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Research World, Volume 8, 2011
Online Version

Article S8.3

Dynamics of Demographic Change and Economic Development: New Methods and New Results

Seminar Leader: Tapas Mishra
Department of Economics, Swansea University, Swansea, UK
t.k.mishra[at]swansea.ac.uk


For more than three centuries, demographic volatility, which refers to uncertainty in demographic factors like human capital, education system, employment rate, age, gender, or income, has been hailed as a prime mover of long term economic fluctuations and business cycles. It is also regarded as the foremost reason for perpetual environmental disasters in the recent times, for example, tsunami and ocean acidification. However, modelling demographic, environmental, and economic growth within a single framework has not been straightforward mainly due to the inherent stochasticities in the evolutionary processes of these systems. The complexity arises because demographic systems have been found to be subjected to stochastic shocks over time as they evolve within a complex broader socio-economic milieu. At different points of time, the demographic system transits (either exogenously or endogenously) to a different state and such transition is not always stationary (i.e., its current state is not independent of its past states) (Azomahou & Mishra, 2009). Moreover, incomplete information about the nature of interactions poses additional problems in modelling. Hence, there is a need of a different approach in order to assess the consequences of stochasticities in demographic-environmental-economic growth systems.

The seminar leader described a modelling approach in which the above interactions could be captured and used the model in order to foresee the nature of economic growth in the long term. This approach, known as ARFIMA (autoregressive fractionally integrated moving average), is a time-series model with its root in understanding and mapping of possible human reactions (i.e., the rational ones often used in economics) to different shocks and their probable evolutionary outcomes in future. In econometrics, this approach is often denoted as stochastic long-memory mechanism and integrates concepts of probability theory, stochastic calculus, stochastic optimisation, spectral analysis, and non-stationary econometrics. The model is described as:



Where,
    L is the lag operator or backshift operator and operates on an element of a time series to produce the previous element. For example, given some time series X = {X1, X2 …}, then LXt = Xt-1, L2Xt = Xt-2, etc for all t > 1 (t: time); hence accordingly, (1-L)Xt = Xt - Xt-1 for all t > 1

    nt represents the time series data of population growth

    d is the difference parameter or the degree of integration, and is used to represent the type of memory (explained later); d can have values between 0 and 1 (both inclusive)

    is the autoregressive (AR) operator of order p. It represents a stochastic process (i.e., the evolution of the process is described by probability distributions; even if the initial condition is known, there are many possibilities the process might go to, but some paths are more probable than others) and it is often used to model and predict various types of natural and social phenomena; (L) Xt = Xt - 1Xt-1 - 2Xt-2 - . . . pXt-p

    á is a constant term

    is a q-th order moving average (MA) operator. Moving average is the average of the last q number of numerical values out of a set that contains a larger number of historical values; (L) Xt = Xt + 1Xt-1 + 2Xt-2 + . . .qXt-q

    are the error terms; the error terms are generally assumed to be independent, identically distributed variables sampled from a normal distribution with zero mean, i.e., = i.i.d (0, ó)
The ARFIMA model is useful for modelling time series with long memory where the underlying variables have a stochastic behaviour. In a time series with long memory the current value is correlated with all past values to varying degrees. Researchers investigating the characteristics of output (such as, Gross Domestic Product) of developed countries have found substantial evidence of long memory (Michelacci & Zaffaroni, 2000). Systems working on short memory parameters would be inadequate in explaining this long memory component of the market. Short-memory systems make use of the last i values for making the forecast in univariate analysis. For example, in most statistical methods, the last i observations are given in order to predict the next observation. Statistically, d < 0.5 represents a short-memory process; 0.5 < d < 1 represents a long-memory process; d = 0 represents a no memory process; and d = 1 represents a perfect memory process.

Demographic variables have recently occupied central place in the explanations of economic growth fluctuations (Kelley & Schimdt, 1995; Mishra, Prskawetz, Parhi, & Diebolt, 2009), therefore, any shock persisting in the growth of output (i.e., stochastic shock) could be interpreted originating from the growth of demographic variables along with technological progress. Demographic variables have been observed to provide stable forecasts of economic growth and also the ability to dynamically predict large-scale societal changes (Creaspo-Cuaresma & Mishra, 2007). Moreover, the importance of time and role of stochastic shocks has been downplayed for a long time, primarily because of underdeveloped statistical and mathematical tools and the lack of high-speed computers (Mishra, 2006).

Considering the above limitations and developments, the seminar leader used the ARFIMA model in order to predict the per capita output growth rate based on demographic factors (e.g., age, birth rates, death rates, life expectancy at birth, etc.), stock variables (e.g., savings, investment returns, state of democracy, inflation, etc.), and the initial state of the economy (e.g., population density and educational attainment, which also represent the environmental condition).

The results provided a better understanding of the economic-demographic and environmental interactions over time, and also contributed to a more accurate forecast of the per capita output growth rate based on the described parameters compared to what the previous modelling efforts could achieve (Azomahou & Mishra, 2009). This provides a testimony about the utility of the approach in an environment characterised by stochastic long-memory, and also taking into account high degree of imperfection in evolving systems. The model can also be used for short-run and long-run prediction.

While the approach is highly ambitious and promises great value in economic analysis (Azomahou & Mishra, 2009), it has its own limitations. Being a well-structured quantitative modelling approach, it may miss out on a multitude of unforeseen and uncertain factors that govern a socio-economic system. However, quantitative modelling has been an advancing field and there is reason to be optimistic about future developments.

References

Azomahou, T. T., & Mishra, T. (2009). Stochastic environmental effects, demographic variation, and economic growth [UNU-MERIT Working Paper 2009-016]. Retrieved September 27, 2010, from http://www.merit.unu.edu/publications/wppdf/2009/wp2009-016.pdf

Crespo-Cuaresma, J., & Mishra, T. (2007). Human capital, age structure and growth fluctuation [IIASA Interim Report IR-07-031]. International Institute for Applied Systems Analysis, Laxenburg, Austria. Retrieved September 27, 2010, from http://www.iiasa.ac.at/Admin/PUB/Documents/IR-07-031.pdf

Kelley, A. C., & Schmidt, R. M. (1995). Aggregate population and economic growth correlations: The role of the components of demographic changes. Demography, 32, 543-555.

Michelacci, C., & Zaffaroni, P. (2000). (Fractional) beta convergence. Journal of Monetary Economics, 45, 129-153.

Mishra, T. K. (2006). Dynamics of demographic change and economic growth. Unpublished doctoral dissertation, Catholic University of Louvain, Belgium.

Mishra, T., Prskawetz, A., Parhi, M., & Diebolt, C. (2009). A note on long-memory in population and economic growth [Working Papers, No. 6, 2009]. Association Françoise de Cliométrie (AFC). Retrieved September 27, 2010, from http://www.cliometrie.org/pdf/wp/AFC_WP_06-2009.pdf


Reported by Mahendra Kumar Shukla; with inputs from Prahlad Mishra, Rahul Thakurta, Soumya Guha Deb; edited by D. P. Dash. [October 24, 2010]


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