Economic performance under diﬀerent monetary policy frameworks

We first outline the major trends in monetary policy frameworks, which are shifts towards inflation targeting and towards frameworks which offer higher degrees of monetary control. We then examine the economic performance (inflation and growth) associated with different frameworks, presenting unconditional and conditional analyses, running regressions weighted by GDP and population as well as by the number of countries, and using predictions of countries’ monetary policy framework choices to address the issue of endogeneity. We find some differences in performance associated with the different monetary policy frameworks, together with a general improvement over time which is explained in part by the trends towards inflation targeting and more precise monetary control but in part, and perhaps more strongly, reflects a more general trend towards better economic performance.


1
Introduction In this paper we explore the economic performance associated with different monetary policy frameworks (MPFs) in advanced and emerging economies, using the classification developed by Cobham (2021). That classification brings together both external (exchange rate) and domestic (money, inflation, GDP) targets, on the one hand, and both announced objectives and realised outcomes, on the other. It has been implemented so far for 26 'advanced' economies, the Euro currency area, 33 'emerging' economies, and developing countries in some, but not all, regions, from 1974 to 2017. Its availability naturally suggests questions about the different levels of economic performance associated with each type of MPF. While there is a significant literature examining the inflation and growth associated with different exchange rate regimes -notably Ghosh et al. (2002) and Husain et al. (2005) -and a separate literature investigating the effect of inflation targeting -e.g. Ball (2010), Walsh (2009) -there is little systematic research across the whole range of monetary policy frameworks, taking in both domestic and external dimensions.
In section 2 we identify the major trends revealed by the classification. In section 3 we examine the implications of weighting the frameworks by GDP and by population, rather than by the number of countries. In sections 4 and 5 we present first unconditional and then conditional analyses of the inflation and economic growth associated with different frameworks. Section 6 uses predictions of countries' MPFs based on Cobham and Song (2020) to allow for possible endogeneity. Section 7 concludes.

2
The classification and what it shows In the classification we use here (explained in detail in Cobham, 2021, pp4-5 The classification starts by asking if the MPF concerned has pre-announced objectives or targets; if so, what those targets are for; whether they are broad or narrow; whether they are stationary or converging; and whether they are attained. Where no such announced targets exist, or announced targets are not attained, the frameworks are divided between 'unstructured', 'loosely structured' and 'well structured' discretion, by reference to the effectiveness of the instruments available to the monetary authorities as well as their (unquantified, maybe even unarticulated) objectives. An important distinction is also made between an exchange rate 'fix', where the monetary authority dominates forex transactions and sets (typically very narrow) margins for transactions, and an exchange rate target where there is an autonomous forex market, and interest rates as well as market intervention are used to influence the rate. Two types of currency board are distinguished, while the category of 'multiple direct controls' is used to cover command economies with no real monetary policy. The key sources of information for the classifications are the reports and papers from the regular Article IV consultations of the IMF with its members.
On this basis 32 different frameworks are defined, but these are then aggregated along two different dimensions. 1 First, an aggregation by target variable (plus the three forms of discretion) puts together, for example, 'loose' and 'full', stationary and converging, inflation targets. Second, an aggregation by degree of monetary control puts together, for example, all loose targeting arrangements in one category, and all full targeting arrangements in another.
