The Effects of Model Specification on Foreign Direct Investment Models: An Application of Count Data Models.

KaSaundra M. Tomlin [*]

Previous studies have drawn a theoretical and empirical connection between foreign direct investment (FDI) and exchange rates using continuous measures of FDI. However, FDI data are often in discrete count form. I take a representative study of the FDI/exchange rate relationship by Jose M. Campa (1993), and I analyze the sensitivity of the results to specification of the dependent variable. Whereas Campa uses a Tobit specification, I use a count data specification to model counts of FDI occurrences. Using data on FDI in the United States from 1982 to 1993, controlling for the traditional determinants of FDI, I find that the results are sensitive across specifications. Significance levels and the magnitude of the coefficients change when going from a continuous Tobit specification to a zero inflated Poisson (ZIP) model designed for count data. Formal statistical testing finds that the ZIP specification likely models the data most properly. Thus, I indicate that misspecification bias from modeling discrete data with continuous distributions is important.

1. Introduction

The rapid rise in foreign direct investment (FDI) over the past few decades has heightened interest in the relationship between FDI flows and exchange rates. For example, several studies have established a connection between the exchange rate level and FDI decisions; the exchange rate level determines multinational firms' expected return, and hence the decision to invest abroad (Froot and Stein 1991; Goldberg and Kolstad 1995; Blonigen 1997; Tomlin 1998).

In these studies, the exchange rate level is a vital determinant of FDI; however, volatile exchange rates are also a determinant, discovered empirically to have a deterrent effect on FDI. Campa (1993) investigates the influence of the exchange rate level and exchange volatility on FDI. Firms invest abroad when expected profits exceed the sunk cost necessary to enter. The entry decision depends on sunk costs, the critical exchange rate level, exchange rate volatility, and other vital determinants. Using a count measure of FDI entries into four-digit standard industrial classification wholesaling industries, Tobit estimates suggest that sunk costs and exchange rate volatility depress FDI and that high exchange rate levels induce FDI during the 1980s. An abundance of research exists in this area; however, one common problem encountered by researchers relates to FDI data difficulties. Some data are aggregated, industry specific, or even discrete in nature.

FDI data are regularly provided in discrete count form, whereas typically studies FDI as a continuous variable. In past research, economists seeking data on complete transactions of FDI at the industry level obtained data from the International Trade Administration (ITA). ITA data have myriad missing values for EDI transactions, leaving only count data to analyze. Although in some cases continuous measures are applicable, count measures provide the actual number of FDI occurrences, thereby differentiating between no entry occurrences and positive events of entry. Moreover, total reliance on continuous measures may create the possibility of significant specification bias.

I take a representative study of FDI by Campa (1993), conduct a systematic examination of the empirical FDI/exchange rate relationship, and analyze the sensitivity of the results to specification of the dependent variable. Whereas Campa (1993) uses a Tobit model, I employ maximum-likelihood techniques to obtain estimates from the zero inflated Poisson model (ZIP). The ZIP model accounts for the discrete nature of the data and excess zeros in the dependent variable. To my knowledge, no one has verified that estimates will improve if more technical distributions are used which model the data better. Hence, I obtain Tobit estimates and use them as a benchmark to compare to ZIP estimates to ascertain the extent to which specification matters. I address two issues in the literature: misspecification bias from modeling discrete data with continuous variable models; and controlling for excess zeros in the dependent variable when using discrete data. Ultimately, the ZIP model presents an opportunity to ameliorate es timates used for policy discussions on the FDI-exchange rate relationship.

I find that the estimates are sensitive to specification. There are salient differences between the Tobit and ZIP estimates. Statistical tests indicate that the ZIP model, which specifically models the discrete nature of the dependent variable, is an appropriate specification for this sample. Statistical significance changes across the two models, and importantly, there are economic differences in the marginal effects as well. Whereas a Tobit specification finds a statistically and economically significant relationship between real exchange rate changes and EDI entry, this is not true for the ZIP specification. The results also suggest that the Tobit model underestimates the negative impact of labor costs and advertising expenses on FDI entry into U.S. wholesaling industries.

2. Specification Issues

Following the Dixit (1989b) model, I present a formal model based on option pricing theory. In recent studies using option pricing analogies, the FDI decision depends on the level of expected profits versus irreversible costs (Dixit 1989b; Campa 1993; Dixit and Pindyck 1994; Kogut and Chang 1996).

Review of the FDI Model

As in the Dixit model, I assert that uncertainty about future returns has a deterrent effect on risk neutral firms. At time t, the firm chooses whether to enter in the current period incurring sunk costs. Let R denote the exchange rate, expressed in units of foreign currency per dollar. The exchange rate is assumed to follow a Brownian motion, given by Equation 2.1:[1]

dR/R = [micro]dt + [sigma]dz.

