Post on 03-Jun-2018
8/12/2019 Forecasting the Real Wage Rate of Palay Farm Workers and Comparing the Mean Real Wage Rate of Male and F
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Mindanao State University- Iligan Institue of Technology
Statistics and Mathematics Department
Tibanga, Iligan City
Forecasting the Real Wage Rate of Palay Farm Workers and Comparing the
Mean Real Wage Rate of Male and Female Palay Farm Workers from Year
1994 to 2011
JOHNIEL E. BABIERA
MS STATISTICS
DAISY LOU LIM POLESTICO, Ph.D
STAT325 : STATISTICAL COMPUTING
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Chapter I
Introduction
Background of the Study
Rice plays a vital role in the lives of the Filipino citizens. One of the basic foods on the
plate of every Filipino is rice. Twenty percent of food expenditures for average Filipino
households is accounted for rice, and 30% for the below average households.
Rice grain or palay is grown in about 3.2 million hectares of land use, providing
livelihood to millions of households engaging in rice-based farming, farm laborers, and
merchants and traders. For this reason, rice is not only a major expenditure but also a source of
income to many households.
Palay farmers play a great role in the basis that they are the common producer of rice.
And, rice farming is facing a great challenge today: dumping the farming and working on the
industry. According to Lita "Ka Lita" Mariano, secretary of general of Alyansa ng Magbubukid sa
Gitnang Luzon, rice farmers force many of them into agricultural labour for rich for rich farmers
and landlords with low wages due to low income in farming.
In connections to this, it is reasonable to study the palay farmers especially about their
wages for they play a great role in producing rice. This study is about the daily real wage rate of
the palay farm workers from year 1975 to 2011. It also includes the daily real wage rate of palay
farm workers disaggregated by gender starting at year 1994 to 2011.
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Real wage is defined as real wage adjusted for the price level, that is
where Nominal wagerate is the amount of money receives from labors. It is the actual money
that you receive and not affected by any inflation rate of any commodities.
Objective of the Study
This paper aims to do the following;
1. Show how the real wage rate changed through the years.2. Forecast values of real wage rate of palay farm workers.3. Compare the means of the real wage rate of male and female workers.
Significance of the Study
This study will provide the readers a closer view on the information about real wage
rate of the palay farm workers. This will help also in comparing the wages of male and female
farm workers of the past few decades. The paper will discuss about some underlying natures of
the real wage rate of the palay farm workers, thus it will help the reader to understand
statistically the nature of the wage rate of the palay farmers. This will also be helpful to some
future studies concerning the wages of the farmers.
Scope and Limitations of the Study
This study is conducted to compare the real wage rate of female and male palay farm
workers and to predict ahead values of their wage rate. The data is the real wage rate per day
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and is presented annually starting in year 1975 to 2011. Disaggregation of the real wage rate
data starts from 1994 to 2011.
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Chapter II
Data and Sampling Design
Table 2.1: Data Description of the real wage data
obs: 37 Real Wage Rate of Palay Farm Workers
vars: 4
size: 666 (99.9% of memory free)
storage display value
variable name type format label variable label
year int %ty Year
wage float %8.0g Real Wage Rate
fwage float %8.0g Female Real Wage Rate
mwage float %8.0g Male Real Wage Rate
Sorted by: year
Table 2.1 shows some descriptions about the real wage data. The data is labeled as Real Wage
Rate of Palay Farm Workers. There 37 observations in which each observation represented by year.
There 4 variables namely; year which represents the year, wage for the real wage rate of palay farm
workers, fwage for real wage rate of female workers, and mwage for real wage rate of male workers.
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Table 2.3 shows that variable fwage is in numeric type characters. There only 18 observations
since there 19 missing values. All these 18 values are unique which means that there are no years in
which the female wage rate is the same. Also, the mean female real wage rate is almost equal to the
median female wage rate which might implies a symmetric distribution of female wage rate.
Table 2.4: Variable mwage Description
mwage
Male Real Wage Rate
type: numeric (float)
range: [126.34,152.95] units: .01
unique values: 18 missing .: 19/37
mean: 138.422
std. dev: 7.75813
percentiles: 10% 25% 50% 75% 90%
127.76 132.62 136.97 144.07 152.56
Table 2.4 shows some descriptions about variable mwage. Variable mwage is in numeric type
characters. There only 18 observations since there 19 missing values. All these 18 values are unique
which means that there are no years in which the male wage rate is the same. Also, the mean male real
wage rate is almost equal to the median male wage rate which might implies a symmetric distribution of
male wage rate.