Full details of these aggregations, which reduce the number of frameworks to 9 in the first case and 4 in the second, are presented in Table 1. Figures 1 and 2 show the results in terms of each of these two aggregations, for advanced and emerging economies together. Figure 1 uses the target variable aggregation and includes as a separate category countries with 'no national framework', that is countries which used another country's currency (Luxembourg, before 1999) or joined the European monetary union (EMU) in or after 1999 so that from then on they have had no national-specific framework, but the Euro area itself is included. What Figure 1 shows clearly is the growth over time of inflation targeting and the decline from the early 1990s of exchange rate targeting; those trends are stronger for the advanced countries but still significant for the emerging economies (see the visualisations at www.monetaryframeworks.org or the graphs in Cobham, 2018). Monetary targeting, on the other hand, is never very important 2 and disappears altogether in the mid-1990s, except where it coexists with exchange rate targeting or inflation targeting as countries tried to fulfil the Maastricht criteria for entry into EMU (all these cases, and the few cases of exchange rate plus inflation targeting, are classified as 'mixed targeting'). Of the three forms of discretion, unstructured is initially most important, but that loses ground to loosely structured which also later declines, while well structured discretion turns out to have very low incidence (possibly because countries with sufficiently coherent and well-organised objectives and instruments turn to inflation targeting instead).   Figure 3 indicates that when weighted by GDP the share of inflation targeting in the second half of the period is much higher, because inflation targeting is largely an advanced economy sport. Figure 4 shows that when the frameworks are weighted by population inflation targeting is much less important, and pride of place goes to loosely structured discretion, which is the framework for China (from 1994) and India (from 1974 to 2013, after which it moves to inflation targeting).
Figures 5 and 6 show the weightings for the DOC aggregation (excluding cases of no national framework). On the GDP weighting intensive and substantial frameworks account for roughly 50% each by the end of the period. 4 On the population weighting intensive frameworks are less than 20% and substantial around 80% by the end of the period, while rudimentary frameworks are over 30% in the first decade. average growth rose in the second but fell sharply in the fourth. In terms of the target variable aggregation, in the first two subperiods unstructured discretion is associated with much worse performance (higher inflation and weaker growth), exchange rate fixing does poorly on inflation but well on growth, and monetary targeting does better than the average on both counts. Performance under inflation targeting is superior in the second subperiod (lowest inflation but growth below monetary targeting and just below exchange rate targeting). In the third subperiod it is also better on inflation but not so good on growth relative to exchange rate and mixed targeting, and less good on inflation but better on growth than loosely structured discretion. In terms of the DOC aggregation, intermediate does poorly on inflation, while intensive does mostly better than substantial frameworks on inflation but not on growth. Table 4 provides similar data for the emerging economies, with the average inflation rising between the first and second subperiods but much lower after that, while growth is best in the third subperiod. Direct controls (and therefore rudimentary frameworks) and exchange rate fixing have high inflation but better than average growth in the first two subperiods (but then disappear), while exchange rate targeting has better inflation and comparable growth.

Inflation and growth: unconditional analysis
Unstructured and loosely structured discretion have much higher inflation and lower growth in the first two subperiods, but loosely structured discretion is closer to the average, particularly on growth, in the later subperiods. Inflation and mixed targeting do better in the two later subperiods but are not always better than exchange rate targeting. Intermediate and substantial frameworks have high inflation in the second subperiod but lower after that, especially substantial. Intensive frameworks do better on inflation and mostly better on growth than substantial frameworks from the second subperiod onwards.

Inflation and growth: conditional analysis
The unconditional outcomes identified in the previous section may reflect country-specific factors rather than any effect of the frameworks. In this section we therefore report the results for panel regressions of both inflation and real GDP per capita growth upon a set of dummies for the monetary policy frameworks together with a set of standard control variables. We do this separately for both advanced and emerging economies using fixed effects estimation, as well as, for both groups combined, using panel regressions weighted by (time varying) real GDP and population. Our regressions cover the full period 1974-2017. 5

Inflation
Tables 5-7 present regression results for inflation using fixed effects estimation. Table 5 presents our main results for both the advanced and emerging economies in our sample, where we test the effect of the MPFs aggregated by target and DOC variables respectively. 6 Our control variables are broad money growth, real GDP growth, trade openness, the government fiscal balance (surplus), an index of Central Bank Independence (CBI) and a terms of trade shock. 7 We use loosely structured discretion (LSD) as our benchmark target variable MPF and substantial as our benchmark DOC variable MPF. Preliminary regression results for the emerging economies were strongly influenced by a relatively small number of episodes where countries had experienced high levels of inflation alongside high broad money growth. For this reason, we also applied a filter to our regressions that removed observations where broad money growth was equal to or exceeded 100% (per annum). 8 Amongst our control variables in Table 5 we find, as anticipated by theory, positive and significant estimated coefficients on broad money growth as well as negative and significant estimated coefficients on real GDP growth. We find the estimated coefficient on openness to be positively signed although insignificant. Standard theory suggests a negative relationship (see Romer, 1993). 9 However, our advanced economy results are in line with those of Husain et al (2005), who find a small positive but insignificant relationship between the variables over 1970-99. We find the estimated coefficient on the government balance is negatively signed but insignificant, 10 that on the CBI Index is insignificant 11 and that on the terms of trade shock is positive but only significant for the emerging economies.
