Chapter 1- Introduction 1.1 Introduction Construction is one of the major contributors for National Economy in any country. In another words, it accounts for a sizable proportion in Gross Domestic Product (GDP) and Gross National Product (GNP). Therefore, this analysis was undertaken to determine the relationship between national economy and construction activities in all segments in Sri Lanka mainly categorized as residential buildings, non-residential buildings and others. These categories cover all types of construction activities in the country including hotels, housing complexes, hospitals, trade centers, towers, schools, other buildings, urban infrastructure including water supply, sewerage and drainage. Also it comprises construction of roads, railways, highways, ports, airports; power & oil storing systems; irrigation, recreation facilities and agriculture systems and telecommunications etc. that indicates input - output flux of national fiscals. As per the definition of United Nations (UN) construction is “an economic activity directed to the creation, renovation, repair or extension of fixed assets in the form of buildings, land improvements of an engineering nature and other such engineering constructions as roads, bridges, dams and so forth”. It is a process that consists of the building or assembling of infrastructure in the fields of architecture and civil engineering. Construction industry involves a broad range of stakeholders and provides substantial employment opportunities to unskilled, semi-skilled and skilled labor markets. It supplements the foreign revenue derived from trade in construction material and engineering services. Further, it has strong linkages with other sectors which positively contribute towards the national income. Construction activities in Sri Lanka has shown fairly upward trend year-on year since 1990. However, after the end of 30 year prolonged war in 2009, construction industry has shown a steep development with an average of 13.0% increase from 2009 to 2013. This has been accelerated specially due to reconstruction activities undertaken in North and East parts of the country and many other development projects carried out around the island. The trend for real GDP and construction sector GDP fluctuation is shown in figure 1 below. § £ UfcftAJW ^1 * > Figure 1 - Construction Sector and overall GDP Growth Rate (Source : CBSL Annual Report 2013) As shown in Table 1.1 below, construction sector has contributed 8.1% to the overall GDP (real) in 2012 and 8.7% in 2013. Similarly, construction subsector has contributed 26.7% towards ‘Industry Sector’ in 2012 and subsequently 27.8% in 2013. Table 1 - Comparison of construction sector in terms of GDP and Industry Sector (Source : CBSL Annual Report 2013) ConstructionIndustry Sector (Real) Construction as % of Industry Sector GDP (Real) ConstructionGDP (Real)Year as % of GDP(Rs. Mn) (Rs. Mn)(Rs. Mn) 23.2%6.6%701,129 162,7902009 2,449,214 23.4%6.7%2010 177,9122,645,542 760,334 24.2%7.1%2011 2,863,715 838,932 203,204 26.7%8.1%2012 247,0913,045,288 925,152 27.8%8.7%282,7422013 3,266,099 1,016,886 2 However, by looking at just the row figures it may be difficult to get a clear understanding of if any money invested in construction industry may bring profits or not at the end. Hence, entrepreneurs and investors are interested to have a reliable and logical approach to be used in the decision making process to determine whether or not there is an obvious link between construction industry investments and constant economic growth of the country to get a feeling about the returns of their investments (ROI). Therefore, the intention of this study is to provide a mathematical approach to assist the decision making process in the context of Sri Lankan economy to identify the correct relationships between the investments in construction activities and the economic indicators of the country. 1.2 About Sri Lanka Sri Lanka is an island located in the Indian Ocean with total land area of 65,610 squire kilo meters and 20.3 million of population with a distribution of 47.4% male and 52.6% female in gender (2012 census). Further, Sri Lanka has recorded 1% of population growth rate (2011). Sri Lanka is strategically located at the cross roads of major shipping routes connecting South Asia, Far East and the Pacific with Europe and the Americas next to the fast growing Indian sub-continent with close proximity to Southeast Asia and the Middle East. As per the Socio Economic Indicators published by Central Bank of Sri Lanka (2013) Ethnic diversity of the country has been reported as Sinhalese - 74.9%, Sri Lankan Tamils — 11.2%, Indian Tamils - 4.2%, Moors - 9.2%, and Other - 0.5% (2012 census) with overall literacy rate (Aged 15 years and above, 2010) 91.9%. (Male - 93.2% and Female - 90.8%) Also the life expectancy (2011) has been reported as average of 74.9 years in total population. Labor force as a percentage to the population has been recorded as 48.2% in the country (exclude Northern and Eastern provinces, 2011) whilst Unemployment percentage out of total labor force has been recorded as 4.2% with the same conditions. Per capita income has been recorded as USD 2,805 (LKR 310,124) in 2011 and this is an increase of 15.73% compared to 2010 and 14.65% compared to 2009. Sri Lanka is rich with natural resources such as graphite, apatite, limestone, dolomite, mica, quartz, calcite, silica sand, gems, mineral sands, clay, hydropower and phosphates. Certain 3 minerals such as Graphite and Silica (mostly monazite) and few verities of gems are mainly exported as row materials with no purification or processing. The Government has emanated the State policy under ‘Mahinda Chinthana’ vision to develop Sri Lanka as one major hub in the South Asian region consist with five sub components such as Maritime, Aviation, Commercial & Tourism, Knowledge and Energy. This is called ‘five-hub concept’ in government strategy plans. However, still the main economic revenue of the country is generated through tourism, apparel & textile, tea, rubber & coconut exports and other agricultural products such as rice production. Further, Sri Lanka receives significant remittance through work force deployed in foreign countries for employment. Most of third world countries are facing the problem of racing funds to improve their capital expenditures. As a developing country, Sri Lanka is also facing for the same issue in terms of inadequacy funds to improve infrastructure facilities in the country. Nevertheless, it’s a challenge to meet global standards and to par with global economic trends specially to attract investors from the outside the country. Therefore, developing of traveling and transportation facilities, aviation, ports, telecommunication, information technology and uninterrupted power solutions are essential and high priority. 1.3 Sri Lankan Economy and Outlook As per Central Bank Statistics for past five years (2009 -2013), Sri Lanka has gained average of 6.7% growth in real GDP. Further, it was noted a sustainable growth trajectory throughout the period and has achieved 7.3% growth in 2013 compared to 6.3% in 2012. (Refer Table 1.2). This has been supported by growth of all sectors including improved earnings from merchandises, service exports and workers’ remittances received in to the country. It was also noted the inflation (Colombo Consumers' Price Index, Department of Census and Statistics, Base 2006/07=100) remained at a single digit level for the fifth consecutive year, recording 6.9 in December 2013 whereas 7.6 in December 2012. Latest reports indicate that this has been further reduced to 5.6 in April 2014. Year-on-year headline inflation too has moved on a decelerating path since March 2013 with the improvements in supply conditions. Continuation of this trend will help to reduce wage pressures in the economy and also to raise investor confidence in the long run. 4 Further, as per World Economic Outlook by IMF (April, 2014) it is noted that, Sri Lanka has made a remarkable progress in comparison to the emerging and developing markets in the Asian continent. Table 2 - World GDP - Real (Source : World Economic Outlook by IMF (April, 2014)) Average 1996-2005 2009 2010 2011 2012 2013 1.0-2.7 1.8 1.4 1.22.9Advanced Economies United States United Kingdom Germany France 1.61.8 2.43.9 -3.0 1.5 1.6-0.6 1.43.9 -4.8 1.2 0.4 0.6-1.6 1.8 2.90.7 -0.1 0.31.6 1.0-1.42.2 2.2 2.1-2.3 2.0 0.70.8Japan Emerging and Developing Asia Bangladesh Bhutan China 6.57.9 6.77.7 9.77.1 6.1 5.85.9 6.4 6.55.4 6.5 55.7 9.3 10.16.9 7.79.2 10.4 9.3 7.79.2 4.48.5 10.3 6.6 4.7India 6.4 6.5 6.3 5.8Indonesia 2.6 4.6 6.2 6.3 7.3Sri Lanka 3.5 8 8.24.3 All sectors of the economy has contributed positively towards the steady growth of DGP and backed by favorable climate conditions prevailed during the year 2013. As a result, GDP in nominal terms has been grew by 14..5% to LKR 8,674 billion (USD 67 billion) in 2013 compared to 15.8% of growth amounting LKR 7,582 billion (USD 59.4 billion) in 2012. This has helped to raise GDP per capita from USD 2,923 in 2012 to USD 3,280 in 2013 by recognizing Sri Lanka as the second highest country for GDP per capita among the SARRC members after Maldives. | UBRAM |5 Figure 2 - GDP Current and Year-On-Year Change % (Source : CBSL) In terms of expenditure, GDP growth supports increasing of consumption as well as investments in the country. Also it was noted interest rates have been reduced from double digit levels to single digit levels by the end of year 2013. This will lead to a positive move of the economy as relatively low interest rates will help to increase resources for investment activities in the future with the expansion in credit growth. Credit to both Industry and Services sectors have been increased by LKR 201.1 billion in 2013. The Central Bank policy introduced in 2013 has resulted to increase declarations of credit obtained from commercial banks in Sri Lanka. Further, it has helped to boost the access to the domestic and global capital markets by the private sector in 2013. As per the preliminary findings of the Household Income and Expenditure Survey (HIES) for 2012/13, population below the Poverty Line ratio has been declined to 6.5% from 8.9% in 2009/2010. This is also a positive trend that indicates the development of Sri Lanka in terms of investor confidence. Further, it was noted that new reforms have been new introduced to simplify the tax system while reducing its inefficiencies and leakages. This will help reducing tax evasion and increase state revenue. As per the CBSL economic indicators, it is observed an increase of labour force by 4.1% in 2013 compared to the previous year. Further, it was noted that labour force participation rate (LFPR) also has increased to 53.8% in 