… Rees's (1963, 1989) seminal work examining the effect of unionization on resource allocation provides a theoretical framework to explore the relationship between minimum wage increases and output. Higher minimum wages are likely to affect GDP ...

Sabia, J. J. (2015). Minimum wages and gross domestic product. Contemporary Economic Policy, 33(4), 587-605.

… regional minimum wages in that year was more than 17%, while the real average wage rose by around 13% and real per capita GDP by around 3.5%. ...

Suryahadi, A., Widyanti, W., Perwira, D., & Sumarto, S. (2003). Minimum wage policy and its impact on employment in the urban formal sector. Bulletin of Indonesian economic studies, 39(1), 29-50.

...In this study we investigate the effect of different price indices on the relation between real GDP growth rates and real minimum wage growth rates …

Sunal, O., & Alp, O. S. (2016). Effect of different price indices on linkage between real GDP growth and real minimum wage growth in Turkey. Journal of Economic & Financial Studies, 4(01), 01-10.

Economic theory suggests that the macroeconomic effect of minimum wage increases on gross domestic product (GDP) is ambiguous. Minimum wage increases may increase labor costs and output prices, reduce firms' profits and job training, and cause adverse employment and hours effects, each of which may reduce in GDP...

Do minimum wages stimulate productivity and growth?

https://wol.iza.org/uploads/articles/221/pdfs/do-minimum-wages-stimulate-productivity-and-growth.pdf

Supporters of the minimum wage say it increases the standard of living of workers, reduces poverty, reduces inequality, and boosts morale. In contrast, opponents of the minimum wage say it increases poverty, increases unemployment because some low-wage workers "will be unable to find work...

Minimum wage - Wikipedia

Thank you so much Gayan for your explanations.

Thank you Mukhlif for your contribution.

Wage is indeed the price for labor. This, minimum wage should not be increased when the value of labor, denoted by productivity, does not increase. Otherwise, just like with other commodities, we just reduce the value of money and heighten inflation. The higher the increase of minimum wage and number of workers, the higher the inflation could be. As a result, increasing minimum wage without improving productivity may increase nominal GDP. However, real GDP may still be unchanged.

Furthermore, increased minimum wage would surely improve workers purchasing power and raise demand. As the level of productivity remains unchanged, aggregate production would stay the same. Increased demand would only induce higher inflation. Living standard of workers may improve after the increase of minimum wage, yet eventually the inflation may exhaust that improvement. Then again, nominal GDP may increase while real GDP may not.

In view of this, increasing minimum wage should be accompanied by increasing labor productivity. In other words, workers need to increase value added of the products to earn higher wage. This can be achieved by providing education/training, improving production methods as well as acquiring higher technologies. Then, we may see nominal and real GDP increased.

Thank you so much Mr.Yudhi for your valuable contribution.I really appreciate. However, the question of wags increasing or not, there is no consensus on the answer on by which to begin. Increasing wages first or increasing productivity/perfomance.

When considering motivation theories, employees give the best of their best when they are motivated.

Best.

Governments usually take increasing minimum wage and increasing productivity as separate policies. Increasing minimum wage is often considered as short term policy, while increasing productivity is seen as medium/long term policy. Many governments increase minimum wage annually to preserve workers purchasing power from inflation of the preceding year. As the increased minimum wage contribute to inflation of the ongoing year, it is infact a vicious circle.On the other hand, improving productivity requires investment for providing education/training and acquiring new technologies. Governments of developing countries concurrently pursue both policies.

The answer to this question is truly ambiguous. There is a set of arguments on both sides supported by theoretical/empirical literature. I believe that conducting empirical research at the country/region/industry level will give us a relatively precise answer… but as far as we are just sharing our opinions here, I believe in the following:

First, businessmen will always try to increase profit, and any policy “threatening” to achieve this goal won’t make them happy. Accordingly, I support the argument that increasing the minimum wage will decrease the profitability of firms due to the increased labor cost. As a response, firing a few employees will do a trick (and/or increased prices or reduced working hours). In this context, losing jobs is expected at a lower level of management and/or low-skilled labor within the organizations. Hence, we got workforce reduction that won’t help GDP to grow (and/or mitigate the severity of poverty/income distribution).

Second, increasing the minimum wage is partially perceived to stimulate worker productivity that by itself complements economic growth. Although it can be true, there are better ways to foster productivity than simply increasing the minimum wage. e.g. performance-based salary that can motivate employees to earn more by working harder/efficiently, thus, stimulating the growth of aggregate output. The list of alternative ways to increase productivity is long enough.

Third, if the real value of an employee is equivalent to what (s)he does, then why to increase the wage for them? Isn’t it better to think about raising our qualification with or without external help and get paid accordingly?

In the end, I believe that it all depends on a firm’s response to the changes, along with the level of these changes. For instance (rough comparison),” in the late 20th century, the U.S. government imposed harsh regulations on pulp and paper industry to reduce environmental damage, while Scandinavian countries adopted similar regulations but more flexible in its essence. As a result, U.S. firms spent more money and time on lawyers to fight against the regulations, find alternative ways to avoid increasing production costs, etc. Basically, everything but innovation/R&D activities. Meanwhile, in Sweden, firms succeed to adopt innovative environmentally friendly technologies and raised the competitiveness of the industry. The reason was the flexibility and/or reasonable deadlines to comply with the regulation changes” (Porter et al. 1995). In the same way, the increasing minimum wage can be roughly interpreted as U.S. type regulations mentioned above, especially for small and medium-size firms in developing countries where management in small businesses is non-existent or let’s say management is just formality (entrepreneurs run their businesses as simple as just buying and selling without proper organizational management/strategic planning). When we deal with these types of firms on a large scale, we cannot expect from them a rational/adequate decision-making process to meet the local/global political/economic challenges. It’s kind of same as designing economic models by assuming mostly rational economic agents, while in practice we have plenty of quasi-rational agents as described in Thaler (2000). These quasi-rational agents and/or above-mentioned entrepreneurs are making simple decisions: Minimum wages increased so let’s increase prices/fire a few employees/increase working hours. Either of it won’t be efficient to stimulate aggregate output growth… But finding the ways to educate society to be more competitive in the labour market, give access to the local/foreign market information to firms to help them expand beyond their comfort zone/keep up with market trends, promote R&D activities, etc is more beneficial for sustainable economic growth.

However, the question is so multidimensional that it’s extremely hard to give a satisfactory answer… as in every research, there is always big bald “but”…

P.S. I apologize for the long and boring answer, it's just my subjective view that I would take into consideration if I were doing research on the topic.

I think it is one of the tools that any government takes in short run to encourage workers to be indulged in productivity. By the end of the day if productivity increases it brings it will definitely increase productivity and hence GDP, but usually it does not happen.