SEN700 Statistical Data Collection and Interpretation

the analysis of statistical data of the United States GDP and other factors like consumer price index, real interest rate, and broad money. The research aims to identify the dependence of the above-mentioned factors on the gross domestic product as the dependent variable and the other three factors as the independent variables.

Hypothesis

H1: There is a positive and significant relationship between Gross Domestic Product and Consumer Price Index

H2: There is a positive and significant relationship between Gross Domestic product and real interest rate

H3: There is a positive and significant relationship between Gross Domestic Product and Broad Money

Parameters and the sample population

The parameters identified for analysis are gross domestic product, consumer price index, interest rate, and broad money.

Gross Domestic Product (GDP)

The Gross Domestic Product can be termed as the value n monetary terms that are attached to all finished goods and services that are manufactured within a particular state’s border in a specific time period [10]. In the United States, the GDP is calculated on a quarterly basis and then annualized for annualized for each quarter [11]. The Gross Domestic Product is, therefore, a broad measurement of the overall economic activity of a nation thereby earning the nickname, the godfather of the indicator world. The Gross Domestic Product is very important in that it is used to gauge the standard of living in a particular country [12]. The uniformity of the Gross domestic product has enabled the economic indicator to be used in comparing the productivity of the numerous nations with an accuracy of the highest degree [13]. GDP is tracked over a long span of time and is used in gauging the economic decline or growth of a nation [14]. As a result, it is an important tool that can be used in determining whether or not a country is in recession. The GDP can be determined primarily using three methods, expenditure approach, the output approach, and the income approach.

Consumer Price Index

The consumer price index (CPI) scrutinizes the weighted average of prices of a basket of consumer services and goods [15]. The CPI is measured by taking the variations in the price of each item in a predetermined basket of services and goods and then averaging them. The CPI changes are used in assigning the changes in price which are associated with the cost of living [16]. Thus, it is the most used statistics in the identification of periods of deflation and inflation. In the United States, the United States Bureau of Labor Statistics is the institution which reports the consumer price index on a monthly basis. The institute has done this since 1913 [17]. The CPI wide use in measuring inflation has made it as an effective tool which is used to determine the efficiency and the effectiveness of the government’s economic policies [18]. The CPI gives citizens, businesses and the government an idea about the changes in price in the economy. Thus, it acts as a guide which ensures the making of informed decisions regarding the economy. The components of the CPI and the CPI itself can be used as a deflator for other economic factors which include hourly or weekly earnings, the worth of a consumer dollar to find its purchasing power and the retail sales [19]. On the other hand, the index is used in adjusting the eligibility levels of people for certain types of government assistance which include social security and automatically providing the cost of living wage adjustment to domestic workers. 

Real interest rate

The real interest rate is identified as an interest rate which has been attuned in order to eliminate the inflation effects so as to replicate the real cost of funds to the borrower and the real yield to an investor or a lender [20]. Thus, it does not take inflation into account. It is normally quoted on loans and bonds. The real interest rate is usually measured as the amount through which the nominal interest rate is greater than the interest rate [21]. The economic indicator reflects the modifications in the purchasing power that is a resultant of an investment which is based on the swings in the inflation rates. The real interest rate in the United States is reported by the United States Federal Reserve [22].

Broad money

Broad money is classified as the most inclusive method that is used in measuring the money supply of a given country [23]. Broad money is the money supply which is the entirety of assets which households and businesses use to make payment or hold as a short-term investment. Broad money does not only include coins and notes but also savings accounts, and deposits in savings accounts [24]. Moreover, broad money may include gilts and treasury bills. Such financial securities are observed as near money since they are more illiquid compared to instant saving accounts and cash. However, broad money does not include assists such as shares and long-term dated securities. Though they can be sold, they are not included since they fall into the category of assets rather than money. Thus, broad money includes M2, M3, and M4 [25].

