An Application of VAR and Almon Polynomial Distributed Lag Models to Insurance Stocks:

Evidence from KSEMuhammad Ayub Siddiqui

FAST School of Business National University of Computer and Emerging Sciences

Islamabad, Pakistan ayub.siddiqui@nu.edu.pk

Abstract—In the time series data, a regressand may respond to regressors with a time lag. This study employs dynamic methodology of Almon Polynomial Distributed-Lag (PDL) model as an application to the stocks of 13 selected insurance companies, using daily data for the period from 1996 to 2008. Realizing the importance of causality in economics and finance, this study focuses on the causal relationship between investment, growth in returns and market uncertainty. The study also employs VAR which is of non-structural approaches amongst the a-theoretic models. In this study I have constrained the coefficients on the distributed lag to lie on a third degree polynomial with the satisfactory test results of near and the far end points of the lag distribution. Generating the series of risk variable through GARCH (p, q) is also an academic contribution of this study. The Almon PDL model may also be considered as an alternative to the lagged regression models. For the PDL avoids the estimation problems associated with the autoregressive models. This study is in a way an attempt to invite researchers and practitioners for the maximum application of these very important dynamic models in economics, business and finance. The results of this study reveal mixed causality among the three variables. The Almon Polynomial Distributed Lag results support the theory of adaptive expectations.

Keywords- Almon PDL; VAR;Causality; Pakistan; Stocks and uncertainty.

I. INTRODUCTION

Causality among the variables has always attracted its significant importance in the domain of economics and finance. Many a methods are applied to test this causality. Granger causality methods have, nevertheless, received attention of the researchers who explore dynamic models relating the financial variables.

This study employs dynamic methodology of Almon Polynomial Distributed-lag model. In the time series data, a regressand may respond to regressors with a certain degree of time lag. Distributed-lag and autoregressive models, when estimated by OLS, pose the issues of serious multicollinearity, inconsistency and simultaneity. In order to avoid biasedness and inconsistency, Almon models are better substitute for the Koyck and autoregressive models. Further to these models, in resolving the issue of pre-specification of lag length and the degree of polynomial in the Almon approach the study

employs Granger causality tests and Akaike or Schwarz information criteria to make out appropriate PDL. The beauty of Polynomial Distributed Lagged models is that they make the static economic theory a dynamic one by taking into account explicitly the role of time. Furthermore, such models help us to distinguish between short-run and long-run response of the dependent variable to a unit change in the value of the explanatory variables. The Almon PDL model may also be considered as an alternative to the lagged regression models, for the PDL avoids the estimation problems associated with the autoregressive models.

In the Almon approach, we have to pre-specify both the lag length and the degree of the polynomial. There are both formal and informal methods1 of choosing lag length and the degree of polynomial. That was one of the realities to apply Almon PDL for financial time series of insurance companies in this study. For estimating short-run and long-run elasticities, these models have proved to be highly useful. Additionally, these models address the topic of causality in economic variables. Though in applied work, the Granger causality modeling has received considerable attention, but one has to exercise great caution in using the Granger methodology because it is very sensitive to the lag length used in the model. This study is in a way an attempt to invite researchers and practitioners for the maximum application of these very important dynamic models in economics, business and finance.

Following the introduction next section reviews a synthesis of investment, risk and returns from the previous studies. Section 3 briefs about VAR and distributed lag methodologies; Findings of the study have been analyzed in Section 4 while Section 5 concludes study with some recommendations.

II. SYNTHESIS OF INVESTMENT, RISK AND RETURNS IN STUDIES

Trading activities in the stock markets help to determine the volume of investment and their impact on the volatility of prices. Risk and volatility of stock prices have randomness in yielding capital gains or loss. Objective of this study was to

1 Akaike or Schwarz information criterion can be used to choose the appropriate format of the model. Please refer to [30] chapter 17 for further details.

