## Introduction: Topic selection and reasons

United States has been a good place for foreign investors. The steady growth and strength of the economy has made US an attractive destination for foreign capital. The GDP has recorded a steady growth for the past 31 years (between 1983 and 2013). The rate of Foreign Direct Investment growth has been moving in the same direction as GDP^{3}. The data from US Department of Commerce indicates that between 1988 and 2010, GDP grew by 181% and FDI by 644%. In 2010, for instance, GDP was14.7 trillion USD and FDI in total was 2.3 trillion USD.

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FDI has been found to have great impact on wages. The positive effects of FDI benefits both average and minimum wage earners. Since these effects are distributed unevenly among the two groups, FDI can widen labor income gap. However, only a few studies have been done on the impact of wages on FDI. This will be dealt with in this paper. Other factors believed to have impact on FDI are inflation, Average Wages, and the standard of living. The average annual wage has been increasing in US in a trend similar to that of FDI. This is shown below:

The question has become of interest because of the trends observed between FDI and a number of macro variables. The standard of living measured using US GDP per capita also showed a trend heading the same direction as Foreign Direct Investment.

The standard of living (STDL) increased with increase in FDI.

The model to be investigated is stated as follows:

- FDI = β
_{0}+ β_{1}GDP + β_{2}AWW + β_{3}INF + β_{4}STDL + ε

Where:

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- FDI = Foreign Direct Investment
- GDP = Gross Domestic Product
- AWW = Average Wage
- INF = Inflation
- STDL = Standard of Living.

## Organization of the paper

The paper gives a brief literature about the topic. This is crucial in digging deeper into what other researchers have found about the topic. The other section is the Conceptual framework. This section will simply describe why the topic is of interest and the signs expected on the relationship between key variables. Any expected bias or complexity is also addressed. The other part of the paper will describe the data used and the source. The characteristics of data will be given including the descriptive statistics. Econometric model will then be presented. The variables are defined and model assumptions described (regarding variance of the error term and covariance between regressors and error term). Description of inappropriateness of Ordinary least Square method in estimating the model will be given. An alternative model to OLS will also be suggested. A model that is not affected by the violation of assumptions of OLS method will be used in this study. The last section will be presentation of results and discussion.

## Literature Review

Yasmin, Hussain and Chaudhary in their study analyzed the volume and determinants of FDI in some emerging economies in the world^{4}. They used a sample of 15 developing countries. The countries comprised of upper middle, lower middle, and lower income earning. Five countries were selected in each category. They used random effect and fixed effect models in identifying the determinants of FDI in those countries. They found urbanization, GDP per capita, Inflation, and wages are significant determinants of FDI. Urbanization was significant because urban areas have products used as inputs and are easily available to investors. The infrastructure facilities and markets are concentrated in urban areas and they facilitate FDI projects. Standard of living was a significant and valid variable because foreign investors are attracted more towards the countries which have higher incomes leading to higher standard of living and greater demand for foreign goods^{4}. They also found GDP to have positive effects on FDI because large markets seem to point to the efficient utilization of resources. This leads to greater absorption capacity which increases demand for goods and services, and economies of scale. Average wage also had a positive effect on FDI. Levels of wages tend to depend on production technique applied by foreign investors. Where wages are high, production level is high because workers are skilled.

Wood (2012) investigated the factors affecting FDI in US real estate and found that GDP and FDI in real estate grew in the same direction^{3}. It was also found that GDP is a significant determinant of FDI in Real Estate. The GDP per capita and the exchange rate were found to be significant drivers of FDI.

## Conceptual Framework

This study was necessitated by the trend that FDI and some macro-variables depicted over the years. FDI and GDP in United States of America have been moving in the same direction for several years. The signs expected are as follows:

- ∆FDI/∆GDP>0 => This means that GDP increase will increase FDI
- ∆FDI / ∆W > 0 => increase in average wages will increase FDI. High wages are given to skilled and productive workers.
- ∆FDI / ∆STDL > 0 => Increase in standard of living will increase FDI. High standard of living increases demand for local and foreign goods and services.
- ∆FDI / ∆INF < 0 => Increase in inflation rate will decrease FDI inflow. It discourages investors from investing in the country where rates have increased. This lowers the inflow of FDI
^{1}.

The variables will be tested empirically and tested for significance.

