# «Discussion Papers Nadja Dwenger Corporate Taxation and Investment: Explaining Investment Dynamics with Firm-Level Panel Data Berlin, ...»

Deutsches Institut für

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Discussion Papers

Nadja Dwenger

**Corporate Taxation and Investment:**

Explaining Investment Dynamics

with Firm-Level Panel Data

Berlin, October 2009

Opinions expressed in this paper are those of the author and do not necessarily reflect

views of the institute.

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© DIW Berlin, 2009

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http://www.diw.de/english/products/publications/discussion_papers/27539.html http://ideas.repec.org/s/diw/diwwpp.html http://papers.ssrn.com/sol3/JELJOUR_Results.cfm?form_name=journalbrowse&journal_id=1079991 Corporate taxation and investment: Explaining investment dynamics with ﬁrm-level panel data Nadja Dwenger∗ September 17, 2009 Abstract Using a ﬁrm-level panel data set I assess whether dynamic models of investment provide an empirically fruitful framework for analyzing tax eﬀects on changes in capital stock. In particular I estimate a one-step error correction model (ECM) complementing the usual estimation of a distributed lag model. A correction term accounts for non-random sample attrition, which has not been considered in previous studies on investment even though most (if not all) panel data sets on ﬁrms are incomplete. Both, ECM and distributed lag model, suggest that user cost of capital and output have an economically and statistically signiﬁcant inﬂuence on capital formation. In the ECM, however, estimates are larger in size and match theoretical predictions more closely. My preferred estimate of -1.3 implies that a decrease in the user cost of capital by 10 percent will increase the ﬁrm’s capital stock by 13 percent, on average. Taking my elasticity estimate to the Corporate Tax Reform 2008 I would expect that the reform only slightly increases capital stock, since the rather strong reduction in corporate income tax rate was partly compensated for by stricter depreciation allowances. Investment dynamics appear to be crucial for the coeﬃcients of cash ﬂow variables in investment equations. While cash ﬂow eﬀects are present in the (ﬁrstdiﬀerenced) distributed lag model, they vanish in the ECM. This leads me to conclude that well documented cash ﬂow eﬀects point at dynamic misspeciﬁcation in previous studies.

Keywords: Taxation; Business investment; User cost of capital; Dynamic speciﬁcation JEL Classiﬁcation: E22; H25; H32 Acknowledgement: I want to thank Stephen Bond, Hermann Buslei, Viktor Steiner, Alfons J. Weichenrieder as well as seminar participants at the Oxford Center for Business Taxation, at the Wissenschaftszentrum Berlin, at the DIW Berlin, and Berliner Netzwerk Arbeitsmarktforschung for valuable comments.

∗ Deutsches Institut f¨r Wirtschaftsforschung Berlin, Department Public Economics, Mohrenu str. 58, 10117 Berlin, Germany, email: ndwenger@diw.de.

1 Introduction In this paper I assess whether dynamic models of investment provide an empirically fruitful framework for analyzing tax eﬀects on changes in the capital stock.

The main focus of the paper is the estimation of an error correction model which allows me to model investment dynamics explicitly. So far, drawing on the work by Chirinko, Fazzari and Meyer (1999), other studies based on micro data have documented a signiﬁcant response of capital spending to its user cost, where the user cost of capital combines prices, corporate income tax, allowances, interest, and depreciation rates. The empirical framework of these estimations, however, is based on autoregressive distributed lag models, where short-run dynamics result from an empirical speciﬁcation search rather than being imposed ex ante; long-term eﬀects are simply calculated as the sum of the coeﬃcients of short-run adjustment.

Under certain testable assumptions, the autoregressive distributed lag model may be reparameterized as an error correction model. While short-run investment dynamics are again found from an empirical speciﬁcation search, the long-term formulation of the capital stock in the error correction model is consistent with a simple neoclassical model of the ﬁrm’s demand for capital. In the error correction model, the long-term level of capital thus equals the optimal capital stock, i.e., the level of capital that maximizes the discounted value of all future income streams.

Since ﬁrms’ optimal capital stock also depends on its user cost, a fall (rise) in the user cost of capital will lead ﬁrms to expand (reduce) their capital stock. Because of quadratic adjustment costs or adaptive expectations, they may not fully adapt in the ﬁrst place but slowly shift their capital stock to the optimal one.1 Both the adjustment process and the long-term equilibrium relationship are distinguishable in the error correction model.

In the following I will estimate two models: the distributed lag model to compare results to the existing literature,2 and the error correction model to learn more These factors would yield a simple speciﬁcation of the form kt = α0 + β1 Xt + β2 Xt−1 + λkt−1 + ut, where kt is the capital stock at time t, β1 and β2 are column vectors of regression coeﬃcients, Xt and Xt−1 are column vectors of explanatory variables at time t and t − 1, and ut is an unobserved error term.

Chirinko et al. (1999) and subsequent work have merely assumed extrapolative expectations about the dynamics of investment. There are several methodological problems which include unobserved ﬁrm heterogeneity, measurement error in the user cost of capital (Goolsbee 2000), simultaneity bias (Goolsbee 1998), and lagged dependent variable in the error correction model. While it seems impossible to control for these factors on the basis of a single cross section, I argue that the user cost elasticity can be identiﬁed by taking advantage of a panel and by using GMM methods. The panel data set I use for the estimations is the Hoppenstedt company database provided by Hoppenstedt ﬁrm information GmbH. The data set covers the years 1987 to 2007 and contains detailed accounting data for a large number of German non-ﬁnancial corporations that are subject to publication requirements.

