The Analysis of Transitions in Economic Performance Using Covariate Dependent Statistical Models

Abstract

The GDP or GNP as a measure of economic performance of a country changes continuously. We can identify the factors that precede its ups and downs. For such forecasting, the use of Markov models are not new, but in this paper, an attempt is made to propose a covariate-dependent Markov model to identify the factors that contribute to the estimation of transition probabilities. The proposed model is employed to estimate the transition probabilities, the factors that contribute to transitions in economic performance, and other relevant characteristics. The cross-country data have been employed for the period 1980–2000 for fitting the model. This can provide a useful model for forecasting the economic performance in both developing and developed countries.

Introduction

The measure of GDP depends on several components such as private consumption, investment, government consumption, changes in inventories, total exports and total imports. It is observed by Swamy and Fikkert (2002) that the determinants of economic growth which rely on cross-country growth regressions may be affected by bias from two sources : (i) omitted variables, and simultaneity. The first one is attributable to country characteristics that affect growth but omitted by the econometricians. The second one is due to the fact that the determinants of growth of GDP, such as investment in physical capital, may also affected by this growth. Currently, there is evidence of relationship between human capital accumulation and economic growth. Asteriou and Agiomirgianakis (2001) demonstrated such relationship between education variables and GDP as well as the causal direction between them for Greece. Similar relationship was observed in other studies based on cross-country data (Barro, 2001; Hanushek and Kimko, 2000). The transition from agrarian to predominantly industrial economy had been successful in raising the pace of economic growth in some Asian countries during the recent past.

In this paper, the growth of GDP has been analyzed in order to identify the factors that contribute to the change in the economic performance. For the purpose of this study, we have employed the cross-country data. Due to missing observations for many variables, we have used only some selected variables that are associated with the change in the economic performance in the cross-country setting. The main objective of this paper is to demonstrate the utility of Markov models in identifying the role of the selected characteristics in explaining the growth in GDP over time. The advantage of such model is that we can use repeated observations to identify the factors that attribute to the change in economic performance.

Data and Methods

We have used the cross-country data for the period 1980–2000. To demonstrate a distinct trend over time, we have taken into consideration data after every five years from the World Development Reports for the years 1980 through to 2000. The gross domestic product (GDP) is considered as the outcome variable, which measures the economic performance of a country. The selected variables are: growth of industry (indgr), population growth (popgr), labor force growth (lfgr), use of energy (eneruse) We have used both linear regression as well as logistic regression models in this study for different time periods. Then a covariate dependent Markov model is used to examine the change in performance in economic growth over time.

Linear Regression Model for Economic Growth

The linear regression model for economic growth is presented here. The outcome variable is GDP and the explanatory variables are: growth of industry (indgr), population growth (popgr), labor force growth (lfgr), use of energy (eneruse). We have employed two different sets of models here, one for each selected year and the other sets of models include the lag variables. The models are shown below for the ith country in the jth year:

• Model 1a:

• Model 1b:

The first model (Model 1a) considers both the outcome and explanatory variables during the same year for the selected countries. However the second model (Model 1b) employs explanatory variables observed five years before the outcome variable. This model is expected to take account of the time-lag in explaining the outcome variable, GDP. The results for Model 1a are displayed in Table 1. It is evident from Table 1 that growth of industry is positively associated (p<0.01) during the period 1980–2000 with a steadily increasing effect on the growth of GDP. Population growth does not show any significant association with the growth of economy. Growth in labor force appears to have no statistical association with growth in GDP. However, use of energy appears to have positive association with economic performance in 1985 (p<0.05).

Table 1.

Estimates of Regression Models for Growth of GDP for Year 1980, 1985, 1990, 1995 and 2000

Model 1b uses the 5-year lag between observed GDP and explanatory variables. Table 2 shows that only growth of industry seems to have positive association with GDP for the years 1985–90 and 1995–2000.

Table 2.

Estimates of Regression Models for Growth of GDP During the Period 1980–1985, 1985–1990, 1990–1995 and 1995–2000

Logistic Regression Models

To explore the underlying association between growth in GDP and the selected explanatory variables, two sets of logistic regression models are fitted in this section. Let us define the following dichotomous variables for the ith country in year j:

Then let us define the following models:

• Model 2a:

• Model 2b:

Then the logistic regression models for both 2a and 2b are:

• Model 2a:

• Model 2b:

Table 3 shows the estimates for Model 2a. It is clearly observed from the results that growth of industry has been positively associated with the growth of GDP for all the years during 1980–2000 (p<0.01). The impact of growth on growth of GDP appears to exert the largest impacts in the years 1990 and 2000. Similarly, growth of labor force shows statistically significant positive association with growth in GDP for the year 1990 (p<0.05).

Table 3.

Estimates of Parameters of Logistics Regression Models for Growth of GDP in 1980, 1985, 1990, 1996 and 2000

Model 2b (Table 4) confirms the result that growth of industry increases the growth of GDP during the periods 1980–85, 1985–90, 1990–1995 and 1995–2000 (p<0.01). However, all other selected variables do not show any statistically significant association with the outcome variable except population growth during 1990–1995.

Table 4.

Estimates for Lagged Logistic Regression Models for Binary Outcomes for the Period 1980 – 2000.

