Note: This table reports p-values of the Wald statistics of the traditional **Granger**-**causality** **test**. h = 0 (i.e. the reduced-form VAR model), lags = (1, 2, 3, 4), assuming homoskedastic idiosyncratic shocks.
Table 2 reports the p-values of the robust **Granger**-**causality** **test** statistics (for ExpW ∗ , M eanW ∗ , N yblom ∗ and QLR ∗ , respectively). We are testing whether the restricted regressor **Granger**-causes the dependent variable in the presence of instabilities. For example, if we consider the dependent variable π and the restricted regressor R, we are testing whether R **Granger**-causes π in a way robust to instabilities across time, i.e. whether the coefficients of lags of R are constant and equal to zero over time. The p- value of the ExpW ∗ statistics in Panel A in Table 2 is 0.01, so the **test** does reject the null at the 5%

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Many economic variables are non-stationary, so a unit root **test**, namely the augmented Dickey-Fuller **test**, was used to analyze the data and ensure stationarity. Following this, the Johansen and Juselius (1988) was used to determine the long-term relationship among the variables. Finally, the famous **Granger** **causality** **test** was applied to examine the **causality** relationship between exports and economic growth, specifically to identify whether exports affect economic growth or if economic growth drives the demand for more exports in the economy.

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Conclusions and Policy implications
Throughout our study, we targeted for main objective to study the impact of the development of the agricultural insurance, measured in term of penetration in the agricultural insurance on the agricultural performance in one representative American countries such us Argentina, during period 2000-2012. To do it, we used the **Granger** **Causality** **Test**. By these tests, we were able to make important results which reflect the reality of the agricultural activity in Argentina. For Argentina, the **test** of stationarity showed that all the variables are stationnary in first difference. The model used to estimate the impact of the agricultural insurance on the agricultural productivity is globally significant. The model is not autocorreleted, homoscedastic and follows a normal distribution, so it can be used for the forecast. From the study led on the Argentina economy concerning the existence or not of an interaction between the activity of agricultural insurance and the agricultural performance, we were able to clear three types of causalities (we schematize the causalities in Figure 1) namely:

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Conclusions and policy implications
Throughout our study, we targeted for main objective to study the impact of the development of the agricultural insurance, measured in term of penetration in the agricultural insurance on the agricultural performance in one representative European countries such us France, during period 2000-2012. To do it, we used the **Granger** **Causality** **Test**. By these tests, we were able to make important which reflect the reality of the agricultural activity in France. For France, the **test** of stationarity showed that all the variables are stationary in first difference. The model used to estimate the impact of the agricultural insurance on the growth of the agricultural production and to estimate the impact of the penetration at the insurance on the agricultural productivity or the one who is used to study the impact of the subsidies of the premiums of agricultural insurance on the growth of the agricultural production are globally significant. The model is not autocorreleted, homoscedastic and follows a normal distribution, so it can be used for the forecast. From the study led on the French economy concerning the existence or not of an interaction between the activity of agricultural insurance and the agricultural performance, we were causalities in Figure 1) namely:

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and of Management of Sousse, Tunisia
the **causality** between the agricultural productivity and the development of the agricultural insurance and this by resorting to an econometric approach using **Granger** **Causality** **Test**. This 2012 for one of the American country to know the United States. We found interesting results in this connection which reflect the state of the agricultural insurance and the implications of its use to allow the preservation of the agricultural performance. Besides, we showed in term of **causality** the implications of the application of the agricultural modalities of risk management on the agricultural in the developed countries, the agricultural insurance acquires a big importance as is used for a long time as one management tool of the agricultural risks. Through our econometric analysis, we try to show the existence or not of a **causality** between the agricultural productivity and the development of the To be made, we shall **test** the existence of a relation of cointegration between the variables which are used and we shall proceed by a study of the stationarity applying **Granger** **causality** **test**, we show the existence of an unidirectional **causality** between the development of the agricultural insurance and the agricultural productivity in the United States and we also identify the existence of an unidirectional **causality** enter the development of the agricultural insurance premiums to United States and the agricultural productivity enters the period 2000-2012.