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synthesize a short term and long term link between the volume of investment, market risk associated with insurance stocks and historical returns from these securities. No theory in finance at the very outset determines the direction of relationship among these three variables. The purpose of this section is to explore studies which examined some sort of relationship among these variables. Stock returns are time dependant and their distribution is leptokurtic and skewed [4]. Volatility of returns is different for opening and closing prices [20]. The reason for this difference in the volatility of returns can be attributed to the trading mechanism of the market for the opening and the closing prices and the time lag between the opening and closing prices [23]. Focusing on the oscillations in the stock market indicators related to the efficiency of the market, changes in stock prices have been observed as dependent on the type and availability of information pertaining to the returns of particular stocks [21]. The volume of investment in the stock market also contributes in the volatility of stock prices and returns [22]. Very frequent crashes in the Karachi Stock Exchange (KSE) in the recent past enumerate mounting volatility of stock prices and stock returns in Pakistan.

Studies have examined various aspects of the volatility of stock prices and stock returns. Campbell [6] made out changing investment/trading volume as one of reasons for increasing volatility of stocks. The stocks traded heavily by the institutional investors create volatility in the market [14]. Jones [15] in their study on the Swedish index examined positive relationship between volatility and the size of investment (number of transactions). Griffin [11] examined the relationship between trading activities and returns of 46 markets and found strong direct and positive relationship between trading volume (the size of investment) and returns. Further in the same area, Blume [3] made out extent of the trading volume as responsible for the losses in S&P stocks in 1987. Song [24] employed three variables such as number of transactions, size of transactions, in order to examine the relationship of volatility and volume (of investment) in the Shanghai Stock Exchange and found number of transactions as the main culprit for the volatility. Findings of [25] about the 54 companies of Turkish stock market were also similar in the sense that trading volume (investment), number of transactions and volatility are integrated and move in the same direction. Sabri [26] and Sabri [27], in a comparative study of emerging and developing markets, observed highly positive correlation between trading volume (investment) and stock price volatility.

Contrary to the findings of other studies, Hu [28] in his cross sectional study for the relation between stock returns and volume on Tokyo Stock Exchange, came out with inverse relation between stock returns and trading volume (of investment). None of the previous studies has employed Almon PDL on the causal relationship of financial variables. This study is an attempt to determine causal relationship among risk, return and change in the capital which is volume of investment. Measuring series of risk variable through GARCH (p, q) is also an academic contribution of this study.

III. METHODOLOGY OF DYNAMIC ECONOMETRIC MODELS2

A. Distributed-Lag Models: The Almon Polynomial Distributed lag (PDL) The Koyck distributed-lag model is extensively used in

research. Coefficients of the lag are assumed to decline geometrically in this model, as the lag length increases. The Koyck distributed-lag models in this restrictive assumption may not be applicable when there is functional relationship between the coefficients and time lags3. The finite distributed-lag model can be presented as follows.

tktktttt uXXXXY ...22110 (1)

This can also be written more precisely as follows.

t

k

iitit uXY

0 (2)

In this expression i is approximated by length of the lag. Hence, i is polynomial function of lag length (i) with degree of polynomial less than length of the lag (k).

mmi iaiaiaiaa .........3

32

210 (3)

On substitution of value of i the above expression changes to

t

k

iit

mmt uXiaiaiaiaaY

0

33

2210 ).........(

(4)

The equation can be further reduced to the estimable form as follows.

t

k

iitit uZaY

0 (5)

Since in the Almon scheme Y is regressed on the constructed variables Z, not the original X variables, thus OLS assumptions seem to hold valid. The estimated parameters have all the desirable statistical properties. Assuming the second degree polynomial, values of i‘s can be obtained from the estimated values of the parameters of the equation (5) as follows:

22

10

2103

2102

2101

00

ˆˆˆˆ...........................

ˆ9ˆ3ˆˆˆ4ˆ2ˆˆ

ˆˆˆˆˆˆ

akaka

aaa

aaa

aaa

a

k

End point restrictions are imposed on i depending upon whether or not the value of independent variable with certain

2 This methodology with certain modification has been adapted from Gujarati [30].3 Shirley Almon in [30], pp. 656-712.

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degree of lag affects the dependant variable 4 . With the application of end point restrictions on the values of i the model becomes Restricted-Least Squares Model. A near end constraint restricts the one-period lead effect of independent variable (x) on dependant variable (y) to be zero. Similarly, far end constraint restricts effect of x on y to die off beyond the number of specified lags. The number of estimated parameters is reduced by the number of restrictions.

