TOTAL POPULATION SIZE PREDICT-Stationary Test

A stationary time series data means the mean of the series does not change with time shift, and standard deviation could be limited in a range.

Obvious increase trend was observed, so difference operation is needed to transfer the unstationary series into stationary one. But what is the difference order?

“Augmented Dickey-Fuller , ADF” test is used in Matlab to test whether the series has a unit root.

2004199819921986198019741968196219561950

2500

2000

1500

1000

500

0

- 500

- 1000

I ndex

C2

Ti me Seri es Pl ot of C2


TOTAL POPULATION SIZE PREDICT- One order difference solution

1 1 2 2 1t t t p t p t tx x x x x t

0 : 1 0 1H

1 : 1 0 1H

P-value is smaller than 0.05, so we reject the null hypothesis. The series does not have unit root.

It passes the AFD test and then come into the model determination part.


After determine the difference order of d=1, the ARIMA model turns into ARMA model. Model determination is based on ACF & PACF.

ACF has a heavy tail and PACF is bobtail, then it is AR(1) model. So based on Box- Jenkins ARIMA(1,1,0)

24222018161412108642

1. 00. 80. 60. 40. 20. 0

- 0. 2- 0. 4- 0. 6- 0. 8- 1. 0

Lag

Auto

corr

elat

ion

Autocorrel ati on Functi on for C1(wi th 5% si gni f i cance l i mi t s f or the autocorrel at i ons)

151413121110987654321

1. 00. 80. 60. 40. 20. 0

- 0. 2- 0. 4- 0. 6- 0. 8- 1. 0

Lag

Part

ial

Auto

corr

elat

ion

Parti al Autocorrel ati on Functi on for C1( wi th 5% si gni f i cance l i mi ts f or t he part i al aut ocorrel at i ons)




Residual check shows a odd points of “1961”. It is far from the normality line. What shall we do?

Transfer? Cut the series?

We cut this series and take only 1962~2007.

10000-1000-2000

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200010000-1000

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8000-800-1600-2400

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Freq

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5550454035302520151051

1000

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-2000

Observati on Order

Resi

dual



Resi dual Pl ots for C1


TOTAL POPULATION SIZE PREDICT- Two order difference solution

AFD test?

2008200319981993198819831978197319681963

750

500

250

0

- 250

- 500

I ndex

C10

Ti me Seri es Pl ot of C10

Decision vector H shows the 1962-2007 part is not a stationary series any more.

And observation shows a decrease trend. So higher order difference is needed.



ARMA is of p=3, q=1 based on Box-Jenkins method

SS = 1114603, MS = 27865.

24222018161412108642

1. 00. 80. 60. 40. 20. 0

- 0. 2- 0. 4- 0. 6- 0. 8- 1. 0

Lag

Auto

corr

elat

ion

Autocorrel ati on Functi on for 2I(wi th 5% si gni f i cance l i mi ts f or the autocorrel at i ons)

1110987654321

1. 00. 80. 60. 40. 20. 0

- 0. 2- 0. 4- 0. 6- 0. 8- 1. 0

Lag

Part

ial

Auto

corr

elat

ion

Parti al Autocorrel ati on Functi on for 2I(wi th 5% si gni f i cance l i mi ts f or the part i al autocorrel at i ons)

4002000-200-400

99

90

50

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Resi dual

Perc

ent

5002500-250-500

400

200

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-200

-400

Fi tted Val ue

Resi

dual

4003002001000-100-200-300

16

12

8

4

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Resi dual

Freq

uenc

y

454035302520151051

400

200

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-200

-400

Observati on Order

Resi

dual



Resi dual Pl ots for 2I


Population increase can be estimated by above function to get future value based on historical ones.

ARIMA Model: C1 Final Estimates of ParametersType Coef SE Coef T PAR 1 0.9138 0.0714 12.88 0.000Constant 124.68 31.32 3.37 0.002Mean 1313.7 390.3Number of observations: 46Residuals: SS = 1773508 (backforecasts excluded) MS = 40307 DF = 44


200720031999199519911987198319791975197119671963

750

500

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I ndex

Data

2IFI TS1

Vari abl e

Ti me Seri es Pl ot of 2I , FI TS1

2046204120362031202620212016201120062001

2500

2000

1500

1000

500

I ndex

Data

1962- 2007C11

Vari abl e

Ti me Seri es Pl ot of 1962- 2007, C11

2017201120051999199319871981197519691963

140000

130000

120000

110000

100000

90000

80000

70000

I ndex

Data

C5C7

Vari abl e

Ti me Seri es Pl ot of C5, C7

1 2 3 121.74 0.8538 0.0203 0.5614 0.5958t t t t ty y y y z


TOTAL POPULATION-Prediction and Deviation Analysis

Future increase and it 95% CI could be predicted, then the total population could be get respectably. MAPE dropped nearly 91%, MSD 99% and MAD 91%.

Method MAPE MSD MADS-curve 0.7 1144129 872

ARIMA(1,1,0) 0.06 6058 73 Improvement( with S-curve ) 0.914286 0.994705 0.916284

(2000-2007)

2008200319981993198819831978197319681963

750

500

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I ndex

Data

2IC19C20C21

Vari abl e

Ti me Seri es Pl ot of 2I , C19, C20, C21

20122007200219971992198719821977197219671962

2500

2000

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I ndex

Data

predpred- l i mpred-up1962-2007

Vari abl e

Ti me Seri es Pl ot of pred, pred- l i m, pred- up, 1962- 2007

20122007200219971992198719821977197219671962

140000

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70000

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Data

total popuC12C13C14

Vari abl e

Ti me Seri es Pl ot of total popu, C12, C13, C14


TOTAL POPULATION PREDICT-ARIMA Result

2012201120102009200820072006200520042003200220012000

138000

136000

134000

132000

130000

128000

126000

C8

Data

C9C10C11C12

Vari abl e

Ti me Seri es Pl ot of C9, C10, C11, C12

Year(unite:1*104)

2008 2009 2010 2011 2012

ARIMA(3,2,1) 132,790 133,404 134,030 134,614 135,186S-curve 134,975 135,918 136,836 137,731 138,603








PART 8: Conclusion


Features: total population population increase what’s right now?

Chinese population takes up nearly 1/4 of the world population.

post-80’s has come into the region of birth peak which keeps a relative high population increase.

health care improved in large extent and people will have a much longer life.

What’s in future? around 2050 China will face a first time population decrease. social problems but also economic challenges will show

up. Economy increase? Social welfare? Stability ?Is it necessary for the government to revise the birth control police to keep China’s population and the increase at a reasonable region?

TOTAL POPULATION PREDICT-Conclusion


Thanks!

Documents

The Analysis and Forecast of Chinese Population