2013 compared to 52.6% in 2012. Although, unemployment rate has recorded high in 2013 this would have been resulted by increased 6 entry from rural females into the labor market seeking local job opportunities which attributing 6.6% of female unemployment rate. By considering all facts above, in overall, the economy of Sri Lankan is expected to continue its growth momentum in the medium term underpinned by increased investment, improved macroeconomic stability and improving global economic conditions. These are favorable indicators for entrepreneurs who look opportunities to invest in Sri Lanka in any sector, including the construction sector as well. 1.4 Construction Sector Contribution to Gross Domestic Product The construction sector share to overall GDP has been improved steadily since 1990. CBSL statistics indicates 13% of average growth (in real terms) in Construction Sector during the past five years (2009 -2013). Further, it was noted the Construction Sector GDP in real terms has achieved 282.7 billion (USD 2.2 billion) in 2013 in comparison to LKR 247 billion (USD 1.9 billion) in 2012. Whilst the highest growth rate of 21.6% recorded in 2012, still the sector has maintained 14.4% of growth in 2013. (Refer figure 1) GDP Construction and Year-On-Year Change Percentage ^ 1,000,000 g 900,000 I 800,000 5 700,000 ^ 600,000 •2 500,000 s 400,000 * 300,000 g 200,000 - 45.00% - 40.00% - 35.00% - 30.00% - 25.00% - 20.00% - 15.00% - 10.00% - 5.00% - 0.00% u 100,000 ft 0 o«—'vor^oooo — n n OnOnOn^>0''0'iO\0'>C'iOnOOOOOOOOOO—<»— *— ONOnOnO'On05^0>CT'OnOOOOOOOOOOOOOO,_^_,_^_I_^^rt__^rv1(NrNcNcN(NtNc- ■t-28 O Share of Constriction in GNP NICs LDSs AICs GNP Per Capita Figure 7 - The Bon curve (Source: Bon 1992) The inverted U-shaped relationship presented by Bon (1992) is very different from the S- shaped relationship found by Turin (1978).Turin,s analysis was mainly focused on developing countries. Bon’s 1992 argument concerns the entire path from LDC (least developed countries) to NIC (newly industrialised countries) to AIC (advanced industrial countries) status. The share of construction in total output first increases and then decreases with economic development, this is called the inverted U-shaped relationship. Ofori (1993) enhanced his previous views in 1980 and suggested that construction industry development as ‘the deliberate and managed process to improve the capacity and effectiveness of the construction industry to meet the national economic demand for building and civil engineering products, and to support sustained national economic and social development objectives.5 In another hand he introduced that the following components: human resource development; materials development; technology development; corporate development; development of documentation and procedures; institution building; and development of operating environment of the industry. Jin et al. (2003) found a non-linear relationship between the shares of construction output in GDP with the GDP per capita. Jin used the statistics across 34 countries and regions to analyses this. construction economics (Wells 1986; Field and OforiIn addition to above many studies on 1988; Bon and Pietroforte 1990; Green 1997; Hillebmndt 2000; Lean 2001; Rameezdeen 2007; Anaman and Amponsah, 2007; Myers 2008; Dlamini 2011) emphasize the important 29 role of the construction sector in national economic growth. They all argue that construction makes a noticeable contribution to the economic output of a country. However, still there are some opposing views also can be noted. Authors such as Wang and Zhou (2000), Tan (2002), Hassan (2002), Kim (2004), and Dlamini (2011) all argue that the construction sector and its related activities are not drivers of economic growth. Also it was noted that Thanuja and Raufdeen (2006) and Thanuja, James and Raufdeen (2013) have conducted a causality test with no mathematical modeling in the same area and the conclusion justifies a strong linkage between national economic growth and the construction industry activities. 30 Chapter 3 - Methodology 3.1 Introduction This chapter describes the data and the methodology used in this study and the impact of the growth of the construction sector to the national economy. 3.2 Selection of Data In this empirical analysis it is used basic set of variables consists of both national economy fiscals and construction sector annual figures from 1990 to 2013. Whilst National Economy Fiscals included variables such as Nominal Gross Domestic Product (GDP) and Balance of Trade (BOT); Construction Sector variables included Construction Gross Domestic Products (CGDP), Gross Fixed Capital Formation for Construction Sector (CGFCF) and All Construction Cost Index (ACINDEX). All the variables are expressed in natural logarithms so that they may be considered elasticity of the relevant variables. Annual observations of GDP, BOT, CGDP, CGFCF were extracted from data published by the Central Bank of Sri Lanka on the annual reports and All Construction Cost Index (ACINDEX) was extracted from The Institute of Construction Training & Development (ICTAD) bulletins. 3.3 Granger Causality Clive J Granger (1969) introduced the Granger causality tests to analyze the effect of one time series on another one. He thought out of the box and said that ‘regressions’ does not only show ‘correlations’ but if certain tests are performed on them they may reveal information about causality. The idea of Granger causality is that a variable X Granger- courses variable Y can be better predicted using the histories of both X and Y than it can be predicted using the history of Y alone. This is shown if the expectation of Y given the history unconditional expectation of Y. It was then widely used in of X is different from the economics. 31 3.3.1 Definition of Granger Causality We say that xt is Granger causal for yt with respect to Fx if the predictor of yt+h based on Fx has smaller based on zt, zx.x... for any h. In other word xt is Granger causal for yt if xt helps predict yt at some stage in the future. variance of the optimal linear variance than the optimal linear predictor of yt-*-h Often you will have that xt Granger causes yt and yt Granger causes xt. In this case we talk about a feedback system. Most economists will interpret a feedback system as simply showing that the variables are related (or rather they do not interpret the feedback system). Sometimes econometricians use the shorter terms “causes" as shorthand for “Granger causes". You should notice, however, that Granger causality is not causality in a deep sense of the word. It just talks about linear prediction, and it only has “teeth" if one thing happens before another. (In other words if we only fmd Granger causality in one direction). In economics you may often have that all variables in the economy react to some un-modeled factor and if the response of xt and yt is staggered in time you will see Granger causality even though the real causality is different. There is nothing we can do about that (unless you can experiment with the economy) Granger causality measures whether one thing happens before another thing and helps predict it and nothing else. Of course we all secretly hope that it partly catches some “real" causality in the process. In any event, you should try and use the full term Granger causality if is not obvious what you are referring to. The definition of Granger causality did not mention anything about possible instantaneous correlation between xt and yt. If the innovation to yt and the innovation to xt are correlated we say there is instantaneous causality. You will usually (or at least often) find instantaneous correlation between two time series, but since the causality (in the “real" sense) can go either usually does not test for instantaneous correlation. However, if you do find Granger feel that the case for “real" causality is stronger if innovations to each series can be thought way, one causality in only one direction you may there is no instantaneous causality, because then the enerated from this particular series rather than part of some vector Of course, if your data is sampled with a long sampling of as actually being g innovations to the vector system period, for example annually, then you would have to the other after such a long lag (you may depending on your application). explain why one variable would only have a story for that or you may not, cause 32 Granger causality is be described by the model, p rticularly easy to deal with in VAR models. Assume that our data can Miyt AuAnA'n A21A22A23 ^A3\AnAi3j yt-1 AUAV yt-k + AUWL ak ak ak ^A.3]A.32 A33 j Hit Mizt + 1Zt-1 U2tZt-k Xt, M 3V / \ J \xt-i) U3t[Xt-k J Also assume that, S11Z12Z13 Z„ = Zl2Z22Z23 Z13 Z23 Z33 This model is a totally general VAR-model - only the data vectors has been partitioned in 3 sub-vectors - the yt and the xt vectors between which can be tested for causality and the zt vector(That could be empty) which we condition on. In this model it is clear that xt does not Granger cause yt with respect to the information set ,k or AU = 0; and A[2 = 0; i =generated by zt if either^{3-0; and^23~0; i - 1, 1,.. .k. Note that this is the way you will test for Granger causality. Usually you will use the VAR approach if you have an econometric hypothesis of interest that states that xt Granger causes yt but yt does not Granger cause xt. 3.3.2 Limitations of Granger Causality . If both X and Fare driven by a commonGranger causality is not necessarily true causality with different lags, one might still accept the alternative hypothesis of Granger causality. Yet, manipulation of one of the variables would not change the other. Indeed, the of variables, and may produce misleading results variables. A similar test involving more third process Granger test is designed to handle pairs when the true relationship involves three variables can be applied with vector auto regression. or more 33 Vector Auto Regression (VAR) Analysis3.4 The vector autoregression (VAR) model is one of the use models for the analysis of multivariate time univariate autoregressive model to dynamic multivariate time series. A way to summarize the dynamics of macroeconomic data is to make use of Vector Auto Regressions. The VAR model has proven to be especially useful for describing the dynamic behavior of economic and financial time series and for forecasting. Therefore, VAR models have become increasingly popular in recent decades. They are estimated to provide empirical evidence on the response of macroeconomic variables to various exogenous impulses in order to discriminate between alternative theoretical models of the economy. It often provides superior forecasts to those from univariate time series models and elaborate theory-based