Firms choose to enter by FDI when the expected profitability from investing abroad exceeds the sunk costs requisite to enter, given by Equation 2.2: [2]

[R.sup.c]/[rho] - [micro] - w/[rho] - [R.sup.c]p/([rho] - [micro])x[beta]([sigma]) [greater than or equal to] [R.sup.c]K. (2.2)

[R.sup.c] is the critical value of the exchange rate that triggers entry. [beta]([sigma]) is a known function of exchange rate volatility, [sigma], and decreasing in [sigma]. The drift of the exchange rate is given by [micro]; p is the dollar price of the good; k is the sunk cost of entry; w is the variable cost in foreign currency of producing the good, and [rho] represents the discount rate. [3] The model suggests that the higher the volatility of the exchange rate, the higher the exchange rate level has to be to trigger foreign firms to exercise the option to enter by FDI. Following from Equations 2.1 and 2.2, a reduced form equation may be developed to describe the impact of the observable variables on entry.

Predictions of the Model

Equation 2.2 suggests that entry is a function of the observable parameters of the formal model: the real exchange rate, drift, standard deviation, sunk costs, advertising expense, and labor costs. Table 1 contains the expected signs of the regressors. The real exchange rate is expected to exert a direct effect on entry. High exchange rate levels are associated with higher expected returns, a condition that implies higher entry rates. The drift of the exchange rate, representing the exchange rate trend, is expected to exert a direct effect on entry as well. Standard deviation represents exchange rate uncertainty. High exchange rate uncertainty tends to deter FDI. Hence, standard deviation is expected to have a negative effect on entry. Sunk costs, advertising expense, and labor costs are expected to exert a negative effect on entry. High sunk costs increases the value of the option to enter, consequently leading to fewer FDI occurrences. Finally, high advertising expenses and labor costs are expected to have an adverse effect on entry rates.

Specification of the Empirical Model

Estimation of the proposed theory introduces a complication because a number of key variables are not directly observed. Specifically, I do not observe the discount rate and the dollar price of the good. However, I do observe the exchange rate, exchange rate volatility, sunk costs, and labor costs. I commence with the benchmark Tobit model by following Campa's methodology, after which I use the ZIP model to determine the extent to which specification matters. The ZIP model, an extension of the standard Poisson regression model, is an appropriate model when the dependent variable consists of nonnegative integer values and a large number of 0 observations. I propose it for this sample because the dependent variable (the annual number of FDI entries by industry) takes on the value of 0 in 57.8% of the observations. If expected discounted profits are less than the sunk cost of entry, the dependent variable would take on a value of zero, representing the foreign firms' decision not to enter. If the expected disco unted profits exceed the sunk cost of entry, a foreign firm decides to enter, and the dependent variable takes on a nonzero value.

The ZIP Model

The standard Poisson model may not accurately assign probability to the outcome of ENTRY = 0 (i.e., no entry occurred) if a separate process is simultaneously at work influencing this outcome. Hence, fitting a simple Poisson model to these data overstates (inflates) the theoretical probability of zero in the Poisson model. [4] If this is the case, an alternative formulation is the ZIP model. For example, in a panel containing the number of entries by FDI, the outcome ENTRY = 0 may arise from two circumstances: ENTRY = 0 is the number of entries by a foreign firm in a certain period. At some other time, the same foreign firm may choose ENTRY = j [greater than] 0; or ENTRY = 0 occurs because a foreign firm never considers entering a U.S. market by FDI regardless of the characteristics that appear in the model. Equation 2.3 is the ZIP regression model to be estimated. The ZIP model extends the Poisson model in the following ways. First, the model alters the zero probability outcomes. Second, the changed zero pr obability induces overdispersion (divergence between the mean and the variance of the distribution). The testing procedure is complicated since the ZIP is not nested with either the Poisson

[ENTRY.sub.i] = 0 with probability [q.sub.i]

[ENTRY.sub.i] [sim] Poisson([[lambda].sub.i]) with probability (1 - [q.sub.i]) so that

Pr ob[ENTRY.sub.i] = 0] = [q.sub.i]+ [1 - [q.sub.i]][R.sub.i](0)

Pr ob[ENTRY.sub.i] = j [greater than] 0] = [1 - [q.sub.i]][R.sub.i](j), where [R.sub.i](entry) = the Poisson probability

[R.sub.i](entry) = the Poisson probability = [e.sup.-[lambda](i)][[[lambda].sup.entry(i)].sub.i]/[entry.sub.i]!, [[lambda].sub.i] = [e.sup.[beta]'[x.sub.i]] (2.3)

or negative binomial models. Consequently, I conduct the Vuong test (1989) for nonnested models, which has some power to distinguish between a "non-Poisson" due to overdispersion of the negative binomial model and the splitting mechanism in the ZIP model. Ultimately, the Vuong test is a test between the standard Poisson and ZIP models.

