## Abstract

We investigate how personal income taxes affect the portfolio share of personal wealth that entrepreneurs invest in their own business. In a portfolio choice model that allows for tax sheltering, we show that lower tax rates may increase investment in entrepreneurial equity at the intensive margin, but decrease it at the extensive margin. Using German panel data, we identify tax effects on the portfolio shares of six asset classes by exploiting tax and entry regulation reforms. Our results indicate that lower taxes drive out businesses that are viable only due to tax sheltering, but increase investment in productive entrepreneurial businesses.

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## Notes

- 1.
The US figures are from Gentry and Hubbard (2004).

- 2.
Consistent with this, Cullen et al. (2018) estimate a higher responsiveness of reported taxable income to a taxpayer’s approval of the current government for income categories that are subject to little third party reporting such as income from small businesses.

- 3.
This could of course consist of a portfolio of risky assets.

- 4.
We are not specifying as yet whether sheltering of business income is due to legal tax avoidance activities such as profit shifting or illegal tax evasion. In practice, it is likely that a mixture of both occurs, although it is of course very hard to find direct evidence due to the very nature of income concealment. However, it is very plausible that income from private businesses, which must be declared by the entrepreneur, can be sheltered more easily than other income types such as wage and salary income or income from interest or dividends, all of which are subject to withholding taxes. This is further discussed below.

- 5.
In general, as is well-known, the effect of a tax reduction on investment in a risky asset with expected return greater than the riskless rate is ambiguous, as it depends on how the risk aversion of the entrepreneur varies with income or wealth. But an increase in that investment is certainly plausible.

- 6.
A tilde denotes a random variable.

- 7.
It is possible to formulate a more complicated model without tax offsets for negative values of portfolio income, but our main conclusion, that tax changes can have opposite effects at the extensive and intensive margins, continues to hold.

- 8.
The zero lower bound on

*k*seems reasonable because short-selling capital in one’s own business would create obvious moral hazard problems. We do not exclude the possibility of borrowing at the riskless rate as long as that does not create a bankruptcy risk, which would then have to be explicitly taken into account in the model. - 9.
Asterisks denote optimal values.

- 10.
If \(r=0\) or we have constant absolute risk aversion the well-known Domar/Musgrave effect (Domar and Musgrave 1944) will imply that

*k*increases with the tax rate. - 11.
A referee has suggested that the main point of the example could be based on a much simpler formulation of the gain from tax avoidance, with a reduction in taxable income in every state of the world fixed at

*F*, and so an increase in net income*tF*. A second referee suggested that there could be a fixed cost of avoidance, say*C*. As long as \((tF-C)>0\) it is true that these suggestions taken together would also support our initial intuition and rationalize the empirical results. We would argue, however, that it is more challenging, as well as more interesting, to ground the argument in a leading model drawn from the tax avoidance literature. This requires that the amount of avoidance is*optimally chosen*in every state of the world that yields a positive return and so provides a conceptually more demanding formal test of the intuition, upon which the numerical example depicted in Fig. 1 is based. Although the simple fixed net benefit case is sufficient for the example, it is useful to show that it is far from being necessary. - 12.
- 13.
This is actually a specialized version of the model of Mayshar (1991), which has a more general specification of the sheltering technology and tax system. But Slemrod ’s model is sufficient for our purposes here.

- 14.
The standard models of tax avoidance typically consider labor income which is always positive so this case does not arise. Of course allowing losses to be exaggerated would increase the attraction of tax avoidance when there is any kind of loss offset, so this assumption here goes some way toward adjusting for the assumption of full loss offset.

- 15.
We are grateful to a referee for pointing out that the same result could be obtained by an appeal to Topkis’ Theorem, since the objective in Eq. (9) is supermodular in \(({\tilde{c}},k{\tilde{e}},t)\).

- 16.
This is not to imply that reducing the tax rate is the best way of dealing with tax evasion or avoidance.

- 17.
This tax calculator takes into account the details of the German tax and benefit system and its changes over time, including, for example, the rules for income splitting by married couples and basic and child allowances. We compute individual marginal tax rates by simulating the additional tax liability due to an additional 1000 Euro of income in a given year and dividing by 1000. By using an increment of 1000 Euro we avoid rounding issues.

