Do exchange rates affect the capital–labour ratio? Panel evidence from Canadian manufacturing industries

Abstract

Using industry-level data for Canadian manufacturing industries from 1981 to 1997, we find empirical evidence of a negative relationship between the capital–labour ratio and the user cost of capital relative to the price of labour. A 10% increase in the user cost of the Machinery and Equipment (M&E) relative to the price of labour results in a 3.3% decrease in the M&E–labour ratio in the long run. Assuming complete exchange rate pass-through into imported M&E prices, the maximum effect of a permanent 10% depreciation in the exchange rate is a 1.7% decline in the M&E–labour ratio. This result implies that the cumulative growth of the M&E–labour ratio during the 1991 to 1997 period would have been 2.3 percentage points higher had the dollar not depreciated. This may appear to be significant, but considering both M&E as a share of total capital and the capital share of nominal output are both approximately one-third, in terms of a simple growth accounting framework, the effect on labour productivity is small.

Notes

¹ See, for example, Oliner and Sichel (2000) and Stiroh (2001).

² See Dupuis and Tessier (2000).

³ They find conflicting evidence on employment adjustments to exchange rate movements for the US and Japan manufacturing industries.

⁴ They find supportive evidence that investment sensitivity to exchange rate movements varies positively to revenue channels.

⁵ Other empirical articles have used panel cointegration techniques to estimate long-run effects of exchange rate changes on input demand. See for example, Chakrabarti (2003) and Hatemi-J and Irandoust (2006) in this journal. However, these articles also focus on one factor input at a time.

⁶ Two other propositions discussed in Lafrance and Schembri (1999–2000) are the Balassa–Samuelson model and the hypothesis of exchange rate sheltering.

⁷ One might argue that changes in the capital–labour ratio, particularly capital deepening in Information and Computer Technology (ICT), would have an indirect impact on labour productivity through the total factor productivity channel. Recent studies suggest that there exists a positive correlation between ICT investment and total factor productivity growth (e.g. Nordhaus, 2002; Parham, 2002). As noted, we assume that total factor productivity is exogenous in our framework.

⁸ The measure of the user cost of capital used in the empirical section of this article takes taxes and investment credits into account. The Appendix shows the expression for the user cost that includes these considerations. User cost not including taxes is shown here for simplicity only. It does not affect the arguments made in this section.

⁹ If imported and domestic capital are substitutable, then the effect of an exchange rate depreciation on the capital–labour ratio would be lessened as firms substitute towards both labour and domestic capital.

¹⁰ Hamermesh and Pfann (1996) provide an extensive survey of the literature on dynamic factor demands.

¹¹ It is straightforward to extend this model to flexible inputs; the extension does not change the main results hereafter.

¹² For example, when labour is flexible with θ _L = 0, the demand for capital at t is a simple linear combination of it is not related to other inputs, . Moreover, the adjustment to the long-run equilibrium follows a constant convergence rate: , where α = (1 − v).

¹³ In general, V is not a diagonal matrix, except in some restrictive production functions.

¹⁴ This is appropriate as long as the deviations of L, K, from some average levels are small. Note that, for any x, if is small.

¹⁵ The manufacturing industries are according to the 1980 Standard Industrial Classification (SIC). The original classification includes 22 manufacturing industries. The refined petroleum and coal products industry is excluded from our sample due to missing data. For details on each industry, see Table 1. The Canadian Productivity Accounts do include data for some other industries, but only the manufacturing sector is disaggregated into so many sub-industries. Given that the panel is relatively short, other industries were not examined.

¹⁶ See Harchaoui and Tarkhani (2002) for more detail on how capital input is constructed.

¹⁷ See Gu et al. (2002) for more detail on how labour input is constructed.

¹⁸ The capital–labour ratio for the 21 manufacturing industries is obtained by aggregating the growth rates of capital and labour separately. Capital growth rates in period t are aggregated using each industry's average nominal cost of capital for t and t − 1 as weights. The growth rate of labour input for the 21 manufacturing industries is similarly calculated. The difference in the aggregate capital and labour input growth rates is then used to create indexes. The relative price of capital for the 21 manufacturing industries is computed in the same way.

¹⁹ One such factor is aggregate demand: when it is weak, both the exchange rate and price of labour decline. The relative price of capital therefore increases for two reasons. First, the exchange rate depreciation increases the price of investment and user cost of capital. Second, the price of labour falls. In this situation, the movement in the relative price of capital can be greater than the exchange rate. In the empirical analysis that follows, demand conditions are accounted for and the relative price of capital is treated as an endogenous variable.

²⁰ Other methods of controlling for changes in the capital–labour ratio due to technological changes have been explored and do not change the conclusions of the article. Results using time-fixed effects, and time-fixed effects and industry-specific effects are available on request.

²¹ One-step GMM is used. Studies have shown that SEs from the two-step GMM are downward biased; thus, Arellano and Bond (1991) recommend the use of one-step GMM for inference.

²² For example, log(r/w) _{it− 2} is used as an instrument for Δlog(r/w) _it . In fact, any lagged level, log(r/w) _{it − j} , j ≥ 2, is a valid instrument. The Arellano and Bond estimates presented in this article use two lagged levels as instruments. The number of lags is restricted because introducing a large number of them leads to an ‘over-fitting’ problem, where the Arellano–Bond estimates tend to move towards the estimates from the within-groups OLS estimator.