simultaneous equations models. Forecasts from VAR models are quite flexible because they can be made conditional on the potential future paths of specified variables in the model. most successful, flexible, and easy to series. It is a natural extension of the In addition to data description and forecasting, the VAR model is also used for structural inference and policy analysis. In structural analysis, certain assumptions about the causal structure of the data under investigation are imposed, and the resulting causal impacts of unexpected shocks or innovations to specified variables on the variables in the model are summarized. These causal impacts are usually summarized with impulse response functions and forecast error variance decompositions. This simple framework provides a systematic way to capture rich dynamics in multiple time series, and the statistical toolkit that came with VARs was easy to use and to interpret. In addition to measuring the broad correlation in the variables of a system, VAR helps us to the lead-lag relationships. VAR is commonly used for forecasting systems of interrelated time series and for analyzing the dynamic impact of random disturbances on the VAR approach side steps the need for structural modeling by variable in the system as a function of the lagged values of all of The estimated VARs are used to calculate the measure system of variables. The modeling every endogenous the endogenous variables in the system percentages of each endogenous explanatory variables and pro innovation to the variable in the ++ ApYt-p + pXt + variable that can be explained by innovations in each of the vides information about the relative importance of each random VAR. The mathematical form of a VAR is Yt = A1Yt-1 34 Where Yt is a k vector of endogenous variables, X, i Ap and (3 are matrices of coefficients to be estimated may vary contemporaneously. is a d vector of exogenous variables, Aj, , and at is a vector of innovations that Multiple Regression and Assumpti Multiple regression is most effect at identifying relationship between a dependent variable and a combination of independent variables when its underlying assumptions are satisfied. In another words, it relies upon certain assumptions about the variables used in the analysis. When these assumptions are not met the results may not be trustworthy. 3.5 ons These assumptions include • The errors are normally distributed • The mean of the errors is zero • Errors have a constant variance • The model errors are independent Each metrics variables are normally distributed, the relationships between metric variables are linear, and the relationship between metric and dichotomous variables is homoscedastic. Failing to satisfy the assumptions does not mean that our answer is wrong. It means that our solution may under-report the strength of the relationships. Outliers can distort the regression results. When an outlier is included in the analysis, it pulls result in a solution that is more accurate for the cases in the data set. It shall be checked for the regression line towards itself. This can outlier, but less accurate for all of the other univariate outliers on the dependent variable and multivariate outliers on the independent of satisfying assumptions and detecting outliers are intertwined. For value on the dependent variable that is an outlier, it will affect the variables. The problems example, if a case has a skew, and hence, the normality of the distribution. Removing an outlier may improve the distribution of a variable. Transforming for a case will be characterized as an outlier. variable may reduce the likelihood that the value 35 The order in which we check assumptions and detect outliers will affect our results because we may get a different subset of eases in the final analysis. In otder to maximize the number of cases available to the analysis, it shall be evaluated assumptions first. It shall be substituted any transformations of variable that enable transformed variables that are required in our analysis to detect us to satisfy the assumptions. It shall be used any outliers. Least Squares Method (LSM)3.6 The Least Squares Methods (LSM) is one of the very popular techniques in statistics due to following reasons. • Most common estimators can be casted within this framework, (i.e — the mean of a distribution is the value that minimizes the sum of squared deviations of the scores. • This method has recognized as very tractable as when the error is independent of an estimated quantity, it can add the squared error and the squared estimated quantity. • Mathematical tools and algorithms are involved in LSM (derivatives, Eigen composition, singular value decomposition) have been well studied for a relatively long time. The Method of Least Squares is a procedure to determine the best fit line to data; the proof simple calculus and linear algebra. The basic problem is to find the best fit straight line y = ax + b given that, for n E {1,........ N}, the pairs (xn; yn) are observed. The method easily generalizes to finding the best fit of the form; uses + ckfk(x);y = a^Cx) + it is not necessary for the functions fk to be linearly in x - all that is needed is that y is to be a linear combination of these functions. define the error associated to saying,(xN;yN)}' we mayGiven data {(x1;* yi), y = ax + bby N E(a,b) = ^On - (axn + b))2 n=l 36 This is just N times the variance of the data set {yx - (aXl + b), ,yn - (axN + b)}. It makes no difference whether or not we study the variance or N times the variance as our error, and note that the error is a function of two variables. The goal is to find values of a and b that minimize the error. In multivariable calculus learn that this requires us to find the values of (a; b) such that, dE we dE db ° Therefore the final solution can be drawn as, S b =-^SJXX a = y - bx It is not necessary to worry about boundary points: as |a| and |b| become large, the fit will clearly get worse and worse. Thus it was not necessary to check on the boundary. Preliminary Analysis3.7 Both graphical representations as well as descriptive statistics were comprehensively employed in examining the data properties. Variables are depicted using scatter plots and line graphs which is useful in identifying characteristics of the series, detecting possible outliers, observations that could be used in the determining the probable transformation to make the seriesmodeling process such as stationary etc. is carried out under Chapter 4 for all the variables and special characteristics of the series. The of central tendency such as arithmetic mean, median and mode and measures of dispersion such as variance, standard deviation and range which are widely known. Further, measures of distribution shape including skewness and kunosis which is normally a concern in most of the economic data series is also considered. A comprehensive descriptive level analysis selected, in order to identify the patterns summary measures included measures 37 3.8 Skewness Skewness is a measure of asymmetry of the distribution of. series around its arithmetic mean and computed by the formula, HW)3 1 = 1 Where d is an estimator for the standard deviation and n is the sample size. The skewness of a symmetric distribution, such as the normal distribution, is zero. A positive value implies positive skewness of the distribution and a negative value implies negative skewness of the distribution. 3.9 Kurtosis Kurtosis measures how sharply peaked the distribution is (peaked ness or flatness of the distribution) of a series and calculated as, i=l Where d an estimator for the standard deviation and n is is the sample size. The kurtosis of the normal distribution is 3. If the kurtosis exceeds 3, the distribution is peaked (leptokurtic) relative to the normal; if the kurtosis is less than 3, the distribution is flat (platykurtic) relative to Normal distribution. 3.10 Cointegration If two or more series are themselves non-stationary, but a linear combination of them is said to be cointegrated. That is if they share a commonstationary, then the series are stochastic drift. spurious or nonsense regressions in timecauseNot concerning about co-integiation may series in modeling. Ms is where ihe usual procedure for resting hypotheses concerning the relationship between non-sta,ionary variables was to run ordinary leas, scares,egress,ons on 38 data which had initially been differenced is i cointegrated. is incorrect if the non-stationary variables are Let Yt - (yi t> • ■ •, yn t)' denote an ( Yt is cointegrated if there exists an (n x ]) vector p = PoYt = PiYi t + • • ■ + pnyn t ~ 1(0) The intuition is that 1(1) time series with a long-run equilibrium relationship cannot drift too far apart from the equilibrium because economic forces will act to restore the equilibrium relationship. Here the individual series are first-order integrated that is 1(1) but some cointegrating vector of coefficients exists to form a stationary linear combination of them. Therefore I such cases Error Correction Models recommended when it comes to the modeling process. 1) vector of 1(1) time series.n x (Pi/---,Pny such that 3.11 Detecting Cointegration - Johansen Cointegration Test Johansen Co-integration test is a technique for testing cointegration of several time series. This test permits more than one cointegrating relationship. It was selected a VAP (p) + Apy( p + e,yt-\i+Axyt ,+ Where y, is an n x 1 vector of variables that are integrated of order one commonly denoted 1(1) and et is an n x 1 vector of innovations. This vector auto regression can be re-written as, pA 2 r,Av +&Ay,=p+n y +t l i=i Where, II = ^Ai = / And 1/ - Aj • j then there exist nxr matrices a and P each stationary. R is the number of co-integrating If the coefficient matrix II has reduced rank r with rank r such that n=aP' and P y* IS 39 relationships, the elements of a known as the adjustment parameters a co~integrating vector .It can be shown that for a are in the vector error correction model and each column of (3 is given r, the maximum likelihood estimator of (3 defines the combination of yt-i that yields the of Ayt with yM after correcting for lagged differences andr largest canonical correlations deterministic variables when present. Johansen theo ry proposes two different likelihood ratio of these canonical correlations and thereby the reduced rank of the ITtests of the significance matrix. 3.12 Trace Test H0 : Cointegration rank is less than or equal to r H0 * There is m cointegrating relations” (i.e., the series are stationary) Where r = 0,1,....., m - 1. T 2ln(l- jj,,)Where J i/ trace /=r+l Where T = sample size and ^ is the largest canonical correlation. Maximum Eigen value statistic test H0: Number of cointegration vectors equal to r H0: Number of cointegration vectors equal to r + 1 where ^max ~ Tl7l(l ^r+l)^ ^ likelihood estimates of the parameters in a vector error-The tests also produce maximum correction (VEC) model of the cointegrated series. 