The Almon technique has a distinct advantage over the Koyck method which has some serious estimation problems. These problems result from the presence of the stochastic explanatory variable Yt-1 and its likely correlation with the disturbance term. As per advice of Gujarati [29], we need to resolve the following practical problems, before applying the Almon technique.

Maximum length of the lag (k) should be determined in advance. Advice of Davidson and MacKinnon [29] has been well taken and the question of lag length has been settled by starting with a very large value of the lag length and then seeing whether the fit of the model deteriorates significantly when it is reduced without imposing any restrictions on the shape of the distributed lag. Additionally, Akaike or Schwarz [29] information criteria are used in order to choose the appropriate lag length and degree of polynomial.

The degree of polynomial (m) should be at least one more than the number of turning points in the curve relating i to i. In the absence of sound theoretical basis, one can use a fairly low-degree polynomial (say, m = 2 or 3) for good results and that is what has been followed in this study on the stocks of insurance companies.

The following section examines results of the model. At the first stage it examines the results of autoregressive models. At the second stage, keeping in view the limitations of autoregressive models-as discussed earlier in this study, Almon model results have been pictured.

B. Vector Autoregresion (VAR) The VAR is generally used for the purpose of forecasting

time series which might be closely related. It is also used in order to analyze dynamic impact of random error terms on the group of variables. The VAR approach to structural modeling is in a way that every endogenous variable in the system is presented as a function of the lagged values of all of the endogenous variables in the system.

The model, in general can be presented as follows: p

ittitit XYY

1 (6)

Where Yt is vector of endogenous variables and Xt is the vector of exogenous variables; while and are the coefficient matrices. In the mathematical expression, µ is vector of innovations (the error term). The error term might be

4 For example, when k <= 0, then kth lagged form of independent variable is not affecting dependant variable.

contemporaneously correlated but without simultaneity leading to the consistent estimates.

IV. RESULTS AND ANALYSIS

A. Vector Auto Regression (VAR) Models Economic theory at times is applied in order to make out

the relationships of time series data variables. In many research cases, economic theory does not provide dynamic relationships of the variables. That is why non-structural modeling deems appropriate for the relationships where direction of causality is indistinct. VAR is one of models in the lines of non-structural approaches.

In this Section, I have estimated three-variable VAR with 4 lags for the endogenous variables. The model also includes investment as exogenous variable. The investment has been defined as change in the capital invested in the two consecutive business days. Lag structure and residual tests were used as diagnostic tests for stability of the roots.

VAR can be used as a better alternative to the simultaneous equation models in the sense that we do not need to distinguish endogenous variables from the exogenous ones, and VAR is rather a method of measuring multi-directional causality test.

Assuming lagged values of uncertainty and returns as determinants of uncertainty in current period the results of VAR have been presented in the Table I (given at the end). An overview of the results signifies impact of risk and low returns on the uncertainty to exist in the subsequent periods. For most of 13 stocks of insurance companies, prevalence of uncertainty in the current period is result of risk and low returns in the past. The external shocks in the stock market in general, shatter confidence of investors. Specifically uncertainty associated with the stocks of small companies such as HICL and HIMCL does not seem to persist due to relatively less amount of capital invested in these stocks for the period under discussion. Nevertheless, significance of low returns and risk as determinant of uncertainty at 90 percent confidence level could not be rejected. For the large and established companies this relationship is significant even with 95 per cent confidence.

Table II reveals impact of lagged values of risk and returns on the current period returns for all the 13 insurance stocks using VAR model. Theoretically high returns in the current period encourage investors to take up more risk and go for high volume of investment. Similarly, there should be negative relationship between the current period rising risk/uncertainty and future returns. Volume of investment and returns from this investment should also move in the same direction. Results reveal significant positive relationship between volume of investment and absolute amount of return from this investment. For the companies such as EFUG, LIBM and PakRe the direction of relationship is correct but not with much significance. Investment in the Jublee stocks looks quite risky on account of negative relation between the volume of investment and returns from these stocks.