²³ See Arellano and Bond (1991) for details on the Sargan test and the test for serial correlation.

²⁴ Although this test was suggested in the context of two-stage least squares, it should provide some indication of whether the instruments are weak in the GMM in a panel-data context.

²⁵ The system GMM estimator outlined in Blundell and Bond (1998) could have been used in place of the Arellano–Bond estimator if the instruments were found to be weak, but, given the size of the F-statistics in this case, it is not necessary. Furthermore, panel unit root tests suggest the capital–labour ratio series cannot be distinguished from a nonstationary series. The validity of using lagged levels as instruments in Blundell and Bond (1998) comes into question. These panel unit root tests, however, are known to lack power when the time-series element of the data is short, as is the case here. Potential problems can be avoided by using lagged differences as instruments, but the Arellano–Bond estimator with differenced instruments does not perform as well as the Arellano–Bond estimator with level instruments in small samples when the data are simply highly persistent. We compare estimates of long-run elasticities that use level instruments with those that use differenced instruments. The estimates (not reported) are found to be similar, and therefore, we provide in our main text only estimates that use level instruments.

²⁶ The results for different lag lengths are shown in Tables A-1–A-3 in the Appendix.

²⁷ The Appendix provides a more detailed description of the process. The expenditure weights used in Statistics Canada's Machinery and Equipment Price Indexes (MEPI) cannot be used, because, even for the post-1986 period, expenditure weights for 1979 to 1983 are used. See Statistics Canada (2003) for more detail.

²⁸ It would be preferable to perform the calculation at the more disaggregate L-level, but these data are not publicly available. Still, the approximation gives numbers similar to the ones calculated by Statistics Canada in the past. For example, Statistics Canada (1982) shows that the import expenditure weight in 1971 was 0.39, which is in line with the value of 0.41 computed using the M-level data. Furthermore, the weight derived from MEPI for the post-1986 period is 0.51. This is close to the value calculated using the M-level data for 1979 (0.49) and 1980 (0.48), but higher than the values in 1981 (0.43), 1982 (0.39) and 1983 (0.43).

²⁹ The imported share of machinery was not calculated for the years after 1997, because the input–output tables based on SIC end in 1997.

³⁰ There is no clear way of testing this assumption, because prices for imported M&E are generally US producer prices from the Bureau of Labour Statistics adjusted for exchange rates, taxes and custom tariffs. See Statistics Canada (2003) for more detail. These constructed imported M&E prices are used in Statistics Canada's calculation of the user cost of capital, which is subject to some error if pass-through is not complete. This measurement error may be another reason why the price of labour has a greater effect on the capital–labour ratio than the user cost of capital.

³¹ A simple way to confirm whether the estimated imported share of M&E is appropriate is to regress the growth in the price of M&E on the growth of the exchange rate. This yields a point estimate of 0.52 with 95% confidence interval bands at 0.45 and 0.60. Furthermore, a regression of the growth in the total price of capital on the growth of the exchange rate yields a point estimate of 0.23 with 95% confidence bands at 0.14 and 0.32. The fraction of imported M&E (0.52) multiplied by the average share of M&E in capital (0.34), 0.18 is within the above confidence bands.

³² The effect of the exchange rate on the M&E–labour ratio measured in this article is due solely to the change in the relative price of capital. Industry output is being held constant. As in the case of the total capital–labour ratio, we find that the long-run effect of industry output on the M&E–labour ratio is zero.

³³ Growth in labour input can be aggregated using the nominal cost of labour, and growth in capital services can be aggregated using the nominal cost of capital, but it is unclear how to aggregate growth in the capital–labour ratio.

³⁴ The predicted logged differences of the M&E–labour ratio cannot be obtained in 1981 and 1982. Therefore, the actual logged differences are used in their place.

³⁵ Since M&E is only one-third of total capital, the total K/L ratio would be only 1.5 percentage points higher in 1997. Furthermore, given that capital's share of nominal Gross Domestic Product (GDP) is one-third, a simple growth accounting framework would suggest that labour productivity would be only 0.5 percentage points higher.

³⁶ A formal way to test this hypothesis is to decompose the user cost into permanent and transitory components using some statistical procedure, such as the Beveridge–Nelson decomposition. In theory, higher estimates of the long-run elasticity would be expected if the observed user cost were replaced by its permanent component. Since only 17 years of annual data are available, such decomposition may not be reliable.

³⁷ The mean of the coefficient of variation across industries is 0.18 for wages and 0.38 for the user cost of capital over the sample period.

³⁸ All the regressors are treated as endogenous. As in the previous regressions, the Sargan test suggests that the moment restrictions are valid, no second-order serial correlation in the error term is found, and the instruments are sufficiently correlated to the regressors. Auxiliary regressions of the regressors on two lagged levels yield F-statistics of 11.29, 26.64 and 29.16 for the user cost of capital, price of labour and price of output, respectively.

³⁹ The effect of the exchange rate can vary across appreciations and depreciations because exchange rate pass-through can be asymmetric. See Yang (2007) for an explanation on how pass-through can be asymmetric.