1. Using the Lazarsfeldian elaboration framework, hypothesise a plausible set of relationships between the variables in the dataset and draw a path diagram to show these. The final outcome variable should be netearn23 and all of the other variables in the dataset should appear in the diagram somewhere.

2. Fit a sequence of up to three regression models, each having netearn23 as the dependent variable, that together help you to evaluate the path model and estimate its parameters. You will probably need to recode some variables. You should show your model results in publication quality tables (not raw Stata output). That is to say, make nice tables in Word to paste in to your report. Interpret the coefficients and how they change in successive models, and any other statistics that the reader would find helpful in understanding what the results mean. You may use a limited number of charts too, if they aid interpretation.

Since the age of industrialization and even well before that, there have been curiosity to realize what characterizes the pay that a given employee gets. In a salary survey conducted by Zabel (2015) to determine what kind of factors influence salaries, several factors such as level of education, overtime working and skills are proposed. For instance, in the study outcome, a job whose position is hardest to fill attracted higher pay compared to that whose market is saturated.

Another research conducted in the mid-1990s indicated that there was a general salary gap between male and females (Aizer, 2010), this therefore, suggests that sex is another factor that is likely to cause salary difference.

The purpose of this study is to:

- Determine whether tall people earn more than others
- Determine if one’s ability to read, sex, parental social class as well as height do influence earnings of an individual

From the purpose of the research, the problem is therefore to examine the factors that affect earnings, i.e. “Is there a relationship between salary and factors such as height, sex, ability to read and social class?”

At the end of our research, we need to answer the following three questions:

- Does height influence an individual’s net earnings?
- Is there a relationship between reading ability, sex, and parental social class?
- Is there a relationship between reading ability, sex, parental social class, and height?

In about the middle period of industrialization, around 1851 in Britain, there begun an exercise to classify the British population according to occupation and industry (Rose, 1995). In general, the population was stratified into the following classes:

- Professional occupations
- Managerial and Technical occupations

- Skilled occupations i.e. “Non-manual” and “Manual”

- Partly skilled occupations
- Unskilled occupations

Therefore, classification according to social classes occurred among working persons and has become the basis of societal class stratification.

Erola and Lehti (2016) in their social paper on social stratification and mobility argue that, “…despite relatively high degree of equality of opportunity in most of the developed countries, family background still influences inheritance of social classes.” As such, the socioeconomic status tend to influence each other, i.e. education, class and income (Crowford and Erve 2015)

In a research on gender and income disparities, Ruel and Hauser (2013) note that there is an identifiable income gap between male and female. More especially, there is a large wealth accumulation gap between married men and married women, such differences are attributed to investment strategies and selection effects. Additionally, households that have a single parent accumulate less wealth compared to those with two parent, i.e. the married (Schmidt and Sevak, 2005).

Past studies indicate that there is little preference for short persons more so short men, according to a study by Gregory in the 1960s. Pinsker (2015) argues that, “an extra inch correlates to an estimated $800 in increased annual earnings.” These differences are attributed to the fallacy that tall persons especially men (gender disparity as well) are often stronger and get picked to do most task which are idealized to require strength. In the post by the Atlantic, it is noted that among men those whose height is between 5’4’’ and 5’6’’ have the steepest earning differences.

According to Tyrrell (2016), height and socioeconomic status are correlated. Earlier on, we noted that socioeconomic status which is majorly determined by one’s income form a basis for social stratification. Consequently, males and females seem to differ in height where men are averagely taller compared to women. The figure below represents the hypothetical relationship between the research variables with net earnings as the outcome variable where the underlying assumptions also include that every individual is influenced by a given parental social class.

## Purpose of the Study

Data for this research is obtained from UK data service. It contains 7 variables i.e.: Gender (Sex), Net earnings, Height, Parental social class, Ability to read, intmth11, and Female

During data cleaning and management, the sex variable is renamed to gender while the female variable is dropped altogether due to its redundant nature, i.e. the female and gender variables serve the same purpose such that they both indicate whether a respondent is male or female. Another variable that is not useful for our data analysis is the intmth11 which is dropped from the dataset. In addition, the netearn23 is renamed to Net earnings, height23 is renamed to Height and read11 to Read. The gender variable is coded such that, 1-Male, 2-Female. The parental social classes are coded from 1:6 with 1 being the highest social class while 6 is the lowest and is renamed to Class from class16.

