7. RESULTS
7.3 M ULTIVARIATE ANALYSIS
The hypotheses are tested in equations 1 and 2 in the OLS model, and in equations 3 and 4 in the FE model (see chapter 6.5). The control variables have been entered stepwise as to investigate possible changes in the effect of each independent variable on the dependent variable and the model as a whole.
7.3.1 Pooled OLS estimation
TABLE 5a: POOLED OLS ESTIMATION EQUATION 1 Variables
Intercept 1.207*** (0.092 0.959*** (0.160) 0.776** (0.279) 1.567*** (0.318)
Structural deficit divergence -0.032** (0.015) -0.020 (0.016) -0.019 (0.019) -0.010 (0.018) Cyclical deficit divergence -0.325*** (0.091) -0.318** (0.093) -0.334** (0.105) -0.381*** (0.102)
Trade intensity 0.715* (0.382) 1.208† (0.625) 0.189 (0.642)
Industrial similarity 0.001 (0.004) -0.004 (0.004)
Capital controls -0.668*** (0.144)
R2 0.055 0.062 0.069 0.137
Adjusted R2 0.049 0.053 0.055 0.121
F statistics 9.633*** 7.155*** 5.003*** 8.617***
Df (residual) 332 324 272 271
N 335 328 277 277
TABLE 5b: POOLED OLS ESTIMATION EQUATION 2 Variables
Intercept 1.043*** (0.075) 0.744*** (0.144) 0.554* (0.279) 1.110*** (0.306)
Primary deficit divergence -0.034* (0.017) -0.025 (0.018) -0.016 (0.020) 0.005 (0.020)
Interest payments divergence -0.044** (0.019) -0.043* (0.020) -0.047* (0.021) -0.039† (0.021)
Trade intensity 0.924* (0.386) 1.469* (0.642) 0.740 (0.062)
Industrial similarity 0.000 (0.004) -0.005 (0.004)
Capital controls -0.601*** (0.152)
R2 0.033 0.044 0.051 0.103
Adjusted R2 0.027 0.035 0.037 0.086
F statistics 5.579** 4.962** 3.646** 6.215***
Df (residual) 332 324 272 271
N 335 328 277 277
† p < .1 * p < .05 ** p < .01 *** p < .001
The pooled OLS estimation is used as a benchmark to which the fixed effects analysis is compared. Table 5a presents the results from the pooled OLS estimation for equation 1. The results show that structural deficit divergence is significantly and negatively correlated with business cycle synchronization only when no control variable is included. Cyclical deficit divergence is significantly and negatively correlated with business cycle synchronization in all equations.
The coefficient of trade intensity is positive in all equations, as is in line with our expectations, however, only significant at a 5% significance level when no more control variable is included. The coefficient of industrial similarity changes between being positive and negative. The variable capital controls is significantly and negatively correlated with business cycle correlation.
Table 5b presents the results from the pooled OLS estimation for equation 2.
Primary deficit divergence is significant and negative only when no control variable is included. Interest divergence is significantly and negatively correlated with business cycle synchronization, however, only at a significance level of 10%
when all control variables are included. The coefficient of trade intensity is positive as is in line with our expectations, however, not significant when all control variables are included. Industrial similarity is not significantly correlated to the dependent variable, while the variable capital controls is significantly and negatively correlated to the dependent variable.
R2 has a value of 5.5% in equation 1a, while adjusted R2 is 4.9%, and these values increase when the control variables are added. For equation 2a the values are 3.3%
and 2.7%, respectively. The low explanatory power of the models is not surprising as it most likely exist relevant variables that are not accounted for in the models.
The FE regressions in tables 6a and 6b suggest that a large fraction on the unexplained variation is country-pair fixed.
7.3.2 Fixed effects estimation
TABLE 6a: FIXED EFFECTS ESTIMATION EQUATION 3 Variables
Intercept 1.1750*** (0.183) -6.019*** (0.871) -7.994*** (1.028) -4.358*** (1.281)
Structural deficit divergence -0.0416 (0.0273) -0.007 (0.027) 0.008 (0.027) 0.052† (0.027) Cyclical deficit divergence -0.243 (0.160) -0.344* (0.139) -0.367* (0.143) -0.422** (0.135)
Trade intensity 24.487*** (2.965) 29.178*** (3.326) 17.785*** (4.088)
Industrial similarity -0.002 (0.014) 0.014 (0.014)
Capital controls -1.111*** (0.257)
R2 0.414 0.601 0.631 0.676
Adjusted R2 -0.208 0.152 0.257 0.342
F statistics 0.666 1.339* 1.685** 2.024***
N 335 328 277 277
TABLE 6b: FIXED EFFECTS ESTIMATION EQUATION 4 Variables
Intercept 1.131*** (0.122) -5.060*** (1.049) -6.781*** (1.260) -4.778*** (1.388)
Primary deficit divergence -0.035 (0.030) 0.016 (0.020) 0.024 (0.0297559) 0.050† (0.030) Interest payments divergence -0.176*** (0.035) -0.079* (0.037) -0.081* (0.039) -0.046 (0.039)
Trade intensity 20.655*** (3.392) 25.721*** (3.805) 19.076*** (4.287)
Industrial similarity -0.015 (0.0141865) -0.001 (0.014)
Capital controls -0.816** (0.267)
R2 0.492 0.595 0.624 0.648
Adjusted R2 -0.048 0.141 0.243 0.286
F statistics 0.911 1.310* 1.638** 1.791***
N 335 328 277 277
† p < .1 * p < .05 ** p < .01 *** p < .001
The results from the fixed effects estimation are mostly in line with the results from the OLS estimation. However, the explanatory power of the models is now much higher. R2 is 41.4% when no control variable is included in equation 3, while adjusted R2 is -20.8%. For equation 4 the values are 49.2% and -4.8%, respectively. A negative adjusted R2 indicates a poor model fit relative to the number of degrees of freedom (Wooldridge, 2009). Adjusted R2 increases when the control variables are added to the model, which indicates better model fit.