Collected data

The nature of the research's data that was used was secondary. The data was acquired from an existing source, that is, the World Bank. Though the data was freely available on the internet, the ownership of the original data had to be acknowledged. Moreover, the data obtained from World Bank was checked to ensure that the data is adequate and relevant. Consequently, it was evaluated through the methodology of data collection, period of data collection, accuracy, the aim of collecting the data, and the data content.

Data collected on the gross domestic product, consumer price index, real interest rate and broad money was quantitative in nature. Moreover, the data was also time series, that is, the data covered a spread of time course (1961 to 2016).

The following are the trends of the collected data.

GDP

It is evident that the United States gross domestic product has been on a constant rise. Thus, it can be deduced that the economy of the United States has been on a constant rise since 1961. However, 2008, the gross domestic product took a slight dip till 2009. However, the economy rebounded successfully to record new highs since 1961.

As of 2016, the United States Gross Domestic Product was recorded at the US $18,624.48 billion. The impressive numbers of the gross domestic product reflect a positive contribution of exports, expenditure, federal government spending, private inventory investment, and local and state government spending [26].

Similarly to the Gross Domestic Product, the consumer price index of the United States has been on a constant rise. Though the rise was marginal between 1961 and 1973, the rise has been tremendous from 1973 to 2015.

Real interest rate

 

The real interest in the United States has been experiencing frequent fluctuation from 1961 to 2016. From a high of 5.58% in 1970, the real interest rate fell drastically to be recorded at an all-time low of -1.28% in 1975. However, the real interest rate changed positively to record a new high of 8.72% in 1981. From then, the real interest rate fell with frequent fluctuations to be recorded at a current real interest rate of 2.21% in 2016.

Broad money as a percentage of the Gross Domestic Product in the United States has been in a relatively constant rise. Broad money was recorded at a low of 59.8% in 1994 having fallen from a high of 76.99% in 1986. However, broad money has been on the rise has to reach a high of 91.06% in 2009 then easing till 2016 where it is recorded at 90.28%.

Tools used for a research study

The statistical tools that were used in the research study with the objective of fining the dependence of gross domestic product on various indecent variables like consumer price index, real interest rates, and broad money are regression analysis, mean, standard deviation, maximum, and minimum.

Descriptive statistics

Descriptive analysis of the data was carried out in order to provide simple summaries regarding the measures.

Table 1.1: descriptive statistics

	Observations	Minimum	Maximum	Mean	Std. Deviation
GDP (current US$ in Billions)	56	563.30	18624.48	6885.2516	5656.74970
Consumer price index	56	13.72	110.07	56.6341	32.31029
Real interest rate (%)	56	-1.28	8.72	3.8500	2.30184
Broad money (% of GDP)	56	59.48	91.06	72.0454	8.38451

Table 1.1 shows a brief of the descriptive results of the collected data. The number of observations made for each variable is 56. Thus, data collected from 1961 to 2017 represent 56 years. The mean of the GDP is US$ 6,885.25 Billion with a standard deviation of US $5,656.75 Billion. In regards to this, the highest amount of GDP recorded in the 56 year period is the US $18,642.48 Billion while the least is the US $563.3 Billion. Hence, the GDP in the United States has ranged from US$ 563.3 Billion to SU $18,624.48 billion.

The mean of the consumer price index in the US from 1961 to 2017 is 56.63 units with a standard deviation of 32.31 units. Consequently, over the 56 years, the consumer price index had a maximum of 110.07 units while the minimum was 13.72 units. Thus, the consumer price index in the United States has ranged from, 13.72 units to 110.07 units between 1961 and 2017.

On the other hand, the real interest rate had an average of 3.85% with a standard deviation of 2.3%. The maximum interest rate observed in the 56 years is 8.72% while the minimum was -1.28%. Thus, over the 56 year period, interest rates in the United States have ranged from -1.28% to 8.72%.

Broad money, as a percentage of the US GDP, had an average of 72.05% with a standard deviation of 8.38%. Consequently, between 1961 and 2017, it experienced a maximum of 91.06% and a minimum of 59.48%. Therefore, broad money as a percentage of the GDP ranged from 59.48% to 91.06%.

