New Loans – An Inference Model
5.3 Multinomial logit model
5.3.1 Model specification
As indicated above, it is questionable whether linear panel data models are appropriate for the question at hand as they are unable to account for the interdependency among creditors.
Fortunately, there are alternatives available. For example, instead of conceptualizing the dependent variable as a continuous measure of the loan volume obtained, one could directly analyze the choices for or against a creditor. Multinomial logit models, for instance, use a discrete variable that captures a range of unordered outcomes as the dependent variable to then estimate the predicted probability that a particular outcome is chosen. This class of models is particularly appealing as it considers the available choices jointly. In other words, the decision-makers are assumed to simultaneously face all of the possible choices and then decide to choose one of the possible outcomes.
It appears straightforward to see how this model might be applied to the question at hand. Governments are presented with loan proposals (see Section 3.3) and need to choose among them. It is therefore reasonable to conceptualize the dependent variable as the choice between BRICs, DACs, IFIs and private creditors and to subsequently estimate whether the type of coalition present affects the predicted probability of choosing one over the other type of creditor.
However, the model assumes that each government chooses only one of the available options but not multiple. As there are instances in my data where governments obtain loans from several creditors in a single year, I am forced to transform the dependent variable. I do so by creating a variable the indicates whether the loan from a particular creditor has been the largest loan obtained by a government in a particular year.
More formally, the latent utility approach that is typically used to motivate multinomial logit models can be directly applied to the question at hand. Each government has a utility Uij associated with each choice of creditor j. That utility Uithas a stochastic part ij and
a systematic part µi. The latter is assumed to be a function of the variables associated with the respective country, such as the type of coalition dominating the domestic political economy (that is, µ)i = Xiβi). The government then chooses among the alternatives in such a way that maximizes its utility, so that
P r(Yi = j) = P r(Uij > Ui`∀`j ∈ J ) (5.2) Assuming a Type I Extreme Value distribution (i.e. a Gumbel distribution) the probability of Equation 5.2 can subsequently be expressed as
P r(Yi= j) = exp(Xiβi
PJ
j=1exp(Xiβj (5.3)
5.3.2 Results
The results of these estimations are presented in Table 5.2. To identify Equation 5.3 the research is required to choose a base category against which the other outcomes are compared. I follow the common practice of choosing the most frequent category as the base category, which in my case is the choice for IFI loans. The table therefore does not display results for this choice, even though it was included in the estimation. Note that the coefficients for the included choices are displayed in separate columns for space considerations, but were actually estimated jointly.
However, because of the functional form of multinomial logit estimators, the interpre-tation of the resulting coefficients is not intuitive. To facilitate the interpreinterpre-tation of the model results I therefore calculate the predicted probabilities across the three coalitions to identify how the type of coalition affects the probability that a loan of a particular creditor is the largest loan obtained in a particular year. Figure 5.2 displays the predicted probabil-ities that a particular coalition obtained its largest loan from one of the four creditors. As can be seen, the results are not convincing. With the exception of the very low predicted probability that BRIC loans are the largest loan obtained by Consumer coalitions, none of
the remaining predicted probabilities are significantly different across coalitions.
5.3.3 Appraisal
The lack of significant results is not surprising. To be sure, the multinomial logit model appears appropriate for the question at hand at first sight because it accounts for the choice amongst the four creditors jointly. However, the model makes the assumption that each government only chooses one of the available creditors – the option that gives it the highest utility. The model cannot accommodate instances in which countries chose to borrow from two or more creditors in the same year. Estimating a multinomial logit model with the loan data available therefore required a transformation of the dependent variable. I addressed this requirement by creating a variable indicating if a government’s loan from a particular creditor was the largest loan obtained in a given year.
