As with capacity, the forecasting of regime type in IFs has multiple elements: (1) a basic statistical formulation; (2) a recognition of country-specific differences (tied in part to path dependencies); and (3) algorithmic specification of a number of additional factors, including global waves and neighborhood effects.

A look at the historical patterns since 1960 of democratization across global regions shows a substantial almost global increase in democracy levels in the late 1970s and 1980s. That suggests reasons that a multi-element and potentially algorithmic forecasting formulation can be useful. Most analyses of democratization place much emphasis on a developmental variable such as GDP per capita. Note, for instance, that the general upward movement of democracy across most developing regions could be forecast with a basic formulation tied to the traditionally-identified development drivers of democracy, including income and education increase. Again, however, this historical pattern, with a clear dip in the early years of the post-1960 period and an accelerated advance in the later decades is consistent with a global wave that a formulation tied only to quite steadily growing long-term developmental variables could not generate. Further, a formulation tied only to such drivers would be unlikely to generate initial conditions for 1960 or 2010 consistent with the actual history, because country and regional values in those years also reflect historical path dependencies.

In building an initial, statistically-based formulation, we looked, as usual, at the power of two highly-correlated long-term development variables (notably GDP per capita and average education years attained by adults). The better broad developmental driving variable proved to be years of adults' education. With additional exploration, however, we found a slight further advantage for the Gender Empowerment Measure, and so replaced the education variable with the GEM (which is, itself, strongly influenced by adults' education). On top of that we found the size of the youth bulge (YTHBULGE) and extent of dependence on energy exports (ENX times the price ENPRI) as a share of GDP to be quite useful (see the discussions in these variables in Chapter 3 of Hughes et al. 2014).

In the equation below, the basic IFs formulation, all terms are significant with T-scores above 2.0 in absolute terms. In earlier work we also explored a linkage to the survival/self-expression dimension of the World Value Survey, but have found that other development variables statistically force it out of the relationship.

where

DEMOCPOLITYBase=basic or initial democracy using the Polity scale (in our case a combined 20-point scale built from historical democracy and autocracy series)

GEM=Gender Empowerment Measure (values below 1 indicate female disadvantage)

YTHBULGE=the youth bulge, the population aged 15–29 as a portion of the entire adult population

ENX=energy exports in physical terms (billion barrels of oil equivalent)

ENPRI=energy price per barrel

GDP=gross domestic product in billion constant 2000 dollars, market prices

democm=an exogenous multiplier for scenario analysis

r=country (geographic region in IFs terminology)

R-squared in 2010 = 0.41

The initial conditions of democracy in countries carry a considerable amount of idiosyncratic, country-specific influence, much of which can be expected to erode over time. Therefore a revised base level is computed that converges over time from the base component with the empirical initial condition built in to the value expected purely on the base of the analytic formulation. The user can control the rate of convergence with a parameter that specifies the years over which convergence occurs ( polconv ) and, in fact, basically shut off convergence by sitting the years very high.

The endogenous movement of this basic calculation can also be overridden by the users via the specification of a target value for democracy some number of standard errors ( democpolitysetar ) above or below the cross-sectional estimation of the formulation and the movement of the basic value to that target over a specified number of years ( democpolityseyrtar ). Such targeting of important variables is done in an algorithm described elsewhere.

Additionally we built structures, largely algorithmic, that allow forecasting with waves of democratization influenced by the impetus provided by systemic leadership, computing the magnitude of the global wave effect for all countries (DemGlobalEffects). Those depend on the amplitude of waves (DEMOCWAVE) relative to their initial condition and on a multiplier (EffectMul) that translates the amplitude into effects on states in the system. Because democracy and democratic wave literature often suggests that the countries in the middle of the democracy range are most susceptible to movements in the level of democracy, the analytic function enhances the affect in the middle range and dampens it at the high and low ends.

The democratic wave amplitude is a level that shifts over time (DemocWaveShift) with a normal maximum amplitude ( democwvmax ) and wave length ( democwvlen ), both specified exogenously, with the wave shift controlled by a endogenous parameter of wave direction that shifts with the wave length (DEMOCWVDIR). The normal wave amplitude can be affected also by impetus towards or away from democracy by a systemic leader (DemocImpLead), assumed to be the exogenously specified impetus from the United States ( democimpus ) compared to the normal impetus level from the U.S. ( democimpusn ) and the net impetus from other countries/forces ( democimpoth ).

Our historical analysis suggests the waves could have magnitudes (trough to peak) of as much as 6 points on the 20-point Polity scale of combined democracy and autocracy, although we found in historical analysis that downward shifts tend to be only one-third as great as upward movements. We found that the swings appear greatest in the anocracies, and that countries with higher incomes appear unaffected by them. We have structured and then "tuned" the general IFs representation of such effects so that the representation appears generally consistent with behavior over our 1960–2010 period of historical analysis. Nonetheless, we have no basis for forecasting the impetus that the U.S. or other systemic leadership might provide in the future, and we therefore set parameters for forecasting so that the effect is neutralized unless model users decide to introduce such an impetus on a scenario basis. The parameter for the U.S. impetus ( democimpus ) is set equal to the parameter for "normal" impetus ( democimpusn ), and that for other sources of impetus ( democimpoth ) is set to 0.