Of the MPF target variables in Table 5, we find the estimated coefficient on ERfix to be positive and significant for advanced, which provides some evidence that over this period inflation was high (in advanced economies) where monetary authorities pursued ERfix relative to those advanced countries which pursued LSD (our benchmark MPF variable). We similarly find some evidence for emerging, but not advanced, economies that MixedTs and ITs are associated with inflation lower than benchmark, and evidence of inflation above benchmark under UD.
We find no significant effects for ERTs, MTs or WSD. For the DOC MPF variables we find MPFs classified as intermediate control have higher inflation relative to those classified as substantial control (the benchmark) across both advanced and emerging economies, and that advanced (but not emerging) economies MPFs classified as intensive control experience lower inflation relative to the benchmark.
Sensitivity: inflation regressions Table 6 presents a basic sensitivity analysis for our findings, by presenting summary results of four regression models which are slight modifications of our chosen specification. For each of our regression models reported in Table 5 (A to D in Table 6), we run four regression models.
First, in Model (1) we exclude the broad money growth filter from the data. Second, in Model (2) we remove the terms of trade shock variable from our chosen specification. Third, to mitigate the possibility of endogeneity in our regressions, Model (3) includes control variables lagged one period rather than using contemporaneous variables, while Model (4) similarly lags our MPF variables by one period. 12 We return to the issue of possible endogeneity with a different approach in the following section. For these modified models, the significance and the signs on the estimated coefficients are broadly similar to those in Table 5. With respect to the MPF target variables, when we introduce lagged control variables (Model 3) for the advanced economy regressions, we find that the estimated coefficient on ERfix is no longer significant while that on ITs becomes significantly negative. We also find that under Model (4) with lagged MPFs the estimated coefficient on UD becomes significant. For emerging economies, we no longer find the estimated coefficient of rudimentary to be significant in any of our four models, and dropping the broad money growth filter results in a loss of significance on the estimated coefficients for MixedTs and UD. 13

Weighted Inflation Regressions
Section 4 presented graphs of the trends in MPFs weighted by GDP and population, instead of by the number of countries. This raises the question of whether the econometric relationships are also affected by the weights used. We therefore re-run our tests using weighted regression techniques, making use of GDP and population as weights. Note that these weights are timevarying. While previous results tell us the average effect per country of different frameworks, these results will show the average effect per unit of economic activity or per unit of population. Table 7 replicates the results of Table 5 (our main inflation regressions for advanced and emerging economies using both target and DOC MPFs), where we run a weighted regression (using both GDP and population weights) over our full sample of countries. 14 The results in Table 7 are broadly comparable to our previous findings when we look across the estimated coefficients on our control variables. Those on broad money growth, real GDP growth and the CBI index are similar to our main results. However, we find evidence that the estimated coefficient on the terms of trade variable is significantly positive (in common with the emerging economies results). We now find the estimated coefficient for the government balance when we use target MPFs to be significantly negative. The estimated coefficients on openness remain insignificant although they are now negative when we apply GDP weights (and population weights using target MPFs). Across the target MPF variables we find some significant differences. Most noticeably MixedTs economies appear to have high inflation relative to the benchmark value, under both GDP and population weights. We also now find significantly positive estimated coefficients on both ERtarget and WSD under GDP weights, and no longer find evidence of positive estimated coefficients on ERFix or rudimentary. In common with our results for the emerging economies in Table 5, the estimated coefficient on UD is positive and significant while on ITs it is negative and significant under population weights. In line with the results in Table 5 we also find the estimated coefficients on MTs and MDC to be insignificant.
