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The transition to Industry 4.0 presumes the use of innovation potential which is also determined by the institutional environment, including the level of corruption and its perception. The post-communist countries of Central and Eastern Europe are characterized by a higher level of corruption and higher share of the shadow economy, which can fundamentally reduce their innovation potential and thus become the brake on the transition to Industry 4.0. The aim of this paper is thus to evaluate the effects of corruption in public administration on the size and structure of the shadow economy, and to determine whether the existence of corruption may affect the transition of a country and society to Industry 4.0. Based on an extended DSGE (Dynamic Stochastic General Equilibrium) model and using the data for the Czech Republic, the paper finds that corruption in public administration has a much more destructive and long-term effect on the capital accumulation than on the size of the workforce. In that sense, corruption can become a significant obstacle to the transition, underlining that the task of public policies is not only to support digitization, robotization, and further development of technologies, but especially to ensure a transparent non-corrupt environment of public administration.