Correlation

A correlation analysis was also adopted. The method is a statistical evaluation which is aimed at determining the strength of a relationship between two continuous variables which are numerically measured [27]. Through the correlation analysis, the researcher gets to know whether it is possible to establish a connection between variables. 

Table 1.2: Correlation

		GDP (current US$ in Billions)	Consumer price index	Real interest rate (%)	Broad money (% of GDP)
GDP (current US$ in Billions)	Pearson Correlation	1
	Sig. (2-tailed)
Consumer price index	Pearson Correlation	.980**	1
	Sig. (2-tailed)	.000
Real interest rate (%)	Pearson Correlation	-.083	.055	1
	Sig. (2-tailed)	.544	.687
Broad money (% of GDP)	Pearson Correlation	.730**	.667**	-.269*	1
	Sig. (2-tailed)	.000	.000	.045
**. Correlation is significant at the 0.01 level (2-tailed).
*. Correlation is significant at the 0.05 level (2-tailed).

From the correlation analysis, it is evident that the Consumer price index and the GDP are positively correlated at 0.98. From this, it can be deduced that consumer price index and the GDP are strongly and positively correlated. The correlation is statistically significant at 0.01 levels (2-tailed).

The real interest rate is weakly and negatively correlated with the GDP, -0.083 correlation. However, the correlation is neither significant at the 0.01 level and the 0.05 level (2-tail). Broad money as a percentage of the GDP is strongly and positively correlated with GDP, 0.73 correlations. On the other hand, the correlation between broad money and GDP can be seen to be significant at the 0.01 level (2-tail).

Statistical model

The study aimed to establish a relationship between dependent variables, which are Gross Domestic Product (GDP), an independent variable, which is the interest rates, consumer price index, and broad money as a percentage of gross domestic products. Thus, Gross Domestic Product= f (interest rates, consumer price index, broad money).

Thus, GDP = β₀ - β₁r +β₂CPI + β₃Bm

β ₀ is assumed to be positive and about the same size as last year's GDP. β ₂ and β3 are also assumed to be positive since it is assumed that CPI and broad money are an increasing factor of GDP.

On the other hand, β1 should be negative since gross domestic product goes down as interest rates go up.

11. Statistical Results

A regression analysis was carried out as seen in the subsequent tables.

1. Regression Results

Table 1.3: Model summary

Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.991a	.982	.981	774.85627
a. Predictors: (Constant), Broad money (% of GDP), Real interest rate (%), Consumer price index

 

From table 1.3, it is seen that the adjusted r squared of the model is 0.981. From this, it can be deduced that 98.1% of the variability in the model is explained by the variables in the model. However, 1.9% of the variability is explained by variables which are not in the model. On the other hand, the R square indicates that the model explains 99.1% of all the variability of the data around its mean.

Table 1.4: Analysis of variance

Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	1728714028.046	3	576238009.349	959.753	.000b
	Residual	31220916.728	52	600402.245
	Total	1759934944.774	55
a. Dependent Variable: GDP (current US$ in Billions)
b. Predictors: (Constant), Broad money (% of GDP), Real interest rate (%), Consumer price index

Consequently, table 1.4 shows that the regression model predicting the dependent variable (GDP) is statistically significant. The deduction is based on the fact that p < 0.000 is less than 0.05. Therefore, the regression model statically and significantly predicts the outcome of the variable GDP. The regression model also shows that there is a goodness of fit between the data. 

Table 1.5: Parameters Estimates

Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta
1	(Constant)	-4960.196	1245.093		-3.984	.000
	Consumer price index	163.975	4.591	.937	35.716	.000
	Real interest rate (%)	-281.030	49.866	-.114	-5.636	.000
	Broad money (% of GDP)	50.535	18.342	.075	2.755	.008
a. Dependent Variable: GDP (current US$ in Billions)

All the parameters used in the model were statically significant except for broad money. The gross domestic product, consumer price index, and the real interest rate have p-values which are less than the significant level of 0.05 (5% probability). However, broad money was deemed to be insignificant since its p-value is more than 0.05 (5% probability).

