Break Point Tests

There is casual evidence for the idea that there might be breaks in the public sector variables during the economic turbulence years of early 1990’s. Therefore, we estimate the following model by OLS for all three country groups (t = calender time)

q_i;t =a_i;t +b_i;tt (11)

Country x l m g r

period I II I II I II I II I II I II I II

Australia .57 1.1 .37 .21 1.4 2.1 4.4 2.7 1.3 1.1 1.6 1.8 5.4 2.4 Austria .84 .67 -.22 -.06 .47 -.22 2.7 1.6 1.3 .42 1.3 .92 3.1 1.9 Belgium .87 .68 .04 .58 -1.3 .10 2.3 2.0 .55 1.1 .78 .73 4.3 2.0 Canada .46 .93 .57 .24 1.1 .33 3.82 1.7 .98 .60 2.1 .65 4.6 2.0 Denmark .57 .74 .39 -.20 1.7 1.1 3.5 1.9 .67 .96 1.4 .78 4.9 2.2 Finland .78 .96 -.01 -.01 1.2 3.1 4.0 1.8 1.9 .82 2.9 .93 5.1 2.1 France .72 .58 -.20 .41 -.86 1.7 .3.8 1.9 1.2 1.0 1.3 .96 4.4 2.1 Germany .54 .43 .56 .30 .97 -.13 2.5 1.3 1.4 .38 1.3 1.2 3.0 1.9 Greece .17 .89 .35 .72 -1.1 .21 8.5 4.8 .32 .84 1.8 1.9 7.6 4.6 Ireland 1.24 2.55 -.04 .97 .12 1.3 5.0 4.2 1.3 3.0 1.7 2.2 5.1 2.4 Italy .95 .57 -.10 .25 .17 .38 6.9 2.4 2.0 .48 2.1 .99 5.9 2.8 Japan 1.4 .40 .43 .26 2.0 1.0 3.5 -.74 1.6 1.2 1.7 1.8 2.7 .48 Netherl. .65 .73 .19 1.0 .69 -.67 2.0 1.7 .65 1.2 .71 -.38 3.2 1.9 New Zeal. .51 1.0 -.29 .31 1.2 2.2 1.5 2.0 .53 1.2 1.6 .22 6.1 2.8 Norway 1.1 1.1 .17 .28 1.3 1.4 3.6 2.9 1.2 1.7 2.1 1.5 5.2 2.7 Portugal 1.4 .72 .48 .39 -1.2 1.9 9.4 3.4 2.4 1.8 2.9 2.4 7.1 2.9 Spain .88 .93 -.22 1.35 1.4 -.57 7.2 3.1 2.2 1.3 2.4 .90 6.0 2.7 Sweden .63 .78 .05 -.56 -.14 1.1 3.9 1.1 .79 .98 1.5 .73 4.7 2.4 Switzerl. .59 .24 1.00 -.09 .44 .69 1.6 .69 .92 .50 3.6 1.5 2.4 1.2

UK .65 1.0 .25 .08 2.4 1.5 4.1 1.5 1.1 1.5 1.9 1.3 5.0 2.5

the US .75 0.83 .37 .01 .05 .61 2.9 2.0 .80 .82 1.6 1.4 3.9 1.9 Average .77 .85 .19 .31 .57 .91 4.1 2.2 1.2 1.1 1.8 1.2 4.8 2.3 Table 5: Averages of each variables over the …rst and second period, as per cents.

PN CS RoW

Variable LR prob. year LR prob. year LR prob. year transf ers 60.53 0.00 1992 26.24 0.00 1983 16.30 0.01 1992 gov⁰t cons: 7.22 0.27 1991 15.44 0.01 1983 3.79 0.76 1997 tax 14.83 0.01 1990 12.08 0.04 1982 23.83 0.00 1990

Table 6: Quandt-Andrews breakpoint tests.

and test for the presence of a break, examining whethera_i;t =a_{i;t 1} andb_i;t =b_{i;t 1} for all t. The Quandt-Andrews unknown breakpoint test seeks the presence of a breakpoint at anyt and reports the maximum of LR-statistic and the year of the breakpoint. The results are presented in Table 6.

The results indicate that both the bene…ts in the North and in the Rest of the World exhibited a break in 1992 while the tax variables exhibited the break already in 1990. There is no evidence of a break in the government expenditures in these two groups. The results for the Catholic South suggest a break in 1983 both in the bene…ts and in the government expenditure variables while the break in the tax variable appears a year earlier. Our …ndings suggest that multiple breaks are present. Yet to have at least one period where no breaks occur, we choose to split our data in 1992.

C Endogeneity

Typically the endogeneity of the instruments can be tested by Granger-causality test, whereby "y should not cause x". While this test is easy to implement, the problem is that it does not control for other variables besides one proposed cause.