This data is available at the countrystat.bas.gov.ph. Real wage data is contained from a national
level database under the employment category. The data can be downloaded in different document file
extensions such as excel file, csv file and html file.
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For the both sexes(wage) real wage rates, the available data is from 1975 to 2011. While, for
disaggregation by gender, the available data is from 1994 to 2011. For investigating the real wage rate of
the palay farm workers, the researcher takes all the 37 values (1975 to 2011) and treats this data as a
time series data. While for the samples in each gender, the researcher takes all 18 real wage rate
values(from 1994 to 2011) in each gender. Thus, all available data presented about the real wage rate of
palay farm workers are taken.
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Chapter III
Results and Discussion
3.1 Comparison of Female and Male Real Wage Rate of Palay Farm Workers
from 1994 to 2011
Table 3.1: Summary of Some Statistics on Female Real Wage
Female Real Wage
Percentiles Smallest
1% 112.96 112.96
5% 112.96 114.01
10% 114.01 115.39 Obs 18
25% 120.04 117.72 Sum of Wgt. 18
50% 123.515 Mean 123.4933
Largest Std. Dev. 6.597696
75% 128.28 128.73
90% 133.8 128.95 Variance 43.52959
95% 137.91 133.8 Skewness .3526006
99% 137.91 137.91 Kurtosis 2.722793
Table 3.1 shows summary of some statistics on real wage of palay farm female workers
recorded from 1994 to 2011. It shows that the least wage recorded in the said time interval is 112.96
Php and the largest is 137.91 Php. The average female wage from 1994 to 2011 is 123.49 Php.
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It seems that, from Table 3.1, the real wage of female play farm workers follows a distribution
which is a flat from the top and positively skewed. This suggests that there seems to be more observed
female real wage which is lesser than the mean, and the variance seems to be large.
Table 3.2: Summary of Some Statistics on Male Real Wage
Male Real Wage
Percentiles Smallest
1% 126.34 126.34
5% 126.34 127.76
10% 127.76 129.24 Obs 18
25% 132.62 131.94 Sum of Wgt. 18
50% 136.97 Mean 138.4217
Largest Std. Dev. 7.75813
75% 144.07 144.55
90% 152.56 147.71 Variance 60.18858
95% 152.95 152.56 Skewness .3732691
99% 152.95 152.95 Kurtosis 2.388167
Table 3.2 shows summary of some statistics on real wage of palay farm male workers recorded
from 1994 to 2011. It shows that the least wage recorded in the said time interval is 126.34 Php and the
largest is 152.95 Php. The average male wage from 1994 to 2011 is 138.24 Php which is seems to be
larger than the average real wage of female workers.
It seems that, from Table 3.2, the real wage of male play farm workers follows a distribution
which is a flat from the top and positively skewed. This suggests that there seems to be more observed
female real wage which is lesser than the mean, and the variance seems to be large.
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Also, the distribution of the real wage for male and female is seems to be the same since their
kurtosis and skewness are almost equal.
Figure 3.1: Real Wage Rates of Male and Female Palay Farm WorkersFigure 3.1 above shows that since 1994 to 2011, it seems that the wage rate of female palay
farm workers is lesser than the wage rate of palay farm male workers. Also, the increasing and
decreasing trend of wage for both sexes is seems to be similar. That is, if the wage increases for male,
then its most likely that the wage for female also increases.
110
120
130
140
150
1995 2000 2005 2010year
Female Wage Rate Male Wage Rate
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Figure 3.2: Histogram with Kernel Density Line of Real Wage Rate of Palay Farm Female Workers
Figure 3.2 shows the histogram and kernel density line of the real wage rate of palay farm
female workers recorded from 1994 to 2011. It seems that most observed real wage values are below
125 Php. Its kernel density line suggests that the distribution of the real wage of female workers seems
to be a distribution with thick tails. This means that its distribution is most likely to be t-distribution, only
that its right tail is less thick than its left tail.