Results discussion

From the regression model, it can be seen that the United States Gross Domestic Product holding all factors constant is the US $-4,960.2 billion.  A negative gross domestic product is an indication that the economy of the United States is experiencing a contraction in the business earnings or sales. Consequently, a negative gross domestic product s an implication that the country’s economy is contracting. The negative gross domestic product, holding all factors constant therefore suggest that the economy of the United States is experiencing the increasing real value of wages, there is a decrease in real income, there are low levels of industrial production in the economy and there is a decline in both retail and wholesale sales.

1. Hypothesis 1

The regression model shows that the consumer price index has a positive impact on the gross domestic product. Therefore, holding all other factors constant, a unit increase in consumer price index increases the level of the gross domestic product by 163.98 units. Since the p-value is less than 0.05, the decision is to accept the null hypothesis. Therefore, the relationship between consumer price index and the gross domestic product is positive and significant.

1. Hypothesis 2

Conversely, the real interest rate is observed to have a negative influence on the gross domestic product. Thus, a unit increase in real interest rate decreases the level of gross domestic product in the US economy by 281.03 units ceteris peribus. However, the real interest rate coefficient is seen to be significant. Thus, we choose to accept the null hypothesis that real interest rate and the gross domestic product is negatively and significantly related.

1. Hypothesis 3

Finally, broad money as a percentage of the GDP is seen to have a positive impact on the gross domestic product. Hence, a unit increase in broad money leads to 50.53 increase in the gross domestic product in the United States. Since the p-value is more than 0.05, we choose to reject the null hypothesis. Thus, the relationship between broad money and the gross domestic product is not positively and significantly significant.

Thus,
   GDP = -4,960.196 + 163.975CPI + 50.535Bm – 281.03r

The consumer price index and the gross domestic product are the two most vital features of a healthy country [28]. From the research, it is evident that the consumer price index positively and significantly affects the gross domestic product. Thus, a steady growth of the consumer price index offsets the negative impacts on the gross domestic product.  When consumer price increases, wages eventually increases since the consumer price index is adapted to adjust income. Adjustment of the consumer price index to adjust tax brackets, retirement benefits, wages, and other important economic indicator is done by the Bureau of Labor and Statistics (BLS) [29].  On the contrary, if the government is slow compared to the market, the gross domestic product will grow fast and the government will not be in a position to make adjustments that the people require to uphold a good quality of life since the cost of living has augmented too fast.

An increase in demand for real goods and services will necessitate more production of real goods and services, therefore, pushing up the gross domestic product of the United States [30]. An increase in demand warrants an increase in money supply and also a decrease in real interest rates. As a result, the gross domestic level of the United States will begin to slowly expand. Therefore, in tandem with the research findings, the decrease in interest rate will lead to an increase in the gross domestic product. Conversely, an increase in broad money will also lead to an increase in the United States gross domestic product.

Conclusions and recommendations

The research has proved that consumer price index and broad money are all increasing factors of gross domestic demand. On the other hand, the real interest rate was a decreasing factor for the gross domestic product. Therefore, an upsurge in the real interest rate leads to a decline in gross domestic demand while a deterioration in the real interest rate leads to an improvement in the gross domestic demand.

Since low-interest rates and an increasing money supply causes inflation, policymakers in the United States should ensure that the two are sustained so far to support the growth of the gross domestic product. Anything in excess will result in an increase in the levels of price without actually adding any economic value.

Future researchers

The research carried out ha proved all the assumption which the researcher had regarding the factors which determine gross domestic product in the United States. However, more research needs to be carried out in order to improve the research. Future researchers can carry out researchers which include more variables which were not included in the regression analysis. Consequently, they should consider other countries and regions in order to ensure that the results are similar across the globe.

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