However, this transformation is highly dubious, for several reasons. First, this trans-formation loses intrans-formation on the additional, yet smaller, loans that a country might have obtained in the same year. For example, Table 5.3 shows that only about a quarter of all country-years chose only one creditor. It would be only for this subset of cases that the dependent variable as conceptualized for the multinomial logit model above would be appropriate. For the remaining 75% of cases the dependent variable used would lose the information on one or more loans that were obtained in the same year, but that were smaller than the respective largest loan acquired.
In addition, the transformation of the dependent variable loses information not only with respect to the number of loans considered, but also truncates qualitative information.
For example, a discrete measure of loan choice disregards whether the largest loan was 1 billion US$ or 10 million US$ as long as either of these two loans are larger than any other loans obtained in that year. Similarly, if two or more loans were acquired, the relative volume of loans is ignored. In other words, it does not matter whether the largest loan was larger by 1 million US$ of 1 billion US$. Clearly, however, the details on the size of
the loans, both absolute and relative, are important information. However, in the context of multinomial logit models such information cannot be incorporated into the dependent variable.
Lastly, the transformation of the dependent variable also makes the assumption that all creditors, in principle, have comparable chances of being the largest loan obtained.
This might be reasonable for the comparison of government’s choice among the traditional creditors. The IFIs, DACs and private creditors have established themselves as creditors to developing countries over a longer period of time. In contrast, BRICs have entered the stage only recently. It is therefore unreasonable to expect that BRICs have the same chance of being the largest loan obtained in a single year as traditional creditors.
BRICs DACs Private Total natural resources rents (% of GDP) -0.078 -0.062 -0.101
(0.060) (0.042) (0.077)
S-score of G5 -23.632** 0.609 6.384
(9.231) (2.442) (8.191)
IMF Membership (dropped) (dropped) (dropped)
. . .
Principal arrears, official creditors (US$) 0.000* -0.000 -0.000 (0.000) (0.000) (0.000) Interest arrears, official creditors (US$) -0.000 -0.000 0.000
(0.000) (0.000) (0.000) Principal arrears, private creditors (US$) -0.000 -0.000 -0.000***
(0.000) (0.000) (0.000) Interest arrears, private creditors (US$) -0.000 0.000 0.000***
(0.000) (0.000) (0.000)
GDP per capita -3.862*** -0.866 -1.477
(1.374) (0.641) (1.246) Revenue, excluding grants (% of GDP) 0.058 -0.013 -0.056
(0.089) (0.058) (0.103) Gov’t consumption expenditure (% of GDP) -0.124 0.125 -0.173
(0.129) (0.091) (0.230) Imports of goods and services (% of GDP) 0.011 -0.076* 0.002
(0.059) (0.040) (0.065) Exports of goods and services (% of GDP) 0.112 0.159*** 0.124*
(0.075) (0.054) (0.073) External debt stocks (% of GNI) -0.067** -0.017 -0.052**
(0.028) (0.017) (0.024)
Table 5.2: Model results of Multinomial Logit analysis.
Corporatist
Capital
Consumer
0 .05 .1 .15 .2 .25
Probability
Corporatist
Capital
Consumer
0 .05 .1 .15 .2
Probability DAC
Corporatist
Capital
Consumer
.35 .4 .45 .5 .55 .6
Probability IFI
Corporatist
Capital
Consumer
.25 .3 .35 .4 .45
Probability Private
Figure 5.2: Predicted probabilities by coalition that the loan obtained from the respective creditor is the largest of all loans obtained.
BRIC only 15 1.66
DAC only 5 0.55
IFI only 171 18.94
Private only 56 6.20
BRIC, DAC 10 1.11
BRIC, IFI 80 8.86
BRIC, Private 20 2.21
DAC, IFI 68 7.53
DAC, Private 18 1.99
IFI, Private 95 10.52
BRIC, DAC, IFI 38 4.21
BRIC, DAC, Private 5 0.55 BRIC, IFI, Private 37 4.10 DAC, IFI, Private 138 15.28
all creditors 87 9.63
no loan 60 6.64
Total 903 100
Table 5.3: Frequency and distribution of creditor set chosen by all governments.