Question

The Labor Share and Data The production function is Cobb-Douglas, Y = F (K, L) = ĀKαL1−α with Ā = 1, depreciation of δ = 0.07 savings rate of 20% and population growth of 1%.

1. Suppose you have data on the total payments to labor and GDP, take the ratio of labor payments over GDP, (wL)/Y, and show the parameter in the model this corresponds to. To answer this, you will have to use the perfect competition assumption that gives us w = [∂F (K,L)] / ∂L.

2. Suppose that instead of Ā being constant, At is growing at a 1% rate. Can you still use (wtLt) / Yt to get the model parameter? What, if any, change to the algebra above do you need to do?

3. In https://fred.stlouisfed.org search for “National income: Compensation of employees,” divide it by “Gross Domestic Product” and plot it. This is pretty close to the number we are looking for, eh?

4. But what’s missing? The line you just found from the data should be a bit lower than the one I showed you in class. The answer is that self- employed people are also part of “labor” but not part of compensation of employees. Suppose that 10% of workers are self employed and they have the same production function. This means your line only shows 90% ofwL. How will this change your estimate of that crucial model parameter from section 1?

Answer 1