On top of the country-specific calculation and the global wave effect sits an (optional) regional or swing state effect calculation (SwingEffects), turned on by setting the swing states parameter ( swseffects ) to 1. The countries set as default neighborhood leaders are Brazil, Indonesia, Mexico, Nigeria, Pakistan, Russian Federation, South Africa, Turkey, and the Ukraine.

The swing effects term has three components. The first is a world effect, whereby the democracy level in any given state (the "swingee") is affected by the world average level, with a parameter of impact ( swingstdem ) and a time adjustment ( timeadj ). The second is a regionally powerful state factor, the regional "swinger" effect, with similar parameters. The third is a swing effect based on the average level of democracy in the region (RgDemoc). The size of the swing effects is further constrained algorithmically by an external parameter ( swseffmax ), not shown in the equation below.

David Epstein of Columbia University did extensive estimation of the parameters (the adjustment parameter on each term is 0.2). Unfortunately, the levels of significance were inconsistent across swing states and regions. Moreover, the term with the largest impact is the global term, already represented somewhat redundantly in the democracy wave effects. Hence, these swing effects are normally turned off (the sweffects parameter is 0 in the Base Case scenario) and are available for optional use.

Further, we anticipated and explored for an impact of internal war on democratization, as discussed in some of the literature. Although there is a cross-sectional relationship, it is weak. Further, when the variable is added to a formulation with a long-term driver such as GEM, it actually reverses sign (more war is associated with greater democracy) and the significance drops further. One of the analytical difficulties is that a number of countries, like India and Israel, are both democratic and prone to internal conflict. Internal conflict conceptualization and measurement probably need refinement to take into consideration the actual threat level that internal war poses to regimes. We have explored the relationship using the PITF data on conflict magnitude rather than simply event occurrence and have found similar difficulties. Given our analysis, we have not built a relationship from intrastate conflict into our forecasting of democracy.

Thus the final equation for democracy adds the global wave effects and the swing effects (both turned off in the base case) to the revised basic calculation of it.

IFs has the capability of doing an historical simulation between 1960 and 2010 so that we can compare with data. We undertook such an analysis using the basic democratization formulation and wave-based modifications to it described above. Although we introduced an historical wave exogenously, no other interventions were made to affect the course of the forecasts for level of democracy. The R-squared in a cross-sectional analysis comparing the IFs regional forecast for 2010 against Polity data was 0.69 and the value across the entire time period was 0.78. That provides a false sense of the accuracy of our historical forecasts, however. At the country level the R-squared in 2010 was only 0.09 and the value over the entire 50-year period was 0.37. IFs expected higher values than proved to be the case for countries including Qatar, Singapore, Cuba, Kuwait, and Belarus. IFs expected lower values than Polity data show for countries including Nigeria, Ethiopia, Bangladesh and Moldova.

Most significantly, IFs failed to anticipate the large rise in democracy in Africa in the 1990s. More generally, however strong our basic formulations for forecasting democracy may become, they are unlikely to foresee the timing of transitions toward or away from democracy. One approach to helping with that is to try to assess the pressures or unmet demand for democracy. As a small step in that direction, and using the concept of democratic deficit that Chapter 2 introduced, the model also computes an expected democracy variable (DEMOCEXP) directly from the equation above without exogenous multiplier or convergence to the function. This is useful for those who wish to see the magnitude of a country's democratic deficit or surplus by comparing DEMOC with DEMOCEXP. In fact, in advance of the Arab spring of 2011, IFs analysis (Cilliers, Hughes, and Moyer 2011) had identified the Middle East and North Africa as having exceptionally large democratic deficits.

Although we use the Polity democracy measure as our central indicator of regime type (including its use in the more general measure of governance inclusiveness) IFs also calculates in a simpler fashion a FREEDOM measure (combining the Freedom House political rights and civil liberties scales into one scale running from least to most free). Specifically, the drivers are GDP per capita and adult educational attainment, our two standard long-term development drivers. Interestingly, the R-squared between the democracy and freedom measures in 2010 (using data from both projects) is 0.686 and that in 2060 (using forecasts of IFs for both measures) is a nearly identical 0.689. This suggests that the long-term driver variables in our formulations are doing a quite good job of representing the similarities and differences in the two measures.

where

FREEDOM=freedom using 14-point Freedom House scale (PL and CL summed), inverted so that higher is more free

GDPPCP=GDP per capita at purchasing power parity in thousand dollars

EDYRSAG15=average years of education for adults aged 15 or older

freedomm=an exogenous multiplier for the model user

R-squared=0.402

Although IFs uses the Polity measure of democracy (DEMOCPOLITY) as its main measure of more formal, electoral inclusion, Freedom House's freedom measure (FREEDOM) is a logical alternative and the second of that measure's sub-dimensions, civil liberties, is a more inclusive measure. We therefore compute it also, using again GDP per capita and educational years (of all adults, not just females) as drivers. And there is a brute force multiplier for it also ( freedomm ). There is no SE targeting mechanism in place for the freedom variable.