## Variable of interest and hypothesis

The variable of interest in this study is Gross Domestic Product and the role it plays in the growth of Foreign Direct Investment in the USA. The trend shown in figure 1 indicated that GDP and FDI grew in the same direction over a long period of time. The US GDP has grown at a steady rate over the past 31 years and the same trend is depicted by FDI. This makes the two variable worthy of empirical examination. The null and alternative hypotheses are stated as follows:

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- Null hypothesis H0: β
_{1}= 0 => meaning that GDP is not a significant determinant of FDI - Alternative hypothesis H1: β
_{1}≠ 0 => meaning that GDP is not a determinant of FDI.

The parameter β_{1} is the coefficient of FDI in the regression model. It measures the marginal effect of GDP on FDI.

## Bias and complexity expected

The use of OLS method is likely to cause problems in model estimation. These challenges arise because of high correlation of variables in the regression model. They are likely to give misleading results. If OLS is used for such kind of data, the results will misguide policy makers.

## Data Description

The data was collected from the US Bureau of Statistics and was analyzed using Eviews software. The data was collected for 31 years between years1983 and 2013. Foreign Direct Investment will be denoted by FDI in the model. The amount of FDI is indicated in billion dollars. The same unit of measure is used for Gross Domestic Product (GDP). Average wage (AWW) only captures the wages that are subject to federal income tax. Inflation (INF) is expressed in percentage. It is the percentage change in general price level from the previous period. The standard of living (STDL) was measured by US GDP per capita. The data used if cross-sectional time series data. The data is collected on the 1^{st} day of every year for the period specified.

## Econometric Model and expected signs of the variables

The econometric model to be used is FDI = β_{0} + β_{1}GDP + β_{2} AWW + β_{3}INF + β_{4}STDL + ε. The variables on the right and on the left hand side of the model are assumed to have a linear relationship. The parameter β_{0} is the intercept of the regression line. It shows the value of FDI when all the other factors in the model are zero. The other parameters β_{i }measures the effect of each independent variable on the dependent variable. The coefficients of GDP, AWW, and STDL are positive but that of INF is expected to be negative. The variables are tested at 95% level of confidence. The t-statistic value and p-value will be used in determining the significance of the variables.

## OLS method unsuitability

OLS is one of the mostly used methods in prediction techniques. However, the method has a lot of pitfalls which make it inappropriate in analyzing some data. The following paragraphs accounts for some of the problems associated with the use of OLS.

### Outliers effects

The method seeks to achieve its objectives by minimizing the sum of square errors. In some cases, the elements in a data set may lie too far from the fitted line. This will have an effect on the parameters being estimated.

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### Non-linearity

OLS is a linear regression model. However, not all systems are linear and may be inappropriate to use OLS in such cases. A linear model will attempt to fit a line in one dimensional set of data which is very unlikely in real world. The relationships in real world tend to be more complicated that what a simple line can describe.

### Dependence among variable

Poor prediction will be experienced when variables are significantly related to each other. There will be poor performance of the testing set.

### There is wrong choice of error function

In OLS method, minimization of the square errors is the main focus. The major challenge is to justify the method used to obtain the square errors. The method of measuring the least square regression errors is unjustifiable. One would wonder why sum of absolute values errors is not used in place of sum of square errors.

### Heteroscedasticity problem

The OLS method assumes equal variance for all variables in the regression model^{5}. The variance is assumed to be constant for all variables. This may not always be the case.

### Omitted variables problem

The OLS method is likely to suffer the problem of model misspecification. If a key explanatory variable is left out of the model, the coefficients and the p-values obtained cannot be relied on. They can give misleading interpretation.

### Multicollinearity problem

This arises when one of the explanatory variables become redundant. This makes the model unreliable and unstable. It causes over-counting type of bias in estimation.

### Normal Distribution Bias

The OLS method assumes that the residuals are normally distributed and this may not be the case always. If this assumption is violated, the p-values of the coefficients are unlikely to be reliable.

## Alternative Model

The problems associated with OLS method could be corrected on case by case basis. However, there are other models which can be used to overcome the challenged. For this paper, the alternative model that is adopted is Instrumental Variables and Two Stage Least Squares. When the regressors are related, the OLS method will fail to give results for parameters. The instrumental variables estimator is used to overcome the challenges of OLS method. A popular form of instrumental variables estimator is two-stage least squares (2SLS)^{2}.

## Results and Discussion

The analysis was done using Ordinary Least Square method and also by 2SLS model. The two models were used to estimate the econometric model stated above. The failure of OLS to give reliable solution due to its limitations led to the use of an alternative method.

