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Annex 1
Description of Regression Models and Results

Standard Regression Using Annual Data

The regression model used to estimate the impact of the 2001–2004 corporate income tax rate reductions on investment is specified as follows:

finance - image


Ii,t = investment by the ith industry during year t in millions of 1997 dollars

Ki,t = capital stock of the ith industry at the end of year t in millions of 1997 dollars (estimated based on straight line depreciation)

UCCnti,t = the non-tax component of the user cost of capital for the ith industry in year t (per cent reduction in return from investment)

TWi,t = the tax component of the user cost of capital for the ith industry in year t, or the "tax wedge" (per cent reduction in return from investment)

Yi,t = gross domestic product of the ith industry in year t in millions of 1997 dollars


i = industry dummy variable for the ith industry


t = time dummy variable for year t

ei,t = error term for the ith industry, year t

Data for investment (I), capital stock (K) and output (Y) are from Statistics Canada.

The user cost variables, UCCnt and TW, were constructed at the Department of Finance. A substantial amount of data was required to calculate these variables—for example, output and investment goods prices, interest rates, depreciation rates, capital cost allowance rates, investment tax credit rates, corporate income tax rates, capital tax rates and sales tax rates. Some of these tax and economic variables are asset and time specific. For example, depreciation rates differ by types of assets, investment tax credits are available in some parts of the country but not in others and tax rates changed over time. Thus these inputs to the UCC and TW variables had to be assembled on an industry-by-industry and year-by-year basis using information on the provincial location and asset mix of each industry.

The investment behaviour of firms is more likely to be affected by the expected than the current value of the UCC and its tax component, or the tax wedge. In most cases, user cost parameters, such as inflation or interest rates, are uncertain so it is assumed that firms form their expectations based on current values. But in the case of tax changes, firms are more likely to react to announced tax changes, provided they are credible. Further, given the long lead times associated with many investments, firms will react to announced tax reductions well before they occur.

In this study, the tax wedge is calculated by including the present value of the corporate income tax rate reductions in each year. For example, in the February 2000 federal budget, a 1-percentage-point reduction in the corporate income tax rate, effective January 1, 2001, was announced. The user cost was therefore updated starting March 2000 to reflect the present value of the coming tax reduction. The same approach was applied for October 2000 to reflect the impact of additional corporate income tax reductions to be phased in from January 1, 2002 to January 1, 2004. As a result, although the major reductions became effective between 2002 and 2004, the largest impact on the tax wedge occurs in late 2000, when the announcement took place. Since the announcement was made late in the year, only a small portion of these discounted reductions are captured in the annual user cost for 2000, with much of the adjustment coming in 2001.

The estimation results are reported in Table A1.1. Results are reported for four different, progressively more elaborate, versions of the model as described in the table notes.

"Dummy" variables are included in versions 3 and 4 to capture the impact of industry-specific influences on the average level of investment of each industry. Certain industries may persistently have higher investment growth than others, due to differing depreciation rates for example, regardless of output and the user cost.

Time "dummies" are included in version 4 to acknowledge that certain common, contemporaneous influences may have affected all industries in particular years, such as the cyclical state of the economy. Their estimated coefficients are not reported here in the interest of conserving space. Statistical tests confirm that inclusion of both industry and time dummy variables in the regression is appropriate.[9]

Table A1.1
Regression Results—Annual Data

  Regression Models
  Version 1 Version 2 Version 3 Version 4

Explanatory Variables Coefficients
Intercept 0.215 0.1881 0.197 0.1191
  (0.015) (0.012) (0.066) (0.037)
Non-tax component of the user cost of -0.072 -0.118 -0.012 -0.3271
 capital (per cent change) (0.075) (0.074) (0.066) (0.112)
Tax component of the user cost of capital -0.135 -0.164 -0.1572 -0.3133
 (per cent change) (0.104) (0.107) (0.094) (0.151)
Output growth   0.5691 0.4591 0.104
    (0.168) (0.146) (0.135)
Proportion of variance explained (R2) 0.06 0.11 0.12 0.28

Version 1—UCC (tax and non-tax components) only explanatory variables.
Version 2—UCC (tax and non-tax components) + output growth.
Version 3—UCC (tax and non-tax components) + output growth + fixed industry effects.
Version 4—UCC (tax and non-tax components) + output growth + fixed industry effects + time dummies.
Number of observations = 301.
Robust standard errors in parentheses.
Dependent variable is real investment as a ratio of end-of-period capital stock.
1 Significant at 1-per-cent level.
2 Significant at 10-per-cent level.
3 Significant at 5-per-cent level.