- 18.
In a robustness check reported in Sect. 6.4, we use updated incomes from 2001 instead.

- 19.
Our usage of a simulated tax rate change as the instrument is similar to the approach taken by parts of the literature on the elasticity of taxable income (Gruber and Saez 2002; Saez et al. 2012; Weber 2014). However, our dependent variables are ownership indicators or portfolio shares of asset classes, not taxable income, so the issues of regression to the mean and income dispersion do not arise in our context. In Sect. 6.4, we run robustness checks with respect to different specifications used in this literature.

- 20.
Net worth is gross wealth minus liabilities. We do not include gross wealth as a control variable because the leverage decision is potentially endogenous.

- 21.
We cannot exploit the lower tax rate on interest income available since 2009 to identify effects of taxes on the choice of specific financial assets because our data do not distinguish between holdings of bonds and stocks.

- 22.
See Fossen and Simmler (2016) for details on the final withholding tax and the tax option for retained earnings.

- 23.
We use directly observed information on asset holdings only. Using imputations provided by the SOEP increases the size of our final estimation sample only slightly and our estimation results do not change much.

- 24.
For the descriptive statistics we use the same sample restrictions as in the econometric estimations (concerning the age and labor market status of the respondents as described above and no missing values in the relevant variables), but we do not limit the sample to individuals observed in two consecutive periods yet, which is required in the first differenced regressions.

- 25.
- 26.
The first stage of the IV regressions has the marginal tax rate as the dependent variable and is identical for all asset classes.

- 27.
The exclusion restrictions are jointly insignificant in the ownership equations of the other assets, although some of these variables are individually significant. It is plausible that regulation of entry into entrepreneurship and the local unemployment rate affect the probability of owning a business, but not necessarily ownership of other assets.

- 28.
In Table 6 in Appendix 3, we report standard errors robust to clustering at the person level. The clustered standard errors turn out to be mostly smaller than the regular standard errors in our 3SLS estimations. Therefore, to be conservative, we report regular standard errors in Table 5. We also estimate bootstrapped standard errors with 200 replications taking into account clustering at the person level and sampling error in the predicted selection correction term. While again some standard errors shrink, this increases the

*p*-value of the coefficient of the marginal tax rate in the business equity equation to 0.057, and the marginal tax rate becomes insignificant in the owner-occupied housing equation. - 29.
A limitation of Shea’s partial \(R^2\) is that it does not allow to formally test for weak instruments. Therefore, for each endogenous regressor, we also conduct Sanderson–Windmeijer’s \(\chi ^2\) and

*F*-test for underidentification and for weak identification. In both versions of the test as well as in a joint*F*-test (not reported in the table), no*p*-value exceeds the 5% significance level, and we can infer that the hypotheses that the endogenous regressors are underidentified or weakly identified are rejected. The method by Sanderson and Windmeijer (2016) is a modification of the tests described by Angrist and Pischke (2009), which we report in the table. - 30.
Note that our linear selection correction model allows interpreting the effect of an increase in the probability of being an entrepreneur (\(Z_{{{it}}} \gamma _m\)) more directly than other selection correction models (see Eq. 20 in “System estimation” in the appendix). If an individual’s probability of being an entrepreneur is 10 percentage points larger, the share this individual invests in own business equity conditional on business ownership is 1.5 percentage points lower.

- 31.
We discuss the effect size in Sect. 6.3.

- 32.
Moreover, in more competitive industries, being an entrepreneur with low productivity motivated by tax sheltering may be less sustainable than in more concentrated industries. Therefore, one might expect the effects to be weaker in more competitive industries. Comparing the services sector to the manufacturing sector is informative in this respect because the services sector is generally less concentrated than the manufacturing sector (e.g., Brülhart and Traeger 2005).

- 33.
To be precise, in services (manufacturing), the coefficient of the marginal tax rate in the ownership equation of business equity is 0.187 (0.113) with a standard error of 0.119 (0.105), and the respective coefficient in the portfolio share equation is − 0.072 (− 0.063) with a standard error of 0.035 (0.061).

