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

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


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


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


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


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


Interpolated Dickey-Fuller



Z(t) -5.596 -3.682 -2.972 -2.618


-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


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


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


---------- Interpolated Dickey-Fuller ---------



Z(t) -0.213 -3.750 -3.000 -2.630


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


---------- Interpolated Dickey-Fuller ---------



Z(t) -4.140 -3.750 -3.000 -2.630


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


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


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


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

[1] ea, ., Tiao, . ., Tsay, R. .(001). A Course in Time Series Analysis. John Wiley and Sons,

Inc., Canada.

[2] Wei, W. W. S. (2006). Time Series Analysis: univariate and multivariate methods. 2nd

ed. Pearson

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
http://countrystat.bas.gov.ph/?cont=10&pageid=1&ma=Q10LEWRShttp://countrystat.bas.gov.ph/?cont=10&pageid=1&ma=Q10LEWRShttp://www.da.gov.ph/index.php/2012-03-27-12-03-56/2012-04-13-12-38-11http://www.da.gov.ph/index.php/2012-03-27-12-03-56/2012-04-13-12-38-11http://economics.wikia.com/wiki/Real_Wageshttp://economics.wikia.com/wiki/Real_Wageshttp://www.ehow.com/info_8239349_definition-nominal-wage-rate.htmlhttp://www.ehow.com/info_8239349_definition-nominal-wage-rate.htmlhttp://www.ehow.com/info_8239349_definition-nominal-wage-rate.htmlhttp://economics.wikia.com/wiki/Real_Wageshttp://www.da.gov.ph/index.php/2012-03-27-12-03-56/2012-04-13-12-38-11http://countrystat.bas.gov.ph/?cont=10&pageid=1&ma=Q10LEWRS

Documents

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