Our original interest is to determine the relationship between net earnings and other predictor variables. Given the three research questions, we fit three regression models with net earnings being the response variables and in the 1^{st} equation height being the only predictor variable. In the 2^{nd} regression equation, reading ability, sex, and parental social class are the predictor variables while in the last equation, all the variables excluding net earnings which is the predictor variable in thee dataset are independent variables as in the equations below:

- Y
_{i}=β_{0}+β1X_{1}+ £_{I}, where: β_{0}is the regression coefficient

β_{1} is the coefficient of predictor variable X_{1} **height**

_{ } £_{i} is the random error term

Y_{i} is the response variable **net earnings**

- Y
_{i}=β_{0}+β_{1}X_{1}+β_{2}X_{2}+ β_{3}X_{3}+£_{I}, where: β_{0}is the regression coefficient

β_{1} is the coefficient of predictor variable X_{1} **reading ability**

β_{2} is the coefficient of predictor variable X_{2} **sex**

β_{3} is the coefficient of predictor variable X_{3} **Parental social class**

_{ } £_{i} is the random error term

Y_{i} is the response variable **net earnings**

- Y
_{i}=β_{0}+β_{1}X_{1}+β_{2}X_{2}+ β_{3}X_{3}+ β_{4}X_{4}+£_{I}, where: β_{0}is the regression coefficient

β_{1} is the coefficient of predictor variable X_{1} **reading ability**

β_{2} is the coefficient of predictor variable X_{2} **sex**

β_{3} is the coefficient of predictor variable X_{3} **Parental social class**

β_{4} is the coefficient of predictor variable X_{4} **height**

_{ } £_{i} is the random error term

Y_{i} is the response variable **net earnings**

To help in answering the research questions, three sets of hypotheses are formulated:

**Null hypothesis**

Taller persons earn just like any other persons

**Alternative hypothesis**

Taller persons earn more than other persons, i.e. there is a relationship between height and net earnings.

**Null hypothesis**

One’s ability to read, parental social status and sex do not affect an individual’s net earnings.

**Alternative hypothesis**

There is significant relationship between one’s ability to read, parental social status and sex and an individual’s net earnings.

**Null hypothesis**

There is no relationship between all the predictor variables i.e. height, sex, parental social class as well as one’s ability to read and net earnings

**Alternative hypothesis**

There is significant evidence that there is a relationship between all the predictor variables i.e. height, sex, parental social class as well as one’s ability to read and net earnings.

**Y**_{i}**=****β**_{0}**+****β****1X**_{1}

From the results in table 1 above, the p-value of F-statistic is 0.000 which is less than the computed F-value 522.14, hence indicating that height is significant in predicting net earnings, in addition, the coefficient of regression is -85.0305 while the coefficient of height is 92.34439. In addition, the adjusted r-squared is 0.1056 which is used to measure the efficiency of the model upon entry of new variables into the regression model. Hence using the regression diagnostics in the regression equation we obtain:

## Research Questions

**Y**_{i}**= ****-85.0305 ****+ ****92.34439****X**** _{1}**,

**X**

**height (cm), we do not include the random errors since they do not affect the expectation. Therefore, for every increase in height by 1 cm, an individual is projected to increase by $7.3.**

_{1 }The p-value for the t-statistic is 0.000<0.05 at 95% confidence interval, we reject the null hypothesis that height does not affect net earnings and conclude that there is significant evidence that height affects net earnings, proving Pinsker (2015) correct.

**Y**_{i}**=****β**_{0}**+****β**_{1}**X**_{1}**+**** β**_{2}**X**_{2}**+ ****β**_{3}**X**_{3}

From table 2 above, the p-value of the t-statistic is 0.000 for sex and reading variables while it is 0.048 for the parental social class variable which are all less than 0.05 at 95% confidence interval. We therefore reject the null hypothesis of no effect between response and predictor variables and conclude that one’s parental social class, ability to read and sex do influence an individual’s net earnings, i.e.