This may result wrong inferences on the endogeneity of the variable x, due to missing variable problem. Using the more general version, whereby "x should be independent of past y conditional on pastx" is probably closer to the true model and mitigates the problem of missing variables. Therefore to test the endogeneity

of the variables we test the following two propositions wherex_j;t is the current value of each cause variablej andy_{i;t k} are the past values of each indicator variables i. As our T = 25 in the full sample and since we work with annual data, we setk = 2, i.e. we have two lags of each variable in the model we test.¹⁸

It is also crucial that indicator variables are independent on each other. Testing it in the presence of non-observed variable, which we expect to a¤ect all indicators is, however, di¢ cult. What one can do is to propose a model where the non-observed variable is replaced by the cause variables as in the instrument variables procedure to control for latent variable’s absence from the model. Therefore we proceed to test the following model where the current values of each indicator variabley_j;t are explained by the lags of all three indicators and the the lags of all proposed causes. In order to save the degrees of freedoms we set the number of lags for indicators to 2 and include only the second lag of each proposed cause variable.

We …rst test the simple Granger causality applied to the pooled, cross-country data of our cause variables. The Granger causality test suggests that our measure of tax is probably caused by real GDP per capita, which seems plausible. The transfers, on the other hand, might be caused by labor force participation and real GDP per capita - again a result in accordance with the expectations. Government consumption might be caused by real GDP per capita and interest rates are caused both by real GDP per capita and currency in circulation. As to indicators, labor force participation might be caused by real GDP per capita and somewhat surpris-ingly might real GDP per capita be caused by real currency in circulation, but not the other way around. According to Granger causality tests, there is some evidence that the proposed causes and indicators are not exogenous.¹⁹

18Other lag lengths were also tested and the results were similar to those reported here.

19All the results presented here are available from the author at request.

tax transf ers gov⁰t cons: interest rate Causes,x_{j;t k} signi…cant signi…cant signi…cant not signi…cant Indicators coef. p-value coef. p-value coef. p-value coef. p-value (GDP = capita)_{t 1} .345 .051*** -.192 .022** .257 .000* .193 .001*

(GDP = capita)_{t 2} -.243 .064*** .210 .115 .193 .028** .017 .782 (currency =capita)_{t 1} .005 .838 -.002 .875 .003 .749 .009 .063***

(currency = capita)_{t 2} -.036 .522 .007 .697 .001 .929 .018 .067***

lf participation_{t 1} .091 .589 -.004 .957 .052 .402 .015 .811 lf participation_{t 2} -.070 .550 .173 .087*** .089 .232 -.007 .878

AdjustedR² .419 .238 .206 .095

F-test 42.69 .000* 18.09 .000* 15.33 .000* 7.33 .000*

Table 7: Results from the general causality test for proposed cause variables *, **

and *** 1, 5 and 10 per cent levels of signi…cance.

Table 7 presents the results from the general causality tests for our proposed causes. Again, for sake of simplicity the tests are applied for the pooled data, whereby we report White heteroscedasticity corrected standard errors. Firstly, as already manifested by Granger causality tests, it appears that real GDP per capita signi…cantly a¤ects all our cause variables, although its impact on tax is weakly signi…cant. In addition, it appears that transfers might be caused by labor force participation and the interest rate is caused by real currency in circulation. The results are in line with Granger causality tests and suggest the proposed causes might be endogenous. Even though one could have expected that the endogeneity would have been more severe than it appears to be.

Table 8 presents the results for indicator variables. Since we are not interested on the e¤ects of our causes for the indicators per se, we suppress the information and present whether there wasany signi…cant cause for the indicators. As it turns out, the second lags of our proposed cause variables seem not to cause real currency per capita. The more interesting result is that, controlling for the cause variables, our indicators seem to be independent on each other. Only the labor force participation seems to be a¤ected by the …rst lag of real GDP per capita. Since the bias introduced by the fact that the indicator variables are not exogenous is far greater than the

GDP = capita currency =capita lf participation Causes,x_{ij;t 2} some signi…cant none signi…cant some signi…cant Indicators coef. p-value coef. p-value coef. p-value (GDP = capita)_{t 1} .404 .000* .028 .908 .261 .001*

(GDP = capita)_{t 2} .023 .743 .493 .105 .082 .132 (currency =capita)_{t 1} .017 .145 -.107 .578 -.006 .435 (currency =capita)_{t 2} .017 .364 -.263 .020** -.030 .370 lf participation_{t 1} .009 .833 .211 .431 .235 .000*

lf participation_{t 2} -.042 .420 -.261 .388 .111 .078***

AdjustedR² .291 .055 .262

F-test 18.50 .000* 2.64 .004* 16.05 .000*

Table 8: Results for the general causality test for indicator variables, *, ** and ***

1, 5 and 10 per cent levels of signi…cance.

bias due to endogeneity of the cause variables, this is a good sign.

To summarize, the endogeneity of our cause and indicator variables is less of a problem than one would have expected. While our results are probably not heavily in‡uenced by the endogeneity bias, the estimated standard errors are instead downsized because of non-normality and small sample size.