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…ndings can be summarized as follows. First, the Homogenous Non **Causality** (HNC) hypothesis from …nancial development to economic growth is very often accepted at 5%
level. We …nd the same result when the panel is split into two subgroups: developed and developing countries. This suggests that either there is no empirical evidence of a causal in‡uence of …nancial depth on economic growth in the short run or that the **causality** from …nance to the real side of the economy is too complex relationship to be identi…ed by a bivariate **Granger** **causality** **test**. Then, our results are then conform to some conclusions of previous empirical studies (Christopoulos and Tsionas, 2004, for example). In terms of economic policy recommendations, it implies that …nancial

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Indeed, one of the main issues of a panel **Granger** **causality** **test** is the heterogeneity of the model and of the **causality** relationship. Let us assume for instance that we **test** the non **causality** from …nancial development (representend by a variable x); to growth (represented by a variable y). For each country; we say that …nancial development measure (x) is causing growth (y) if we are better able to predict growth using all available information than if the information apart from x had been used (**Granger**, 1969). But, when growth and …nancial development are observed on N countries, the issue consists in determining the optimal information set used to forecast y: Several solutions could be adopted. The most general is to **test** the **causality** from the variable x (…nancial development) observed on the i th country to the variable y (growth) observed for the j th country, with j = i or j 6 = i: It implies that we can identify a **causality** relationship when the past values of the …nancial development indicator for France give an information about the future values of growth for Japan. In this paper, we use a more restrictive solution derived from the time series analysis. We say that there is **causality** from …nancial development to growth if and only if, the past values of the variable x observed on the i th country improve the forecasts of growth for this country i only. The cross sectional information is then only used to improve the speci…cation of the model and the power of tests as in unit root **test** literature. In this contexte, we propose to distinguish between the heterogeneity of the model and the heterogeneity of the causal relationships from x to y. Indeed, the model may be di¤erent from an country to another, whereas there exists a causal relationship from x to y for all countries. On the contrary, it may be exist a **causality** relationships only for a sub-group of countries.

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The outcomes contained in this article should be useful tips for other researchers using considered variants of the Toda-Yamamoto **test** in their practical applications. The presented results ensure that bootstrap based on leveraged residuals is often an eﬀective tool for **Granger** **causality** **test**- ing, which allows avoidance of the problem of over-rejection of the con- sidered null hypothesis. However, the conducted simulation study con- firms that this method cannot be used without a second thought, since it is likely to fail for specific models.

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In order to re-enforce the **Granger**-**causality** **test** results, we apply two complementary strategies. The first one, let us call it indirect approach, assumes that the variables are stationary or can be made stationary by differencing. It makes use of pre-testing for unit roots and cointegration and, depending on the outcomes, testing for **causality** is undertaken within VAR models of different specifications. When both series are deemed I(0), a VAR model in levels is used. When one of the series is found I(0) and the other one I(1), VAR is specified in the level of the I(0) variable and in the first difference of the I(1) variable. When both series are determined I(1) but not cointegrated, the proper model is VAR in terms of the first differences. Finally, when the series are cointegrated, we can use a vector error correction (VECM) model or, for a bivariate system, a VAR model in levels. Obviously, the weakness of this strategy is that incorrect conclusions drawn from preliminary analyses might be carried over onto the **causality** tests. In the light of the unit-root and cointegration **test** results, this possibility must be taken seriously. The ambiguities of pre- testing might have great impact on the final conclusions regarding **Granger**-**causality**, unless different VAR specifications lead to the same results . The second strategy, let us call it direct approach, is free of this problem. It is based on the procedure of Toda and Yamamoto (1995) which does not rely so heavily on pre-testing, though some knowledge of the maximum order of integration and of the lag structure is still required.