Figure 3.3: Histogram with Kernel Density Line of Real Wage Rate of Palay Farm Male Workers
0
.02
.04
.06
.08
110 120 130 140Female Real Wage
0
.01
.02
.03
.04
.05
120 130 140 150 160Male Real Wage
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Figure 3.3 shows the histogram and kernel density line of the real wage rate of palay farm male
workers recorded from 1994 to 2011. It seems that there is more observed real wage values that are
between 133 php and 139 php. Its kernel density line suggests that the distribution of the real wage of
male workers seems to be a distribution with very thick tails. This means that its distribution is most
likely to be t-distribution.
Comparing the distribution of male and female real wage, it seems that their distributions are
the same with t-distribution, only that the distribution of male real wage has thicker tails and more peak
than the female real wage distribution.
Figure 3.4: Normality plot of Female Real Wage Rate
Figure 3.4 shows the normality plot for real wage rate of palay farm female workers. It seems
that there are more dots below the 45 degree line which suggests that the distribution is seem to be
positively skewed. Also, the distribution of the dots around the line seems to be near to the line which
suggests that real wage of female workers seems to follow a normal distribution.
110
120
130
140
110 115 120 125 130 135Inverse Normal
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Figure 3.5: Normality plot of Male Real Wage Rate
Figure 3.5 shows the normality plot for real wage rate of palay farm male workers. It can be
observed that there are more dots below the 45 degree line which suggests that the distribution is seem
to be skewed to right. Moreover, the distribution of the dots around the line seems to be near to the
line which suggests that real wage of male workers seems to be normally distributed.
Table 3.3 : Summary on Normality Test of Real Wage Rate for Female and Male Workers
Shapiro-Wilk W test for normal data
Variable | Obs W V z Prob>z
fwage | 18 0.97346 0.583 -1.079 0.85965
mwage | 18 0.95952 0.890 -0.234 0.59233
Table 3.3 shows the summary statistic on normality test for fwage(female real wage) and
mwage(male real wage). At 0.05 level of significance, the two variables are found to be normally
120
130
140
150
160
125 130 135 140 145 150Inverse Normal
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distributed. This means that real wages of palay farm workers for both female and male follow a normal
distribution
Table 3.4: Summary on Test for Equality of Variance Between fwage and mwage
Variance ratio test
Variable | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
fwage | 18 123.4933 1.555092 6.597696 120.2124 126.7743
mwage | 18 138.4217 1.828609 7.75813 134.5636 142.2797
combined | 36 130.9575 1.729507 10.37704 127.4464 134.4686
ratio = sd(fwage) / sd(mwage) f = 0.7232
Ho: ratio = 1 degrees of freedom = 17, 17
Ha: ratio < 1 Ha: ratio != 1 Ha: ratio > 1
Pr(F < f) = 0.2556 2*Pr(F < f) = 0.5113 Pr(F > f) = 0.744
Table 3.4 shows the summary statistic and test result on test for equality of variance between
fwage and mwage. The standard deviation of fwage, which is 6.5977, is lesser than mwage, which is
7.7581. But, at 0.05 level of significance, it is found that there is no significance difference between the
variance of fwage and variance of mwage. This means that there is no evidence that their variances are
not equal.
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Table 3.5: Summary on two mean-comparison test between fwage and mwage
Two-sample t test with equal variances
Variable | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
fwage | 18 123.4933 1.555092 6.597696 120.2124 126.7743
mwage | 18 138.4217 1.828609 7.75813 134.5636 142.2797
combined | 36 130.9575 1.729507 10.37704 127.4464 134.4686
diff | -14.92833 2.400442 -19.80662 -10.05005
diff = mean(fwage) - mean(mwage) t = -6.2190
Ho: diff = 0 degrees of freedom = 34
Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
Pr(T < t) = 0.0000 Pr(|T| > |t|) = 0.0000 Pr(T > t) = 1.0000
Table 3.5 shows summary on two sample t-test for comparing the means of fwage and mwage.
It shows that the difference between the means of fwage and mwage is -14.92883. This suggests that
the mean of the fwage is less than the mean of mwage. At 0.05 level of significance, mean of the fwage
is significantly different to mean of mwage. And to be exact, the mean of fwage is significantly less than
the mean of mwage. This means that the female workers in palay farms have lesser real wage rate than
to male workers.
