cross-sectional average of the observations. Specifically, the exponent _α_ is given by ̃ _Std._ ( ̃ _xt_ ) = _O_ ( _N_<sup>_α−_1</sup> ), where _xt_ is a simple cross-sectional average of observations _xit, i_ = 1 _,_ 2 _, ...n_ ; _t_ = 1 _,_ 2 _, ..., T_ . The exponent takes a value between 0 and 1. A value of 1 indicates strong cross-sectional dependence, of the type usually captured with (strong) factor models.<sup>18</sup> Table 2 reports the Pesaran CD test statistic and the exponent of cross-sectional dependence of the dependent and independent variables of the model, for both the advanced-country and the full sample. The CD test statistic for equity returns is above 100 for both samples, overwhelmingly rejecting the null. For the other variables, the statistic also provides evidence against weak dependence, although to a more limited extent. In both country samples, the highest CD statistic, aside from that of equity prices, corresponds to GDP growth.

Table 2: Cross-sectional dependence

|||Adv<br>|anced countries<br>||
|---|---|---|---|---|
||Equity returns|GDP growth|∆Real interest rate|Real credit growth|
|Pesaran CD statistic|104.788|13.091|11.340|7.905|
|Exponent of CSD|1.002|0.961|0.892|0.861|
||(0.905, 1.099)|(0.907, 1.015)<br>A|(0.823, 0.960)<br>ll countries|(0.822, 0.899)|
|Pesaran CD statistic|131.365|63.542|10.529|39.201|
|Exponent of CSD|0.983|0.973|0.829|0.941|
||(0.879, 1.085)|(0.839, 1.106)|(0.796, 0.862)|(0.892, 0.991)|

Notes: Equity returns are measured by the first difference of the log of real equity price indices, GDP growth is the first difference of the log of real GDP, ∆Real interest rate is the first difference of the real interest rate, and Real credit growth is the first difference of the log of the real credit stock. ’Exponent of CSD’ is the exponent of cross-sectional dependence, and values in parenthesis are its 95% confidence bands. The sample period covers 1995:1-2016:3.

Table 2 also reports the exponent of cross-sectional dependence along with 95% confidence bands, for both the advanced and full country samples. For equity prices, the estimated value of _α_ is 1 in the advanced-country sample and .98 in the full sample. In both cases, the 95% confidence region reaches well above 1, providing clear indication of the presence of strong common factors in the equity returns data.

The table also shows that the exponent of cross-sectional dependence of GDP growth is very close to 1 in both country samples, with the confidence region including unity in both cases. This agrees with the evidence that GDP growth around the world reflects a common factor (Kose, Otrok and Whiteman (2003)). Finally, for the interest rate and credit variables the estimated exponents of cross-sectional dependence are below .9, 18In a portfolio setting, the degree of cross-sectional dependence of asset returns can be viewed as a measure of the extent of risk (non-)diversification associated with an equally-weighted portfolio. More broadly, in a general factor model setting the exponent of cross-sectional dependence can be interpreted as the rate at which the factor loadings (fail to) die off as cross-sectional sample size increases, see Bailey, Kapetanios and Pesaran (2015).

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