3.13 Selection of the lag length nsidering the VAR lag order selection criteria of the The optimum lag length is arrived by co lag structure. The available criterias are 40 • Sequential modified LR • Final prediction error • Akaike information criterion The Akaike Information smaller values are Preferred. It is computed as, test statistic Criterion (AIC) is used in model selection processes and AIC = -2-+ — n n Where l is the Log likelihood and k is the number of parameters in the model and n i; the sample size. • Schwarz information criterion This is an alternative to the Akaike Information Criterion that imposes a larger penalty for additional coefficients. It is calculated as, l _ k log (n) SC = -2 —+n n Smaller values are preferred in this criterion also. • Hannan-Quinn information criterion l 2k log (log (n)) HQ= -2- + 7171 This criterion also imposes another penalty function for unimportant inclusions to the model. Commonly selected lag by the available techniques the model while taking more emphasis on Akaike criterion and Hannan-Quinn information criterion which are widely employed. is considered as the best possible lag of information criterion, Schwarz information 41 Chapter 4 - Analysis of Data 4.1 Introduction In this chapter the methodology elaborated in chapter 3 is implemented to the selected variables described under notation section. Gross Domestic Product (GDP) and Balance of Trade (BOT) have been selected to reflect the national economic statistics whilst Construction Sector of Gross Domestic Product (CGDP), Gross Fixed Capital Formation for Construction Sector (CGFCF) and All Construction Cost Index (ACINDEX) have been selected to reflect construction outputs. In order to understand the characteristics of the variables the graphical as well as summary measures were studied at first. Then the series was tested to determine whether the assumptions are met and the given regressions are explained our objective reflecting any unidirectional bidirectional relationship between construction outputs and national economic statistics. A keen attention was paid to safeguard the characteristics and real behavior of row data. Hence, transformations deemed unnecessary as it results to compromise the details and smoothness of variables particularly used in this analysis. Then the residual tests were tested for unit root, serial correlation, heteroscedasticity and multivariate normality to validate the model. Finally, the conclusion was arrived based on the test results. consist of 24 data elements from year 1990 to 2013. TheIt was obtained a sample information such as CGFCF is only published annually. Hence, for higher accuracy and reliability, the stud, was based on published annual dam b, the respective national authorities , , . , . observations of GDP, BOT, CGDP, CGFCF wereduring the mentioned period above. Observ tral Bank of Sri Lanka on the annual reports fromextracted from data published by the Cen 2009 - 2013 and All Construction Cost Index (ACINDEX) of Construction Training & Development (ICTAD) bulletins. extracted from The Institutewas 4.2 Notation Let, Abbr: GDPic Product (Nominal)• Gross Domestic • Construction Sector of Gross Dome • Balance of Trade - Abbr: BOT Stic Product (Nominal) - Abbr: CGDP 42 . Gross Fixed Capital Formation for Const . All Construction Cost Index ruction Sector - Abbr: CGFCF - Abbr: ACINDEX 43 Graphical Representation of the Vari4.3 ables plot of each series was checked plot the graphs. parately to identify the trend. E-views have been used to GDP CGDP 10,000.000 1.000,000 8,000.000- 800,000- 6,000,000- 600.000- 4,000,000- 400.000- 2,000,000- 200,000- ® i i i i ■ i i i i i i i i i i i i i—i—i—i—i—r~ 90 92 94 96 98 00 02 04 06 08 10 12 P. I ( i i I I i i i I I I i i fill I I i T90 92 94 96 98 00 02 04 06 08 10 12 BOT CGFCF 0 2,000,000 1,600,000--2,000- 1,200,000--4,000- 800,000--6,000- 400,000--8,000- °90T^^4 ‘ 96'98'00 02 ‘ 04'06 ‘ 08 ‘ 10'12-10,000 90'92'94'96'98 ‘ 00'02'04 06'08'10 12 ACINDEX 120" j j |j j i i i i ^ 90 92 94 96 98 00 variablesFigure 8 - Time series line plots of the 44 When observing the scattered plots of the vari with their trends indicating possible consist anables, all of them are fairly concentrated along ence in variance except BOT. Testing for Ganger Causality4.4 The Granger Causality was «ed for the Mowi„g ^ ^ N„u Hypothcs|s M ^ ppeared m different lag levels (1 to 7) depicted below. Howe combinations where national versa. a ver, it was considered only the economy can be compared with construction sector and vice It has been selected Gross Domestic Product (GDP) and Balance of Trade (BOT) to express the national economic statistics whilst Construction Sector of Gross Domestic Product (CGDP), Gross Fixed Capital Formation for Construction Sector (CGFCF) and All Construction Cost Index (ACINDEX) have been chosen to reflect construction sector outputs. Then the associations between the variables were tested In this study, only the combinations of variables were considered from the opposing sector and the combinations of variables from the same sector were omitted. Hence following relationships have been used to analyse and express the causality relationship between GDP & CGDP, GDP & CGFCF, GDP & ACINDEX, BOT & CGDP, CGFCF & BOT and ACINDEX & BOT. It has been disregarded the combinations that indicate relationships between the same sector variables such as GDP & BOT, CGFCF & CGDP, ACINDEX & CGDP and CGFCF & ACINDEX. Table 5 - Causality Test in different Lag Levels between GDP and CGDP GDP Does Not Cause CGDPrr.np Does Not Cause GDPLag ProbabilityF-StatisticProbabilityF-Statistic 0.8337 0.9493 0.04527 0.05222 0.2796 0.4791 1.23513 0.76871 1 2 0.97740.065220.00855.820953 0.06493.037790.01335.208694 0.02284.98107 19.9189 8.3356 0,0229 0.05244.97484 4.83161 5 0.0024 6 0.11130.09310.10357 st and 2nd lags of CGDP 45 an unidirectional relationship from GDP relationship observed that t0 in lag 6. However, there ivambte GDP o, CGDP depend Therefore this was not examined this father as i relationship between these two variables to fb is no recent on resent past data (lag 1 or 2) it would not able to identify any short term recast any trend. Table 6 - Causality Test in different Lag Le,e„ between GDP turd CGFCF CGFCF Does Not Caiisp QDPLag GDP Does Not Cause CGFCFF-Statistic Probability F-Statistic Probability1 1.32122 0.61141 0.2639 6.71212 0.01752 0.5541 4.20032 0.03293 0.92367 0.4549 1.68143 0.21654 1.72011 0.2154 1.88107 0.184 5 5.43141 7.09323 17.4166 0.0179 2.38259 0.1319 6 0.0242 3.07376 0.1192 7 0.0554 5.06661 0.1747 It was noted no causal relationship exists among first four lag levels from CGFCF to GDP. Although, there is a unidirectional relationship from CGDP to GDP in lag 5 and 6, still this was not examined further as it would not able to identify any long or short term relationship from CGFCF to GDP in causality. However there was a unidirectional relationship from GDP to CGFCF both in lag 1 and 2. Hence, we examined this relationship further. Table 7 — Causality Test in different Lag Levels between GDP and CGFCF GDP Does Not Cause ACINDEXACINDEX Does Not Cause GDPLag ProbabilityF-StatisticProbabilityF-Statistic 0.93090.007710.19741.777961 0.77880.253750.43382 0.87748 0.6650.536320.03143.939063 0.02444.308230.01784.764584 0.069 0.3587 3.22285 1.42001 0,0717 0.1033 3.16916 3.34224 5 6 0.055717.30990.05467 17.6715 lationship from ACCINDEX to GDP in lag 3 & 4 and in lag 4, still this was not examined relationship among these two Although, there is a unidirectional re unidirectional relationship from fata, as it would not able to identify any k>"8 or short tern, GDP to ACCINDEX variables. 46 Table 8 - Causality Test in different Lag LeveIs between BOT and CGDP —^IDowNolCaus^CDP r-Statistic Lag _ CGDP Does Not Cause BOT F-Statistic____ Probabilil 7,99639 19.158 3.07867 1.25566 ~~ 1.86712 1.2015 Probabilil 1 14,5153 6.20009 6.80489 3.57876 4.32161 3.42797 0.0011 0.0095 0.0046 0.0104 0.00004 0.0621 0.3442 0.2061 2 3 4 0.0425 0.0334 0.09886 0.42957 7.59064 0.1213 2.37194 0.3284 Table 4.4 indicates productive and meaningful bi-directional CGDP and CGDP to BOT. At the outset this indicates that there among variables BOT and CGDP in short run. Hence, it was tested further to understand long term relationship. causal relationship from BOT to would be a relationship Table 9 - Causality Test in different Lag Levels between CGFCF and BOT CGFCF Does ^ot Cause BOT BOT Does Not Cause CGFCFLag F-Statistic Probability F-Statistic Probability 1 16.6491 0.0006 0.88755 0.3574 0.5615 0.58060.000012 24.5656 0.02174.437290.01273 5.20794 0.09142.637590.20914 1.75006 0.05743.483460.09785 2.75479 0.06514.312710.08786 3.6645 0.09919.442050.2183.92563 There is a positive short term unidirectional relationship from CGFCF to BOT in lag 1 to 3. investigated further to understand any Although there is a unidirectional relationship from BOT to CGFCF in lag 3, this examined further as i. would not able to identify any long or short tenn teladonship here. n ACINDEX and BOT mathematical long term relationship. was not This was Table 10 — Causality Test in different Lag Levels betv ACINDEX Does Not Cause_BQT Probabili BOT Does Not Cause ACINDEX F-Statistic ProbabililLag F-Statistic 0.42320.668540,0067 0,0006 0,1987 0,8584 0.6097 9.132461 0.2441.53437 0.0518 0.1424 0.1949 11.75642 3.29993 2.14952 1.9292 3 1.7717 0,32062 0.74817 4 5 47 6 0.43009 4J190T 0.8332 0.2092 7 0.64395 0.98016 0.6981 0.5915 A short term unidirectional and 2. No causal relationship can be noted vi causal relationshi•P exists between ACINDEX and BOT in lag 1 ice versa from BOT to ACINDEX. 4.5 Summary Measures of the variables Table 11 - Summary Measures GDP CGDP BOT CGFCF ACINDEXMean 2559349. 201638.3 -2930.529 401720.9 268.9344 Median 1494642. 97730.50 -1548.650 170657.0 202.4125 Maximum 8673870. 894683.0 -702.5000 1631404. 590.4250 Minimum 321784.0 21541.00 -9710.000 35239.00 100.0000 Std. Dev. 2456862. 231775.7 2666.122 464442.0 154.9524 Skewness 1.164400 1.667581 -1.531855 1.382934 0.748164 Kurtosis 3.186333 5.006492 4.114979 3.740262 2.116075 Jarque-Bera 5.458027 15.14931 10.62950 8.198015 3.020321 Probability 0.000513 0.004919 0.016589 0.2208750.065284 As the values of the variable are in different scales it is less meaningful in comparing summary measures of the variables. When considering the shape of the distributions, according to the Jarque-Bera statistics all the variables do not look normally distributed. Ho: Distribution is Normally Distributed Hi: Distribution is not Normally Distributed bability is less than 0.05 at 5% significance. almost close to zero indicating their all Reject the null hypothesis when pro Further, skewnesses of the variable distributions are the variables are normally distributed. 