## Abstract

We apply border discontinuity analysis to measure the impact of marginal tax rates on capital income, property, sales, and income on establishment entry on either side of state borders. Establishments are more likely to enter on the side of the border with the lower marginal tax rates. The biggest differences in start-up rates are at borders with the largest tax rate differences, with property tax rate differences mattering most. We rank borders by the differences in start-ups due to tax structure, and we rank states by their distortionary tax structures. The greatest distortion in start-ups due to tax rates is at the Wyoming-Idaho border with an 8.6% lower probability of start-ups on the Idaho side. The most distortionary tax structure is Rhode Island’s at 14.2% lower probability of entry, but it is not as heavily disadvantaged at the border because its neighbor, Connecticut, has the third most distortionary tax structure.

## Plain English Summary

State tax rates affect start-ups at state borders. State taxes on property, sales, personal income, and corporate income affect the side of the border start-ups tend to select. A state with a one-point higher tax rate in each of the four taxes will have a 3.2% lower probability of a start-up than its neighboring state. Property taxes have the greatest adverse effect on start-ups because new firms must pay property taxes, even if they have no sales or income. The greatest distortion in start-ups due to tax rates is Wyoming’s 8.6% advantage compared to Idaho. Some states with the most distortionary tax structures are not disadvantaged at their borders because their neighbors also have high tax rates. Rhode Island has the most distortionary tax structure, but it is not as heavily disadvantaged at the border because its neighbor, Connecticut, has the third most distortionary tax structure.

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## Notes

Corporate tax rates apply to C-corporations. Personal income tax rates apply to both as they tax the income earned from S-corporations and they also tax the dividends distributed to shareholders by C-corporations. The overwhelming majority of start-ups are S-corporations.

The advantage of summing the tax effects rather than focusing on each individual tax rate is that the tax rates may not be set independently. In particular, states with low (or no) income tax or sales tax may set higher rates on property tax rates. It is the joint tax rates that create the economic climate for start-ups and not an individual tax in isolation.

We do not add local tax rates. Local tax rates would endogenously reflect local economic outcomes. Moreover, available information on local taxes represents averages and not marginal tax rates and add further endogeneity to our preferred state marginal tax rates.

For example, a city with a 50% assessment level and a $4/100 nominal property tax rate would have the same effective rate as a city with a 100% assessment level and a $2/100 property tax rate.

Data on tax reciprocity was taken from Rork and Wagner (2012) supplemented by information summarized by TaxAct, Inc. https://www.taxact.com/support/category/300042/download-help-tax-support-taxact. Data on minimum wages was compile by the U.S. Department of Labor https://www.dol.gov/agencies/whd/state/minimum-wage/history

The full list is in the appendix.

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## Acknowledgements

We are grateful for partial research support under USDA-NIFA grant 2018-68006-27639 and a grant from the Charles Koch Foundation.

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## Appendix

### Appendix

### 1.1 Equating conditional logit with Poisson regression

Consider N investors, \(i=1, ..., N\), each of whom chooses their business location from C spatially differentiated choices, \(c= 1, ..., C\). The profit of the establishment \(i\) from industry *k* entering in year \(t\) at area \(c\) is given by

where \({{\boldsymbol{Z}}}_{{\boldsymbol{i}}{\boldsymbol{c}}{\boldsymbol{k}}{\boldsymbol{t}}}\) is a vector of explanatory variables including area-specific, industry-specific attributes, and entrepreneur’s characteristics. Without loss of generality, we focus on one industry and subtract the subscript *k* in profit function. The profit function will be:

Establishment \(i\) will choose the site \(c\) that gives the highest expected profit. When the shocks \({\varepsilon }_{ict}\) have standard Type I extreme value distributions, the probability of choosing site \(c\) is \({P}_{ict}\) given by

From Guimaraes et al. (2003), the conditional logit model is equivalent to Poisson regression in two situations.

1. \({Z}_{ict}={Z}_{ct}\), the conditional logit model is equivalent to Poisson regression model (Guimaraes et al., 2003). This is a strong assumption assuming individual choice is exclusively determined by a set of choice-specific variables common to all decision-makers. This assumption can be relaxed by assuming the choice-specific variables are common to groups of individuals.

2. \({Z}_{ict}={Z}_{gct}\)**,** with \(g=\mathrm{1,2},\ldots , G\), where \(G\) is the number of different groups of investors. There could be 107 groups of investors as that is the number of pairs of states that share a border. Or we could specify 1212 groups of investors, that is the number of paired counties who border one another on either side of a state line.

Let \({d}_{ict}=1\) in the case investor \(i\) picks choice \(c\) at time \(t\), and \({d}_{ict}=0\) otherwise. Then we can write the log likelihood of the conditional logit model as

where \({n}_{gct}\) is the number of establishments from group \(g\) that select location \(c\) at time \(t\). Alternatively, we can let \({n}_{gct}\) be independently Poisson-distributed with

where \(\left[\boldsymbol{\alpha },{\boldsymbol{\beta}}\right]\) is the vector of parameters to be estimated and \({{\boldsymbol{d}}}_{{\boldsymbol{g}}{\boldsymbol{c}}{\boldsymbol{t}}}\) is a vector of \(G\) group’s dummy variables, each one assuming the value 1 if the observation that locates in *c* at time *t* belongs to group *g*. Consequently, the log likelihood for the Poisson model is

From the first-order conditions with respect to the \({\alpha }_{g}\), we obtain

And so, \(exp\left({\alpha }_{g}\right)=\frac{\sum_{t=1}^{T}\sum_{c=1}^{C}{n}_{gct}}{\sum_{t=1}^{T}\sum_{c=1}^{C}exp\left({{\boldsymbol{\beta}}}^{\boldsymbol{^{\prime}}}{{\boldsymbol{Z}}}_{{\boldsymbol{g}}{\boldsymbol{c}}{\boldsymbol{t}}}\right)}\). We can substitute \({\alpha }_{g}\) in (A4) to get

where \({n}_{g}=\sum_{t=1}^{T}\sum_{c=1}^{C}{n}_{gct}\) measures the number of establishments of group \(g\) in the sample, and \(N=\sum_{t=1}^{T}\sum_{g=1}^{G}\sum_{c=1}^{C}{n}_{gct}\), represents the total number of establishments in the sample. Compare this with the likelihood function of the conditional logit model

Comparing (A7) and (A3), it is apparent that the solutions to \(\left[\boldsymbol{\alpha },{\boldsymbol{\beta}}\right]\) are identical because the two probability functions are identical except that the Poisson probability function has a constant term, \(-N+\sum_{t=1}^{T}\sum_{g=1}^{G}\sum_{c=1}^{C}\left({n}_{gct}\mathrm{log}{n}_{g}\right)-\sum_{t=1}^{T}\sum_{g=1}^{G}\sum_{c=1}^{C}\left({n}_{gct}\mathrm{log}{n}_{gct}!\right)\). Hence, the conditional logit is equivalent to the Poisson model under these simplifying assumptions.

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(Fig. 1)

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Chen, Y., Duncan, K.D., Ma, L. *et al.* How relative marginal tax rates affect establishment entry at state borders.
*Small Bus Econ* **60**, 1081–1103 (2023). https://doi.org/10.1007/s11187-022-00624-7

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DOI: https://doi.org/10.1007/s11187-022-00624-7