Dummy Variable Model in pooling Data & a production model in Agriculture and Industry Sectors in Egypt

Transcription

1 Dummy Variable Model in pooling Data & a production model in Agriculture and Industry Sectors in Egypt (Dr: Khaled Abd El-Moaty Mohamed El-Shawadfy) lecturer of statistic in Institute of productivity zagazig university 1-1 Introduction In these article two models was estimated using panel data, first full model where all coefficient are constant, second Dummy variables model where intercept coefficient variant through individuals. Using data of Gross Domestic production (GDP), investment in million L.E and number of labor in thousands unit in relation to agriculture and industry sectors in Egypt through (ministry of planning 2000). This article consists of the following parts: 1-2 the theoretical models 1-3 Model with all coefficients constant (Full Model) 1-4 Dummy Variable Models, in addition to conclusion and recommendations, reference and appendix. 1-2 The theoretical models The problem of hetroscedasticity and autocorrelation have been discussed extensively in the literatures,hoch, I.(1962),Goodnight,J.and Wallace (1972) it has been noted that the first problem might be a reasonable assumption when using cross sectional data while the latter frequently occurs when using time series data. Thus when combining the two types of data it seems reasonable to set up a model that captures both effects. Havenner, A.and Swamy,P.A.V.P.(1981). The model is Y i = X i B + e i, i=1,2,,n (1.1) Where Y i =(y i1, y i2,, y it ), X i is a (T x K) matrix of observations on K explanatory variables for the ith individual. B=(B 1, B 2,,B K ) / is a vector of parameters to be estimated, and the disturbance e i =(e i1, e i2,, e it ) / is such that E(e i ) = 0. E(e i e j )=ψ where the covariance matrix results from the firstorder autoregressive process. This model assumes that:

2 a) The coefficients are the same for all individuals. b) The disturbance vector for a given individual follows a first-order autoregressive process. c) The variance of the disturbance can be different for different individuals. d) The disturbances for different individuals are (contemporaneously correlated) While the dummy variable model can be written as Y i = ( B + μ i ) J T +X si B s +e i (1.2) Where Y i =(y i1, y i2,, y it ) /, e i =(e i1, e i2,, e it ) /, J T = (1,1,,1) / and is of dimension (Tx1), and X si contains values of the explanatory variables except for the constant and is of dimension (TxK / ),where K / =K-1. The intercepts B 1i = B + μ I are assumed to be fixed parameters which, along with the slop coefficients B s = (B 2, B 3,, B k ) / need to be estimated, e i =(e i1, e i2,, e it ) / is such that E(e i ) = 0. E (e i e j ) =ψ where the covariance matrix results from the first-order autoregressive process 1-3Modle with all coefficients constant (Full Model) The aim of this article is building and estimation a production model using data of Gross Domestic production GDP as a dependent variable, investment and labor as explanatory variables. The comparison between last two theoretical models in logarithm transformation will do. The model is: LnY it =B 1 Ln X 1it + B 2 Ln X 2it + U it (1-3) Where LnY it is a logarithm of GDP for sector i (two sector) in time t (40 year ) Ln X 1it is the logarithm of investment for sector i (two sector) in time t(40 year ) Ln X 2it is the logarithm of labor for sector i (two sector) in time t(40 year ) 2

3 B 1, B 2 are parameters to be estimated without constant term and the coefficients are the same for all sectors U it is a disturbance term follows a first-order autoregressive process. When apply the model using data Table (I) in appendix the results appear in the following table (1-1) Table (1-1) Results for Full Model Variables Prais-Winsten Β (P.W) P.value Cochrane- Orcutt Β (C.O) P.value Ln X Ln X F R D.W From Table (1)first the two methods appear that all B`s take the expected positive signs which prove the direct relationship between gross domestic production GDP( LnY )and each of investment(ln X 1 ) and labor (Ln X 2 ) 3