- 34.
We are grateful to a referee for suggesting that we consider the following type of example.

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## Acknowledgements

We thank Alan Auerbach, Martin Biewen, Robin Boadway, Thiess Buettner, Julie B. Cullen, Ryo Ishida, Eric Ohrn, David Rowell, Emmanuel Saez, Thanasis Stengos, Danny Yagan, participants at the 2016 Workshop on Self-Employment/Entrepreneurship and Public Policy at Oslo Fiscal Studies, the 2017 Annual Congress of the International Institute of Public Finance in Tokyo, the 2017 Annual Congress of the European Economic Association in Lisbon, the 2017 Annual Conference of the German Economic Association in Vienna, the 2017 Annual Seminar of the European Group of Risk and Insurance Economists in London, the 2017 Annual MaTax Conference in Mannheim, the 2017 Annual Conference of the Canadian Public Economics Group in Kingston, ON, the 2017 Annual Conference of the National Tax Association in Philadelphia, PA, the 2018 CESifo Area Conference on Applied Microeconomics in Munich, the 2018 Annual Conference of the International Association for Applied Econometrics in Montréal, QC, the G-Forum 2018 Annual Interdisciplinary Conference on Entrepreneurship, Innovation and SMEs in Stuttgart, the 2018 Annual Meetings of the Southern Economics Association in Washington, DC, as well as seminar participants at Freie Universitaet Berlin, University of Bath, University of California-Berkeley, University of Canterbury, University of Guelph, University of Hohenheim, University of Nevada-Reno, and University of Tuebingen, for valuable comments. Rostam-Afschar also thanks the University of California, Berkeley, for support as a visiting scholar while working on the project, and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) for financial support (Project-ID 403041268—TRR 266 Accounting for Transparency). The usual disclaimer applies. Declarations of interest: none. A prior version of this paper was entitled “How Do Entrepreneurial Portfolios Respond to Income Taxation?”

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## Appendices

### Appendix 1: Necessary and sufficient conditions

Necessary and sufficient conditions under which we predict opposite signs of the effects of a tax change at the extensive and intensive margins are, for the Slemrod (2001) model:

There exists a critical value \(k_{C}>0\) such that at the given tax rate:

where \({\tilde{c}}^{*}=\gamma (k_{C}{\tilde{e}},t),\) and the expectation is taken with respect to the distribution of \({\tilde{e}}\).

In words, there exists a positive *k*-value \((k_{C})\) at which expected utility is equal to that at \(k=0\) and is strictly increasing at that point. Intuitively, the tax gain from tax sheltering for all positive realizations of \({\tilde{e}}\) must be sufficient to compensate for the negative net returns in some states.

If condition (15) is satisfied, using the certainty equivalent of the left hand side, the entrepreneur will have a risk premium \(\rho _{C}>0\) such that

implying

with \(E[{\tilde{c}}-a({\tilde{c}},k_{C}{\tilde{e}})]>0.\) This tells us that this case is more likely to arise the higher the tax rate, the greater the expected value of sheltered income net of transactions costs, the less risk averse the entrepreneur, and the smaller the absolute value of the (negative) expected net return.

Note that if \(t=1,\) in this model, as long as the net return from sheltering *any* business income is positive, we must have \(k>0,\) since then

Therefore, by continuity of \({\tilde{y}}_{T}\) in *t*, there must exist an interval of *t*-values sufficiently close to 1 for which condition (15) is satisfied. On the other hand, at \(t=0\) these conditions cannot be satisfied, and again by continuity there will be an interval of *t*-values at which the corner solution is optimal. How large these respective intervals are is determined by the parameters of the model.

### Appendix 2: Derivation of the estimation equations

### Selection correction

Equation (11) describes portfolio shares at the intensive margin, where Eqs. (12) and (13) are the equations of selection into ownership of a particular asset. To avoid clutter, we suppress the asset class indices in this subsection and assume that the individual fixed effects have already been eliminated by partialling out from the linear selection and share equations. \(X_{{{it}}}\) and \(Z_{{{it}}}\) are row vectors which conform to the column vectors of unknown coefficients \(\beta\) and \(\gamma\), respectively. The *X*’s and *Z*’s are assumed to be exogenous in this appendix to focus on selection.