An advantage of using panel data is that it is possible to control for unobservable industry- and time-specific effects on investment, such as a higher trend rate of investment and general cyclical conditions. However, there is still a possibility that variables that may help explain time-series variation in investment have been omitted, which could result in biased estimates of the coefficients on the included variables.[10] For example, if the regression equation leaves out an important determinant of investment and this variable is correlated with the tax wedge, the coefficient on the tax wedge will be biased since it indirectly captures the effect of the omitted variable. An omitted variable is by definition part of the error term, so in this example a potential problem could be identified by checking if the tax wedge is correlated with the error term. Statistical tests reject the hypothesis that the tax wedge is correlated with the error term.[11]

It is also important that the statistical significance of the coefficient estimates, as indicated by their standard errors, be measured without bias, in order to avoid drawing erroneous conclusions about the relationship between the explanatory variables and investment. Two conditions are required to obtain unbiased standard errors: that the residuals have constant variance and that they be uncorrelated with each other. Statistical tests reject the hypothesis of constant variance and no serial correlation in the errors at the 5-per-cent level of significance. The reported standard errors are adjusted to correct for these problems.

Since the industries in the data set vary substantially by size, it is possible that the estimated coefficient on the tax wedge is not accurately capturing the impact on aggregate investment. For example, it is possible that only the small industries in the data set responded favourably to the tax reduction, with the result that the impact on aggregate investment is much smaller than implied by the estimated coefficient. This possibility was tested by including small and large industry interaction variables on the tax wedge in the regression equation. The estimated coefficients were not statistically different for large and small industries.

The results confirm the strong and statistically significant influence of taxes on investment. The coefficient estimate on the tax wedge indicates that a 10-per-cent reduction in the tax wedge is associated with an approximately 3-per-cent increase in the real capital stock.[12] There is only a 1-per-cent probability that the true value of the coefficient on the tax wedge is zero and a 5-per-cent probability that the true value of the UCC coefficient is zero. As discussed below, however, it was not possible to model adequately the response of investment over time to a change in the tax wedge, which likely causes the annual model to understate the impact of tax reductions on investment.


The difference-in-differences (DD) approach directly exploits the natural experiment nature of the corporate income tax rate reductions: some industries (i.e. services) were affected by the tax changes while others (i.e. manufacturing) were not. The study uses regression analysis to examine whether the difference in investment performance between affected and unaffected industries changed as a result of the tax reductions.

The previous regression approach considered each of the years in the sample interval as giving rise to a separate observation; the DD regression analysis used here looks at two periods only—before the tax reductions were announced (1997–1999) and after (2000–2004). Industry-by-industry differences in the growth rate of the capital stock before and after the tax reductions were regressed on the corresponding percentage changes in the tax wedge along with additional control variables to capture other factors that may have caused growth in the capital stock in the affected industries to vary relative to the unaffected industries. These control variables include the relative price of capital, output growth, industry fixed effects as well as a "catch-all" post–tax reduction dummy variable.

The tax component of the UCC has a large, statistically significant impact on the capital stock, implying that the tax reductions provided a strong stimulus for investment (Table A1.2). A 10-per-cent reduction in the tax wedge is associated with an approximately 7-per-cent increase in the capital stock.

Table A1.2
Difference-in-Differences Regression Results

  Regression Models
  One Two

Explanatory Variables Coefficients
Tax component of the user cost of capital -0.7271 -0.7082
 (per cent change) (0.218) (0.266)
Post–tax cut period dummy 0.0242 0.016
  (0.013) (0.025)
Output growth   -0.099
Relative price of capital (per cent change)   -0.027
Proportion of variance explained (R2) 0.577 0.584

Fixed effect estimates are not reported.
Number of observations = 86.
Robust standard errors are in parentheses.
1 Significant at 1-per-cent level.
2 Significant at 5-per-cent level.

Comparison of the Two Approaches

Investment is a dynamic process, with firms taking several years to reach their new optimal capital stock. The potential benefit of specifying an annual investment model is the ability to capture the short-term dynamics of investment decisions. In practice, however, specifying the dynamic structure is difficult in general and not feasible in our case given the short time period of our sample.[13] The annual model should include adjustment costs and allow investment to respond over several years to a tax change. Given the relatively small number of annual observations available, these features were excluded from the stylized model used in this study. As a result, the annual approach likely understates the true impact of tax changes on investment.