In spite of a variety of advantages, the use of a long panel data set implies one major problem, which is sample attrition. The longer the sequence of years, the more likely it is that ﬁrms drop out of the sample. Observations on ﬁrms may be missing for several reasons, including bankruptcy, cessation of business, merger, falling below thresholds which aﬀect publication requirements, etc.. In theory, if ﬁrms are randomly missing, the investment function may be estimated using the incomplete panel data set as if it was complete. In practice, estimates can be biased without an appropriate correction if ﬁrms are missing for certain speciﬁc reasons which are, conditional on the explanatory variables included in the investment equation, not independent of the determinants of the decision to invest. In papers on investment, the fact that most (if not all) panel data sets on ﬁrms are incomplete, and the potential bias associated with this fact, have received little attention. To address the concern of non-random sample attrition, I include a correction term drawing on the work by Wooldridge (1995, 2002).

Estimating the ﬁrst-diﬀerenced distributed lag model, I ﬁnd a long-term user cost elasticity of -0.6. These estimates compare to what was documented for Germany in the literature (Chatelain, Hernando, Generale, von Kalckreuth and Vermeulen 2001, Harhoﬀ and Ramb 2001, von Kalckreuth 2001). The only study and no adjustment costs. This assumption leads to a distributed lag model which does not include the lagged dependent variable. Further, Chirinko et al. (1999) estimate the investment equation in rates of changes to account for large diﬀerences in ﬁrm size, i.e., they estimate a ﬁrst-diﬀerenced distributed lag model.

with lower estimates for Germany is the study by Ramb (2007). Using the method of simulated marginal tax rates (Graham 1996), Ramb estimates a long-term elasticity of the simulated marginal tax rate to investment activity between -0.2 and

-0.1.3 The estimation of the error correction model yields a robust, statistically signiﬁcant, and relatively large point estimate of the user cost elasticity. The point estimate of the long-term elasticity of -1.3 implies that a decrease in the user cost of capital by 10 percent will increase capital by 13 percent. Further, I ﬁnd that ﬁrms quickly adjust to the new optimal capital stock: about half of the gap between existing and optimal capital stock is closed within a year.

Interestingly, well-known cash ﬂow eﬀects are present in the distributed lag model but vanish in the error correction model. This ﬁnding conﬂicts with the view that cash ﬂow eﬀects can be seen as evidence for the importance of ﬁnancial constraints (see, e.g., Fazzari, Hubbard and Petersen 1988, 2000). In fact, it suggests that in the distributed lag model, cash ﬂow may act as a proxy for omitted expected future proﬁtability variables (e.g., Kaplan and Zingales 1997, 2000; Bond, Elston, Mairesse and Mulkay 2003) which becomes insigniﬁcant once the investment equation is dynamically correctly speciﬁed.

The remainder of the paper is organized as follows. The next section brieﬂy describes the user cost of capital and argues that the user cost provides suﬃcient variation to identify the user cost elasticity. The data set I use in the study and the empirical methodology are introduced in Section 3. Estimation results of the ﬁrst-diﬀerenced distributed lag model and the error correction model are presented in Section 4. Section 5 summarizes my main results and concludes.

In Ramb’s study, the simulated tax rate is solely driven by the tax rate, loss oﬀsetting rules, and the (simulated) tax base. All other eﬀects incorporated in the user cost of capital such as depreciation allowances are assumed to be identical for all ﬁrms. For this reason, Ramb’s estimate is not directly comparable to the studies estimating the user cost elasticity, the present paper included.

** 2 Firm-speciﬁc variation in the UCC**

My goal is to estimate the user cost elasticity of investment. Identiﬁcation of this elasticity comes from the user cost of capital (U CC), which varies across ﬁrms and over time. The deﬁnition of the U CC in this study is standard and based on the work by Jorgenson (1963), Hall and Jorgenson (1967), and King and Fullerton (1984). Following their approach, the U CC is the minimal rate of return a ﬁrm must earn on investments before taxes, i.e., it is the discount rate a ﬁrm should use in evaluating investment projects. As earnings from the investment are taxed and because the tax system provides for some allowances for investment goods, the U CC is not only a function of economic variables but also of taxation. This introduces further variation as major reforms in the tax system have taken place in Germany in recent years. In the following, I will brieﬂy present the way I calculate the user cost of capital. In doing so, I will also introduce those features of the German tax system that are particularly relevant for the decision to invest.

The U CCi,j,a,t for ﬁrm i in industry j with asset a at time t is given by

output price at time t. The ratio of these price indices reﬂects capital gains (or losses) that may occur if capital goods’ prices are expected to rise (fall) relative to the prices of output goods. Capital gains alleviate the eﬀect of economic dee preciation (δj,a,t ) in lowering the asset’s value. Assets are assumed to deteriorate exponentially, which renders the economic depreciation rate invariant to the interest rate (Auerbach 1983). Information on economic depreciation is available at the industry-level for two diﬀerent assets a, property with buildings and ﬁxed tangible assets.