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Table 3.6: Summary of Some Statistics on Real Wage Rate
Real Wage
Percentiles Smallest
1% 88.88 88.88
5% 90.68 90.68
10% 93.17 90.91 Obs 37
25% 103.98 93.17 Sum of Wgt. 37
50% 120.61 Mean 118.8176
Largest Std. Dev. 16.92116
75% 131.27 138.97
90% 138.97 140.21 Variance 286.3258
95% 145.19 145.19 Skewness -.2445813
99% 147.23 147.23 Kurtosis 1.869183
Table 3.6 shows summary on some statistics about real wage rate of palay farm workers
recorded from 1975 to 2011. It shows that the least wage recorded from the given time interval is 88.88
Php and the largest in 147.23 Php. The average wage from 1975 to 2011 is 118.82 Php.
Table 3.6 also shows that the distribution of the real wage of palay farm workers is seems to be
flat from top and skewed to left. This suggests that most of the real wage recorded is greater than the
average and the variance is seems to be large.
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3.2 Investigating and Modeling the Real Wage Rate of Palay Farm Workers from
year 1975 to 2011
Figure 3.6: Histogram with Kernel Density Line of Real Wage Rate of Palay Farm Workers
Figure 3.6 shows the histogram and kernel density line of the real wage rate of palay farm
workers recorded from 1975 to 2011. It seems that there more observed real wage values are greater
than 120. Also, it seems that the distribution of the real wage rate of the palay farm workers is a bi-
modal distribution with thick tails. This might implies that there are two groups with a large density of
frequency, and these are a group with values less than 100 and the group of those values between 120
and 137. This also suggests that the distribution seems to be a non-normal distribution.
0
.01
.02
.03
80 100 120 140 160Real Wage
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Figure 3.7: Normality plot of Real Wage Rate
Figure 3.7 shows the normality plot for real wage rate of palay farm workers. The distribution of
the dots below and above the 45 degree line is seems to be the same which suggest that the distribution
of the real wage is most likely to be symmetric. In addition, the distribution of the dots around the line
seems to be close to the line which suggests that its distribution is most likely a normal distribution.
Table 3.7: Normality test for the Real Wage Rate
Shapiro-Wilk W test for normal data
Variable | Obs W V z Prob>z
wage | 37 0.94755 1.953 1.402 0.08048
Table 3.7 shows the summary statistic on normality test for wage. At 0.05 level of significance,
the real wage rate is found to be normally distributed. This means that real wages of palay farm workers
follow a normal distribution
80
100
120
140
160
80 100 120 140 160Inverse Normal
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Figure 3.8: Historical plot of Real Wage Rate
Figure 3.8 shows the real wage rate of palay farms workers from 1974 to 2011. The highest
value of real wage occurred during 1997. It also shows that the series seems to have a non-constant
mean since in year 1980s to 1990s there is a long increase trend in the real wage. Also, it seems that
the series has a non-constant variance. These observations suggest that the series seems to be non-
stationary.
Table 3.8: Stationary test for Real Wage Rate
Dickey-Fuller test for unit root Number of obs = 36
Interpolated Dickey-Fuller
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
Z(t) -1.262 -3.675 -2.969 -2.617
MacKinnon approximate p-value for Z(t) = 0.6463
80
100
120
140
160
1970 1980 1990 2000 2010year
Real Wage Rate of Palay Farm Workers
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Table 3.8 shows the Dickey-Fuller test for unit root or stationary result for real wage. The test
statistics is greater than compared to the three critical regions and its p-value is not less than any
desired level of significance. This means that the series wage is a non-stationary series.
Figure 3.9: Historical plots of the first difference of real wage rate
Figure 3.9 shows the first difference of real wage rate. The figure shows that the series seems to
have a constant mean which is around zero. Though there is seems to have a few indication of non-
constant variance, the overall impression for this series is that it is seems to be a stationary series
Table 3.9: Stationary test for the first difference of real wage
Dickey-Fuller test for unit root Number of obs = 35
Interpolated Dickey-Fuller
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
Z(t) -5.596 -3.682 -2.972 -2.618
MacKinnon approximate p-value for Z(t) = 0.0000
-20
-10
0
10
20
30
1970 1980 1990 2000 2010year
First Difference of Real Wage Rate
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Table 3.9 shows the Dickey-Fuller test or unit root or stationary result for first difference real
wage. The test statistic is significant at 0.05 alpha or level of significance. This means that the first
difference real wage series is a stationary series.