## Ordinary Least Square Method

The regression model estimated was stated as follows:

- FDI = β
_{0}+ β_{1}GDP + β_{2}W + β_{3}I + β_{4}STDL + ε

The estimation by Eviews yielded the following results:

### Descriptive Statistics

The descriptive statistics are used in explaining the characteristics and shape of a data set. The mean and median according to the table above shows that the series were not normally distributed. For a normal distribution, the mean and median should be equal. The series for FDI and GDP were skewed to the right while that of AWW, INF, and STDL were skewed to the left. This is interpreted using the signs of the coefficients of skewness. When the coefficient is negative, the distribution is skewed to the left. The distribution is skewed to the right when the coefficient is positive. The probability (P-value) of Jacque-Bera test also shows that all the series were not normally distributed. The p-values were greater than the level of significance (0.05) and, therefore, the null hypothesis could not be rejected. The null hypothesis in this case was that the series is not normally distributed. By failing to reject the null hypothesis means that the series is not normally distributed. This was the case in all variables in the model.

### Model estimation

According to OLS results, the equation was estimated as follows:

- FDI = -5.28E+11 + 0.007204 GDP – 3482962. AWW + 1.60E+10 INF + 17125628 STDL

The p-values of the coefficients of the variables in the model showed that all the variables were insignificant determinants of Foreign Direct Investment. The p-values were all greater than the level of significance (0.05). However, the p-value of F-statistics showed that the variables are jointly significant.

## Instrumental Variables and Two Stage Least Squares (2SLS)

This model is used because it is not affected by the violation of assumptions of OLS method. The model uses instrumental variables in estimating the model. An instrumental variable is a variable correlated with other regressors in the model but not highly correlated with the error term^{2}. In this study, the independent variables were all identified as instruments. This condition means that the model was over-identified. The selection of Instrumental Variables is described by correlation matrix below.

## Correlation of variables

The table below shows the level of correlation of the variables in the model.

The table is clear that the variables are highly correlated. At least there is a pair that is highly correlated. This is a necessary condition when using Two Stage Least Squares (2SLS) model. There is no correlation between the independent variables and the error term. The correlation is too close to zero. RESID is the error term of the regression estimated using OLS. This means that the variables qualify to be used as instrumental variables.

## Instrumental Variables and 2-Stage-Least Squares Output

The p-values of the independent variables show that the variables are insignificant. The decision rule is that if the p-value of less than the level of significance, the variable is significant. In this case, the p-values are greater than the level of significance (5%) meaning that the variables are insignificant. The null hypothesis for every variable was that the variable is insignificant. The null hypothesis could not be rejected. However, the overall significance of variables shows that they were jointly significant. The solution by OLS showed that variables are significant jointly but insignificant individually. This shows that the two models yielded same results. However, the marginal effects of 2SLS model were improved. The series were not normally distributed as expected in OLS method.

## References

Kiat, Jason. *The effect of exchange rate and inflation on foreign direct investment and its relationship with economic growth in South Africa*. Pretoria: University of Pretoria, 2008.

Kleibergen, Frank, and Zivot, Eric. “Bayesian and classical approaches to instrumental variable regression”. *Journal of Econometrics*, 114 (2003): 29 – 72

Wood, Brian. *Factors Affecting Foreign Investment in Us Real Estate*. New York: Johns Hopkins University, 2012.

Yasmin, Hussain, and Chaudhary Muhammad. “Analysis of Factors Affecting Foreign Direct Investment in Developing Countries.” *Pakistan Economic and Social Review Volume XLI* 1, No. 2 (2003): 59-75.

Yujarati Damodar. *Basic Econometrics*. New Delhi: Cengage Learning, 2005.

## Footnotes

1 – Jason Kiat, *The effect of exchange rate and inflation on foreign direct investment and its relationship with economic growth in South Africa* (Pretoria: University of Pretoria, 2008), 5.

2 – Frank Kleibergen and Eric Zivot. “Bayesian and classical approaches to instrumental variable regression”. *Journal of Econometrics*, 114 (2003): 29 – 72

3 – Brian Wood, *Factors Affecting Foreign Investment In Us Real Estate* (New York: Johns Hopkins University, 2012), 45.

4 – Hussain Yasmin and Muhammad Chaudhary, “Analysis of Factors Affecting Foreign Direct Investment in Developing Countries,” *Pakistan Economic and Social Review Volume XLI* 1, No. 2 (2003): 61

5 – Damodar Yujarati, *Basic Econometrics* (New Delhi: Cengage Learning, 2005), 852.