Methodology of econometrics involving three stages

1. Specification of the model using a specific stochastic equation, together with *a priori* theoretical expectations about the sign and size of the parameters of the function.

2. Data collection on the variables of the model and estimation of the coefficients of the function, using appropriate econometric techniques.

3. Evaluation of the estimated coefficients of the function, based on economic statistical and econometric criteria.

Time series is a collection of observations made sequentially over time. The first step of the analysis is to plot the observations (time plot) to obtain descriptive measures of the properties of the series.

In this review the causal (independent) variable is Foreign Direct Investment (FDI) and Exports and Imports are the dependent variables. The questions to be answered through the critical analysis of literature is: Does Foreign Direct Investment from the United States, non-United States partners, and local investment affect exports from the technology sector in Costa Rica, generating export led platform? or does Foreign Direct Investment from the United States, non-United States partners, and local investment affect from the technology sector in Costa Rica generating an import substitution platform?

This study will use the econometric procedure to analyze the relationship between FDI, imports and exports, and respective equations.

**A- The first step** for the Granger causality is to test the time series data for stationarity

i- Use unit root test ADF

ii- Use unit root test PP

iii- Use Lumsdaine and Papell's (LP) model to consider possible breaks in the time series.

If structural break(s) exist in the series, the ADF test statistics may have been biased toward the non-rejection of a unit root when the series is trend stationary within each of the sub-periods (Perron, 1997). Therefore, Lumsdaine and Papell's (LP) model is applied to detect two-time structural breaks in the unit root analysis, and the result of stationarity of each time series by using the LP approach replaces the result from ADF and PP tests. The structural break may occur by reflecting, for example, a country's policy reforms or slowdown in growth (Perron, 1997). If the break date(s) is/are located in the same year as the occurrence of the incident, then we may conclude that the time series was affected immediately by this structural break. Similarly, if the break date(s) is/are located in the year after the incident occurred, we may interpret this time series was affected gradually by this structural break (Valadkhani, Pahlavani & Layton, 2005). The LP approach is an improved version of the ADF test, increased by two endogenous breaks.

**B- The second step** is the cointegration testing for bivariate and multivariate models related to FDI and exports and FDI and imports. This analysis will use Johansen and Jesulius's (1990) approach to the number of cointegrating vectors if two variables are *I*(1). The cointegration test of maximum likelihood based on the Johansen-Jesulius test is developed based on a VAR approach initiated by Johansen (1988).

For Hypotheses 1, 2, 3, 4, 5 and 6) the study will investigate if there exists long-run relationships of the following form:

**(19) H1 EXP = ****β****1 ****+**** ****β****2 ****FDI****U.S.*** ***+ u**

where EXP is exports from the technology sector, FDIU.S. is Foreign Direct Investment from the United States to the technology sector, **β****1** the unknown constant parameter, parameter **β****2** is the slope coefficient, and** u** is the random disturbance, error, or stochastic term.

**(20) H3 EXP = ****β****1 ****+**** ****β****3****FDI****N-U.S.*** ***+ u**

where EXP is exports from the technology sector, FDIN-U.S. is Foreign Direct Investment from non United States countries to the technology sector, **β****1** the unknown constant parameter, parameter **β****3** is the slope coefficient, and** u** is the random disturbance, error, or stochastic term.

**(21) H5. EXP = ****β****1 ****+**** ****β****4 ****DI*** ***+ u**

where EXP is exports from the technology sector, DI is Domestic Investment to the technology sector, **β****1** the unknown constant parameter, parameter **β****4** is the slope coefficient, and** u** is the random disturbance, error, or stochastic term.

** (22) H2. IMP = ****β****1 ****-**** ****β****2 ****FDI****U.S.*** ***+ u**

where IMP is imports from the technology sector, FDIN-U.S. is Foreign Direct Investment from United States to the technology sector, **β****1** the unknown constant parameter, parameter **β****2** is the slope coefficient, and** u** is the random disturbance, error, or stochastic term.

**(23) H4. IMP = ****β****1 ****-**** ****β****3****FDI****N-U.S.*** ***+ u**

where IMP is imports from the technology sector, FDIN-U.S. is Foreign Direct Investment from non United States countries to the technology sector, **β****1** the unknown constant parameter, parameter **β****3** is the slope coefficient, and** u** is the random disturbance, error, or stochastic term.

**(24) H6. IMP = ****β****1 ****-**** ****β****4 ****DI*** ***+ u**

where IMP is imports from the technology sector, DI is Domestic Investment to the technology sector, **β****1** the unknown constant parameter, parameter **β****4** is the slope coefficient, and** u** is the random disturbance, error, or stochastic term.

For multivariate model (Hypothesis 7 and 8), the search for the long-run relationship will take the following form:

**(25) H7. EXP = ****β****1 ****+**** ****β****2 ****FDI****U.S.*** ***+ β****3****FDI****N-U.S.*** ***+ ****β****4 ****DI*** *** ****+ u**

where EXP is exports from the technology sector, FDIU.S. is Foreign Direct Investment from the United States, FDINN-U.S.is Foreign Direct Investment from non-United States countries to the technology sector, DI is domestic investment to the technology sector, and β1, β2, β3 and β4 are the unknown constant parameters. The parameters β2, β3 and β4 are the slope coefficients,** **and** u** is the random disturbance, error, or stochastic term.

**(26) H8. IMP = ****β****1 ****-**** ****β****2 ****FDI****U.S.*** ***- β****3****FDI****N-U.S.*** ***+ ****β****4 ****DI*** *** ****+ u**

where IMP is imports from the technology sector, FDIU.S. is Foreign Direct Investment from the United States, FDINN-U.S.is Foreign Direct Investment from non-United States countries to the technology sector, DI is domestic investment to the technology sector, and β1, β2, β3 and β4 are the unknown constant parameters. The parameters β2, β3 and β4 are the slope coefficients, and **u** is the random disturbance, error, or stochastic term.

If a series forms a long-run equilibrium relationship, and even if the series may contain stochastic trends (i.e. non-stationary, *I*(1)), they will move closely together over time. Therefore, the existence of cointegration implies a long-run equilibrium with an economic system that converges over time (Harries, 1995, p. 22).