## Abstract

Regression analysis is the statistical technique commonly used in econometric modeling and carrying out economic forecasts. This study sought to assess the precision multiple linear regression in evaluating the evolution in real GDP per capita in the USA between 1998 and 2011 using expenditure approach. Three macroeconomic variables were used; Gross domestic product, net investment and final consumption. Net investment and final consumption are model regressors predicting GDP. The researcher used MS Excel to carry out all the statistical analysis on the data. The analysis result shows weak linear development GDP increment. Small fluctuations were observed around the fitted trend line implying that the data follows the lognormal distribution. The conclusion drawn from the analysis is despite large relative growth over the selected period, there is slow economic development.

## Keyword: GDP per capita, aggregate, multiple regression, regressors

Introduction

Evolution of Real GDP per capita has been studied by most economists since early 1930s. The most influential work is that relating aggregate macroeconomic factors and national accounting. Charles Hall (19-53) introduced the idea of GDP per capita evolution in two-components. This economist identified net investment and final consumption as being key macroeconomic variables that affect the growth of real GDP of a country. The justification behind the selection of these variables is that they are less responsive to the usual business cycle. They are therefore efficient in forecasting the GDP growth in short-run and long-run.

Further still, Charles Hall (19-53) proposed an econometric regression model which describes how GDP growth is explained based on net investment and final consumption only. According to the proposed model, fluctuations observed are due to social-economic factors such as the demographic structures within the economy at a given time. By implication, it can be concluded that if there are no significant changes in the structure and composition of the population, relative growth of the GDP per capita will be statistically insignificant.

Classical economic theory holds that growth of real Gross Domestic Product of a given country using expenditureis a function of than five macroeconomic variables; consumption, investments, government expenditure, exports and imports. Multiple linear regression can be used with all the variables stated to estimate GDP. However, the cost of obtaining this data is not economically viable in empirical research in academia and even in practice. Also, the computation effort using all the five variables is quite demanding and complex.

This study is devoted to decomposing the growth of Gross domestic product into two components without oversimplifying the real situation; net investment and final consumption only, taking demographic structure of the economy as the only social-economic factor.

## Literature Review

The fundamental challenge in economics is to explain with precision the causes of economic growth and development (Baumol 415-426). The most straightforward indicator for economic growth is the GDP per capita which is computed by dividing total GPD by the entire population of the country. It is evident that such an indicator is likely to oversimplify the reality. Now the question one asks is then what precisely remains to be explained? We are aware that in the normal business cycle, economic growth is associated with different rates of growth. Sometimes there is rapid economic growth while at some points there is sluggish economic growth. Why? It is also important to interrogate why economic growth rate is not a universal concept.

The modern literature explains that we can measure economic growth rate by the total output from the economy. This theory guides our thinking to view economic growth as a factory capable of transforming input into finished useful products (outputs). The essential factors of production which are herein referring to as inputs are three; 1) labor, 2) natural resources such as land and 3) capital. Labor includes both skilled and semi-skilled fueled by entrepreneurship (Deardorff 209-236). Natural resources in most cases are the immovable factors of production such as land and water sources. These factors of production can be homogenous to more than one economy say neighboring countries can share most natural resources. The GDP growth can still be different to countries having the same factors of production. Such variation can be explained in terms of different technology levels.

GDP per capita growth model in the United States of America was developed and used by Kitov (288-298). The model uses external parameter to make a probabilistic forecast of the observed progress of the gross domestic product and its components. According to this model, there is a direct implication that it is possible to increase the real GDP per capita growth without disturbing economic structure within the society.

The model used by Kitov (288-298) fails to show the link between external parameters (labour, land and capital) and economic growth rate in a universal sense. The failure of this model in explaining the nature of economic growth especially during and after the financial crisis in 2008 has brought disturbing questions in modern economics as to whether evolution of real GDP can be sufficiently described based on resource availability and technology.

Emerging markets and developing economies particularly in the Middle East and Asia Minor have struggled with the question; do they lack the potential to grow their economy or are they unable to reach their full potential. This has shifted the perspective from looking at the growth in real GDP in terms of resources and technology to private and public investment, final consumption and other social-economic factors.