Growth Table 8 presents our main regression results for growth. Our dependent variable is percentage growth in per capita GDP, our control variables are the ratio of investment to GDP, openness, tax to GDP ratio, government balance as a percentage of GDP, (log of) population, population growth, level of schooling and terms of trade shocks. 15 We use the same benchmark MPF variables as we did in the inflation regressions and continue to apply our broad money growth filter.
The signs and significance of the estimated coefficients on the control variables in Table 8 are broadly in line with theory. Surprise findings for the advanced (but not emerging) economies are that the estimated coefficients on the investment ratio are not significantly positive, those on schooling are negative and those on population are not significantly positive. 16 Looking at the target MPFs we find evidence in emerging economies that MixedTs, ITs and MDC economies enjoy growth higher than the LSD benchmark, but UD economies experience relatively lower growth. For advanced economies we also find evidence that ITs economies enjoy higher growth relative to the LSD benchmark. For the DOC MPFs we find evidence within the emerging economies that rudimentary and intensive have growth higher than the substantial benchmark, and that intermediate economies have lower than benchmark growth.
We find no evidence of similar effects in the advanced economies.

Sensitivity: growth regressions
As with our inflation regressions we develop a basic sensitivity analysis by presenting, in Table   9, the results of regressions run on slightly modified versions of our four main regression equations (from Table 8). We present 4 modifications (models 1 to 4) that correspond to those we made to our inflation regressions. Again, if we focus on the MPF variables we can see most of the results of our main growth regressions (Table 8) hold across our four alternative models.
Significant differences apply to the advanced economies under model (3), where the significance of the estimated coefficients on both MixedTs and ITs changes, and to the emerging economies under model (4), where the estimated coefficients on MixedTs, ITs and WSD become insignificant. 17 Weighted Growth Regressions Table 10 presents the results of a weighted regression analysis of our growth variable for advanced and emerging economies together, again using both GDP weights and population weights for both target and DOC MPF variables. The results are broadly similar to those found in the main regressions although there are some differences. In terms of the control variables, in common with the main results we find the estimated coefficients on the government balance to be positive and significant and on population growth to be negative and significant in all the weighted regressions. We also find the estimated coefficients on the investment ratio and terms of trade variable to be significant and positive. We no longer find the estimated coefficients on the tax ratio, population or schooling to be significant. In addition, we find that the signs on the estimated coefficients vary with the weighting scheme for openness, tax ratio and schooling, and that, contrary to our main results, the estimated coefficient on openness under population weighting and using DOC MPFs is negative.
The estimated coefficients on the MPF variables are also close to those in the main regressions in most cases. As with the main results, for the target variables, we find the estimated coefficients on MDC and ITs to be significant and those on ERtarget and ERfix to be insignificant. We find a positive estimated coefficient on MixedTs only when we use GDP weights and a significantly negative estimated coefficient on UD only under population weights. Contrary to the results in Table 8, we also find significantly positive coefficients on MTs and WSD under GDP weighting. For the DOC MPFs we find the estimated coefficients on rudimentary and intensive to be positive and significant as they were in the main regressions for emerging economies, and intermediate to have a negatively signed and insignificant estimated coefficient as was the case for the advanced economies.

Instrumental variables estimation of inflation performance
As noted in our sensitivity analysis above, it is possible there is an endogeneity issue with our inflation regressions. In particular, countries with low and stable inflation could choose to announce inflation targets and so become classified as ITs. In this case, the MPF variables are influenced by the contemporaneous inflation rate, rather than the prior choice of the ITs framework leading to better inflation performance. Similarly, poor inflation performance might encourage a country not to declare inflation targets in which case it would be more likely to be classified as loosely structured discretion. In our inflation regressions the endogeneity issue is likely to be mitigated by the low variance of the MPF variables: if MPFs do not change frequently, they are less likely to be influenced by short-term changes in inflation. Moreover, it is hard to tell a convincing story as to why the choice of frameworks other than ITs and LSD should be 'caused' by their inflation performance, and even harder to tell comparable stories for growth performance. indicators (Jaggers and Marshall, 2009) and dummy variables to capture whether a country has historically suffered high levels of inflation, whether it is an emerging economy and whether it is a fuel exporter; none of these variables are likely to be caused by current inflation. They find their model is able to predict 75% of countries' MPF choices. See Cobham and Song (2020) for further details and motivation.