48 4.6 Vector Autoregression Estim We tested Vector Autoregression Estimates for diffe relationship equation explaining its model variables. Since at 5% significance level, the value of the test statistics reject the null hypothesis. ates rent lag levels in each variable to build its own lags and the lags of the other a evolution based on are greater than 0.05 we do not 4.6.1 VAR Estimate - Lag 1 Table 12 - VAR Estimate (Lag 1) Vector Autoregression Estimates Date: 05/16/14 Time: 20:04 Sample (adjusted): 1991 2013 Included observations: 23 after adjustments Standard errors in () & t-statistics in [ ] GDP CGDP BOT CGFCF ACINDEX GDP(-l) 1.203189 (0.19856) [ 6.05965] 0.067967 (0.02606) [ 2.60788] 1.002809 (0.17733) [ 5.65501] -11.67808 (3.64348) [-3.20520] -0.131513 (0.11735) [-1.12065] -515.4916 (157.638) [-3.27009] 26978.38 (14641.3) [ 1.84262] 0.997348 0.996568 -0.002142 (0.00176) [-1.21774] 0.073310 (0.05711) [ 1.28365] 4.85E-05 (2.6E-05) [ 1.86845] 0.004218 (0.38859) [ 0.01085] 5.96E-05 (0.00018) [0.33741] 0.037204 (0.01197) [3.10777] -0.106635 (1.35102) [-0.07893] CGDP(-l) -0.004714 (0.00363) [-1.29996] -7.584921 (7.98397) [-0.95002] -0.029640 (0.24596) [-0.12051] -0.016547 (0.00792) [-2.08870] 12.50492 (10.6418) [ 1.17507] -2000.654 (988.401) [-2.02413] 0.908264 0.881283 21.71853 (27.7583) [ 0.78242] -0.236662 (0.89407) [-0.26470] 446.6763 (1200.99) [0.37192] -56824.98 (111546.) [-0.50943] 0.998616 0.998208 BOT(-l) -0.000268 (0.00012) [-2.29825] 0.748119 (0.25716) [ 2.90919] -3.093559 (345.434) [-0.00896] -31637.81 (32083.6) [-0.98611] CGFCF(-l) 0.932789 (0.15690) [ 5.94524] ACINDEX(-l) -2.283689 (14.5724) [-0.15671] C 0.993958 0.992181 0.996826 0.995893^■squared Mi- R-squared 49 Sum sq. resids S.E. equation F-statistic Log likelihood Akaike AIC Schwarz SC Mean dependent S.D. dependent 1.85E+U 104308.7 2452.551 -294.9269 26.16756 26.46377 2656634. 2464360. 3.19E+09 13691.30 1278.758 -248.2232 22.10637 22.40258 209468.7 233716.4 14522620 924.2682 33.66288 -186.2264 -266.2666 16.71534 17.01156 -3027.400 2682.509 1.53E+10 3156.763 30001.79 13.62688 1067.827 559.3125 -89.23638 23.67536 8.281425 23.97158 8.577640 417654.9 276.2793 468124.8 154.1039 Determinant resid covariance (dof adj.) Determinant resid covariance Log likelihood Akaike information criterion Schwarz criterion 7.54E+32 1.66E+32 -1016.375 90.98915 92.47023 It is noted AIC (Akaike information criterion) in lag 1 is 90.99 and SIC (Schwarz information criterion) is 92.47. It shall be chosen the lag length that minimizes AIC and SIC for the VAR model. Therefore it was tested the second lag length of the VAR (Vector Autoregression) model and then test the correlations of residuals. 4.6.2 VAR Estimate - Lag 2 Table 13 - VAR Estimate (Lag 2) Vector Autoregression Estimates Date: 05/16/14 Time: 20:10 Sample (adjusted): 1992 2013 Included observations: 22 after adjustments Standard errors in () & t-statistics in [ ] CGFCF ACINDEXBOTCGDPGDP 0.254942 0.000107-0.0081170.103286 10 12471) (0.00851) (0.24380) (0.00013) [0.82819] [-0.95398] [ 1.04570] [0.80656] 0.008920 (0.00745) (0.21342) (0.00012) [ 1.19761] [-0.94598] [-0.22098] -0.060623 3.84E-05 1.376091 (1.09535) [ 1.25630] GDP(-l) -0.201886 -2.57E-05-0.029637-0.453766 (0.95884) (0-109H) [-0.47325] [-0.27148] 1.516740 GDP(-2) -0.027805 tO 04342) (1.24410) (0.00068) [-0.64036] [-0.04873] [ 0.05657] -1.429155 -0.000952/ ' <58S [0.87328] [ 2.38329J -1.829311 (1.02932) CGDP(-l) (01)7023) (2.01221) (0.00110) '-6.036992 (9.04052) CGDP(-2) Vi \V50 V* [-0.66777] 108.7569 [-1.77720] [0.97076] -1.090161 [-0.71024] [-0.86669] BOT(-l) U.36710] [-0 094001 n'Si (17'7067) (0.00967) L y4°°] [-1-76406] [0.78757] [0.68532] 76.57792 1.632175 (84.0353) (9.56799) [0.91126] [0.17059] 13.94529 0.006624 BOT(-2) -0.856162 -16.75054 (0.65280) (18.7043) (0.01021) [-1.31151] [-0.89554] [0.18064] -2.529798 -0.356966 0.007776 r 131ml r(?'?i<56) (°-01498) (0-42921) (0.00023) [ -31187] [-1.62583] [0.51908] [0.02554] [-1.00227] ,4'5.49544 0.731724 -0.041732 1.545865 0.000329 (2.60046) (0.29608) (0.02020) (0.57880) (0.00032) [ 1.74952] [2.47137] [-2.06587] [2.67080] [ 1.04251] 3791.441 -242.0887 (5031.06) (572.820) (39.0824) (1119.80) (0.61128) [0.75361] [-0.42263] [0.16487] [0.61315] [2.25625] 0.001844 CGFCF(-l) 0.010963 -0.000235 CGFCF(-2) ACINDEX(-l) 6.443437 686.6023 1.379196 ACINDEX(-2) -2090.701 -87.12927 -6.415008 -691.1034 -0.704977 (6771.39) (770.969) (52.6016) (1507.16) (0.82273) [-0.30876] [-0.11301] [-0.12195] [-0.45855] [-0.85687] -16759.30 26474.00 -2716.995 -20001.55 32.10987 (323555.) (36838.9) (2513.45) (72015.9) (39.3122) [-0.05180] [ 0.71864] [-1.08098] [-0.27774] [0.81679] 0.998573 0.995976 0.997275 0.992318 6.67E+09 1986.678 24618.86 13.43901 769.5173 272.2499 -80.75159 23.36727 8.341054 23.91279 8.886575 434899.7 283.8193 471604.3 153.3265 C 0.947266 0.899326 8121025. 859.2293 19.75935 -172.2248 -246.0399 16.65680 17.20232 -3119.686 2708.007 0.998504 0.997144 1.74E+09 12593.50 734.0740 -231.2926 22.02660 22.57212 217874.7 235630.7 0.998950 0.997995 1.35E+11 110608.3 1046.393 -279.0945 26.37223 26.91775 2760466. 2470322. R-squared Adj. R-squared Sum sq. resids S.E. equation F-statistic Log likelihood Akaike AIC Schwarz SC Mean dependent S.D. dependent Determinant resid covariance (dof adj-) Determinant resid covariance Log likelihood Akaike information criterion Schwarz criterion 1.98E+31 6.18E+29 -910.6413 87.78557 90.51318 51 Subsequent lag length indicates lag 2 is a better modification. However, the optimal level. a minimizati n of A1C to 87.78 and SIC to 90.51. Therefore 11 Was checked the third lag length also to determine 4.6.3 VAR Estimate - Lag 3 Table 14 - VAR Estimate (Lag 3) Vector Autoregression Estimates Date: 05/16/14 Time: 20:11 Sample (adjusted): 1993 2013 Included observations: 21 after adjustments Standard errors in () & t-statistics in [ ] GDP CGDP BOT CGFCF ACINDEX GDP(-l) 3.479916 0.481880 -0.020749 0.568011 0.000313 (1.04949) (0.13531) (0.01162) (0.17954) (0.00012) [3.31582] [3,56140] [-1.78615] [3.16378] [2.58861] -2.795751 -0.296971 0.026988 -0.463770 -0.000346 (0.72258) (0.09316) (0.00800) (0.12361) (8.3E-05) [-3.86910] [-3.18776] [3.37431] [-3.75181] [-4.16299] GDP(-2) 2.220802 0.203470 -0.016464 0.212530 0.000328 (0.65113) (0.08395) (0.00721) (0.11139) (7.5E-05) [ 3.41070] [2.42377] [-2.28429] [ 1.90801] [4.37848] -2.752454 -0.001998 GDP(-3) -1.172407 0.108677-14.71995 (5.63501) (0.72650) (0.06237) (0.96398) (0.00065) [-261223] [-1.61377] [ 1.74236] [-2.85530] [-3.07882] 0.002025 CGDP(-l) -0.136078 1.9054851.890045 Cl 20954) (0.10384) (1.60492) (0.00108) [ 1.56261] [-1.31039] [ 1.18728] [ 1.87482] -0.003503 18.40258 (9.38165) [ 1.96155] CGDP(-2) ;31„87847 'altm (°02S (iS (0-00108) [-3,39136] [-3.99H2] [2.18849] [-3.49654] [-3.23658] 0.004236 CGDP(-3) 22.51751-1.223029 (0 65508) (10.1242) (0.00681) [-1.86700] [2.22413] [0.62171] 0 979886 -39.11709 (093648) (14.4732) (0.00974) [ L04635] [-2.70272] [-3.18353] 0.014354 4.69837194 46554 -31.60142 BOT(-l) -0.031011 (8496043) (^077) [-2.35953] [-2.89716] BOT(-2) 41.10457-0.928631-4.72664558.58385BOT(-3) 52 [0.63880] [-0399761 /n!'513) 05.6888) (0.01056) 0.39976] [-0.91479] [2.62000] [ 1.35941] 1.637064 0.114167 0-38149) (0.17811) [ 1.18500] [0.64099] 0.691693 0.403583 (1-54640) (0.19937) [0.44729] [2.02427] 2.529342 (3.01340) (0.38851) (0.03336) [ 0.83937] [ 0.29998] [-0.37603] -5538.957 -1627.047 (5148.39) (663.763) (56.9872) (880.734) (0.59277) [-1.07586] [-2.45125] [0.85188] [-1.51256] [0.17884] 44.00800 -715.5223 (8190.13) (1055.92) (90.6560) (1401.08) (0.94299) [0.00537] [-0.67763] [0.18571] [0.56920] [-0.24916] -2793.643 38.12013 -11.34743 -587.3804 -0.172266 (4485.93) (578.354) (49.6544) (767.407) (0.51650) [-0.62276] [0.06591] [-0.22853] [-0.76541] [-0.33353] 179380.2 -7302.263 115130.0 105.7062 CGFCF(-l) -0.027313 (0.01529) (0.23633) (0.00016) [-1 -78615] [ 4.63084] [ 2.61845] -0.015273 (0.01712) (0.26454) (0.00018) [-0.89228] [ 1.84481] [-0.74670] -0.012543 1.094410 0.000416 CGFCF(-2) 0.488031 -0.000133 CGFCF(-3) 0.116545 0.993829 -7.81E-05 (0.51550) (0.00035) [ 1.92789] [-0.22509] ACINDEX(-l) 48.54597 -1332.166 0.106009 ACINDEX(-2) 16.83539 797.4952 -0.234959 ACINDEX(-3) 702294.7 (462760.) (59662.0) (5122.26) (79164.3) (53.2809) [ 1.51762] [3.00661] [-1.42559] [ 1.45432] [ 1.98394] 0.988952 0.955808 1651538. 574.7239 29.83821 -148.1610 15.63438 16.43021 -3218.500 2733.938 C 0.999913 0.999616 0.999650 0.998463 3.94E+08 178.6931 8882.331 5.978179 3813.817 867.2633 -205.6575 -52.27976 21.11024 6.502834 21.90607 453323.3 475068.8 0.999801 0.999206 2.24E+08 6694.144 1678.373 -199.7181 20.54458 21.34041 226893.3 237527.1 0.999890 0.999560 1.35E+10 51922.24 3027.443 -242.7369 24.64161 25.43743 2871665. 2474264. R-squared Adj. R-squared Sum sq. resids S.E. equation F-statistic Log likelihood Akaike AIC Schwarz SC Mean dependent S.D. dependent 7.298661 291.6857 152.4960 determinant resid covariance (dof adj-) Determinant resid covariance Log likelihood Akaike information criterion Schwarz criterion 1.20E+26 9.21E+22 -704.1970 53 It was noted that the relative quality of Akaik values in the third lag level. Those h lag values. « (AIC - ave been minimized 74.68) and Schwarz (SIC - 78.66) and optimized compared to first two 4.7 Proposed Models Based o. .he values chained tough the above VAR ^ reMom were identified. However these relationships to be tested further against model assumptions. Model 1 - GDP — 3.31582 GDP( 1) — 3.86910 GDP(-2) + 3.41070 GDP(—3) - 2.61223 CGDP(-l) + 1.96155 CGDP(-2) - 3.39136 CGDP(-3) - 2.35953 B0T(—2) Model 2 - CGDP = 3.56140 GDP(-l) - 3.18776 GDP(-2) - 2.42377 GDP(-3) - 3.99112 CGDP(-3) - 2.89716 B0T(-2) + 2.02427 CGFCF(-2) - 2.45125 ACINDEX(-l) + C Here, C = 3.00661 Model 3 - BOT = 3.37431 GDP(-2) - 2.28429 GDP(-3) + 2.18849 CGDP( 3) Model 4 - - 3 .75181 GDP(—2) - 2.85530 CGDP(-l) 2.22413 B0T(-1) - 2.70272 BOT(-2) 4.63084 CGFCF(-l) CGFCF = 3.16378 GDP(-l) - 3.49654 CGDP(-3) + + 2.62000 B0T(-3) + Model 5 - „ .,-QQ rnp(-2) + 4.37848 GDP(-3) 4 W 923658 CGDP(-3) - 3,8353 BOT(-2,ACINDEX = 2.58861 GDP(-l) " + 3.07882 CGDP(-l) - + 2.61845 CGFCF(-l) + C Here, c = 1.98394 54 4.8 Testing of assumptions Series of tests were undertaken to determine violate one or more of multiple linear not met the results may not be trust whether above mentioned multiple regressions regression assumptions. When these assumptions Y' ^ome the key assumption were tested as below. are • Variables are Normally distributed. • Assumption of a Linear Relationshi Variable(s). • Variables are measured without error (Reliably) • Assumption of Homoscedasticity p between the Independent and Dependent 4.8.1 Model 1 In model I, we noted the GDP has the following relationship. GDP = 3.31582 GDP(-l) - 3.86910 GDP(-2) + 3.41070 GDP(-3) - 2.61223 CGDP(-l) + 1.96155 CGDP(-2) - 3.39136 CGDP(-3) - 2.35953 B0T(—2) It shows the current year GDP is linked to the previous year GDP, CGDP and BOT. Further analysis was undertaken. Since at 5% significance level, the value of the test statistics greater than 0.05, we do not reject the null hypothesis.are Model 1.1 - the significance of the lagged variables It was used a lagged regression model to test identified in the VAR model 1. for Model 1 (1st Iteration) Table 15 - Least Squares estimate Dependent Variable: GDP Method: Least Squares Date: 06/12/14 Time: 16:21 Sample (adjusted): 1993 2013 Included observations: 21 after adjus^m^^ Std. Error 86033.50 Prob.t-Statistic .1,441611 CoefficientVariable 0.1731 -124026.8C 55 GDP(-l) GDP(-2) GDP(-3) CGDP(-l) CGDP(-2) CGDP(-3) B0T(-2) 1-314008 -1-232275 1-677201 -3.598568 11.49616 -15.26034 -68.99373 0.364276 0.748251 0.556039 2.497096 4.543061 4.067904 78.24270 3.607174 -1.646874 3.016337 -1.441101 2.530487 -3.751400 -0.881791 0.0032 0.1235 0.0099 0.1732 0.0251 0.0024 0.3939 ^squared 0.999292 Mean dependent ™ S.E. of regression 816«iS Akait^ZZn Sum squared resid 8.67E+10 Schwarz criterion Log likelihood -262.2762 Hannan-Quinn criter. F-statistic 2621.857 Durbin-Watson stat Prob(F-statistic) 0.000000 2871665. 