In order to understand the role of net investment, final consumption and population dynamics in economic progress, it is important to understand the underlying economic theory behind each of the three variables. Most importantly, we need clearly understand how econometric, Mathematical and Statistical tools can be applied to make forecast accurately.

## Economic Model

This study used three macroeconomic model; GDP per capita, net investment and final consumption. Each of these variables is a function of other economic variables. Investment is a process of allocating money in business enterprises with the aim of getting better returns. Total investment consists of two components namely autonomous investment and induced investment (also called endogenous investment). Investment is a function of income of the investor. However, autonomous investment is independent of income.

I=α+βY

Where I=Investment

α=Autonomous investment

β=Investment (also called endogenous investment) and

Y= Income

Consumption is the final utilization of goods and services produced within an economy. Consumption is key in driving economic growth because it motivates aggregate demand. The consumption level of individuals is a function of income. It is however important to understand that disposable income is the proportion of income that is available to an individual and they are free to either spend or save.

Total consumption has two components; autonomous and induced consumption. Autonomous consumption is independent of the disposable income. Marginal propensity to consume is a ratio of average change in total consumption to average change in total income of the consumer Baumol (415-426). Induced consumption if the coefficient to marginal propensity to consume as shown in the model below.

C=a+byd

Where C=total consumption

a= Autonomous consumption

b=∆C∆Y= Marginal propensity to consume

yd= Disposable income

In this study, population dynamics and other social-economic factors that affect the real GDP growth rate will be absorbed in the error term u.

The purpose of this research was to decompose GDP per capita into two components; net investment and final consumption the model become

GDP=I+C+u

GDP=α+βY+a+yd*∆C∆Y+u

Where u is the stochastic term in the model assumed to be normally distributed with mean zero and constant variance and also uncorrelated with all the other variables under study.

## Empirical Methodology

This section presents the theoretical framework of the based on the aggregate economic variables to be used in the analysis. Investment is a function of income and specific need of the economy which is often determined by the population structure, composition and size. According to the accelerator principle, more earnings in the economy motivates endogenous investments. Consumption is also a function of income.

There are three basic theories explaining determinants of consumption; absolute income hypothesis, relative income hypothesis, and permanent income hypothesis. These approaches may vary in nonessential minor details, but the converging concept underpinning all of them is that income is a crucial variable to consider in consumption model. This section presents variable description, preliminary data analysis and regression equation used in the estimation of real GDP per capita growth rate.

## Variable description

In this study, we are focusing on three macroeconomic variables; GDP per capita, net investment and final consumption in USA from 1998 to 2011. Since the main task in this research is estimating the GDP per capita, this is taken to be an endogenous variable. In econometric modeling, and endogenous variable is dependent on a set of exogenous variables. Therefore, there are two exogenous variables in this study; net investment and final consumption.

It is important to note that given a set of econometric model in which investment function and consumption functions are involved, they are often identified as endogenous variables and in each case, household income in presented as an exogenous variable. Having income as a common variable in both investment and consumption functions creates endogeneity problemMerton (288-298). This is because when we form an autoregressive model including all the exogenous variables, there is a high probability that these variables will correlate with the stochastic term.

## Preliminary Data Analysis

This research used secondary data from published sources. The collected information was first summarized in Microsoft Excel and later exported to econometric analysis software called E-vies for further analysis of the data. First, the descriptive statistics and histogram for the three variables in our regression model was performed in MS Excel. A time series plot for the three variables was produced using E-vies software.

Descriptive statistics gives a summary of the three measures of central tendency for each variable, measures of dispersion and moments. Measures of central tendency are the mean, mode and median, measures of dispersion are the variance, standard deviation and the range. The third and fourth moments are the skewness and kurtosis respectively. The table below gives a descriptive summary statistics of GDP per capita, net investment and final consumption.

The mean for GDP between 1998 and 2011 is equal to $ 347095.70, final consumption is $ 290705.10 and net investment is $ 60394.70. The distribution of these variables can be best understood by looking at the skewness and kurtosis coefficients. For a normally distributed data, the coefficient of skewness is zero while the kurtosis is 3. Form the data above all the three variables are negatively skewed. This is indicated by the negative figure in the skewness.

A histogram gives visual display of the comparison among the three variables for the entire period of study. Below is the histogram showing comparative distribution of the data in table 1 above.