Markov Model

The covariate dependent Markov model was proposed by Muenz and Rubinstein (1985) and then Islam and Chowdhury (2006) extended the model for higher order. Let us give a brief overview of the model here from Muenz and Rubinstein and Islam and Chowdhury. See these papers for more details.

Let us consider a two state Markov chain for a discrete time binary sequence as follows:

where π₀₀ =1−π₀₁ and π₁₀ =1−π₁₁. Here, 0 and 1 are the two possible outcomes of a dependent variable, Y. Each row of the above transition probability matrix provides a model on the basis of conditional probabilities. For instance, the probability of a transition from 0 at time t _j−1 to 1 at time t _j is π₀₁ = P(Y_j=1| Y_j−1=0) and similarly the probability of a transition from 1 at time t _j−1 to 1 at time t _j is π₁₁=P(Y_j=1| Y_j−1=1). It is evident that π₀₀ +π₀₁ = 1 and similarly, π₁₀ +π₁₁ =1.

For covariate dependence, let us define the following notations:

Then the transition probabilities can be defined in terms of function of the covariates as follows:

• Model for Increase in the Growth of GDP

• Model for Decrease in the Growth of GDP

Table 5 shows the summary of the results for both increase and decrease in the growth of GDP for covariate dependent Markov models. As expected, growth of industry is positively associated with increase in GDP growth (p-value<0.01) and negatively associated with decrease in GDP growth during the period 1980–2000. Although there is no association between growth in population and increase in GDP growth, while there is positive association between population growth and decrease in GDP growth. Use of energy appears to have no significant association with increase or decrease in GDP growth during the long duration from 1980 to 2000.

Table 5.

Covariate Dependent Markov Model for Increasing and Decreasing in the Growth of GDP for the Period 1980–2000

Summary and Conclusion

This paper examines the factors influencing the change in economic growth of countries. The economic performance of countries may depend on factors related to capital investment, investment on human capital accumulation, expenditure on health, and many other factors that are associated directly or indirectly with the economic growth. This paper provides only a preliminary overview of the problems associated with the relationship with growth in GDP. The main purpose of this paper is to demonstrate different techniques that can be employed to explain such relationships. Due to data limitations, some of the important variables could not be used.

In this paper, three different methods have been used: (i) regression models, (ii) logistic regression models, and (iii) Markov models with covariate dependence. First two models take account of both cross-section data as well as data with a lag of five years. The third model uses the Markov model for explaining the transitions from low or moderate economic performance to high performance as well as transition from high economic performance to moderate or low performance. It is surprising that in all these models, it appears that growth in industry is the most dominating factor in explaining the growth in GDP. In some models, the role of growth in labor force seems to have statistically significant association. For the East Asian economies, the transition to high performance was preceded by the demographic transitions that led to high growth of labor force during the period of population momentum. The Markov models reveals the findings more explicitly due to use of repeated measures of economic performance. It provides two sets of equations for increase in the growth of GDP as well as decrease in the growth of GDP from the same model and thus the role of variables can be determined for both directions in the change of economic performance. With more detailed data, the advantage of the covariate dependent Markov model will be more precise and obvious.

Kholodilin and Silverstovs (2006) pointed out that the GDP reflects the state of the overall economy. According to them, in a developed economy like Germany, the share of the components have been changed drastically, and the industrial production represents less than 50% of the contemporary German economy. They noted that the service sector plays an ever increasing role in the economy. The regression models based on cross-national data displays a positive association between growth in industry and growth of GDP. These results are confirmed by both the logistic regression models with or without lagged variables. Similarly, the results based on the covariate dependent Markov models show that during the longer duration from 1980 to 2000, there is positive association for increase in higher growth attributable to growth in industry. The short and long term shifts in the growth of GDP can be of interest in terms of changes in the growth of industry as compared to that of other sectors such as service.

Dawson (2006) included the growth rate of the labor force to explain the cumulative growth rate of the real per capita GDP on the basis of cross-country data and observed that the labor force growth is associated negatively with the growth in per capita GDP. However, it is observed from the covariate dependent Markov models that labor growth is not associated with the increase or decrease in the growth of GDP for the period 1980–2000. However, there exists an opposite impact on the growth of GDP in developing and developed countries. In the near future, it is expected that due to stagnation or decrease in labor supply deriving from past low fertility will pose difficulties in the most developed countries (McDonald and Kippen, 2001). This will necessitate adjustments in the major components of the GDP in order to minimize the impact of such transition in the labor force composition.

In the presence of the labor force growth in the model, population growth does not show any significant association with the growth in GDP. Barro (2001) showed that the quality of human capital accumulation is quantitatively much more important for analyzing the growth in GDP. Hanushek and Kimko (2000) observed that the direct measures of labor force quality are strongly related to growth. Galor and Weil (2000) indicated that the relationship between income and population growth has been changed dramatically during the recent past and even the poor countries are experiencing relatively higher population growth rate. Campos and Coricelli (2002) described transition in economy as the simultaneous change of economic structures and the dependence upon the coherent economic reforms. They also pointed out the necessity of future research with emphasis on economically meaningful contributions of labor. They further emphasized on the more reliable estimates of physical and human capital and labor contributions to growth. This may provide us with the improved understanding of the sources of this process of transition and relative contributions of the underlying determinants.