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The relationship between military spending and economic inequality is not well documented within the empirical literature, while numerous studies have uncovered the linkages between military spending and other macroeconomic variables, such as economic growth, unemployment, purchasing power parity, black market premium, poverty and investment. The purpose of this article is to examine the causal relationship between military spending and inequality using BVC and SIPRI data across 58 countries from 1987 to 1999. Panel unit root tests indicate that two inequality measures (Theil and EHII) under consideration are likely to be non-stationary. The authors’ work addresses the adverse implications of modeling with non-stationary variables, since this omission casts serious doubt on the reliability of the relationship between military spending and inequality. The recent developed panel **Granger** non-**causality** tests provide no evidence to support the causal relationship in either direction between the military spending and the change in economic inequality. The results are consistently robust to alternative data sources for military spending, to alternative definitions of the inequality measures, to the log transformation of the military spending, to the deletion of some data points, and to the division of OECD and non-OECD countries. Finally, the impulse responses and variance decompositions based on the panel vector autoregressive regression model are consistent with the findings relied on **Granger** non-**causality** tests.

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Second, for liquidity of the stock markets indicators we found no **Granger** **causality** relation which Implies that the liquidity of stock markets does not **Granger** cause inward FDI inflows That results are true for the aggregate level data used in the current study for all countries . At the other extreme we found significant direction of **causality** from FDI to liquidity of stock markets among lower middle income countries There are two interpretations of this results First, FDI can be positively correlated with the number of firms in capital markets, since foreign investors might want to finance part of their investment with external capital or might want to recover their investment by selling equity in capital markets. Second, given that foreign investors partly invest through purchasing existing equity, the liquidity of stock markets will likely rise.

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Second, for liquidity of the stock markets indicators we found no **Granger** **causality** relation which Implies that the liquidity of stock markets does not **Granger** cause inward FDI inflows That results are true for the aggregate level data used in the current study for all countries . At the other extreme we found significant direction of **causality** from FDI to liquidity of stock markets among lower middle income countries There are two interpretations of this results First, FDI can be positively correlated with the number of firms in capital markets, since foreign investors might want to finance part of their investment with external capital or might want to recover their investment by selling equity in capital markets. Second, given that foreign investors partly invest through purchasing existing equity, the liquidity of stock markets will likely rise.

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dimensional cases (A 1 model, E 1 and E 5 error term) are in line with results presented in table 4.
The outcomes contained in table 5 and 6 also lead to some interesting regularities and provide no significant reason for rejection of Hypothesis 1 or Hypothesis 2. Firstly, they confirmed the hypothesis that TY **test** based on asymptotic distribution theory tends to over- reject the null hypothesis also when there exist cointegration between considered variables 17 . Secondly, they provided basis for claiming that the application of bootstrap methods leads to reduction of actual **test** size in comparison to asymptotic method. However, this reduction is still insufficient for A 2 algebraic structure and E 3 error distribution scheme (still over- rejection) and too intensive for A 3 and E 2 case (under-rejection, worse performance in comparison to χ 2 distribution on 5% and 10% significance levels).

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The misspecification of lag parameter caused much worse performance of TY **test** when asymptotic theory was applied. In general the performance of the bootstrap method has not worsened in such significant way.
The results contained in this paper support the hypothesis that asymptotic distribution theory performs better for longer time series. However, except for the case of spherical multivariate normal distribution of error term, this type of significant improvement has not been observed. Furthermore, **test** results obtained in cases of high size distortion of bootstrap- based technique brought no clear suggestion about the relationship between number of bootstrap replications and actual size of **test**.

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Conclusions
Companies listed on the NewConnect alternative market are characterized by higher values of risk measures than companies traded on the main WSE market. Such results affect the expectations of investors and suggest that those companies may have different goals. It was assumed that the direction of liquidity – profitability relation- ship will be opposite on the markets taken into consideration. The results brought different answers than expected and it was found that on both markets the influence of profitability on liquidity is higher than the influence of liquidity on profitability. It is not according to the theory that says that liquidity affects profitability. It does, but the opposite statement is true as well. Moreover, it is stronger. The findings show that, according to the **Granger** **causality** tests, the influence of profitability on liquidity is higher than the influence of liquidity on profitability. Additionally, both mature and growing companies, focus on profitability and value maximization.