3. Data

Below is a description of the specific data to be used, which is comparable to Campa's (1993) data set. Entry, the dependent variable, is defined as the actual number of firms that entered a wholesale trade industry classified at the four-digit SIC code from 1982 to 1993. These data were obtained from the U.S. Department of Commerce, International Trade Administration Foreign Direct Investments in the United States: Completed Transactions for 1982 to 1993. In total, the wholesale sector had 1062 entries by FDI.

The independent variables are the Real Exchange Rate, Standard Deviation, Sunk Costs, Advertising Expense, and Labor Costs. All exchange rate data are from the Federal Reserve Bank of St. Louis, defined as the trade-weighted exchange index of the U.S. dollar. All variables were averaged to obtain an annual measure of the exchange rate variable in question. A rise in the index indicates a real appreciation of the dollar. I investigate one assumption with respect to how investors determine their exchange rate expectations: adaptive expectations. With adaptive expectations, I construct the exchange rate variables using data two years before investing at time t. There is no assumption a priori about how investors form these expectations. Sunk Costs was obtained from Dun & Bradstreet's Industry Norms and Key Business Ratios (several issues). Sunk Costs are measured by fixed assets to net wealth by four-digit SIC code for wholesale industries. The second proxy for sunk costs is Advertising Expense. These data were obtained from the U.S. Federal Trade Commission, Bureau of Economics, Statistical Report: Annual Line of Business Report 1977, Washington, D.C. (1985). Advertising Expense is the ratio of total advertising expenditures to sales by the average firm in that industry in 1977. Labor Costs are unit labor costs from the U.S. Bureau of Labor Statistics: Monthly Labor Review. It is the average of 11 countries' unit labor costs with respect to the United States. [5]

4. Results and Statistical Tests

Table 3 contains the marginal effects from the Tobit estimation, the same procedure Campa (1993) used. The Tobit results serve as a benchmark for comparison to the ZIP results to show specification matters. [6] All the variables have the correct sign, with the exception of Drift, the same problem Campa (1993) encountered. With respect to Drift he indicates this "troublesome" result may be because the exchange rate behavior is unpredictable.

In Table 3, the Tobit model estimates suggest that at the sample means, a 10% increase in the Real Exchange Rate may lead to a 8.64% increase in entry rates. [7] Drift has the wrong sign, negative, although it is statistically significant. The total effect of Drift on FDI entries is close to zero. Standard Deviation is statistically insignificant. Hence, rejecting the hypothesis that high exchange rate uncertainty deters FDI. If Sunk Costs rise by 10%, entry rates may decline by 3%. Advertising Expense represents a form of sunk costs, an unrecoverable Cost once incurred. Advertising Expense is statistically significant at the 1% level. The marginal effects computed at the sample means suggest that a rise in Advertising Expense by 10% may cause entry rates to decline by 2%. Labor Costs has a negative significant effect on FDI. At the sample means, if Labor Costs rise by 10%, entry rates may fall by 10.6%. This result supports the hypothesis that high labor costs deter FDI. Next, I use the ZIP model, which is designed for discrete data, in lieu of a continuous model such as Tobit.

The ZIP model was run to determine how robust the empirical results were across the Tobit and ZIP specifications. To test the appropriateness of the ZIP model, I conduct the Vuong test. The Vuong statistic is distributed standard normal. A value greater than 1.96 favors the ZIP model. In Tables 3 and 4, the Vuong statistics are 15.1900 and 12.3612 for the large and small sample, respectively. Both are greater than 1.96, a finding that favors the ZIP model. [8]

In Table 3, there are salient differences between the benchmark Tobit and ZIP estimates. The marginal effects from the ZIP regression provide the magnitude of the coefficients. [9] This robustness check leads to interesting implications. The estimates between the two specifications are incongruous. Taking into account the excess number of zeros in the dependent variable and the discrete nature of the data, the Real Exchange Rate and Sunk Costs are no longer statistically significant. In terms of economic significance, the magnitudes of the coefficients change. For example, the ZIP model suggests that an increase in Labor Costs by 10% would decrease entry rates by 14.95%; the Tobit model predicts a decline of 10.6%. For select industries, this would lead to an underestimate of one FDI occurrence. The coefficient on Advertising Expense is larger than in the benchmark case. At the sample means, if Advertising Expense increases by 10%, entry rates may decline by 3.3%. This is a difference of about 1.3% between t he Tobit and ZIP estimates.