We make use of a slightly modified version of that model 18 to generate predicted MPFs over a slightly extended data sample . Note we are unable to extend the period further back due to unavailability of data. This smaller sample size, relative to that used in section 5, limits the number of observations, and for this reason we do not attempt to generate predictions for MDC, ERfix, MTs and rudimentary. We also remove the CBI Index and Openness from our set of controls as these variables are strongly correlated (in the case of the CBI Index perfectly collinear) with the explanatory variables used to generate our predicted MPFs. Table   11 shows the results of re-running our main inflation regressions for the advanced economies over the sample together with those obtained by replacing our MPF variables with those predicted by our version of the Cobham and Song model. Table 12 provides a similar analysis for the emerging economies.
As between the main inflation regressions in Table 5 and the 'actual' results in Tables 11 and   12, there are few sharp differences. For the advanced economies there are no differences of sign or significance for the control variables and differences of significance only for intermediate and intensive. For the emerging economies the government balance becomes significant in Table 12. However, the crucial issue in Tables 11 and 12 is the similarity or otherwise between the actual and predicted MPF results in each case. In Table 11 for the advanced economies, the results are generally very close, as between columns (1) and (2)  periods. 20 Thus, reverse causality should not be a serious concern for ITs in emerging economies. Overall, at this stage we think it is reasonable to assume from these results that there is not a serious endogeneity problem here.

Discussion and conclusions
We have now presented a wide range of results on the economic performance associated with different monetary policy frameworks. Table 13 summarises the results, first from the   unconditional analysis in Tables 3-4, then from the conditional analysis of inflation from   Tables 5-7, supported by the IV approach in Tables 11-12, and finally from the conditional analysis for growth in Tables 8-10. These findings are of considerable interest.
For the target variables it is clear, first of all, that multiple direct controls (MDC), exchange rate fixing (ERfix) and unstructured discretion (UD) have poor inflation records. What is perhaps surprising is that MDC and ERfix are mostly associated with relatively good growth: it seems that planning and controls do (sometimes) deliver. Second, we find that exchange rate targeting (ERtargets) has a mixed record: there is some evidence of good performance for emerging economies on the unconditional analysis but this disappears in the conditional results.
Third, monetary targeting (MTs) is not particularly good for inflation, but not bad for growth, while mixed targeting (MixedTs) seems good for growth, but less clearly good on inflation.
Fourth, inflation targeting (ITs) is mostly associated with lower inflation, more clearly for emerging than for advanced economies, and generally with higher growth. Fifth, loosely structured discretion (LSD) does relatively well on the unconditional analysis, and in the conditional analysis, where it is the benchmark, it remains superior to many of the frameworks (but not always to ITs or MixedTs), while well structured discretion (WSD) is mostly associated with lower inflation and higher growth.
For the degree of control variables, which are wider and more heterogeneous, rudimentary MPFs are associated with relatively good inflation and growth. Intermediate MPFs are associated with higher inflation and lower growth. Intensive MPFs mostly but not always do better than substantial MPFs.
We have shown that the standard results, implicitly weighted by the number of countries, are not radically different from those obtained when we weight by GDP or population: given the prevalence of the former procedure, this is reassuring. There are few large differences between the unconditional and conditional results on economic performance, and our use of MPFs predicted by the Cobham and Song (2020) model suggests that there are no serious issues of endogeneity.