The last period risk seems to have significantly positive impact on the returns in the current period for the companies such as AICL, EFUL and MTLA. The value of uncertainty

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with two periods lag negatively affects current return from the securities for most of the stocks. With the increase in time lag, negative impact of risk on current period returns becomes significant MTLA and Jublee. For rest of the stocks impact of risk on current period returns dwindles. Current period returns are independent of lagged values of returns in most of the cases. However, the returns from the stocks of AICL Ins., HMICL and JubleeL are significantly affected by their returns in the recent past. Based on the results shown in the Table 2 we cannot clearly generalize the direction of causal relationship between the current period returns and their lagged values. It varies from stock to stock.

B. Ploynomials Distributed Lag Models Results The results obtained from Almon technique are presented in

the Table III without end-point restrictions and Table IV with end-point restrictions. For illustration we assume that given the volume of investment, growing uncertainty determines growth in returns from investment in stocks. Furthermore we assume that can be approximated by the third degree polynomial at the initial results. Nevertheless, applying the Akaike and Schwarz information criteria appropriate degree of the model was applied.

In Pakistan there are 5 business days in a week in the KSE. Friday being the congregation day, the business activities are observed to be below the normal level as compared to the other working days. Therefore, starting from Monday through Thursday the business activities are on swing. Given this context we estimated the models with three periods lag and arrived at the appropriateness of two period lag. From the three estimated z-variables (PDL), most of the coefficients have shown individually statistical significance at 5 percent level. Significance of z-coefficients and the values of Durbin-d, correct specification of the models without multicollinearity and autocorrelation was checked. 's have been estimated from the z-variables coefficients and their values are reported in the tables 3 and 4.

Variances of these two sets of coefficients are related according to the following equation:

)ˆ,ˆ(2)ˆ()ˆ(2

0

2pj

j pj

pjj

ji aaCoviaVariVar

(7)

The equation reveals interdependence of variances of the two categories of coefficients but they may not have necessarily the same signs and magnitudes on account of covariance terms.

Assuming that the values of explanatory variable in the current and the distant periods have least impact on the current value of dependant variable, end-point restrictions are generally applied. In the model of current study I have applied far-end-restrictions on 's assuming that risk existing today shall gradually fade up in the far subsequent period’s returns from the given volume of investment. For the most of the insurance stocks this restriction is significantly rejected except the stocks of AICL Ins., JubleeL Ins. and PakRe. Insurance. Very vivid conclusion can be drawn for these stocks. Once a risk arises, it persists quite for some time and continues

affecting the returns from the investment in these stocks. The linear combination of the coefficients reported in the last column of the tables satisfies condition of no multicollinearity.

The results also support adaptive expectations indicating partial adjustment in the values of the coefficients.

V. CONCLUSIONS AND RECOMMENDATIONS

Causality among the economic variables has always been at the core of studies. Events and shocks are contiguous to macroeconomic indicators for a certain period of time. For instance, 9/11 is still referred to have effects on economic indicators. In the time-series data, this contiguity of effect is of more concern. The lead-lag relationship is more common for the time series data. In the time series econometrics, multivariate causality is tested through vector auto-regression (VAR) which has been applied in this study for not having any priori distinction between endogenous and exogenous variables namely investment, risk and returns.

The VAR results signify uncertainty in the current period in consequent upon the risk and low returns in the near past for most of the 13 stocks of insurance companies. The lag effect of uncertainty does not persist in the following periods for the insurance stocks with relatively less amount of investment in the market. But for such a lag effect the confidence interval is relatively wide (at 10 percent). This relationship is more significant for the companies with relatively big investment. The stocks yielding high returns encourage investors to subsequently go for high risky investment in the KSE of Pakistan.

Significantly positive relationship between volume of investment and absolute amount of return has been proved in this study for most of the insurance stocks. These results are in accordance with findings of Roll [22], Jones [15] and Sabri [26] and Sabri [27]. However, some of the insurance companies this relationship can not be proved.

