**1. Introduction**

A seemingly unrelated regression (SUR) system, originally proposed by Zellner (1962), comprises multiple individual regression equations that are correlated with each other. Zellner's idea was to improve estimation efficiency by combining several equations into a single system. Contrary to SUR estimation, the ordinary least squares (OLS) estimation loses its efficiency and will not produce best linear unbiased estimates (BLUE) when the error terms between the equations in the system are correlated. This method has a wide range of applications in economic and financial data and other similar areas (Shukur 2002; Srivastava and Giles 1987; Zellner 1962). For example, Dincer and Wang (2011) investigated the effects of ethnic diversity on economic growth. Williams (2013) studied the effects of financial crises on banks. Since it considers multiple related equations simultaneously, a generalized least squares (GLS) estimator is used to take into account the effect of errors in these equations. Barari and Kundu (2019) reexamined the role of the Federal Reserve in triggering the recent housing crisis with a vector autoregression (VAR) model, which is a special case of the SUR model with lagged variables and deterministic terms as common regressors. One might also consider the correlations of explanatory variables in SUR models. Alkhamisi and Shukur (2008) and Zeebari et al. (2012, 2018) considered a modified version of the ridge estimation proposed by

Hoerl and Kennard (1970) for these models. Alkhamisi (2010) proposed two SUR-type estimators by combining the SUR ridge regression and the restricted least squares methods. These recent studies demonstrated that the ridge SUR estimation is superior to classical estimation methods in the presence of multicollinearity. Srivastava and Wan (2002) considered the Stein-rule estimators from James and Stein (1961) in SUR models with two equations.

In our study, we consider preliminarily test and shrinkage estimation, more information on which can be found in Ahmed (2014), in ridge-type SUR models when the explanatory variables are affected by multicollinearity. In a previous paper, we combined penalized estimations in an optimal way to define shrinkage estimation (Ahmed and Yüzba¸sı 2016). Gao et al. (2017) suggested the use of the weighted ridge regression model for post-selection shrinkage estimation. Yüzba¸sı et al. (2020) gave detailed information about generalized ridge regression for a number of shrinkage estimation methods. Srivastava and Wan (2002) and Arashi and Roozbeh (2015) considered Stein-rule estimation for SUR models. Erdugan and Akdeniz (2016) proposed a restricted feasible SUR estimate of the regression coefficients.

The organization of this paper is as follows: In Section 2, we briefly review the SUR model and some estimation techniques, including the ridge type. In Section 3, we introduce our new estimation methodology. A Monte Carlo simulation is conducted in Section 4, and our economic data are analysed in Section 5. Finally, some concluding remarks are given in Section 6.