In general these findings confirm that the monetary policy frameworks which are conventionally regarded as 'better' are associated with somewhat better inflation and growth outcomes, while 'worse' frameworks are associated with poorer outcomes. One exception to this is that some of the poor frameworks do well on growth. It should also be noted that inflation targeting does not consistently score more highly than other 'better' frameworks, a finding which is broadly in line with the conclusion reached by Ball (2010) on the basis of his own work and the work he surveys (see also Cobham and Song, 2021). Furthermore there is a clear general improvement in performance, at least up to the GFC, which also means that the benchmarks used in the regression analysis are improving over time. 21 Indeed, from closer examination of Tables 3 and 4 it is arguable that this general improvement outweighs the smaller differences between ITs and the other 'better' frameworks.
To sum up, then, we have identified in this paper the economic performance, in terms of inflation and growth, associated with different monetary policy frameworks. There are clear improvements over time in the general performance, at least up to the GFC, which are partly related to the trend towards inflation targeting but also, perhaps more strongly, reflect the improving performance associated with other frameworks, notably the loosely structured discretion and substantial MPFs that we use as benchmarks.
Notes 1 Cobham (2018) suggests that users of the MPF data may wish to make their own aggregations along other dimensions. 2 There are no examples in the dataset of (successful) monetary targeting in emerging economies, and few among the advanced countries. Several episodes of announced monetary targets, e.g. the UK 1977-87 and many emerging country cases, are not classified as monetary targeting because of the repeated failure to hit the targets. 3 Cobham (2018) contains an analysis of durations by the full menu of frameworks and distinguishes between advanced and emerging economies. 4 It should be noted that the Euro area is classified here as loose inflation targeting and therefore substantial. 5 We have also run unreported regressions for the subperiods 1974-1984, 1985-2007 and 1999-2017. These subperiods correspond respectively to the first and second, the second and third, and the third and fourth of the subperiods used in Tables 3 and 4. A particular problem is that when a country's MPF does not change through a period, its effect is taken into the (collinear) country fixed effect. We report only the full period results to mitigate this issue. Although this issue influences subperiod results there is a reasonable correspondence between them and our full period results. 6 Year dummies and a constant term are included in our regressions, reported t-statistics are calculated using cluster-robust standard errors. 7 Note that the inflation variable used in our regression is ln(1+pi), where pi is the inflation rate, and we similarly transform the broad money growth variable. Our terms of trade shock is the standard deviation of the previous 5 years of exports as a capacity to import. The choice of control variables broadly follows existing literature on the impact of the exchange regime upon inflation, such as Ghosh et. al (2002) and Husain et. al (2005). Our data for both the inflation and growth regressions comes from World Development Indicators (WDI), except for the CBI index variable which comes from Garriga (2016). Our broad money growth data in the main comes from WDI, but is supplemented by data from International Financial Statistics and central banks including the ECB. See Table A1 in the appendix for variable definitions. Note we have extended the endpoint of the Garriga data from 2012 to 2017 by assuming no changes in the index she calculates beyond 2012. Table A2 in the appendix shows the number of observations for each MPF in each subperiod. 8 The filter removes 62 observations from our data, 2 from the advanced economies and 60 from the emerging economies. The bulk of missing observations are from South American economies (e.g. episodes of very high money growth in Argentina, Brazil, Chile and Peru) and in some instances from ex-communist economies (such as Poland, Bulgaria and Romania). The main impact upon our inflation results of not using the filter is in the emerging economies, where the estimated coefficients on broad money growth increase to close to unity and those on real GDP growth fall to less than negative unity. We include the impact of not including this filter in our sensitivity analysis later in the paper. Full results are available on request from the authors. 9 Available empirical evidence is mixed: where researchers use long-term averages, the relationship is usually found to be negative (see inter alios Lane, 1997;Campillo and Miron, 1997;and Wynne and Kersting, 2007), but where researchers make use of annual data with standard time series or panel estimation techniques, a positive relationship is often established (see inter alios Alfaro, 2005, andSamimi et. al., 2012). 