The risk lovers enjoyed significant returns in the leading period for taking risk of investment in AICL, EFUL and MTLA in the past. At the same time, uncertainty with two periods lag negatively affects returns in the current period for most of the stocks and this negative impact of risk looks significant for MTLA and Jublee. But this relationship can not be generalized for all the companies. Returns from these securities in the period t were found independent of their lagged values for most of the cases with the exception of the stocks of AICL Ins., HMICL and JubleeL.

The study concludes that stock price volatility is mainly caused by the trading frequency and the trading volume of the insurance stocks. In terms of skewness of returns from the insurance stocks, results of this study are similar to the findings of Bollerslev and others [4]. Volatility of returns from the insurance stocks is not similar for opening and closing prices [30]. For the space saving, these results have not been reported. Reasons for the asymmetric volatility might be the same as reported by [23]. Regarding the relationship between volume of investment and volatility my results are similar to Rolls [22], [15] and [11] in spite of different methodology. Investment in

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the stock market also contributes in the volatility of stock prices and returns.

The findings of this study can be helpful in predicting volatility of the stock prices and stock returns in relation with the capital invested in these stocks. The study also recommends applying panel data models in order to explore and further strengthen the type of causal relationship among number of trades, volume of investment, volatility in the stock market and returns from the stocks. Nonlinear models are also recommended to be applied to test relationship of these variables. In this regard the study can be extended to increased number of stocks to generalize the relationships discussed in the study.

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TABLE I. VAR MODEL RESULTS

VAR Model: H = C(1,1)*H(-1) + C(1,2)*H(-2) + C(1,3)*H(-3) + C(1,4)*H(-4) + C(1,5)*R(-1) + C(1,6)*R(-2) + C(1,7)*R(-3) + C(1,8)*R(-4) + C(1,9) + C(1,10)*I

Companies H(-1) H(-2) H(-3) H(-4) R(-1) R(-2) R(-3) R(-4) I AGIC Ins. 0.386* - 0.00078 0.0071 0.019 - 0.024* 0.0048* 0.0008 - 0.00018 - 5.76e-010 AICL Ins. 0.870* - 0.167* 0.134* - 0.081* - 0.0009 - 0.002* - 0.002* - 0.0002 - 2.2e-011*

Century Ins. 0.911* 0.064 - 0.003 - 0.035 - 0.003* - 0.0001 - 0.0002 0.0001 6.16e-010* EFUG Ins. 0.36* 0.034 - 0.03 0.006 0.001* 6.17 - 7.17 2.33 - 7.03e-012 EFUL Ins. 0.846* - 0.299* 0.098* - 0.023 - 0.033* - 0.008* 0.0007 - 0.0002 - 9.5e-010 HICL Ins. - 0.038 - 0.051 - 0.039 - 0.016 - 0.091* - 0.012* - 0.008 - 0.006 - 1.4e-008*

HMICL Ins. 0.042 0.017 - 0.038 - 0.061 - 0.136* 0.023 - 0.008 - 0.013 5.9e-009 ITTGEN Ins. 0.685* - 0.108 0.113 - 0.052 - 0.015* 0.005* - 0.0003 0.002 3.7e-010

LIBM Ins. 0.514* 0.229 - 0.207 - 0.184 - 0.008* - 0.002 0.0007 - 0.003* 1.1e-008 MTLA Ins. 1.158* - 0.251* - 0.039 0.099 - 0.003* - 0.002 - 0.0007 - 0.002* - 2.8e-009 Jublee Ins. 0.933* - 0.163* 0.238* - 0.055* - 0.076* - 0.032* - 0.051* - 0.099* - 1.1e-007*

JubleeL Ins. 0.788* 0.0133 - 0.0144 - 0.011 0.001* 0.0005* - 0.0001 - 0.0002 - 3.6e-011 PakRe. Ins. 1.11* 0.005 - 0.149* 0.027 - 0.0023 0.0112* 0.008* 0.0005 1.8e-010

* Significant at less than 5% level of significance. Intercept is not reported for space saving.