Table 6a presents the results from the fixed effects estimation for equation 3. The results show that the coefficient of structural deficit divergence changes between being positive and negative. The coefficient of cyclical deficit divergence is significant and negative for all equation, except when no control variable is included, as in line with our expectations. Trade intensity is, as expected, significantly and positively related to business cycle synchronization, industrial similarity is not significant in any equations, while the variable capital controls is significantly and negatively correlated with the dependent variable.
Table 6b presents the results from the fixed effects estimation for equation 4. The coefficient of primary deficit divergence alters between being positive and negative, and is never significant. Interest payments divergence is significantly and negatively correlated with business cycle synchronization except when all control variables are included. Trade intensity is significantly and positively related to business cycle synchronization, industrial similarity is not significant, while the variable capital controls is significantly and negatively correlated with the dependent variable.
7.3.3 Robustness checks
We explore the robustness of our findings to: a) differences in the entry order of control variables; b) sample selection; c) inclusion of other controls; and d) a different measure of the dependent variable. The performed robustness-check analyses are all fixed effects estimations.
Differences in the entry order of control variables
orders. Consequently, we have performed five additional analyses. The results from these can be found in tables 8-12 in appendix 9. The general pattern of the results is the same irrespective of the entry order of the control variables.
Sample selection
There are missing observations in the sample, and especially the first period is missing quite a lot of observations which may constitute a concern. To check the robustness of the variables we conduct a fixed effect analyses in which observations from the first period are deleted. The results can be found in table 13 in appendix 10, and do not differ considerably from the analysis based on all three periods.
Some of the observations are calculated based on means of yearly data. Several of these means are calculated without a fully complete data set. To check whether this may have caused bias in our estimations we perform a fixed effect analysis in which we delete observations based on means of data from fewer than three years.
The results are to be found in table 14 in appendix 10, and the main results do not differ considerably from the analysis based on all available observations.
We exclude the three countries not sharing the euro as a common currency, namely Denmark, Sweden, and the UK. Doing this changes the results on the affect of cyclical deficit divergence on the dependent variable. Cyclical deficit divergence is now only negative and significant at a 10% level when all control variables are included in the analysis. It is difficult to interpret why this happens.
However, the integration process is not uniform across Europe. European countries have joined the EU and the EMU at different points in time, and this seems to influence our results. Nevertheless, as the three non-euro countries are under the obligation of complying with regulations in the SGP, we choose to include these countries in our analysis. The results of the regressions excluding Denmark, Sweden, and the UK from the sample is to be found in table 15 in appendix 10.
Inclusion of other controls
In order to reduce possible bias caused by the fact that one or more independent variables may be correlated with an omitted variable that we have not accounted
for in the analysis, we include the value of the dependent variable from an earlier period as a control (Yt-1). Using lagged dependent variables as proxy variables provides a simple way to account for historical factors that cause current differences in the dependent variable that are difficult to account for in other ways (Wooldridge, 2009). The lagged Y variable switches between having a positive and a negative value, and is overall not significance. This indicates that this variable might not belong in the model. The results of the regressions with the lagged Y variable are to be found in table 16 in appendix 11.
We also conduct a fixed effect analysis in which we include time dummies with period 1 as the reference period. The results show that the dummy variable for period 2 is significantly and positively related to business cycle synchronization when none or one control variable is included in equations 3 and 4. The dummy variable for period 3 is significantly and positively related to business cycle synchronization except when all control variables are included in equation 3. In addition, including the time dummies make most of the effects of the independent variables and the control variables disappear. This indicates that there exists an average change over time for all country pairs in which the country pairs become more similar when it comes to all our variables. The effects we have found may be claimed to be driven by common trends. The results of the fixed effect analysis with time dummies are to be found in table 17 in appendix 11.
Different measure of dependent variable
We conduct a fixed effects analysis in which we make use of the transformed business cycle correlation coefficient composed by the HP filter instead of the CF filter. The results are to be found in table 18 in appendix 12. The analysis yields basically the same results with respect to the sign of the coefficients, but now almost all coefficients become significant. Nevertheless, as we know the HP filter tends to give imprecise estimates of the trend at end-point series, and that we yet have used all estimated cyclical components in our analysis, we choose not to base our interpretation on the results obtained with the HP filter.
7.3.4 Summary of results
cycles. The variable structural deficit divergence is most often not significantly correlated with business cycle synchronization. In addition, the sign of its coefficient changes between being positive and negative. Hence, we find no support for hypothesis 1.
Hypothesis 2 stated that divergence of the cyclical deficit between two EMU countries has a negative effect on the synchronization of these countries’ business cycles. The variable cyclical deficit divergence is significantly and negatively correlated with business cycle synchronization in most of our regressions. Thus, we claim to have found support for hypothesis 2.
Hypothesis 3 stated that divergence of the primary deficit between two EMU countries has a negative effect on the synchronization of these countries’ business cycles. The variable primary deficit divergence is most often not significantly correlated with business cycle synchronization, and the sign of its coefficient changes between being positive and negative. Hence, we find no support for hypothesis 3.
Hypothesis 4 stated that divergence of interest payments between two EMU countries has a negative effect on the synchronization of these countries’ business cycles. The variable interest payments divergence is significantly and negatively correlated with business cycle synchronization in most of our regression. Thus, we claim to have found support for hypothesis 4.