The DD approach, although based on fewer observations, circumvents this problem by considering the full post–tax reform period in which firms are expected to respond. The DD estimate, therefore, captures most, if not all, of the adjustment that firms make to their capital stock in response to the tax changes announced in Budget 2000. As a result, while our tax wedge elasticity estimates range from about -0.3 under the annual approach to about -0.7 under the DD approach, a higher weight should be attached to the DD estimate.

Annex 2
Studies of the Influence of the User Cost of Capital on Investment

There have been two waves of empirical work testing the linkage between the user cost of capital and investment. The first occurred from the 1960s to the early 1990s and failed to find a statistically significant relationship between the UCC and investment. The second, which makes use of more sophisticated statistical techniques and of firm-level data to take advantage of higher variance than in economy-wide data, has generally found a statistically significant relationship between the UCC and business investment.

An ongoing challenge in the empirical literature has been measuring the expected user cost—the key decision variable for a forward-looking firm. To reduce the likelihood of measurement error and therefore potential bias in the user cost elasticity estimates, some economists have studied investment during periods of tax reform. The key advantage of tax reform periods is that they represent discernible changes in tax rates, allowing the researcher to minimize the error associated with measuring expected tax effects on user costs.

The most widely studied tax reforms have been those of 1991 in Sweden and 1986 in the U.S. The Swedish reform, labelled by Agell, Englund and Södersten (1996) as the most "far-reaching reform in any industrialized country in the post-war period" (p. 643), saw a major broadening of the value-added sales tax, combined with significant reductions in the corporate and personal tax rates for middle- to high-income individuals. Auerbach, Hassett and Södersten (1995) examine whether these tax changes had any effect on investment and conclude that the impact was likely minor.

The U.S. tax reform of 1986 also introduced sweeping changes to the tax code. On the corporate side, the corporate income tax rate was reduced from 46 per cent in 1985 to 34 per cent in 1988, depreciation lives were lengthened and the investment tax credit was repealed. Cummins and Hassett (1992) find a strong relationship between the tax changes and investment as a result of the U.S. tax reform. They estimate user cost elasticity of -1.1 for equipment and -1.2 for structures (Table A2.1). The authors argue that their exploitation of the tax reform period, as well as their use of firm-level data, allow them to overcome measurement errors common in earlier macro-level studies. Cummins, Hassett and Hubbard (1996) apply this approach to tax reforms in 14 countries in the Organisation for Economic Co-operation and Development. They find evidence of significant investment responses to taxes in 12 of the 14 countries studied, including in Canada during the 1987 tax reform, but do not provide a direct estimate of the response of investment to a change in the user cost of capital.

Based on these more recent studies, it would appear that tax rate changes have a significant impact on investment, although the range of estimates varies widely. Table A2.1 shows that the elasticity of investment (and in the long run, the capital stock) with respect to the UCC ranges from -.25 to -1.2 in studies based on U.S. and Canadian data.

Table A2.1
The Sensitivity of Investment to the User Cost of Capital

Study Dependent Variable1 User Cost Elasticity2 Data

Cummins and Hassett (1992) Investment divided by the capital stock -1.1 (machinery and
-1.2 (structures)
U.S. 1986 tax reform.
Firm-level data, 1987
Caballero, Engel and
Haltiwanger (1995)
Investment -0.72 U.S.
plant-level data,
Cummins, Hassett and
Hubbard (1994)
Investment divided by the capital stock -0.66 Years of major tax
reforms in U.S.
firm-level data,
Chirinko, Fazzari and
Meyer (1999)
Investment divided by the capital stock -0.25 U.S. firm-level panel
data, 1981–1991
Chirinko, Fazzari and
Meyer (2002)
Capital stock -0.4 U.S. firm-level panel
data, 1974–1992
ab Iorwerth and Danforth (2004) Investment -0.97 (M&E) Canadian aggregate
data, 1984–2002
Schaller (2007)3 Capital stock -0.9 (M&E) Canadian aggregate
data, 1962–1999
This study3 Change in the capital stock -0.73 Canadian industry-
level data,

1 Investment and capital stock are measured in real terms. The capital stock is measured at the end of the previous period relative to investment in the current period.