Figure 3.10: Autocorrelations of first difference of real wage
Figure 3.10 shows the autocorrelations of the first difference of real wage. As shown in the
figure, there are no significant spikes at 0.05 level of significance. This means that the autocorrelations
of the first difference wages are insignificantly not equal to zero for time lags greater than or equal to
one. This also means that the possible model does not contain a moving average operator or the series
do not follows a possible moving average process.
-.
-
.
0.0
0
0.2
0
0.4
0
0 5 10 15Lag
Bartlett's formula for MA(q) 95% confidence bands
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Figure 3.11: Partial Autocorrelations of first difference on real wage
Figure 3.11 shows the partial autocorrelations of first difference on real wage. As shown in the
figure, there are two significant lags or spikes. This means that, at these lags (8 and 15), the partial
autocorrelations of the first difference wages are significantly not equal to zero. The first significant lag
is at lag 8, but as observed, this lag is seems to be very close to the region of non-significant lags. The
second significant lag is at lag 15 but this lag is least possible to be with the model since most likely the
maximum lag to be considered is at lag 8 or lag 9 and below.
From figure 3.10 and 3.11, the possible model for the first difference of real wage is ar(8).
-.
-.
0.00
0.2
0
0.4
0
0 5 10 15Lag
95% Confidence bands [se = 1/sqrt(n)]
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Table 3.10: Summary Statistic of AR(8) on first difference of real wage
ARIMA(8,0,0) regression
Sample: 1976 - 2011 Number of obs = 36
Wald chi2(1) = 1.55
Log likelihood = -118.6659 Prob > chi2 = 0.2133
| OPG
D.wage | Coef. Std. Err. z P>|z| [95% Conf. Interval]
wage |
_cons | 1.236258 1.05448 1.17 0.241 -.8304846 3.303001
ARMA |
ar |
L8. | -.2954817 .2374475 -1.24 0.213 -.7608703 .1699069
sigma | 6.470049 .6519128 9.92 0.000 5.192323 7.747774
Table 3.10 shows the summary statistic of AR(8) as possible model of the first difference of real
wage. As shown in the table, the coefficient for constant value is not significant which means that the
model does not contain a constant value. In addition, the coefficient for lag 8 is not significant which
means the model may not contain the ar(8) operator. Dropping the constant and the ar lag 8 coefficient;
the possible model left is just the first difference equation plus some error which characterize a random
walk model.
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Table 3.11: Test for White Noise series in first difference real wage
Portmanteau test for white noise var:D.wage
Portmanteau (Q) statistic = 14.0215
Prob > chi2(16) = 0.5971
Table 3.11 shows the result of Portmanteau test for white noise in the first difference of real
wage. Since the probability is greater than to the 0.05 level of significance, then it means that the first
difference of real wage series follows a white noise process.
Table 3.12: Summary Statistic of Random Walk Model
ARIMA regression
Sample: 1976 - 2011 Number of obs = 36
Log likelihood = -119.5498
OPG
D.wage Coef. Std. Err. z P>z [95% Conf. Interval]
wage
_cons 1.168333 1.169062 1.00 0.318 -1.122987 3.459653
/sigma 6.698545 .5390402 12.43 0.000 5.642045 7.755044
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Table 3.12 shows the summary statistic on fitting the wage series on random walk model or
arima(0,1,0). It shows that the p-value of the constant for the model is insignificant which means that
the model do not contain a deterministic trend.
This means that the fitted model for the wages is given by
where represents the wage(real wage) at time and is a random error at time t. The model
implies that the current value for the real wage rate depends on the last year real wage and a random
error. For the basic assumption of time series modeling, the random errors, , must be from a white
noise process, then we should check whether these errors satisfies the assumption.
Table 3.13: White Noise Test for residuals
Portmanteau test for white noise var:res1
Portmanteau (Q) statistic = 14.0215
Prob > chi2(16) = 0.5971
Table 3.13 shows the result of Portmanteau test for white noise for the residuals of the model . Since the probability is greater than to the 0.05 level of significance, then it means that
the residuals follow a white noise process.
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Figure 3.12: Fitted and observed real wages
Figure 3.12 shows the real wages and the fitted values(y prediction). As observed in the figure,
the values of fitted very near to the actual observed values of real wage. Also, the fitted and the actual
values are both inside in the 95% confidence interval.
