The horizontal line on the graphs marks the U.S. level of multifactor productivity. As the graph shows, the underlying relationship between multifactor productivity (MFP)and tax wedge is fitted with quadratic equation. Total tax wedge explains about 34.5 percent of the variation in multifactor productivity index across OECD countries. The trend exerts a decreasing MFP as the tax wedge rises and, after reaching a local minimum, a slight increase alongside the proporional rise in tax wedge. The relevant question is at which rate of tax wedge the MFP reaches the minimum. Setting the first-order derivate to zero (dy/dx=0) yields 0.0016x-0.0488=0. Rearranging the equation yields x=30.5. The first-order derivative implies that MFP reaches the minimum at 30.5 percent tax wedge. The estimate sample-based tax elasticity of productivity ((dy/dx)(x/y)) is 1.78. The elasticity indicates that 1 percentage point increase in tax wedge would reduce the multifactor productivity in a sample country by 1.78 percent, ceteris paribus. In other words, the estimated slope coefficient suggests that a 1 percentage point increase in tax wedge would widen the MFP gap between the average country and the US by additional 0.05 index points.
In economic terms, MFP would decrease as long as the countries in the sample would exert less than 30.5 percent tax wedge. In the horizon after the local minimum (30.5 percent), MFP would initially increase but at a smaller rate than before the function would reaches the minimum point. At 20 percent tax wedge (close to Japanese level), the expected decrease in MFP would be 0.0168 index point. At 40 percent tax wedge, the expected increase in MFP would be 0.0152 index point. Economically, the relationship between MFP and tax wedge should not be interpreted as a mixed effect of tax wedge on MFP. In countries, where tax wedge exceeds 30.5 percent (Austria, Denmark, Sweden, Belgium etc.) , the multifactor productivity is close to the U.S. level. The only country with higher MFP level than the United States is Luxembourg. In these countries, the average number of annual hours worked per worker is lower than in the U.S. Hence, hourly productivity output is higher. The following graph illustrates the relationship between annual hours worked (per worker) and MFP level.
Average annual hours worked per worker and multifactor productivity relative to the US
As the graph illustrates, there is a negative relationship between average annual hours worked and MFP. The estimated regression coefficient suggests that an increase in annual hours worked by 100 hours would reduce MFP level (compared to the U.S) by 0.06 index points. As expected, the implied elasticity of productivity is negative. Taking the average values ov both variables, an increase in average annual hours worked (per worker) by 1 percent would reduce the MFP relative to the U.S level by 1.16 percent, ceteris paribus.
The conclusion is that there is a significant and negative impact of tax wedge on multifactor productivity. Taking the differences in annual hours worked into account, tax wedge alone explains almost 35 percent of the differential in multifactor productivity across the OECD. The findings suggest that there is a relatively strong substitution effect in labor supply. The finding is underlined by the fact that higher tax wedge would correspondingly reduce annual hours worked. However, the interpretation should be taken with a grain of warning. As previous empirical studies have shown, there is a widespread disparity in the distribution of working hours in formal and household sector of the economy. A sizeable proportion of working hours in household sector of the economy is not officially measured. Consequently, a blick of distortion of the real relationship between labor supply and tax wedge, in its broadest sense, is a major impediment to the measurement of labor supply dynamics. These estimates will, in a large part, determine the future research of the effect of taxation on labor productivity.
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