TABLE II. IMPACT OF LAGGED VALUES OF RISK AND RETURNS ON THE CURRENT PERIOD RETURNS

VAR Model: R = C(2,1)*H(-1) + C(2,2)*H(-2) + C(2,3)*H(-3) + C(2,4)*H(-4) + C(2,5)*R(-1) + C(2,6)*R(-2) + C(2,7)*R(-3) + C(2,8)*R(-4) + C(2,9) + C(2,10)*I

Companies H(-1) H(-2) H(-3) H(-4) R(-1) R(-2) R(-3) R(-4) I AGIC Ins. 1.484 - 0.124 0.948 0.839 - 0.034 0.084 - 0.018 0.017 7.61e-008* AICL Ins. 2.618* - 4.32* 3.66* - 0.783 0.206* 0.032 0.033 - 0.007 4.89e-009*

Century Ins. - 4.29 1.12 - 0.31 2.69 - 0.117* - 0.019 - 0.104* 0.035 7.08e-008* EFUG Ins. - 20.8 21.16 - 3.91 0.894 - 0.02 0.044 - 0.02 - 0.02 6.7e-009 EFUL Ins. 3.09* - 1.43* 0.600 - 0.070 - 0.324* - 0.017 - 0.006 - 0.011 5.7e-008* HICL Ins. - 0.005 0.166 - 0.227 - 0.209 - 0.028 - 0.009 0.037 - 0.0006 2.43e-007*

HMICL Ins. 0.239 0.152 - 0.296 0.217 0.168* - 0.029 0.003 0.039 3.8e-007* ITTGEN Ins. - 3.01 0.929 0.112 - 1.68 0.093 0.0004 - 0.027 0.025 - 2.1e-008

LIBM Ins. 21.42 - 35.1* - 15.5 18.5 0.123 - 0.064 - 0.024 - 0.085 2.7e-007 MTLA Ins. 5.60* - 10.19* 16.21* - 11.58* - 0.136* - 0.025 - 0.094 - 0.016 - 1.03e-008 Jublee Ins. - 0.026 0.372* - 0.296* - 0.0169 - 0.143* - 0.206* - 0.123* 0.028 - 5.5e-007*

JubleeL Ins. - 3.12 8.16 - 5.21 - 1.60 0.170* - 0.014 - 0.004 0.021 2.4e-008* PakRe. Ins. - 3.72* 3.01* - 0.145 1.01 - 0.205* - 0.224* - 0.039 - 0.034 2.3e-008

* Significant at less than 5% level of significance. Intercept is not reported for space saving.

TABLE III. PDL-RESULTS WITHOUT END POINT RESTRICTIONS

Companies I PDL01 PDL02 PDL03 0 1 2 3 i

AGIC Ins. 1.24E07* 3.587* -2.542* 0.779* 6.9094* 3.5873* 1.8246* 1.6213** 13.943* AICL Ins. 5.22E09* 0.0715 -1.742* 1.429* 3.2419* 0.0715 -0.242 2.302* 5.374*

Century Ins. -8.95E08** 8.5069* -19.702* 6.773* 34.982* 8.507* -4.421** -3.805 35.262* EFUG Ins. 1.89E09 -120.388* 95.86* -32.1* -248.34* -120.4* -56.63* -57.06* -482.407* EFUL Ins. 9.05E08* 1.923* -6.08* 3.32* 11.32* 1.93* -0.84* 3.02* 15.413* HICL Ins. 3.19E07* 3.746* -1.39* 0.061 5.21* 3.75* 2.41* 1.19* 12.56*

HMICL Ins. 3.23E-07 2.263* -0.458* -0.299* 2.42* 2.26* 1.51* 0.15 6.347* ITTGEN

Ins. -2.49E08 5.575* -5.771* 2.266* 13.61* 5.58* 2.070 3.096 24.354*

LIBM Ins. -1.12E07 15.887 -17.34* -2.696 30.53* 15.88 -4.15 -29.58** 12.69 MTLA Ins. 1.24E-07 -5.764* -10.69* 10.47* 15.39* -5.76* -5.98* 14.74* 18.39* Jublee Ins. -7.75E07* -0.489* -0.0028 0.98* 0.49* -0.49* 0.49* -- 0.49*

JubleeL Ins. 2.79E08* -18.335* 1.085 21.46* 2.04 -18.33* 4.21 -- -12.08 PakRe. Ins. 4.23E08 1.202* 1.190* -0.94* -0.93 1.20* 1.45* -0.18 1.548

* Significant at <= 5% level of significance. ** Significant at <= 10% level of significance.