Table 3.14: Five-ahead values for the Real Wage Rate
Forecast Real Wage
140.1383
141.3067
142.475
143.6433
144.8117
80
100
120
140
160
1970 1980 1990 2000 2010year
Real Wage y prediction, one-step
lower limit (95% C.I) upper limit (95% C.I)
Fitted vs Observed Real Wage Rate
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Table 3.14 shows the five forecasted values for the real wage rate of the palay farm workers.
The real wage at year 2011 is 138.97 Php and it expected to increase to 140.14 Php and expected to
increase for the next 4 years.
3.3 Investigating and Modeling the Real Wage Rate of Palay Farm Workers from
year 1980 to 1999
Figure 3.13: Real Wages of Palay Farm Workers from 1980 to 1999
Figure 3.13 above is the cut of series of the wage rate of the palay farm workers from figure 3.8.
That is, the series in the figure represents the wage rate from 1980 to 1999. As we observe in the figure
3.13, the wage rate seems to show a general increasing trend. This might implies that from 1980 to
1999, the wage rate of the palay farm workers increases over time.
First we apply the 3-year moving-averaging to see the general trend of this series by observing
the series of the 3-year averages. The 3-year moving-averages is given by the model
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where represents the 3-year moving average at time .
Figure 3.14: Observed and 3-year Moving-averages values
Figure 3.14 above shows the wages and 3-year moving-averages from 1980 to 1999. Looking at
the moving-averages, it seems that the wage have a clear increasing trend from 1980 to 1999. That is, it
seems that from 1980, the average 3-year wage rate increases over time. The series for wages shows
80
100
120
140
160
1980 1985 1990 1995 2000year
wage Moving-averages(3-year)
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some small ups and downs but it seems to have increasing trend, as an over-all impression. The 3-year
averages support this increasing trend of the wages.
Now, using the arima modeling , we investigate the autocorrelations and partial
autocorrelations of the wages from 1980 to 1999.
Figure 3.15: Autocorrelations and Partial Autocorrelations of Wages
Figure 3.15 above shows that the autocorrelations of the wage rate series decays very slowly
and its partial autocorrelations cuts-off at lag 1. This might implies that the partial autocorrelations of
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the wages are converges to zero at time lags greater than 1. This suggests that the wage series may
follows an AR(1) process.
But before we model the wage series into AR(1) model, we should check first if the wage follows
a stationary series.
Table 3.15: Stationary Test for the wage series
Dickey-Fuller test for unit root Number of obs = 19
---------- Interpolated Dickey-Fuller ---------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
Z(t) -0.213 -3.750 -3.000 -2.630
MacKinnon approximate p-value for Z(t) = 0.9370
The Augmented Dickey-Fuller test for unit root test in table 3.15 results to a non-significant p-
value at . This means that wage is not stationary series.
Since the wage series is not stationary, we can apply the differencing method for transformation
so that the wages will be stationary.
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Figure 3.16: First Difference Wages
Observing figure 3.16, it seems that the first difference of wages are fluctuating about a fixed
mean level, that is around 2-3 difference in wage rate. Also, the variability of the observed points is
constant over time. These observations suggest that the series of first difference of wage rate might be a
stationary series.
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Table 3.16: Stationary Test for First Difference Wages
Dickey-Fuller test for unit root Number of obs = 18
---------- Interpolated Dickey-Fuller ---------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
Z(t) -4.140 -3.750 -3.000 -2.630
MacKinnon approximate p-value for Z(t) = 0.0008
The Augmented Dickey-Fuller test for unit root test in table 3.16 results to significant p-value at
. This means that wage is stationary series.
Since the first difference wages is now stationary, then we can now investigate its
autocorrelations and partial autocorrelations.
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Figure 3.17: Autocorrelations and Partial Autocorrelations of First Difference Wages
Figure 3.17 shows that the autocorrelations of the first difference are insignificant starting at
time lags. Also, the partial autocorrelations of the first difference wages are also insignificant at time lag
1 and onwards. These observations characterize a series which follows a white noise process. This
means that the first difference wages series might follow a white noise process.
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Table 3.17: White Noise Test for First Difference Wages
Portmanteau test for white noise
Portmanteau (Q) statistic = 6.6805
Prob > chi2(7) = 0.4629
The Portmanteau test for white noise in table 3.17 shows an insignificant statistic at ,
which confirms that the first difference wage series is indeed from a white noise process.
