If real GDP declined for several years, the capital-to-labor ratio will increase. Let's examine the reasons why.
First, we'll define real GDP. It's the value of all the goods and services produced by an economy, expressed in base-year prices. Real GDP has also been adjusted for inflation, and it lets us know how well an economy is really doing. Basically, real GDP lets governments know what a currency's purchasing power is. For example, what is the amount of goods and services one unit of money can buy? If the purchasing power of a currency falls, then consumers will buys less. So, falling real GDP can lead to a recession.
Now, for the capital-to-labor ratio. A high capital-to-labor ratio means that companies are favoring capital over labor. In a recession (when real GDP continues to decline), companies are motivated to automate many of their more labor-intensive tasks. This will save on labor costs (employee wages and benefits) and perhaps, keep the company competitive through a rough economic period. Today, there is furious debate about whether robots will take all of our jobs in the ensuing decades. Read U.S. News' article: Are Robots Taking Our Jobs?
The capital-to-labor ratio is calculated by dividing fixed assets over direct labor (fixed assets/ direct labor). When real GDP continues to decline, companies will look to shore up on their capital investments, and they will hire fewer workers (labor). So, the numerator of the equation (fixed assets) will rise, while the denominator of the equation (labor) will fall. This will lead to a higher capital-to-labor ratio.
To reiterate, if real GDP declines for several years, this will lead to a higher capital-to-labor ratio.
The capital to labor ratio is a measurement that compares the amount of capital present in the economy to the amount of labor. When the amount of capital rises, the value of the ratio rises if the amount of labor does not rise by a similar amount. When the amount of labor rises, the value of the ratio falls if the amount of capital does not rise by a similar amount.
During a deep recession (when real GDP has been declining for several years), the labor force generally becomes smaller. This has certainly been the case (as seen in this link) during the recent “great recession.” If the labor force shrinks, the denominator of the capital to labor ratio gets smaller. If the denominator gets smaller and the numerator (amount of capital) does not fall by a similar amount, the value of the ratio as a whole will increase. During a recession, the amount of capital in the economy does not rise as quickly as it would in good times. However, it should not fall by a tremendous amount because capital does not tend to disappear quickly. Therefore, in a prolonged recession, we should expect to see a gradual decline in capital and a deep decline in labor. This means that the capital to labor ratio will increase in this situation.