Derivation of Quarterly GDP, Investment Spending, and Government Expenditure Figures from Annual Data: The Case of Pakistan

Rashid, Abdul and Jehan, Zanaib (2013): Derivation of Quarterly GDP, Investment Spending, and Government Expenditure Figures from Annual Data: The Case of Pakistan.

Abstract

In this paper we convert annual GDP, investment spending, and government expenditure data into quarterly figures for Pakistan using observed annual time-series data for the period 1971-2010. Three different econometric disaggregation techniques, namely the Denton (1970) approach, the Chow-Lin (1971) framework, and the cubic spline interpolation method, are used for quarterisation. We use quarterly consumer price index (CPI) and industrial production index (IPI) as the indicator variables while disaggregating annual frequency data into quarterly frequency data. The time series properties of estimated quarterly series are examined using different unit root tests. Correlation estimates indicate that interpolated quarterly series using all three methods are highly correlated. Time series plots illustrate that while the series quartered using the Denton approach and the Chow-Lin procedure exhibit similar trends. However, the quarterisation based on the farmer approach is more variable as compared to that based on the later approach. The data set is given in the appendix and the estimation codes for all three methods are available from the authors.

• Item Type: MPRA Paper
• Language: English
• Keywords: Quarterly GDP; Quarterly investment; Quarterly government expenditures; Disaggregation methods, Quarterisation; Quarterly Data; Pakistan; the Denton approach; the Chow-Lin framework; the Cubic Spline interpolation process
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy

References

Arby, M. F. (2008), “Some issues in the National Income Accounts of Pakistan (Rebasing, Quarterly and Provincial Accounts and Growth Accounting)”, PhD Dissertation, Pakistan Institute of Development Economics, Islamabad.

Arby, M. F. and Batool, I. (2007), Estimating quarterly gross fixed capital formation”, SBP Working Paper No. 17.

Bengaliwala, K. (1995), “Temporal and regional decomposition of National Accounts of Pakistan”, PhD Dissertation, Department of Economics, University of Karachi.

Boot, J. C. B., Fiebes, W., and Lisman, J. H. C. (1969), “Further methods of derivation of quarterly figures from annual data,” Applied Statistics, 16, 65-75.

Chan, W., (1993), “Disaggregation of annual time-series data to quarterly figures: A comparative study”, Journal of Forecasting, 12, 677-88.

Chow, G. C. and Lin, A.(1971), “Best linear unbiased interpolation, distribution and extrapolation of time series by related series,” Review of Economics and Statistics, 53, 372-5.

Denton, F. T. (1970), “Quadratic minimization procedures for adjusting monthly or quarterly time series to independent annual totals”, McMaster University Department of Economics Working Paper 70-01.

Denton, F. T. (1971), “Adjustment of monthly or quarterly series to annual totals: An approach based on quadratic minimization”, Journal of the American Statistical Association, 66, 92–102.

Engle, R. F. and Granger, C. W. J. (1987), “Co-integration and error correction: Representation, estimation, and testing”, Econometrica, 55, 251-276.

Fernandez, R. B. (1981), “A methodological note on the estimation of time series”, Review of Economics and Statistics, 63, 471-6.

Friedman, M. (1962), “The interpolation of time series by related series” ,Journal of the American Statistical Association, 57, 729–57.

Guerrero, V. M. (1989),“Temporal disaggregation of time series: An ARIMA approach”, International Statistical Review, 58, 29-46.

Harvey, A. C. and Pierse, R. G., (1984), “Estimating missing observations in economic time series”, Journal of the American Statistical Association, 79, 125-31.

Johansen, S. (1990), “Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models”, Economterica, 59, 1551-1580.

Kemal, A. R. and Arby, M. F. (2004), “Quarterisation of annual GDP of Pakistan,” Statistical Papers Series No 5, PIDE, Islamabad.

Kwiatkowski, D., Phillips, P.C.B., Schmidl, P. and Shin, Y. (1992),“Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root?”, Journal of Econometrics, 45, 159–178.

Lisman, J.H.C. and J. Sandee (1964), “Derivation of quarterly figures from annual data”,Applied Statistics, 13, 87-90

Litterman, R. B. (1983), “A random walk, Markow model for the distribution of time series”, Journal of Business and Economics Statistics, 1, 169-73.

Marcellino, M. (1999), “Some consequences of temporal aggregation in empirical analysis”,Journal of Business and Economic Statistics, 17,129-136.

Newey, W. and West, K. (1994), “Automatic lag selection and the construction of unit root tests with good size and power”, Econometrica, 66, 1519-1954.