The competitiveness of national economies is increasingly dependent on their ability to produce and use knowledge, as knowledge, education, and innovation are the main indicators of economic growth in a globalizing world. Many countries have adopted policies related to the production of knowledge and its transformation into wealth that stimulates the growth and competitiveness of their economies. Through our study, we measured some knowledge economy (KE) variables for a sample of 20 developing countries. During the period (1996–2020), using panel data, the estimate was made using three models: the cumulative regression model, the fixed-effects model, and the random-effects model. The results of the statistical tests indicated that the fixed-effects model is the appropriate model, and that the estimates of the proposed model parameters do not contradict the assumptions of economic theory, nor do they contradict the practical reality. In addition, the results showed that 93% one of the changes that occur in economic growth in the developing countries under study is due to the dependence on the knowledge economy. It became clear through the study that the use of cross-sectional time-series models increases the accuracy of statistical forecasting, because it considers the information with a time dimension in the time series, as well as the cross-sectional dimension in different units. Our study found a positive impact on economic growth of the internet and mobile phone users, control of corruption, political stability, foreign direct investment, and the total value of international trade. Additionally, spending on education, patents for residents, and trade openness had a negative impact on economic growth. Accordingly, the knowledge economy in developing countries contributed greatly to their economic growth and had a prominent role in maintaining high rates of growth for decades. Our study contributes by expanding the scope of developing countries in deciding to focus on the important indicators in the knowledge economy (KE), so that they can increase the added value of their economic growth.