Daniel Bennett and Dr. Richard Evans, Department of Economics

The purpose of this research is to verify the implications of common economic models which predict that increases in taxation will lead to increases in net exports. I find that tax increases have a positive impact on net exports, but that the estimated impact is likely unreliable due to imperfect estimation methods and the simplicity of the model. The initial attempt revealed several difficulties some of which could be overcome and others requiring further research. This report will explain my model, how the data for the estimation was obtained, the process of estimation, and my conclusions.

To analyze how taxes affect net exports I built a simple macroeconomic model of an open economy. The model considers the decisions of households and firms. Households try to maximize their happiness also called utility by consuming domestic and foreign goods. Households are constrained in how much they consume by a budget. Firms seek to maximize profits by hiring labor and capital to produce output. Solving the firm and household’s problem leads to an equation describing the movement of net exports which depends on the parameters of the model. The reduced form of the equation is given by,

where
NX_t is net exports, Y_t is total output, e_t is the exchange rate, g_t is government expenditures, T_t is the tax rate, and E_t is a random variable which takes account of unanticipated shocks to the economy. The’s are parameters of the model. is interpreted as the impact of he tax rate on the level net exports. The parameters can be estimated directly using a statistical procedure called ordinary least squares (OLS).OLS however is not best procedure in this instance however because  is determined by our model. Since  is also on the right hand side of the above equation OLS will give biased and inconsistent estimates of the parameters. I addressed this problem by using an instrumental variables (IV) strategy. This statistical procedure estimates the parameters in two stages. First estimating the following equation,

where  and  are capital and labor respectively. Then using the predicted values of obtained from this estimation it is possible to obtain consistent estimates of the first equation.

Originally I intended to use data from the Organization for Economic Co-operation and Development (OECD). The OECD has data on more than 20 developed countries. Estimating the relationship for more than one country would show that the results are not unique to a specific region. Unfortunately however the OECD does not keep enough data to perform an IV estimation. Because the estimates are not reliable under OLS I had to look for new data. Since the main focus of my question was how tax increases in the United States would affect net exports, I decided to focus on U.S. data. The Bureau of Economic Analysis (BEA) and the Federal Reserve Board (Fed) both keep detailed macroeconomic databases. I obtained data on exchange and interest rates from the Fed and the rest of my data from the BEA. To allow for easy interpretation of results, I put all of the data in terms of percent change from the previous year. Another major problem was deciding how to define the tax rate. Since there are many different tax rates for different economic activities I decided to define the effective tax rate as the percent of total output collected by the government in taxes. This however also has a problem Changes in the tax rate as I have defined it can be caused by changes in output not just changes in legislation. To take this into account I threw out all changes in the tax rates less than 5 percent. Since GDP grows on average at 3 percent per year, larger changes in the tax rate are almost certainly the result of changes in the tax code.

Having collected the data I estimated the equations using three different IV estimators, namely two stage least squares (2SLS), Limited Information Maximum Likelihood (LIML), and the Generalized Method of Moments (GMM). These estimators can all be optimal under different circumstances, but similar estimates from each method suggest that the results are not an artifact of the estimation procedure. Results are given in table one, and since the estimates were almost identical only the 2SLS estimates are reproduced.

The table shows that a tax increase does have a positive impact on the amount of net exports. The effect however is not statistically
different than zero. While it may be the case that there is actually no affect there are several reasons to suspect that these estimates are inaccurate. First notice that although the tax rate and total output have the predicted signs, government spending, the exchange rate, and the interest rate all have signs that are the opposite of what we would expect. There are several possible explanations for these results. If the instruments used, namely the capital stock and labor hours, affect the amount of net exports through channels other than through affecting total output the IV estimates, regardless of the estimator used, will be biased and inconsistent. Another explanation is that since the government usually taxes in order to spend more, spending and taxes almost never move in isolation. This makes it difficult to estimate the isolated effect of taxes on net exports. Finally it could be the case that the model is just not robust enough to correctly predict the interactions that determine net exports. All of these problems can be overcome. New instruments can be discovered, more data for more countries over a longer period of time can be acquired, and more complex models can be designed, but all of these improvements will require further research to accomplish. My attempts to overcome these issues are ongoing. A recent paper by Robert Barro¹ estimates the effect of government spending on total output using defense spending as an instrument for his estimations. Building on his and similar work is a promising avenue for eventually finding a suitable answer to this important question.

References

1. Barro R., Redlick C. “Macroeconomic Effects From Government Purchases and Taxes”, The Quarterly Journal of Economics (2011) 126 (1): 51-102.