The series is highly characterizing a random walk model since its a limited process of AR(1)
process with slowly decaying autocorrelation lags(see figure 3.15) and insignificant autocorrelation lags
on its differenced series(see figure 3.17). This means that we can fit the wages in to a random walk
model or arima(0,1,0).
Table 3.18: Summary Statistic of Random Walk Model fitting on Wages
ARIMA regression
Sample: 1981 - 1999 Number of obs = 19
Log likelihood = -56.87383
| OPG
D.wage | Coef. Std. Err. z P>|z| [95% Conf. Interval]
wage |
_cons | 2.594737 1.111471 2.33 0.020 .4162943 4.77318
/sigma | 4.827945 1.337679 3.61 0.000 2.206143 7.449747
Table 3.18 shows that the model contains a significant deterministic trend which is equal to
2.595. This means that our final model for the wages from 1980 to 1999 is given by
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This means that the wage rate of the palay farm workers depends on its preceding year value and to a
random error with additional of a constant 2.595.
Figure 3.18: Diagnostic plots
Figure 3.18 that the standardized residuals seem to fluctuate around zero level with constant
variance. This suggests that the residuals might be from a normal distribution. The autocorrelations of
the residuals are insignificant at lags 0 and onwards. This means that the residuals an uncorrelated.
Moreover, the dots on Ljung-Box statistic plots are insignificant (above p-value 0.05 line) which might
implies that the residuals are independently distributed.
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Table 3.19: Test for Independent Distributions of Residuals
Box-Pierce test
data: residuals
X-squared = 0.0281, df = 1, p-value = 0.8668
Box-Pierce test chi-squared statistic in table 3.19 is an insignificant at , which means
that the residuals of the model is independently distributed.
Table 3.20: White Noise Test for Residuals
Portmanteau test for white noise
Portmanteau (Q) statistic = 6.6805
Prob > chi2(7) = 0.4629
The Portmanteau test for white noise in table 3.20 shows an insignificant statistic at ,
which confirms that the residuals follow a white noise process. This means that the model
satisfies the assumptions of having a white noise residuals.
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Figure 3.19: Wages, Fitted values, and 3-year Moving-averages
Figure 3.19 shows the fitted values of wages and the 3-year moving average. The fitted values
shows the predicted value of wage rate of palay farm workers at specific year whole the 3-year moving
averages shows the average wage rate of palay farm workers at every 3 years.
3.4 Statistical Software
Graphs, tables and statistical inference results were obtained using the statistical softwares
STATA11 SE and R-program.
80
120
140
1980 1985 1990 1995 2000
year
wage Moving-averages(3-year)
Fitted values for arima(0,1,0)
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Chapter IV
Summary and Recommendations
4.1 Summary
Palay farm workers plays great role in the Philippines since they are the main producer of rice.
Real wage rate of palay farm workers shows an increasing trend since 1975 to 2011 and it is expected to
ton increase for the next five years. Also, their real wage rate follows a random walk model in which the
ahead value of real wage rate depends on its past year value and a random error.
In comparison of the real wage rate of male and female workers of palay farms, it is found that
the real wage rate of male workers are significantly greater than of female workers. But, the real wage
rate of female and male workers has the same trend of real wage rate with respected to time. That is,
they both increases and decreases with time.
4.2 Recommendations
The researcher of this paper recommends the following for future works and more effectiveness
of the research;
1. Focus on the studying the inflation rate and nominal wage rate as factors affecting real wagerate simultaneously.
2. Apply multivariate modeling(preferably vector time series modeling ) for variables nominalwage rate, real wage rate, and inflation rate.
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Bibliography
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Inc., Canada.
[2] Wei, W. W. S. (2006). Time Series Analysis: univariate and multivariate methods. 2nd
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Education, Inc., USA.
[3] http://countrystat.bas.gov.ph/?cont=10&pageid=1&ma=Q10LEWRS
[4] http://www.da.gov.ph/index.php/2012-03-27-12-03-56/2012-04-13-12-38-11
[5] http://economics.wikia.com/wiki/Real_Wages
[6] http://www.ehow.com/info_8239349_definition-real-wage-rate.html
[7] http://www.tcd.ie/Economics/staff/frainj/main/MSc%20Material/
TimeSeriesAnalysis/UNIVAR4.PDF
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