**Y**_{i}**=** **98.70261 ****+****0.4898992****X**_{1}**-22.15094X**_{2}**-.5285474X**_{3}

Such that holding all other factors constant, an increase in 1 parental social class level increases individual net earnings by $98.2 while a female worker earns $76.6 less than a male worker. The ability of an individual to read has a positive relationship with net earnings where, assuming that all other factors are constant one earns approximately $99.2 more than a person who does not know how to read.

**Y**_{i}**=****β**_{0}**+****β**_{1}**X**_{1}**+**** β**_{2}**X**_{2}**+ ****β**_{3}**X**_{3}**+**** β**_{4}**X**_{4}

From the regression diagnostics in table 3, the adjusted R-squared statistic increases upon entry of height into the regression model from 0.1617 to 0.1638 indicating that the height variable improves the model. Moreover, Sex, Read and Height variables are significant in predicting net earnings given that they have p-value for t-statistic being less than 0.05 while that of parental social class is 0.104>0.05 at 95% confidence interval.

The regression coefficient intercept is 61.30585 while the coefficient of Read variable is 0.468691, Sex variable is -19.2853, we assume the parental class variable since it is not significant in the regression model while that of height variable is 19.43205. We therefore obtain a regression equation of the form:

**Y**_{i}**=**61.30585 **+**0.468691**X**** _{1}**-19.2853

**X**

_{2}**+**

**9.43205**

**X**

_{4}Hence from the resulting equation it is clear that there is a positive relationship between ability to read and height variables and net earnings while sex has a negative relationship with net earnings.

**Conclusion**

In conclusion, several factors are significant in influencing an individual’s net earnings. For instance, from our results, one’s sex plays a huge part in determining their net income, i.e. there is an income disparity that is defined by gender where women and men do not earn the same income. On the other hand, we notice that an increase in height has a positive effect on the income an individual gets However, taking a look at the third regression results, we realize that some factors when taken together cause others to be less significant in predicting an individual’s net income. Consider the 2^{nd} regression results where, in the absence of height variable, parental social class influenced individual net earnings whereas upon introduction of the height variable parental social class becomes insignificant in predicting net earnings.

Therefore, can safely conclude that taller persons earn on average more and that there is a relationship between one’s sex and ability to read and net earnings as it is also with height.

Upon completion of this research, it is recommended that research into what leads to the income disparity between male and female to be conducted so as to determine the underlying causes.

**References**

Aizer, A. (2010) The gender Wage Gap and Domestic Violence. American economic review, 100(4), pp. 1847-1859. DOI:10.1257/aer/100.4.1847

Crowford, C. & Erve, L. (2015). Does Higher education Level the Playing Field? Socioeconomic Differences in Graduate Earnings. Education sciences, 5(4), pp. 380-412.

Erola, J. & Lehti, H. (2016). Parental Education, class and income over early life course and children’s achievement. Research in Social Stratification and Mobility, 44(6), pp. 33-43. DOI: 10.1016/j.rssm.2016.01.003

Pinsker, J. (2015). The Financial Perks of Being Tall. Available from: https://www.theatlantic.com/amp/article/393518/

Rose, D. (1995). **Official Social Classifications in the UK**. Available from: https://sru.soc.surrey.ac.uk/SRU9.html

Ruel, E. & Hauser, R. (2013). Explaining the Gender Wealth Gap. Demography, 50(4), pp. 1155-1176. DOI: 10.1007/s13524-012-0182-0

Schmidt, L. &Sevak, P. (2005). Gender, Marriage, and asset Accumulation in the United States. Working papers, 109(3), pp. 33-54

Tyrrell, J. (2016). **Height, Body mass index and Socioeconomic status: Mendelian ****randomization Study in UK Biobank**. Available from: https://www.bmj.com/content/352/bmj.i582

Zabel,R. (2016). **A profession in need of change: Results from the 2016 survey**. Available from: https://www.isa.org/intech/20161006

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