2474264. 25.74059 26.13850 25.82695 2.281746 The following variables were noted GDP(-l), GDP(-3), CGDP(-2) and CGDP(-3). as significant during the lagged regression model 1.1. Model 1.2 - Based on the output, of model 1.1, GDP was regressed again with GDP(-l) GDP(-3) CGDP(- 2) and CGDP(-3) Table 16 - Least Squares estimate for Model 1.1 (2nd Iteration) Dependent Variable: GDP Method: Least Squares Date: 06/12/14 Time: 16:25 Sample (adjusted): 1993 2013 Included observations: 21 after adjustments _____ _ Prob.Std. Error t-StatisticCoefficientVariable 4.569668 0.0003 2.569405 0.0199 1.697494 0.1078 -2.679911 0.0158 2871665. 2474264. 25.82582 26.02477 25.86899 0.847234 0.185404 0.716986 0.279047 4.955498 2.919302 -9.960046 3.716558 GDP(-l) GDP(-3) CGDP(-2) CGDP(-3) Mean dependent var S D. dependent var Akaike info criterion ^■-squared Adjusted R-squared 0.998673 S-E. of regression 90142.58 rriterion S«m squared resid 1.38E+11 Schwarz cr ^ J;°8 likelihood -267.1711, Hannan-Q urbin-Watson stat pL.88492^ * 0.998872 56 The following variables were noted as si CGDP(-3). S1gnificant from model 1.2. GDP(-l), GDP(-3), and lyTndel 1.3 - Based on the output, of model 1.2, GDP CGDP(-3) was regressed again with GDP(-l) GDP(-3) and Table 17 - Least Squares estimate for Model 1.2 (3rd I Dependent Variable: GDP Method: Least Squares Date: 06/12/14 Time: 16:30 Sample (adjusted): 1993 2013 Included observations: 21 after adjustments teration) Variable Coefficient Std. Error t-Statistic Prob. GDP(-l) GDP(-3) CGDP(-3) 1.065655 0.140287 7.596239 0.453002 0.243504 1.860347 -4.515170 1.972940 -2.288548 0.0344 0.0000 0.0793 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat 0.998681 Mean dependent var 2871665. 0.998534 S.D. dependent var 94736.68 Akaike info criterion 25.88715 1.62E+11 Schwarz criterion -268.8151 Hannan-Quinn criter. 25.91954 2.017691 2474264. 26.03637 The following variables were noted as significant from model 1.3. GDP(-l) and CGDP(-3). Model 1.4- Based on the output, of model 1.3, GDP was regressed again with GDP(-l) and CGDP(-3). Table 18 - Least Squares estimate for Model 1.3 (4th Iteration) Dependent Variable: GDP Method: Least Squares Date: 06/29/14 Time: 15:55 Sample (adjusted): 1993 2013 Included observations: 21 after adjustments Std. Error 0.088068 1.632085 Meandependent var Prob.t-Statistic 14.49149 -1.354626 CoefficientVariable 0.0000 0.19141.276242 -2.210864 GDP(-l) ^CGDP(-3) Squared 2871665. 0.998427 57 Adjusted R-squared 0.998344 S.E. of regression 100685.1 Sum squared resid 1.93E+11 Log likelihood -270.6616 Durbin-Watson stat 2.296031; S-P-dependent var Akatkemfo criterion 25 96778 Schwarz criterion 26 06 25 Hannan-Quinn criter. 2474264. 25.98937 At the end it has been received a reland GDp previous ,ear. This concluded «ha. ,be c„M GDP depend „„ly « „ p„viou5 year GOP and does not have a relationship with any other construction relationship was disregarded. 1 which is the output parameters. Hence, this 4.8.2 Model 2 In model 2, it was noted that the CGDP has the following relationship. CGDP = 3.56140 GDP(-l) - 3.18776 GDP(-2) - 2.42377 GDP(-3) - 3.99112 CGDP(-3) - 2.89716 B0T(-2) + 2.02427 CGFCF(-2) - 2.45125 ACINDEX(-l) + C Further analysis was undertaken. Since at 5% significance level, the value of the test statistics are greater than 0.05, we do not reject the null hypothesis. Model 2.1 - Based on the output, of VAR model 2, CGDP was regressed again with GDP(-l), GDP(-2), GDP(-3), CGDP(-3), BOT(-2), CGFCF(-2) and ACINDEX(-l). Table 19 - Least Squares estimate for Model 2 (1st Iteration) Dependent Variable: CGDP Method: Least Squares Date: 06/12/14 Time: 16:13 Sample (adjusted): 1993 2013 Included observations: 21 after adjustmen s Std. Error 9925.878 0.017682 0.031069 0.029970 0.285563 2.114318 Prob.t-Statistic 10.34744 18.32022 -6.992929 5 928900 .10.81191 .10.36373 ! CoefficientVariable 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 102707.5 0.323930 -0.217260 0.177691 -3.087483 -21.91222 C GDP(-l) GDP(-2) GDP(-3) CGDP(-3) BOT(-2) 58 CGFCF(-2) ACINDEX(-l) 0-542623 -1360.750 0.069937 101.7535 7.758750 -13.37301 Adjusted R-squared 0.999387 var S.E. of regression 5880.578 Akaike^f^ V3r Sum squared resid 4.50E+08 Schwarz Miwihood " hJsss* 0.000000 Durb,"-Wa's»”® All the variables concludSini^S3^" 0.0000 0.0000jAsquared 226893.3 237527.1 n°n 20.47903 20.87694 20.56539 3.016022 F-statistic Prob(F-statistic) assumption test was undertaken. Testing of Stationarity of the model residuals with A Ho: Residuals are non-stationary (There is a unit root) Hi: Residuals are stationary (There is no unit root) ugmented Dickey-Fuller test Table 20 - Augmented Dickey-Fuller test for model 2.1 Null Hypothesis: RES2 has a unit root Exogenous: None Lag Length: 1 (Automatic based on SIC, MAXLAG=4) t-Statistic Prob.* -6.387454Augmented Dickey-Fuller test statistic Test critical values: 1% level 5% level 10% level -2.692358 -1.960171 -1.607051 ^MacKinnon (1996) one-sided p-values. Warning: Probabilities and critical values calculated for observations and may not be accurate for a sample size of Augmented Dickey-Fuller Test Equation Dependent Variable: D(RES2) Method: Least Squares Date: 06/29/14 Time: 16:35 Sample (adjusted): 1995 2013 included observations: 19 after adjustments^ Std. Error Prob.t-Statistic -6.387454 2.512285 Variable Coefficient RES2(-1) aaaJXRES2(-l)) Squared 0.0000 0.02240.359566 0.206786 ^Td^ndent var -2.296711 0.519505 0.821985 -15.34085 59 Adjusted R-squared 0.811514 S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat 1.967183 S.D. dependent*... . . 8676.206 AKaike info criterion 19.40513 Schwarz criterion Hannan-Quinn criter. var3766.777 2.41 E+08 -182.3487 19.5045419.42195 P value < 0.05 we reject H0 Since at 5% significance level, the p-value of the Augmented Dickey-Fuller test statistic (0.0000) is less than 0.05 stationary. reject the null hypothesis. Therefore, the residuals arewe Serial Correlation - Correlogram of Residuals (Q statistics) Ho: No serial correlation exists in residuals Hi : There exists serial correlation in residuals 1Date: 06/12/14 Time: 16:18 Sample: 1993 2013 Included observations: 21 AC PAC Q-Stat ProbAutocorrelation Partial Correlation 1 -0.510 -0.510 6.2703 0.012 2 -0.123 -0.516 6.6534 0.036 3 0.333 -0.047 9.6245 0.022 4 -0.392 -0.404 13.997 0.007 5 0.333 0.045 17.348 0.004 6 -0.180 -0.272 18.390 0.005 7 0.057 0.159 18.503 0.010 8 0.060 -0.148 18.635 0.017 9 -0.273 -0.154 21.642 0.010 10 0.355 -0.086 27.179 0.002 11 -0.166 0.022 28.512 0.003 12 -0.121 -0.223 29.292 0.004 C =3 I CE= □l Cl cc= [ c cc Figure 9 - Correlogram of Residuals for model 2.1 concluded that there exists serialless than 0.05 it wasSince some of the p-values correlation between residuals. are Breusch-Godfrey Serial Correlation LM Test Ho: No serial correlation exists in residuals in residualsHi : There exists serial correlation 60 Tabk 21 - Breusch-Godfrey Serial Correlation LM T Breusch-Godfrey Serial Correlation LM Test: estfor model 2.1 F-statistic Obs*R-squared 11.20109 14.08428 Prob. F(2,l 1) Prob. Chi-Square(2) 0.0022 0.0009 Test Equation: Dependent Variable: RESID Method: Least Squares Date: 06/12/14 Time: 16:21 Sample: 1993 2013 Included observations: 21 Presample missing value lagged residuals set to zero. Variable Coefficient Std. Error t-Statistic Prob. C 2869.090 6252.025 0.458906 0.013343 0.013172 1.012991 0.016753 0.024809 0.675262 -0.046913 0.021945 -2.137717 0.253073 0.190368 1.329385 0.433999 1.338486 0.324246 -0.037874 0.044632 -0.848583 -19.70464 63.85451 -0.308586 -1.121400 0.243080 -4.613288 -0.808731 0.283000 -2.857701 0.6552 0.3328 0.5135 0.0558 0.2106 0.7518 0.4142 0.7634 0.0007 0.0156 GDP(-l) GDP(-2) GDP(-3) CGDP(-3) BOT(-2) CGFCF(-2) ACINDEX(-l) RESID(-l) RESID(-2) 0.670680 Mean dependent var -1.46E-10 4741.073 R-squared Adjusted R-squared 0.401237 S.D. dependent var 3668.633 Akaike info criterion 19.55878 20.05617S.E. of regression Sum squared resid Log likelihood F-statistic 1.48E+08 Schwarz criterion -195.3672 Hannan-Quinn criter. 19.66673 2.489130 Durbin-Watson stat 0.078051 1.693209 Prob(F-statistic) Breusch-Godfrey Serial Correlation LMSince at 5% significance level, the p-value of the is lesser than 0.05 the null hypothesis was rejected.Test: statistic (0.0022) is , this was notserial correlation among residuals. Therefore That means this relationship has investigated further. 4-8.3 Model 3 In model 3, it was noted that the BOT has the following relationship. 61 BOT = 3.37431 GDP(—2) - 2-28429 GDP(—3) + 2.18849 CGDP(-3) Further analysis was undertaken. Si are greater than 0.05, we do not reject the nee at 5 ^ significance level, the value of the test statistics null hypothesis. Model 3.1 - Based on the output, of VAR model 3, BOT CGDP(-3). was regressed with GDP(-2), GDP(-3) and Table 22 - Least Squares estimate for Model 3 (1st Iteration) Dependent Variable: BOT Method: Least Squares Date: 05/16/14 Time: 20:22 Sample (adjusted): 1993 2013 Included observations: 21 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C -125.8388 428.0259 -0.293998 0.7723 0.005463 0.002124 2.572653 0.0198 -0.008555 0.003181 -2.689744 0.0155 0.007538 0.026119 0.288601 0.7764 GDP(-2) GDP(-3) CGDP(-3) 0.898872 Mean dependent var -3218.500 2733.938 R-squared Adjusted R-squared 0.881026 S.D. dependent var 943.0050 Akaike info criterion 16.70566 15117393 Schwarz criterion -171.4095 Hannan-Quinn criter. 