Corporate taxes and the demand for labor and capital in developing countries

Abstract

This article provides evidence about the impact of corporate taxation on both labor and capital demand by private companies in a developing economy, using firm level data from Chile. Our results show that higher corporate tax rates reduce not only the demand for capital, but also the demand for labor due to complementarities between both inputs. An interesting element of the results presented in this article is the asymmetry between the effects of taxation according to company size. The impact on labor demand is significantly higher in large corporations than in small enterprises, while the demand for capital is more responsive to corporate tax changes in small firms. We can explain these results based on differences in credit constraints according to firm size.

Appendix

1.1 A. Measuring the capital stock and depreciation rate

The construction of the capital stock in the micro dataset follows a reversal version of the perpetual inventory method. Let us define:

• S = buildings (e), machinery (m) or vehicles (v);

• $K^{s}_{{it}}$ = capital stock type s of firm i at year t;

• $I^{s}_{{it}}$ = investment type s of firm i at year t;

• δ^s = type s depreciation rate.

Our dataset has available data on annual investment plus capital stock at the end of the sample. Capital stock data in other periods might be missing. In order to construct the series of capital stock in each firm, we assume the following annual depreciation rates:

• δ^e: buildings, 2%;

• δ^m: machinery, 8%;

• δ^v: vehicles, 15%.

We assume that the capital stock type s in a firm follows the traditional law of motion:

$$ K^{s} _{{i(t + 1)}} = K^{s} _{{it}} {\text{ (1}} - \delta ^{s} )\,+\,I^{s} _{{it}} {\text{.}} $$

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Also, let T be the final period of our sample; as we have available $K^{s}_{{iT}}$, we may obtain $K^{s}_{{iT - 1}}$ as follows:

$$ K^{s} _{{iT - 1}} = (K^{s} _{{iT}} - I^{s} _{{iT - 1}} )/(1 - \delta ^{s} ). $$

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By recursion, we may obtain the sequence of capital stock as in:

$$ K^{S}_{{it}} = {\left( {\frac{1} {{1 - \delta ^{s} }}} \right)}^{{T - t}} K^{S}_{{it}} - {\sum\limits_{j = T - 1}^t {{\left( {\frac{1} {{1 - \delta ^{s} }}} \right)}^{{T - j}} I^{S}_{{ij}} } }. $$

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Once we obtain the series of each type of capital stock per firm, we obtain the total capital stock per firm by adding up the all the types of capital as in:

$$ K_{{it}} = K^{e} _{{it}} + K^{m} _{{it}} + K^{v} _{{it}} . $$

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The average depreciation rate is calculated as:

$$ \delta _{{it}} = [(E_{{it}} *\delta ^{e} ) + (M_{{it}} *\delta ^{m} ) + (V_{{it}} *\delta ^{v} )]/(E_{{it}} + M_{{it}} + V_{{it}} ); $$

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where E _it , M _it , V _it are capital stock in buildings, machinery and vehicles in year t, respectively.

1.2 B. The reduced form equations

This section presents the cost-minimization problem faced by the firm. We assume the firms use labor, capital, and an imported intermediate good in the production of the final good. The firm has a Cobb-Douglas production function of the form

$$ Y = AK^{{\alpha _{K} }} L^{{\alpha _{L} }} M^{{\alpha _{M} }} , $$

where Y, K, L and M are output, capital, labor, and an intermediate imported good. Let w, c, and x denote the wage, the cost of capital and the price of the imported good. Following the user cost of capital approach we assume the cost of capital is given by $c = {\left( {r + \delta - {\left( {p^{e}_{{t + 1}} - p_{t} } \right)}} \right)}{\left( {1 - \tau } \right)},$ where r is the relevant interest rate, δ is the depreciation rate, $p^{e}_{{t = 1}} - p$ is the expected capital gain and τ correspond to the corporate tax rate. Then, we can write the following cost minimization problem of the firm:

$$ {\mathop {\min }\limits_{K,L,M} }cK + wL + xM\quad {\text{Subject}}\,{\text{to}}\;Y = AK^{{\alpha _{K} }} L^{{\alpha _{L} }} M^{{\alpha _{M} }} ; $$

with the associated first-order conditions:

$$ \begin{aligned}{} & \frac{w} {c} = \frac{{\alpha _{L} K}} {{\alpha _{K} L}}; \\ & \frac{w} {x} = \frac{{\alpha _{L} M}} {{\alpha _{M} L}}. \\ \end{aligned} $$

Rearranging the first-order conditions and replacing them into the production function leads to the following labor demand equation:

$$ \log \,L^{d} = \beta _{0} - \beta _{1} \log \,w + \beta _{2} \log \,c + \beta _{3} \log \,x + \beta _{4} \log \,Y; $$

where

$$ \begin{aligned}{} & \beta _{0} = { - {\left( {\log \,A + \alpha _{K} \log \frac{{\alpha _{K} }} {{\alpha _{L} }} + \alpha _{M} \log \frac{{\alpha _{M} }} {{\alpha _{L} }}} \right)}} \mathord{\left/ {\vphantom {{ - {\left( {\log \,A + \alpha _{K} \log \frac{{\alpha _{K} }} {{\alpha _{L} }} + \alpha _{M} \log \frac{{\alpha _{M} }} {{\alpha _{L} }}} \right)}} {{\left( {\alpha _{L} + \alpha _{K} + \alpha _{M} } \right)}}}} \right. \kern-\nulldelimiterspace} {{\left( {\alpha _{L} + \alpha _{K} + \alpha _{M} } \right)}}; \\ & \beta _{1} = {{\left( {\alpha _{K} + \alpha _{M} } \right)}} \mathord{\left/ {\vphantom {{{\left( {\alpha _{K} + \alpha _{M} } \right)}} {{\left( {\alpha _{L} + \alpha _{K} + \alpha _{M} } \right)}}}} \right. \kern-\nulldelimiterspace} {{\left( {\alpha _{L} + \alpha _{K} + \alpha _{M} } \right)}}; \\ & \beta _{2} = {\alpha _{K} } \mathord{\left/ {\vphantom {{\alpha _{K} } {{\left( {\alpha _{L} + \alpha _{K} + \alpha _{M} } \right)}}}} \right. \kern-\nulldelimiterspace} {{\left( {\alpha _{L} + \alpha _{K} + \alpha _{M} } \right)}}; \\ & \beta _{3} = {\alpha _{M} } \mathord{\left/ {\vphantom {{\alpha _{M} } {{\left( {\alpha _{L} + \alpha _{K} + \alpha _{M} } \right)};}}} \right. \kern-\nulldelimiterspace} {{\left( {\alpha _{L} + \alpha _{K} + \alpha _{M} } \right)};} \\ & \beta _{4} = 1 \mathord{\left/ {\vphantom {1 {{\left( {\alpha _{L} + \alpha _{K} + \alpha _{M} } \right)}.}}} \right. \kern-\nulldelimiterspace} {{\left( {\alpha _{L} + \alpha _{K} + \alpha _{M} } \right)}.} \\ \end{aligned} $$

Finally, replacing c and using the approximation log(1 − τ) ≈ −τ, we obtain the conditional labor demand function, Eq. 6 in the text, as in:

$$ \log \,L^{d} = \beta _{0} - \beta _{1} \log \,w + \beta _{2} \log {\left( {r + \delta } \right)} + \beta _{3} \log \,x + \beta _{4} \log \,Y - \beta _{5} \tau . $$

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In Eq. 6 we assume that there are no capital gains. This assumption is necessary because we do not have such data for each firm in our microeconomic dataset.