The data was finally exported to E-views software and a time series plot for the data in table 1 above. A time series plot displays trend components for each of the three variables in the study. The table below shows the simultaneous trend in GDP per capita (Green line), net investment (Red line) and final consumption (Blue line)

## Regression Equation

The study used a multiple linear regression model of the form

y=β0+β1X1+β2X2

## Where; β0 is the intercept, while β1 and β2 are the coefficients on the first and second independent variables

They convey the marginal effect of each independent variable on the dependent variable. As noted earlier, increasing net investment and final consumption increases GPD per capita. This gives an indication that we expect coefficients β1 and β2 will have positive signs.

The aim of this study is to decompose GDP per capita evolution into two components; net investment and final consumption. The validity of the coefficients in the above regression model were tested at 5% level of significance. We test the hypothesis below and reject the null hypothesis whenever p-value is less that the level of significance.

HO: β1=β2=0

## H1: β1≠β2≠0

Rejecting the null hypothesis implies that implies that indeed net investment and final consumption significantly influence GDP per capita evolution.

Data Description

The study used times series data from secondary sources. The data collection began with obtaining figures relating to household income then the economic models for investment and consumption stated earlier used to estimate net investment and final consumption. Since these endogenous variables were taken as exogenous variables in the final model of analysis, population figures were taken into consideration to avoid multi colinearity problem (Deardorff (209-236). However, demographic dynamics were not displayed because they were involved in the computation of GDP per capita, thus remaining silent as social economic factors.

Since we are using time series data, the regression equation y=β0+β1X1+β2X2

## Is appropriate to perform forecasting

Below is the summary out of the regression analysis of our data.

Therefore, the regression model is

y=8927.57+1.17X1+0.28X2

## Results

At 95% confidence level, we reject the null hypothesis. This is because the p-value for the independent variables is less than 5% level of significance. The power of the test in this hypothesis based on the p-value is that the p-value less than the specified level of significance indicate the probability of a rare event occurring in the sample. Therefore, we conclude that net investment and final consumption significantly influence GDP per capita evolution.

We note that the independent variables have coefficients with positive signs. The coefficient of 1.17 on the first independent variable implies that 1 per cent increase in final consumption leads to a corresponding increase in GPD per capita by 1.17 per cent. Similarly, 1 percent increase in net investment leads to a corresponding increase in GDP per capita by 0.28 per cent. The correlation between the dependent variable and each independent variable can be further understood by the computing the correlations as presented in the table below.

Clearly, each independent variable has a high positive correlation with the dependent variable. Final consumption correlates with GDP per capita by 0.99 while net investment correlates with the GDP Per capita by 0.92 which are very strong positive correlation. This in general can be summarized that increase in either of the independent variables leads to increase in dependent variables.

## Conclusion

Regression analysis is an econometric analysis technique that is widely used to study how one or a set of independent variables affects one dependent variable. The precision of this econometric method can be realized when there is a good blend of economic theory and statistics and probability theory. In this study, the economic theory relating to macroeconomic variables was used with multiple regression analysis to build a forecasting model using Microsoft Excel and an econometric E-views software. The task was to decompose the fluctuation of the GDP per capita between 1998 and 2011 into two components; net investment and final consumption.

The regression model shows that there is positive correlation among the three variables. The interpretation of the coefficient in regression model shows that increase in each of the independentvariablesincreases GDP per capita by a certain percentage. We notice that final consumption increase GDP more significantly compared to net investment. These findings can be used by policy makers and governments for planning for their population not only in the United States but also in other developed and developing economies. High correlation between net investment and final consumption also raises questions that inspire further research.

## Works Cited

Baumol, William J. "Macroeconomics of unbalanced growth: the anatomy of urban crisis." The American economic review (1967): 415-426.

Deardorff (209-236)

Deardorff, Alan V. "A framework for analysis in international macroeconomics." WeltwirtschaftlichesArchiv 113.2 (1977): 209-236.

Hall, Charles AS. "Integrating Concepts and Models Development Economics with Land use Change in the Tropics." Environment, Development and Sustainability 8.1 (2006): 19-53.

Kitov, Ivan. "Real GDP per capita in developed countries." Available at SSRN 886664 (2006): 288-298

Merton, Robert C. "Financial innovation and the management and regulation of financial institutions." Journal of Banking & Finance 19.3 (1995): 461-481.