4.2.4Hours Worked

Labor input (L) is represented by hours worked. It is the product of the number of full time equivalent employees (N) times the yearly sum of average weekly hours (H). Thus

Lits = Nits + Hits ; Lit = Nit + Hit ; Lts = Nts + Hts and Lt = Nt + Ht(4.29)

The Bureau of Labor Statistics (BLS 1999) provides data on the number of full time equivalent employees by 2-digit industries for the years 1977 to 1997 (N it). The corresponding number of average weekly hours was also obtained from BLS, but by 1-digit industry only. I assume that 1-digit industry average weekly hours can be used as a proxy for the more detailed 2-digit average weekly hours. Considering a year is constituted of 52 weeks, the yearly number of hours is equal to the weekly average hours times 52. This is the procedure I used to obtain data for variable H it. Finally, multiplying the number of employees (N it) by the number of hours (H it) gives data for annual aggregate industry labor input (L it). The corresponding national variable is obtained according to the following relation:

L t = Σi Lit.(4.30)

Problems arise once again when data for the state industry level (L its) are constructed. BLS provides data on variable N its for only 45% of my dataset (25,061 cases over 55,692), and on H its for 20% only. Thus, I need to find a procedure to estimate L its.

In order to do so, I use an approach similar to the one used to estimate K its, which is described in the previous section. I introduce the following hypothesis to be tested:

Lit / Yit ≅ Lits / Yits (4.31)

⇔Lits / Lit ≅ Yits / Yits (4.32)

I create variables PROPL and PROPY equal to the left hand side and right hand side of equation 4.32, respectively. Thus, I want to test whether these two variables are equal. To test this hypothesis, I use the 20% of data that are available for L its and I run a paired sample t-test on variables PROPLPROPY. Results appear in Table 4.5. They indicate that I can reject the hypothesis that these two variables have similar values at the 1% level (t-statistic is 23.32). Hence, the differences are significant but, on average, of moderate size. Thus, the assumption of equality might be a workable way forward, and the proportion of hours worked in industry i in state s (L its/ L it), is assumed to be equal to the proportion of output for that same industry in that same state (Y its/ Y it). I can then compute data for variable L its according to equation 4.32 since it is the only unknown variable in that equation. Finally, I obtain data on state labor variable (L ts) by simple aggregation of state industry labor variable such as:

L ts = Σi L its(4.33)

Table 4.5Significance of the Labor-to-Output Ratio Hypothesis
PROPL PROPY
Mean 0.0373 0.0317
Standard Error 0.00043 0.00038
N 11,138 11,138
Mean of Differences 0.0055
95% Confidence Interval of the Differences LowerUpper 0.0050.006
t-test for the differences = 0 23.32
Probability value (2-tailed) 0.000