16J4884 50.36816 Durbin-Watson stat PB8BBI 0.000000 S.E. of regression Sum squared resid Log likelihood F-statistic 16.90462 Prob(F-statistic) significant during the lagged regression model 3.1.The following variables were noted as GDP(-2) and GDP(-3). Model 3.2 - , BOT was regressed with GDP(-2) and GDP(-3) Based on the output, of model 3.1 Table 23 - Least Squares estimate for Model 3.1 (2nd Iteration) Dependent Variable: BOT Method: Least Squares Date: 06/12/14 Time: 15:44 Sample (adjusted): 1993 2013 Included observations: 21 after adjustmen 62 Variable Coefficient 0.005543 0.002034 -0.008140 0.002368 Std. Error t-Statistic Prob. GDP(-2) GDP(-3) 2.724796 0.0134 -3.438068 0.0028 R-squared 0.895906 Mean dependent var -3218 500 Adjusted R-squared <3890428 S.D. dependent vat 2733 938 S.E. of regress,on 904.9805 Akaike info criterion 16.54410 Sum squared resid 15560803 Schwarz criterion Log likelihood -171,7130 Hannan-Quinn criter Durbin-Watson stat fl.752762 16.64357 16.56569 It was identified that both the variables were significant. Testing of Stationarity of the model residuals with Augmented Dickey-Fuller test H0: Residuals are non-stationary (There is a unit root) Hi : Residuals are stationary (There is no unit root) Table 24 - Augmented Dickey-Fuller test for model 3.2 Null Hypothesis: RES has a unit root Exogenous: None Lag Length: 0 (Automatic based on SIC, MAXLAG=4) t-Statistic Prob.* mm-3.883453Augmented Dickey-Fuller test statistic -2.685718 -1.959071 -1.607456 1% levelTest critical values: 5% level 10% level ♦MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(RES) Method: Least Squares Date: 06/12/14 Time: 15:49 Sample (adjusted): 1994 2013 Included observations: 20 after adjustments Coefficient -0.980827 0.252564 Prob.Std. Error t-Statistic Variable -3.883453 0.0010 RES(-l) 116.4395 1192.150Mean dependent var S.D. dependent var 0.436910R-squared Adjusted R-squared 0.436910 63 S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat 1.817203 15205251i « Schwarz criterion 163.7930 Hannan-Quinn criter. 16.47930 16.52908 16.48902 P value < 0.05 we reject H0 Since at 5% significance level, (0.0005) is less than 0.05 we stationary. the p-value of the Augmented Dickey-Fuller test statistic reject the null hypothesis. Therefore, the residuals are Serial Correlation - Correlogram of Residuals (Q statistics) H0: No serial correlation exists in residuals Hi : There exists serial correlation in residuals Date: 06/12/14 Time: 15:46 Sample: 1993 2013 Included observations: 21 AC PAC Q-Stat ProbAutocorrelation Partial Correlation 1 -0,001 -0.001 2.E-05 0.996 2 0.063 0.063 0.1017 0.950 3 0.010 0.011 0.1046 0.991 4 0.232 0.229 1.6330 0.803 5 -0.394 -0.418 6.3300 0.275 6 -0.141 -0.170 6.9710 0.324 7 -0.269 -0.285 9.4725 0.220 8 -0.079 -0.132 9.7029 0.287 9 -0.154 0.074 10.656 0.300 10 -0.064 -0.168 10.838 0.370 11 0.015 0.049 10.849 0.456 12 0,181 -0.001 12.603 0.399 l] Zl=] c= cc dcz c[ ]c c[ I □ Figure 10 - Correlogram of Residuals for model 3.2 spike could be observed lay beyond the confidence intervals. This greater than the significance level of 0.05. Hence, then; is As per the correlogram no was confirmed by all p values no serial correlation in the residuals of the model. are Breusch-Godfrey Serial Correlation LM Test Ho: No serial correlation exists in residuals 64 H, : There exists serial correlation in residuals Table 25 - Breusch-Godfrey Serial Correlation LM T Breusch-Godfrey Serial Correlation LM Test: est for model 3.2 F-statistic Obs*R-squared 0.110073 0.065147 Prob. F(2,17) Prob. Chi-Square(2) 0.9680 Test Equation: Dependent Variable: RESID Method: Least Squares Date: 06/12/14 Time: 16:05 Sample: 1993 2013 Included observations: 21 Presample missing value lagged residuals set to zero. Variable Coefficient Std. Error t-Statistic Prob. GDP(-2) GDP(-3) RESID(-l) RESID(-2) 0.000956 0.002952 0.323686 0.7501 -0.001101 0.003419 -0.321946 0.7514 0.014643 0.284464 0.051476 0.9595 0.183232 0.395700 0.463059 0.6492 0.003102 Mean dependent var -84.83256 877.7720 950.5995 Akaike info criterion 16.72171 15361870 Schwarz criterion -171.5779 Hannan-Quinn criter. 16.76488 1.765551 R-squared Adjusted R-squared -0.172821 S.D. dependent var S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat 16.92066 5% significance level, the p-value of the Breusch-Godfrey Serial Correlation LM do not reject the null hypothesis. Therefore, Since at Test: statistic (0.8964) is greater than 0.05 there is no serial correlation among residuals. we 65 Correlogram Squared Residuals Date: 06/12/14 Time: 1 SiST" Sample: 1993 2013 Included observations: 21 Autocorrelation Partial Correlation AC PAC Q-Stat Prob 1 0.057 0.057 0.0780 0.780 2 -0.174 -0.177 0.8440 0.656 3 -0.140 -0.122 1.3690 0.713 4 0.066 0.052 1.4928 0.828 5 0.391 0.359 6.1022 0.296 6 -0.041 -0.085 6.1566 0.406 7 0.045 0.205 6.2277 0.513 8 -0.098 -0.072 6.5878 0.582 9 -0.103 -0.132 7.0119 0.636 10 -0.072 -0.250 7.2399 0.703 11 -0.083 -0.105 7.5706 0.751 12 -0.036 -0.256 7.6398 0.813 C c c c ] J [ ] □ c [ c c c n= [ : i= Figure 11 - Correlogram Squared Residuals for model 3.2 As per the correlogram of squad residuals, no spike could be observed lay beyond the confidence intervals. This was confirmed by the all the p values are greater than the significance level of 0.05. Hence, there is no squared serial correlation in the residuals of the model. White’s Heteroskedasticity H0: No Heteroskedasticity exists in residuals H, : There exists Heteroskedasticity in residuals Table 26 - White’s Heteroskedasticity test for model 3.2 Heteroskedasticity Test: White 6.2039 0.1826 0.1431 1.704572 Prob. F(3,17) Prob. Chi-Square(3) Prob. Chi-Square(3) F-statistic Obs*R-squared Scaled explained SS 5.426489 4.856172 Test Equation: Dependent Variable: RES1DA2 Method: Least Squares Date: 06/12/14 Time: 15:59 66 Sample: 1993 2013 Included observations: 21 Variable Coefficient Std. Error t-Statistic Prob. C 453473.9 317528.1 -1.37E-05 1-428138 0.17140.3197 0.3113 0.3046 GDP(-2)A2 GDP(-2)*GDP(-3) 3.23E-05 GDP(-3)A2 1.34E-05 -1.025139 3.10E-05 1.043662 1.79E-05 -1.058576-1.89E-05 R-squared 0-231246 Mean dependent var Adjusted R-squared 0.095584 S.D. dependent var S.E. of regression 1193121. Akaike info criterion Sum squared resid 2.42E+13 Schwarz criterion Log likelihood -321.4127 Hannan-Quinn criter. 31 03487 F-statistic 1.704572 Durbin-Watson stat 0.203866 740990.6 1254586. 30.99169 31.19064 2.202519 Prob(F-statistic) Since at 5% significance level, the p-value of the White’s Heteroskedasticity Test (0.2039) is greater than 0.05 we do not reject the null hypothesis. Hence, there is no squared serial correlation in the residuals of the model. Normality Test (Jarque-Bera Test) 8 Series: Residuals Sample 1993 2013 Observations 217- 6- -84.83256 -145.4721 1736.390 -2305.723 877.7720 -0.255947 3.643344 Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis 5- 4- 3- 2- Jarque-Bera 0.591437 Probability 0.7439971- 0 1000 _________ -2000 __ ________ Figure 12 - Jarque-Bera test for model 3.2 Ho: Residuals are normal Hj: Residuals are not normal 67 Since at 5% significance level, the p-value of the J 0.05 we do not reject the null hypothesis. Th arque-Bera Test (0.591437) is greater than erefore, residuals are normal. 4.8.4 Model 4 In model 4, iit was noted that the CGFCF has the following relationship. CGFCF= 3.16378 GDP(-l) - 3 .75181 GDP(-2) - 2.85530 CGDP(-l) 3.49654 CGDP(—3) + 2.22413 BOT(-l) - 2.70272 BOT(-2) + 2.62000 BOT(-3) + 4.63084 CGFCF(-l) Since at 5% significance level, the value of the test statistics are greater than 0.05 we do not reject the null hypothesis. Model 4.1 - Based on the output, of VAR model 4, CGFCF was regressed with GDP(-l), GDP(-2), CGDP(-l), CGDP(-3), BOT(-l), BOT(-2), BOT(-3) and CGFCF(-l). Table 27 - Least Squares estimate for Model 4 (1st Iteration) Dependent Variable: CGFCF Method: Least Squares Date: 06/12/14 Time: 16:48 Sample (adjusted): 1993 2013 Included observations: 21 after adjustments Prob.Coefficient Std. Error t-StatisticVariable 0.233340264.34 1.255171 0 100733 0.455100 0.6572 0.140642 0.241130 0.8135 0.480564 -1.750981 0.882093 -1.185661 50538.63 0.045844 0.033913 -0.841458 -1.045863 12.38537 13.99309 -0.563484 12.81848 55.19842 19.37538 1.740107 0.355327 C GDP(-l) GDP(-2) CGDP(-l) CGDP(-3) BOT(-l) BOT(-2) BOT(-3) CGFCF(-l) 0.1054 0.2587 0.885106 0.3935 -0.043959 0.9657 2.848895 0.0147 4.897199 0.0004 453323.3 475068.8 23.06836 23.51602 23.16551 0.998794 Mean dependent var 0^997990 S.D. dependent var 21300.36 Akaike info criterion 5.44E+09 Schwarz criterion -733 2178 Hannan-Quinn criter. Durbin-Watson stat R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic 1242.095 68 Prob(F-statistic) 0.000000 Only BOT(-3) and CGFCF(-l) was significant among the considered variables. Model 4.2 - Based on the output, of model 4.1 CGFCF was regressed again with BOT(-3) and CGFCF(- 1). Table 28 - Least Squares estimate for Model 4.1 (2nd Iteration) Dependent Variable: CGFCF Method: Least Squares Date: 06/12/14 Time: 16:49 Sample (adjusted): 1993 2013 Included observations: 21 after adjustments Variable Coefficient Std. Error t-Statistic Prob. BOT(-3) CGFCF(-l) 13.42734 8.118632 1.653892 0.1146 1.252350 0.037088 33.76698 0.0000 0.995774 Mean dependent var 453323.3 475068.8 R-squared Adjusted R-squared 0.995551 S.D. dependent var S.E. of regression Sum squared resid Log likelihood ______ Durbin-Watson stat 2.330218 31686.54 Akaike info criterion 23.65556 1.91 E+l 0 Schwarz criterion -246.3834 Hannan-Quinn criter. 23.67715 23.75504 Only CGFCF(-l) was significant out of the considered variables. Model 4.3 - Based on the output, of 4.2, CGFCF was regressed again with CGFCF(-1). estimate for Model 4.2 (3rd Iteration)Table 29 - Least Squares Dependent Variable: CGFCF Method: Least Squares Date: 06/12/14 Time: 16:50 Sample (adjusted): 1991 2013 Included observations: 23 after adjustments Coefficient 1.194746 0.012682 Prob.Std. Error t-Statistic Variable 94.20515 0.0000 CGFCF(-l) 417654.9Mean dependent var0.995469R-squared 69 Adjusted R-squared 0.995469 S.E. of regression Sum squared resid Log likelihood 23K sss-270 3596 ^chwarz criterion 23.64585 Durbin-Watson stat 2.814910 nan'Qumn criter- 23.60890 This results also pretty much similar to the means Construction Gross Fixed Capital Format! year CGFCF value. This concluded that current CGFCF depend only on the previous year CGFCF and does not have a relationship with an, other national economic parameter,. results which were received in the 1st model. That (CGFCF) depends only on the previousion 4.8.5 Model 5 In model 5, it was noted that the ACINDEX has the following relationship. ACINDEX = 2.58861 GDP(-l) - 4.16299 GDP(-2) + 4.37848 GDP(-3) + 3.07882 CGDP(-l) - 3.23658 CGDP(-3) - 3.18353 BOT(-2) + 2.61845 CGFCF(-l) + C Since at 5% significance level, the value of the test statistics are greater than 0.05 we do not reject the null hypothesis. Model 5.1 - Based on the output, of VAR model 5, ACINDEX was regressed with GDP(-l), GDP(-2), GDP(-3), CGDP(-l), CGDP(-3), BOT(-2) and CGFCF(-l). Table 30 - Least Squares estimate for Model 5 (1st Iteration) Dependent Variable: ACINDEX Method: Least Squares Date: 06/12/14 Time: 16:51 Sample (adjusted): 1993 2013 Included observations: 21 after adjustments Prob.Std. Error t-StatisticCoefficientVariable 7.188275 0.0000 7.396763 0.0000 -2.664242 0.0195 4117436 0.0012 -4.968231 0.0003 -8.110277 0.0000 -3.198533 0.0070 1.971038 0.0704 66.05422 9.189162 0.000275 3.71E-05 -0.000176 6.59E-05 0.000203 4.92E-05 -0.001251 0.000252 -0.002752 0.000339 -0.025065 0.000193 C GDP(-l) GDP(-2) GDP(-3) CGDP(-l) CGDP(-3) BOT(-2) CGFCF(-l) 0.007836 9.81E-05 70 R-squared Adjusted R-squared 0.997073 8.250676 884.9575 -69.07839 974.1878 0.000000 0.998097 Mean dependent var 291.6857 T?’