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2 Time Series Causal Models
The basic idea of **Granger** **causality** is quite simple. Suppose that we have three sets of time series W t , Y t , and Z t , and that we have a prediction of Y t+1 based on lagged values of Y t and Z t . Then we want to improve the prediction by including the lagged values of W t . If the second prediction is better, then the lagged values of W t contain information for forecasting Y t+1 that is not in the past of Y t and Z t . In this case we say W t **Granger** causes Y t . If Z t includes already a large set of carefully chosen explanatory variables, W t seems to contain certain unique information for predicting Y t+1 . This justifies why we say W t **Granger** causes Y t . If Z t is empty, we refer it to bivariate **Granger** **causality**, otherwise to multivariate **Granger** **causality** 4 . Suppose that two time series, say W t and Y t , are mutually **Granger** causal to each other. We want to give a causal explanation that leads to the dependence implied by the **Granger** **causality** **test**. The mutual **Granger** **causality** relation may be an effect that these two time series are indeed causal to each other. It may also be that the two time series are driven by one or more common cause processes, say Z t , at different lags. Therefore to give a causal explanation to the **Granger** **causality** relation we need to take all these potentially relevant time series into account.

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Previously, the question what legitimate conclusions can be drawn from an application of **Granger**-**causality** when the scholar has no prior theoretical knowledge has never been considered. On the one hand, the existence of **Granger**-**causality** is usually tested when the theory on (eventually causal) mechanisms connecting the two time series is insufficient or does not exist. On the other hand, a review of the literature conducted below shows some serious pitfalls of the method. It is shown in the paper that in case of limited knowledge on the investigated phenomenon, one cannot judge whether the relation discovered by **Granger**-**causality** **test** is true or erroneous due to e. g.

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The concept of **Granger**-**Causality** (GC) is widely used to draw inference concerning
**causality** in applied economics. Stationary series are the term of reference used in GC testing, which is generally studied by means of a standard Dickey-Fuller **test**. We prove that, when the Data Generating Process (DGP) of the variables is either Broken-Trend Stationary (BTS) or Broken-Mean Stationary (BMS), correct inference can not be drawn from a standard **Granger**-**Causality** **test** and may identify inexistent causal relationships, even if the former variables are differenced. Asymptotic and finite-sample evidence in this sense is provided.

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regression, while its empirical size of the **test** is acceptable. We will be concerned with the improvement of the power of the LA-VAR approach in the paper.
The present paper proposes sequential testing procedures for the **Granger** non-**causality** in levels VAR’s regression. It is a suitable combination of the LA-VAR approach and the Std-VAR approach. Theorem 1 of Toda and Phillips (1993) gives a certain rank condi- tion on a sub-matrix of a cointegrating matrix for the Wald statistic in the levels VAR’s to be asymptotically chi-square distributed. If the condition is satisﬁed, we should use the Std-VAR approach rather than the LA-VAR approach, since the former is obviously asymptotically more eﬃcient. Dolado and Lutkepohl (1996) showed in small sample ex- periments with a simple 2-variate VAR model that the empirical power of the **test** of the Std-VAR approach can be signiﬁcantly greater than that of the LA-VAR approach in some cases, when the rank condition is satisﬁed. On the other hand, if the rank condi- tion is not satisﬁed, we should use the LA-VAR approach, since the Std-VAR approach cannot be used in this case because its Wald statistic has a non-standard asymptotic dis- tribution and cannot be properly tested. Obviously, the above testing procedure should be more powerful than the **test** solely based upon the LA-VAR approach, since it adopts the Std-VAR approach whenever it is applicable.

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