І П Булєєв - Вісник донецького університету - страница 11
Exports equation 0 1 2 3 4 3 2 1 55.300 18.417* 5.789 1.974
81.479 73.046 134.99
26.180* 19.251 54.689
7.763 2.581 18.587
1.974 0.004 2.554
" The number of cointegration vectors and the number of variables are denoted by r and n, respectively. * The null hypothesis is accepted for the first time.
Starting with the most restrictive model (and concentrating on Imports equation and the trace state statistic) the rank test statistic of 141.74 exceeds its 95 per cent critical value of 53.12 in Osterwald-Lenum (1992, Table 1*). Then proceed to the next most restrictive model (keeping the same value of r) which again exceeds its critical value of 47.21 in Osterwald-Lenum (Table 1). Moving throw the table row by row from left-to-right, the first time the null is accepted is indicated by the *. Thus, for both of the tested models we accepted that there is one cointegration vector. In the levels of the data in the model of aggregate import there are linear deterministic trends (i.e. intercept and trend in cointegration equation and no trend in VAR), while in the levels of the data in the model of aggregate export we decided that there are no linear trends (i.e. the intercept is restricted to the long-run model).
Long-run cointegrating vector estimates
The next step is to report the cointegrating vectors. In order to interpret the estimated cointegrating vectors, it is a common practice to normalize them on one of the variables by setting its estimated coefficients equal to 1. Since our interest is to obtain long-run trade elasticities, we normalize the cointegrating vectors on m in the import-demand equation and x in export-supply equation. This practice enables us to read the elasticities directly from cointegrating vectors. The coefficients are given in Table 4. Excluding the intercept and the world income coefficient in export-supply equation all long-run coefficients are significant and have the expected signs (the only exception is nominal exchange rate). The demand of Bulgarian aggregate imports would, therefore, appear to be income, relative price and nominal exchange rate elastic and trend (incorporating the impact of other factors) inelastic in the long run. According to the estimated cointegration relationships, the long-run elasticity of imports with respect to domestic GDP is 6.74 and with respect to relative price and the nominal exchange rate is -2.04 and -2.00 respectively. These results are parallel with the thought that the imports is elastic in domestic income.
_Table 4. Estimated long-run parameters_
Akaike information criterion (AIC)
ВІСНИК ДОНЕЦЬКОГО УНІВЕРСИТЕТУ, СЕР. В: ЕКОНОМІКА І ПРАВО, ВИП.2, 2007
Schwarz criterion (BIC)
Hannan-Quinn criterion (HQC)
Note: In the brackets are shown expected signs of the coefficients. The long-run equilibrium relations are:
m = - 49.026+6.735y - 2.038rpm - 2.002nex - 0.12trend; x = 0.192 + 0.836yw - 0.546rpx- 2.036ulc.
The long-run relationship of exports with respect to unit labor costs is elastic, whereas relative prices are inelastic. Meanwhile exports remain unaffected by world income. Table 4 suggests that exports decreases in unit labor costs and relative prices. The long-run elasticity of exports with respect to world income is 0.84 and with respect to relative price and the unit labor costs is -0.54 and -2.04 accordingly.
Price elasticity is high enough, therefore, the Marshall-Lerner condition is satisfied. This is due to the fact that sum of absolute values of import and export own prices elasticity add up to more than one. Our long-run approach determines the existence of the Marshall-Lerner condition that lends support for the notion that devaluations of the Bulgarian lev could improve Bulgarian trade balance.
Estimation of error-correction models (ESM)
Once a cointegration relationship is established, then an ECM can be estimated to determine the short-run dynamic behavior of Bulgarian imports and exports. According to Engle and Granger (1987), cointegrated variables must have a vector error-correction models (VECM) representation. The major advantage of the VECM representation is that it avoids problems of spurious correlation between dependant and independent variables and makes use of any short- and long-run information on data. Table 5 presents the Granger-causality results in the VECM framework. The lag length for each variable and the sequence in which variables are entered in the VECM were selected using Akaike information (AIC), Schwartz Bayesian (BIC) and Hannan-Quinn (HQC) criterion respectively.
Following Hendry's (1995) general-to-specific modeling approach, we first include 4 lags of all variables and 1 lag of the error correction term (EC), and then gradually eliminate the insignificant variables. Specification of general error correction models is as follows:
n n n n
Am = в +YJPnAmt + ^в2іАУ( , + YjP3Arpmt , + YjP4lAriext + PEC 1 + є; (7)
i=1 i=0 i=0 i=0
n n n n
Axt = Цв11Лс( +Yd0'2i4ywt i + He3,Arpxt +YJe4lAulct i + P5ECt 1 + є. (8)
i=1 i=0 i=0 i=0
After experimenting with the general form of ECM, the following ECMs are found to fit data best (Table 5). The symbol A is the first difference operator and the regressor ECt-1 corresponds to the one period lagged error-correction term. The ECt-i term carries the theoretically predicted sign and is significant at the 1% level in both models. This suggests the validity of a long-run equilibrium relationship among the variables in tested equations. With the dynamic specification of the model, the short-run dynamics are influenced by the deviation from the long-run relationship as capture by ECt-i.