"Elasticity" is defined as the percentage change in investment, or the capital stock, arising from a 1-per-cent change in the user cost of capital. A negative elasticity indicates that a decrease in the UCC causes an increase in investment. Since a permanent increase in investment will, over time, raise the capital stock by the same percentage, the reported elasticities are comparable whether they refer to investment or the capital stock.


The elasticity of the capital stock is calculated using the coefficient on the tax component of the user cost of capital. This can still be interpreted as a user cost elasticity since a given percentage change in the tax wedge changes the overall user cost of capital by the same percentage.


ab Iorwerth, A. and Danforth, J. (2004). "Is Investment Not Sensitive to Its User Cost? The Macro Evidence Revisited." Department of Finance Working Paper 2004-05.

Agell, J., Englund, P. and Södersten, J. (1996). "Tax Reform of the Century—The Swedish Experiment." National Tax Journal, Vol. 49, No. 4, pp. 643–64.

Auerbach, A., Hassett, K. and Södersten, J. (1995). "Taxation and Corporate Investment: The Impact of the 1991 Swedish Tax Reform." National Bureau of Economic Research Working Paper 5189.

Caballero, R., Engel, E. and Haltiwanger, J. (1995). "Plant-Level Adjustment and Aggregate Investment Dynamics." Brookings Papers on Economic Activity 2, Macroeconomics, pp. 1–54.

Chirinko, R., Fazzari, S. and Meyer, A. (1999). "How Responsive Is Business Capital Formation to Its User Cost? An Exploration With Micro Data." Journal of Public Economics, Vol. 74, No. 1, pp. 53–80.

Chirinko, R., Fazzari, S. and Meyer, A. (2002). "That Elusive Elasticity: A Long-Panel Approach to Estimating the Price Sensitivity of Business Capital." 10th International Conference on Panel Data, Berlin, July 5–6, 2002.

Cummins, J. and Hassett, K. (1992). "The Effects of Taxation on Investment: New Evidence From Firm Level Panel Data." National Tax Journal, Vol. 45, pp. 243–51.

Cummins, J., Hassett, K. and Hubbard, G. (1994). "A Reconsideration of Investment Behavior Using Tax Reforms as Natural Experiments." Brookings Papers on Economic Activity, Vol. 2, pp. 1–74.

Cummins, J., Hassett, K. and Hubbard, G. (1996). "Tax Reforms and Investment: A Cross-Country Comparison." Journal of Public Economics, Vol. 62, pp. 237–273.

Karlsson, S. and Löthgren, M. (2000). "On the Power and Interpretation of Panel Unit Root Tests." Economics Letters, Vol. 66, pp. 249–55.

Schaller, H. (2007). "The Long-Run Effect of Taxes, Prices, and the Interest Rate on the Capital Stock." Carleton University Working Paper.

Stanford, J. (2005). "Protesting Too Much: The Rhetoric and Reality of Corporate Tax Cuts" (pdf



For example, see Stanford (2005). [Return]


See "Assessing the Impact of the 2001–2004 Tax Reductions on Business Investment," Department of Finance Working Paper, forthcoming.  [Return]


See Annex 2 for a summary of these studies. [Return]


Note also that the corporate income surtax adds 1.12 percentage points to the general corporate income tax rate. [Return]


For a non-technical description of regression analysis, see Sykes, Alan O., "An Introduction to Regression Analysis," University of Chicago Law School Working Paper in Law and Economics (pdf

). [Return]


Resource industries are excluded from the analysis because they benefited from the tax reductions over a different time horizon than other industries and because investment in resource industries is affected by different factors than in other industries. [Return]


This involves including dichotomous, or "dummy," variables for each year and for each industry. [Return]


Using the capital stock, which is accumulated investment, as the dependent variable allows for a phased investment response even though there are only two DD time periods—before and after the tax reduction announcement.  [Return]


A Breusch–Pagan test strongly rejects the hypothesis of random effects and an F-test confirms the joint significance of the industry dummies. [Return]


Other factors that could cause biased coefficients include simultaneity bias—in this case the possibility that causality between investment and the user cost may run in both directions—and mismeasurement of explanatory variables. Neither of these factors is likely to affect the tax wedge, which is the variable of primary interest. [Return]


Hausman tests were performed, which examine the F-statistic on the predicted change in a variable when it is added to the regression.  [Return]


See Chirinko, Fazzari and Meyer (1999) for a discussion of how to interpret the coefficient on the tax wedge in equation 1. [Return]


See Chirinko, Fazzari and Meyer (2002) for the problems associated with estimating time series investment equations. [Return]

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