10 Standard theory predicts a negative relationship here. Husain et al also find a negative but insignificant coefficient for advanced economies -although significant and negative for emerging. Blanchard and Fischer (1989, Ch10) and Drazen and Helpman (1990) suggest a model where there might be a positive relationship. This is because the relationship between a fiscal deficit and inflation is influenced by the impact of today's deficit upon expected money growth. High deficits may lead to the expectation of high future inflation or indeed low future inflation depending upon the future response of government. 11 While earlier work found that inflation was negatively related to CBI, at least for industrial countries, doubts arose about this in later work, e.g. Crowe and Meade (2007). Garriga (2016) found a significant negative relationship for some but not all samples, in panel regressions which included fixed effects but no other control variables. 12 Note that for the advanced economies, since there are only two observations where broad money growth exceeds 100%, the results of regression model (1) (in columns A and B) are very close to those presented in columns (1) and (2) of Table 5. 13 We also find some minor changes regarding the significance of the control variables. In particular, use of lagged control variables influences the significance of the estimated coefficient on (a) real growth for advanced economies and (b) the government balance in emerging economies. The use of lagged target MPFs also results in a significant estimated coefficient on government balance for emerging economies and the terms of trade estimated coefficient becomes insignificant for emerging economies (again using target MPFs) if we drop the broad money growth filter. 14 We use the areg command in the Stata statistical software package. 15 As was the case with our inflation regressions our choice of control variables is strongly influenced by existing literature such as Ghosh et. al (2002) and Husain et. al (2005). Note we do not include a convergence or 'catch-up' variable such as the ratio of a country's starting GDP relative to that in the US. This is because such a variable will be constant across time within a given country and therefore excluded (subsumed into the fixed effect) from the fixed effect regression. Note that all the data used in this regression come from the World Bank, except for the schooling data which comes from the Barro and Lee updated dataset (http://www.barrolee.com). Note the latter data end in 2010, although by centring we extend the data to 2012. This means our effective sample runs from 1974 to 2012. See Table A1 in the Appendix for further detail on the variable definitions. 16 A standard finding in empirical work is that schooling has a positive impact upon per-capita growth rates (see inter alios Barro, 2013 al. find a negative relationship between the investment ratio and growth. 17 The results of our sensitivity analysis have a greater impact upon our control variables. Use of model (3) results in changes to the significance of the estimated coefficients on the investment ratio, openness and government balance in both advanced economy regressions as well as on population in the DOC regressions. It also results in significant changes to estimated coefficients for the emerging economy regressions (using target MPFs) on the investment ratio, terms of trade and openness, as well as on the investment ratio and terms of trade using DOC MPFs. Model (4) also leads to a change in the estimated coefficient on population growth in the emerging economies and on the investment ratio in advanced economies (using target MPFs). We can also see that removing the broad money growth filter (model 1) has some impact upon our emerging economies results, estimated coefficients on population and schooling change (using DOC MPFs) as well as on population growth (using both target and DOC MPFs). 18 The method used by Cobham and Song requires the setting of benchmark MPF variables to generate point estimates. Their benchmarks are ERtargets and intermediate. In keeping with our earlier analysis we use LSD and substantial as our benchmarks here. 19 The inverse of the differenced covariance variance matrix is not positive definite and this may limit the accuracy of the tests.  Table 3, that is from 1974-84 through 1985-1998 to 1999-2007, and from the second to the third of these in Table 4. The average scores for the benchmarks -LSD and substantial -are also given there.   1974-1998 1985-2007 1999-2014 Tables for insertion into text       Table  A1, MPF variables in Table 1.  1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 Table A1, MPF variables in Table 1.     Table A1, MPF variables in Table 1.      Table 7 MixedTs higher for emerging and occasionally for advanced, higher for GDP weighted LSD (benchmark) WSD higher emerging and GDP weighted rudimentary higher emerging and both weights intermediate lower emerging only substantial (benchmark) intensive higher emerging and pop-weighted Notes: these are summaries in each case of a considerable number of results as indicated by the table numbers; for the unconditional analysis the judgments are relative to the (advanced/emerging) averages, for the conditional analysis the judgments are on significance relative to the benchmarks.