<u>1</u> _n_ where _G_ ( _η_ ) = _nT_ � _i_ = _r_ +1<sup>_μi_(</sup><sup>_S−_�</sup><sup>_K_</sup> _k_ =1<sup>_Zkδk_)(</sup><sup>_S−_�</sup><sup>_K_</sup> _k_ =1<sup>_Zkδk_)</sup><sup>_′_.TheQMLestimatoris</sup> derived from the optimization problem in equation (5). The estimate of the factor loadings Ψ is computed from the eigenvectors associated with the first _r_ largest eigenvalues of ( _S −_<sup>�</sup><sup>_K_</sup> _k_ =1<sup>_Zkδk_)(</sup><sup>_S−_�</sup><sup>_K_</sup> _k_ =1<sup>_Zkδk_)</sup><sup>_′_.</sup> The estimate of _FT_ is obtained analogously by switching _T_ and _n_ .

The QML estimator of the regression coefficients is consistent and asymptotically normal. However, it may be asymptotically biased owing to an incidental parameters problem, specifically due both to the presence of predetermined regressors (the lagged dependent variable) and to the interaction between the spatial effects and the factor loadings. To tackle this problem, Shi and Lee (2017) develop a bias correction that yields an asymptotically normal, properly-centered estimator. The estimations reported below using common factors employ the bias-corrected estimator.

# **3 Data**

We assess the international comovement of equity returns using a balanced panel data – set comprising 40 advanced and emerging countries over 1995:1 to 2016:3 a total of 3,480 quarterly observations. Because advanced countries tend to exhibit higher real and financial openness, as well as larger and more liquid financial markets, than other countries, we consider separately a subsample of 25 advanced economies, comprising 2,175 observations. Table A1 in the appendix provides the complete list of countries.

Following Hirata, Kose, Otrok and Terrones (2013), we measure equity prices by the stock market price index for each country. Real equity returns are then given by the first difference of the log of equity prices deflated by the consumer price index.<sup>9</sup> We collect the equity price index data from the OECD Statistics Database, except in the cases of Argentina, Hong Kong and Peru, for which we draw the data from Investing.com.<sup>10</sup> Figure 1 depicts the cross-country average of the real equity returns. It displays very similar fluctuations over the two country samples, including a sharp decline around the fourth quarter of 2008, at the onset of the global crisis.

As already mentioned, we consider three covariates of equity returns: real GDP, short term interest rates and private credit. The GDP data comes from the OECD Statistics Database and the International Financial Statistics (IFS) of IMF and complemented with national statistics sources as well as the Federal Reserve Bank of St. Louis Economic Data (FRED). Credit is measured by domestic credit to the private sector, drawn from DataStream, complemented with FRED and the Bank for International Settlements (BIS). All the variables are measured in real terms, using the consumer price index as deflator.

> 9An alternative would be to express equity returns in nominal terms in a common currency – e.g., U.S. dollars. However, this would automatically introduce additional commonality in the returns across countries, reflecting the movements in the exchange rate of the currency in question. To avoid it, we opt for working with real returns instead.

> 10For Argentina we use the Merval stock price index, for Hong Kong we use the Hang Seng stock market index, and for Peru we use the S&P/BVL Peru General Index.

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