.dependent var 152.4960 Akaike info criterion 7.340799 Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat S.E. of regression Sum squared resid Log likelihood F-statistic 7.738712 7.427156 2.058199Prob(F-statistic) Out of the regression the lagged variables CGDP(-3), and BOT(-2) were significant. of GDP(-l), GDP(-2), GDP(-3), CGDP(-l), Model 5.2 - Based on the output, of model 5.1, ACINDEX CGDP(-l), CGDP(-3) and BOT(-2). was regressed with GDP(-l), GDP(-2), Table 31 - Least Squares estimate for Model 5.1 (2nd Iteration) Dependent Variable: ACINDEX Method: Least Squares Date: 06/12/14 Time: 16:52 Sample (adjusted): 1993 2013 Included observations: 21 after adjustments Coefficient Std. Error t-Statistic Prob.Variable 0.0000 4.01E-05 7.199364 0.0000 7.24E-05 -2.464380 0.0273 5.29E-05 3.453221 0.0039 _ 0.0010 0.000288 -8.079840 0.0000 0.008580 -2.781380 0.0147 60.17156 9.544545 6.304288 0.000288 -0.000178 0.000183 -0.001059 0.000255 -4.152937 -0.002327 -0.023864 C GDP(-l) GDP(-2) GDP(-3) CGDP(-l) CGDP(-3) BOT(-2) 291.6857 152.4960 7.507037 7.855211 7.582599mm R-squared 0.997529 Mean dependent var Adjusted R-squared 0.996470 S.D. dependent var 9.060996 Akaike info criterion 1149.423 Schwarz criterion -71.82389 Hannan-Quinn criter. 941.8227 Durbin-Watson stat 0.000000 ____ _ S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) All the variables were significant in the regression. Therefore the model was reconstructed as below. 71 ACINDEX = 60.17156 + 0-000288 GDP(-i) _ 0-000183 GDP(—3) _ 0.000178 GDP(—2) 0-001059 CGDP(-l) _ 0.002327 CGDP(-3) + ~ 0.023864 BOT(-2) Testing of Stationary of the model residuals with A Ho: Residuals are non-stationary (There is a unit root) H, : Residuals are stationary (There is no unit root) Table 32 - Augmented Dickey-Fuller test for model 5.2 Null Hypothesis: RESS has a unit root Exogenous: None Lag Length: 0 (Automatic based on SIC, MAXLAG=4) ugmented Dickey-Fuller test t-Statistic Prob.* Augmented Dickey-Fuller test statistic -3.983851 &.0004 Test critical values: 1% level 5% level 10% level -2.685718 -1.959071 -1.607456 * MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(RESS) Method: Least Squares Date: 06/12/14 Time: 16:54 Sample (adjusted): 1994 2013 Included observations: 20 after adjustments Prob.Coefficient Std. Error t-StatisticVariable 0.00080.221402 -3.983851-0.882031RESS(-l) -0.628209 10.08396 6.905333 6.955120 6.915052 R-squared 0.452910 Mean dependent var Adjusted R-squared 0.452910 S.D. dependent var S.E. of regression 7.458653 Akaike info criterion Sum squared resid 1056.999 Schwarz criterion Log likelihood -68.05333 Hannan-Quinn enter. Durbin-Watson stat 2.058722 P value < 0.05 we reject Ho 1 nf the Augmented Dickey-Fuller test statistic significance Therefore the residuals aie stationary.Since at 5% (0.0004) is less than 0.05 we 72 Serial Correlation - Correlo gram of Residuals (Q statistics) Date: 06/12/14 Time: 16:52 Sample: 1993 2013 Included observations: 21 Autocorrelation Partial Correlation AC PAC Q-Stat Prob 1 0.116 0.116 0.3277 2 0.022 0.009 0.3400 3 -0.008 -0.012 0.3418 4 -0.283 -0.285 2.6175 0.624 5 -0.039 0.029 2.6623 0.752 6 -0.034 -0.025 2.6986 0.846 7 0.064 0.081 2.8379 0.900 8 -0.009 -0.117 2.8407 0.944 9 -0.285 -0.308 6.1038 0.729 10 -0.105 -0.074 6.5852 0.764 11 -0.215 -0.178 8.8252 0.638 12 -0.098 -0.098 9.3369 0.674 3 3 0.567 0.844 0.952d d ] ] C d d c [ c c c [ Figure 13 - Correlogram of Residuals for model 5.2 Ho: No serial correlation exists in residuals Hj : There exists serial correlation in residuals As per the correlogram no spike could be observed lay beyond the confidence intervals. This confirmed by the all the p values are greater than the significance level of 0.05. Hence, there is no serial correlation in the residuals of the model. was Breusch-Godfrey Serial Correlation LM Test Ho: No serial correlation exists in residuals Hi : There exists serial correlation in residuals Table 33 - Breusch-Godfrey Serial Correlation LM Test for model 5.2 Breusch-Godfrey Serial Correlation LM Test: 0,7454 0.60540.301211 Prob. F(2,12)Prob. Chi-Square(2)F-statisticObs*R-squared 1.003845 Test Equation: Dependent Variable: RESID Method: Least Squares Date: 06/12/14 Time: 16:53 73 Sample: 1993 2013 Included observations: 21 Presample missing value lagged residual Variable s set to zero. Coefficient Std. Error t-Statistic -0.014021 -0.531136 0.424461 0.092083 0.228398 -0.000230 0.000456 -0.504876 0.001660 0.009399 0.176573 0.419591 0.550101 -0.048538 0.540794 -0.089753 Prob. C -0.141107 10.06374 -3.18E-05 5.99E-05 4.21E-05 9.91E-05 6.02E-06 6.54E-05 6.47E-05 0.000283 0.9890 0.6050 0.6787 0.9282 0.8232 0.6228 0.8628 0.4603 0.9300 GDP(-l) GDP(-2) GDP(-3) CGDP(-l) CGDP(-3) BOT(-2) RESID(-l) RESID(-2) 0.762753 R-squared 0.047802 Mean dependent Adjusted R-squared -0.586996 S.D. dependent var S.E. of regression Sum squared resid Log likelihood F-statistic var 1.44E-13 7.580973 9.550211 Akaike info criterion 7.648531 1094.478 Schwarz criterion -71.30957 Hannan-Quinn criter. 7.745683 0.075303 Durbin-Watson stat 2.067602 0.999458 8.096183 Prob(F-statistic) Since at 5% significance level, the p-value of the Breusch-Godfrey Serial Correlation LM Test: statistic (0.7454) is greater than 0.05 we do not reject the null hypothesis. Therefore, there is no serial correlation among residuals. Correlogram Squared Residuals Date: 06/12/14 Time: 16:56 Sample: 1993 2013 Included observations: 21 AC PAC Q-Stat ProbPartial CorrelationAutocorrelation 1 0 024 0.024 0.0141 0.905 2 -0 200 -0.201 1.0326 0.597 3 -0 180 -0.177 1.9017 0.593 4 0.091 0.059 2.1377 0.710 5 -0.022 -0.100 2.1524 0.828 6 -0.103 -0.115 2.4971 0.869 7 -0.136 -0.145 3.1371 0.872 8 -0.206 -0.314 4.7177 0.787 ss as as s „ .(WW -0.126 6.4® 0.836 c□ cc l] : cc cc c[= ]□ c c[ 12 -0.120 -0.131cc d Residuals for model 5.2 Figure 14 - Correlogram Square 74 As per the correlogram of squared confidence intervals. This significance level of 0.05. model. residuals, spike could be observed lay beyond the p values are greater than the correlation among squared residuals of the no was confirmed by the all the Hence, there is no White’s Heteroskedasticity Ho. No Heteroskedasticity exists in residuals Hi : There exists Heteroskedasticity in residuals Table 34 - White’s Heteroskedasticity test for model 5.2 Heteroskedasticity Test: Breusch-Pagan-Godfrey F-statistic Obs*R-squared Scaled explained SS 3.254095 Prob. Chi-Square(6) 1.097443 Prob. F(6,14) 6.717518 Prob. Chi-Square(6) 0.4109 0.3478 0.7763 Test Equation: Dependent Variable: RESIDA2 Method: Least Squares Date: 06/12/14 Time: 16:58 Sample: 1993 2013 Included observations: 21 Coefficient Std. Error t-Statistic Prob.Variable 85.97946 0.059370 0.9535 0.0950 0.3165 0.9659 0.4199 0.6554 0.5001 5.104587 0.000646 0.000361 1.790631 -0.000678 0.000652 -1.038910 -2.08E-05 0.000476 -0.043554 -0.001908 0.002296 -0.831054 0.001183 0.002595 0.455999 -0.053505 0.077291 -0.692259 C GDP(-l) GDP(-2) GDP(-3) CGDP(-l) CGDP(-3) BOT(-2) 54.73444 82.80799 R-squared 0.319882 Mean dependent var Adjusted R-squared 0.028403 S.D. dependent var S.E. of regression 81.62354 Akaike info criterion 1.90331 Sum squared resid 93273.62 Schwarz criterion 2.-5149 Log likelihood -117.9848 Hannan-Quinn enter. 1L97888 F-statistic 1.097443 Durbin-Watson stat -.659743 Prob(F-statistic) 0.410888 ___I 75 Since at 5% significance level, greater than 0.05 we do squared residuals of the model. the p-value of the White’s Heteroskedasticity Test (0.4109) is not reject the null hypothesis. Hence, there is no correlation among Normality Test (Jarque-Bera Test) ' Series: Residuals Sample 1993 2013 Observations 21 i 6- 5- Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis 1.44e-13 -1.464088 18.96103 -11.21831 7.580973 0.620250 3.179886 4- 3- 2- 1 - Jarque-Bera 1.374799 Probability 0.502882 0 -10 -5 0 5 10 15 20 Figure 15 - Jarque-Bera test for model 5.2 Since at 5% significance level, the p-value of the Jarque-Bera Test (0.502882) is greater than 0.05 we do not reject the null hypothesis. Therefore, residuals are normal. 76 Chapter 5 - Conclusion In general terms, the construction sector plays vital role in Sri Lankan industry sector has contributed positively towards the GDP noted the construction sector GDP growth country. economy and the entire growth year-on-year. Also it was always higher than overall GDP growth in thewas However, during our exercise to derive mathematical approach to express a relationship between construction sector output and national economic fiscals, It was noted two long term relationships as below. BOT = 0.005543 GDP(-2) - 0.008140 GDP(-3) and; ACINDEX = 60.17156 + 0.000288 GDP(-l) - 0.000178 GDP(-2) + 0.000183 GDP(-3) - 0.001059 CGDP(-l) - 0.002327 CGDP(-3) - 0.023864 BOTC-2) Therefore, it could be concluded that Balance of Trade (BOT) has a relationship between previous year Gross Domestic Products (GDP) and a year before. In another words last two year GDP figures have influenced this year BOT figures. Further, it explains that all construction cost index (ACINDEX) has an impact from last three GDP figures plus CGDP figures of last year and two years before plus BOT figures of two years before. year Therefore it is evident that an existence of a strong relationship between construction activity with the decisionand economic growth in Sri Lanka. Further, this conclusion is par statements provided by the previous researchers through their studies. 77 5.1 Recommendation and further studies In this study it was determined that there exists a long term relationship between BOT and ACINDEX using a VAR model for annual data since 1990 to 2013. recommended to use the fitted model in determining relationships among those Therefore it is variables. However, no relationships were identified GDP, CGDP and for CGFCF methodology followed in this study. 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