4 From Table (1) using Cochrane- Orcutt method it can be seen that all Β (C.O)`s are highly significant with significant t less than 0.05 except B 1 (Estimate coefficient of Ln X1) and adjusted R 2 =0.845 and F = (Indicates that the regression is significant in general). In the same table using Prais-Winsten method notice that all Β (P.W)`s are highly significant with significant t less than 0.05 without exception. In addition to adjusted R 2 =.927 greater than its value in Cochrane- Orcutt method and D.W value =1.991 is more close to 2 value than the same value in Cochrane- Orcutt method.then the estimated full model using praiswinsten is better than the other using Cochrane- Orcutt method. So the estimated full model is LnY =.517 Ln X Ln X 2 (1-4) In appendix (1) diagram (1) appears the goodness fitting of Prais- Winsten method in relative to Cochrane-Orcutt method. 1-4 Dummy Variable Model Using two dummy variables S 1, S 2 to indicate agriculture sector and industry sector respectively in model (1-1) to become model (1.3) LnY it = B 01 S 1 + B 02 S 2 B 1 Ln X 1it + B 2 Ln X 2it + U it (1-5) 4

5 Which S 1 takes one values relating agriculture sector observations and zero value relating industry sector observations. Thus S 2 takes one value relating industry sector observations and zero value relating agriculture sector observations. When apply the model (1-3) in the same data in appendix the results appear at the following table (1-2) Table (1-2) Results for Dummy Variable Model Variables Prais-Winsten Β (P.W) P.value Cochrane- Orcutt Β (C.O) P.value Ln X LnX S S F R D.W From Table(1-2) The results of Cochrane-Orcutt method notice that 2 estimated parameters of Ln X1 and LnX2 are not significant, R =.85 and the value of D.W =1.14 indicating that autocorrelation problem still exists. The results of Prais-Winsten method all estimated parameters are significant and have expected signs. D.W=2.04 statistic is optimum value 5

6 2 where indicate that autocorrelation problem was disappeared. R =.94 and value is significant. So the estimated Dummy variable model is LnY = S S Ln X Ln X 2 (1-6) Where B 01 = and B 02 = but the true effect of the individual sector μ i calculated as it is: μ i = B 0 - B 0i Then μ 1 =( )/ = μ 2 =( )/ = Thus, the model (1-6) can rewrite as: LnY 1 = Ln X Ln X 2 LnY 2 = Ln X Ln X 2 (agriculture sector) (industry sector). (1-7) 1-5 Conclusion and Recommendations 1) The study appear that the dummy variable model give results better than model with all coefficients constant, where adjusted R square is bigger, Durbin Watson (D.W) is more closed to 2 value, 2) Dummy variable model allows estimation of Individuals Effects, where μ 1 = is the effect of agriculture sector in GDP and μ 2 = is the effect of industry sector. 3) The study prove that the agriculture sector has a positive effect in GDP, otherwise it prove that the industry sector has a negative effect in GDP. 4) The results of Prais-Winsten method was better than the Cochrane-Orcutt method 6

7 References 1 - Goodnight, J.and Wallace, T.D. (1972),Operational Techniques and Tables for Making Weak Use Tests For Restrictions in Regressions, Econometrica,40, Havenner, A. and Swamy,P.A.V.B.(1981) A Random Coefficient Approach to Seasonal Adjustment of Economic Time Series,Journal of Econometrics,15, Hoch, I.(1962), Estimation of Production Function Parameters Combining Time Series and Cross Section Data, Econometrica, 30(1), Hausman, J.A.(1981), Panel Data and Unobservable Individuals Effects, Econometrica 43(4), Theil, H.(1971), Principles of Econometrics, New York John Wiley. 7

8 Appendix Table I Agriculture Sector Industry Sector Year Labor Gdps Invest Labor Gdps Invest S1 S

9 Full Model Diagram (1) demonstrates the true values of GDP and its predicted values of Cochran- Orcutt method and Prais- Winsten method Ln(Y) Fit (C.O) Fit (P.W) YEAR 9

10 Dummy Variable Model Diagram (2) demonstrates the true values of GDP and its predicted values of Cochran- Orcutt method and Prais- Winsten method Ln(Y) Fit(C.O) Fit (P.W) YEAR 10