Table 4 contains the marginal effects from the Tobit and ZIP estimations for a smaller sample size of seven years. This is to verify that the observed differences are not a result of a larger sample size. [10] The estimates reveal that the Tobit regression still reports the Real Exchange Rate as statistically significant, although statistically insignificant in the ZIP regression. The Real Exchange Rate is no longer statistically significant once one accounts for the discrete nature of the data. This is the same result found in the large sample. Drift has the wrong sign, although it is statistically significant.

The primary hypothesis in Campa's research was that exchange rate uncertainty deters FDI. Standard Deviation, representing exchange rate uncertainty, remains statistically insignificant across specifications and sample size. Roberts and Tybout (1997) note Campa's finding that sunk costs deter FDI entry is consistent with the hysteresis model. [11] Here, Advertising Expense has a negative significant effect on FDI, which implies a presence of hysteresis, given Advertising Expense is a proxy for sunk costs. The magnitude of the coefficient is about the same for the small and large sample under the ZIP. The Tobit model tends to underestimate the effect of Advertising Expense on Entry by about 4%, predicting one less entry than the ZIP estimation. Labor Costs is statistically insignificant under the Tobit and ZIP. It appears to some degree the empirical results depend on sample size.

Weak exchange rate links to FDI in U.S. wholesaling sectors found here may be because FDI in the distributional stages of U.S. industries are linked to intense export activity, not necessarily exchange rate changes. In addition, the reason we observe negative significant effects of labor and advertising costs on FDI is that distributional activities are subject to substantial expenses that may be sunk in the host market (Yamawaki 1991). [12] Yamawaki (1991) lists activities such as marketing, providing technical assistance and after-sales services to customers, maintenance of repair facilities, and service personnel training. Hence, the observance of weak exchange rate links may be plausible if the primary reason for FDI into U.S. wholesaling sectors is to accommodate exports.

5. Conclusion

Previous studies have drawn a theoretical and empirical connection between FDI and exchange rates; however, consideration for count data models is sparse. The empirical results confirm that estimates are sensitive to specification. This study takes a representative study of FDI and analyzes the robustness of previous empirical studies with respect to specification of FDI as the dependent variable. When shifting from a Tobit to a ZIP model, significance levels change and the magnitude of the coefficients changes. Using a count data sample of FDI into the United States from 1982 to 1993, maximum-likelihood estimates confirm that high advertising and labor costs deter FDI; however, there is little support for the notion that the exchange rate level or exchange rate uncertainty matters. Ultimately, the conclusion is that attention toward the choice of model specification is necessary to avoid misspecification bias from modeling discrete data with continuous distributions.

(*.) Department of Economics, College of Business Administration, University of Central Florida, P.O. Box 161400, Orlando, FL 32816-1400, USA; E-mail [e-mail].

I thank Bruce Blonigen, Wes Wilson, and Van Kolpin for helpful comments. I also thank Jose Campa for the data he was able to provide. Any errors or omissions are my own.

Received April 1998; accepted October 1999.

(1.) Here. dz is an increment of the standard Weiner process, uncorrelated across time, and at any one instant satisfying E(dz) 0 and E(d[z.sup.2]) = dt where E denotes the expectations operator (Dixic 1989b). For a detailed explanation on this process see Dixit and Pindyck (1994).

(2.) See Dixit (1989a) or Campa (1993) for details of the model.

(3.) Following Campa (1993), output is normalized to 1.

(4.) See Greene (2000) for the technical details of the model.

(5.) Those countries are Japan, U.K., France, Canada, Sweden, Belgium, Denmark, Germany, Norway, Netherlands, and Italy.

(6.) The marginal effects for the Tobit model are given by [partial]E[entry/x]/[partial]x = [phi]([beta]'x/[sigma])[beta].

(7.) All the results discussed above relate to the total effect. I compute the total effect using the marginal effects and the sample means in Tables 2, 3, and 4.

(8.) I also ran the model using the zero inflated negative binomial model (ZIPNEG), which accounts for overdispersion; however, the Vuong test indicated that the ZIPNEG was not the favorable model.

(9.) The marginal effects are computed at the sample means of the data. The marginal effects are given by: [partial]E[entry / x]/[partial]x = [lambda][beta]. This computation accounts for the splitting effect and overlap between the splitting model and base negative binomial model. See Greene (2000) for discussion.

(10.) Other small samples yield similar results.

(11.) Campa (1993) notes that FDI in the United States in the l980s might have shown hysteresis effects. Specifically, he remarks that "hysteresis refers to the failure of foreign firms that entered the U.S. market while the dollar was revaluing in the first half of the 1980s to exit once the dollar returned to its original level due to the sunk costs that could not be recovered upon exit" (p. 614).

(12.) Yamawaki (1991) found that the effect of exports on distributional activity is weak. Conversely, he found that the influence of distributional activity on exports is strong and robust. He used employment in U.S. distributional subsidiaries as a proxy for FDI in U.S. wholesale trade industries.

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