Table 5. Estimated error-correction models
Dependant variable: Am
Dependant variable: Ax
Jt - 2
t - 2
Adj. R-squared F-statistic Akaike AIC Schwarz SC
Durbin-Watson statistic LMF
Jarque-Bera White (No Cross Terms) ARCH , ARCH , JDoornik-Hansen
0.936 62.335 -3.474 -3.177 2.198
2.715 (0.257) 113.92 (0.161)
0.80 (0.44), -1.61 (0.13) 0.63 (0.54), -1.35 (0.20)
Adj. R-squared F-statistic Akaike AIC Schwarz SC
Jarque-Bera White (No Cross Terms)
ARCH [i], ARCH ,
0.709 10.746 -3.398 -3.099 2.657
2.068 (0.189) 2.794 (0.247)
0.41 (0.68), 0.59 (0.57) -0.05 (0.96), -0.90 (0.39)
Three (two) asterisks indicate the significance levels at 1 percent (5 percent) respectively. ( ) is p-value
The equations are well determined, as can seen from the results of specifications tests reported in the lower part of the Table. Diagnostic test statistics show no evidence of misspecification of functional form, no serial correlation, nor any problem of heteroscedasticity and no problem of non-normality in residuals. The Breusch-Godfrey LMF test rejects the presence of serial correlation up to fourth order. The Jarque-Bera statistic and Doornik-Hansen Chi-square statistic confirm normality of residuals. ARCH test and White test reject first, second, third and fourth order heteroscedasticity in the disturbance term at one per cent significant level. In the above estimated imports model intercept, volume of import (lagged one quarter), real GDP (lagged two quarters) and relative price (lagged two quarters) have emerged as the major determinants of the import-demand function of Bulgaria. Surprisingly, the aggregate import volume in short-run is found to be (positively) price inelastic, the coefficient estimate being 0.471. The value of income elasticity of demand for imports lagged one and two quarters (i.e. cumulative coefficient) is grater than unity, implying that the demand for imports increases more than proportionately to the increase in
In the exports model, volume of export (lagged one quarter), world income (lagged two and three quarters) and unit labor costs (lagged one and two quarters) have all emerged as significant determinants of the aggregate export-supply function for Bulgaria. The value of world income elasticity of supply of exports lagged two and three quarters is grater than unity, therefore in short run Bulgarian exports increases more than proportionately to the increase in world income. Our estimates suggest a high negative elasticity of export to the unit labor costs.
The speed of adjustment (measured by the coefficient of the ECu term) is quite rapid, and 39.7 % of imports disequilibrium and 74.5 % of export disequilibrium are eliminated in one quarter. These results indicate that the adjustment of aggregate imports and exports to any change in the right side variables of the model does not take a long time to return to equilibrium.
5. Summary and conclusions
In our empirical analysis of the aggregate import-demand and the export-supply functions for Bulgaria, cointegration and error correction modeling approaches have been used. The results reveal that the real volume of import demanded and its determinants namely relative prices, real domestic GDP and nominal exchange rate, as well the volume of export supplied and its determinants namely world income, relative prices and unit labor costs are cointegrated. We have determined a unique equilibrium relationship in both models. The determinants domestic GDP, relative prices and nominal exchange rate in the import model and unit labor costs in export model found to be elastic, relative export prices - inelastic, and world income - insignificant in long run.
In the estimated ECM, volume of import (lagged one quarter), real GDP (lagged two quarters), and relative price (lagged two quarters) have emerged as the major determinants of the import-demand function of Bulgaria. Only domestic GDP (lagged one quarter) is elastic in short run. On the other side, volume of export (lagged one quarter), world income (lagged two and three quarters) and unit labor costs (lagged one and two quarters) have all emerged as significant determinants of the aggregate export-supply function for Bulgaria. World income variables lagged two and three quarters are elastic in short run. The estimated coefficients of the error correction term (-0.397 and -0.745 respectively) indicate a high speed of adjustment to equilibrium.
Our econometric estimates of the aggregate import-demand function suggest that Bulgarian import is positively correlated with the relative import changes lagged two quarters (0.471). The value of income elasticity of demand for imports lagged one and two quarters is 1.615 and 0.906 respectively. Thus, income elasticity is grater than price elasticity of demand for imports. Bulgarian export is positive correlated with world income (lagged two and three quarters), but negatively connected with unit labor costs (lagged one and two quarters). However, world income elasticity is grater than unit labor elasticity, what is meaning that the increase of world income could be a strong stimulus for Bulgarian exports growth. The results indicate also that Marshall-Lerner condition is easily to be satisfied for Bulgarian case, denoting devaluation is appropriate to correct the trade imbalance.
Data definition and source
All data are quarterly over 2001:I - 2007:I period and collected from the following sources:
a. International Financial Statistics of the International Monetary Fund, various issues.
b. Bulgarian National Statistical Institute. Variables:
M = import volume. Nominal imports are deflated by import price index (2000=100) to obtain this measure. All data are from source b.
Y = real domestic GDP. Nominal GDP are deflated by the domestic price level (CPI,
2000=100). All data are from source a. PM = index of unit value of imports, 2000 =100, source b. PD = index of domestic price level measured by CPI, 2000=100, source a. NEX = index of nominal effective exchange rate, 2000=100, source b. X = export volume. Nominal exports are deflated by export price index (2000=100) to
obtain this measure. All data are from source b. YW= world income. This variable is proxied by the index of industrial production in
Industrial countries. Data are from source a. PX = index of unit value of exports, 2000=100, source b.
PXW = export unit value index (2000=100) of the IMF's "industrial countries"
aggregate. Data are from source a. ULC = seasonally unadjusted unit labor costs index, 2000=100, source b.
В статье рассматривается коинтеграционный анализ внешней торговли Республики Болгария.
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