Assume that the expected value of the error of the intensive regression is zero, \(E(u_{{{it}}})=0\), and its variance is \(E(u_{{{it}}}u_{jt})=\sigma ^2_u {\text { for }} i=j\), and zero otherwise. The expected value of the selection threshold is equal to \(E(\nu _{{{it}}})=\mu _{\nu }\), its variance is \(E[(\nu _{{{it}}}-\mu _{\nu })(\nu _{jt}-\mu _{\nu })]=\sigma ^2_{\nu } {\text { for }} i=j\), and zero otherwise. The covariance between the error of the intensive regression and the selection threshold is \(Cov(u_{{{it}}},\nu _{jt})=E(u_{{{it}}}\nu _{{{it}}})-E(u_{{{it}}})E(\nu _{{{it}}})=\rho \sigma _{\nu } \sigma _u {\text { for }} i=j\), and zero otherwise. Assume the expected value of the error of the intensive regression conditional on the value of the selection threshold is \(E(u_{{{it}}}|\nu _{{{it}}})=\rho (\nu _{{{it}}}-\mu _{\nu })\sigma _u/\sigma _{\nu }.\)

By assuming the conditional expectation of \(u_{{{it}}}\) given \(\nu _{{{it}}}\) is linear in \(\nu _{{{it}}}\) we can use the decomposition

where \(\varepsilon _{{{it}}}\) and \(\nu _{{{it}}}\) are uncorrelated. Substituting this in \(y_{{{it}}}=X_{{{it}}}\beta +u_{{{it}}}\) gives

Then, the conditional mean is

If \(\nu _{{{it}}}\) is a standard normally distributed random variable with mean \(\mu _{\nu }=0\) and variance \(\sigma ^2_{\nu }=1\), then it follows (Heckman 1979) that

and the estimation equation is:

where \(\delta\) and \(\beta\) are the parameters to be estimated.

Following Olsen (1980) instead, if \(\nu _{{{it}}}\) is uniformly distributed over the interval [0, 1], then \(E(\nu _{{{it}}})=\mu _{\nu }=\frac{1}{2}\) and \(V(\nu _{{{it}}})=\frac{1}{12}\), so \(\sigma _{\nu }=\frac{1}{2\sqrt{3} }.\) Using the equation for the conditional mean as above with these values gives

Using \(E(\nu _{{{it}}}|\nu _{{{it}}}<Z_{{{it}}}\gamma )= Z_{{{it}}}\gamma E(\nu _{{{it}}}) = Z_{{{it}}}\gamma /2\) we can write

From this follows

### System estimation

Based on the assumption of a normally distributed error term in the selection equation, Shonkwiler and Yen (1999) show that the conditional mean of \(y_{{{mit}}}\) for individual *i* in equation \(m=1,\ldots ,M\) is

Because \(E(y_{{{mit}}}|X_{{{it}}},\nu _{{{mit}}}\ge Z_{{{it}}}\gamma _{m})=0\), the unconditional mean of \(y_{{{mit}}}\) for the *m*th equation, which can be estimated based on the full sample, is

In our case, we have analogously for the uniform distribution

and

### Marginal effects

Under the assumptions listed above, the marginal effects for a variable \(x_{itk}\) that is an element of both \(Z_{{{it}}}\) and \(X_{{{it}}}\) conditional on selection are

and the unconditional marginal effects are

### Appendix 3: Supplementary tables

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### Cite this article

Fossen, F.M., Rees, R., Rostam-Afschar, D. *et al.* The effects of income taxation on entrepreneurial investment: A puzzle?.
*Int Tax Public Finance* **27, **1321–1363 (2020). https://doi.org/10.1007/s10797-020-09606-5

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### Keywords

- Taxation
- Entrepreneurship
- Portfolio choice
- Tax sheltering
- Investment

### JEL Classification

- H24
- H25
- H26
- L26
- G11