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Modeling the Contribution of Industry to Gross Domestic Product of Bangladesh

Tanvir Khan
Senior Officer
Uttara Bank Limited, Core Banking Solution Implementation Project,

Md. Arafat Rahman
Research Associate
Implementation of Monitoring and Evaluation (M & E), for IFC ( World Bank Group) at A.D.S.L

Abstract/ Executive Summary:

To analyze the contribution of industry to a macroeconomic variable, GDP, is an important concern in economics. It plays major role in the government and industrial sector of Bangladesh. A time series model can provide a reasonable benchmark to evaluate the value-added of economic theory relative to the pure explanatory power of the past behavior of the variable; recent developments in time series analysis suggest that more sophisticated time series models could provide more accurate benchmarks for economic models. In this paper the feature of yearly data on industrial contribution to GDP from fiscal year 1979-1980 to 2011-2012 is presented. There are two methods named Auto-Regressive Integrated Moving Average (ARIMA) and Holt’s linear trend method are fitted to our data set. In this study Box Jenkings method were used to construct ARIMA model. The goodness of fit is determined via Akaike Information criterion and Bayesian information criterion. By comparing the measures of error we can see that ARIMA model is a better model than Holt’s linear trend model to forecast contribution of industry to GDP of Bangladesh.

Keywords: GDP, ARIMA Model, Holt’s Model

Location: In Bangladesh

Start Date: 00-00-2011

End Date: 00-00-2012

Program Area: Socio-economic and Policy

Commodity: Micro-finance, Income generation

Objectives:

To identified ARIMA model as a reasonable model to forecast the yearly growth rate of GDP of Bangladesh.

Methodology:

The basis of the Box-Jenkins approach for modeling time series data is consists of three phases. Identification is the first step in this process which is broadly classified into two categories: data preparation and model selection. In data preparation, part data is transformed to stabilize variance and differences of data are considered to obtain stationary series. In model selection, part data is examined by checking ACF (Auto Correlation Function) and PACF (Partial Autocorrelation Function) to identify potential model. ACF plot is frequently used to identify whether or not seasonality is present in a given time series data to identify an appropriate model for specific situations and to determine if data are stationary. The general non-seasonal model is known as ARIMA (p, d, q) where p is order of autoregressive part, d is degree of first differencing involved, q is order of moving average part. The second step of Box-Jenkins approach is modeling time-series data by estimating parameters and testing the significance. This step involves the estimation of the parameters to fit potential models and to select a suitable criterion which can be used to determine the best model among plausible models. This criterion is well known as Akaike's Information Criterion (AIC) developed in 1974 defined as: AIC = (-2log L+2 m) (2) Where, L is the maximized likelihood function and m is the number of parameters estimated in the model. The model which attains minimum AIC value is considered as the best model. After choosing the most appropriate model, parameters are estimated by using the method of maximum Likelihood. The method of maximum likelihood finds the values of the parameters, which maximizes the likelihood function. Computer programs for fitting ARIMA models will automatically find appropriate initial estimates of the parameters and then successfully refine them until the optimum values of the parameters are found. A test of significance of the estimated parameters is done from the parameter estimate and its standard error. Some of the estimated parameters may have been found insignificant (p-value larger than 0.05). If so, a revised model is considered dropping the insignificant explanatory variables. In the diagnostic checking step check the autocorrelation function (ACF) of residual. This is usually done by correlation analysis through the residual ACF plots and the goodness-of-fit test by means of Chisquare (χ2) statistic. If the residuals are correlated, then the model should be re-considered as discussed in step one. Otherwise, the model is adequate to represent the time series data.

Source of Information: Tanvir Khan, Md.Arafat Rahman, Int. J. Eco. Res., 2013, v4i2, 66 - 76; ISSN: 2229-6158

Article Link (Online Journal):

Funding Source:

1.

Budget:

Total Budget (Tk.) :

Achievement/Findings:

In this paper, we have used statistical methods to collect, analyze, explain and present various aspects of time series data on industrial contribution to GDP of Bangladesh. Various combinations of the autoregressive, moving average and linear trend models were considered. Among the various models, ARIMA (3, 2, 0) is found to be the best model with the lowest AIC and BIC values. We do not merely accept the values of information criteria as sole confirmation, but rather gain further confirmation through various statistical tests. These include test for goodness of fit and Ljung-Box test for error independence. Furthermore, we clearly show the way to model any time-series data by ARIMA and Holt’s linear smoothing model. A close look of the plots of our actual and simulated time series data also confirms the steps of a proper time series modeling. We conclude that ARIMA is a better univariate model for predicting industry contribution to GDP of Bangladesh comparing Holt’s linear smoothing model based on their measures of error.

Knowledge Management: Journal