211

TABLE IV. PDL-RESULTS WITH END POINT RESTRICTIONS

Companies I PDL01 PDL02 0 1 2 3 i

AGIC Ins. 1.23E-07* (1.22E-07*)

4.114* (4.021*)

-0.98* (-2.349*)

3.136* (6.705*)

4.317* (4.020*)

3.542* (2.008*)

0.812 (0.668)

11.81* (13.41*)

AICL Ins. 5.25E-09* (5.27E-09*)

0.472 (1.192**)

-0.034 (-1.031**)

0.437 (2.434*)

0.805 (1.192**)

1.103** (0.372)

1.331 (-0.025)

3.68** (3.972**)

Century Ins. -8.45E-08 (-8.91E-08**)

18.472* (10.207*)

-5.282* (-18.724*)

13.189* (34.04*)

15.813* (10.21*)

7.872* (-3.411)

-10.635* (-6.813*)

26.24* (34.02*)

EFUG Ins. 2.29E-09 (1.78E-09)

-141.79* (-138.5*)

33.95* (87.13*)

-107.8* (-239.3*)

-147.8* (-138.5*)

-119.8* (-65.05*)

-23.8 (-18.87)

-399.18* (-461.8*)

EFUL Ins. 9.15E-08* (8.92E-08*)

3.287* (3.361*)

-0.866* (-4.867*)

2.42* (9.47*)

3.11* (3.36*)

2.069* (-0.257)

-0.704 (-1.378*)

6.897* (11.20*)

HICL Ins. 3.47E-07* (3.20E-07*)

4.128* (3.77*)

-0.9578* (-1.39*)

3.17* (5.202*)

4.43* (3.77*)

3.76* (2.42*)

1.188* (1.166*)

12.55* (12.56*)

HMICL Ins. 2.79E-07 (3.54E-07**)

2.420* (1.919*)

-0.597* (-0.555*)

1.823* (2.45*)

2.45* (1.92*)

1.889* (1.336*)

0.131 (0.696*)

6.29* (6.39*)

ITTGEN Ins. -2.50E-08 (-2.48E-08)

7.185* (6.79*)

-1.756* (-5.075*)

5.429* (12.81*)

7.35* (6.79*)

5.756* (2.655)

0.652 (0.391)

19.19* (22.64*)

LIBM Ins. 1.50E-08 (-2.76E-07)

32.38* (5.794)

-10.072* (-20.79*)

22.31* (32.87*)

24.47* (5.794)

6.495 (-8.713)

-31.63* (-10.64)

21.65 (19.31)

MTLA Ins. 6.25E-08 (5.48E-08)

-1.978 (2.1471)

0.891 (-3.93**)

-1.08 (7.147*)

-0.39 (2.147)

2.082 (-0.711)

6.34** (-1.43)

6.94 (7.157)

Jublee Ins. -8.51E-07* (-7.92E-07*)

-0.207* (-0.006)

0.096* (-0.147*)

-0.111** (0.215*)

-0.029 (-0.006)

0.246* (-0.078)

-- 0.1067 (0.132)

JubleeL Ins. 2.73E-08* (2.73E-08*)

-12.86* (-7.65**)

4.352* (-2.61)

-8.51* (-1.83)

-8.314* (-7.65**)

0.584 (-7.04**)

-- -16.24** (-16.51**)

PakRe. Ins. 4.24E-08 (4.18E-08)

0.553 (0.6183)

-0.1098 (0.754)

0.443 (-0.456)

0.667 (0.618)

0.67** (1.05*)

0.4542 (0.846*)

2.234** (2.061)

* Significant at <= 5% level of significance. ** Significant at <= 10% level of significance.

Values in parentheses are the results with far-end-point restriction. The other values reveal results of the near-end-point restriction.

212